![RULES OF THUMB: SUMMARY
Although experienced engineers know where to find information
and how to make accurate computations, they also keep a minimum
body of information in mind on the ready, made up largely of
shortcuts and rules of thumb. The present compilation may fit into
such a minimum body of information, as a boost to the memory or
extension in some instances into less often encountered areas. It is
derived from the material in this book and is, in a sense, a digest of
the book.
An Engineering Rule of Thumb is an outright statement
regarding suitable sizes or performance of equipment that obviates
all need for extended calculations. Because any brief statements are
subject to varying degrees of qualification, they are most safely
applied by engineers who are substantially familiar with the topics.
Nevertheless, such rules should be of value for approximate design
and cost estimation, and should provide even the inexperienced
engineer with perspective and a foundation whereby the reason-
ableness of detailed and computer-aided results can be appraised
quickly, particularly on short notice such as in conference.
Everyday activities also are governed to a large extent by rules
of thumb. They serve us when we wish to take a course of action
but are not in a position to find the best course of action. Of interest
along this line is an amusing and often useful list of some 900 such
digests of everyday experience that has been compiled by Parker
(Rules of Thumb, Houghton Mifflin, Boston, 1983).
Much more can be stated in adequate summary fashion about
some topics than about others, which accounts in part for the
spottiness of the present coverage, but the spottiness also is due to
ignorance and oversights on the part of the author. Accordingly,
every engineer undoubtedly will supplement or modify this material
in his own way.
COMPRESSORS AND VACUUM PUMPS
1. Fans are used to raise the pressure about 3% (12in. water),
blowers raise to less than 40 psig, and compressors to higher
pressures, although the blower range commonly is included in
the compressor range.
2. Vacuum pumps: reciprocating piston type decrease the pressure
to 1 Torr; rotary piston down to 0.001 Torr, two-lobe rotary
down to 0.0001 Torr; steam jet ejectors, one stage down to
lOOTorr, three stage down to 1 Torr, five stage down to
0.05 Torr.
3. A three-stage ejector needs 1OOlb steam/lb air to maintain a
pressure of 1 Torr.
4. In-leakage of air to evacuated equipment depends on the
absolute pressure, Torr, and the volume of the equipment, V
cuft, according to w = kVz3 lb/hr, with k = 0.2 when P is more
than 90 Torr, 0.08 between 3 and 20 Torr, and 0.025 at less than
1 Torr.
5. Theoretical adiabatic horsepower (THP) = [(SCFM)T1/8130a]
[(PJPJ - 11, where Tt is inlet temperature in °F+ 460 and
a = (k - 1)/k, k = CJC,,.
6. Outlet temperature & = T,(P,/P,)“.
7. To compress air from lOO”F, k = 1.4, compression ratio = 3,
theoretical power required = 62 HP/million tuft/day, outlet
temperature 306°F.
8. Exit temperature should not exceed 350-400°F; for diatomic
gases (C,/C, = 1.4) this corresponds to a compression ratio of
about 4.
9. Compression ratio should be about the same in each stage of a
multistage unit, ratio = (PJPi)““, with n stages.
10. Efficiencies of reciprocating compressors: 65% at compression
ratio of 1.5, 75% at 2.0, and 80-85% at 3-6.
11. Efficiencies of large centrifugal compressors, 6000-100,000
ACFM at suction, are 76-78%.
12. Rotary compressors have efficiencies of 70%, except liquid liner
type which have 50%.
CONVEYORS FOR PARTICULATE SOLIDS
1. Screw conveyors are suited to transport of even sticky and
abrasive solids up inclines of 20” or so. They are limited to
distances of 150ft or so because of shaft torque strength. A
12in. dia conveyor can handle 100@3000cuft/hr, at speeds
ranging from 40 to 60 ‘pm.
2. Belt conveyors are for high capacity and long distances (a mile or
more, but only several hundred feet in a plant), up inclines of
30” maximum. A 24in. wide belt can carry 3OOOcuft/hr at a
speed of lOOft/min, but speeds up to 6OOft/min are suited to
some materials. Power consumption is relatively low.
Bucker elevators are suited to vertical transport of sticky and
abrasive materials. With buckets 20 x 20 in. capacity can reach
1000 cuft/hr at a speed of 100 ft/min, but speeds to 300 ft/min
are used.
Drug-type conveyors (Redler) are suited to short distances in any
direction and are completely enclosed. Units range in size from
3 in. square to 19 in. square and may travel from 30 ft/min (fly
ash) to 250 ft/min (grains). Power requirements are high.
Pneumatic conveyors are for high capacity, short distance (400 ft)
transport simultaneously from several sources to several
destinations. Either vacuum or low pressure (6-12psig) is
employed with a range of air velocities from 35 to 120ft/sec
depending on the material and pressure, air requirements from 1
to 7 cuft/cuft of solid transferred.
COOLING TOWERS
1. Water in contact with air under adiabatic conditions eventually
cools to the wet bulb temperature.
2. In commercial units, 90% of saturation of the air is feasible.
3. Relative cooling tower size is sensitive to the difference between
the exit and wet bulb temperatures:
AT('F) 5 15 25
Relative volume 2.4 1.0 0.55
4. Tower fill is of a highly open structure so as to minimize pressure
drop, which is in standard practice a maximum of 2 in. of water.
5. Water circulation rate is l-4gpm/sqft and air rates are
1300-1800 lb/(hr)(sqft) or 300-400 ft/min.
6. Chimney-assisted natural draft towers are of hyperboloidal
shapes because they have greater strength for a given thickness;
a tower 250 ft high has concrete walls 5-6 in. thick. The enlarged
cross section at the top aids in dispersion of exit humid air into
the atmosphere.
7. Countercurrent induced draft towers are the most common in
process industries. They are able to cool water within 2°F of the
wet bulb.
8. Evaporation losses are 1% of the circulation for every 10°F of
cooling range. Windage or drift losses of mechanical draft towers](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-13-320.jpg)
![2 INTRODUCTION
% of Total Project Time
Figure 1.1. Progress of material commitment, engineering
manhours, and construction [Matozzi, Oil Gas. J. p. 304, (23 March
1953)].
% of Total Project Time
Figure 1.2. Rate of application of engineering manhours of various
categories. The area between the curves represents accumulated
manhours for each speciality up to a given % completion of the
project [Miller, Chem. Eng., p. 188, (July 1956)].
For a typical project, Figure 1.1 shows the distributions of
engineering, material commitment, and construction efforts. Of the
engineering effort, the process engineering is a small part. Figure
1.2 shows that it starts immediately and finishes early. In terms of
money, the cost of engineering ranges from 5 to 15% or so of the
total plant cost; the lower value for large plants that are largely
patterned after earlier ones, and the higher for small plants or those
based on new technology or unusual codes and specifications.
1.4. SOURCES OF INFORMATION FOR PROCESS DESIGN
A selection of books relating to process design methods and data is
listed in the references at the end of this chapter. Items that are
especially desirable in a personal library or readily accessible are
identified. Specialized references are given throughout the book in
connection with specific topics.
The extensive chemical literature is served by the bibliographic
items cited in References, Section 1.2, Part B. The book by
Rasmussen and Fredenslund (1980) is addressed to chemical
~engineers and cites some literature not included in some of the
other bibliographies, as well as information about proprietary data
banks. The book by Leesley (References, Section 1.1, Part B) has
much information about proprietary data banks and design
methods. In its current and earlier editions, the book by Peters and
Timmerhaus has many useful bibliographies on classified topics.
For information about chemical manufacturing processes, the
main encyclopedic references are Kirk-Othmer (1978-1984),
McKetta and Cunningham (1976-date) and Ullmann (1972-1983)
(References, Section 1.2, Part B). The last of these is in German,
but an English version was started in 1984 and three volumes per
year are planned; this beautifully organized reference should be
most welcome.
The most comprehensive compilation of physical property data
is that of Landolt-Bornstein (1950-date) (References, Section 1.2,
Part C). Although most of the material is in German, recent
volumes have detailed tables of contents in English and some
volumes are largely in English. Another large compilation,
somewhat venerable but still valuable, is the International Critical
Tables (1926-1933). Data and methods of estimating properties of
hydrocarbons and their mixtures are in the API Data Book
(1971-date) (References, Section 1.2, Part C). More general
treatments of estimation of physical properties are listed in
References, Section 1.1, Part C. There are many compilations of
special data such as solubilities, vapor pressures, phase equilibria,
transport and thermal properties, and so on. A few of them are
listed in References, Section 1.2, Part D, and references to many
others are in the References, Section 1.2, Part B.
Information about equipment sizes and configurations, and
sometimes performance, of equipment is best found in manufac-
turers’ catalogs. Items 1 and 2 of References, Section 1.1, Part D,
contain some advertisements with illustrations, but perhaps their
principal value is in the listings of manufacturers by the kind of
equipment. Thomas Register covers all manufacturers and so is less
convenient at least for an initial search. The other three items of
this group of books have illustrations and descriptions of all kinds of
chemical process equipment. Although these books are old, one is
surprised to note how many equipment designs have survived.
1.5. CODES, STANDARDS, AND
RECOMMENDED PRACTICES
A large body of rules has been developed over the years to ensure
the safe and economical design, fabrication and testing of
equipment, structures, and materials. Codification of these rules
has been done by associations organized for just such purposes,
by professional societies, trade groups, insurance underwriting
companies, and government agencies. Engineering contractors and
large manufacturing companies usually maintain individual sets of
standards so as to maintain continuity of design and to simplify
maintenance of plant. Table 1.1 is a representative table of contents
of the mechanical standards of a large oil company.
Typical of the many thousands of items that are standardized in
the field of engineering are limitations on the sizes and wall
th,icknesses of piping, specifications of the compositions of alloys,
stipulation of the safety factors applied to strengths of construction
materials, testing procedures for many kinds of materials, and so
on.
Although the safe design practices recommended by profes-
sional and trade associations have no legal standing where they have
not actually been incorporated in a body of law, many of them have
the respect and confidence of the engineering profession as a whole
and have been accepted by insurance underwriters so they are
widely observed. Even when they are only voluntary, standards
constitute a digest of experience that represents a minimum re-
quirement of good practice.
Two publications by Burklin (References, Section 1.1, Part B)
are devoted to standards of importance to the chemical industry.
Listed are about 50 organizations and 60 topics with which they are
concerned. National Bureau of Standards Publication 329 contains
about 25,000 titles of U.S. standards. The NBS-SIS service
maintains a reference collection of 200,000 items accessible by letter
or phone. Information about foreign standards is obtainable
through the American National Standards Institute (ANSI).
A listing of codes and standards bearing directly on process](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-21-320.jpg)
![1.9. SAFETY OF PLANT AND ENVIRONMENT 7
TABLE 1.4. Safety Factors in Equipment Design: Results of a Questionnaire
Equipment Design Variable
Range of Safety
Factor 1 % )
Compressors, reciprocating piston displacement
Conveyors, screw diameter
H a m m e r m i l l s power input
Filters, plate-and-frame area
Filters, rotary area
Heat exchangers, shell and tube for area
liquids
Pumps, centrifugal impeller diameter
Separators, cyclone diameter
Towers, packed d i a m e t e r
Towers, tray d i a m e t e r
Water cooling towers volume
B Based on pilot plant tests.
[Michelle, Beattie, and Goodgame, Chem. Eng. frog. 50,332 (1954)).
11-21
8-21
15-21”
ll-218
14-20’
11-18
7-14
7-11
11-18
lo-16
12-20
only to a certain accuracy. AT may be uncertain because of possible
fluctuations in regulated steam and tower pressures. A, the effective
area, may be uncertain because the submergence is affected by the
liquid level controller at the bottom of the column. Accordingly,
dq dU dA d(AT)
-=7+x+ A T ’
4
that is, the fractional uncertainty of q is the sum of the fractional
uncertainties of the quantities on which it is dependent. In practical
cases, of course, some uncertainties may be positive and others
negative, so that they may cancel out in part; but the only safe
viewpoint is to take the sum of the absolute values. Some further
discussion of such cases is by Sherwood and Reed, in Applied
Mathematics in Chemical Engineering (McGraw-Hill, New York,
1939).
It is not often that proper estimates can be made of
uncertainties of all the parameters that influence the performance or
required size of particular equipment, but sometimes one particular
parameter is dominant. All experimental data scatter to some
extent, for example, heat transfer coefficients; and various cor-
relations of particular phenomena disagree, for example, equations
of state of liquids and gases. The sensitivity of equipment sizing to
uncertainties in such data has been the subject of some published
information, of which a review article is by Zudkevich [Encycl.
Chem. Proc. Des. 14, 431-483 (1982)]; some of his cases are:
1. Sizing of isopentane/pentane and propylene/propane splitters.
2. Effect of volumetric properties on sizing of an ethylene
compressor.
3. Effect of liquid density on metering of LNG.
4. Effect of vaporization equilibrium ratios, K, and enthalpies on
cryogenic separations.
5. Effects of VLE and enthalpy data on design of plants for
coal-derived liquids.
Examination of such studies may lead to the conclusion that some
of the safety factors of Table 1.4 may be optimistic. But long
experience in certain areas does suggest to what extent various
uncertainties do cancel out, and overall uncertainties often do fall in
the range of lo-20% as stated there. Still, in major cases the
uncertainty analysis should be made whenever possible.
1.9. SAFETY OF PLANT AND ENVIRONMENT
The safe practices described in the previous section are primarily for
assurance that the equipment have adequate performance over
anticipated ranges of operating conditions. In addition, the design
of equipment and plant must minimize potential harm to personnel
and the public in case of accidents, of which the main causes are
a. human failure,
b. failure of equipment or control instruments,
c. failure of supply of utilities or key process streams,
d. environmental events (wind, water, and so on).
A more nearly complete list of potential hazards is in Table 1.5, and
a checklist referring particularly to chemical reactions is in Table
1.6.
Examples of common safe practices are pressure relief valves,
vent systems, flare stacks, snuffing steam and fire water, escape
hatches in explosive areas, dikes around tanks storing hazardous
materials, turbine drives as spares for electrical motors in case of
power failure, and others. Safety considerations are paramount in
the layout of the plant, particularly isolation of especially hazardous
operations and accessibility for corrective action when necessary.
Continual monitoring of equipment and plant is standard
practice in chemical process plants. Equipment deteriorates and
operating conditions may change. Repairs sometimes are made with
“improvements” whose ultimate effects on the operation may not
be taken into account. During start-up and shut-down, stream
compositions and operating conditions are much different from
those under normal operation, and their possible effect on safety
must be taken into account. Sample checklists of safety questions
for these periods are in Table 1.7.
Because of the importance of safety and its complexity, safety
engineering is a speciality in itself. In chemical processing plants of
any significant size, loss prevention reviews are held periodically by
groups that always include a representative of the safety depart-
ment. Other personnel, as needed by the particular situation, are
from manufacturing, maintenance, technical service, and possibly
research, engineering, and medical groups. The review considers
any changes made since the last review in equipment, repairs,
feedstocks and products, and operating conditions.
Detailed safety checklists appear in books by Fawcett and
Wood (Chap. 32, Bibliography 1.1, Part E) and Wells (pp.
239-257, Bibliography 1.1, Part E). These books and the large one
by Lees (Bibliography 1.1, Part E) also provide entry into the vast
literature of chemical process plant safety. Lees has particularly
complete bibliographies. A standard reference on the properties of
dangerous materials is the book by Sax (1984) (References, Section
1.1, Part E). The handbook by Lund (1971) (References, Section
1.1, Part E) on industrial pollution control also may be consulted.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-26-320.jpg)
![10 INTRODUCTION
EXAMPLE 1.2-(continued)
Superheater
12 rows of 2$-in. OD tubes (0.165-in. thick),
17.44 ft long
Rows in line and spaced on 3$in. centers
23 tubes per row spaced on 6-in. centers
S = 3150 sqft
A, = 133 sqft
Boiler
25 rows of 2&in. OD tubes, approx 18 ft long
Rows in line and spaced on 3$-in. centers
35 tubes per row spaced on 4-m. centers
s = 10,308 sqft
A, = 85.0 sqft
Economizer
10 rows of 2-in. OD tubes (0.148-in. thick),
approx 10 ft long
Rows in line and spaced on 3-m. centers
47 tubes per row spaced on 3-m centers
S = 2460 sqft
A, = 42 sqft
Air heater
53 rows of 2-in. OD tubes (0.083-in. thick),
approx 13 ft long
Rows in line and spaced on 2$-in. centers
41 tubes per row spaced on 3&n. centers
S = 14,809 sqft
A, (total internal cross section area of 2173 tubes)
= 39.3 sqft
A, (clear area between tubes for crossflow of air)
= 70 sqft
Air temperature entering air heater = 80°F
(a)
lb)
Steam out
Downcomer
not Heated
I
(c) Gas Steam Coil
Outlet Air Heater
t /
II II II
Fire 1.4. Steam boiler and furnace arrangements. [Steam,
Babcock and Wilcox, Barberton, OH, 1972, pp. 3.14, 12.2 (Fig. 2),
and 25.7 (Fig. 5)]. (a) Natural circulation of water in a two-drum
boiler. Upper drum is for steam disengagement; the lower one for
accumulation and eventual blowdown of sediment. (b) A two-drum
boiler. Preheat tubes along the Roor and walls are connected to
heaters that feed into the upper drum. (c) Cross section of a
Stirling-type steam boiler with provisions for superheating, air
preheating, and flue gas economizing; for maximum production of
550,000 Ib/hr of steam at 1575 psia and 900°F.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-29-320.jpg)
![42 PROCESS CONTROL
EXAMPLE 3.1
Constants of PID Controllers from Response Curves to a Step
Input
The method of Ziegler and Nichols [Tram ASME, (Dec. 1941)] will
be used. The example is that of Tyner and May (Process
Engineering Control, Ronald, New York, 1967). The response to a
change of 2 psi on the diaphragm of the control valve is shown. The
full range of control pressure is from 3 to 15 psi, a difference of
12psi, and the range of temperature is from 100 to 2OO”F, a
difference of 100°F. Evaluate the % displacement of pressure as
Am = 100(2/12) = 16.7%.
From the curve, the slope at the inflection point is
R = 17.5/100(7.8 - 2.4) = 3.24%/min,
and the apparent time delay is the intercept on the abscissa,
L = 2.40 min.
The values of the constants for the several kinds of controllers are
Proportional: 100/K, = % PB = lOORL/Am = 100(3.24)(2.4)/
16.7 = 46.6%.
Proportional-integral: % PB = llORL/Am = 51.2%
Ki=L/0.3=8min
Proportional-integral-derivative:
% PB = 83RLIAm = 38.6%,
Ki = 2L = 4.8 min,
Kd = 0.5L = 1.2 min.
These are approximate instrument settings, and may need to be
adjusted in process. PB is proportional band.
A recent improvement of the Ziegler-Nichols method due to
Yuwana and Seborg [AZChE J. 28, 434 (1982)] is calculator
programmed by Jutan and Rodriguez [Chem. Eng. 91(18), 69-73
(Sep. 3, 1984)].
170
t
Am (t) = 2 psig
r-----------------------------------------
Time (min) --+
case, details of detectors and transmitters as well as all other
elements of a control system are summarized on instrument
specification forms. The simplified coding used in this chapter is
summarized on Figure 3.4.
CASCADE (RESET) CONTROL
Some control situations require interacting controllers. On Figure
3.19(d), for instance, a composition controller regulates the setpoint
of the temperature controller of a reactor and on Figure 3.15(g) the
set point of the reflux flow rate is regulated by composition or
temperature control. Composite systems made up of regions that
respond with varying degrees of speed or sluggishness are
advantageously equipped with cascade control. In the reactor of
Figure 3.19(b), the temperature T-I-1 of the vessel contents
responds only slowly to changes in flow rate of the heat transfer
medium, but the temperature TT-2 of the HTM leaving the cooling
coil is comparatively sensitive to the flow rate. Accordingly,
controller TC-2 is allowed to adjust the setpoint of the primary
controller TC-1 with an overall improvement in control of the
reactor temperature. The controller being reset is identified on
flowsheets.
3.2. INDIVIDUAL PROCESS VARIABLES
The variables that need to be controlled in chemical processing are
temperature, pressure, liquid level, flow rate, flow ratio, com-
position, and certain physical properties whose magnitudes may be
influenced by some of the other variables, for instance, viscosity,
vapor pressure, refractive index, etc. When the temperature and
pressure are fixed, such properties are measures of composition
which may be known exactly upon calibration. Examples of control
of individual variables are shown in the rest of this chapter with the
various equipment (say pumps or compressors) and processes (say
distillation or refrigeration) and on the earlier flowsketches of this
and the preceding chapters, but some general statements also can
be made here. Most control actions ultimately depend on regulation
of a flow rate with a valve.
TEMPERATURE
Temperature is regulated by heat exchange with a heat transfer
medium (HTM). The flow rate of the HTM may be adjusted, or the
condensing pressure of steam or other vapor, or the amount of heat
transfer surface exposed to condensing vapor may be regulated by
flooding with condensate, which always has a much lower heat
transfer coefficient than that of condensing vapor. In a reacting
system of appropriate vapor pressure, a boiling temperature at
some desired value can be maintained by relluxing at the proper
controlled pressure. Although examples of temperature control
appear throughout this chapter, the main emphasis is in the section
on heat exchangers.
P R E S S U R E
Pressure is controlled by regulating the flow of effluent from the
vessel. The effluent may be the process stream itself or a non-
condensable gas that is generated by the system or supplied for
blanketing purposes. The system also may be made to float on the
pressure of the blanketing gas supply. Control of the rate of
condensation of the effluent by allowing the heat transfer surface to
flood partially is a common method of regulating pressure in
fractionation systems. Throttling a main effluent vapor line usually
is not done because of the expense of large control valves. Figure
3.5 shows vacuum production and control with steam jet ejectors.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-61-320.jpg)
![60 PROCESS CONTROL
*
W
Figure 3.24. Control of positive displacement compressors, rotary and reciprocating. (a) Flow control with variable speed drives. (b) Pressure
control with bypass to the suction of the compressor. (c) Reciprocating compressor. SC is a servomechanism that opens some of suction
valves during discharge, thus permitting stepwise internal bypass. The clearance unloader is controllable similarly. These built-in devices may
be supplemented with external bypass to smooth out pressure fluctuations.
acceptable limits. Two other aids are available to control of recip-
rocating units.
1. Valve unloading, a process whereby some of the suction valves
remain open during discharge. Solenoid or pneumatic unloaders
can be operated from the output of a control instrument. The
stepwise controlled flow rate may need to be supplemented with
controlled external bypass to smooth out pressure fluctuations.
2. Clearance unloaders are small pockets into which the gas is
forced on the compression stroke and expands into the cylinder
on the return stroke, thus preventing compression of additional
gas.
Figure 3.24 shows control schemes for rotary and reciprocating
compressors. Vacuum pumps are compressors operating between a
low suction pressure and a fixed discharge pressure, usually
REFERENCES
1. Chemical Engineering Magazine, Practical Process Instrumentation and
Control, McGraw-Hill, New York, 1980.
2. D.M. Considine, Process Instruments and Controls Handbook, McGraw-
Hill, New York, 1985.
atmospheric. Mechanical pumps are used for small capacities, steam
jet ejectors for larger ones. Ejectors also are used as ther-
mocompressors to boost the pressure of low pressure steam to an
intermediate value. Control of suction pressure with either mech-
anical or jet pumps is by either air bleed [Fig. 3.5(a)] or suction
line throttling [Fig. 3.5(c)]; air bleed is the more economical process.
Up to five jets in series are used to produce high vacua. The steam
from each stage is condensed by direct contact with water in baro-
metric condensers or in surface condensers; condensation of steam
from the final stage is not essential to performance but only to avoid
atmospheric pollution. In a single stage ejector, motive steam flow
cannot be reduced below critical flow in the diffuser, and water to
the barometric condenser must not be throttled below 30-50% of
the maximum if proper contacting is to be maintained. Control by
throttling of steam and water supply, as on Figure 3.5(b), is subject
to these limitations.
3. B. Liptak, Instrumentation in the Process Industries, Chilton, New York,
1973.
4. F.G. Shinskey, Process Control Systems, McGraw-Hill, New York, 1979.
5. F.G. Shinskey, Distillation Control, McGraw-Hill, New York, 1984.
6. M.R. Skrokov (Ed.), Mini- and Microcomputer Control in Industrial
Processes, Van Nostrand Reinhold, New York, 1980.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-79-320.jpg)
![64 DRIVERS FOR MOVING EQUIPMENT
hundred degrees of superheat. In larger sixes turbines may be
convenient sources of low pressure exhaust steam in the plant.
From multistage units, steam may be bled at several reduced
pressures. When the expansion is to subatmospheric conditions, the
operation is called condensing because the exhaust steam must be
condensed before removal from the equipment. Although the
efficiency of condensing turbines is less, there is an overall reduction
of energy consumption because of the wider expansion range.
Several parameters affect the efficiency of steam turbines, as
shown partially on Figure 4.1. Closer examination will need to take
into account specific mechanical details which usually are left to the
manufacturer. Geared turbines [the dashed line of Fig. 4.1(b)] have
higher efficiencies, even with reduction gear losses, because they
operate with especially high bucket speeds. For example, for a
service of SOOHP with 3OOpsig steam, a geared turbine has an
efficiency of 49.5% and one with a direct drive at 1800 rpm has an
efficiency of 24%.
The flow rate of steam per unit of power produced is
represented by
2545
m=-q(H2-Hl)
lb/HP hr
3412
= - Wz - 4)
lb/kWh
with the enthalpies in Btu/lb. The efficiency is 9, off Figure 4.1, for
example. The enthalpy change is that of an isentropic process. It
may be calculated with the aid of the steam tables or a Mollier
diagram for steam. For convenience, however, special tables have
been derived which give the theoretical steam rates for typical
combinations of inlet and outlet conditions. Table 4.3 is an
abbreviated version.
Example 4.1 illustrates this kind of calculation and compares
the result with that obtained by taking the steam to behave as an
ideal gas. For nonideal gases with known PVT equations of state
and low pressure heat capacities, the method of calculation is the
same as for compressors which is described in that section of the
book.
On a Mollier diagram like that with Example 4.1, it is clear that
expansion to a low pressure may lead to partial condensation if
insufficient preheat is supplied to the inlet steam. The final
condition after application of the efficiency correction is the
pertinent one, even though the isentropic point may be in the
two-phase region. Condensation on the blades is harmful to them
and must be avoided. Similarly, when carbon dioxide is expanded,
possible formation of solid must be guarded against.
When gases other than steam are employed as motive fluids,
the equipment is called a gas expander. The name gas turbine
usually is restricted to equipment that recovers power from hot
TABLE 4.3. Theoretical Steam Rates for Typical Steam Conditions (Ib/kWh)”
IC(I 25(1 410 6llO 600 Xi0 X50 000 Yoo 1,200 l,?jO 1,250 1,450 I ,ijO I ,x00 2 , 4 0 0
Initid tamp, “F
Z6C.Y ioo hi0 ii0 x25 x25 YOO x25 9oll x25 Y00 Y50 X25 YjO I000 I000
E:haut Initial cnth:alpv, I3tu/lh
prc5t,re 1,IYj.i 1 , 2 6 1 . X 1,114.Y 1,379.hI,-t!t.4 I.4tO.6I,-Ijj.j
t,-WX.-l 1.451.61,jY-i.T 1.43X.4 I,-KX.I1,2X2.7I,-Ml.ll,GW.Il,Mt.-t
inf fg ill)
2 . 0 I O . 5 2 o.oio 7.X31 7.0X3 6.761 6,.5x0 6.2X2 6 .i j 5 6.256 (,.-l.il h.l!? 5.Y-H 6.40X 5.YCO 5.6fa 5,633
2 . 5 IO.XX Y. 343 x . 0 3 ; 7.251 6.Yl6 h.i?l h.-tl5 6.6Y6 6.3xX 6.5X-l 6 . 2 5 6 6.061 6.536 6.01-t S.77? 5.i33
i.396 i.052 6.XJi 6.ilO fi.XIY 6..iO? 6.G.v 6 . 3 6 2 6.162 6.64x 6.112 5.w j.XIY
3 . 0 t 1.20
4.0 I I . 7 6
IlJill’g,lgc
i 21.6Y
I O ?!.Yi
20 2 X . 6 1
30 31.6Y
40 3Y.!Y
50 -Ki.(Hl
60 5 3 . 9 0
l6.5i
I7.YO
!O.+t
!?.Yj
2 5 . 5 2
2 X . 2 1
31.07
13.01
13.X3
lj.13
16.73
18.0X
19.42
2 0 . 7 6
i.frH 7.2x2
I .Oj t0.42
I.# I O . 9 5
2.6X II.‘)0
3.61 12.75
+.31 13.5-t
5 . 3 6 l-I.30
6. IX 15.05
I ’
7.05x
Y.H.38
I O . 1 0
I I . 1 0
Il.XO
12.46
1 3 . 0 ;
1 3 . 6 6
6.iX i.026 6.X9-l 6.541 6.332 6.27i 6.OIZ j.Y6?
Y.?XX
Y.iOj
IO.43
I I.OX
I I .h6
I ? . ? !
t2.i-t
Y.i55
IO.202
t O.YX?
II.67
lZ.!c-+
12.00
13.47
6.W
Y. ?IW
Y.flli
I O . 3 2 7
IO.YC?
Il.i?
1 2 . 0 6
12.57
Y.!Yi
Y. xi
IO.-Km
I I.OYS
II.fi-wJ
12.16
I2.64
X.X20
0.1X0
Y.XOI
IO.341
10.x31
II.2X-t
Il.71
x.+Yl
x.x10
0.415
9.Y22
10.1Xu
lO.XOt-+
I I . 2 0
Y.2IX
Y.jY?
IO.240
Io.xoI
II.?W
I l . 7 7 9
I?.?-!
X.351
X.673
Y.227
‘).7(L)
IO.11-t
lO..i31
lO.YO
7.x7-t
X.ISX
X.&l2
Y.057
9.427
Y.767
IO.OX
i.il3
7.97j
X.-121
x . 7 9 9
Y.136
Y.-t-t!
9 . 7 2 7
i5 69.-t 3i.7; ??.XI I;.40 I6.l6 I-1.50 Il.51 I-t.?X 11.30 13.1-t 1 2 . 3 2
X0 i5.Y 37.47 23.51 17.x0 In.54 I-t.78 1 3 . 7 7 l-I.55 13.55 1 3 . 5 6 12.52
IO0 -ti.?l 26.46 IY.43 IX.05 IJ.Xfi I-t.77 I5.iY I-t.50 l-t.42 l!.2i
I25 j7.XX 30.59 21.56 20.03 17.22 I6.04 16.X7 IS.70 15.46 I-t.Ii
Ii0 76.5 35.40 2 3 . 8 3 22.1-t I X . 6 1 I i . 3 3 IX.IX Ih.Yl l&-t7 IC.06
I60 X6.X 3i.j; 2 4 . 7 9 23.03 19.17 17.X5 I X . 7 1 17.41 Ih.XX l.i.41
Ii5 41.16 2 6 . 2 9 24.43 20.04 I X . 6 6 l9.j? I X . 1 6 17.4X Ij.Yi
200 4x.24 29.w 2 6 . 9 5 21.53 20.05 20.9I 19.45 IX.-tX 1fi.X-l
2 5 0 6 Y . l 35.40 32.x9 24.7X 23.0x 23.YO 22.2-t 20.57 1X.6X
XX) 4 2 . 7 2 GO.62 2X. 50 2 6 . 5 3 2 7 . 2 7 25.37 22.iY 20.62
wo 7 2 . 2 6 7 . 0 3X.05 ?5.43 3 5 . 7 1 3 2 . 2 2 2 7 . 8 2 2 4 . 9 9
-tLj x-t.2 7X.3 41.0x 3 X . 2 6 3X.33 3 5 . 6 5 29.2-t 2 6 . 2 1
6c4) i x . 5 73.1 6 X . 1 1 63.-t 4 2 . 1 0 37.03
‘From Theoretical Steam Rate Table-Compatible with the 1967 ASME Steam Tables, ASME, 1969.
I I . 7 7
I I . 9 5
1 2 . 6 5
13.51
I-k.35
l-t.69
lj.20
16.05
17.x1
19.66
23.X2
?-l.YX
35.?0
12.X5
t 3.05
13.X3
l-l.76
15.65
tr5.00
16.j2
Ii.?9
19.11
2 0 . 8 9
24.7-I
2 5 . 7 X
?-l.jO
Il.-I? IO.53 t o . 1 2
I I . 6 0 Io.6; I O . 2 5
12.2-t I I . 2 1 10.73
1 3 . 0 1 11.x-t II.?X
1 3 . 7 5 12.44 I l.XO
I4.0j 12.6X 12.00
I-+.-tY 13.03 1 2 . 2 9
IS.23 1 3 . 6 2 Il.77
16.73 1-1.7x 1 3 . 6 9
IX.?X t5.95 l4..i9
21.64 I X . 3 9 16.41
2 2 . 5 5 19.03 16.X7
30. I6 24.06 2 0 . 2 9](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-83-320.jpg)
![4.3. COMBUSTION GAS TURBINES AND ENGINES 65
EXAMPLE 4.1
Steam Requirement of a Turbine Operation
Steam is fed to a turbine at 614.7 psia and 825°F and is discharged at
64.7 psia. (a) Find the theoretical steam rate, Ib/kWh, by using the
steam tables. (b) If the isentropic efficiency is 70%, find the outlet
temperature. (c) Find the theoretical steam rate if the behavior is
ideal, with C,/C, = 1.33.
(a) The expansion is isentropic. The initial and terminal
conditions are identified in the following table and on the graph.
The data are read off a large Mollier diagram (Keenan et al., Steam
Tables, Wiley, New York, 1969).
Point P fF H S
1 614.7 825 1421.4 1.642
2 64.7 315 1183.0 1.642
3 64.7 445 1254.5 1.730
AH, = H2 - HI = -238.4 Btu/lb
Theoretical steam rate = 3412/238.4 = 14.31 lb/kWh. This value is
checked exactly with the data of Table 4.3.
(b) H3 - HI = 0.7(H, - HI) = -166.9 Btu/lb
H3 = 1421.4 - 166.9 = 1254.5 Btu/lb
The corresponding values of T3 and S, are read off the Mollier
diagram, as tabulated.
(c) The isentropic relation for ideal gases is
AH= & RTl[(P2/Pl)(k~‘)~k - l]
= 1’9;f5285) [(64.7/614.7)“-25 - l]
= -4396 Btu/lbmol, -244 Btu/lb.
f
F
1 ?@
v
1.64 1.73
ENTROPY , BTU/(LB)(F)
combustion gases. The name turboexpander is applied to machines
whose objective is to reduce the energy content (and temperature)
of the stream, as for cryogenic purposes.
Gas expanders are used to recover energy from high pressure
process gas streams in a plant when the lower pressure is adequate
for further processing. Power calculations are made in the same way
as those for compressors. Usually several hundred horsepower must
be involved for economic justification of an expander. In smaller
plants, pressures are simply let down with throttling valves
(Joule-Thomson) without attempt at recovery of energy.
The specification sheet of Table 4.4 has room for the process
conditions and some of the many mechanical details of steam
turbines.
4.3. COMBUSTION GAS TURBINES AND ENGINES
When a low cost fuel is available, internal combustion drivers
surpass all others in compactness and low cost of installation and
operation. For example, gas compression on a large scale has long
been done with integral engine compressors. Reciprocating engines
also are widely used with centrifugal compressors in low pressure
applications, but speed increasing gears are needed to up the
300-6OOrpm of the engines to the 3000-10,OOOrpm or so of the
compressor.
Process applications of combustion gas turbines are chiefly
to driving pumps and compressors, particularly on gas and oil
transmission lines where the low thermal efficiency is counter-
balanced by the convenience and economy of having the fuel on
hand. Offshore drilling rigs also employ gas turbines. Any hot
process gas at elevated pressure is a candidate for work recovery in
a turbine. Offgases of catalytic cracker regenerators, commonly at
45 psig and as high as 1250”F, are often charged to turbines for
partial recovery of their energy contents. Plants for the manufacture
of nitric acid by oxidation of ammonia at pressures of 100 psig or so
utilize expanders on the offgases from the absorption towers, and
the recovered energy is used to compress the process air to the
reactors.
Combustion gas turbine processes are diagrammed on Figure
4.2 and in Example 4.2. In the basic process, a mixture of air and
fuel (or air alone) is compressed to 5-10 atm, and then ignited and
burned and finally expanded through a turbine from which power is
recovered. The process follows essentially a Brayton cycle which is
shown in Figure 4.2 in idealized forms on TS and PV diagrams. The
ideal process consists of an isentropic compression, then heating at
constant pressure followed by an isentropic expansion and finally
cooling at the starting pressure. In practice, efficiencies of the
individual steps are high:
Compressor isentropic efficiency, 85%
Expander isentropic efficiency, 85-90%
Combustion efficiency, 98%](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-84-320.jpg)
![70 T R A N S F E R O F S O L I D S
EXAMPLE 5.1
Conditions of a Coal Slurry Pipeline
Data of a pulverized coal slurry are
c, = 0.4,
D = 0.333 ft,
f= 0.0045 (Blasius’ eq. at N, = 105),
s = 1.5.
Mesh size 24 48 100 Mixture
dhn) 0.707 0.297 0.125 0.321
Weight fraction 0.1 0.8 0.1 1
u, Wsec) 0.164 0.050 0.010 0.0574
The terminal velocities are read off Figure 5.1, and the values of the
mixture are weight averages.
The following results are found with the indicated equations:
item Eq. 24 48 1 0 0 M i x t u r e
“C 5.1 7.94 5.45 3.02
k 5.6 5.8 20.6 1.36 6.27 2.89 9.38 1.25 3.39
WIAPL 5.11 1.539
ApStAp, 5.13 1.296
Eq. (5.1): u;= 34.6(0.4)(0.333)dm
=3232,
Eq. (5.6): u=8.41u,=125u
qcjYom5 ”
4 32.2(1.5 - 1) d,, _ O.O704d,,
= 1.5391,
Eq. (5.13): s= 1 + 0.272(0.4)
0.0045(0.333)32.2(0.5) ’ 3
L (0.0574)2(3.39) 1
= 1.296.
100
6Ll
4 0
10
6
fii 4
”
E
0 2
i
5
0 1
5
F 0 6
0 4
c
u-l
0 2
01
0 06
0 0 4
0 0 2
0 0 1
0 006
0 0 0 4
0 0 0 2
0 001
01
Sphere diameter, cm
Figure 5.1. Settling velocities of spheres as a function of the ratio ot
densities of the two phases. Stokes law applies at diameters below
approximately 0.01 cm (based 011 a chart of La&e et al., Chemical
Engineering Handbook, McGraw-Hill, New York, 1984, p. 5.67).
With coal of sp gr = 1.5, a slurry of 40 ~01% has a sp gr = 1.2.
Accordingly the rule, AP,/AP, = sp gr, is not confirmed accurately
by these results. For particles of one size, Eqs. (5.7) and (5.8) combine to
APs/APr = 1 + ~OOC,[(U,D/U~)~~‘~~,
consistent units. (5.10)
The drag coefficient is The pressure drop relation at the critical velocity given by Eq. (5.1)
is found by substitution into Eq. (5.7) with the result
CD = 1.333gd(s - 1)/u:. (5.8)
A&/APL = 1 + $$[(l/uJvgd(s - 1)/C,]‘.3.
I,
(5.11)
For mixtures, a number of rules has been proposed for evaluating
the drag coefficient, of which a weighted average seems to be
favored,
With Eq. (5.10) the result is
APJAP, = 1 + 1/Co,.3. (5.12)
lG=cw*vG (5.9) With the velocity from Eq. (5.6), Eq. (5.7) becomes
where the wi are the weight fractions of particles with diameters di. A&/APL = 1 + 0.272C,[fgD(s - 1)/~:6]‘.~ (5.13)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-89-320.jpg)
![5.2. PNEUMATIC CONVEYING 71
IO’
IO0
fii
07
a”
>: IO
-1
.E
g
ii
.-
>
10-Z
10-3
I
F
0-2
I I I r I 1 I
r slope = - 0.51
Shear rate, I/set
(a)
IO’ IO2
Shear rate, I/set
(b)
IO3
Figure 5.2. Non-Newtonian behavior of suspensions: (a) viscosity as a function of shear rate, 0.4 wt % polyacrylamide in water at room
temperature; (b) shear stress as a function of shear rate for suspensions of TiO, at the indicated ~01% in a 47.1 wt % sucrose solution whose
viscosity is 0.017 Pa set (Denn, Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1980).
and, for one-sized particles, 5.2. PNEUMATIC CONVEYING
APs/APL = 1+ 0.394Cu[cfD/u,)~&7j72]‘~3. (5.14)
These several pressure drop relations hardly appear consistent, and
the numerical results of Example 5.1 based on them are only
roughly in agreement.
From statements in the literature, it appears that existing slurry
lines were designed on the basis of some direct pilot plant studies.
Nonsettling slurries are formed with fine particles or plastics or
fibers. Although their essentially homogeneous nature would
appear to make their flow behavior simpler than that of settling
slurries, they often possess non-Newtonian characteristics which
complicate their flow patterns. In Newtonian flow, the shear stress
is proportional to the shear strain,
Granular solids of free-flowing natures may be conveyed through
ducts in any direction with high velocity air streams. In the normal
plant, such lines may be several hundred feet long, but dusty
materials such as fly ash and cement have been moved over a mile
in this way. Materials that are being air-veyed include chemicals,
plastic pellets, grains, and powders of all kinds. The transfer of
catalysts between regenerator and reactor under fluidized conditions
is a common operation. Stoess (1983) has a list of recommendations
for about 150 different materials, of which Table 5.1 is a selection.
Basic equipment arrangements are represented in Figure 5.3.
The performance of pneumatic conveyors is sensitive to several
characteristics of the solids, of which the most pertinent ones are
stress = ~(strain),
1. bulk density, as poured and as aerated,
2. true density,
but in other cases the relation between these two quantities is more
complex. Several classes of non-Newtonian behavior are recognized
for suspensions. Pseudoplastic or power-law behavior is represented
by
stress = k(strain)“, n<l,
where k is called the consistency index. Plastic or Bingham behavior
is represented by
3. coefficient of sliding friction ( = tangent of the angle of repose),
4. particle size distribution,
5. particle roughness and shape,
6. moisture content and hygroscopicity, and
7. characteristics such as friability, abrasiveness, flammability, etc.
Sulfur, for example, builds up an electrostatic charge and may
introduce explosive risks.
stress = k, + ~(strain),
where n is called the plastic viscosity. Data for some suspensions
are given on Figure 5.2.
The constants of such equations must be found experimentally
over a range of conditions for each particular case, and related to
the friction factor with which pressure drops and power
requirements can be evaluated. The topic of nonsettling slurries is
treated by Bain and Bonnington (1970) and Clift (1980). Friction
factors of power-law systems are treated by Dodge and Metzner
(1959) and of fiber suspensions by Bobkowitz and Gauvin (1967).
In comparison with mechanical conveyors, pneumatic types
must be designed with greater care. They demand more power
input per unit weight transferred, but their cost may be less for
complicated paths, when exposure to the atmosphere is undesirable
and when operator safety is a problem. Although in the final
analysis the design and operation of pneumatic conveyors demands
the attention of experienced engineers, a design for orientation
purposes can be made by the inexpert on the basis of general
knowledge and rules of thumb that appear in the literature. An
article by Solt (1980) is devoted entirely to preventive trouble-
shooting.
Some basic design features are the avoidance of sharp bends, a
minimum of line fittings, provision for cleanout, and possibly
electrical grounding. In many cases equipment suppliers may wish
to do pilot plant work before making final recommendations. Figure](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-90-320.jpg)
![5.2. PNEUMATIC CONVEYING 73
&
Pickup (a)
Vent
MateJial In Filter Receiver
LJI”“Y~l
and Motor Rotary
Valve
yq-p)
L ,
itch
Rotary Valve
Collector
ifi3
Venturi I
c
Process Machine
Collector
3
3
Figure 5.3. Basic equipment arrangements of pneumatic conveying systems. (a) Vacuum system
with several sources and one destination, multiple pickup; (b) pressure system with rotary valve
feeder, one source and several destinations, multiple discharge; (c) pressure system with Venturi
feed for friable materials; (d) pull-push system in which the fan both picks up the solids and
delivers them [ufier F. J. Gerchow, Chem. Eng. (17 Feb. 1975, p. Ss)].
Piping usually is standard steel, Schedule 40 for 3-7 in. IPS and
Schedule 30 for 8-12 in. IPS. In order to minimize pressure loss and
abrasion, bends are made long radius, usually with radii equal to 12
times the nominal pipe size, with a maximum of 8ft. Special
reinforcing may be needed for abrasive conditions.
feeders, positive pressure systems are limited to about 12 psig.
Other feeding arrangements may be made for long distance transfer
with 90-125psig air. The dense phase pulse system of Figure 5.4
may operate at lo-30 psig.
Linear velocities, carrying capacity as tuft of free air per lb of
solid and power input as HP/tons per hour (tph) are listed in Table
OPERATING CONDITIONS
5.1 as a general guide for a number of substances. These data are
for 4-, S-, and 6-in. lines; for 8-in. lines, both Sat. and HP/tph are
Vacuum systems usually operate with at most a 6 psi differential; at reduced by 15%, and for lo-in. by 25%. Roughly, air velocities in
lower pressures the carrying power suffers. With rotary air lock low positive pressure systems are 2OOOft/min for light materials,](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-92-320.jpg)
![TRANSFER OF SOLIDS
Hose Connec Inns
W!th Qwck Couplings
- Medium L o o p - -
- Long LOOP
ll
Figure 5.4. Sketch of pilot plant arrangement for testing pneumatic
conveying under positive pressure (Kruu.s, Pneumatic Conveying of
Bulk Materials, McGraw-Hill, New York, 1980).
3000-4000 ft/min for medium densities such as those of grains, and
XJOOft/min and above for dense materials such as fly ash and
cement; all of these velocities are of free air, at atmospheric
pressure.
Another set of rules for air velocity as a function of line length
Material
inlet
To receiving hopper
Figure 5.5. Concept of dense phase transfer of friable materials, by
intermittent injection of material and air pulses, air pressures
normally lo-30 psig and up to 90 psig (Sturteuant Engineering Co.,
Boston, MA).
and bulk density is due to Gerchow (1980) and is
ft/min
Line length
w 55 Ib/cuft 55-85 85-115
200 4000 5000 6000
500 5000 6000 7000
1000 6000 7000 8000
Conveying capacity expressed as ~01% of solids in the stream
usually is well under 5 ~01%. From Table 5.1, for example, it is
about 1.5% for alumina and 6.0% for polystyrene pellets, figured at
atmospheric pressure; at 12psig these percentages will be roughly
doubled, and at subatmospheric pressures they will be lower.
POWER CONSUMPTION AND PRESSURE DROP
The power consumption is made up of the work of compression of
the air and the frictional losses due to the flows of air and solid
through the line. The work of compression of air at a flow rate ML
and C,/C, = 1.4 is given by
WC = 3.5(53.3)(7- + 460)m:[(Pz/q)0~2”57 - l] (ft lbf/sec)
(5.15)
with the flow rate in lb/set.
Frictional losses are evaluated separately for the air and the
solid. To each of these, contributions are made by the line itself, the
elbows and other fittings, and the receiving equipment. It is
conservative to assume that the linear velocities of the air and solid
are the same. Since the air flow normally is at a high Reynolds
number, the friction factor may be taken constant at f, = 0.015.
Accordingly the frictional power loss of the air is given by
w,=~P,m:/p,=(u2/2g)[1+2n,+4n,+(0.015/D)(L+~Li)]m:
(ft lbf/sec). (5.16)
The unity in the bracket accounts for the entrance loss, n, is the
number of cyclones, nr is the number of filters, L is the line length,
and Li is the equivalent length of an elbow or fitting. For long
radius bends one rule is that the equivalent length is 1.6 times the
actual length of the bend. Another rule is that the long bend radius
is 12 times the nominal size of the pipe. Accordingly,
Li = 1.6(nRi/2) = 2.5R, = 2.5D;ft, with 0:’ in inches.
(5.17)
The value of g is 32.2 ft lb m/(lbf sec2).
The work being done on the solid at the rate of ml lb/set is
made up of the kinetic gain at the entrance (w2), the lift (ws)
through an elevation AZ, friction in the line (wJ, and friction in the
elbow (ws). Accordingly,
w, = $ ml (ft lbf/sec) . (5.18)
The lift work is
8
w,=Az-mmj=Azmj
8,
(ft lbf/sec). (5.19)
The coefficient of sliding friction f, of the solid equals the tangent of
the angle of repose. For most substances this angle is 30-45” and](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-93-320.jpg)
![76 TRANSFER OF SOLIDS
the value off, is 0.58-1.00. The sliding friction in the line is
w, = f, Lrni (ft lbf/sec) , (5.20)
where L is the line length.
Friction in the curved elbows is enhanced because of
centrifugal force so that
w, =h$ (y)m: = O.O488f,u*mi (ft lbf/sec) (5.21)
The total frictional power is
wf=w1+w*+w3+wq+wg,
and the total power consumption is
(5.22)
w = 5$;.$) W/(ton/hr)l, (5.23)
where 17 is the blower efficiency. Pressure drop in the line is
obtained from the frictional power, the total flow rate, and the
density of the mixture:
AP= Wf
144(mA + ml) pm (Psi). (5.24)
The specific air rate, or saturation, is
saturation = 0.7854(60)0*
(cuft/min of air)/(lb/min of solid)], (5.25)
where the velocity of the air is evaluated at atmospheric pressure.
Example 5.2 makes the calculations described here for power
and pressure drop, and compares the result with the guidelines of
Table 5.1.
5.3. MECHANICAL CONVEYORS AND ELEVATORS
Granular solids are transported mechanically by being pushed along
or dragged along or carried. Movement may be horizontal or
vertical or both. In the process plant distances may be under a
hundred feet or several hundred feet. Distances of several miles
may be covered by belts servicing construction sites or mines or
power plants. Capacities range up to several hundred tons/hr. The
principal kinds of mechanical conveyors are illustrated in Figures
5.7-5.13 and will be described. Many construction features of these
machines are arbitrary. Thus manufacturers’ catalogs are the
ultimate source of information about suitability for particular
services, sizes, capacities, power requirements and auxiliaries,
Much of the equipment has been made in essentially the present
form for about 100 years by a number of manufacturers so that a
body of standard practice has developed.
PROPERTIES OF MATERIALS HANDLED BELT CONVEYORS
The physical properties of granular materials that bear particularly
on their conveying characteristics include size distribution, true and
bulk densities, and angle of repose or coefficient of sliding friction,
but other less precisely measured or described properties are also of
concern. A list of pertinent properties appears in Table 5.2. The
elaborate classification given there is applied to about 500 materials
in the FMC Corporation Catalog 100 (1983, pp. B.27-B.35) but is
too extensive for reproduction here. For each material the table
also identifies the most suitable design of screw conveyor of this
These are high capacity, relatively low power units for primarily
horizontal travel and small inclines. The maximum allowable
inclination usually is 5-15” less than the angle of repose; it is shown
as “recommended maximum inclination” in Table 5.3 for some
substances, and is the effective angle of repose under moving
conditions.
The majority of conveyor belts are constructed of fabric,
rubber, and wire beads similarly to automobile tires, but they are
made also of wire screen or even sheet metal for high temperature
company’s manufacture and a factor for determining the power
requirement. An abbreviated table of about 150 substances appears
in the Chemical Engineers Handbook (1984, p. 7.5). Hudson (1954,
pp. 6-9), describes the characteristics of about 100 substances in
relation to their behavior in conveyors. Table 5.3 lists bulk
densities, angles of respose at rest, and allowable angles of
inclination which are angles of repose when a conveyor is in motion;
references to more extensive listings of such data are given in this
table.
The angle of repose is a measure of the incline at which
conveyors such as screws or belts can carry the material. The
tangent of the angle of repose is the coefficient of sliding friction.
This property is a factor in the power needed to transfer the
material by pushing or dragging as in pneumatic, screw, flight, and
Redler equipment.
Special provisions need to be made for materials that tend to
form bridges; Figure 5.13(a) is an example of a method of breaking
up bridges in a storage bin so as to ensure smooth flow out.
Materials that tend to pack need to be fluffed up as they are pushed
along by a screw; adjustable paddles as in Figure 5.7(d) may be
sufficient.
SCREW CONVEYORS
These were invented by Archimedes and assumed essentially their
present commercial form a hundred years or so ago. Although the
equipment is simple in concept and relatively inexpensive, a body of
experience has accumulated whereby the loading, speed, diameter,
and length can be tailored to the characteristics of the materials to
be handled. Table 5.4, for example, recognizes four classes of
materials, ranging from light, freeflowing, and nonabrasive
materials such as grains, to those that are abrasive and have poor
flowability such as bauxite, cinders, and sand. Only a portion of the
available data are reproduced in this table.
Lengths of screw conveyors usually are limited to less than
about 150 ft; when the conveying distance is greater than this, a belt
or some other kind of machine should be chosen. The limitation of
length is due to structural strength of the shaft and coupling. It is
expressed in terms of the maximum torque that is allowable.
Formulas for torque and power of screw conveyors are given in
Table 5.4 and are applied to selection of a conveyor in Example 5.3.
Several designs of screws are shown in Figure 5.7. The basic
design is one in which the pitch equals the diameter. Closer spacing
is needed for carrying up steep inclines, and in fact very fine pitch
screws operating at the relatively high speeds of 350 rpm are used to
convey vertically. The capacity of a standard pitch screws drops off
sharply with the inclination, for example:
Angle (degrees)
Percent of capacity
<8 20 30 45
100 55 30 0
Allowable loadings as a percentage of the vertical cross section
depend on the kind of material being processed; examples are
shown in Table 5.4.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-95-320.jpg)
![5.3. MECHANICAL CONVEYORS AND ELEVATORS 77
EXAMPLE 5.2
Size aud Power Requirement of a Pneumatic Transfer Line
A pneumatic transfer line has 300 ft of straight pipe, two long radius
elbows, and a lift of 5Oft. A two-stage cyclone is at the receiving
end. Solid with a density of 125 Ib/cuft is at the rate of 10 tons/hr
and the free air is at 5000 ft/min. Inlet condition is 27 psia and
100°F. Investigate the relation btween line diameter and power
requirement.
On a first pass, the effect of pressure loss on the density of the
air will be neglected.
Mass flow rate of solid:
ml = 20,000/3600 = 5.56 Ib/sec.
Mass flow rate of air:
rn: = ~~(0.075)0’ = 4.91D*Ib/sec.
Density of air:
on = 0.075 & = 0.138 Ib/cuft.
( .>
Density of mixture:
Pm =
(4 + 4)
mLlp, + dl~,
(mi + 5.56)
=mL/0.138 + 5.56’125
Linear velocity of air at inlet:
u =z + =45.37fps.
( >
Assume air and solid velocities equal. Elbow radius = 120.
Elbow equivalent length,
L, = 1.6(n’2)(120) = 30.20
Power for compression from 14.7 psia and 560 R to 27 psia,
k/(/c - 1) = 3.5,
w, = 3.5RT,[(P,/P,)“~2857 - l]mi
= 3.5(53.3)(560)[(27/14.7)“~2857 - 1]4.910’
= 973050’ ft lbf/sec.
Frictional contribution of air
w1 =$ [5 + (0.015/0)(300 + 2(30.2)D]mi
= [(45.4)2’64.4][5.9 + (4.5’D)](4.91DZ)
= 157.102(5.9 + 4.5’0)
For the solid, take the coefficient of sliding friction to be f, = 1.
Power loss is made up of four contributions. Assume no slip
velocity;
w,=w*+w,+w,+w,
= [u2/2g + AZ +f,L + 2(0.0488)f,u2]mj
= 5.56[45.4”64.4 + 50 + 300 + 2(0.0488)45.4’]
= 3242.5ft lbf/sec.
Total friction power:
wf = 3242.5 + 157.10’(5.9 + 4.5/D).
Pressure drop:
AP-
Wf
I Pm psi
144(m: + m,)
Fan power at 9 = 0.5:
p = 550;.$0)
= sHP/tph,
saturation = 5000(n’4)D2
20, ooo/60
= 11.78D2SCFM/(lb/min).
1 PS D (RI In: pm w, w,
3 0.2557 0.3210 2.4808 6362 3484
4 0.3356 0.5530 1.5087 10,959 3584
5 0.4206 0.8686 1.0142 17,214 3704
6 0.5054 1.2542 0.7461 24,855 3837
3 10.2 3.58 0.77
4 6.1 5.29 1.33
5 4.1 7.60 2.08
6 2.9 1 0 . 4 4 3.00
From Table 5.1, data for pebble lime are
sat = 1.7 SCFM/(lb/min)
power = 3.0 HP/TPH
and for soda ash:
sat = 1.9 SCFM/(lb/min)
power = 3.4 HP/TPH.
The calculated values for a 4in. line are closest to the recom-
mendations of the table.
services. A related design is the apron conveyor with overlapping For bulk materials, belts are troughed at angles of 20-45”. Loading
pans of various shapes and sizes (Fig. 5.8), used primarily for short of a belt may be accomplished by shovelling or directly from
travel at elevated temperatures. With pivoted deep pans they are overhead storage or by one of the methods shown on Figure 5.9.
also effective elevators. Discharge is by throwing over the end of the run or at intermediate
Flat belts are used chiefly for moving large objects and cartons. points with plows.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-96-320.jpg)
![80 TRANSFER OF SOLIDS
Shear
(a)
pin
(d) (e)
Figure 5.7. A screw conveyor assembly and some of the many kinds of screws in use. (a) Screw conveyor assembly with feed hopper
and discharge chute. (b) Standard shape with pitch equal to the diameter, the paddles retard the forward movement and promote
mixing. (c) Short pitch suited to transfer of material up inclines of as much as 20”. (d) Cut flight screws combine a moderate mixing
action with forward movement, used for light, fine, granular or flaky materials. (e) Ribbon flights are suited to sticky, gummy or
viscous substances.
EXAMPLE 5.3
Sizing a Screw Conveyor
Dense soda ash with bulk density 6Olb/cuft is to be conveyed a
distance of 100 ft and elevated 12 ft. The material is class II-X with
a factor F = 0.7. The bearings are self-lubricated bronze and the
drive is V-belt with 7) = 0.93. The size, speed, and power will be
selected for a rate of 15 tons/hr.
Q = 15(2000)/60 = 500 cuft/hr.
According to Table 5.4(a) this capacity can be accommodated by a
12 in. conveyor operating at
o = (500/665)(50) = 37.6 rpm, say 40 rpm
From Table 5.4(c) the bearing factor is
s = 171.
Accordingly,
1; = [171(40) + 0.7(500)(60)]100 + 0.51(12)(30,000)/106
= 2.97 HP
motor HP = G@/q = 1.25(2.97)/0.93 = 3.99,
torque = 63,000(2.97)/40 = 4678 in. lb.
From Table 5.4(d) the limits for a 12 in. conveyor are 10.0 HP
and 6300 in. lb so that the selection is adequate for the required
service.
A conveyor 137 ft long would have a shaft power of 4.00 HP
and a torque of 6300 in. Ibs, which is the limit with a 2 in. coupling;
a sturdier construction would be needed at greater lengths.
For comparison, data of Table 5.5 show that a 14 in. troughed
belt has an allowable speed of 267fpm at allowable inclination of
19” (from Table 5.3), and the capacity is
2.67(0.6)(38.4) = 61.5 tons/hr,
far more than that of the screw conveyor.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-99-320.jpg)
![82 TRANSFER OF SOLIDS
TABLE 5.5-(continued)
(c) Power to Drive Empty Conveyor
18
16
I I
Ml#lt,nlv Chnrt
60”
or-1 1 ’ ’ I I I I I I
0 400 800 1200 1600 2000 2400
Length of Conveyor in Feet
particularly suited to a process. Capacity and power data for bucket
machines are given in Table 5.6. Flight and apron conveyors are
illustrated in Figure 5.11.
CONTINUOUS FLOW CONVEYOR ELEVATORS
One design of a drag-type of machine is the Redler shown on Figure
5.12. They function because the friction against the flight is greater
than that against the wall. Clearly they are versatile in being able to
transfer material in any direction and have the often important
merit of being entirely covered. Circular cross sections are available
but usually they are square, from 3 to 30 in. on a side, and operate
at speeds of 30-250 ft/min, depending on the material handled and
the construction. Some data are shown in Table 5.7. Most dry
granular materials such as wood chips, sugar, salt, and soda ash are
handled very well in this kind of conveyor. More difficult to handle
are very fine materials such as cement or those that tend to pack
such as hot grains or abrasive materials such as sand or crushed
stone. Power requirement is dependent on the coefficient of sliding
friction. Factors for power calculations of a few substances are
shown in Table 5.7.
The closed-belt (zipper) conveyor of Figure 5.13 is a carrier
that is not limited by fineness or packing properties or abrasiveness.
Of course, it goes in any direction. It is made in a nominal 4-in.
size, with a capacity rating by the manufacturer of O.O7cuft/ft of
travel. The power requirement compares favorably with that of
open belt conveyors, so that it is appreciably less than that of other
types. The formula is
HP = O.OOl[(L,/30 + 5)~ + (L,/16 + 2L,)T], (5.26)
where
u = ft/min,
T = tons/hr,
L, = total belt length (ft),
L, = length of loaded horizontal section (ft),
L, = length of loaded vertical section (ft).
Speeds of 2OOft/min or more are attainable. Example 5.5 shows
that the power requirement is much less than that of the Redler
conveyor.
(a)
Figure 5.9. Some arrangements of belt conveyors (Stephens-Adamson Co.) and types of idlers
(FMC Corp.). (a) Horizontal conveyor with discharge at an intermediate point as well as at the
end. (b) Inclined conveyor, satisfactory up to 20” with some materials. (c) Inclined or retarding
conveyor for lowering materials gently down slopes. (d) A flat belt idler, rubber cushion type. (e)
Troughed belt idler for high loadings; usually available in 20”, 35”, and 45” side inclinations.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-101-320.jpg)
![88 TRANSFER OF SOLIDS
h-d
Feed hopper
r Screw conveyer
Belt dwe
in)
Figure 5X%-(continued)
Fabric
C h a m b e r ’
Comparison of Redler and Zippered Belt Conveyors
Soda ash of bulk density 30 lb/tuft is to be moved 120ft
horizontally and 30 ft vertically at the rate of 350 cuft/hr. Compare
power requirements of Redler and zippered belt conveyors for this
service.
A 3-in Redler is adequate:
HP = $$ [X4(120) + 6.5(30) + 201 = 8.31.
For a closed belt,
350
u=-=83.3fpm,
0.07(60)
350
u = 60(n,4)(3,12)2 = 118.8 fpm,
which is well under the 200 fpm that could be used,
which is within the range of Table 5.7(a),
L, = 300, L, = 120, L, = 30.
Use Eq. (5.26):
tons/hr = 350(30)/2000 = 5.25
HP = 0.001{(300/30 + 5)83.3 + [120/16 + 2(30)]5.25}
Take constants from Table 5.7(b) for a Redler. = 1.60.
R E F E R E N C E S
1. T.H. Allegri, Materials Handling Principles and Practice, Van Nostrand
Reinhold, New York, 1984.
2. A.G. Bain and S.T. Bonnington, The Hydraulic Transport of Solids by
Pipeline, Pergamon, New York, 1970.
3. M.V. Bhatic and P.N. Cheremisinoff, Solid and Liquid Conveying
System, Technomic, Lancaster, PA, 1982.
4. A.J. Bobkowicz and W.G. Gauvin, The effects of turbulence in the flow
characteristics of model tibre suspensions, Chem. Eng. Sci. 22, 229-247
(1967).
5. R. Clift, Conveyors, hydraulic, Encycl. Chem. Process. Des. 11, 262-278
(1980).
6. H. Colijn, Mechanical Conveyors for Bulk Solidz, Elsevier, New York,
1985.
7. Conveyor Equipment Manufacturers Association, Belt Conveyors for
Bulk Materials, Van Nostrand Reinhold, New York, 1979.
8. D.W. Dodge and A.B. Metzner, Turbulent flow of non-newtonian
systems, AIChE .I. 5, 189 (1959).
9. G.H. Ewing, Pipeline transmission, in Marks’ Mechanical Engineers
Handbook, McGraw-Hill, New York, 1978, pp. 11.134-11.135.
10. FMC Corp. Material Handling Equipment Division, Catalog 100, Homer
City, PA, 1983.
11. F.J. Gerchow, Conveyors, pneumatic, in Encycl. Chem. Process. Des.
l&278-319 (1980); Chem. Eng., (17 Feb. 1975, 31 Mar. 1975).
12. H.V. Hawkins, Pneumatic conveyors, in Marks’ Mechanical Engineers
Handbook, McGraw-Hill, New York, 1978, pp. 10.50-10.63.
l3. J.W. Hayden and T.E. Stelson, Hydraulic conveyance of solids in pipes,
in Zandi, Ref. 27, 1971, pp. 149-163.
14. W.G. Hudson, Conveyors and Related Equipment, Wiley, New York,
1954.
15. E. Jacques and J.G. Montfort, Coal transportation by slurry pipeline, in
Considine (Ed.), Energy Technology Handbook, McGraw-Hill, New
York, 1977, pp. 1.178-1.187.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-107-320.jpg)
![94 FLOW OF FLUIDS
EXAMPLE 6.3
Units of the Energy Balance
In a certain process the changes in stored energy and the friction are
AE = - 135 ft lbf/lb
= 3 6 4 . 6 2 , 364.66,
w =364.6=kgf=37.19-.
m kgf
s kg 9.806N kg
rvf = 13 ft lbf/lb.
The net work will be found in several kinds of units:
At sea level, numerically lbf = lb and kgf = kg.
Accordingly,
w, = -(AE + wr) = 122 ft Ibf/lb,
ft lbf 4.448N2.204 lb m
w, = 122~~~~
lbf k g 3.28ft
w = ,,,!+f&~fm= 37,19-
kgf m
s lb lbf kg 3.28ft kg ’
as before.
and the simpler form of the energy balance becomes
AE + W, = -W,. (6.17)
The units of every term in these energy
alternately:
balances are
ft Ib,/lb with g, = 32.174 and g in ft/sec* (32.174 at sea level).
N m/kg = J/kg with g, = 1 and g in m/se? (1.000 at sea level).
kg, m/kg with g, = 9.806 and g in m/se? (9.806 at sea level).
Example 6.3 is an exercise in conversion of units of the energy
balances.
The sign convention is that work input is a negative quantity
and consequently results in an increase of the terms on the left of
Eq. (6.17). Similarly, work is produced by the flowing fluid only if
the stored energy AE is reduced.
6.3. LIQUIDS
Velocities in pipe lines are limited in practice because of
1. the occurrence of erosion.
2. economic balance between cost of piping and equipment and the
cost of power loss because of friction which increases sharply
with velocity.
Although erosion is not serious in some cases at velocities as high as
lo-15ft/sec, conservative practice in the absence of specific
knowledge limits velocities to 5-6 ft/sec.
Economic optimum design of piping will be touched on later,
but the rules of Table 6.2 of typical linear velocities and pressure
drops provide a rough guide for many situations.
The correlations of friction in lines that will be presented are
for new and clean pipes. Usually a factor of safety of 20-40% is
advisable because pitting or deposits may develop over the years.
There are no recommended fouling factors for friction as there are
for heat transfer, but instances are known of pressure drops to
double in water lines over a period of 10 years or so.
In lines of circular cross section, the pressure drop is
represented by
D,, = 4(cross section)/wetted perimeter.
For an annular space, D,, = Dz - D,.
In laminar flow the friction is given by the theoretical Poiseuille
equation
f = WN,,, Nne < 2100, approximately. (6.19)
At higher Reynolds numbers, the friction factor is affected by the
roughness of the surface, measured as the ratio e/D of projections
on the surface to the diameter of the pipe. Values of E are as
follows; glass and plastic pipe essentially have E = 0.
E (R) E (mm)
Riveted steel
Concrete
Wood stave
Cast iron
Galvanized iron
Asphalted cast iron
Commercial steel or
wrought iron
Drawn tubing
0.003-0.03 0.9-9.0
0.001-0.01 0.3-3.0
0.0006-0.003 0.18-0.9
0.00085 0 . 2 5
0.0005 0 . 1 5
0.0004 0 . 1 2
0 . 0 0 0 1 5 0.046
0.000005 0 . 0 0 1 5
The equation of Colebrook [J. Inst. Civ. Eng. London, 11, pp.
133-156 (1938-1939)] is based on experimental data of Nikuradze
[Veer. Dtsch. Zng. Forschungsh. 356 (1932)].
Nae > 2100. (6.20)
Other equations equivalent to this one but explicit in f have been
devised. A literature review and comparison with more recent
experimental data are made by Olujic [Chem. Eng., 91-94, (14
Dec. 1981)]. Two of the simpler but adequate equations are
f =1.6364 ln
H
?+:)I-’
Re
[Round, Can. J. C&m. Eng. 58, 122 (1980)],
I=(-. [
- 2
0 86861n &-2.18021n &+!$
III (6.22)
Re
For other shapes and annular spaces, D is replaced by the hydraulic [Schacham, Ind. Eng. Chem. Fundam. 19(5), 228 (198O)J. These](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-113-320.jpg)
![6.3. LIQUIDS 95
TABLE 6.2. Typical Velocities and Pressure Drops in Pipelines
Liquids (psi/lOOft)
LiquidzPwrhin
Bubble Point
Light Oils
and Water “%p,”
Pump suction
Pump discharge
Gravity flow to or from
tankage, maximum
Thermosyphon reboiler
inlet and outlet
0 . 1 5
2 . 0
(or 5-7 fps)
0 . 0 5
0 . 2
0 . 2 5 0 . 2 5
2.0 2.0
(or 5-7 fps) (or 3-4fps)
0 . 0 5 0 . 0 5
Gases (psi/lOOft)
Pressure (psig)
o-300ft 300-600ft
Equivalent Length Equivalent Length
-13.7(28 in.Vac) 0 . 0 6 0 . 0 3
-12.2(25 in.Vac) 0 . 1 0 0 . 0 5
-7.5(15 in.Vac) 0 . 1 5 0 . 0 8
0 0 . 2 5 0 . 1 3
5 0 0 . 3 5 0 . 1 8
100 0 . 5 0 0 . 2 5
150 0 . 6 0 0 . 3 0
200 0 . 7 0 0 . 3 5
500 2 . 0 0 1.00
Steam psi/lOOft Maximumft/min
Under 50 psig 0 . 4 1 0 , 0 0 0
Over 50 psig 1.0 7000
Steam Condensate
To traps, 0.2 psi/l 00 ft. From bucket traps, size on the basis of 2-3
times normal flow, according to pressure drop available. From
continuous drainers, size on basis of design flow for 2.0 psi/100 ft
Control Valves
Require a pressure drop of at least 10 psi for good control, but values as
low as 5 psi may be used with some loss in control quality
Particular Equipment Lines (R/see)
Reboiler, downcomer (liquid)
Reboiler, riser (liquid and vapor)
Overhead condenser
Two-phase flow
Compressor, suction
Compressor, discharge
Inlet, steam turbine
Inlet, gas turbine
Relief valve, discharge
Relief valve, entry point at silencer
3-7
35-45
25-100
35-75
75-200
loo-250
120-320
150-350
0.5v,"
KS
a v, is sonic velocity.
three equations agree with each other within 1% or so. The
Colebrook equation predicts values l-3% higher than some more
recent measurements of Murin (1948), cited by Olujic (Chemical
Engineering, 91-93, Dec. 14, 1981).
For orientation purposes, the pressure drop in steel pipes may
be found by the rapid method of Table 6.3, which is applicable to
highly turbulent flow for which the friction factor is given by von
Karman’s equation
f = 1.3251[ln(D/e) + 1.3123)]-*. (6.23)
Under some conditions it is necessary to employ Eq. (6.18) in
differential form. In terms of mass flow rate,
(6.24)
Example 6.4 is of a case in which the density and viscosity vary
along the length of the line, and consequently the Reynolds number
and the friction factor also vary.
FITTINGS AND VALVES
Friction due to fittings, valves and other disturbances of flow in pipe
lines is accounted for by the concepts of either their equivalent
lengths of pipe or multiples of the velocity head. Accordingly, the
pressure drop equation assumes either of the forms
AP = f(L + c Li)pu2/2gJ, (6.25)
AP = [f(L/D) + c K]w2/2gc. (6.26)
Values of equivalent lengths Li and coefficients K, are given in
Tables 6.4 and 6.5. Another well-documented table of Ki is in the
Chemical Engineering Handbook (McGraw-Hill, New York, 1984
p. 5.38).
Comparing the two kinds of parameters,
K, = fLJD (6.27)
so that one or the other or both of these factors depend on the
friction factor and consequently on the Reynolds number and
possibly E. Such a dependence was developed by Hooper [Chem.
Eng., 96-100, (24 Aug. 1981)] in the equation
K = KJNRe + K,(l + l/D), (6.28)
where D is in inches and values of K, and K, are in Table 6.6.
Hooper states that the results are applicable to both laminar and
turbulent regions and for a wide range of pipe diameters. Example
6.5 compares the several systems of pipe fittings resistances. The K,
method usually is regarded as more accurate.
O R I F I C E S
In pipe lines, orifices are used primarily for measuring flow rates but
sometimes as mixing devices. The volumetric flow rate through a
thin plate orifice is
A, = cross sectional area of the orifice,
/3 = d/D, ratio of the diameters of orifice and pipe.
For corner taps the coefficient is given by
cd = 0.5959 + 0.0312/12.’ - 0.184@
+ (0.0029~2s)(106/Re,)0~7s (6.30)
(International Organization for Standards Report DIS 5167,
Geneva, 1976). Similar equations are given for other kinds of orifice
taps and for nozzles and Venturi meters.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-114-320.jpg)
![100 FLOW OF FLUIDS
TABLE 6.6. Velocity Head Factors of Pipe Fittings’ 6.5. OPTIMUM PIPE DIAMETER
Elbows
ValWS
Fitting type K1 Kc.2
- -
Standard (RID = 1 I, screwed 800 0.40
Standard (RID = 1). flanged/welded 800 0.25
Long-radius (RID = 1.5). all types 800 0.20
30” 1 Weld (90” angle) 1,000 1 . 1 5
Mitered 2 Weld (45” angles) 800 0.35
elbows 3 Weld (30’ angles) 800 0.30
(RID-1.5) 4 Weld (22X” angles) 800 0.27
5 Weld (18” angles) 800 0.25
Standard (R/D = 1). all types 500 0.20
15O
Long-radius (RID = 1.5). all types 500 0.15
Mitered, 1 weld, 45’ angle 500 0.25
Mitered, 2 weld, 22X” angles 500 0.15
Standard (R/D = 1). screwed 1,000 0.60
180” Standard (RID = 1). flanged/welded 1,000 0.35
Long radius (RID = 1.5). all types 1,000 0.30
Jsed
Standard, screwed 500 0.70
Long-radius, screwed 800 0.40
as
Standard, flanged or welded 800 0.80
!Ibow
Stub-in-type branch 1,000 1 .oo
+Jn- Screwed 200 0.10
-hrough Flanged or welded 150 0.50
ee Stub-in-type branch 100 0.00
Sate, Full line size, p = 1 .O 300 0.10
Iall, Reduced trim, p = 0.9 500 0.15
1lug Reduced trim, p = 0.8 1,000 0.25
Globe, standard 1,500 4.00
Globe, angle or Y-type 1,000 2.00
diaphragm, dam type 1,000 2.00
3utterflv 800 0.25
Lift 2,000 10.00
:heck Swing 1,500 1.50
Tilting-disk 1,000 0.50
Note: Use R/D = 1.5 values for R/D = 5 pipe bends, 45’ to 180’.
Use appropriate tee values for flow through crossas.
a Inlet, flush, K = 160/N,, + 0.5. Inlet, intruding, K = 160/N,, = 1.0.
Exit, K = 1 .O. K = K,/NRe + K,(l + l/D), with D in inches.
[Hooper, Chem. Eng. 96-100 (24 Aug. 1981)].
from Eqs. (4)-(10) with the aid of the Newton-Raphson method
for simultaneous nonlinear equations.
Some simplification is permissible for water distribution
systems in metallic pipes. Then the Hazen-Williams formula is
adequate, namely
Ah = AP/p = 4.727L(Q/130)‘-852/D4~87w (6.31)
with linear dimensions in ft and Q in cuft/sec. The iterative solution
method for flowrate distribution of Hardy Cross is popular.
Examples of that procedure are presented in many books on fluid
mechanics, for example, those of Bober and Kenyon (Fluid
Mechanics, Wiley, New York, 1980) and Streeter and Wylie (Fluid
Mechanics, McGraw-Hill, New York, 1979).
With particularly simple networks, some rearrangement of
equations sometimes can be made to simplify the solution. Example
6.7 is of such a case.
In a chemical plant the capital investment in process piping is in the
range of 25-40% of the total plant investment, and the power
consumption for pumping, which depends on the line size, is a
substantial fraction of the total cost of utilities. Accordingly,
economic optimization of pipe size is a necessary aspect of plant
design. As the diameter of a line increases, its cost goes up but is
accompanied by decreases in consumption of utilities and costs of
pumps and drivers because of reduced friction. Somewhere there is
an optimum balance between operating cost and annual capital cost.
For small capacities and short lines, near optimum line sizes
may be obtained on the basis of typical velocities or pressure drops
such as those of Table 6.2. When large capacities are involved and
lines are long and expensive materials of construction are needed,
the selection of line diameters may need to be subjected to
complete economic analysis. Still another kind of factor may
need to be taken into account with highly viscous materials:
the possibility that heating the fluid may pay off by reducing the
viscosity and consequently the power requirement.
Adequate information must be available for installed costs of
piping and pumping equipment. Although suppliers quotations are
desirable, published correlations may be adequate. Some data and
references to other published sources are given in Chapter 20. A
simplification in locating the optimum usually is permissible by
ignoring the costs of pumps and drivers since they are essentially
insensitive to pipe diameter near the optimum value. This fact is
clear in Example 6.8 for instance and in the examples worked out
by Happel and Jordan (Chemical Process Economics, Dekker, New
York, 1975).
Two shortcut rules have been derived by Peters and
Timmerhaus (1980; listed in Chapter 1 References) for optimum
diameters of steel pipes of l-in. size or greater, for turbulent and
laminar flow:
D = 3.9Q”.45po.‘3, turbulent flow, (6.32)
D = 3.0Q”.36po.18, laminar flow. (6.33)
D is in inches, Q in cuft/sec, p in lb/tuft, and p in cP. The factors
involved in the derivation are: power cost = O.O55/kWh, friction
loss due to fittings is 35% that of the straight length, annual fixed
charges are 20% of installation cost, pump efficiency is 50%, and
cost of l-in. IPS schedule 40 pipe is $0.45/ft. Formulas that take
additional factors into account also are developed in that book.
Other detailed studies of line optimization are made by Happel
and Jordan (Chemical Process Economics, Dekker, New York,
1975) and by Skelland (1967). The latter works out a problem in
simultaneous optimization of pipe diameter and pumping tem-
perature in laminar flow.
Example 6.8 takes into account pump costs, alternate kinds of
drivers, and alloy construction.
6.6. NON-NEWTONIAN LIQUIDS
Not all classes of fluids conform to the frictional behavior described
in Section 6.3. This section will describe the commonly recognized
types of liquids, from the point of view of flow behavior, and will
summarize the data and techniques that are used for analyzing
friction in such lines.
VISCOSITY BEHAVIOR
The distinction in question between different fluids is in their
viscosity behavior, or relation between shear stress r (force per unit
area) and the rate of deformation expressed as a lateral velocity](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-119-320.jpg)
![6.6. NON-NEWTONIAN LIQUIDS 101
EXAMPLE 6.5
Comparison of Pressure Drops in a Line with Several Sets of
Fittings Resistances
The flow considered is in a 12-inch steel line at a Reynolds number
of 6000. With E = 0.00015, Round’s equation gives f = 0.0353. The
line composition and values of fittings resistances are:
Table 6.6
Table 6.4 Table 6.5
L K K, 4 K
Line 1000
6 LR ells 0.25 ii0 075 0.246
4 tees, branched fi 0.5 150 0 . 1 5 0 . 5 6 7
2 gate valves, open
1 globe valve
3470 0.05 300 0 . 1 0 0 . 1 5 8
5.4 1500 4 . 0 0 4 . 5 8
1738 9.00 8.64
Table 6.4, &=;(1738)=61.3,
Table 6.5,
A P
0
=f+ K,
= 0~035w~) + gJ0 = 44
1
3
. ,
Table 6.6,
A P
0
= 35.3 + 8.64 = 43.9.
The value K = 0.05 for gate valve from Table 6.5 appears to be
low: Chemical Engineering Handbook, for example, gives 0.17,
more nearly in line with that from Table 6.6. The equivalent length
method of Table 6.4 gives high pressure drops; although
convenient, it is not widely used.
EXAMPLE 6.6 Friction factor:
A Network of Pipelines in Series, Parallel, and Branches: the
Sketch, Material Balances, and Pressure Drop Equations
Pressure drop:
Jj = 1.6364/[1n(c/D, + 6.5/(NnJij)]‘.
Pressure drops in key lines:
hei = (8plg,n2)f;iLijQ;/D, = k&L,Q;/D;.
Q,
” *
3 7 6
Reynolds number:
(Ge)ij = JQ,jPlnDijP. (4
App12 = PI - f’z - &L,,Q:,lD:, = 0,
Apa3 = P2 - P3 - kf,,L,,Q$JD& = 0,
Ap,, = P2 - Ps = kf~~)L~~)(Q~))‘/(D~))5
= kf~~~L~~~(Q~~~)2/(D~~)5
= kf~~)L~)(Q~~))2/(D~))5
App4s = P4 - P5 - kfd5 L,, Q&/L& = 0,
Ap,, = Ps - Ps - kf,&L!:dD:, = 0
N o d e Material Balance at Node:
1 c&,-cl,,-Q,,=O
2 Q,,-Q,,-Q~~-Q~~-Q~~=O
3 Q,,+Q,,-OS,=0
4 Q,4-Q40-Q45=0
5
Q + Ql” + Q’2’ + Q’3’
2s - Qs, - Qss = 0
6 Q;;+Q:,“-Q;;=O
Overall Q,,+Q,,-Q,,-Q,,-Q,,=O
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(1‘3
(17)
EXAMPLE 6.7
Flow of Oil in a Branched Pipeline
The pipeline handles an oil with sp gr = 0.92 and kinematic viscosity
of 5centistokes(cS) at a total rate of 12,00Ocuft/hr. All three
pumps have the same output pressure. At point 5 the elevation is
100 ft and the pressure is 2 atm gage. Elevations at the other points
are zero. Line dimensions are tabulated following. The flow rates in
each of the lines and the total power requirement will be found.
Line L (ft) D (ft)
14 1000 0.4
24 2000 0.5 =
34 1500 0.3
4 5 4000 0.75
Q, + Q, + Q3 = Q., = 12,000/3600 = 3.333 cfs
N -3L-
4Q 23,657Q
zz-
Re nDV nD(5/92,900) D
59,142&r
47,313(2,,
78,556Q2,,
31,542Q2,,
(1)
(2)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-120-320.jpg)
![102 FLOW OF FLUIDS
EXAMPLE 6.7-(continued)
E = 0.00015 ft,
h = 8fL2Q: = 0.0251fLQ2,DS ft,
f gcn D
Q,[ 1 + 1.2352 fi
(,,I” + 0.3977($1’2] = Q4 = 3.333,
(3)
(4)
(5)
(6)
(7)
(8)
1.6364
’ = [ln(2.03(10-‘)/D + 6.5/NRJ2.
For line 45,
(N& = 31542 (3.333) = 105,140,
f4 = 0.01881,
@f 145 =
0.02517(0.01881)(4000)(3.333)2 = 88,65 ft,
(o.75)5
Procedure:
1.
2.
3.
4.
5.
As a first trial assume fi = f2 =f3, and find fJ, = 1.266 from Eq.
(8).
Find Q, and Q3 from Eqs. (6) and (7).
With these values of the Qi, find improved values of the f; and
hence improved values of Q2 and Q3 frog Eqs. (6) and (7).
Check how closely Q, + Q2 + Q3 - 3.333 = 0.
If check is not close enough, adjust the value of Q, and repeat
the calculations.
The two trials shown following prove to be adequate.
Q, 0, Q, 0.3 10/3-a, f,
1.2660 1.5757 0.4739 3.3156 0.0023 0.02069
1.2707 1.5554 0.5073 3.3334 0.0001 0.02068
Summary :
Line &#. f a 4
I
14 75,152 0.02068 1.2707 82.08
24 60,121 0.02106 1.5554 82.08
34 99,821 0.02053 0.5073 82.08
45 105,140 0.01881 3.3333 88.65
hf14 = kf24 = 5 34 =
0.02517(0.02068)(1000)(1.2707)2 = 82.08 ft.
(o.4)5
Velocity head at discharge:
s=&&$=O.SSft.
Total head at pumps:
2(2117)
hp = 0.92(62.4) + loo
+ 0.88 + 82.08 + 88.65
= 345.36 ft.
0.92(62.4)(10/3)345.36
= 66,088 ft lb/set
120.2 HP, 89.6 kW.
1 0 ! ExarilF-le 6 7 ; t 1 ow in a ts t-at-,
chcd PIPeline
20 REAU Dl,D2>D3,Ll>L2,L3
30 DATA .4,.5,.3>1000>2000>1500
48 INFIJT Ql
50 Q2=1.2352$Ql
60 Q3=.397i*Ql
70 R1=59142561
8 0 R2=47313*Ql
90 R3=78556*Ql
100 Fl=1.6364/L#G~.135f.00015~Dl
+6.51Rl>^2
110 F2=1.6364/LOGC.l35*.00015~D2
+6.5.‘R2)*2
120 F3=1.6364iLOGC.135Y.00015~D3
+6.5/R3)*2
1 3 0 Q2=1,2352SQl*CFl~F2>^.5 ! i m
p r o v e d v a l u e
1 4 0 Q3=.3977%Ql%CFl/F3>‘.5 ! imp
r o v e d v a l u e
1 5 0 X=10/3-G!l-Q2-Q3 ! s h o u l d b e
l e s s t h a n 0 . 0 0 0 1
1 6 0 DISF XpQl>G!2,Q3
1 7 0 GOTO 4 0 ! c h o o s e a n o t h e r val
UQ o f 121 i f condi?icln o f s t e
P 1 5 0 i s n o t s a t i s f i e d
180 END.
Characteristics of the alternate pump drives are:
Economic Optimum Pipe Size for Pumping Hot Oil with a
Motor or Turbine Drive
A centrifugal pump and its spare handle 1OOOgpm of an oil at
500°F. Its specific gravity is 0.81 and its viscosity is 3.OcP. The
length of the line is 600 ft and its equivalent length with valves and
other fittings is 9OOft. There are 12 gate valves, two check valves,
a. Turbines are 36OOrpm, exhaust pressure is 0.75 bar, inlet
pressure is 20 bar, turbine efficiency is 45%. Value of the high
pressure steam is $5.25/10OOlbs; that of the exhaust is
$0.75/1000 lbs.
h. Motors have efficiency of 90%, cost of electricity is $O.O65/kWh.
and one control valve. Cost data are:
Suction pressure at the pumps is atmospheric; the pump head
exclusive of line friction is 120 psi. Pump efficiency is 71%. Material
of construction of line and pumps is 316 SS. Operation is 8000 hr/yr.
1. Installed cost of pipe is 7.50 $/ft and that of valves is 600D”.7 $
each, where D is the nominal pipe size in inches.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-121-320.jpg)
![EXAMPLE 6.8-(continued)
2. Purchase costs of pumps, motors and drives are taken from
Manual of Economic Analysis of Chemical Processes, Institut
Francais du Petrole (McGraw-Hill, New York, 1976).
3. All prices are as of mid-1975. Escalation to the end of 1984
requires a factor of 1.8. However, the location of the optimum
will be approximately independent of the escalation if it is
assumed that equipment and utility prices escalate approximately
uniformly; so the analysis is made in terms of the 1975 prices.
Annual capital cost is 50% of the installed price/year.
The summary shows that a 6-in. line is optimum with motor
drive, and an B-in. line with turbine drive. Both optima are
insensitive to line sizes in the range of 6-10 in.
Q = 1000/(7.48)(60) = 2.2282 cfs, 227.2 m3/hr,
N -4Qp -4(2.2282)(0.81)(62.4)-71,128
Re nDp n(O.O00672)(3)D D ’
0.135(0.00015) 6 . 5 0 2
D
+71,128 1
Pump head:
h = 120(144) 8fLQ’
p O.gl(62.4) +$$
= 341.88 + 124.98f /Ds ft.
Motor power:
p =C?P~ = 2.22fWO.W h
WI 17,vm p 550(0.71(0.90)) p
= 0.3204h,, HP
Turbine power:
p = 2’2282(50’54) h
r 550(0.71) p
= 0, 2883h ,,, HP.
Steam
6.6. NON-NEWTONIAN LIQUIDS 103
= 10.14 kg/HP (from the “manual”)
= 10.14(0.2883)(2.204)h,/1000 = 0.006443hp, 1000 lh/hr.
Power cost:
O.O65(8000)(kw), $/yr,
Steam cost:
4.5(8000)(lOOOlb/hr), $/yr.
Installed pump cost factors for alloy, temperature, etc (data in the
“manual”)
= 2[2.5(1.8)(1.3)(0.71)] = 8.2.
Summary:
IPS 4 6 6 10
D (ft) 0.3355 0.5054 0.6651 0.8350
1OOf 1 a9 1.67 1.89 1.93
hp (it) 898 413 360 348
Pump efficiency 0.71 0.71 0.71 0.71
motor (kW) 214.6 98.7 86.0 83.2
Steam, 1000 Ib/hr 5.97 2.66 2.32 2.25
Pump cost, 2 installed 50,000 28,000 28,000 28,000
Motor cost, 2 installed 36,000 16,000 14,000 14,000
Turbine cost, 2 installed 56,000 32,000 28,000 28,000
Pipe cost 18,000 27,000 36,000 45,000
Valve cost 2 3 , 7 5 0 3 1 , 5 4 6 3 8 , 5 8 4 4 5 , 1 0 7
Equip cost, motor drive 1 2 7 , 7 5 0 9 3 , 5 4 6 1 0 7 , 5 8 4 1 2 3 , 1 0 7
Equip cost, turbine drive 1 4 7 , 7 5 0 1 0 9 , 5 4 6 1 2 1 , 5 8 4 1 3 7 , 1 0 7
Power cost ($/yr) 1 1 1 , 5 9 2 5 1 , 3 2 4 4 4 , 7 2 0 4 3 , 2 6 4
Steam cost ($/yr) 2 0 8 , 4 4 0 9 5 , 7 6 0 8 3 , 5 2 0 8 0 , 8 3 4
Annual cost, motor drive 1 7 5 , 4 6 7 9 8 , 0 9 7 9 8 , 5 1 2 1 0 4 , 8 1 7
Annual cost, turbine drive 2 8 2 , 3 1 5 1 5 0 , 5 3 3 1 4 4 , 3 1 2 1 4 9 , 3 8 7
gradient, f = du/dx. The concept is represented on Figure 6.2(a):
one of the planes is subjected to a shear stress and is translated
parallel to a fixed plane at a constant velocity but a velocity gradient
is developed between the planes. The relation between the variables
may be written
r = F/A = p(du/dx) = pLj, (6.34)
where, by definition, p is the viscosity. In the simplest case, the
viscosity is constant, and the fluid is called Newtonian. In the other
cases, more complex relations between z and y involving more than
one constant are needed, and dependence on time also may be
present. Classifications of non-Newtonian fluids are made according
to the relation between r and + by formula or shape of plot, or
according to the mechanism of the resistance of the fluid to
deformation.
The concept of an apparent viscosity
CL, = r/P (6.35)
is useful. In the Newtonian case it is constant, but in general it can
be a function of t, 9, and time 0.
Non-Newtonian behavior occurs in solutions or melts of
polymers and in suspensions of solids in liquids. Some t-p plots are
shown in Figure 6.2, and the main classes are described following.
1. Pseudoplastic liquids have a z-9 plot that is concave
downward. The simplest mathematical representation of such
relations is a power law
r=Kp”, n<l (6.36)
with n < 1. This equation has two constants; others with many more
than two constants also have been proposed. The apparent viscosity
is
pa = z/p = K/j+‘. (6.37)
Since n is less than unity, the apparent viscosity decreases with the
deformation rate. Examples of such materials are some polymeric
solutions or melts such as rubbers, cellulose acetate and napalm;
suspensions such as paints, mayonnaise, paper pulp, or detergent
slurries; and dilute suspensions of inert solids. Pseudoplastic
properties of wallpaper paste account for good spreading and
adhesion, and those of printing inks prevent their running at low
speeds yet allow them to spread easily in high speed machines.
2. Dilatant liquids have rheological behavior essentially](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-122-320.jpg)
![opposite those of pseudoplastics insofar as viscosity behavior is
concerned. The t--P plots are concave upward and the power law
applies
t=Kf”, n>l, (6.38)
but with n greater than unity; other mathematical relations also
have been proposed. The apparent viscosity, ,u. = KY-l, increases
with deformation rate. Examples of dilatant materials are
pigment-vehicle suspensions such as paints and printing inks of high
concentrations; starch, potassium silicate, and gum arabic in water;
quicksand or beach sand in water. Dilatant properties of wet
cement aggregates permit tamping operations in which small
impulses produce more complete settling. Vinyl resin plastisols
exhibit pseudoplastic behavior at low deformation rates and dilatant
behavior at higher ones.
3. Bingham plastics require a finite amount of shear stress
before deformation begins, then the deformation rate is linear.
Mathematically,
r = to + /&(dU/dx) = to + ,uBj, (6.39)
where pL8 is called the coefficient of plastic viscosity. Examples of
materials that approximate Bingham behavior are drilling muds;
suspensions of chalk, grains, and thoria; and sewage sludge.
Bingham characteristics allow toothpaste to stay on the brush.
4. Generalized Bingham or yield-power law fluids are
represented by the equation
t=t,+Kf”. (6.40)
Yield-dilatant (n > 1) materials are rare but several cases of
0.50
0.45
0 . 4 0
0.35
‘, 0 . 3 0
I
g 0.25
.
b
l/l- 0.20
z
6 0.15
b
al 0.10
6
I -
1 I I I I I I
Shear Rate , sec.’
8267
1377
c ”
918
0 20 4 0 60 80 100 120 140 160
Duration of Shear, min
Figure 6.3. Time-dependent rheological behavior of a rheopectic
fluid, a 2000 molecular weight polyester [after Steg and Katz, J.
Appl. Polym. Sci. 9, 3177 (1965)].
6.6. NON-NEWTONIAN LIQUIDS 105
yield-pseudoplastics exist. For instance, data from the literature of a
20% clay in water suspension are represented by the numbers
to = 7.3 dyn/cm*, K = 1.296 dyn(sec)“/cm’ and n = 0.483 (Govier
and Aziz, 1972, p. 40). Solutions of OS-5.0% carboxypolymethylene
also exhibit this kind of behavior, but at lower concentrations the yield
stress is zero.
5. Rheopecticfluids have apparent viscosities that increase with
time, particularly at high rates of shear as shown on Figure 6.3. Figure
6.2(f) indicates typical hysteresis effects for such materials. Some
examples are suspensions of gypsum in water, bentonite sols, vanadium
pentoxide sols, and the polyester of Figure 6.3.
6. Z’hixotropic fiuio!.s have a time-dependent rheological
behavior in which the shear stress diminishes with time at a constant
deformation rate, and exhibits hysteresis [Fig. 6.2(f)]. Among the
substances that behave this way are some paints, ketchup, gelatine
solutions, mayonnaise, margarine, mustard, honey, and shaving
cream. Nondrip paints, for example, are thick in the can but thin on
the brush. The time-effect in the case of the thixotropic crude of
Figure 6.4(a) diminishes at high rates of deformation. For the same
crude, Figure 6.4(b) represents the variation of pressure gradient in
a pipe line with time and axial position; the gradient varies fivefold
over a distance of about 2 miles after 200 min. A relatively simple
relation involving five constants to represent thixotropic behavior is
cited by Govier and Aziz (1972, p. 43):
7J = (PO + cd)?, (6.41)
M/d0 = a - (a + by)A. (6.42)
The constants pO, a, b, and c and the structural parameter I are
obtained from rheological measurements in a straightforward
manner.
7. Viscoelastic fluids have the ability of partially recovering
their original states after stress is removed. Essentially all molten
polymers are viscoelastic as are solutions of long chain molecules
such as polyethylene oxide, polyacrylamides, sodium carboxy-
methylcellulose, and others. More homely examples are egg
whites, dough, jello, and puddings, as well as bitumen and napalm.
This property enables eggwhites to entrap air, molten polymers to
form threads, and such fluids to climb up rotating shafts whereas
purely viscous materials are depressed by the centrifugal force.
Two concepts of deformability that normally are applied only
to solids, but appear to have examples of gradation between solids
and liquids, are those of shear modulus E, which is
E = shear stress/deformation, (6.43)
and relaxation time 0*, which is defined in the relation between the
residual stress and the time after release of an imposed shear stress,
namely,
T= roexp(-8/O*). (6.44)
A range of values of the shear modulus (in kgf/cm’) is
Gelatine
0.5% solution 4 x lo-lo
10% solution (jelly) 5 x lo-*
Raw rubber 1.7 x lo2
Lead 4.8x 10”
Wood (oak) 8~10~
Steel 8~10~](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-124-320.jpg)
![106 FLOW OF FLUIDS
E 5
i?! 4
iz 3
Duration of
Pkmbino Crude Oil,
Temperature 44.5;F
lO-2
I ,I I I,l,, IOI I
lo 20 30 50 70 100 200 300 500
(a)
0.0032
0.0028
T
z
0 0.0024
21;
; 0.0020
z
d
; 0.0016
e
7
z
OL:
0.0012
O.OOOE
0.0004
b)
Rate of Shear, s+ IO ,sec-’
Figure 6.4. Shear and pipeline flow data of a thixotropic Pembina
crude oil at 44.5”F. (a) Rheograms relating shear stress and rate of
shear at several constant durations of shear (Ritter and Govier,
Can. J. Chem. Eng. 48, 505 (1970)]. (b) Decay of pressure gradient
of the fluid flowing from a condition of rest at 15,000 barrels/day in
a 12 in. line [Ritter and B&y&y, SPE Journal 7, 369 (1967)].
and that of relaxation time (set) is
Water 3 x 1o-6
Castor oil 2 x 1o-3
Copal varnish 2x 10
Colophony (at 55°C) 5x 10
Gelatine, 0.5% solution 8~10~
Colophony (at 12°C) 4x 10s
Ideal solids cc
Examples thus appear to exist of gradations between the properties
of normally recognized true liquids (water) and true solids.
Elastic properties usually have a negligible effect on resistance
to flow in straight pipes, but examples have been noted that the
resistances of fittings may be as much as 10 times as great for
viscoelastic liquids as for Newtonian ones.
PIPELINE DESIGN
The sizing of pipelines for non-Newtonian liquids may be based on
scaleup of tests made under the conditions at which the proposed
line is to operate, without prior determination and correlation of
rheological properties. A body of theory and some correlations are
available for design with four mathematical models:
rw = Kp”, power law, (6.45)
rw = zy + PBY1 Bingham plastic, (6.46)
r,=q,+Kjf’, Generalized Bingham or
yield-power law, (6.47)
z, = K’@/D)“’ Generalized power law
(Metzner-Reed) (AZChE J. 1,434, 1955).
(6.48)
In the last model, the parameters may be somewhat dependent on
the shear stress and deformation rate, and should be determined at
magnitudes of those quantities near those to be applied in the plant.
The shear stress r,,, at the wall is independent of the model and
is derived from pressure drop measurements as
z, = DAPI4L. (6.49)
Friction Factor. In rheological literature the friction factor is
defined as
(6.50)
This value is one-fourth of the friction factor used in Section 6.3.
For the sake of consistency with the literature, the definition of Eq.
(6.50) will be used with non-Newtonian fluids in the present section.
Table 6.2 lists theoretical equations for friction factors in
laminar flows. In terms of the generalized power law, Eq. (6.48),
f=+= K’(SV/D)“’
PV I% PV2/2tTc
16
= D”‘V2-“‘p/g,K’8”‘-l~
By analogy with the Newtonian relation, f = 16/Re, the
denominator of Eq. (6.52) is designated as a modified Reynolds
number,
Re,, = D”‘V2-“‘p,gcK’8”‘-l~ (6.53)
The subscript MR designates Metzner-Reed, who introduced this
form.
Scale Up. The design of pipelines and other equipment for
handling non-Newtonian fluids may be based on model equations
with parameters obtained on the basis of measurements with
viscometers or with pipelines of substantial diameter. The shapes of
plots of t, against p or W/D may reveal the appropriate model.
Examples 6.9 and 6.10 are such analyses.
In critical cases of substantial economic importance, it may be
advisable to perform flow tests-Q against BP-in lines of
moderate size and to scale up the results to plant size, without
necessarily trying to fit one of the accepted models. Among the
effects that may not be accounted for by such models are time](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-125-320.jpg)
![6.6. NON-NEWTONIAN LIQUIDS 107
EXAMPLE 6.9
Analysis of Data Obtained in a Capillary Tube Viscometer
Data were obtained on a paper pulp with specific gravity 1.3, and
are given as the first four columns of the table. Shear stress t, and
deformation rate 7 are derived by the equations applying to this
kind of viscometer (Skelland, 1967, p. 31; Van Wazer et al., 1963,
p. 197):
r, = D API4L,
. 3n’+l 8
- -
'= 4n' D
(7
d 144
n”d ln(8V/D)
The plot of log r, against log (8V/D) shows some scatter but is
approximated by a straight line with equation
rw = 1.329(8V/D)“.5*.
Since
f = (2.53/2.08)(8V/D),
the relation between shear stress and deformation is given by the
equation
t, = 1.203i,“.51
0.15 14 0.20 3200 464 8.57
0.15 14 0.02 1200 46.4 3.21
0.30 28 0.46 1950 133.5 5.22
0.30 28 0.10 860 29.0 2.30
0.40 28 1.20 1410 146.9 5.04
Parameters of the Bingham Model from Measurements of
Pressure Drops in a Line
Data of pressure drop in the flow of a 60% limestone slurry of
density 1.607g/ml were taken by Thomas [Znd. Eng. Chem. 55,
18-29 (1963)]. They were converted into data of wall shear stress
r, = DAP/4L against the shear rate 8V/D and are plotted on the
figure for three line sizes.
The Buckingham equation for Bingham flow in the laminar
region is
The second expression is obtained by neglecting the fourth-power
term. The Bingham viscosity ,ur, is the slope of the plot in the
laminar region and is found from the terminal points as
pB = (73-50)/(347-O) = 0.067 dyn set/cm’.
From the reduced Buckingham equation,
ra = 0.75t, (at 8V/D = 0)
= 37.5.
Accordingly, the Bingham model is represented by
rw = 37.5 +0.067(81/‘/D), dyn/cm’
with time in seconds.
Transitions from laminar to turbulent flow may be identified off
a 4.04 cm dia _
2
,, 7.75 cm dia
3
0
0 200 400 600 -, 800
SHEAR RATE Ev/D, SAC
the plots:
D = 2.06 cm, 8V/D = 465, V = 120 cm/set
4.04 215, 109
7.75 (critical not reached).
The transition points also can be estimated from Hanks’ correlation
[AZChE .I. 9, 45, 306 (1963)] which involves these expressions:
xc = (%/LL
He = D*q,p/&,
x,/(1 - x,)~ = He/16,800,
Re,, = (1 - $x, + fxd)He&,.
The critical linear velocity finally is evaluated from the critical
Reynolds number of the last equation with the following results;](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-126-320.jpg)
![108 FLOW OF FLUIDS
EXAMPLES 6.1~(continued)
D (cm) 1O-4 H e
2 . 0 6 5 . 7
4.04 2 2 . 0
7 . 7 5 81 .O
xc %, v,
0.479 5 6 3 5 114(120)
0.635 8945 93 (109)
0.750 14,272 77
The numbers in parentheses correspond to the break points on the
figure and agree roughly with the calculated values.
The solution of this problem is based on that of Wasp et al.
(1977).
dependence, pipe roughness, pipe fitting resistance, wall slippage,
and viscoelastic behavior. Although some effort has been devoted
to them, none of these particular effects has been well correlated.
Viscoelasticity has been found to have little effect on friction in
straight lines but does have a substantial effect on the resistance of
pipe fittings. Pipe roughness often is accounted for by assuming that
the relative effects of different roughness ratios E/D are represented
by the Colebrook equation (Eq. 6.20) for Newtonian fluids. Wall
slippage due to trace amounts of some polymers in solution is an
active field of research (Hoyt, 1972) and is not well predictable.
The scant literature on pipeline scaleup is reviewed by
Heywood (1980). Some investigators have assumed a relation of the
form
z, = DAPI4L = kV”/Db
and determined the three constants K, a, and b from measurements
on several diameters of pipe. The exponent a on the velocity
appears to be independent of the diameter if the roughness ratio
E/D is held constant. The exponent b on the diameter has been
found to range from 0.2 to 0.25. How much better this kind of
analysis is than assuming that a = b, as in Eq. (6.48) has not been
established. If it can be assumed that the effect of differences in E/D
is small for the data of Examples 6.9 and 6.10, the measurements
should plot as separate lines for each diameter, but such a
distinction is not obvious on those plots in the laminar region,
although it definitely is in the turbulent region of the limestone
slurry data.
Observations of the performance of existing large lines, as in
the case of Figure 6.4, clearly yields information of value in
analyzing the effects of some changes in operating conditions or for
the design of new lines for the same system.
Laminar Flow. Theoretically derived equations for volumetric
flow rate and friction factor are included for several models in Table
6.7. Each model employs a specially defined Reynolds number, and
the Bingham models also involve the Hedstrom number,
He = z,pD’/& (6.54)
These dimensionless groups also appear in empirical correlations of
the turbulent flow region. Although even in the approximate Eq.
(9) of Table 6.7, group He appears to affect the friction factor,
empirical correlations such as Figure 6.5(b) and the data analysis of
Example 6.10 indicate that the friction factor is determined by the
Reynolds number alone, in every case by an equation of the form,
f = 16/Re, but with Re defined differently for each model. Table
6.7 collects several relations for laminar flows of fluids.
Transitional Flow. Reynolds numbers and friction factors at
which the flow changes from laminar to turbulent are indicated by
the breaks in the plots of Figures 6.4(a) and (b). For Bingham
models, data are shown directly on Figure 6.6. For power-law
liquids an equation for the critical Reynolds number is due to
Mishra and Triparthi [Z’runs. ZChE 51, T141 (1973)],
Re, = 1400(2n + 1)(5n + 3)
c (3n + 1)2 . (6.55)
The Bingham data of Figure 6.6 are represented by the equations of
Hanks [AZChE J. 9, 306 (1963)],
(Re,),=e(l-i*,+fxf),
H e
- - -
(1 -x;,)” - 16,800.
(6.56)
(6.57)
They are employed in Example 6.10.
Turbulent Flow. Correlations have been achieved for all four
models, Eqs. (6.45)-(6.48). For power-law flow the correlation of
Dodge and Metzner (1959) is shown in Figure 6.5(a) and is
represented by the equation
$= ,n:$,, log,,[Re,.f(‘~“‘“)] -s.
These authors and others have demonstrated that these results can
represent liquids with a variety of behavior over limited ranges by
TABLE 6.7. Laminar Flow: Volumetric Flow Rate, Friction
Factor, Reynolds Number, and Hedstrom Number
Newtonian
f = 16/Re, Fie = DVply
Power Law [Eq. (6.491
(1)
Q+p-)(g”
f = 16lRe’
Bingham Plastic [Eq. (6.4611
iTD3t
Q=L
32~~
Re, = DVple,
He = toD2pl&
1 fHe 4
-=---+J& (solveforfl
R% 1 6 SRe,
f= 96Rei
6Re, + He
[neglecting (s,/rw14 in Eq. (91
(5)
(6)
(7)
(8)
(9)
&neralized Bingham (Yield-Power Law) [Eq. (6.4711
Qua& (y(l-5)
x[l*[l+$y)(l+ny] (10)
f=g(l-gJ
111 (11)
IRe’ bv Ea. (4) and He by Eq. (7)I](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-127-320.jpg)
![10,000
R E Y N O L D S N U M B E R , Re,,
(a)
6.7. GASES 109
IO’ IO’ IO’ IO’
B i n g h a m R e y n o l d s N u m b e r . Re,
lb)
Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids. (a)
r, = K’(8V/D)“‘, with K’ and n’ constant or dependent on T,: l/$= [4.0/(n;)“.‘5~log,o[Re,.f(
For pseudoplastic liquids represented by
n *)I - 0.40/(n')'.', [Dodge and Metzner,
AIChE J. 5, 189 (1959)]. (b) For Bingham plastics, Re, -
- DVplp,, He = t,D p/p* [Hanks and Dadia, AIChE J. 17,554 (1971)].
evaluating K’ and n’ in the range of shear stress z,,, = DAP/4L that
will prevail in the required situation.
Bingham flow is represented by Figure 6.5(b) in terms of
Reynolds and Hedstrom numbers.
Theoretical relations for generalized Bingham flow [Eq. (6.47)]
have been devised by Torrance [S. Afr. Me&. Eng. 13, 89 (1963)].
They are
2.69
n-2.95 +Fln(l-x)
>
+ F In(Re~~1-“‘2) + y (%I - 8) (6.59)
with the Reynolds number
Re, = D”V2-“p/8”m’K
and where
(6.60)
x = ro/5,. (6.61)
In some ranges of operation, materials may be represented
approximately equally well by several models, as in Example 6.11
where the power-law and Bingham models are applied.
6.7. GASES
The differential energy balances of Eqs. (6.10) and (6.15) with the
friction term of Eq. (6.18) can be integrated for compressible fluid
flow under certain restrictions. Three cases of particular importance
are of isentropic or isothermal or adiabatic flows. Equations will be
developed for them for ideal gases, and the procedure for nonideal
gases also will be indicated.
I S E N T R O P I C F L O W
In short lines, nozzles, and orifices, friction and heat transfer may
be neglected, which makes the flow essentially isentropic. Work
transfer also is negligible in such equipment. The resulting theory is
a basis of design of nozzles that will generate high velocity gases for
Figure 6.6. Critical Reynolds number for transition from laminar to
turbulent flow of Bingham fluids. The data also are represented by
Eqs. (6.56) and (6.57): (0) cement rock slurry; (A) river mud
slurries; (0) clay slurry; (P) sewage sludge; (A) ThO, slurries; (m)
lime slurry. [Hanks and Pratt, SPE Journal, 342-346 (Dec. 1967)].
power production with turbines. With the assumptions indicated,
Eq. (6.10) becomes simply
dH + (l/g& du = 0, (6.62)
which integrates into
HZ-HI++-u;)=O. (6.63)
c
One of these velocities may be eliminated with the mass balance,
+I = u,A,/V, = u,A,/V, (6.64)
so that
u; - u: = (rizV,/A,)*[l - (A2VI/A,V2)*].
For ideal gases substitutions may be made from
H2 - HI = C,( T, - TI)
(6.65)
(6.66)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-128-320.jpg)
![110 FLOW OF FLUIDS
and
T*/T, = (P2/Pl)‘k-“‘k = (VJV,)“. (6.67)
After these substitutions are made into Eq. (6.63), the results may
be solved for the mass rate of flow as
At specified mass flow rate and inlet conditions Pr and VI, Eq.
(6.68) predicts a relation between the area ratio AZ/Al and the
pressure ratio P,/P, when isentropic flow prevails. It turns out that,
as the pressure falls, the cross section at first narrows, reaches a
minimum at which the velocity becomes sonic; then the cross
section increases and the velocity becomes supersonic. In a duct of
constant cross section, the velocity remains sonic at and below a
critical pressure ratio given by
p, 2
-4 1
kl(k+ 1)
4 k+l .
(6.69)
The sonic velocity is given by
u,=vamms+.> (6.70)
where the last result applies to ideal gases and M, is the molecular
weight.
ISOTHERMAL FLOW IN UNIFORM DUCTS
When elevation head and work transfer are neglected, the
mechanical energy balance equation (6.13) with the friction term of
Eq. (6.18) become
fu2
VdP + (l/g& du + ~ dL = 0.
W’
(6.71)
Make the substitutions
u=GJp=GV (6.72)
and the ideal gas relation
V = PIVl/P and dV/V = -dP/P
so that Eq. (6.71) becomes
(6.73)
(6.74)
This is integrated term-by-term between the inlet and outlet
conditions,
and may be rearranged into
p2=p23V,G2 fL
2 1
g,[20+4~)1 (6.76)
(6.75)
In terms of a density, pm, at the average pressure in the line,
(6.77)
The average density may be found with the aid of an approximate
evaluation of P2 based on the inlet density; a second trial is never
justified. Eqs. (6.76) and (6.77) and the approximation of Eq.
(6.76) obtained by neglecting the logarithmic term are compared in
Example 6.12. The restriction to ideal gases is removed in Section
6.7.4.
ADIABATIC FLOW
The starting point for development of the integrated adiabatic flow
energy balance is Eq. (6.71) and again ideal gas behavior will be
assumed. The equation of condition of a static adiabatic process,
PVk = const, is not applicable to the flow process; the appropriate
EXAMPLE 6.11
Pressure Drop in Power-Law and Bingham Plow
A limestone slurry of density 1.693 g/mL is pumped through a 4-in.
(152 mm) line at the rate of 4 ft/sec (1.22 m/set). The pressure drop
(psi/mile) will be calculated. The slurry behavior is represented by
a. The power-law with n = 0.165 and K = 34.3 dyn sec”.165/cm2
(3.43 Pa sec0.r6’).
h. Bingham model with to= 53 dyn/cm2 (5.3 Pa) and pa = 22cP
(0.022 Pa set).
Power law:
Re’ = D”V2-“p/8”-1K
= (0.152)“~165(1.22)1~835(1693)(8)o.835/3.43
=2957,
f = 0.0058 [Fig. 6.6(a)]
A P 4fpV= 4(0.0058)(1693)(1.22)=
-=-=
L 2gcD 2(0.152)
= 192.3 N/(m’)(m) [gC = kgm/sec=/N],
+ 192.3(14.7/101,250)1610 = 45.0 psi/mile.
Bingham:
Re
I3
= Dvp = 0.152(1.22)(1693) = 14 270
0.022 7 3
UR
He = tbD2p/pi = 5.3(0.152)2(1693)/(0.022)2
= 428,000,
critical Re, = 12,000 (Fig. 6.5),
f = 0.007 [Fig. 6.6(b)],
AP 0.007
L = 0.0058 45.0 = 54.3 psi/mile.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-129-320.jpg)
+%=O
1 2 1
(6.85)
(6.86)
In terms of the inlet Mach number,
M, = u,/~g~kRTIM, = GV,/~g~kRTJM,,
the result becomes
(6.87)
l- v
(:)‘I +Tln(z)‘. ( 6 . 8 8 )
When everything else is specified, Eqs. (6.86) or (6.88) may be
solved for the exit specific volume V,. Then P2 may be found from
Eq. (6.81) or in the rearrangement
!g+l+(~M~)[l-(!5)2],
11 1
from which the outlet temperature likewise may be found.
(6.89)
Although the key equations are transcendental, they are
readily solvable with hand calculators, particularly those with
root-solving provisions. Several charts to ease the solutions before
the age of calculators have been devised: M.B. Powley, Can. J.
Chem. Eng., 241-245 (Dec. 1958); C.E. Lapple, reproduced in
Perry’s Chemical Engineers’ Handbook, McGraw-Hill, New York,
1973, p. 5.27; 0. Levenspiel, reproduced in Perry’s Chemical
Engineers’ Handbook, McGraw-Hill, New York, 1984, p. 5.31;
Hougen, Watson, and Ragatz, Thermodynamics, Wiley, New York,
1959, pp. 710-711.
In all compressible fluid pressure drop calculations it is usually
justifiable to evaluate the friction factor at the inlet conditions and
to assume it constant. The variation because of the effect of
temperature change on the viscosity and hence on the Reynolds
number, at the usual high Reynolds numbers, is rarely appreciable.
NONIDEAL GASES
Without the assumption of gas ideality, Eq. (6.71) is
dP+~dV+fcZdL=O
V gc V 20 ’
(6.90)
In the isothermal case, any appropriate PVT equation of state may
be used to eliminate either P or V from this equation and thus
permit integration. Since most of the useful equations of state are
pressure-explicit, it is simpler to eliminate P. Take the example of
one of the simplest of the non-ideal equations, that of van der
Waals
P=&-$,
of which the differential is
Substituting into Eq. (6.90),
(6.91)
(6.92)
(6.93)
Although integration is possible in closed form, it may be more
convenient to perform the integration numerically. With more
accurate and necessarily more complicated equations of state,
numerical integration will be mandatory. Example 6.13 employs the
van der Waals equation of steam, although this is not a particularly.
suitable one; the results show a substantial difference between the
ideal and the nonideal pressure drops. At the inlet condition, the
compressibility factor of steam is z = PV/RT = 0.88, a substantial
deviation from ideality.
6.6. LIQUID-GAS FLOW IN PIPELINES
In flow of mixtures of the two phases in pipelines, the liquid tends
to wet the wall and the gas to concentrate in the center of the
channel, but various degrees of dispersion of each phase in the
other may exist, depending on operating conditions, particularly the
individual flow rates. The main patterns of flow that have been
recognized are indicated on Figures 6.7(a) and (b). The ranges of
conditions over which individual patterns exist are represented on
maps like those of Figures 6.7(c) and (d). Since the concept of a](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-130-320.jpg)
![112 FLOW OF FLUIDS
EXAMPLE 6.12
Adiabatic and Isothermal Flow of a Gas in a Pipeline
Steam at the rate of 7000 kg/hr with an inlet pressure of 23.2 barabs
and temperature of 220°C flows in a line that is 77.7mm dia and
30.5 m long. Viscosity is 28.5(10e6)N set/m’ and specific heat ratio is
k = 1.31. For the pipe, E/D = 0.0006. The pressure drop wih be
found in (a) isothermal flow; (b) adiabatic flow. Also, (c) the line
diameter for sonic flow will be found.
VI = 0.0862 m3/kg,
G=7000/(3600)(~~/4)(0.0777)*=410.07 kg/m*sec,
Re
1
-DG-0.0777(410.07)=l,12(106)
P 28.5(10-6)
f = 1.6364/[1n(0.13.5)(0.0006) + 6..5/l.2(106)J2 = 0.0187.
Inlet sonic velocity:
us1 = vg=kRT,/M,,, = Vl(l.31)(8314)493.2/18.02 = 546 m/set
M,=u,/u,,= GV,/u,,= 410.07(0.0862)/546=0.0647.
As a preliminary calculation, the pressure drop will be found
by neglecting any changes in density:
:. P2 = 23.2 - 5.32 = 17.88 bar.
(a) Isothermal fIow. Use Eq. (6.76):
F = 2(23.2)(10’)(0.0862)(410.07)* = 6.726(10”),
p;-?!p(g+&)]l’z
2
= 10’
23.2(10’)
0.0187(305)/2(0.0777)+ Inp
2
= 17.13(10’) N/m*,
and
AP = 23.2 - 17.13 = 5.07 bar.
When the logarithmic term is neglected,
P2= 17.07(10)5N/m2.
(b) Adiabatic flow. Use Eq. (6.88):
0.0187(305)
0.0777 >
73.4 =182.47 l-
Equation (6.89) for the pressure:
= 1 + o’31(20;y)2 [l - (1.2962)‘]
AP=23.2- 17.89=5.31 bar.
(c) Line diameter for sonic flow. The critical pressure ratio is
kl(k-I)
= 0.5439, with k = 1.31,
G=7000/3600-2.4757
(n/4)oZ D2 ’
M =~=2.4757(0.0862)=3.909(10-4)
l us, 546D* D* ’ (4
Equation (6.89) becomes
0.5439(V2/Vl) = 1 + O.l183M:[l- (V,/V,)*],
fL/D =0.0187(305)/D = 5.703510
= rhs of Eq. (6.88).
Procedure
(3)
(4)
1. Assume D.
2. Find Ml [Eq. (2)].
3. Find VJV, from Eq. (6.89) [Eq. (3)].
4. Find rhs of Eq. (6.88) [Eq. (l)].
5. Find D = 5.7035/[rhs of Eq. (6.88)] [Eq. (4)].
6. Continue until steps 1 and 5 agree.
Some trials are:
Eq.(6.69) Eq.(6.66)
D 4 WV, rhs D
0.06 0.1086 0.5457 44.482 0.1282
0.07 0.0798 0.5449 83.344 0.06843
0.0697 0.08046 0.5449 81.908 0.06963
:. D = 0.0697 m.
1 0 ! Example 6. 12. Line dia for
sonic f l o w
2 0 K=1.31
3 0 I N P U T D ! ( T r i a l v a l u e >
4 0 M=.0003909/ll~~2 ! CEq 2)
5 0 I N P U T ‘J ! C=Vl/VZ>
$9”
8 0
1::
110
GOSIJP 1 3 0
I F ABS~X1~>=.0001
F=l/Z/KX<K-1+2fM*2
CK+l)x’2/KtLOG{V’Z)
Ol=S . 7 0 3 5 / F
OISP D>Dl
THEN 50
zJ*:(l-v*2)+
! (Es 11
GOTO 3 0 ! (For ano
t h e r t r i a l
value of D if it i s n o t cl0
s e enough t o c a l c u latcd Dl>
120 END
1 3 0 Xl=- < 5439~V~+l+~K-l>~Z~K*N*
2%Cl-l/V^2)
1 4 0 DISP X l
150 RETURN](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-131-320.jpg)
![particular flow pattern is subjective and all the pertinent variables
apparently have not yet been correlated, boundaries between
regions are fuzzy, as in (d).
It is to be expected that the kind of phase distribution will
affect such phenomena as heat transfer and friction in pipelines. For
the most part, however, these operations have not been correlated
yet with flow patterns, and the majority of calculations of two-phase
flow are made without reference to them. A partial exception is
annular flow which tends to exist at high gas flow rates and has been
studied in some detail from the point of view of friction and heat
transfer.
The usual procedure for evaluating two-phase pressure drop is
to combine pressure drops of individual phases in some way. To this
end, multipliers $+ are defined by
In the following table, subscript L refers to the liquid phase, G to
the gas phase, and LO to the total flow but with properties of the
liquid phase; x is the weight fraction of the vapor phase.
Subscript R e AP/L e2
G DGxIPL, f,G2x2/2g Dp, (APILV(APIL),
L DG(1 - x)lpL tG2(1 -x~J$P, (APILMAPIL),
LO DGh, h,G=l2g&, W/U/W/L),,
In view of the many other uncertainties of two phase flow
correlations, the friction factors are adequately represented by
64/Re, Re < 2000, Poiseuille equation,
f = {0.32/Re0.“, Re > 2000, Blasius equation.
(6.95)
(6.96)
HOMOGENEOUS MODEL
The simplest way to compute line friction in two-phase flow is to
adopt some kinds of mean properties of the mixtures and to employ
the single phase friction equation. The main problem is the
assignment of a two-phase viscosity. Of the number of definitions
that have been proposed, that of McAdams et al. [Trans. ASME
6.8. LIQUID-GAS FLOW IN PIPELINES 113
64, 193-200 (1942)] is popular:
1 lkVo-ph~S~ = X/k + (1 -x)//k.
The specific volumes are weight fraction additive,
(6.97)
VtWO-phW = xv, + (1 - x)V, (6.98)
so that
11Ptwo+3se =x/p, + (1 - X)IPL, (6.99)
where x is the weight fraction of the gas. Pressure drops by this
method tend to be underestimated, but are more nearly accurate at
higher pressures and higher flow rates.
With the Blasius equation (6.96), the friction factor and the
pressure gradient become, with this model,
(6.100)
A P fG2
-r = 2g,D[xlp, + (1 - X)lPJ
(6.101)
A particularly simple expression is obtained for the multiplier in
terms of the Blasius equation:
APlL 1 - x + XPJP,
-=
“‘= (AP/L),, (1 -x + xpJno)“.25.
Some values of $“,a from this equation for steam are
x P = 0.669 bar P = 10.3 bar
0.01 3.40 1.10
0.10 12.16 1.95
0.50 80.2 4.36
High values of multipliers are not uncommon.
(6.102)
EXAMPLE 6.13
Isothermal Flow of a Nonideal Gas
The case of Example 6.12 will be solved with a van der Waals
equation of steam. From the CRC Handbook of Chemistry and
Physics (CRC Press, Boca Raton, FL, 1979),
a = 5.464 atm(m3/kg mol)* = 1703.7 Pa(m3/kg)2,
b = 0.03049 m3/kg mol = 0.001692 m3/kg,
RT = 8314(493.2)/18.02 = 2.276(105) N m/kg.
Equation (6.93) becomes
+0.0187(410.07)2(305)=o
2(0.0777) ’
qb =f+62 [(v ~o,,~l~9)2+5'52$-4)+0.0272]~+ l-0
The integration is performed with Simpson’s rule with 20
intervals. Values of V, are assumed until one is found that makes
4 = 0. Then the pressure is found from the v dW equation:
2.276(10') 1703.7
- -
‘=(V,- 0.00169) V;
Two trials and, a linear interpolation are shown. The value
P2 = 18.44 bar compares with the ideal gas 17.13.
v, cp s
0.120 -0.0540
0.117 +0.0054
0.1173 0 18.44bar](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-132-320.jpg)
![114 FLOW OF FLUIDS
Bubble
Plug
Stratified Dispersed
Wavy
(a)
Bubbly
I k g rn-*s-‘1
Churn
(b)
Annular Dispersed
Dispersed flow IDBI
StratIfled
flow(SSJ
(4
Figure 6.7. Flow patterns and correlations of flow regimes of liquid-gas mixtures in pipelines. (a) Patterns in horizontal liquid-gas flow. (b)
Patterns in vertical liquid-gas flow. (c) Correlations of ranges of flow patterns according to Baker [Oil Gas J. 53(U), 185 (1954)], as
replotted by Bell et al. [Chem. Eng. Prog. Symp. Ser. 66, 159 (1969)]; u is surface tension of the liquid, and u, that of water. (d) Flow
regimes of water/air at 25°C and 1 atm [Tuirel and Dukler, AIChE J. 22, 47 (1976)]; the fuzzy boundaries are due to Mandhane et al. [Int. J.
Two-Phase Flow 1, 537 (1974)].
SEPARATED FLOW MODELS
Pressure drop in two-phase flow is found in terms of pressure drops
of the individual phases with empirical multipliers. The basic
relation is
The last term is the pressure drop calculated on the assumption that
the total mass flow has the properties of the liquid phase.
Some correlations of multipliers are listed in Table 6.8.
Lockhart and Martinelli distinguish between the various combina-
tions of turbulent and laminar (viscous) flows of the individual
phases; in this work the transition Reynolds number is taken as
1000 instead of the usual 2000 or so because the phases are
recognized to disturb each other. Item 1 of Table 6.8 is a guide to
the applicability of the Lockhart-Martinelli method, which is the
oldest, and two more recent methods. An indication of the
attention that has been devoted to experimentation with two phase
flow is the fact that Friedel (1979) based his correlation on some
25,000 data points.
Example 6.14 compares the homogeneous and Lockhart-
Martinelli models for the flow of a mixture of oil and hydrogen.
O T H E R A S P E C T S
The pattern of annular flow tends to form at higher gas velocities;
the substantial amount of work done on this topic is reviewed by](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-133-320.jpg)
![6.8. LIQUID-GAS FLOW IN PIPELINES 115
TABLE 6.8. Two-Phase Flow Correlations of Pressure Drop
1. Recommendations
R /PG G (kg/m* set) Correlation
ilOO0
>lOOO
>lOOO
all Friedel
>I00 C h i s h o l m - B a r o c z y
<IO0 Lockhart-Martinelli
2. Lockhart-Martinelli Correlation
8
1oc
10
’ 0.01 0 10 1.00 1 0 100
PARAMETER X
$J:=r+CIX+lIX=
$&=l +cx+xz
X2 = WIU,I(APIL),
Liquid Gas Subscript C
Turbulent Turbulent tt 2 0
Viscous T u r b u l e n t vt 12
Turbulent Viscous tv 10
Viscous Viscous w 5
3. Chisholm-Baroczy Correlation
& = 1 + (y’- ,)[Bx’2-““z(1 -x)(*-“)‘* + x*~“] = (AP/L)/(AP/L),
n = 0.25
v’= (AP/L),,/(APIL),,
B = 55/G0.=, 0 < Y < 9.5
= 5201 YG”‘5, 9.5 < Y < 28
= 15,000/Y2G0.5, Y > 28
Fr = G’/g,Dp$
We = G2Dlp,a
x= weight fraction gas
4. Friedel Correlation
&=E+
3.24FH
Fr0’045We0’035 ’
E=(, -.&+x2pLfGo
P&o’
FE xo.78(1 - x)‘--,
,q= (~)o~9’(~)o~“(t -zr”, x= weight fraction gas
1. (P.B. Whalley, cited by G.F. Hewitt, 1982). 2. [Lockhart and Martinelli, Chem. Eng. Prog. 45,
39-48 (1949); Chisholm, Int. J. Heat Mass Transfer 10, 1767-1778 (1967)]. 3. [Chisholm, ht. J.
Heat Mass Transfer 16, 347-348 (1973); Baroczy, Chem. Eng. Prog. Symp. Ser. 62, 217-225
(1965)]. 4. (Friedel, European Two Phase Flow Group Meeting, Ispra, Italy, Paper E2, 1979, cited
by G.F. Hewitt, 1982).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-134-320.jpg)
![116 FLOW OF FLUIDS
EXAMPLE 6.14
Pressure Drop and Void Fraction in Liquid-Gas Flow
A mixture of an oil and hydrogen at 500psia and 200°F enters a
3 in. Schedule 40 steel line. Data are:
Oil: 140,000 Ib/hr, 51.85 Ib/cuft, 2700 cfh, viscosity 15 cP.
Hydrogen: 800 Ib/hr, 0.142 Ib/cuft, 5619 cfh,
2.5(10p7) lbf sec/sqft.
viscosity
The pressure drop in 1OOft of line will be found, and also the
voidage at the inlet condition.
ReG = n(0.2557)(32.2)(2.5)(10-7) = 137’500J
; = 0.00059.
Round equations:
1.6434
f= [ln(O.l35s/D + 6.5/Re]‘=
0.0272, liquid,
0.0204, gas,
(AI’lL), = 8friz
8(0.0272)(38.89)*
jt2g,pD5 = ~r’(32.2)(51.85)(0.2557)~
= 18.27 psf/ft,
8(0.0204)(0.222)’
(AP~‘)G = K~(32.2)(o.142)(o.2557)5 = 0.1663 P*f/fta
X2 = 18.27/0.1633 = 111.8.
Lockhart-Martinelli-Chisholm:
c = 20 for TI regime (Table 6.8),
+:=1+;++=2.90,
:. (AP/L) two phase = &AP/L), = 2.90(18.27)
= 53.0 psf/ft, 36.8 psi/100 ft.
Check with the homogeneous model:
x = 140 or+ 8oo = 0.0057 wt fraction gas,
4(39.11)
Re =n(32.2)(0.2557)3.85(10-j) = 157’100
f = 0.0202,
BP 8(0.0202)(39.11)2
7 = ~~‘(32.2)(16.86)(0.2557)’ = 42’2 psf’ft’
compared with 53.0 by the LMC method.
Void fraction by Eq. (6.104):
EC = 1 - l/h = 1 - l/Vz% = 0.413,
compared with input flow condition of
QG 5619
’ = m = 5619 + 2700 = oh75’
Method of Premoli [Eqs. (6.105) and (6.106)]:
Surface tension u = 20 dyn/cm, 0.00137 lbf/ft,
We=DG2= 16ti*
&PLO n2gcD3tw
16(38.89)*
= n2(32.2)(0.2557)3(51.85)(0.00137) = 64’118’
Re = 19,196,
E, = 1.578(19196)-“~‘9(51.85/0.142)o~22 = 0.8872,
E, = 0.0273(6411.8)(19196)-“~5*(51.85/0.142)-o~o* = 7.140,
y = 5619/2700 = 2.081,
yE, = 2.081(7.140) = 14.86.
Clearly, this term must be less than unity if Eq. (6.105a) for S is to
be valid, so that equation is not applicable to this problem as it
stands. If yE, is replaced by y/E, = 0.2914, then
S=1+0.8872 E-
(.
0.5
0.2914 = 2.02,
and the voidage is
5619
’ = 5619 + 2.02(2700) = o’51J
which is a plausible result. However, Eqs. (6.105) and (6.105a) are
quoted correctly from the original paper; no numerical examples
are given there.
Hewitt (1982). A procedure for stratified flow is given by
Cheremisinoff and Davis [AZChE J. 25, 1 (1979)].
Voidage of the holdup in the line is different from that given by
the proportions of the incoming volumetric flows of the two phases,
but is of course related to it. Lockhart and Martinelli’s work
indicates that the fractional gas volume is
&=1-l/&, (6.104)
where #L is defined in Table 6.8. This relation has been found to
give high values. A correlation of Premoli et al. [Termotecnica 25,
17-26 (1971); cited by Hewitt, 19821 gives the void fraction in terms
of the incoming volumetric flow rates by the equation
EC = Q,/(Q, + SQ3, (6.105)
where S is given by the series of equations
S = 1 + E,[y/(l + YE,) - yE,]‘“,
E, = 1.578 Re-0.‘9(p,/p,)0.22,
(6.105’)
E, = 0.0273 We Re-“~51(p,/p,)-o~08,
Y = QclQu Re = DG/pL, We = DG*/up,.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-135-320.jpg)
![6.9. GRANULAR AND PACKED BEDS 117
Direct application of these equations in Example 6.14 is not
successful, but if E, is taken as the reciprocal of the given
expression, a plausible result is obtained.
6.9. GRANULAR AND PACKED BEDS
Flow through granular and packed beds occurs in reactors with solid
catalysts, adsorbers, ion exchangers, filters, and mass transfer
equipment. The particles may be more or less rounded or may be
shaped into rings, saddles, or other structures that provide a
desirable ratio of surface and void volume.
Natural porous media may be consolidated (solids with holes in
them), or they may consist of unconsolidated, discrete particles.
Passages through the beds may be characterized by the properties of
porosity, permeability, tortuosity, and connectivity. The flow of
underground water and the production of natural gas and crude oil,
for example, are affected by these characteristics. The theory and
properties of such structures is described, for instance, in the book
of Dullien (Porous Media, Fluid Transport and Pore Structure,
Academic, New York, 1979). A few examples of porosity and
permeability are in Table 6.9. Permeability is the proportionality
constant k in the flow equation u = (k/p) dP/dL.
Although consolidated porous media are of importance in
chemical engineering, only unconsolidated porous media are
incorporated in process equipment, so that further attention will be
restricted to them.
Granular beds may consist of mixtures of particles of several
sizes. In flow problems, the mean surface diameter is the
appropriate mean, given in terms of the weight fraction distribution,
xi, by
When a particle is not spherical, its characteristic diameter is taken
as that of a sphere with the same volume, so that
D, = (6V,/n)‘“. (6.107)
SINGLE PHASE FLUIDS
Extensive measurements of flow in and other properties of beds of
particles of various shapes, sizes and compositions are reported by
TABLE 6.9. Porosity and Permeability of Several
Unconsolidated and Consolidated Porous Media
Media p”l%ty
0
Perme;.jility
Bed saddles 68-83 1.3 x 1om3-3.9 x 1o-3
W i r e c r i m p s 68-76 3.8 x 1O-5-1.Ox lo+
Black slate powder 57-66 4.9 x 10-‘“-1.2 x 10-S
Silica powder 37-49 1.3 x 10-‘“-5.1 x lo-l0
Sand (loose beds) 37-50 2.0 x 1O-7-1.8~ lo-’
Soil 43-54 2.9x1o-9-1.4x1o-7
Sandstone (oil sand) 8-38 5.0 x lo-‘*-3.o x 1oe
Limestone, dolomite 4-10 2.0 x 10-“-4.5x 1o-‘O
Brick 12-34 4.8 x lo-“-2.2 x 1O-9
Concrete 2-7 1.0 x 1O-9-2.3 x IO-’
Leather 56-59 9.5 x 10-‘“-1.2 x 1o-9
Cork board - 3.3 x 1o-6-1.5x w5
Hair felt - 8.3 x IO-‘-l.2 x 1O-5
Fiberglass 88-93 2.4 x 10-7-5.1 x lo-’
Cigarette filters 17-49 1.1 x 1o-5
Agar-agar - 2.0 x 10-‘“-4.4 x 1o-9
fA.E. Scheidegger, Physics of Flow through Porous Media,
University of Toronto Press, Toronto, Canada, 1974).
Leva et al. (1951). Differences in voidage are pronounced as Figure
6.8(c) shows.
A long-established correlation of the friction factor is that of
Ergun (Chem. Eng. Prog. 48, 89-94, 1952). The average deviation
from his line is said to be f20%. The friction factor is
= 150/Re, + 1.75
with
ReP = D,G/p(l- E).
(6.108)
(6.109)
(6.110)
l PRESENT WORK
A WENTZ & THODOS”)
0.9
0.0
i5
5 05
‘Z
::
t
Smooth, mixed
-h Fused olundum
‘f g’
/ I
h i 1
a I
I II h I1 -0.75
rJn
-L.”
-1.0
-3.0 - 1.5
-4.0 -2.0
-6.0 -3’o
-0.0 -4.0
Ratio of porhcle to tube diameter, 2
/I.
b)
Figure 6.8. Friction factors and void fractions in flow of single phase
fluids in granular beds. (a) Correlation of the friction factor,
Re = D,G/(l - 8)~ and f, = [g,D,E3/pu’(l - &)J(AP/L =
150/Re + 4.2/(Re)1’6 [Sato et al., J. Chem. Eng. Jpn. 6, 147-152
(1973)]. (b) Void fraction in granular beds as a function of the ratio
of particle and tube diameters [Leva, Weintraub, Grummer,
Pollchik, and Starch, U.S. Bur. Mines Bull. 504 (1951)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-136-320.jpg)
![118 FLOW OF FLUIDS
The pressure gradient accordingly is given by
AP
-=
L 1 (6.111)
For example, w h e n D =O.O05m, G = SOkg/m*sec, g, =
1 kgm/N set’, p = 800 kg/m’, p = 0.010 N set/m’, and E = 0.4, the
gradient is AP/L = 0.31(105) Pa/m.
An improved correlation is that of Sato (1973) and Tallmadge
(AZChE J. 16, 1092 (1970)] shown on Figure 6.8(a). The friction
factor is
f, = 150/Re, + 4.2/ReF (6.112)
with the definitions of Eqs. (6.108) and (6.110). A comparison of
Eqs. (6.109) and (6.112) is
9 5 50 500 5000
$ Ergun) 31.8 4.80 2.05 1.78
$, (Sate) 33.2 5.19 1.79 1.05
In the highly turbulent range the disagreement is substantial.
TWO-PHASE FLOW
Operation of packed trickle-bed catalytic reactors is with liquid and
gas flow downward together, and of packed mass transfer
equipment with gas flow upward and liquid flow down.
Concurrent flow of liquid and gas can be simulated by the
homogeneous model of Section 6.8.1 and Eqs. 6.109 or 6.112, but
several adequate correlations of separated flows in terms of
Lockhart-Martinelli parameters of pipeline flow type are available.
A number of them is cited by Shah (Gas-Liquid-Solid Reactor
Design, McGraw-Hill, New York, 1979, p. 184). The correlation of
Sato (1973) is shown on Figure 6.9 and is represented by either
4 = (APLo/AP,)o.5 = 1.30+ 1.85(X)-‘.*‘, 0.1 <X(20,
(6.113)
or
log10 APL, 0.70
AP, + APc = [log*o(x/1.2)]* + 1.00 ’
where
X = ~@PIL),I(APIL),
The pressure gradients for the liquid and vapor phases are
calculated on the assumption of their individual flows through the
bed, with the correlations of Eqs. (6.108)-(6.112).
The fraction h, of the void space occupied by liquid also is of
interest. In Sato’s work this is given by
h, = 0.40(a,)“3x0.22,
where the specific surface is
(6.116)
a, = 6(1 - &)/Dp. (6.117)
Additional data are included in the friction correlation of
Specchia and Baldi [Chem. Eng. Sci. 32, 515-523 (1977)], which is
represented by
fm = ’
(6.118)
X
(a)
X
b)
Figure 6.9. Pressure drop gradient and liquid holdup in liquid-gas
concurrent flow in granular beds. [Sato, Hirose, Takuhashi, and
Toda, J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (a) Correlation of
the two phase pressure drop gradient AP/L, 4 = 1.30 + 1.85X-o.85.
(b) Correlation of frictional holdup h, of liquid in the bed; a, is the
specific surface, l/mm, d is particle diameter, and D is tube
diameter. h, = 0.4~~‘~~~~.
Inf,, = 7.82 - 1.30 ln(Z/~‘~‘) - 0.0573[ln(Z/@‘)]‘. (6.119)
The parameters in Eq. (6.119) are
Z = (Re,)1.‘67/(Re,)0-767, (6.120)
w=z [z pg”‘. (6.121)
Liquid holdup was correlated in this work for both nonfoaming and
foaming liquids.
Nonfoaming, h, = 0. 125(Z/~‘~‘)~0~3*2(u~D~/~)o-65, (6.122)
Foaming, h, = 0.06(Z/~‘~1)-o~‘72(u,D,/~)o~65. (6.123)
The subscript w in Eq. (6.121) refers to water.
Countercurrent flow data in towers with shaped packings are
represented by Figure 13.37. The pressure drop depends on the
viscosity of the liquid and on the flow rates and densities of the
liquid and gas, as well as on characteristics of the packing which are
represented here by the packing factor P. Nominally, the packing
factor is a function of the specific surface a, and the voidage E, as
F = as/e3, (6.124)
but calculated values are lower than the experimental values shown
in the table by factors of 2-5 or so. Clearly the liquid holdup
reduces the effective voidage to different extents with different
packings. The voidages of the packings in the table range from 70 to](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-137-320.jpg)
![6 . 1 0 . G A S - S O L I D T R A N S F E R 119
95%, whereas voidages obtained with small spherical or cylindrical
packings normally used as catalysts are less than 40% or so, which
makes them impractical for countercurrent operation. However,
catalysts are made in the forms of rings or saddles when very low
pressure drop or countercurrent operation is desirable.
Even when they are nominally the same type and size, packings
made by different manufacturers may differ substantially in their
pressure drop and mass transfer behavior, so that manufacturers
data should be obtained for final design.
Many data on individual packings are given by Billet
(Distillation Engineering, Chemical Pub. Co., New York), in
Chemical Engineers Handbook (McGraw-Hill, New York, 1984, p.
18.23) and with Figure 13.37.
The uppermost line of Figure 13.37(a) marks the onset of
flooding which is the point at which sharp increase of pressure drop
obtains on a plot against liquid rate. Flooding limits also are
represented on Figure 13.36; in practice, it is customary to operate
at a gas rate that is 70% of that given by the line, although there are
many data points below this limit in this correlation.
Mesh or other open structures as vessel packing have attractive
pressure drop and other characteristics, but each type has quite
individual behavior so that it is best to consult their manufacturer’s
data.
6.10. GAS-SOLID TRANSFER
Equipment for pneumatic conveying is described in Section 5.2
along with some rules for calculating power requirements. Here the
latter topic will be supplemented from a more fundamental point of
view.
CHOKING VELOCITY
Although the phenomena are not clearcut, partial settling out of
solids from the gas stream and other instabilities may develop below
certain linear velocities of the gas called choking velocities. Normal
pneumatic transport of solids accordingly is conducted above such a
calculated rate by a factor of 2 or more because the best
correlations are not more accurate. Above choking velocities the
process is called dilute phase transport and, below, dense phase
transport.
What appears to be the best correlation of choking velocities is
due to Yang [AZChE J. 21, 1013-1015 (1975)], supplemented by
Punwani et al. and Yang (cited by Teo and Leung, 1984, pp.
520-521). The choking velocity Or,, and voidage E, are found by
simultaneous solution of the equations
G,/P, = (us, - u,)(l- &c) (6.125)
or
E, = 1 - WP,(% - ‘A) (6.126)
and
gD(er4-‘- 1) = 3.41(10’)(p,/p,)2.“(u,, - U,)2,
where G, is the mass rate of flow of solid per unit cross section and
the other terms are defined in Table 6.10. When E, from Eq. (6.126)
is substituted into Eq. (6.127), the single unknown in that equation
is readily found with a root solving routine. For the case of Example
6.15, G, = 29.6 kg/m2 set, U, = 0.45 m/set, p, = 1282 kg/m3, and
pg = 1.14 kg/m3. Accordingly, Ug,, = 1.215 m/set and E, = 0.9698.
TABLE 6.10. Equations for the Calculation of Pressure Drop in
Gas-Solid Transport
Solid Friction Factor c According to Various Investigators
investigator
Stemerding (1962)
Reddy and Pei (1969)
Van Swaaij, Buurman, and
van Breugel (1970)
Capes and Nakamura (1973)
Konno and Saito (1969)
f
0.003 (1)
O.O46U,’ c-3
O.O8OlJ,’ (3)
0.048U;z (4)
0.0285vgD U,’ (5)
Yang (1978). vertical
Yang (1976). horizontal
Free Setting Velocity
63)
UrL%okes~ =
SaJP-Pf), K<3,3 Ki3.3 (9)
1 Gr
Utiintemediete) =
0,,53g0.7’D’.‘4(p -p )O.”
P P f
9 4.3
PP kc
, 3.3<K<43.6 (10)
U 43.6 < K < 2360 (11)
Particle Velocity
Investigator 0,
Hinkle (1953) u, - 4 (12)
IGT (1978) UJl - 0.68D~&5p;0-zD-o’M) (13)
Yang (1976) (14)
Voidage
E = 1 - 4lfl,lnD~(p, - p,,u, (15)
Notation: U, is a fluid velocity, U, is particle velocity, U, is particle
free settling velocity, f& is mass rate offlow of solid, D = pipe diameter,
0, is particle diameter, g = 9.806 m/set at sea level.
(Klinzing, Gas-So/id Transport, McGraw-Hill, New York, 1981).
PRESSURE DROP
The relatively sparse data on dense phase transport is described by
Klinzing (1981) and Teo and Leung (1984). Here only the more
important category of dilute phase transport will be treated.
The pressure drop in simultaneous flow of gas and solid
particles is made up of contributions from each of the phases. When
the particles do not interact significantly, as in dilute transport, the
overall pressure drop is represented by
AP = p,(l - .z)Lg + p&g +
2fgP&L + %P,(l - +q
D
D
(6.128)
for vertical transport; in horizontal transport only the two frictional
terms will be present. The friction factor f, for gas flow is the
normal one for pipe flow; except for a factor of 4, it is given by Eq.
(6.19) for laminar flow and by the Round equation (6.21) for
turbulent flow. For the solid friction factor f,, many equations of](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-138-320.jpg)
![120 FLOW OF FLUIDS
EXAMPLE 6.15 Eq. (6.128),
Pressure Drop in Flow of Nitrogen and Powdered Coal
Powdered coal of 100 ym dia and 1.28 specific gravity is transported
vertically through a l-in. smooth line at the rate of 15g/sec. The
carrying gas is nitrogen at 1 atm and 25°C at a linear velocity of
6.1 m/set. The density of the gas is 1.14 kg/m3 and its viscosity is
1.7( lo-‘) N set/m’. The equations of Table 6.10 will be used for the
various parameters and ultimately the pressure gradient AP/L will
be found:
AP/L = 9.806[1282(1- 0.9959) + 1.14(0.9959)]
+(2/0.0254)[0.0076(1.14)(6.1)2
+0.0031(1282)(0.0041)(5.608)2]
= 51.54 + 11.13 + 25.38 + 40.35 = 128.4 Pa/m.
With Eqs. (5) and (13), no trial calculations are needed.
Eq. @h K = 1O-4
9.806(1.14)(1282- 1.14)
[1.7(10-y
1/3=3,67
Eq. (lo) u =0.153(9.806)"~71(0.0001)1~14(1282- l.l4)'.'l
) f
1.14°.Z9[1.7(10--5)]0.43
= 0.37 m/set (0.41 m/set by Stokes’ law),
Eq. (15), E = l-
0.015
(~/4)(0.0254)~(1282- l.l4)U,
=l-0.0231
Up '
E q . (14), U, =6.1-0.45~l+f,U;/2(9.806)(0.0254)
= 6.1- 0.4561+ 2.007fU;
(1)
(11)
Eq, (7), f, = 0.003y - El [ “,-,“‘2;“]-“‘79
(III)
P
Equations (I), (II), and (III) are solved simultaneously with the
results:
E = 0.9959 and Up = 5.608,
For the calculation of the pressure drop,
f, = 0.0031 (Yang equation),
Ref- orrp,- 0.0254(6.1)(1.14) = 1o
390,
Pf 1.7(10-5) ’
Therefore, Round’s Eq. (6.21) applies:
fr = $fRound=0.0076,
Eq. (13), Up = 6.1[1 - 0.68(0.0001)“~92(1282)o~5
x (1.14)-“~2(0.0254)-o~54]
= 5.88 m/set,
Eq. (15), E = 1 - 0.0231/5.78 = 0.9960,
Eq. (5), f, = 0.0285~9.806(0.0254)/5.88 = 0.00242.
Therefore, the solid frictional gradient is obtained from the
calculated value 40.35 in the ratio of the friction factors.
(AP/L)so,idfriction = 40.35(0.00242/0.0031) = 31.5 Pa/m.
10
ZT:
4 0
5 0
6 0
ifi
3 0
! E x a m p l e 6 . 1 5 . P r e s s u r e dt-o
P i n flow o f nitroscn a n d P O
wdered c o a l
INPUT U
E=l-.0231/U ! (Es I)
F=.003251*~1-E~/E”3*(.45t(l-
E)~‘<6.1-Ujj*-. 9 7 3 ! (Es 111)
G=-U+6.1-.45*<1+2.007*F#U*2>
*.S ! (should = 0>
PRINT “U=“j U
PRINT “G=” j G
GOTrJ 20 ! (if G is not suffi
c i e n t l r c l o s e to zero)
END
u = 5 . 6 0 8
- -
L--. 0 0 0 0 5 9 3 4 8 0 6 1
varying complexity have been proposed, of which some important
ones are listed in Table 6.10.
These equations involve the free settling velocity Cl,, for which
separate equations also are shown in the table. At lower velocities
Stokes’ law applies, but corrections must be made at higher ones.
The particle velocity U, is related to other quantities by Eqs.
(12)-(14) of the table, and the voidage in turn is represented by Eq.
(15). In a review of about 20 correlations, Modi et al. (Proceedings,
Powder and Bulk Solids Handling and Processing Conference,
Powder Advisory Center, Chicago, 1978, cited by Klinzing, 1981)
concluded that the correlations of Konno and Saito (1969) and of
Yang (1976, 1978) gave adequate representation of pneumatic
conveying of coal. They are applied in Example 6.15 and give
similar results there.
6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES
As the flow of fluid through a bed of solid particles increases, it
eventually reaches a condition at which the particles are lifted out of
permanent contact with each other. The onset of that condition is
called minimum fluidization. Beyond this point the solid-fluid mass
exhibits flow characteristics of ordinary fluids such as definite
viscosity and tlow through lines under the influence of hydrostatic
head difference. The rapid movement of particles at immersed
surfaces results in improved rates of heat transfer. Moreover,
although heat transfer rate between particles and fluid is only
moderate, l-4 Btu/(hr)(sqft)(“F), the amount of surface is so great,
lO,OOO-150,000 sqft/cuft, that temperature equilibration between
phases is attained within a distance of a few particle diameters.
Uniformity of temperature, rapid mass transfer, and rapid mixing of
solids account for the great utility of fluidized beds in process
applications.
As the gas flow rate increases beyond that at minimum
fluidization, the bed may continue to expand and remain homo-
geneous for a time. At a fairly definite velocity, however, bubbles
begin to form. Further increases in flow rate distribute themselves
between the dense and bubble phases in some ways that are not
well correlated. Extensive bubbling is undesirable when intimate
contacting between phases is desired, as in drying processes or solid
catalytic reactions. In order to permit bubble formation, the](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-139-320.jpg)
![6 . 1 1 . FLUIDIZATION O F B E D S O F P A R T I C L E S W I T H G A S E S 121
0.5
Gas velocity. m/s
(a)
Fluldizing rate. U/U,,
bl
I*= pvr’(G~-Gn~)/Gm/ I
Figure 6.10. Characteristics of gas-solid fluidization. (a) Schematic of the progress of pressure drop and bed height with increasing velocity,
for “normal” and “abnormal” behavior. For normal systems, the rates at minimum fluidization and minimum bubbling are the same. (b)
Behavior of heat transfer coefficient with gas flow rate analogous to part (a). The peak depends on the density and diameter of the particles
(Botteril, Fluid Bed Heat Transfer, Academic, New York, 1975). (c) Bed expansion ratio as a function of reduced flow rate and particle size.
The dashed line is recommended for narrow size range mixtures (Leva, 1959, p. 102). (d) Correlation of fluctuations in level, the ratio of the
maximum level of disturbed surface to average level (Leva, 1959, p. 105). (e) Bed voidage at minimum fluidization (Leua, 1959). Agarwal
and Storrow: (a) soft brick; (b) absorption carbon; (c) broken Raschig rings; (d) coal and glass powder; (e) Carborundum; (f) sand. U.S.
Bureau of Mines: (g) round sand, $+ = 0.86; (h) sharp sand, Gs = 0.67; (i) Fischer-Tropsch catalyst, & =0.58; (j) anthracite coal,
& = 0.63; (k) mixed round sand, Gs = 0.86. Van Heerden et al.: (I) coke; (m) Carborundum.
rate at minimum fluidization (Leva, 1959): G,,
(&ZoetIicient C in the equation for mass flow
= CDzg,p,(p, - pF)/p and C = 0.0007 Re- (g) Minimum bubbling and fluidization
velocities of cracking catalysts (Hurriott and Simone, in Cheremisinoff and Gupta, Eds., Handbook of Fluids in Motion, Ann Arbor Science,
Ann Arbor, MI, 1983, p. 656). (h) Minimum fluidization and bubbling velocities with air as functions of particle diameter and density
[Geldart, Powder Technol. 7, 285 (1973)]. (i) Transport disengagement height, TDH, as a function of vessel diameter and superficial linear
velocity [Zenz and Weil, AIChE J. 4, 472 (1958)]. (j) Good fluidization conditions (W.V. Battcock and K.K. Pillai, “Particle size in
Pressurised Combustors,” Proc. Fifth International Conference on Fluidised Bed Combustion, Mitre Corp., Washington D.C., 1977).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-140-320.jpg)
![124 FLOW OF FLUIDS
Mean particle diameter d, (urn)
Figure 6.12. Characteristics of four kinds of groups of particles classified by Geldart [Powder Technol. 6,
201-205 (1972); 7, 285-292 (1973)]. The boundary between A and B is represented by the equation
d, = 44,000p~‘&9/g(p, - pF) and that between B and D by (pS - pF) 2: = lo- kg/m.
Feature Group C Group A Group B G r o u p D
Distinguishing
word or phrase
E x a m p l e
Particle size for
ps = 2.5 g/cm3
Channeling
Spouting
Collapse rate
Expansion
Bubble shape
Rheological
character of
dense phase
Solids mixing
Gas back mixing
Slugging mode
Effect of ds
(within group)
on hydrodynamics
Effect of particle
size distribution
Cohesive
Flour
520pm
Severe little
N o n e n o n e
- s l o w
Low because high; initially
of channeling bubble-free
channels, no flat base,
bubbles spherical cap
high yield
stress
very low
very low
flat raining
plugs
unknown
unknown
aeratable
fluid cracking
catalyst
2O<ds a90ym
apparent viscosity
of order 1 poise
high
high
a x i s y m m e t r i c
appreciable
appreciable
bubble readilv spoutable
SO<& s650pm
negligible
shallow beds only
rapid
m e d i u m
rounded with
small
indentation
apparent viscosity
of order 5 poise
m e d i u m
m e d i u m
mostly axi-
symmetric
m i n o r
negligible
>650 pm
negligible
readily
rapid
m e d i u m
rounded
a p p a r e n t
viscosity of
order 10
poise
l o w
l o w
mostly wall
slugs
u n k n o w n
can cause
segregation
Solids of practical interest often are mixtures of a range of
particle diameters, but, for convenience, correlations are expressed
in terms of a single size which is almost invariably taken as the
surface average diameter given by
d, = l/c xidi, (6.129)
where xi is the weight fraction of the material having a diameter di
measured by screen analysis. Particles that deviate substantially
from a spherical shape are characterized as having the diameter of a
sphere with the same volume as the particle. The sphericity is
defined as the ratio
+ = (surface of a sphere)/(surface of the
particle with the same volume) (6.130)
and is always less than unity. Accordingly, the relation between the
effective particle size dp and that found by screen analysis is
dp = Wscreen. (6.131)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-143-320.jpg)
![6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES 125
EXAMPLE 6.16
Dimensions of B Fluidiied Bed Vessel
A fluidized bed is to hold 10,000 kg of a mixture of particles whose
true density is 1700 kg/m3. The fluidizing gas is at 0.3 m3/sec, has a
viscosity of 0.017cP or 1.7(E - 5) Nsec/m* and a density of
1.2 kg/m3. The size distribution of the particles is
d (rm) 252 178 126 89 70 50 30 10
x(wtfrac- 0.088 0.178 0.293 0.194 0.113 0.078 0.042 0.014
tion)
IJ, (m/se4 3.45 1.72 0.86 0.43 0.27 0.14 0.049 0.0054
The terminal velocities are found with Stokes’ equation
u, = dPD - .Q) d2 =
18/J p
9.81(~$~2)~lp 12) [dp (pm)]‘.
(a) The average particle size is
d, = 1
/
x (xJdJ = 84.5 ym.
(b) With d,, = 84.5 and density difference of 1699 kg/m3, the
material appears to be in Group A of Figure 6.12.
(c) Minimum fluidization velocity with Eq. (6.133)
%zf =
O.O093[84S(E - 6)]‘.82(1700 - l.2)“.94
[1.7(E - 5)]0.*8(1.2)0.~
= 0.0061 m/set,
and with Eqs. (6.134) and (6.135),
- -
Ar = 1.2(1700 1.2)(9.81)[84.5(E 6)J3 = 41 75
[1.7(E - 5)]’ . 7
R e , = V(27.2)*+ 0.0408(41.75) - 27.2 = 0.0313,
u,b _ P Remf- l.7(E - 5)(0.0313)
dPP 84.5(E - 6)(1.2) = o’0052 m’sec’
Use the larger value, umf = 0.0061, as the conservative one.
(d) Minimum bubbling velocity, with Eq. (6.136)
u,,,* = 33(84.5)(E - 6)[1.2/1.7(E - 5)]“.’ = 0.0085 m/set,
:. U,b lhzf = 0.0085/0.0061= 1.39.
From Eq. (6.139)
c,,- 82[1.7(E - 5)]“.6(l.2)o.06
u,,,~ - 9.81[84.5(E - 6)]‘.3(170fI - 1.2) = 1’35’
which is in rough agreement.
(e) Voidage at minimum bubbling from Eq. (6.138):
[1.7(E - 5)]2 0.5
9.81[84.5(E - 6)]3(1700)2
= 0.1948,
:. E,,,~ = 0.469.
It is not certain how nearly consistent this value is with those at
minimum fluidization read off Figure 6.10(e). Only a limited
number of characteristics of the solids are accounted for in Eq.
(6.138).
(f) Operating gas velocity. The ratios of entraining and
minimum fluidizing velocities for the two smallest particle sizes
present are
0.049/0.0061= 8.03, for 30 pm,
0.0054/0.0061= 0.89, for 10 pm.
Entrainment of the smallest particles cannot be avoided, but an
appreciable multiple of the minimum fluidizing velocity can be used
for operation; say the ratio is 5, so that
Uf =5u mf = 5(0.0061) = 0.0305 m/set.
(g) Bed expansion ratio. From Figure 6.10(c) with d, =
84.5 pm or 0.0033 in. and Gf /G,,,f = 5,
R =
I
1.16, by interpolation between the full lines,
1.22, off the dashed line.
Take R = 1.22 as more conservative. From Eq. (6.140) the ratio of
voidages is
E,,,~/E,,,~ = 5’.** = 1.42.
From part (e), E,~ =0.469 so that cmf =0.469/1.42 = 0.330.
Accordingly, the ratio of bed levels is
L,,/L, = (1 - ~,,,~)/(l- E,,,~) = 0.67/0.531= 1.262.
Although the value of E,,,~ appears somewhat low, the value of R
checks roughly the one from Figure 6.10(c).
(h) Fluctuations in level. From Figure 6.10(d), with d, =
0.0033 in., the value of m’ = 0.02, so that
r = exp[0.02(5 - 1)] = 1.083.
(i) TDH from Figure 6.10(i). At ur = u,~ - 4(0.0061) =
0.0244 m/set, the abscissa is off the plot, but a rough extrapolation
and interpolation indicates about 1.5 m for TDH.
(j) Dimensions of the bed and vessel. With a volumetric flow
rate of 0.3 m3/sec, the required diameter is
D = dO.3/(0.305)(n/4) = 3.54 m.
With a charge of 10,000 kg of solids and a voidage at minimum
bubbling of 0.469, the height of the minimum bubbling bed is
loo00
L = 1700(1- 0.469)(n/4)D2 = “13 m’
This value includes the expansion factor which was calculated
separately in item (g) but not the fluctuation parameter; with this
correction the bed height is
Lb = 1.13(1.083) = 1.22 m.
The vessel height is made up of this number plus the TDH of 1.5 m
or
vessel height = 1.22 + 1.5 = 2.72 m.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-144-320.jpg)
![126 FLOW OF FLUIDS
Minimum Fluidizafion. The fundamental nature of this
phenomenon has led to many correlations for its prediction. That of
Leva (1959) applies to Reynolds numbers Re, = dPG,,,f/p < 5, and
is
Gmf = 688D’.8* [PAPS - PF)1°.94
P Po.88
(6.132)
in the common units G,,,f in lb/(hr)(sqft), DP in inches, densities in
lb/tuft, and viscosity in cP. In SI units it is
LI
mf
= 0.0093d~“(p, - pf)o.94
~"~88pfo.M
(6.133)
The degree of confidence that can be placed in the correlation is
indicated by the plot of data on which it is based in Figure 6.10(f).
An equation more recently recommended by Grace (1982) covers
Reynolds numbers up to 1000:
Re,f = d+,,,plp = 4(27.2)‘+ O.O408(Ar) = 27.2, (6.134)
where
Ar = P(P, - p)&ld
Here also the data show much scatter, so that pilot plant
determinations of minimum fluidization rates usually are advisable.
Minimum Bubbling Conditions. Minimum bubbling velocities
for Group B substances are about the same as the minimum
fluidization velocities, but those of Group A substances are
substantially greater. For Group A materials the correlation of
Geldart and Abrahamsen [Powder Technol 19, 133 (1978)] for
minimum bubbling velocity is
u,,,~ = 33dP(p/p)Po.‘.
For air at STP this reduces to
(6.136)
umb = lOOd,. (6.137)
For cracking catalysts represented on Figure 6.10(g), Harriott and
Simone (1983) present an equation for the ratio of the two kinds of
velocities as
(6.138)
The units of this equation are SI; the coefficient given by
Cheremisinoff and Cheremisinoff (1984, p. 161) is incorrect. Figures
6.10(g) and (h) compare the two kinds of velocities over a range of
particle diameters. Voidage at minimum bubbling is correlated by
an equation of Cheremisinoff and Cheremisinoff (1984, p. 163):
&,/(l - E,,,~) = 47.4(gd;p;/p2)-o?
Bed Expansion and Fluctuation. The change of bed level with
increasing gas rate is represented schematically in Figure 6.10(a).
The height remains constant until the condition of minimum
fluidization is reached, and the pressure drop tends to level off.
Then the bed continues to expand smoothly until some of the gas
begins to disengage from the homogeneous dense phase and forms
bubbles. The point of onset of bubbling corresponds to a local
maximum in level which then collapses and attains a minimum.
With increasing gas rate, the bed again continues to expand until
entrainment develops and no distinct bed level exists. Beyond the
minimum bubbling point, some fraction of the excess gas continues
through the dense phase but that behavior cannot be predicted with
any accuracy.
Some smoothed data of expansion ratio appear in Figure
6.10(c) as a function of particle size and ratio of flow rates at
minimum bubbling and fluidization. The rather arbitrarily drawn
dashed line appears to be a conservative estimate for particles in the
range of 100 pm.
Ordinarily under practical conditions the flow rate is at most a
few multiples of the minimum fluidizing velocity so the local
maximum bed level at the minimum bubbling velocity is the one
that determines the required vessel size. The simplest adequate
equation that has been proposed for the ratio of voidages at
minimum bubbling and fluidization is
h,b lG?f = (G,,,,/G,,f)o’2* (6.140)
= 2. 64cc~.89po.5~/go.22d~06(pp _ p)0.22
(6.141)
The last equation results from substitution of Eq. (6.138) into
(6.140). Then the relative bed level is found from
LmbIL, = (1 - %,f)/(l - &,,,b). (6.142)
Either E,,,~ or E,,,~ must be known independently before Eq. (6.141)
can be applied, either by application of Eq. (6.139) for .smb or by
reading off a value of E,~ from Figure 6.8(c) or Figure 6.10(e).
These values are not necessarily consistent.
At high gas velocities the bed level fluctuates. The ratio of
maximum disturbed level to the average level is correlated in terms
of Gf/Gmf and the particle diameter by the equation
r = expb’(Gf - G,,fYGmfl, (6.143)
where the coefficient m’ is given in Figure 6.10(d) as a function of
particle diameter.
Freeboard. Under normal operating conditions gas rates
somewhat in excess of those for minimum fluidization are
employed. As a result particles are thrown into the space above the
bed. Many of them fall back, but beyond a certain height called the
transport disengaging height (TDH), the entrainment remains
essentially constant. Recovery of that entrainment must be
accomplished in auxiliary equipment. The TDH is shown as a
function of excess velocity and the diameter of the vessel in Figure
6,10(i). This correlation was developed for cracking catalyst
particles up to 400 pm dia but tends to be somewhat conservative at
the larger sizes and for other materials.
Viscosity. Dense phase solid-gas mixtures may be required to
flow in transfer line catalytic crackers, between reactors and
regenerators and to circulate in dryers such as Figures 9.13(e), (f).
In dilute phase pneumatic transport the effective viscosity is nearly
that of the fluid, but that of dense phase mixtures is very much
greater. Some data are given by Schiigerl (in Davidson and
Harrison, 1971, p. 261) and by Yates (1983). Apparent viscosities
with particles of 50-550 pm range from 700 to 1300 cP, compared
with air viscosity of 0.017 CP at room temperature. Such high values
of the viscosity place the flow definitely in the laminar flow range.
However, information about friction in flow of fluidized mixtures
through pipelines is not easy to find in the open literature. Someone
must know since many successful transfer lines are in operation.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-145-320.jpg)
![7.2. PUMP THEORY 131
electrical motor control. Double-ported valve (d) gives better
control at large flow rates; the pressures on the upper and lower
plugs are balanced so that less force is needed to move the stem.
The single port (e) is less expensive but gives a tighter shutoff and is
generally satisfactory for noncritical service. The reverse acting
valve (f) closes on air failure and is desirable for reasons of safety in
some circumstances.
7.2. PUMP THEORY
Pumps are of two main classes: centrifugal and the others. These
others mostly have positive displacement action in which the
discharge rate is largely independent of the pressure against which
they work. Centrifugal pumps have rotating elements that impart
ie / r - J
or’ ’ ’ ’ ’ ’ ’ ’ ’
0 0.2 0.4 0.6 iii3 1.0
(h)
Figure 7.1-(conthued)
high velocity initially and high pressure head ultimately to the
liquid. Elements of their theory will be discussed here. A glossary
of pump terms and terms relating primarily to centrifugal pumps are
defined in the Glossary at the end of this chapter. The chief
variables involved in pump theory are listed here with typical units:
D, diameter of impeller (ft or m),
H, output head (ft or m),
n, rotational speed (l/set),
i, output power (HP or kW),
Q, volumetric discharge rate (cfs or m3/sec),
p, viscosity (Ib/ft set or N sec/m2),
p, density (Ib/cuft or kg/m3),
E, surface roughness (ft or m).
BASIC RELATIONS
A dimensional analysis with these variables reveals that the
functional relations of Eqs. (7.1) and (7.2) must exist:
gWn2D2 = 9dQlnD3, D=npl~, &ID)>
PJpn3D5 = &(QlnD3, D’npJp, E/D).
The group D2nplp is
roughness ratio. Three
named
the Reynolds number and E/D is the
new groups also have arisen which are
capacity coefficient, C, = Q/no’,
head coefficient, C, = gHln2D2,
power coefficient, Ck = i/pn3D5.
(7.1)
(7.2)
(7.3)
(7.4)
(7.5)
The hydraulic efficiency is expressed by these coefficients as
17 = gHpQ/P = C,C,/C,. (7.6)
Although this equation states that the efficiency is independent of
the diameter, in practice this is not quite true. An empirical relation
is due to Moody [ASCE Trans. 89, 628 (1926)]:
q2 = 1 - (1 - ~,)(D,/D,)“-25. (7.7)
Geometrically similar pumps are those that have all the
dimensionless groups numerically the same. In such cases, two
different sets of operations are related as follows:
QJQ, = (n2/4(4/Dd3J
H,IH, = (n24/nlDl)z,
. .
P,lP, = (p21pl)(nzlnl)3(4/Dl)5.
(7.8)
(7.9)
(7.10)
The performances of geometrically similar pumps also can be
represented in terms of the coefficients C,, C,, C,, and 7. For
instance, the data of the pump of Figure 7.2(a) are transformed into
the plots of Figure 7.2(b). An application of such generalized curves
is made in Example 7.1.
Another dimensionless parameter that is independent of
diameter is obtained by eliminating D between C, and C, with the
result,
N, = nQ”.5/(gH)o.‘5. (7.11)
This concept is called the specific speed. It is commonly used in the](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-150-320.jpg)
![7.2. PUMP THEORY 133
EXAMPLE~.~ Some values are
Operating Points of Single and Double Pumps in Parallel and
Series
The head loss in a piping system is represented by the equation
H, =50+6.0(Q/100)2+ H,,,
where & is the head loss in the control valve. The pump to be used
has the characteristic curve of the pump of Figure 7.7(b) with an
8 in. impeller; that curve is represented closely by the equation
O/100 0.8 1.0 1.2 1.286
H" 10.88 7.00 2.28 0
4 59.92
(b) In parallel each pump has half the total flow and the same
head H,:
HP = 68 - OS(Q/lOO) - 4.5(Q/100)2.
The following will be found (see Figure 7.17):
(a) The values of H, corresponding to various flow rates Q gpm.
(b) The flow rate and head on the pumps when two pumps are
connected in parallel and the valve is wide open (H, = 0).
(c) The same as (b) but with the pumps in series.
(d) The required speed of the pump at 80gpm when no control
valve is used in the line.
5O+6.O(Q/1OO)2=68-(O.5/2)(Q/1OO)-(4.5/4)(Q/1OO)2,
:. Q = 157.2 gpm, H, = 64.83 ft.
(c) In series each pump has the same flow and one-half the
total head loss:
~(50+6.0(Q/100)2]=68-0.5(Q/100)-4.5(Q/100)2,
:. Q = 236.1 gpm, H, = 83.44 ft.
Series flow allows 50% greater gpm than parallel.
(a) The operating point is found by equating e, and HP from
which
H, = 68 - 0.5(Q/lOO) - 4.5(Q/lOO)* - [50 + 6.O(Q/lOO)‘].
(d) H,=50+4.8=54.8,
H,=(68-0.4- 2.88)(n/1750)2,
:. n = 175Odm = 1610 rpm.
mixed units
N, = (rpm)(gpm)“.“/(ft)“~“. (7.12)
For double suction pumps, Q is one half the pump output.
The net head at the suction of the pump impeller must exceed a
certain value in order to prevent formation of vapor and resulting
cavitation of the metal. This minimum head is called the net
positive suction head and is evaluated as
NPSH = (pressure head at the source)
+ (static suction head)
- (friction head in the suction line)
- (vapor pressure of the liquid). (7.13)
Usually each manufacturer supplies this value for his equipment.
(Some data are in Figure 7.7.) A suction specific speed is defined as
S = (rpm)(gpm)“~“/(NPSH)” “. (7.14)
Standards for upper limits of specific speeds have been
established, like those shown in Figure 7.6 for four kinds of
pumps. When these values are exceeded, cavitation and resultant
damage to the pump may occur. Characteristic curves correspond-
ing to widely different values of iV, are shown in Figure 7.3 for
several kinds of pumps handling clear water. The concept of specific
speed is utilized in Example 7.3. Further data are in Figure 7.6.
Recommendations also are made by the Hydraulic Institute of
suction specific speeds for multistage boiler feed pumps, with
S = 7900 for single suction and S = 6660 for double suction. Thus
the required NPSH can be found by rearrangement of Eq. (7.14) as
NPSH = [(rpm)(gpm)0.5/S]4’3. (7.15)
For example, at 35OOrpm, lOOOgpm, and S = 7900, the required
NPSH is 34 ft.
For common fluids other than water, the required NPSH
usually is lower than for cold water; some data are shown in Figure
7.16.
PUMPINGSYSTEMS
The relation between the flow rate and the head developed by a
centrifugal pump is a result of its mechanical design. Typical curves
are shown in Figure 7.7. When a pump is connected to a piping
system, its head must match the head loss in the piping system at
the prevailing flow rate. The plot of the flow rate against the head
loss in a line is called the system curve. The head loss is given by the
mechanical energy balance,
(7.16)
where H, is the head loss of a control valve in the line.
The operating point may be found as the intersection of plots
of the pump and system heads as functions of the flow rate. Or an
equation may be fitted to the pump characteristic and then solved
simultaneously with Eq. (7.16). Figure 7.17 has such plots, and
Example 7.2 employs the algebraic method.
In the normal situation, the flow rate is the specified quantity.
With a particular pump curve, the head loss of the system may need
to be adjusted with a control valve in the line to make the system
and pump heads the same. Alternately, the speed of the pump can
be adjusted to make the pump head equal to that of the system.
From Eq. (7.9) the relation between speeds and pump heads at two](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-152-320.jpg)
![136 FLUID TRANSPORT EQUIPMENT
EXAMPLE 7.3
Check of Some Performance Curves with the Concept of
Specific Speed
(a) The performance of the pump of Figure 7.7(b) with an 8in.
impeller will be checked by finding its specific speed and
comparing with the recommended upper limit from Figure
7.6(b). Use Eq. (7.12) for N,
Clearly the performance curves are well within the recom-
mended upper limits of specific speed.
(b) The manufacturer’s recommended NPSH of the pump of Figure
7.7(c) with an 8 in. impeller will be checked against values from
Eq. (7.15) with S = 7900:
0 kwm) 100 150 200
H Vt) 490 440 300
NPSH (mfgr) 1 0 18 35
NPSH [Eq. (7.15)j 7.4 9.7 11.8
The manufacturer’s recommended NPSHs are conservative.
Q (gpm) 100 200 300
H (fi) 268 255 225
IV, (calcd) 528 776 1044
Ns [Fig. 7.10(a)] 2050 2150 2500
NPSH 5 7 13
1 / I VtZeroft I
H = total head(,a’; (first stage) H= total head,ft (f!rst stage)
(b)
H= totaiheod,ft (first stage) H= total head, ft (first stage)
(cl (d)
Figure 7.6. Upper specific-speed limits for (a) double-suction pumps (shaft through impeller
eye) handling clear water at 85°F at sea level, (b) single-suction pumps (shaft through impeller
eye) handling clear water at 85°F at sea level, (c) single-suction pumps (overhung-impeller
type) handling clear water at 85°F at sea level, (d) single-suction mixed- and axial-flow pumps
(overhung-impeller type) handling clear water at 85°F at sea level. (Hydraulic Institute,
Cleveland, OH, 1957).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-155-320.jpg)
![7 . 3 P U M P C H A R A C T E R I S T I C S 137
I! ! ! ! ! ! ! !.!
mo- cum E-6994-2
rm3X2XBk m( CSO
u P-1757-1 -OIL 8k’
U. L GALLONS PER MINLITE
(a)
U. S. GALLONS PER MINUTE
b)
(c)
Figure 7.7. Characteristic curves of centrifugal pumps when operating on water at 85°F (Allis Chalmers Co.). (a) Single suction, 1750 rpm. (b)
The pump of (a) operated at 3500 ‘pm. (c) Multistage, single suction, 3550 rpm.
The basic types of centrifugals are illustrated in Figure 7.9. A centrifugal vane action; the propeller confers high rates of flow but
volute is a gradually expanding passage in which velocity is partially the developed pressure is low. Figure 7.3(b) represents a typical
converted to pressure head at the outlet. The diffuser vanes of axial pump performance.
Figures 7.9(b) and 7.10(d) direct the flow smoothly to the periphery. The turbine impeller of Figure 7.10(h) rotates in a case of
The volute design is less expensive, more amenable to use with uniform diameter, as in Figure 7.12(j). As Figure 7.4(a) demon-
impellers of different sizes in the same case, and, as a consequence, strates, turbine pump performance resembles that of positive dis-
by far the most popular construction. Diffuser construction is used placement types. Like them, turbines are essentially self-priming,
to a limited extent in some high pressure, multistage machines. The that is, they will not vapor bind.
double suction arrangement of Figure 7.9(d) has balanced axial All rotating devices handling fluids require seals to prevent
thrust and is favored particularly for severe duty and where the leakage. Figure 7.13 shows the two common methods that are used:
lowered NPSH is an advantage. Multistage pumps, however, are stuffing boxes or mechanical seals. Stuffing boxes employ a soft
exclusively single suction. packing that is compressed and may be lubricated with the pump
Some of the many kinds of impellers are shown in Figure 7.10. liquid or with an independent source. In mechanical seals, smooth
For clear liquids, some form of closed impeller [Figure 7.10(c)] is metal surfaces slide on each other, and are lubricated with a very
favored. They may differ in width and number and curvature of the small leakage rate of the pump liquid or with an independent liquid.
vanes, and of course in the primary dimension, the diameter. Performance capability of a pump is represented on diagrams
Various extents of openness of impellers, [Figs. 7.10(a) and (b)] are like those of Figure 7.7. A single point characterization often is
desirable when there is a possibility of clogging as with slurries or made by stating the performance at the peak efficiency. For
pulps. The impeller of Figure 7.10(e) has both axial propeller and example, the pump of Figure 7.7(c) with a 9 in. impeller is called a](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-156-320.jpg)
![0.8
0.7
0.4
0.3
200,
20 100 200 300
HEAD, FEET OF LIQUID
Figure 7.11. Approximate efficiencies of centrifugal pumps in terms
of GPM and head in feet of liquid.
Valve open on
forward stroke
Valve open on
reverse stroke
(a)
j/j--
i
(cl
7.4. CRITERIA FOR SELECTION OF PUMPS 141
identifies impeller and case size and other details which are stated in
a catalog. Each combination of head and capacity will have an
efficiency near the maximum of that style. Although centrifugal
pumps function over a wide range of pressure and flow rates, as
represented by characteristic curves like those of Figures 7.2 and
7.7, they are often characterized by their performance at the peak
efficiency, as stated in the previous section. Approximate
efficiencies of centrifugal pumps as functions of head and capacity
are on Figure 7.11 and elsewhere here.
Centrifugal pumps have a number of good qualities:
1. They are simple in construction, are inexpensive, are available in
a large variety of materials, and have low maintenance cost.
2. They operate at high speed so that they can be driven directly by
electrical motors.
3. They give steady delivery, can handle slurries and take up little
floor space.
Some of their drawbacks are
4. Single stage pumps cannot develop high pressures except at very
high speeds (10,000 rpm for instance). Multistage pumps for high
T i m e
(b)
k-- Cyfinder No.’ f kylinder N o . 3
L Cylinder No. 2 -4
hi)
D I S C H A R G E
S U C T I O N ’
OISCHARGE
4
ION
S C R E W S C R E W
Figure 7.12. Some types of positive displacement pumps. (a) Valve action of a double acting reciprocating piston pump. (b) Discharge curve
of a single acting piston pump operated by a crank; half-sine wave. (c) Discharge curve of a simplex double acting pump as in (a). (d)
Discharge curve of a duplex, double acting pump. (e) An external gear pump; characteristics are in Figure 7.8(c). (f) Internal gear pump; the
outer gear is driven, the inner one follows. (g) A double screw pump. (h) Peristaltic pump in which fluid is squeezed through a flexible tube
by the follower. (i) Double diaphragm pump shown in discharge position (BIF unit of General Signal). (j) A turbine pump with essentially
positive displacement characteristics (data on Fig. Z 4(a)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-160-320.jpg)
![7 . 5 . E Q U I P M E N T F O R G A S T R A N S P O R T 143
Head in feet
o 2 5 I50 I75 ~i00~150~200~250 300~400~500~Above 500
20 .. Single sucfion Either double sucfion
40 -.
I
or mu/tistoge
Fi
75 .-
200--
i’
(r
2 Either
400-. single or
daub/e suction
- Mu/C-
,s 600--
sfoge
2 lOOO--
‘: 2000 -.
g 2500 -.
‘> 4000 --
6000 -. Double s&ion
8000 -.
l0,000
(a)
of 50-1OOOatm or more. Some performance data are shown in
Figure 7.5.
Diaphragm pumps [Fig. 7.12(i)] also produce pulsating flow.
They are applied for small flow rates, less than 100 gpm or so, often
for metering service. Their utility in such applications overbalances
the drawback of their intrinsic low efficiencies, of the order of 20%.
Screw pumps [Fig. 7.12(g)] are suited for example to high
viscosity polymers and dirty liquids at capacities up to 2000 gpm and
pressures of 200 atm at speeds up to 3000 rpm. They are compact,
quiet, and efficient. Figure 7.4(d) shows typical performance data.
Gear pumps [Figs. 7.12(e) and (f)] are best suited to handling
clear liquids at a maximum of about 1OOOgpm at 150atm. Typical
performance curves are shown in Figure 7.4(c).
Peristaltic pumps [Fig. 7.12(h)] move the liquid by squeezing a
tube behind it with a rotor. Primarily they are used as metering
pumps at low capacities and pressures in corrosive and sanitary
services when resistant flexible tubes such as those of teflon can be
used, and in laboratories.
Turbine pumps [Figs. 7.9(f), 7.12(i), and 7.4(a)] also are called
regenerative or peripheral. They are primarily for small capacity
and high pressure service. In some ranges they are more efficient
than centrifugals. Because of their high suction lifts they are suited
to handling volatile liquids. They arc not suited to viscous liquids or
abrasive slurries.
7.5. EQUIPMENT FOR GAS TRANSPORT
Gas handling equipment is used to transfer materials through pipe
lines, during which just enough pressure or head is generated to
overcome line friction, or to raise or lower the pressure to some
required operating level in connected process equipment. The main
classes of this kind of equipment are illustrated in Figures 7.18 and
7.19 and are described as follows.
u.s.gallonsperrmnute
(b)
Figure 7.14. Range of applications of various kinds of pumps. (a)
Range of applications of single and double suction pumps
(Allis-Chalmers Co.). (b) Recommended kinds of pumps for
various kinds of head and flow rate (Fairbanks, Morse, and Co.).
pressures are expensive, particularly in corrosion-resistant mate-
rials
5. Efficiencies drop off rapidly at flow rates much different from
those at peak efficiency.
6. They are not self-priming and their performance drops off
rapidly with increasing viscosity. Figure 7.15 illustrates this ef-
feet
On balance, centrifugal pumps always should be considered first in
comparison with reciprocating or rotary positive displacement
types, but those do have their places. Range of applications of
various kinds of pumps are identified by Figure 7.14.
Pumps with reciprocating pistons or plungers are operated with
steam, motor or gas engine drives, directly or through gears or
belts. Their mode of action is indicated on Figure 7.12(a). They are
always used with several cylinders in parallel with staggered action
to smooth out fluctuations in flow and pressure. Figure 7.5(c) shows
that with five cylinders in parallel the fluctuation is reduced to a
maximum of 7%. External fluctuation dampers also are used.
Although they are self-priming, they do deteriorate as a result of
cavitation caused by release of vapors in the cylinders. Figure 7.4(e)
shows the NPSH needed to repress cavitation. Application of
reciprocating pumps usually is to low capacities and high pressures
1.
2 .
3 .
4 .
5 .
6 .
Fans accept gases at near atmospheric pressure and raise the
pressure by approximately 3% (12in. of water), usually on air
for ventilating or circulating purposes.
Blowers is a term applied to machines that raise the pressure to
an intermediate level, usually to less than 40 psig, but more than
accomplished by fans.
Compressors are any machines that raise the pressure above the
levels for which fans are used. Thus, in modern terminology they
include blowers.
Jet compressors utilize a high pressure gas to raise other gases at
low pressure to some intermediate value by mixing with them.
Vacuum pumps produce subatmospheric pressures in process
equipment. Often they are compressors operating in reverse but
other devices also are employed. Operating ranges of some
commercial equipment are stated in Table 7.3.
Steam jet ejectors are used primarily to evacuate equipment but
also as pumps or compressors. They are discussed in Section 7.7.
Application ranges of fans and compressors are indicated on
Figures 7.20 and 7.21. Some of these categories of equipment now
will be discussed in some detail.
F A N S
Fans are made either with axial propellers or with a variety of radial
vanes. The merits of different directions of curvature of the vanes
are stated in Figure 7.24 where the effect of flow rate of pressure,
power, and efficiency also are illustrated. Backward curved vanes
are preferable in most respects. The kinds of controls used have a
marked effect on fan performance as Figure 7.23 shows. Table 7.4
shows capacity ranges and other characteristics of various kinds of](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-162-320.jpg)
![150 FLUID TRANSPORT EQUIPMENT
6t ~istbn o;mb 1
0.6
sN,=Nfi,/H’
0.3 I)* = IHI k 3fl$
N = sneed. mm
- 8 = fi0w ft3&
H = head. ft
D = Impeller diameter, ft
dh
0.1 I c
0.1 0.3 0.6 1 3 6 10 30 60 100 300 6001000 3OGO 10,003
Specific speed, N,
Figure 7.21. Operating ranges of single-stage pumps and compressors [Balje, Trans. ASME, J. Eng. Power. 84, 103 (1962)].
Example: atmospheric air at the rate of 100,000 SCFM is compressed to 80,000 ft Ibf/ft (41.7 psig) at 12,000 rpm; calculated
N, = 103; in the radial flow region with about 80% efficiency, D, = 1.2-1.6, so that D = 2.9-3.9 ft.
150
0 140
2 130
a
6
120
53 110
E 100
s 90
“u 80
5 7 0
a 6 0
D 50
g 40
330
g 20
10
40 50 60 70 80 90 100 1 1 0 120 1 3 0
PERCENT DESIGN VOLUME
(a)
160
’
140
I I III1
.. ?? 99
PERCENT,
PEAK EFFICIENCY
w”46 m
60
4 0 60 60 100 120 140 160
PERCENT. INLET VOLUME
Figure 7.22. Performances of dynamic compressors: (a) Axial compressor. (b) Centrifugal compressor. All quantities are expressed as
percentages of those at the design condition which also is the condition of maximum efficiency (De Lava1 Engineering Handbook,
McGraw-Hill, New York, 1970).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-169-320.jpg)
![7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 1%
TABLE 7.9. Five Rotary Compressors for a Common Service
Liquid
Liner
Suction loss 6, 9 . 3 5 1.32
Discharge loss 6, 7 . 3 5 1.04
Intrinsic corr. S 1 . 1 8 5 1 . 0 2 3
Adiabatic eff. qsd 8 5 . 6 9 7 . 7
Slippage W, (%) 2 8 . 5 18.6
Slip eff. vs (%) 7 1 . 5 8 3 . 4
Thermal eff. (%)
qt 8 9 . 2 9 3 . 7
Volumetric eff. E,, 8 8 . 0 8 5 . 7
Displacement (cfm) 1 4 , 7 0 0 1 1 , 6 5 0
Rotor dia. (in.) 2 6 . 6 2 6 . 2
Commercial size, d x L 25 x 25 22x33
Speed (rpm) 3 , 5 0 0 1 , 2 5 0
Motor (HP) 1,100 800
Service factor 1.09 1.11
Discharge temp “F 309 270
‘Twin 32.5 x 65 or triplet 2 6 . 5 x 3 3 ( 6 6 7 rpm) are more realistic.
bTwin 32 x 32 (613 rpm) alternate where L= d.
(Evans, 1979).
is the ratio of heat capacities at constant pressure and constant
volume and
C”=R-C,.
A related expression of some utility is
T,/T, = (P2/P,)‘k-“‘k.
(7.22)
(7.23)
Since k ordinarily is a fairly strong function of the temperature, a
suitable average value must be used in Eq. (7.20) and related ones.
Under adiabatic conditions the flow work may be written as
W=H,-H,=
I
9
V dP. (7.24)
4
Upon substitution of Eq. (7.20) into Eq. (7.24) and integration, the
isentropic work becomes
(7.25)
TABLE 7.10. Specifications of Liquid Liner Compressors
Pressure Capacity Motor
tpsi) (cuftfmin) 0-W
5 1020 4 0
K - 6 10 990 6 0
1 5 870 7 5
2 0 650 100
621 2 6
1251 120
1256
i 3 5
440
621
1251 8 0
1256
2 3
110
410
7;
4 0
100
1 0
5 0
i
570
3500
1750
1750
3500
1750
1750
0 . 8 9 0 . 9 0 1.40
0 . 7 0 0 . 7 0 1.10
1 . 0 1 6 1 . 0 1 6 1 . 0 2 5
9 8 . 5 9 8 . 5 9 7 . 9
11.8 11.8 3 . 0
8 8 . 2 8 8 . 2 9 7 . 0
9 5 . 8 9 5 . 5 4 2 . 5
89.1 8 9 . 9 9 6 . 6
1 1 , 2 2 0 1 1 , 1 2 0 1 0 , 3 7 0
2 7 . 0 6 5 . 0 4 5 . 5
22 x 33 46 x 92a 43~48~
593 284 378
750 750 1,400
1.10 1.12 1.10
262 263 120
In multistage centrifugal compression it is justifiable to take the
average of the inlet and outlet compressibilities so that the work
becomes
~=H*-Hl=(~)(~)RT,[(~)‘k-l”k-I]. ( 7 . 2 6 )
When friction is present, the problem is handled with empirical
eficiency factors. The isentropic compression efficiency is defined as
17s =
isentropic work or enthalpy change
actually required work or enthalpy change
(7.27)
Accordingly,
W = AH = WJs = (AH),/n,. (7.28)
When no other information is available about the process gas, it is
justifiable to find the temperature rise from
AT = (AT),/rl,
so that
(7.29)
T, = T,(l + (l/q,)[(P2/PI)‘k-“‘k - 11. (7.30)
A case with variable heat capacity is worked out in Example
7.5.
For mixtures, the heat capacity to use is the sum of the mol
Gas Compression, Isentropic and True Final Temperatures
With k = 1.4, PJPI = 3 and 9, = 0.71; the final temperatures are
(T2)S = 1.369Tt and G= 1.519T, with Eqs. (7.24) and (7.31).
(Nash Engineering Co.).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-174-320.jpg)
![156 FLUID TRANSPORT EQUIPMENT
fraction weighted heat capacities of the pure components,
c, = &Cpi. (7.31)
REAL PROCESSES AND GASES
Compression in reciprocating and centrifugal compressors is
essentially adiabatic but it is not frictionless. The pressure-volume
behavior in such equipment often conforms closely to the equation
PV” = P, V; = const . (7.32)
Such a process is called polytropic. The equation is analogous to the
isentropic equation (7.20) but the polytropic exponent n is different
from the heat capacity ratio k.
Polytropic exponents are deduced from PV measurements on
the machine in question. With reciprocating machines, the PV data
are recorded directly with engine indicators. With rotary machines
other kinds of instruments are used. Such test measurements usually
are made with air.
Work in polytropic compression of a gas with equation of state
PV = zRT is entirely analogous to Eq. (7.26). The hydrodynamic
work or the work absorbed by the gas during the compression is
w,, = f vdP = (-&IRTl[ (;)“I’” - I]. (7.33)
Manufacturers usually characterize their compressors by their
polytropic efficiencies which are defined by
(7.34)
The polytropic work done on the gas is the ratio of Eqs. (7.33) and
(7.34) and comprises the actual mechanical work done on the gas:
W, = W,,,q, = (&)zIRTl[ ($‘n-l”n - I] (7.35)
Losses in seals and bearings of the compressor are in addition to
Wp; they may amount to l-3% of the polytropic work, depending
on the machine.
The value of the polytropic exponent is deduced from Eq.
(7.34) as
(7.36)
The isentropic efficiency is
77 = isentropic work [Eq. (7.25)]
s actual work [Eq. (7.35)]
= (P*/PJ’k-“‘k - 1
(P*/P,)(“-‘1’” - 1
(P*/P#-“‘k - 1
= (pz/pl)‘~-“‘% - 1
(7.37)
(7.38)
(7.39)
The last version is obtained with the aid of Eq. (7.34) and relates
the isentropic and polytropic efficiencies directly. Figure 7.27(b) is a
plot of Eq. (7.39). Example 7.6 is an exercise in the relations
between the two kinds of efficiencies.
MAXIMUM HEAD PER STAGE (FT-LB/LB)
@ 00
4 00
60 00
+
00 00 00” 00
d’ 96 8. ,%P
is-’ 3 0 4 0 5 0 6 0 7 0 80 9 0 t o o
t4OLECULAR YEIGH,
(a)
10 3 0 4 0 so 60 7 0 80
Head, It-lb/lb (multiply by 1000)
(b)
H = 5 ft/stage
K= 0.50-0.65, empirical coefficient
u = 600-900 ft / set, impeller peripheral speed
H = 10,000 with average values K = 0.55 and u = 765 fl ! set
(cl
Figure 7.26. Several ways of estimating allowable polytropic head
per stage of a multistage centrifugal compressor. (a) Single-stage
head as a function of k, molecular weight, and temperature (Elliott
Co.). (b) Single-stage head as a function of the nature of the gas
(NGPSA Handbook, Gas Processors Assn, Tub, OK, 1972),
obtained by dividing the total head of the compressor by number of
stages. H = Ku*/32.2 ft/stage, K = 0.50-0.65, empirical coefficient,
u = 600-900 ft/sec, impeller peripheral speed, and H = 10,000 with
average values K = 0.55 and u = 765 ft/sec. (c) An equation and
parameters for estimation of head.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-175-320.jpg)
![7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 1%
4.0 I I I I I I I I I i
1’
5 /
g I /
E
saturation /
CUrYe -y
g 3.0
/
/
z
b
/’
i2 / /
e
3
/
/,
.i4
%
1.0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -.--0s 0.9 1.0
In terms of a known isentropic efficiency the final temperature TZ
then is found by trial from
(Aff)slv, = j--y CL dT + AH; - AH;. (7.49)
In these equations the heat capacity CL is that of the ideal gas
state or that of the real gas near zero or atmospheric pressure. The
residual properties AS; and AH; are evaluated at (5, Ti) and AS;
and AH; at (Pa, Tz). Figure 7.28 gives them as functions of reduced
temperature T/T, and reduced pressure P/P,. More accurate
methods and charts for finding residual properties from appropriate
equations of state are presented in the cited books of Reid et al.
(1977) and Walas (1985).
For mixtures, pseudocritical properties are used for the
evaluation of the reduced properties. For use with Figure 7.28,
Kay’s rules are applicable, namely,
(7.50)
(7.51)
but many equations of state employ particular combining rules.
Example 7.8 compares a solution by this method with the
assumption of ideal behavior.
(a)
EFFICIENCY
The efficiencies of fluid handling equipment such as fans and
compressors are empirically derived quantities. Each manufacturer
will supply either an efficiency or a statement of power requirement
for a specified performance. Some general rules have been devised
for ranges in which efficiencies of some classes equipment usually
fall. Figure 7.27 gives such estimates for reciprocating compressors.
Fan efficiencies can be deduced from the power-head curves of
Figure 7.24. Power consumption or efficiencies of rotary and
reciprocating machines are shown in Tables 7.7, 7.8, and 7.9.
Polytropic efficiencies are obtained from measurements of
power consumption of test equipment. They are essentially
independent of the nature of the gas. As the data of Figure 7.27
indicate, however, they are somewhat dependent on the suction
volumetric rate, particularly at low values, and on the compression
ratio. Polytropic efficiencies of some large centrifugal compressors
are listed in Table 7.6. These data are used in Example 7.9 in the
selection of a machine for a specified duty.
The most nearly correct methods of Section 7.6.4 require
knowledge of isentropic efficiencies which are obtainable from the
polytropic values. For a given polytropic efficiency, which is
independent of the nature of the gas, the isentropic value is
obtained with Eq. (7.39) or Figure 7.27(b). Since the heat capacity
is involved in this transformation, the isentropic efficiency depends
on the nature of the substance and to some extent on the
temperature also.
TEMPERATURE RISE, COMPRESSION RATIO,
VOLUMETRIC EFFICIENCY
lb)
Figure 7.28. Residual entropy and enthalpy as functions of reduced
properties. (a) Residual entropy. (b) Residual enthalpy. Drawn by
Smith and Vun Ness (Introduction to Chemical Engineering
Thermodynamics, McGraw-Hill, New York, 1959) from data of
Lydersen et al. For illustrative purposes primarily; see text for other
sources.]
The isentropic temperature
for ideal gases by
For
by
(T& = T,(P2/Pl)‘k-“‘k.
polytropic compression
(7.52)
the final temperature is given directly
& = T,(P,/P,)‘“-“‘” (7.53)
in terms of compression ratio is given](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-178-320.jpg)
![7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 161
EXAMPLE 7.9
Selection of a Centrifugal Compressor
A hydrocarbon mixture wtth molecular weight 44.23 is raised from
41°F and 20.1 psia to 100.5psia at the rate of 24001bmol/hr. Its
specific heat ratio is k = 1.135 and its inlet and outlet
compressibilities are estimated as z1 = 0.97 and z, = 0.93. A size of
compressor will be selected from Table 7.6 and its expected
performance will be calculated:
2400 lb mol/hr = 1769 lb/min,
10,260 cfm
From Table 7.6, the smallest compressor for this gas rate is # 38M.
Its characteristics are
&= 8100 rpm at lo-12 K ft/stage
11,=0.77
rfg::;f5
z: = 0.97
1769 Ib/min
10260 cfm
Accordingly,
n - l k - l 0.135
-=-=
k% 1.135(0.77)
= 0.1545.
n
Using Eq. (7.35) for the polytropic head,
HP = (zg(&)RTl[ (g-“‘“- l]
= 0.95(g3(+3(501,[5~~~545 - 11
=39430 ft.
From Figure 7.26(a), the max head per stage is 9700, and from
Figure 7.26(b) the min number of stages is about 4.5. Accordingly,
use five stages with standard 10,000 ft/stage impellers. The required
speed with the data of Table 7.6 is
speed = 8100~39430/10,000(5) = 7190 rpm.
Power absorbed by the gas is
Pgas =
kH,
33,OOOQ
= 1W3%4W = 2745 HP,
33,000(0.77)
Friction losses ~3% max;
:. total power input = 2745/0.97 = 2830 HP max.
or alternately in terms of the isentropic efficiency by stages, accordingly, the compression ratio of each stage is
(A ZLua, = T2 - T = WLntropiclvs (7.54)
so that
P. /E = (P /P)"".
,+1 , " 1 (7.56)
Example 7.11 works out a case involving a nonideal gas and
interstage pressure losses.
T2 = Tl + (AT),/q, = T,{l + (1/11,)[(P2/P~)(‘-‘)‘~ - l]}. (7.55)
The final temperature is read off directly from a thermo-
dynamic diagram when that method is used for the compression
calculation, as in Example 7.7. A temperature calculation is made
in Example 7.10. Such determinations also are made by the general
method for nonideal gases and mixtures as in Example 7.8 and for
ideal gases in Example 7.4.
In centrifugal compressors with all stages in the same shell, the
allowable head rise per stage is stated in Table 7.6 or correlated in
Figure 7.26. Example 7.9 utilizes these data.
Volumetric Eficieuq. For practical reasons, the gas is not
completely discharged from a cylinder at each stroke of a
reciprocating machine. The clearance of a cylinder is filled with
compressed gas which reexpands isentropically on the return stroke.
Accordingly, the gas handling capacity of the cylinder is less than
the product of the cross section by the length of the stroke. The
volumetric efficiency is
Compression Ratio. In order to save on equipment cost, it is
desirable to use as few stages of compression as possible. As a rule,
the compression ratio is limited by a practical desirability to keep
outlet temperatures below 300°F or so to minimize the possibility of
ignition of machine lubricants, as well as the effect that power
requirement goes up as outlet temperature goes up. Typical
compression ratios of reciprocating equipment are:
Large pipeline compressors 1 Z-2.0
Process compressors 1.5-4.0
Small units up to 6.0
For minimum equipment cost, the work requirement should be
the same for each stage. For ideal gases with no friction losses
between stages, this implies equal compression ratios. With it
n, =
suction gas volume
cylinder displacement
= 1 -f,[(WPYk - 11,
where
(7.57)
L=
clearance volume
cyhnder displacement volume ’
For a required volumetric suction rate Q (cfm), the required
product of cross section A, (sqft), stroke length L, (ft), and speed N
(rpm) is given by
A,L,N = Q/v,. (7.58)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-180-320.jpg)
![164 FLUID TRANSPORT EQUIPMENT
condensables are removed with a cold water spray. The tail pipes of
the condensers are sealed with a 34ft leg into a sump, or with a
condensate pump operating under vacuum. Surface condensers
permit recovery of valuable or contaminating condensates or steam
condensate for return as boiler feed. They are more expensive than
barometries, and their design is more complex than that of other
kinds of condensers because of the large amounts of nonconden-
sables that are present.
As many as six stages are represented on Figure 7.30,
combined with interstage condensers in several ways. Barometric
condensers are feasible only if the temperature of the water is below
its bubblepoint at the prevailing pressure in a particular stage.
Common practice requires the temperature to be about 5°F below
the bubblepoint. Example 7.13 examines the feasibility of installing
intercondensers in that process.
AIR LEAKAGE
The size of ejector and its steam consumption depend on the rate at
which gases must be removed from the process. A basic portion of
such gases is the air leakage from the atmosphere into the system.
Theoretically, the leakage rate of air through small openings, if
they can be regarded as orifices or short nozzles, is constant at
vessel pressures below about 53% of atmospheric pressure.
However, the openings appear to behave more nearly as conduits
with relatively large ratios of lengths to diameters. Accordingly
sonic flow is approached only at the low pressure end, and the air
mass inleakage rate is determined by that linear velocity and the
low density prevailing at the vessel pressure. The content of other
gases in the evacuated vessel is determined by each individual
process. The content of condensables can be reduced by interposing
a refrigerated condenser between process and vacuum pump.
Standards have been developed by the Heat Exchange Institute
for rates of air leakage into commercially tight systems. Their chart
is represented by the equation
m = kVU3 (7.59)
where m is in lb/hr, V is the volume of the system in tuft, and the
EXAMPLE 7.11
Three-Stage Compression with Intercooling and Pressure Loss
between Stages
Ethylene is to be compressed from 5 to 75atm in three stages.
Temperature to the first stage is 60”F, those to the other stages are
100°F. Pressure loss between stages is 0.34 atm (5 psi). Isentropic
efficiency of each stage is 0.87. Compressihilities at the inlets to the
stages are estimated from Figure 7.29 under the assumption of
equal compression ratios as z, = 0.98, zr = 0.93, and z, = 0.83. The
interstage pressures will be determined on the basis of equal power
load in each stage. The estimated compressibilities can be corrected
after the pressures have been found, but usually this is not found
necessary. k = C,lC, = 1.228 and (k - 1)/k = 0.1857.
Z,,=O.98
t
P,=75
With equal power in each stage
Tota1 ‘Ower = 0.1857(2545)0.87
3(0.98)(1.987)(520) [ (l225)” ls5’- 1]
“s3L[(;)“‘857-‘] = 1.34 HP/(lb mol/hr).
= 0.98(520)[(PI/5)o-'857- 11
I I
=0.93(560){((p,_P;34))o~lP57- 1) 32-
= 0,83(560){(75/(P, - 0.34)]".'857- 1)
CL
x
‘
Values of PI will be assumed until the value of P2 calculated by
equating the first two terms equals that calculated from the last two
t
“I ;i
3 0
terms. The last entries in the table are the interpolated values.
A
a”
pr 1+2 2+3
12 27.50 28.31
12.5 29.85 28.94
13.0 32.29 29.56
12.25 -28.6+
27
12
I I
12.5 13
p, -](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-183-320.jpg)
![7.7. EJECTOR AND VACUUM SYSTEMS 165
TABLE 7.11. Estimated Air Leakages Through Connections,
Valves, Stuffing Boxes Etc. of Process
Equipmenta
Type Fitting
Estimated
Average
Air Leakage
W/W
Screwed connections in sizes up to 2 in.
Screwed connections in sizes above 2 in.
Flanged connections in sizes up to 6 in.
Flanged connections in sizes 6 in. to 24 in. including
m a n h o l e s
0.1
0 . 2
0 . 5
0 . 8
Flanged connections in sizes 24 in. to 6 ft
Flanged connections in sizes above 6ft
Packed valves up to i in. stem diameter
Packed valves above f in. stem diameter
Lubricated plug valves
Petcocks
Sight glasses
Gage glasses including gage cocks
Liquid sealed stuffing box for shaft of agitators,
pumps, etc. (per in. shaft diameter)
1.1
2.0
0 . 5
1.0
0.1
0 . 2
1.0
2.0
0 . 3
Ordinary stuffing box (per in. of diameter)
Safety valves and vacuum breakers (per in. of
nominal size
1.5
1.0
‘For conservative practice, these leakages may be taken as sup-
plementary to those from Eq. (7.59). Other practices allow 5lb/hr for
each agitator stuffing box of standard design; special high vacuum
mechanical seals with good maintenance can reduce this rate to
l-2 Ib/hr.
[From C.D. Jackson, Chem. Eng. Prog. 44, 347 (194811.
coefficient is a function of the process pressure as follows:
Pressure (Torr) >90 20-90 3-20 l - 3 <l
k 0.194 0 . 1 4 6 0 . 0 8 2 5 0 . 0 5 0 8 0 . 0 2 5 4
For each agitator with a standard stuffing box, 5 lb/hr of air leakage
is added. Use of special vacuum mechanical seals can reduce this
allowance to l-2 lb/hr.
For a conservative design, the rate from Eq. (7.59) may be
supplemented with values based on Table 7.11. Common practice is
to provide oversize ejectors, capable of handling perhaps twice the
standard rates of the Heat Exchange Institute.
Other Gases. The gas leakage rate correlations cited are based
on air at 70°F. For other conditions, corrections are applied to
evaluate an effective air rate. The factor for molecular weight M is
fM = 0.375 ln(M/2) (7.60)
EXAMPLE 7.12
Equivalent Au Rate
Suction gases are at the rate of 120lb/hr at 300°F and have a
molecular weight of 90. The temperature factor is not known as a
function of molecular weight so the value for air will be used. Using
Eqs. (7.61) and (7.62),
m = 120(0.375) ln(90/2)[1- 0.00024(300-70)]
= 161.8 Ib/hr equivalent air.
STEAM CONSUMPTION
The most commonly used steam is 1OOpsig with 10-15” superheat,
the latter characteristic in order to avoid the erosive effect of liquids
on the throats of the ejectors. In Figure 7.31 the steam
consumptions are given as lb of motive steam per lb of equivalent
air to the first stage. Corrections are shown for steam pressures
other than 100 psig. When some portion of the initial suction gas is
condensable, downward corrections to these rates are to be made
for those ejector assemblies that have intercondensers. Such
corrections and also the distribution of motive steam to the
individual stages are problems best passed on to ejector
manufacturers who have experience and a body of test data.
and those for temperature T in “F of predominantly air or
predominantly steam are
fA = 1 - O.O0024(T - 70), for air, (7.61)
fs = 1 - O.O0033(T - 70), for steam. (7.62)
An effective or equivalent air rate is found in Example 7.12.
Figure 7.31. Steam requirements of ejectors at various pressure
levels with appropriate numbers of stages and contact interconden-
sers. Steam pressure lOOpsig, water temperature 85°F. Factor for
65 psig steam is 1.2 and for 200 psig steam it is 0.80 (Worthington
Corp).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-184-320.jpg)
![166 FLUID TRANSPORT EQUIPMEN
EXAMPLE 7.13
Interstage Condensers
A four-stage ejector is to evacuate a system to 0.3 Torr. The
compression ratio in each stage will be
(P4/Po)“4 = (760/0.3)1’4 = 7.09.
The individual stage pressures and corresponding water bubblepoint
temperatures from the steam tables are
Discharge of stage 0 1 2 3 4
T o r r 0.3 2.1 15.1 107 760
“F 1 4 6 3 . 7 1 2 7 . 4
The bubblepoint temperature in the second stage is marginal with
normal cooling tower water, particularly with the practical
restriction to 5°F below the bubblepoint. At the discharge of the
third stage, however, either a surface or barometric condenser is
quite feasible. At somewhat higher process pressure, two interstage
condensers may be practical with a four-stage ejector, as indicated
on Figure 7.31.
Chffuser
Figure 7.32. Progress of pressures, velocities, enthalpies and
entropies in an ejector (Co&on and Richardson, Chemical
Engineering, Pergamon, 1977, New York, Vol. I).
GLOSSARY FOR CHAPTER 7
PUMP TERMS
Head has the dimensions [F][L]/[M]; for example, ft lbf/lb or ft; or
N m/kg or m:
a. pressure head = APIp;
b. velocity head = Au2/2g,;
c. elevation head = Az(g/g,), or commonly AZ;
d. friction head in line, Hr = f (L./D)u2/2gc;
e. system head H, is made up of the preceding four items;
f. pump head equals system head, H, = H,, under operating
conditions;
When barometric condensers are used, the effluent water
temperature should be at least 5°F below the bubblepoint at the
prevailing pressure. A few bubblepoint temperatures at low
pressures are:
Absolute (in. H g ) 0 . 2 0 . 5 1.0 2.0
Bubblepoint “F 3 4 . 6 5 8 . 8 7 9 . 0 101.1
Interstage pressures can be estimated on the assumption that
compression ratios will be the same in each stage, with the suction
to the first stage at the system pressure and the discharge of the last
stage at atmospheric pressure. Example 7.13 examines at what
stages it is feasible to employ condensers so as to minimize steam
usage in subsequent stages.
E J E C T O R T H E O R Y
The progress of pressure, velocity, and energy along an ejector is
illustrated in Figure 7.32. The initial expansion of the steam to point
C and recompression of the mixture beyond point E proceed
adiabatically with isentropic efficiencies of the order of 0.8. Mixing
in the region from C to E proceeds with approximate conservation
of momenta of the two streams, with an efficiency of the order of
0.65. In an example worked out by Dodge (1944, pp. 289-293) the
compounding of these three efficiencies leads to a steam rate five
times theoretical. Other studies of single-stage ejectors have been
made by Work and Haedrich (1939) and DeFrate and Hoer1 (1959)
where other references to theory and data are made.
The theory is in principle amenable to the prediction of steam
distribution to individual stages of a series, but no detailed
procedures are readily available. Manufacturers charts such as
Figure 7.31 state only the consumption of all the stages together.
g. static suction head equals the difference in levels of suction
liquid and the centerline of the pump;
h. static suction lift is the static suction head when the suction level
is below the centerline of the pump; numerically a negative
number.
NPSH (net positive suction head) = (pressure head of
source) + (static suction head) - (friction head of the suction
line) - (vapor pressure of the flowing liquid).
Hydraulic horsepower is obtained by multiplying the weight
rate of flow by the head difference across the pump and converting
horsepower. For
;ipm)(sp gr)(ft)/3960.
example, HHP = (gpm)(psi)/l714 =](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-185-320.jpg)
![REFERENCES 167
Brake horsepower is the driver power output needed to
operate the pump. BHP = HHP/(pump efficiency).
Driver horsepower, HP = BHP/(driver efficiency) =
HHP/(pump efficiency)(driver efficiency).
TERMS CONCERNING CENTRIFUGAL AND RELATED PUMPS
Axial flow is flow developed by axial thrust of a propeller blade,
practically limited to heads under 50 ft or so.
Centrifugal pump consists of a rotor (impeller) in a casing in
which a liquid is given a high velocity head that is largely converted
to pressure head by the time the liquid reaches the outlet.
Characteristic curves are plots or equations relating the
volumetric flow rate through a pump to the developed head or
efficiency or power or NPSH.
Diffuser type: the impeller is surrounded by gradually
expanding passages formed by stationary guide vanes [Figs. 7.2(b)
and 7.3(d)].
Double suction: two incoming streams enter at the eye of the
impeller on opposite sides, minimizing axial thrust and worthwhile
for large, high head pumps [Fig. 7.2(b)].
Double volute: the liquid leaving the impeller is collected in
two similar volutes displaced 180” with a common outlet; radial
thrust is counterbalanced and shaft deflection is minimized,
resulting in lower maintenance and repair, used in high speed
pumps producing above 500 ft per stage.
Impeller: the rotor that accelerates the liquid.
a. Open impellers consist of vanes attached to a shaft without any
REFERENCES
Compressors
1. Compressors in Encyclopedia of Chemical Processing and Design,
Dekker, New York, 1979, Vol. 10, pp. 157-409.
2. F.L. Evans, Compressors and fans, in Equipment Design Handbook for
Refineries and Chemical Plants, Gulf, Houston, 1979, Vol. 1, pp. 54-104.
3. H. Gartmann, DeLaval Engineering Handbook, McGraw-Hill, New
York, 1970, pp. 6.61-6.93.
4. R. James, Compressor calculation procedures, in Encyclopedia of
Chemical Processing and Design, Dekker, New York, Vol. 10, pp.
264-313.
5. E.E. Ludwig, Compressors, in Applied Process Design for Chemical and
Petrochemical Plants, Gulf, Houston, 1983, Vol. 3, pp. 251-396.
6. R.D. Madison, Fan Engineering, Buffalo Forge Co., Buffalo, NY, 1949.
I. H.F. Rase and M.H. Barrow, Project Engineering of Process Plants,
Wiley, New York, pp. 297-347.
Ejectors
1. L.A. DeFrate and V. W. Haedrich, Chem. Eng. Prog. Symp. Ser. 21,
43-51 (1959).
2. B.F. Dodge, Chemical Engineering Thermodynamics, McGraw-Hill, New
York, 1944, pp. 289-293.
3. F.I. Evans, Equipment Design Handbook for Refineries and Chemical
Plants, Gulf, Houston, 1979, Vol. 1, pp. 105-117.
4. E.E. Ludwig, lot. cit., Vol. 1, pp. 206-239.
5. R.E. Richenberg and J.J. Bawden, Ejectors, steam jet, in Encyclopedia
of Chemical Processing and Design, Dekker, New York, Vol. 17, pp.
167-194.
6. L.T. Work and V.W. Haedrich, Ind. Eng. Chem. 31,464-477 (1939).
Piping
1. ANSI Pioine Code. ASME. New York, 1980.
form of supporting sidewall and are suited to handling slurries
without clogging [Fig. 7.2(a)].
b. Semienclosed impellers have a complete shroud on one side
[Fig. 7.3(c)]; they are essentially nonclogging, used primarily in
small size pumps; clearance of the open face to the wall is
typically 0.02 in. for 10 in. diameters.
c. Closed impellers have shrouds on both sides of the vanes from
the eye to the periphery, used for clear liquids [Fig. 7.3(b)].
Mechanical seals prevent leakage at the rotating shaft by sliding
metal on metal lubricated by a slight flow of pump liquid or an
independent liquid [Figs. 7.4(c) and (d)].
Miied flow: develops head by combined centrifugal action and
propeller action in the axial direction, suited to high flow rates at
moderate heads [Fig. 7.3(e)].
Multistage: several pumps in series in a single casing with the
objective of developing high heads. Figure 7.6(c) is of characteristic
curves.
Performance curves (see characteristic curves).
Single suction: the liquid enters on one side at the eye of the
impeller; most pumps are of this lower cost style [Fig. 7.2(c)].
Split case: constructed so that the internals can be accessed
without disconnecting the piping [Fig. 7.2(a)].
Stuffmg box: prevent leakage at the rotating shaft with
compressed soft packing that may be wetted with the pump liquid
or from an independent source [Figs. 7.4(a) and (b)].
Volute type: the impeller discharges the liquid into a
progressively expanding spiral [Fig. 7.2(a)].
2.
3.
4.
5.
6.
7.
8.
9.
10.
S. Chalfin, Control valves, Encyclopedia of Chemical Processing and
Design, Dekker, New York, 1980, Vol. 11, pp. 187-213.
F.L. Evans, Equipment Design Handbook for Refineries and Chemical
Plants, Gulf, Houston, 1979, Vol. 2; piping, pp. 188-304; valves, pp.
315-332.
J.W. Hutchinson, ISA Handbook of Control Valves, Inst. Sot. America,
Research Triangle Park, NC, 1976.
R.C. King, Piping Handbook, McGraw-Hill, New York, 1967.
J.L. Lyons, Encyclopedia of Values, Van Nostrand Reinhold, New York,
1975.
Marks’ Standard Handbook for Mechanical Engineers, McGraw-Hill,
New York, 1987.
Perry’s Chemical Engineers’ Handbook, McGraw-Hill, New York, 1984.
R. Weaver, Process Piping Design, Gulf, Houston, 1973, 2 Vols.
P. Wing, Control valves, in Process Instruments and Controls Handbook,
(D.M. Considine, Ed.), McGraw-Hill, New York, 1974.
.^
11. R.W. Zappe, Value Selection Handbook, tiulf, Houston, pp. IY.~-19.60,
1981.
Pumps
1. D. Azbel and N.P. Cheremisinoff, Fluid Mechanics and Fluid Operations,
Ann Arbor Science, Ann Arbor, MI, 1983.
2. N.P. Cheremisinoff, Fluid Flow: Pumps, Pipes and Channels, Ann Arbor
Science, Ann Arbor, MI, 1981.
3. F.L. Evans, lot. cit., Vol. 1, pp. 118-171.
4. H. Gartmann, DeLnval Engineering Handbook, McGraw-Hill, New
York, 1970, pp. 6.1-6.60.
5. I.J. Karassik and R. Carter, Centrifugal Pump Selection Operation and
Maintenance, F.W. Dodge Corp., New York, 1960.
6. I.J. Karassik, W.C. Krutsch, W.H. Fraser, and Y.J.P. Messina, Pump
Handbook, McGraw-Hill, New York, 1976.
7. F.A. Kristal and F.A. Annett, Pumps, McGraw-Hill, New York, 1940.
8. E.E. Ludwig, lot. cit., Vol. 1, pp. 104-143.
9. S. Yedidiah, Centrifugal Pump Problems, Petroleum Publishing, Tulsa.
OK. 1980.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-186-320.jpg)
![8
HEAT TRANSFER AND HEAT EXCHANGERS
B
asic concepts of heat transfer are reviewed in this
chapter and applied primarily to heat exchangers,
which are equipment for the transfer of heat
between two fluids through a separating wall.
Heat transfer a/so is a key process in other specialized
equipment, some of which are treated in the next and other
chapters. The three recognized modes of heat transfer are by
conduction, convection, and radiation, and may occur
simultaneously in some equipment.
8.1. CONDUCTION OF HEAT
In a solid wall such as Figure 8.1(a), the variation of temperature
with time and position is represented by the one-dimensional
Fourier equation
For the most part, only the steady state condition will be of concern
here, in which the case the partial integral of Eq. (8.1) becomes
assuming the thermal conductivity k to be independent of
temperature. Furthermore, when both k and A are independent of
position,
Q=-Kay=+,-7”), (8.3)
in the notation of Figure 8.1(a).
Equation (8.3) is the basic form into which more complex
situations often are cast. For example,
Q =%,,,, y
when the area is variable and
(8.4)
Q =WA%,,, (8.5)
in certain kinds of heat exchangers with variable temperature
difference.
THERMAL CONDUCTIVITY
Thermal conductivity is a fundamental property of substances that
basically is obtained experimentally although some estimation
methods also are available. It varies somewhat with temperature. In
many heat transfer situations an average value over the prevailing
temperature range often is adequate. When the variation is linear
with
k = k,(l + CUT),
the integral of Eq. (8.2) becomes
Q&/A) = k,[T, - 7” + OSa(T: - T;)]
= k,(T, - T,)[l + OSa(T, + T&l,
(8.6)
(8.7)
which demonstrates that use of a value at the average temperature
gives an exact result. Thermal conductivity data at several
temperatures of some metals used in heat exchangers are in Table
8.1. The order of magnitude of the temperature effect on k is
illustrated in Example 8.1.
(a) lb)
(4 (0
Figure 8.1. Temperature profiles in one-dimensional conduction of
heat. (a) Constant cross section. (b) Hollow cylinder. (c) Composite
flat wall. (d) Composite hollow cylindrical wall. (e) From fluid A to
fluid F through a wall and fouling resistance in the presence of
eddies. (f) Through equivalent fluid films, fouling resistances, and
metal wall.
169](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-188-320.jpg)
![170 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.1. Thermal Conductivities of Some Metals
Commonly Used in Heat Exchangers
is the logarithmic mean radius of the hollow cylinder. This concept
tkBtu/(hr)(sqft)(“F/ft)l
is not particularly useful here, but logarithmic means also occur in
other more important heat transfer situations.
Temperature (“F)
Metal or Alloy -100 7 0 200 1000
Steels
Carbon
ICriMo
410
304
316
Monel400
Nickel 200
lnconel 600
Hastelloy C
Aluminum
Titanium
Tantalum
C o p p e r
Yellow brass
Admiralty
- 3 0 . 0 2 7 . 6 22.2
- 19.2 19.1 18.0
- 13.0 14.4 -
- 9 . 4 10.0 13.7
8.1 9 . 4 - 13.0
11.6 12.6 13.8 2 2 . 0
- 3 2 . 5 3 1 . 9 3 0 . 6
- 8 . 6 9.1 14.3
- 7 . 3 5.6 10.2
- 131 133 -
11.8 11.5 10.9 12.1
- 3 1 . 8 - -
225 225 222 209
5 6 6 9 - -
5 5 6 4 - -
HOLLOW CYLINDER
As it appears on Figure 81(b), as the heat flows from the inside to
the outside the area changes constantly. Accordingly the equivalent
of Eq. (8.2) becomes, for a cylinder of length N,
dT
Q = -kN(2~r)-,
d r
of which the integral is
Q = 2~kNT, - G)
WJr,)
(8.8)
This may be written in the standard form of Eq. (8.4) by taking
A,,, = 2nLNr,, (8.10)
and
L=r,-r,, (8.11)
where
r,, = (5 - rdlW21rd (8.12)
EXAMPLE 8.1
Conduction through a Furnace Wall
A furnace wall made of fire clay has an inside temperature of
1500°F and an outside one of 300°F. The equation of the thermal
conductivity is k = 0.48[1 + 5.15(E - 4)T] Btu/(hr)(sqft)(“F/ft).
Accordingly,
Q(L/A) = 0.48(1500 - 300)[1+ 5.15(E - 4)(900)] = 0.703.
If the conductivity at 300°F had been used, Q(L/A) = 0.554.
COMPOSITE WALLS
The flow rate of heat is the same through each wall of Figure 8.1(c).
In terms of the overall temperature difference,
Q = uA(T, - T,),
where I/ is the overall heat transfer coefficient and is given by
1 1 1 1
i?==k,lL,+m+k,/L;
(8.14)
The reciprocals in Eq. (8.14) may be interpreted as resistances to
heat transfer, and so it appears that thermal resistances in series are
additive.
For the composite hollow cylinder of Figure 8.1(d), with length
N,
2nN( Tl - T4)
’ = In(r,/r,)/k, + ln(r,/r,)/k, + ln(r,/r,)/k, ’
(8.15)
With an overall coefficient Ui based on the inside area, for example,
Q = 2zNrJJ,(T, - T4) = 2x~~~,~ T4) .
I I
On comparison of Eqs. (8.15) and (8.16), an expression for the
inside overall coefficient appears to be
1nWd 1nWJ ln(r4/r3)
-+-+
k, kb kc 1 (8.17)
In terms of the logarithmic mean radii of the individual cylinders,
1
jj = I;
[
1 1 1
karmo/(r2 - 4 + kbrmb/(r3 - 3) + kcrmc/(rd - 4 I ’
which is similar to Eq. (8.14) for flat walls, but includes a ratio of
radii as a correction for each cylinder.
FLUID FILMS
Heat transfer between a fluid and a solid wall can be represented
by conduction equations. It is assumed that the difference in
temperature between fluid and wall is due entirely to a stagnant film
of liquid adhering to the wall and in which the temperature profile is
linear. Figure 8.1(e) is a somewhat realistic representation of a
temperature profile in the transfer of heat from one fluid to another
through a wall and fouling scale, whereas the more nearly ideal
Figure 8.1(f) concentrates the temperature drops in stagnant fluid
and fouling films.
Since the film thicknesses are not definite quantities, they are
best combined with the conductivities into single coefficients
h=k/L (8.18)
so that the rate of heat transfer through the film becomes
Q = hA A T. (8.19)
Through the five resistances of Figure 8.1(f), the overall heat](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-189-320.jpg)
![8.1. CONDUCTION OF HEAT 171
EXAMPLE 8.2
Effect of Ignoring the Radius Correction of the Overall Heat
Transfer Coefticit%t
The two film coefficients are 100 each, the two fouling coefficients
are 2000 each, the tube outside diameter is 0.1 ft, wall thickness is
0.01 ft, and thermal conductivity of the metal is 30:
Basing on the inside area,
ui = [l/100 + l/2000 + [(30/0.01)(0.0448/0.04)1-’
+ 0.8/100 + 0.8/2000]-’ = 52.0898.
rr/ro = 0.04/0.05 = 0.8,
r,,, = (0.05 -0.04)/m 1.25 = 0.0448,
r,,,/ro = 0.8963,
U, = [l/100(0.8) + l/2000(0.8) + l/(30/0.01)(0.8963)
+ l/100 + l/2000]-’ = 41.6721.
Ignoring the corrections,
U = (2/100 + 2/2000 + l/30/0.01)-’ = 46.8750.
The last value is very nearly the average of the other two.
transfer coefficient is given by
L=L+L+-
1 1 1
U h, h, k,/L,+h,+h,’
(8.20)
where r,,, is the mean radius of the cylinder, given by Eq. (8.12).
Since wall thicknesses of heat exchangers are relatively small
and the accuracy of heat transfer coefficients may not be great, the
ratio of radii in Eq. (8.21) often is ignored, so that the equation for
the overall coefficient becomes simply
where L, is the thickness of the metal.
If the wall is that of hollow cylinder with radii r, and r,, the !=L+L+-
1 1 1
(8.22)
overall heat transfer coefficient based on the outside surface is
U h, h, k,/L,+h,+h,’
The results of the typical case of Example 8.2, however, indicate
1 1 1 1 1 1
-=-+-+
U, hl(ri/r,) hz(ri/ro) (k3/L3)(rm/d ’ h,+h, ’
(8.21)
that the correction may be significant. A case with two films and
two solid cylindrical walls is examined in Example 8.3.
EXAMPLE 8.3
A Case of a Composite WaII: Optimum Insulation Thickness
for a Steam Line
A 3 in. IPS Sched 40 steel line carries steam at 500°F. Ambient air is
at 70°F. Steam side coefficient is 1000 and air side is
3 Btu/(hr)(sqft)(“F). Conductivity of the metal is 30 and that of
insulation is 0.05 Btu/(hr)(sqft)(“F/ft). Value of the steam is
$5,00/MBtu. cost of the insulation is $1.5/(yr)(cuft). Operation is
8760 hr/yr. The optimum diameter d of insulation thickness will be
found.
Pipe:
do = 0.2917 ft,
d, = 0.2557 ft,
ln(d,/d,) = 0.1317.
Insulation:
In(d,/dJ = ln(d/0.2917). (1)
Heat transfer coefficient based on inside area:
1 -’
+52 ’
1
Steam cost:
C, = 5(10@)(876O)Q/A,
= 0.0438Q/Ai, $ (yr)(sqft inside).
(2)
(3)
la
2@
3 8
48
59
! Example 8 . 5 . Drt imum incul
a? ion ?hickness
R E A D Dl..D2
DHTH .2317,.2557
INPUT I3
Ul=.@@l,D2+. 1307/3a+LOG<D..‘Dl
j~.a5+1/3d
IJ=lfUl~trE
8=430SU
cl=.a438*C;
C2=1 .5XCD^2-UlA2),D2’2
C=Cl+C2 ! Creq’d t o he m i n i m
urn)
P R I N T U S I N G 120 i D,UzC1,C2..
ff0
128 hIAGE .UDD,X.~ .DDU,X,DrJ.DD..X..
DD.DD,X,DD.DDDD
138 r,oTo 48
148 E N D
h
h =3
T
T = 70 F](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-190-320.jpg)
![172 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE 8.3-(continued)
D u 3 c2 3 + c2
- -
,490 .354- 6 . 6 6 3 . 5 6 1 0 . 2 1 4 7
,494 ,349 6.57 3 . 6 5 1 0 . 2 1 1 8
,495 ,347 6 . 5 4 3 . 6 7 10.2117 -w
,496 .346 6 . 5 2 3 . 6 9 1 0 . 2 1 1 8
.500 ,341 6 . 4 3 .3.78 1 0 . 2 1 4 8
Insulation cost:
C, = 1.5K.lA;
...I I -
= 1.5(d2 - 0.2917a)
(0.2557)’ ’
$/(yr)(sqft inside).
Total cost:
C = C, + C2* minimum. (5)
Substitute Eqs. (2)-(4) into Eq. (5). The outside diameter is the
key unknown.
The cost curve is fairly flat, with a minimum at d = 0.50 ft,
corresponding to 1.25 in. thickness of insulation. Some trials are
shown with the computer program. A more detailed analysis of
insulation optima is made by Happel and Jordan [C/rem. Process
&on., 380 (1975)], although their prices are dated. Section 8.12
also discusses insulation.
Heat transfer coefficients are empirical data and derived
correlations. They are in the form of overall coefficients U for
frequently occurring operations, or as individual film coefficients
and fouling factors.
8.2. MEAN TEMPERATURE DIFFERENCE
In a heat exchanger, heat is transferred between hot and cold fluids
through a solid wall. The fluids may be process streams or
independent sources of heat such as the fluids of Table 8.2 or
sources of refrigeration. Figure 8.2 shows such a process with inlet
and outlet streams, but with the internal flow pattern unidentified
because it varies from case to case. At any cross section, the
differential rate of heat transfer is
dQ = U(T - T’) dA = -mcdT = m’c’ dT’.
The overall heat transfer rate is represented formally by
(8.23)
Q = UA(AT),. (8.24)
The mean temperature difference (AT), depends on the terminal
temperatures, the thermal properties of the two fluids and on the
flow pattern through the exchanger.
TABLE 8.2. Properties of Heat Transfer Media
Figure 8.2. Terminal temperatures and temperature differences of a
heat exchanger, with unidentified internal flow pattern.
SINGLE PASS EXCHANGER
The simplest flow patterns are single pass of each fluid, in either the
same or opposite directions. Temperature profiles of the main kinds
of thermal behavior are indicated on Figure 8.3(a). When the
unbroken lines [cases (a)-(e)] are substantially straight, the mean
temperature is expressed in terms of the terminal differences by
(8.25)
This is called the logarithmic mean temperature difference. The
temperature profiles are straight when the heat capacities are
Medium Trade Name Phase “F
atm,
gag= Remarks
Electricity
Water
Water
Flue gas
Diphenyl-diphenyl oxide eutectic
-
-
-
Dowtherm A
Di + triaryl cpds
Ethylene glycol, inhibited
Dimethyl silicones
Mixed silanes
Aromatic mineral oil
Chlorinated biphenyls
Molten nitrites and nitrates of K and Na
Sodium-potassium eutectic
Mercury
Dowtherm G
Dow SR-1
Dow Syltherm
800
H y d r o t h e r m
Mobiltherm,
Mobil
Therminol,
M o n s a n t o
Hi-Tee, DuPont
vapor
liquid
gas
liquid or
vapor
liquid
liquid
liquid
100-4500 -
200-I 100 O-300
300-400 6-15
100-2000 o-7
450-750 o-9
-
-
-
-
nontoxic, carbonizes at high temp
20-700 o-3 sensitive to oxygen
-4O--250 0 acceptable in food industry
-40-750 0 low toxicity
liquid -50-675 0
liquid 100-600 0
liquid 50-600 0
liquid
liquid
vapor
3 0 0 - 1 1 0 0 0
1 0 0 - 1 4 0 0 0
600-1000 O-12
react with oxygen and moisture
not used with copper based materials
toxic decomposition products
resistant alloys needed above 850°F
stainless steel needed above 1000°F
low pressure vapor, toxic, and expensive](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-191-320.jpg)
![TABLE 8.3. Formulas for Mean Temperature Difference and
Effectiveness in Heat Exchangers
T --r B-METHOD
1. Parallel or countercurrent flow,
(AT), = (A T),,,g,,,san = (AT, - AT,)/ln(AT,/AT,).
2. In general,
o r
(AT), = fl(J - T),
where Fand @ depend on the actual flow paths on the shell and tube
sides and are expressed in terms of these quantities:
P= (T, - 7;)/(T;‘- T) = actual heat transfer/
(maximum possible heat transfer),
R=(T - 7-J/(7-:, - 6’) = m’c’/mc.
3. Number of transfer units, N or NTU, is
N = UAIC,,, = P/S,
where Cr,,i, is the smaller of the two values mc or m’c’ of the
products of mass rate of flow times the heat capacity.
In parallel flow, P= NO = {I - expl-N(1 + C)]}/(l + C).
In countercurrent flow, P = NO = (1 - expl-N/l - C)]]/{ 1 - C exp
[-NC1 - C)l).
One shell pass and any multiple of two tube passes,
Two shell passes and any multiple of four tube passes,
Rfl,
2(R-1) I-PR I/
In
2/P - 1 - R + (2/P)d(l - P)(l - PR) f fi
I
2/P-I-R+(2/P)v(l-P)(l-PR)-fi
8. Cross flow,
(a) Both streams laterally unmixed, P= 1 - exp{[exp( - NCn) - l]/Cn),
where n = Nmo.*‘.
(b) t$z)th;mams mixed, P= {I/]1 -exp(-N)] + C/[l - exp(-NC)]-
(c) Gna, mixed, Crni, unmixed, P= (l/C){1 -exp[-C(1 - eeN)]},
Id) &, mixed, C,,,,, unmixed, P= 1 - exp{-(l/C)[l - exp(-NC)]}.
9. For more complicated patterns only numerical solutions have been
made. Graphs of these appear in sources such as Heat Exchanaer
Design Handbook (HEOH, j983) and Kays and London (1984). -
8.3. HEAT TRANSFER COEFFICIENTS 179
method to be described, however, may be more convenient in such
a case.
One measure of the size of heat transfer equipment is the number
of transfer units N defined by
N = UAIC,,, (8.30)
where Cmin is the smaller of the two products of mass how rate and
heat capacity, mc or m’c’. N is so named because of a loose analogy
with the corresponding measure of the size of mass transfer
equipment.
A useful combination of P and N is their ratio
N UA(T; - ?J - UA(T; - TJ (T; - 7J’
(8.31)
where (T, - T) is the temperature change of the stream with the
smaller value of mc. Thus 0 is a factor for obtaining the mean
temperature difference by the formula:
(AT),,, = O(T; - I;)
when the two inlet temperatures are known.
(8.32)
The term P often is called the exchanger effectiveness.
Equations and graphs are in Table 8.3 and Figure 8.4. Many graphs
for 0, like those of Figure 8.7, may be found in the Heat Exchanger
Design Handbook (HEDH, 1983). When sufficient other data are
known about a heat exchange process, an unknown outlet
temperature can be found by this method directly without requiring
trial calculations as with the F-method. Example 8.5 solves such a
problem.
SELECTION OF SHELL-AND-TUBE NUMBERS OF PASSES
A low value of F means, of course, a large surface requirement for
a given heat load. Performance is improved in such cases by using
several shells in series, or by increasing the numbers of passes in the
same shell. Thus, two l-2 exchangers in series are equivalent to one
large 2-4 exchanger, with two passes on the shell side and four
passes on the tube side. Usually the single shell arrangement is
more economical, even with the more complex internals. For
economy, F usually should be greater than 0.7.
E X A M P L E
A shell side fluid is required to go from 200 to 140°F and the tube
side from 80 to 158°F. The charts of Figure 8.5 will be used:
P = (200 - 140)/(200 - 80) = 0.5,
R = (158 - 80)/(200 - 140) = 1.30.
For a l-2 exchanger, F = 0.485:
2-4 0.92
4-8 0.98
The 1-2 exchanger is not acceptable, but the 2-4 is acceptable. If
the tube side outlet were at 160 instead of 158, F would be zero for
the l-2 exchanger but substantially unchanged for the others.
8.3. HEAT TRANSFER COEFFlClENTS
Data are available as overall coefficients, individual film coefficients,
fouling factors, and correlations of film coefficients in terms of](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-198-320.jpg)
![180 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE 8.4
Performance of a Heat Exchanger with the F-Method
Operation of an exchanger is represented by the sketch and the
equation
Q/UA = 50 = F(AT),,
JZE-
T
200
120
The outlet temperature of the hot fluid is unknown and designated
by T. These quantities are formulated as follows:
p = 200 - T
200-80
R = 200 - T
120-80’
T - 80 - (200 - 120)
(AThm =ln[(T - 80)/(200 - 120)]
F is represented by the equation of Item 6 of Table 8.3, or by
Figure 8.4(a). Values of T are tried until one is found that satisfies
G - 50 - F(A?fT),, = 0. The printout shows that
T = 145.197.
The sensitivity of the calculation is shown in the following
tabulation:
T P R (AT),, F G
145.0 0.458 1.375 72.24 0.679 0.94
145.197 0.457 1.370 72.35 0.691 0.00061
145.5 0.454 1.363 72.51 0.708 -1.34
10 ! ExamPle 8 .4. T h e F - m e t h o d
20 SHORT F..R>F>Tl
30 INFIJT T
;)-’ (‘=(200-T>,120
58 R=<289-T2/48
68 Tl=(T-169>.~LOG((T-802,88r
70 E=<RA2+1:>*.5
80 F=E,~(R-lI*LOG((l-Fj,~l-F*R~~
9 0 F=F~LOG~~2-F%~R+l-Ejj~<2-P~<
R+l+Ej)j
95 G=5Gj-F$Tl
100 P R I N T “T=“;T
110 P R I N T “G=“jG
120 P R I N T “F=“;F
130 P R I N T “R=“;R
140 P R I N T “F=“;F
150 P R I N T “Tl=“iTl
160 GOTO 3 0
170 E N D
ZZ 145.197
.88240286
EZ i.5701
45669
physical properties and operating conditions. The reliabilities of
these classes of data increase in the order of this listing, but also the
ease of use of the data diminishes in the same sequence.
O V E R A L L C O E F F I C I E N T S
The range of overall heat transfer coefficients is approximately
lo-200 Btu/(hr)(sqft)(“F). Several compilations of data are
available, notably in the Chemical Engineers Handbook (McGraw-
Hill, New York, 1984, pp. 10.41-10.46) and in Ludwig (1983, pp.
70-73). Table 8.4 qualifies each listing to some extent, with respect
to the kind of heat transfer, the kind of equipment, kind of process
stream, and temperature range. Even so, the range of values of U
usually is two- to three-fold, and consequently only a rough
measure of equipment size can be obtained in many cases with such
data. Ranges of the coefficients in various kinds of equipment are
compared in Table 8.5.
FOULING FACTORS
Heat transfer may be degraded in time by corrosion, deposits of
reaction products, organic growths, etc. These effects are accounted
for quantitatively by fouling resistances, l/hf. They are listed
separately in Tables 8.4 and 8.6, but the listed values of coefficients
include these resistances. For instance, with a clean surface the first
listed value of U in Table 8.4 would correspond to a clean value of
U= l/(1/12-0.04) =23.1. How long a clean value could be
maintained in a particular plant is not certain. Sometimes fouling
develops slowly; in other cases it develops quickly as a result of
process upset and may level off. A high coefficient often is
desirable, but sometimes is harmful in that excessive subcooling
may occur or film boiling may develop. The most complete list of
fouling factors with some degree of general acceptance is in the
TEMA (1978) standards. The applicability of these data to any
particular situation, however, is questionable and the values
probably not better than f50%. Moreover, the magnitudes and
uncertainties of arbitrary fouling factors may take the edge off the
importance of precise calculations of heat transfer coefficients. A
brief discussion of fouling is by Walker (1982). A symposium on this
important topic is edited by Somerscales and Knudsen (1981).
INDIVIDUAL FILM COEFFICIENTS
Combining individual film coefficients into an overall coefficient of
heat transfer allows taking into account a greater variety and range
of conditions, and should provide a better estimate. Such individual
coefficients are listed in Tables 8.6 and 8.7. The first of these is a
very cautious compilation with a value range of 1.5- to 2-fold.
Values of the fouling factors are included in the coeflicient listings
of both tables but are not identified in Table 8.7. For clean service,
for example, involving sensible heat transfer from a medium organic
to heating a heavy organic,
U = 10,000/(57 - 16 + 50 - 34) = 175](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-199-320.jpg)
![8.3. HEAT TRANSFER COEFFICIENTS 181
B NTU, = AU/C,
1. 0 1.0
a 6
-; 0.5
I-
F -
G I a 4
c-
0 . 3
4. 0
,I
5. 0
a 0. 2
0. I R =
%
=
0 1)i - (Tq Jo
T; (T2)” m(T2)i
0. 0
0. 0 0 . I 0 . 2 0. 3 0 . 4 0 . 5 8. 6 0. 7 0 . 0 0. 9 1.0
(a)
e NTU, = AU/C,
F-c-
s-4
$7
Q A -
t
-
1.0 0 . 2 0 . 3 0 . 4 0. 5 a 0 0. 8 I.0
as
1.2
0. e
I. 4
0 . 7
1.6
0. e
1. a
0.5
0 . 4
a 3
0 . 2
al
a0
a 0 1. 1 a 2 a 3 a.4 a 5 0.0 a 7 a e a s 1.0
C2 (T,)i-(T,)o
R= c, = (T,)o-(T,)i
B P . Thermal Effectiveness =
CT2 j. - (T, )i
(T1 ), _ (TzJ,
b)
Figure 8.7. 8 correction charts for mean temperature difference: (a) One shell pass and any multiple of two tube passes. (b) Two shell passes
and any multiple of four tube passes. [(HEDH, 1983); after Mueller in Rohsenow and Hartnett, Handbook of Heat Transfer, Section 18,
McGraw-Hill, New York, 1973. Other cases also are covered in these references.]](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-200-320.jpg)
![182 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE 8.5
Application of the Effectiveness and the tl Method
Operating data of an exchanger are shown on the sketch. These
data include
UA = 2000,
m’c’ = 1000, mc = 800,
C = Cmin/Cmax = 0.8.
The equation for effectiveness P is given by item 6 of Table 8.3 or it
can be read off Figure 8.4(a). Both P and 19 also can be read off
Figure 8.4(a) at known N and R = CJC, = 0.8. The number of
transfer units is
N = lJA/C,,, = 2000/800 = 2.5,
C = Cmin/Cmax = 0.8,
D=m=1.2806,
2
‘=l+ C + D[l + exp(-ND)]/1 - exp(-ND)
= 0.6271,
0 = P/N = 0.2508,
AT, = 0(200 - 80) = 30.1,
Q = UA(AT), = 2000(30.1) = 60,200,
= 800(200 - T2) = lOOO( T; - 80),
:. T2 = 124.75,
T; = 140.2.
T, also may be found from the definition of P:
P =
actual AT = ?!k% = 0.6271
max possible AT 200 - 80 ’
:. T2 = 124.78.
With this method, unknown terminal temperatures are found
without trial calculations.
compared with a normal value of
CJ = 10,000/(57 + 50) = 93,
where the averages of the listed numbers in Table 8.6 are taken in
each case.
METAL WALL RESISTANCE
With the usual materials of construction of heat transfer surfaces,
the magnitudes of their thermal resistances may be comparable with
the other prevailing resistances. For example, heat exchanger
tubing of 1/16in. wall thickness has these values of l/h, = L/k for
several common materials:
Carbon steel l/h,=1.76~10-~
Stainless steel 5.54 x w4
Aluminum 0.40 x 1o-4
Glass 79.0 x 1o-4
which are in the range of the given film and fouling resistances, and
should not be neglected in evaluating the overall coefficient. For
example, with the data of this list a coefficient of 93 with carbon
steel tubing is reduced to 88.9 when stainless steel tubing is
substituted.
DIMENSIONLESS GROUPS
The effects of the many variables that bear on the magnitudes of
individual heat transfer coefficients are represented most logically
and compactly in terms of dimensionless groups. The ones most
pertinent to heat transfer are listed in Table 8.8. Some groups have
ready physical interpretations that may assist in selecting the ones
appropriate to particular heat transfer processes. Such interpreta-
tions are discussed for example by Grober et al. (1961, pp.
193-198). A few are given here.
The Reynolds number, Dup/p = pu*/(pu/D), is a measure of
the ratio of inertial to viscous forces.
The Nusselt number, hL/k = h/(k/L), is the ratio of effective
heat transfer to that which would take place by conduction through
a film of thickness L.
The Peclet number, DGC/k = GC/(k/D) and its modification,
the Graetz number wC/kL, are ratios of sensible heat change of the
flowing fluid to the rate of heat conduction through a film of
thickness D or L.
The Prandtl number, Cp/k = (p/p)/(k/pC), compares the rate
of momentum transfer through friction to the thermal diffusivity or
the transport of heat by conduction.
The Grashof number is interpreted as the ratio of the product
of the buoyancy and inertial forces to the square of the viscous
forces.
The Stanton number is a ratio of the temperature change of a
fluid to the temperature drop between fluid and wall. Also,
St = (Nu)/(Re)(Pr).
An analogy exists between the transfers of heat and mass in
moving fluids, such that correlations of heat transfer involving the
Prandtl number are valid for mass transfer when the Prandtl
number Cp/k is replaced by the Schmidt number ,u/pkd. This is of
particular value in correlating heat transfer from small particles to
fluids where particle temperatures are hard to measure but
measurement of mass transfer may be feasible, for example, in
vaporization of naphthalene.
8.4. DATA OF HEAT TRANSFER COEFFICIENTS
Specific correlations of individual film coefficients necessarily are
restricted in scope. Among the distinctions that are made are those
of geometry, whether inside or outside of tubes for instance, or the
shapes of the heat transfer surfaces; free or forced convection;
laminar or turbulent flow; liquids, gases, liquid metals, non-
Newtonian fluids; pure substances or mixtures; completely or
partially condensable; air, water, refrigerants, or other specific
substances; fluidized or fixed particles; combined convection and
radiation; and others. In spite of such qualifications, it should be](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-201-320.jpg)
![8.4. DATA OF HEAT TRANSFER COEFFICIENTS 185
TABLE 8.5. Ranges of Overall Heat Transfer Coefficients in Various Types of
Exchangers [U Btu/(hr)(sqft)(“F)]’
Equipment Process u
Shell-and-tube exchanger IFig.
8.4c)l
Double-pipe exchanger [Fig. 8.4(a)] gas (I atm)-gas (1 atm)
Irrigated tube bank
Plate exchanger [Fig. 8.8(a)]
Spiral exchanger [Fig. 8.8fc)l
Compact [Fig. 8.6(h)]
Stirred tank, jacketed
Stirred tank, coil inside
a 1 Btu/(hr)(sqft)(“F) = 5.6745 W/m’ K.
Data from (HEDH, 1983).
gas (1 atm)-gas (1 atm)
gas (250 atm)-gas (250 atm)
liquid-gas (1 atm)
liquid-gas (250 atm)
liquid-liquid
liquid-condensing vapor
gas (250 atm)-gas (250 atm)
liquid-gas (250 atm)
liquid-liquid
water-gas (1 atm) 3-10
water-gas 1250 atm) 25-60
water-liquid 50-160
water-condensing vapor 50-200
water-gas (1 atm) 3-10
water-liquid 60-200
liquid-liquid 120-440
liquid-condensing steam 160-600
gas (1 atm)-gas (1 atm) 2-6
gas (1 atm)-liquid 3-10
liquid-condensing steam 90-260
boiling liquid-condensing steam 120-300
water-liquid 25-60
liquid-condensing steam
water-liquid
l - 6
25-50
2-12
35-70
25-200
50-200
2-6
25-90
35-l 00
50-250
120-440
go-210
borne in mind that very few proposed correlations are more
accurate than f20% or so.
Along with rate of heat transfer, the economics of practical
exchanger design requires that pumping costs for overcoming
friction be taken into account.
DIRECT CONTACT OF HOT AND COLD STREAMS
Transfer of heat by direct contact is accomplished in spray towers,
in towers with a multiplicity of segmented baffles or plates (called
shower decks), and in a variety of packed towers. In some processes
heat and mass transfer occur simultaneously between phases; for
example, in water cooling towers, in gas quenching with water, and
in spray or rotary dryers. Quenching of pyrolysis gases in transfer
lines or towers and contacting on some trays in fractionators may
involve primarily heat transfer. One or the other, heat or mass
transfer, may be the dominant process in particular cases.
Data of direct contact heat transfer are not abundant. The
literature has been reviewed by Fair (1972) from whom specific data
will be cited.
One rational measure of a heat exchange process is the number
of transfer units. In terms of gas temperatures this is defined by
Tg,in - T,,out
Ng = (Tg - Unean
(8.33)
The logarithmic mean temperature difference usually is applicable.
For example, if the gas goes from 1200 to 150°F and the liquid
countercurrently from 120 to 400”F, the mean temperature
difference is 234.5 and Ng = 4.48. The height of a contact zone then
is obtained as the product of the number of transfer units and the
height H, of a transfer unit. Several correlations have been made of
the latter quantity, for example, by Cornell, Knapp, and Fair (1960)
and modified in the Chemical Engineers Handbook (1973, pp.
18.33, 18.37). A table by McAdams (1954, p. 361) shows that in
spray towers the range of H, may be 2.5-10 ft and in various kinds
of packed towers, 0.4-4 ft or so.
Heat transfer coefficients also have been measured on a
volumetric or cross section basis. In heavy hydrocarbon fraction-
ators, Neeld and O’Bara (1970) found overall coefficients of 1360-
3480 Btu/(hr)(“F)(sqft of tower cross section). Much higher values
have been found in less viscous systems.
Data on small packed columns were correlated by Fair (1972)
in the form
Ua = CG”L”, Btu/(hr)(cuft)(OF), (8.34)
where the constants depend on the kind of packing and the natures
of the fluids. For example, with air-oil, 1 in. Raschig rings, in an
8 in. column
L/a = 0.083G0~94L0~25. (8.35)
When G and L are both 5000 lb/(hr)(sqft), for instance, this formula
gives Ua = 2093 Btu/(hr)(cuft)(a).
In spray towers, one correlation by Fair (1972) is
h,a = 0.043G0.8L0-4/Z0.5 Btu/(hr)(cuft)(“F). (8.36)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-204-320.jpg)
![186 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.6. Typical Ranges of Individual Film and Fouling Coefficients [h Btu/(hr)(sqft)(OF)]
Fluid and Process Conditions P (atm) (AT),,,,, (“F) 104h lo44
Sensible
Water
Ammonia
Light organics
Medium organics
Heavy organics
Heavy organics
Very heavy organics
Very heavy organics
G a s
G a s
G a s
liquid
liquid
liquid
liquid
liquid heating
liquid cooling
liquid heating
liquid cooling
l - 2
10
100
7.6-11.4 6-14
7.1-9.5 O-6
28-38 6-11
38-76 9-23
23-76 11-57
142-378 11-57
189-568 23-170
378-946 23-170
450-700 O-6
140-230 O-6
57-113 O-6
Condensing transfer
Steam ammonia
Steam ammonia
Steam ammonia
Steam ammonia
Steam ammonia
Light organics
Light organics
Light organics
Medium organics
Heavy organics
Light condensable mixes
Medium condensable mixes
Heavy condensable mixes
all condensable
1% noncondensable
4% noncondensable
all condensable
all condensable
p u r e
4% noncondensable
p u r e
narrow range
narrow range
narrow range
narrow range
m e d i u m r a n g e
0.1
0.1
0.1
1
10
0.1
0.1
IO
1
4.7-7.1 O-6
9.5-14.2 O-6
19-28 O-6
3.8-5.7 O-6
2.3-3.8 O-6
28-38 O-6
57-76 O-6
8-19 O-6
14-38 6-30
28-95 II-28
23-57 O - I I
38-95 6-23
95-190 11-45
Vaporizing transfer
Water
Water
Ammonia
Light organics
Light organics
Medium organics
Medium organics
Heavy organics
Heavy organics
Very heavy organics
p u r e
narrow range
p u r e
narrow range
p u r e
narrow range
narrow range
4 5 5.7-19
3 6 3.8-14
3 6 11-19
36 14-57
2 7 19-76
3 6 16-57
2 7 23-95
3 6 23-95
2 7 38-142
6-12
6-12
6-12
6-12
6-17
6-17
6-17
11-28
II-45
II-57
2 0 2 7 57-189
Light organics have viscosity il cP, typically similar to octane and lighter hydrocarbons.
Medium organics have viscosities in the range l-5cP. like kerosene, hot gas oil, light crudes, etc.
Heavy organics have viscosities in the range 5-100 cP, cold gas oil, lube oils, heavy and reduced crudes, etc.
Very heavy organics have viscosities above 100 cP, asphalts, molten polymers, greases, etc.
Gases are all noncondensables except hydrogen and helium which have higher coefficients.
Conversion factor: 1 Btu/(hr)(sqft)(“F) = 5.6745 W/m* K.
(After HEDH, 1983, 3.1.4-4).
In a tower with height Z = 30ft and with both G and L at
5000 lb/(hr)(cuft), for example, this formula gives h,n = 21.5.
In liquid-liquid contacting towers, data cited by Fair (1972)
range from KK-12,000 Btu/(hr)(cuft)(“F) and heights of transfer
units in the range of 5 ft or so. In pipeline contactors, transfer rates
of 6000-60,00OBtu/(hr)(cuft)(“F) have been found, in some cases
as high as 200,000.
In some kinds of equipment, data only on mass transfer rates
may be known. From these, on the basis of the Chilton-Colburn
analogy, corresponding values of heat transfer rates can be
estimated.
NATURAL CONVECTION
Coefficients of heat transfer by natural convection from bodies of
various shapes, chiefly plates and cylinders, are correlated in terms
of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the
most usual situations, of which heat losses to ambient air are the
most common process. Simplified equations are shown for air.
Transfer of heat by radiation is appreciable even at modest
temperatures; such data are presented in combination with
convective coefficients in item 16 of this table.
FORCED CONVECTION
Since the rate of heat transfer is enhanced by rapid movement of
fluid past the surface, heat transfer processes are conducted under
such conditions whenever possible. A selection from the many
available correlations of forced convective heat transfer involving
single phase fluids, including flow inside and outside bare and
extended surfaces, is presented in Table 8.10. Heat transfer
resulting in phase change, as in condensation and vaporization, also
is covered in this table. Some special problems that arise in
interpreting phase change behavior will be mentioned following.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-205-320.jpg)
![188 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.8. Dimensionless Groups and Units of Quantities
Pertaining to Heat Transfer
S y m b o l N u m b e r G r o u p
realized heat transfer to the heat transfer that would be obtained if
the fin were at the bare tube temperature throughout. The total
heat transfer is the sum of the heat transfers through the bare and
the extended surfaces:
B i Biot
F o Fourier
GZ Graetz
G r Grashof
N U Nusselt
P e Peclet
P r Prandtl
R e Reynolds
S C S c h m i d t
St Stanton
hL/k
ke/pCL’
wC/kL
D3p2gPAT/p2
hD/k
DGC/k = (Re)(Pr)
Wk
DGIP, DUPIY
d&
hC/G = (Nu)/(Re)(Pr)
Notation Name and Typical Units
C heat capacity ]Btu/flb)(“F), cal/(g)(“C)]
D diameter (ft, m)
9 acceleration of gravity [ft/(hr)‘, m/set’]
G mass velocity [lb/(hr)(ft)2, kg/set)(m)‘]
h heat transfer coefficient [Btu/(hr)(sqft)(“F),
W/(m)2(sec)l
k thermal conductivity [Btu/(hr)(sqft)(‘F/R),
cal/(sec)(cm2)(C/cm)]
4, diffusivity (volumetric) [ft*/hr, cm*/sec]
L length (f-t, cm)
T, AT temperature, temperature difference (“F or “R, “C or K)
” linear velocity (ft/hr, cm/set)
IJ overall heat coefficient (same as units of h)
B”
mass rate of flow (Ib/hr, g/set)
Thermal expansion coefficient (l/“F, l/C)
8 time (hr. set)
P viscosity [lb/(ft)(hr), g/(cm)(sec)]
P density [lb/(f$, g/(cm)3]
can exist in any particular case. Transition between modes
corresponds to a maximum heat flux and the associated critical
temperature difference. A table of such data by McAdams (Heat
Trunsmission, McGraw-Hill, New York, 1954, p. 386) shows the
critical temperature differences to range from 42-90°F and the
maximum fluxes from 42-126 KBtu/(hr)(sqft) for organic sub-
stances and up to 410KBtu/(hr)(sqft) for water; the nature of the
surface and any promoters are identified. Equations (40) and (41) of
Table 8.10 are for critical heat fluxes in kettle and thermosyphon
reboilers. Beyond the maximum rate, film boiling develops and the
rate of heat transfer drops off very sharply.
Evaluation of the boiling heat transfer coefficient in vertical
tubes, as in thermosyphon reboilers, is based on a group of
equations, (42)-(48), of Table 8.10. A suitable procedure is listed
following these equations in that table.
EXTENDED SURFACES
When a film coefficient is low as in the cases of low pressure gases
and viscous liquids, heat transfer can be improved economically by
employing extended surfaces. Figure 8.6 illustrates a variety of
extended surfaces. Since the temperature of a fin necessarily
averages less than that of the bare surface, the effectiveness likewise
is less than that of bare surface. For many designs, the extended
surface may be taken to be 60% as effective as bare surface, but this
factor depends on the heat transfer coefficient and thermal
conductivity of the fin as well as its geometry. Equations and
corresponding charts have been developed for the common
geometries and are shown, for example, in HEDH (1983, Sec.
2.5.3) and elsewhere. One chart is given with Example 8.6. The
efficiency n of the extended surface is defined as the ratio of a
A, is the tube surface that is not occupied by fins. Example 8.6
performs an analysis of this kind of problem.
8.5. PRESSURE DROP IN HEAT EXCHANGERS
Although the rate of heat transfer to or from fluids is improved by
increase of linear velocity, such improvements are limited by the
economic balance between value of equipment saving and cost of
pumping. A practical rule is that pressure drop in vacuum
condensers be limited to OS-l.0 psi (25-50 Torr) or less, depending
on the required upstream process pressure. In liquid service,
pressure drops of 5-10 psi are employed as a minimum, and up to
15% or so of the upstream pressure.
Calculation of tube-side pressure drop is straightforward, even
of vapor-liquid mixtures when their proportions can be estimated.
Example 8.7 employs the methods of Chapter 6 for pressure drop in
a thermosiphon reboiler.
The shell side with a number of segmental baffles presents more
of a problem. It may be treated as a series of ideal tube banks
connected by window zones, but also accompanied by some
bypassing of the tube bundles and leakage through the baffles. A
hand calculation based on this mechanism (ascribed to K.J. Bell) is
illustrated by Ganapathy (1982, pp. 292-302), but the calculation
usually is made with proprietary computer programs, that of HTRI
for instance.
A simpler method due to Kern (1950, pp. 147-152) nominally
considers only the drop across the tube banks, but actually takes
account of the added pressure drop through baffle windows by
employing a higher than normal friction factor to evaluate pressure
drop across the tube banks. Example 8.8 employs this procedure.
According to Taborek (HEDH, 1983, 3.3.2), the Kern predictions
usually are high, and therefore considered safe, by a factor as high
as 2, except in laminar flow where the results are uncertain. In the
case worked out by Ganapathy (1982, pp. 292-302), however, the
Bell and Kern results are essentially the same.
8.8. TYPES OF HEAT EXCHANGERS
Heat exchangers are equipment primarily for transferring heat
between hot and cold streams. They have separate passages for the
two streams and operate continuously. They also are called
recuperators to distinguish them from regenerators, in which hot
and cold streams pass alternately through the same passages and
exchange heat with the mass of the equipment, which is in-
tentionally made with large heat capacity. Recuperators are used
mostly in cryogenic services, and at the other extreme of tem-
perature, as high temperature air preheaters. They will not be
discussed here; a detailed treatment of their theory is by Hausen
(1983).
Being the most widely used kind of process equipment is a
claim that is made easily for heat exchangers. A classified directory
of manufacturers of heat exchangers by Walker (1982) has several
hundred items, including about 200 manufacturers of shell-and-tube
equipment. The most versatile and widely used exchangers are the
shell-and-tube types, but various plate and other types are valuable
and economically competitive or superior in some applications.
These other types will be discussed briefly, but most of the space
following will be devoted to the shell-and-tube types, primarily](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-207-320.jpg)
![190 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.10. Recommended Individual Heat Transfer Coefficient Correlations’
A. Single Phase Streams
a. Laminar Flow, Re c 2300
Inside tubes
Nu, = $3.663 + 1.61a Pe(d/L), 0.1 < Pe(d/L) i IO4
Between parallel plates of length L and separation distance s
Nu, = 3.7% +
0.0156(Pe(s/L)]‘.‘4
1 + 0.058[Pe(s/L)]0.M Pr”.17 ’
0.1 < Pe(s/L) < IO3 (2)
In concentric annuli with d inside, d, outside, and hydraulic diameter d,, = d, - di. I, heat
transfer at inside wall; II, at outside wall; Ill, at both walls at equal temperatures’
0.19[Pe(d,,/L)]0~8
1 +0.117[Pe(d,,/L)]0.467
(3)
(4)
(5)
6)
(7)
Casell:
Case Ill:
b. Turbulent Flow, Re > 2300
Inside tubes
Nu = 0.012(Re0-87 - 280) Prc4
(8)
(9)
(IO)
(11)
Concentric annuli: Use d,, for both Re and Nu. Nurub. from Eqs. (IO] or (11)
Case I:
Case II: (13)
Case III:
1 + qJd, (14)
Across one row of long tubes: d = diameter, s = center-to-center distance, a = s/d,
R%.L = wL/qv
Wvow = 0.3 + ~Nu:.,,m + Nu:turb
Nu~,,am = 0.664GPr’”
‘%tur,, = 0.037 Re$ Pr/[l + 2.443 Re;ci’(Pr2’3 - I)]
Nu~,ra,., = ~Llh
(15)
(161
(17)
(18)
(‘9)
“Special notation used in this table: (Y = heat transfer coefficient (W/m* K) (instead of h),
Q = viscosity (instead of ,n), and (Y = thermal conductivity (instead of k).
(Based on HEDH, 1983).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-209-320.jpg)
![8 . 6 . T Y P E S O F H E A T E X C H A N G E R S 193
EXAMPLE 8.6
Sizing an Exchanger with Radial Finned Tubes
A liquid is heated from 150 to 190°F with a gas that goes from 250
to 200°F. The duty is 1.25 MBtu/hr. The inside film coefficient is
200, the bare tube outside coefficient is h, = 20 Btu/(hr)(sqft)(“F).
The tubes are 1 in. OD, the fins are 5 in. high, 0.038 in. thick, and
number 72/ft. The total tube length will be found with fins of steel,
brass, or aluminum:
LMTD = (60 - 50)/1n(60/50) = 54.8,
u, = (l/20 + l/200))’ = 18.18.
Fin surface:
A, = 72(2)@/4)[(2.25* - 1)/144] = 3.191 sqft/ft.
Uncovered tube surface:
A, = (n/12)[1 - 72(0.038/12)] = 0.2021 sqft/ft,
AJA, = 3.191/0.2021= 15.79,
yh = half-fin thickness = 0.038/2(12) = 0.00158 ft.
Abscissa of the chart:
n = (re - r,)e = [(2.25 - 1)/24]~20/0.00158k
=5.86/G,
rJrb = 2.25,
A, = QlWT(l+ vL/A,)
= 1.25(10”)/18.18(54.8)(1+ 15.7917) sq ft.
Find 9 from the chart. Tube length, L = AJO. ft.
k x q A,, L
Steel 26 1.149 0.59 121.6 602
Brass 6 0 0 . 7 5 6 0 . 7 6 9 6 . 5 4 7 7
Al 120 0.535 0.86 86.1 426
EXAMPLE 8.7
Pressure Drop on the Tube Side of a Vertical Thermosiphon
Reboiler
Liquid with the properties of water at 5 atm and 307°F is reboiled at
a feed rate of 28OOIb/(hr)(tube) with 30wt % vaporization. The
tubes are 0.1 ft ID and 12 ft long. The pressure drop will be figured
at an average vaporization of 15%. The Lockhart-Martinelli,
method will be used, following Example 6.14, and the formulas of
Tables 6.1 and 6.8:
Liquid V a p o r
rh (Ib/hr) 2 3 8 0 4 2 0
F Ob/ft hr) 0.45 0.036
P Wcufi) 5 7 . 0 0 . 1 7 2
R e 6 7 3 4 0 1 4 8 5 4 4
f 0.0220 0.0203
Af/L (psi/ft) 0.00295 0.0281
X2 = 0.00295/0.0281= 0.1051,
c=20,
& = 1 + 20/X + l/X’ = 72.21,
(AP/L) two phase = 72.21(0.00295) = 0.2130,
AP = 0.2130(12) = 2.56 psi, 5.90 ft water.
---
D
T T
i 4
Average density in reboiler tubes is
2800
pm = 2380157 + 420/O. 172
= 1.13 Ib/cuft.
Required height of liquid in tower above bottom of tube sheet
p,h = 2.56(144) + 1.13(12),
h = 382.2157 = 6.7 ft.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-212-320.jpg)
![8.7. SHELL-AND-TUBE HEAT EXCHANGERS 1%
(a)
(i) Parallel and counter flows
d-- -r- -r-‘f--:
I I I
m
I4 f
I f :
I 1 I
---*L--r-- -
(ii) Countercurrent flows
jgTJTJQ-->
-------- --
(iii) Parallel flows throughout
(b)
(cl
L I
Figure 8.8. Plate and spiral compact exchangers. (a) Plate heat
exchanger with corrugated plates, gaskets, frame, and corner
portals to control flow paths. (b) Flow patterns in plate exchangers,
(i) parallel-counter flows; (ii) countercurrent flows; (iii) parallel
flows throughout. (c) Spiral exchanger, vertical, and horizontal
cross sections.
Forced draft arrangement, from below the tubes, Figure 8.4(h),
develops high turbulence and consequently high heat transfer
coefficients. Escape velocities, however, are low, 3 m/set or so, and
as a result poor distribution, backmixing and sensitivity to cross
currents can occur. With induced draft from above the tubes, Figure
8.4(g), escape velocities may be of the order of 10 m/set and better
flow distribution results. This kind of installation is more expensive,
the pressure drops are higher, and the equipment is bathed in hot
air which can be deteriorating. The less solid mounting also can
result in noisier operation.
Correlations for friction factors and heat transfer coefficients
are cited in HEDH. Some overall coefficients based on external
bare tube surfaces are in Tables 8.11 and 8.12. For single passes in
cross flow, temperature correction factors are represented by Figure
8.5(c) for example; charts for multipass flow on the tube side are
given in HEDH and by Kays and London (1984), for example.
Preliminary estimates of air cooler surface requirements can be
made with the aid of Figures 8.9 and 8.10, which are applied in
Example 8.9.
DOUBLE-PIPES
This kind of exchanger consists of a central pipe supported within a
larger one by packing glands [Fig. 8.4(a)]. The straight length is
limited to a maximum of about 20 ft; otherwise the center pipe will
sag and cause poor distribution in the annulus. It is customary to
operate with the high pressure, high temperature, high density, and
corrosive fluid in the inner pipe and the less demanding one in the
annulus. The inner surface can be provided with scrapers [Fig.
8.4(b)] as in dewaxing of oils or crystallization from solutions.
External longitudinal fins in the annular space can be used to
improve heat transfer with gases or viscous fluids. When greater
heat transfer surfaces are needed, several double-pipes can be
stacked in any combination of series or parallel.
Double-pipe exchangers have largely lost out to shell-and-tube
units in recent years, although Walker (1982) lists 70 manufacturers
of them. They may be worth considering in these situations:
1. When the shell-side coefficient is less than half that of the tube
side; the annular side coefficient can be made comparable to the
tube side.
2. Temperature crosses that require multishell shell-and-tube units
can be avoided by the inherent true countercurrent flow in
double pipes.
3. High pressures can be accommodated more economically in the
annulus than they can in a larger diameter shell.
4. At duties requiring only 100-200 sqft of surface the double-pipe
may be more economical, even in comparison with off-the-shelf
units.
The process design of double-pipe exchangers is practically the
simplest heat exchanger problem. Pressure drop calculation is
straightforward. Heat transfer coefficients in annular spaces have
been investigated and equations are cited in Table 8.10. A chapter
is devoted to this equipment by Kern (1950).
8.7. SHELL-AND-TUBE HEAT EXCHANGERS
Such exchangers are made up of a number of tubes in parallel and
series through which one fluid travels and enclosed in a shell
through which the other fluid is conducted.
CONSTRUCTION
The shell side is provided with a number of baffles to promote high
velocities and largely more efficient cross flow on the outsides of the](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-214-320.jpg)
![196 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.11. Overall Heat Transfer Coefficients in Air Coolers [U Btu/(hr)(“F)(sqft of outside bare tube sutface)]
Material
Liquid Coolers Condensers
Heat-Transfer Heat-Transfer Heat-Transfer
Coefficient,
[Btu/(hr) Vt%Wl
Coefficient, Coefficient,
Material (Btu/(hr)(ft?(“F)l Material [Btu/(hr)(rt2WF)l
Oils, 20” API IO-16
200°F avg. temp lo-16
300°F avg. temp 13-22
400°F avg. temp 30-40
Oils, 30” API
150°F avg. temp
200°F avg. temp
300°F avg. temp
400°F avg. temp
12-23
25-35
45-55
50-60
Oils, 40” API
150°F avg. temp
200°F avg. temp
300°F avg. temp
400°F avg. temp
25-35
50-60
55-65
60-70
Heavy oils, 8-14”API
300°F avg. temp
400°F avg. temp
Diesel oil
K e r o s e n e
Heavy naphtha
Light naphtha
Gasoline
Light hydrocarbons
Alcohols and most
organic solvents
Ammonia
Brine, 75% water
Water
50% ethylene glycol
and water
6-10
lo-16
45-55
55-60
60-65
65-70
70-75
75-80
70-75
100-120
go-110
120-140
100-120
Vapor Coolers
Steam
Steam
10% noncondensibles
20% noncondensibles
40% noncondensibles
Pure light hydrocarbons
Mixed light hydrocarbons
Gasoline
Gasoline-steam mixtures
Medium hydrocarbons
Medium hydrocarbons
w/steam
Pure organic solvents
Ammonia
140-150
100-110
95-100
70-75
80-85
65-75
60-75
70-75
45-50
55-60
75-80
100-110
Heat-Transfer Coefficient [Btu/(hr)(f?)(“F)]
Material
Light hydrocarbons
Medium hydrocarbons and organic solvents
Light inorganic vapors
Air
Ammonia
Steam
H y d r o g e n
100%
75% vol
50% vol
25% vol
[Brown, Chem. Eng. (27 Mar. 1978)].
10 psig 50 psig 100 psig 300 psig 500 psig
15-20 30-35 45-50 65-70 70-75
15-20 35-40 45-50 65-70 70-75
IO-15 15-20 30-35 45-50 50-55
8-10 15-20 25-30 40-45 45-50
IO-15 15-20 30-35 45-50 50-55
10-15 15-20 25-30 45-50 55-60
20-30 45-50 65-70 85-95 95-100
17-28 40-45 60-65 80-85 85-90
15-25 35-40 55-60 75-80 85-90
12-23 30-35 45-50 65-70 80-85
TABLE 8.12. Overall Heat Transfer Coefficients in Condensers,
Btu/(hr)(sqft)(OF)a
V a p o r
Liquid Coolants
Coolant Btu/(hrkqfWF)
Alcohol
Dowtherm
Dowtherm
Hydrocarbons
high boiling under vacuum
low boiling
intermediate
kerosene
k e r o s e n e
naphtha
naphtha
Organic solvents
Steam
Steam-organic azeotrope
Vegetable oils
water 100-200
tall oil 60-80
Dowtherm 80-120
water 18-50
water 80-200
oil 25-40
water 30-65
oil 20-30
water 50-75
oil 20-40
water 100-200
water 400-1000
water 40-80
water 20-50
Air Coolers
V a p o r
Btu/(hr)
(bare sqft)(“F)
Ammonia 100-120
Freons 60-80
Hydrocarbons, light 80-100
Naphtha, heavy 60-70
Naphtha, light 70-80
Steam 130-140
“Air cooler data are based on 50mm tubes with aluminum fins
16-18 mm high spaced 2.5-3 mm apart; coefficients based on bare tube
surface. Excerpted from HEDH, 1983.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-215-320.jpg)
![a00
,000 I II
I I
I BROWS.u:IZO I I
WOO
3mo
I
I I
3 ROWS.U=l00
2om 8 I
M II I‘hl I.
40 I
II II II l--d?-+
(b)
10
(a)
:x4, , ( ( , , , , , , , , , ( ,
Figure 8.9. Required surfaces of air coolers with three
rows of tubes. (a) CJ = 140. (b) U = 120. (c) CJ = 100.
(d) CJ= 80. (e) CJ = 60. [Lerner, Hyd. Proc., 93-100
(Fed. 1972)].
” ” “I I I ”
3 ROWS.U:60
I ! ! ! ! ! ! ! N-U_U
II I I I I IIIU
.
40 40
II il II III 11%
3 0
1
al
30
2 0
10 I
5 I) I
lel
(4](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-216-320.jpg)
![8.7. SHELL-AND-TUBE HEAT EXCHANGERS 1%
EXAMPLE 8.9
Estimation of the Surface Requirements of an Au Cooler
An oil is to be cooled from 300 to 150°F with ambient air at 90”F,
with a total duty of 20 MBtu/hr. The tubes have 5/8 in. fins on 1 in.
OD and 2-5/16 in. triangular spacing. The tube surface is given by
A = 1.33NwL, sqft of bare tube surface,
N = number of rows of tubes, from 3 to 6,
W = width of tube bank, ft,
L = length of tubes, ft.
According to the data of Table 8.12, the overall coefficient may be
taken as U = 60 Btu/(hr)(oF)(sqft of bare tube surface). Exchangers
with 3 rows and with 6 rows will be examined.
Approach = 150 - 90 = 60”F,
Cooling range = 300 - 150 = 15O”F,
From Figure 8.9(f), 3 rows,
A = 160 sqft/MBtu/hr)
+ 160(20) = 3200 sqft
= 1.33(3)WL.
tubes. Figure 8.4(c) shows a typical construction and flow paths.
The versatility and widespread use of this equipment has given rise
to the development of industrywide standards of which the most
widely observed are the TEMA standards. Classifications of
equipment and terminology of these standards are summarized on
Figure 8.11.
Baffle pitch, or distance between baffles, normally is 0.2-1.0
times the inside diameter of the shell. Both the heat transfer
coefficient and the pressure drop depend on the baffle pitch, so that
its selection is part of the optimization of the heat exchanger. The
window of segmental baffles commonly is about 25%, but it also is a
parameter in the thermal-hydraulic design of the equipment.
In order to simplify external piping, exchangers mostly are built
with even numbers of tube passes. Figure 8.12(c) shows some
possible arrangements, where the full lines represent partitions in
one head of the exchanger and the dashed lines partitions in the
opposite head. Partitioning reduces the number of tubes that can be
accommodated in a shell of a given size. Table 8.12 is of such data.
Square tube pitch in comparison with triangular pitch accommo-
dates fewer tubes but is preferable when the shell side must be
cleaned by brushing.
Two shell passes are obtained with a longitudinal baffle, type F
in Figures 8.11(a) or 8.3(c). More than two shell passes normally
are not provided in a single shell, but a 4-8 arrangement is
thermally equivalent to two 2-4 shells in series, and higher
combinations are obtained with more shells in series.
ADVANTAGES
A wide range of design alternates and operating conditions is
obtainable with shell-and-tube exchangers, in particular:
l Single phases, condensation or boiling can be accommodated in
either the tubes or the shell, in vertical or horizontal positions.
l Pressure range and pressure drop are virtually unlimited, and can
be adjusted independently for the two fluids.
When W = 16 ft, L = 50 ft.
Two fans will make the ratio of section length to width,
25/16= 1.56 which is less than the max allowable of 1.8. At
7.5 HP/100 sqft,
Power=F7.5=60HP.
From Figure 8.10(c), 6 rows,
A = 185 sqft/(MBtu/hr)
+ 185(20) = 3700 sqft.
= 1.33(6)WL.
When W = 16 ft, L = 29 ft.
Since L/W = 1.81, one fan is marginal and two should be used:
Power = [16(29)/100]7.5 = 34.8 HP.
The 6-row construction has more tube surface but takes less
power and less space.
Thermal stresses can be accommodated inexpensively.
A great variety of materials of construction can be used and may
be different for the shell and tubes.
Extended surfaces for improved heat transfer can be used on
either side.
A great range of thermal capacities is obtainable.
The equipment is readily dismantled for cleaning or repair.
TUBE SIDE OR SHELL SIDE
Several considerations may influence which fluid goes on the tube
side or the shell side.
The tube side is preferable for the fluid that has the higher
pressure, or the higher temperature or is more corrosive. The tube
side is less likely to leak expensive or hazardous fluids and is more
easily cleaned. Both pressure drop and laminar heat transfer can be
predicted more accurately for the tube side. Accordingly, when
these factors are critical, the tube side should be selected for that
fluid.
Turbulent flow is obtained at lower Reynolds numbers on the
shell side, so that the fluid with the lower mass tlow preferably goes
on that side. High Reynolds numbers are obtained by multipassing
the tube side, but at a price.
DESIGN OF A HEAT EXCHANGER
A substantial number of parameters is involved in the design of a
shell-and-tube heat exchanger for specified thermal and hydraulic
conditions and desired economics, including: tube diameter,
thickness, length, number of passes, pitch, square or triangular; size
of shell, number of shell baffles, baffle type, baffle windows, baffle
spacing, and so on. For even a modest sized design program, Bell
(in HEDH, 1983, 3.1.3) estimates that 40 separate logical designs
may need to be made which lead to 240 = 1.10 x 10” different paths
through the logic. Since such a number is entirely too large for
normal computer processing, the problem must be simplified with](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-218-320.jpg)
![204 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE 8.10 Use 16 ft tubes on la in. square pitch, two pass, 33 in. shell
Process Design of a Shell-and-Tube Heat Exchanger
An oil at the rate of 490,000 lb/hr is to be heated from 100 to 170°F
with 145,000 Ib/hr of kerosene initially at 390°F. Physical properties
L/D = 16/(33/12) = 5.82,
are
Oil 0.85spgr.3.5cP at 135°F. 0.49spht
Kerosene 0.82 sp gr, 0.4 CP at 2Oo"F, 0.61 sp ht
oil, 100 F
490000 pph
170F
*
kerosene
2WF
145000 pph
Kerosene outlet:
T = 390 - (490,000/145,000)(0.49/0.61)(170 - 100)
= 2OO”F,
LMTD = (220 - lOO)/ln 2.2 = 152.2,
P = (170 - 100)/(390 - 100) = 0.241,
R = (390 - 200)/(170 - 100) = 2.71.
From Figure 8.5(a), F = 0.88, so a 1-2 exchanger is satisfactory:
AT = 152.2(0.88) = 133.9.
From Table 8.6, with average values for medium and heavy
organics,
U = 104/(57 + 16 + 50 + 34) = 63.7,
Q = 490,000(0.49)(170 - 100) = 1.681(10’) Btu 1 hr,
A = Q/lJAT = 1.681(10’)/63.7(133.9) = 197Osqft,
1970/0.2618 = 7524.8 ft of 1 in. OD tubing.
Use 1: in. pitch, two tube pass. From Table 8.13,
D,he,, (number of tubes)
Required
L (ft) N o . T u b e s Triangular S q u a r e
a 940
12 627 35(608) 37E4)
::
470
376
which is near standard practice. The 20 ft length also is acceptable
but will not be taken.
The pressure drops on the tube and shell sides are to be
calculated.
Tube side: 0.875in. ID, 230 tubes, 32ft long: Take one velocity
head per inlet or outlet, for a total of 4, in addition to friction in the
tubes. The oil is the larger flow so it will be placed in the tubes.
ti = 490,000/230 = 2130.4 lb/(hr)(tube).
Use formulas from Table 6.1
Re = 6.314(2130.4)/0.875(3.5) = 4392,
f = 1.6364/[ln(5(10-‘)/0.875 + 6.5/4392)]’ = 0.0385,
APf= 5.385(10-8)(2130)‘(32)(0.0385)/0.85(0.875)s
= 0.691 psi.
Expansion and contraction:
AP, = 4p(u2/2q,) = 4(53.04)(3.26)‘/(64.4)(144) = 0.243 psi,
:. APtube = 0.691 + 0.243 = 0.934 psi.
Shellside. Follow Example 8.8:
D,, = 1.2732(1.25/12)‘/(1/12) - l/12 = 0.0824 ft,
B = 1.25 ft between baffles,
E = 0.25/12 ft between tubes,
D, = 33/12 = 2.75 ft shell diameter,
A, = 2.75(1.25)(0.25/12)/(1.25/12) = 0.6875 sqft,
G, = 145,000/0.6875 = 210,909 lb/(hr)(sqft),
Re = 0.0824(210,909)/0.4(2.42) = 17,952,
f = 0.0121(17,952)-“.‘9 = 0.00188,
AP,,,,, -
- O.oO188(21O,9O9)‘(2.75)(13)/5.22(1O’o)(O.82)(O.O824)
= 0.85 psi.
The pressure drops on each side are acceptable. Now it remains
to check the heat transfer with the equations of Table 8.10 and the
fouling factors of Table 8.6.
CONDENSER CONFIGURATIONS
The several possible condenser configurations will be described.
They are shown on Figure 8.14.
Condensation Inside Tubes: Vertical DownJlow. Tube dia-
meters normally are 19-25 mm, and up to 50 mm to minimize
critical pressure drops. The tubes remain wetted with condensate
which assists in retaining light soluble components of the vapor.
Venting of noncondensables is positive. At low operating pressures,
larger tubes may be required to minimize pressure drop; this may
have the effect of substantially increasing the required heat transfer
surface. A disadvantage exists with this configuration when the
coolant is fouling since the shell side is more difficult to clean.
Condensation Inside Tubes: Vertical Upflow. This mode is
used primarily for refluxing purposes when return of a hot
condensate is required. Such units usually function as partial
condensers, with the lighter components passing on through. Reflux
condensers usually are no more than 6-loft long with tube
diameters of 25 mm or more. A possible disadvantage is the
likelihood of flooding with condensate at the lower ends of the
tubes.
Condensation Outside Vertical Tubes. This arrangement
requires careful distribution of coolant to each tube, and requires a
sump and a pump for return to a cooling tower or other source
of coolant. Advantages are the high coolant side heat transfer](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-223-320.jpg)
![208 HEAT TRANSFER AND HEAT EXCHANGERS
TABLE 8.14. A Guide to the Selection of Reboilers
Reboiler Type
Process Conditions
Kettle or
Internal
Horizontal Vertical
Shell-Side Tube-Side
T h e r m o s i p h o n T h e r m o s i p h o n
Forcad
F l o w
Operating pressure
Moderate
Near critical
Deep vacuum
Design AT
Moderate
Large
Small (mixture)
Very small (pure component)
Fouling
Clean
Moderate
H e a v y
Very heavy
Mixture boiling range
Pure component
N a r r o w
W i d e
Very wide, with viscous liquid
E
B-E
B
G
Rd
P
P
G
G
F
G
R
R
G
R
F
F
G
G
Rd
P
G
G
G
B
Rd
Rd
B
G - R d
Rd
P
G
B
B
Rd
G
B
B
E
E
E
F-P G - R d P B
a Category abbreviations: B, best; G, good operation; F, fair operation, but better choice is
possible; Rd. risky unless carefully designed, but could be best choice in some cases; R, risky
because of insufficient data; P, poor operation; E, operable but unnecessarily expensive.
(HEDH, 1983, 3.6.1).
weight fraction vaporized should be in the range of 0.1-0.35 for
hydrocarbons and 0.02-0.10 for aqueous solutions. Circulation may
be controlled with a valve in the supply line. The top tube sheet
often is placed at the level of the liquid in the tower. The flow area
of the outlet piping commonly is made the same as that of all the
tubes. Tube diameters of 19-25 mm diameter are used, lengths up
to 12ft or so, but some 20ft tubes are used. Greater tube lengths
make for less ground space but necessitate taller tower skirts.
Maximum heat fluxes are lower than in kettle reboilers.
Because of boiling point elevations imposed by static head, vertical
thermosiphons are not suitable for low temperature difference serv-
ices.
Shell side vertical thermosiphons sometimes are applied when
the heating medium cannot be placed on the shell side.
FORCED CIRCULATION REBOILERS
Forced circulation reboilers may be either horizontal or vertical.
Since the feed liquid is at its bubblepoint, adequate NPSH must be
assured for the pump if it is a centrifugal type. Linear velocities in
the tubes of 1%20ft/sec usually are adequate. The main
disadvantages are the costs of pump and power, and possibly severe
maintenance. This mode of operation is a last resort with viscous or
fouling materials, or when the fraction vaporized must be kept low.
CALCULATION PROCEDURES
Equations for boiling heat transfer coefficients and maximum heat
fluxes are Eqs. (37) through (48) of Table 8.10. Estimating values
are in Tables 8.4-8.7. Roughly, boiling coefficients for organics are
300 Btu/(hr)(sqft)(“F), or 1700 W/m2 K; and for aqueous solutions,
1000 Btu/(hr)(sqft)(“F), or 5700 W/m2 K. Similarly, maximum
fluxes are of the order of 20,000 Btu/(hr)(sqft), or 63,000 W/m*, for
organics; and 35,000 Btu/(hr)(sqft) or 110,000 W/m*, for aqueous
systems.
The design procedure must start with a specific geometry and
heat transfer surface and a specific percentage vaporization. Then
the heat transfer coefficient is found, and finally the required area is
calculated. When the agreement between the assumed and
calculated surfaces is not close enough, the procedure is repeated
with another assumed design. The calculations are long and tedious
and nowadays are done by computer.
Example 8.12 summarizes the results of such calculations made
on the basis of data in Heat Exchanger Design Handbook (1983).
Procedures for the design of kettle, thermosiphon and forced
circulation reboilers also are outlined by Polley (in Chisholm, 1980,
Chap. 3).
8.10. EVAPORATORS
Evaporators employ heat to concentrate solutions or to recover
dissolved solids by precipitating them from saturated solutions.
They are reboilers with special provisions for separating liquid and
vapor phases and for removal of solids when they are precipitated
or crystallized out. Simple kettle-type reboilers [Fig. 8.4(d)] may be
adequate in some applications, especially if enough freeboard is
provided. Some of the many specialized types of evaporators that
are in use are represented on Figure 8.16. The tubes may be
horizontal or vertical, long or short; the liquid may be outside or
inside the tubes, circulation may be natural or forced with pumps or
propellers.
Natural circulation evaporators [Figs. 18.16(a)-(e)] are the
most popular. The forced circulation type of Figure 18.16(f) is most
versatile, for viscous and fouling services especially, but also the
most expensive to buy and maintain. In the long tube vertical
design, Figure 816(d), because of vaporization the liquid is in
annular or film flow for a substantial portion of the tube length, and
accordingly is called a rising film evaporator. In falling film](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-227-320.jpg)
![210 HEAT TRANSFER AND HEAT EXCHANGERS
Noncondensoble
qm outlet
Feed
id)
J L
1
Product
(e)
P’Pe
P--&CL- Body
Swrl breaker
Feed
Inlet
Mother
llqua
Cnculatlon I
Evqmotor crystallmr Va‘“um ‘lxhg crystal llzer
(9)
Figure 8.1~(continued)
THERMAL ECONOMY
Thermal economy is a major consideration in the design and
operation of evaporators. This is improved by operating several
vessels in series at successively lower pressures and utilizing vapors
from upstream units to reboil the contents of downstream units.
Figure 8.17 shows such arrangements. Thermal economy is ex-
pressed as a ratio of the amount of water evaporated in the
complete unit to the amount of external steam that is supplied. For
a single effect, the thermal economy is about 0.8, for two effects it is
1.6, for three effects it is 2.4, and so on. Minimum cost usually is
obtained with eight or more effects. When high pressure steam is
available, the pressure of the vapor can be boosted with a steam jet
compressor [Fig. 8.16(c)] to a usable value; in this way savings of
one-half to two-thirds in the amount of external steam can be
achieved. Jet compressor thermal efficiencies are 20-30%. A
possible drawback is the contamination of condensate with
entrainment from the evaporator. When electricity is affordable, the
pressure of the vapor can be boosted mechanically, in compressors
with efficiencies of 70-75%.
Because of the elevation of boiling point by dissolved solids,
the difference in temperatures of saturated vapor and boiling
solution may be 3-10°F which reduces the driving force available
for heat transfer. In backward feed [Fig. 8.17(b)] the more
concentrated solution is heated with steam at higher pressure which
makes for lesser heating surface requirements. Forward feed under
the influence of pressure differences in the several vessels requires
more surface but avoids the complications of operating pumps
under severe conditions.
Several comprehensive examples of heat balances and surface](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-229-320.jpg)
![214 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE&W
Peak Temperatures
tube spacings the peak temperatures are:
An average flux rate is 12,OOOBtu/(hr)(sqft) and the inside film Center-to-center/diameter 1 1.5 2 2.5 3
coefficient is 2OOBtu/(hr)(sqft)(“F). At the position where the
Peak (“F) 1036 982 9 5 8 9 4 8 9.22
average process temperature is 850”F, the peak inside film For heavy liquid hydrocarbons the upper limit of 950°F often is
temperature is given by T = 850+ 12,000”R/200. At the several adopted.
convection, and heat recovery sections of the heater to the heat
released by combustion. The released heat is based on the lower
heating value of the fuel and ambient temperature. With standard
burners, efficiencies may be in the range 6t-80%; with radiant
panels, 80-82%. Within broad limits, any specified efficiency can be
attained by controlling excess air and the extent of recovery of
waste heat.
An economical apportionment of heat absorption between the
radiant and convection zones is about 75% in the radiant zone. This
can be controlled in part by recirculation of flue gases into the
radiant chamber, as shown in Figure 8.19(b).
Because of practical limitations on numbers and possible
locations of burners and because of variations in process
temperatures, the distribution of radiant flux in a combustion
chamber is not uniform. In many cases, the effect of such
nonuniformity is not important, but for sensitive and chemically
reacting systems it may need to be taken into account. A method of
estimating quickly a flux distribution in a heater of known
configuration is illustrated by Nelson (1958, p. 610). A desired
pattern can be achieved best in a long narrow heater with a
multiplicity of burners, as on Figure 17.16 for instance, or with a
multiplicity of chambers. A procedure for design of a plug flow
heater is outlined in the Heat Exchanger Design Handbook (1983,
3.11.5). For most practical purposes, however, it is adequate to
assume that the gas temperature and the heat flux are constant
throughout the radiant chamber. Since the heat transfer is
predominantly radiative and varies with the fourth power of the
absolute temperature, the effect of even substantial variation in
stock temperature on flux distribution is not significant. Example
8.14 studies this problem.
DESIGN OF FIRED HEATERS
The design and rating of a fired heater is a moderately complex
operation. Here only the completely mixed model will be treated.
For this reason and because of other generalizations, the method to
be described affords only an approximation of equipment size and
performance. Just what the accuracy is, it is hard to say. Even the
relatively elaborate method of Lobo and Evans (1939) is able to
predict actual performance only within a maximum deviation of
16%.
EXAMPLE 8.14
Effect of Stock Temperature Variation
A combustion chamber is at 2260”R. a stock enters at 106O”R and
leaves at 136O”R. Accordingly, the heat fluxes at the inlet and outlet
are approximately in the ratio (2.264 - 1.064)/2.264 - 1.364) =
1.095. The small effect of even greater variation in flux on a mild
cracking operation is illustrated in Figure 8.22.
Pertinent equations and other relations are summarized in
Table 8.16, and a detailed stepwise procedure is listed in Table
8.17. A specific case is worked out in detail in Example 8.15.
Basically, a heater configuration and size and some aspects of the
performance are assumed in advance. Then calculations are made
of the heat transfer that can be realized in such equipment.
Adjustments to the design are made as needed and the process
calculations repeated. Details are given in the introduction to
Example 8.16. Figures 8.20, 8.21, and 8.22 pertain to this example.
Some of the approximations used here were developed by
Wimpress (1963); his graphs were converted to equation form for
convenience. Background and more accurate methods are treated
notably by Lobo and Evans (1939) and more briefly by Kern (1950)
and Ganapathy (1982). Charts of gas emissivity more elaborate than
Figure 8.23 appear in these references.
An early relation between the heat absorption Q in a radiant
zone of a heater, the heat release Q,, the effective surface A, and
the air/fuel ratio R lb/lb is due to Wilson, Lobo, and Hottel [Znd.
Eng. Chem. 24, 486, (1932)]:
Q,/Q = l+ (R/Q~)~. (8.45)
Although it is a great simplification, this equation has some utility in
appraising directional effects of changes in the variables. Example
8.16 considers changes in performance with changes in excess air.
Heat transfer in the radiant zone of a fired heater occurs largely
by radiation from the flue gas (90% or so) but also significantly by
convection. The combined effect is represented by
Q/A = W’; - T:) + h,(T, - T,), (8.46)
where Tg and T, are absolute temperatures of the gas and the
receiving surface. The radiative properties of a gas depend on its
chemical nature, its concentration, and the temperature. In the
thermal range, radiation of flue gas is significant only from the
triatomic molecules H,O, CO,, and SO,, although the amount of
the last is small and usually neglected. With fuels having the
composition C,H,, the ratio of partial pressures is p&pco, = 1.
In Figure 8.23, the emissivity of such a gas is represented as a
function of temperature and the product PL of the partial pressures
of water and carbon dioxide and the path of travel defined by the
mean beam length. Item 8 of Table 8.16 is a curve fit of such data.
When other pertinent factors are included and an approxima-
tion is introduced for the relatively minor convection term, the heat
transfer equation may be written
Q/aA,F = 1730[(T,/1000)4 - (T,/1000)4] + 7(T, - T,). (8.47)
Here the absorptivity depends on the spacing of the tubes and is
given by item 5 of Table 8.16. The cold plane area A, is the
product of the number of tubes by their lengths and by the
center-to-center spacing. The combination cuA, is equal to the area
of an ideal black plane that has the same absorptivity as the tube](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-233-320.jpg)
![8.11. FIRED HEATERS 217
TABLE 8.17--(continued)
19. The partial pressure P of CO, + H,O is given in terms of the excess air by Eq. (6)
20. The product PL is found with the results of Steps 18 and 19
21. The mean tube wall temperature T in the radiant zone is given in terms of the inlet and
outlet process stream temperatures by
J = 100 + 0.5(T, + T2)
22. The temperature Tg of the gas leaving the radiant zone is found by combining the
equations of the radiant zone heat transfer [Eq. (111 and the radiant zone heat balance IEq.
(211. With the approximation usualty satisfactory, the equality is
The solution of this equation involves other functions of T,, namely, the emissivity &J by
Eq. (8). the exchange factor F by Eq. (9) and the exit enthalpy ratio C&/Q, by Eq. (4)
23. The four relations cited in Step 22 are solved simultaneously by trial to find the
temperature of the gas. Usually it is in the range 1500-1800°F. The Newton-Raphson
method is used in the program of Table 8.18. Alternately, the result can be obtained by
interpolation of a series of hand calculations
24. After 7, has been found, calculate the heat absorbed Q, by Eq. (1)
25. Find the heat flux
Q/A = Q~l4actiant
and compare wit!1 value specified in Step 8. If there is too much disagreement, repeat the
calculations with an adjusted radiant surface area
26. By heat balance over the convection zone, find the inlet and outlet temperatures of the
process stream
27. The enthalpy of the flue gas is given as a function of temperature by Eq. (4). The
temperature of the inlet to the convection zone was found in Step 23. The enthalpy of the
stack gas is given by the heat balance [Eq. (3)], where all the terms on the right-hand side
are known. 4/Q” is given as a function of the stack temperature T, by Eq. (4). That
temperature is found from this equation by trial
28. The average temperature of the gas film in the convection zone is given in terms of the
inlet and outlet temperatures of the process stream and the flue gas approximately by
T=05 T +T + (T,,-T,,)-(T,-LA
[
f . L1 LO
Inl(T,, - TL,V(7i- TLoH 1
The flow is countercurrent
29. Choose the spacing of the convection tubes so that the mass velocity is
G = 0.3-0.4 Ib/(sec)(sqft free cross section). Usually this spacing is the same as that of
the shield tubes, but the value of G will not be the same if the tubes are finned
30. The overall heat transfer coefficient is found with Eq. (10)
31. The convection tube surface area is found by
A, = QJU, (LMTD)
and the total length of bare of finned tubes, as desired, by dividing A,by the effective
area per foot
32. Procedures for finding the pressure drop on the flue gas side, the draft requirements and
other aspects of stack design are presented briefly by Wimpress.
[Based partly on the graphs of Wimpress, Hydrocarbon Process. 42(10), 115-126 (196311.
EX A M P L E 8.15
Design of a Fiied Heater
The fuel side of a heater used for mild pyrolysis of a fuel oil will be
analyzed. The flowsketch of the process is shown in Figure 8.20,
and the tube arrangement finally decided upon is in Figure 8.21.
Only the temperatures and enthalpies of the process fluid are
pertinent to this aspect of the design, but the effect of variation of
heat flux along the length of the tubes on the process temperature
and conversion is shown in Figure 8.22. In this case, the substantial
differences in heat flux have only a minor effect on the process
performance.
Basic specifications on the process are the total heat release
(102.86 MBtu/hr), overall thermal efficiency (75%), excess air
(25%), the fraction of the heat release that is absorbed in the
radiant section (75%), and the heat flux (10,000 Btu/(hr)(sqft).
In the present example, the estimated split of 75% and a](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-236-320.jpg)
![218 HEAT TRANSFER AND HEAT EXCHANGERS
EXAMPLE t.lS-(continued)
radiant rate of 10,000 lead to an initial specification of 87 tubes, but
90 were taken. The final results are quite close to the estimates,
being 77.1% to the radiant zone and 99OOBtu/(hr)(sqft) with 90
tubes. If the radiant rate comes out much different from the desired
value, the number of tubes is changed accordingly.
Because of the changing temperature of the process stream, the
heat flux also deviates from the average value. This variation is
estimated roughly from the variation of the quantity
p = 1730(7-i - T;) + 7.0( Tg - TL),
where the gas temperature T,, in the radiant zone is constant and
TL is the temperature of the process stream, both in “R. In
comparison with the average flux, the effect is a slightly increased
preheat rate and a reduced flux in the reaction zone. The inside skin
temperature also can be estimated on the reasonable assumptions of
heat transfer film coefficients of more than 100 before cracking
starts and more than 200 at the outlet. For the conditions of this
example, with Q/A = 9900 and Tg = 2011”R, these results are
obtained:
T,(“Fl Wm h ‘LJF)
547 1.093 >lOO <655
724 1 >lOO ~823
900 1.878 >200 <943
The equation numbers cited following are from Table 8.16. The
step numbers used following are the same as those in Table 8.17:
1.
2.
3.
4.
5.
Flow rate = 195,394/3600(0.9455)(62.4) = 0.9200 cfs,
velocity = 5.08 fps in 6-S/8 in. OD Schedule 80 pipe.
Short radius return bends have 12 in. center-to-center.
?j = 0.75.
Fraction excess air = 0.25.
From the API data book and a heat of cracking of
332 Btu/(lb gas + gasoline):
&,a = 0.9(590) + 0.08(770) + 0.02(855) = 609.6 Btu/lb,
Q fOfa, = 195,394(609.6 - 248) + 19,539(332) = 77.14(E6).
6. Heat released:
Q, = 77.14/0.75 = 102.86(E6) Btu/lb.
7. Radiant heat absorption:
QR = 0.75(77.14)(E6) = 57.86(E6).
8. (Q/A) rad = 10,000 Btu/(hr)(sqft), average.
9. Radiant surface:
A = 57.86(E6)/10,000 = 5786 sqft.
11. Tube length = 5786/1.7344 = 3336 ft; 40 foot tubes have an
exposed length of 38.5ft; N =3336/38.5 =86.6, say 92
radiant tubes.
12. From Eq. (11) the flue gas rate is
G, = 102.85(1020) = 104,907 Ib/hr.
With four shield tubes, equilateral spacing and 3 in. distance
to walls,
104,907(12)
' =3600(38.5)(27.98)
= 0.325 Ib/sec sqft.
13. The 90 radiant tubes are arranged as shown on Figure 8.22:
4 shields, 14 at the ceiling, and 36 on each wall. Dimensions
of the shell are shown.
14. A, = (38.5)(1)(90 - 4) = 3311 sqft.
15. Inside surface of the shell is
A, = 2[20(37 + 38.5) + 37(38.5)] = 5869 sqft.
Refractory surface,
A, = 5869 - 3311 = 2558 sqft.
16. (Center-to-center)/OD = 12/6.625 = 1.81,
(Y = 0.917, single rows of tubes [Eq. (5)].
17. Effective absorptivity:
aA, =4(38.5)(l) + 0.917(3311) = 3190 sqft,
A,/cxA, = 255813190 = 0.8018.
18. Mean beam length:
L=(2/3)(20 x 37 x38.5)"3=20.36.
19. From Eq. (6), with 25% excess air,
P = 0.23.
20. PL = 0.23(20.36) = 4.68 atm ft.
21. Mean tube wall temp: The stream entering the radiant
section has absorbed 25% of the total heat.
H, = 248 + 0.25(77.14)(E6)/195,394 = 346.7,
Tl = 565”F,
T, = 100 + (565 + 900)/2 = 832.5.
22-X Input data are summarized as:
PL = 4.68,
D, = 0.8018,
Dz = 0.25,
T, = 832.5,
Q, = QJaA, = 102.86(E6)/3190 = 32,245.
From program “FRN-l”,
T, = 1553.7,
F= 0.6496 [Eq. (9)],
+ 7(T, - T,))
= 3190(0.6496)(28,679) = 59.43(E6).
Compared with estimated 57.86(E6) at 75% heat absorption](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-237-320.jpg)
![8.12. INSULATION OF EQUIPMENT 219
EXAMPLE 8.1s(continued)
in the radiant section. Repeat the calculation with an
estimate of 60(E6)
HI = 248 + (77.14 - 60)(E6)/195,394 = 335.7,
T, = 542,
T, = 100 + OS(542 + 900) = 821,
Tg = 1550.5,
From (Eq. (4),
T, = 920°F.
28-31.
LMTD = 735.6
mean gas film temp is
F = 0.6498,
QR = 3190(0.6498)(28,727) = 5955(E6).
Interpolating,
0 auumad T, ‘i T. Qe.,cd Q/A
q = 0.5(400 + 547 + 735.6) = 841.3.
Since G = 0.325 lb/(sec)(sqft),
V, = 5.6 Btu/(hr)(sqft)(“F) [(Eq. (lo)],
57.88 565 832.5 1553.7 59.43
A =
1764(E6)
= 4282
60.00 542 821 1550.5 59.55 conv 735.6(5.6) SqfL
Interpolation [547 1551.2 59.50 99001 4282
= 64.1 bare tubes
26-21. 1.7344(38.5)
QcOnv = (77.14 - 59.50)(E6)
= 17.64(E6).
Fraction lost in stack gas
or 16 rows of 4 tubes each. Spacing the same as of the shield
tubes.
Beyond the first two rows, extended surfaces can be
installed.
Q,/Q, = 1 - 0.02 - 0.75 = 0.23. Total rows = 2 + 14/2 = 9.
bank, and is called the equivalent cold plane area. Evaluation of the
exchange factor F is explained in item 9 of Table 8.16. It depends
on the emissivity of the gas and the ratio of refractory area A, to
the equivalent cold plane area aA,. In turn, A,,, = A -A,, where
A is the area of the inside walls, roof, and floor that are covered by
refractory.
In the convection zone of the heater, some heat also is trans-
ferred by direct radiation and reflection. The several contribu-
tions to overall heat transfer specifically in the convection zone of fired
heaters were correlated by Monrad [Znd. Eng. Chem. 24,505 (1932)].
The combined effects are approximated by item 10 of Table 8.16,
which is adequate for estimating purposes. The relation depends on
the temperature of the gas film which is taken to be the sum of the
average process temperature and one-half of the log mean
temperature difference between process and flue gas over the entire
tube bank. The temperature of the gas entering the convection zone
is found with the trial calculation described in Steps 22-23 of Table
8.17 and may utilize the computer program of Table 8.18.
8.12. INSULATION OF EQUIPMENT
Equipment at high or low temperatures is insulated to conserve
energy, to keep process conditions from fluctuating with ambient
conditions, and to protect personnel who have occasion to approach
the equipment. A measure of protection of the equipment metal
against atmospheric corrosion also may be a benefit. Application of
insulation is a skilled trade. Its cost runs to 8-9% of purchased
equipment cost.
In figuring heat transfer between equipment and surroundings,
it is adequate to take account of the resistances of only the
insulation and the outside film. Coefficients of natural convection
are in Table 8.9 and properties of insulating materials at several
EXAMPLE 8.16
Application of the Wilson-Lobo-Hottel Equation
In the case of Example 8.15, 25% excess air was employed,
corresponding to 19.0lb/air/lb fuel, the heat release was
Qr = 102.86(106) Btu/hr, and aA, = 3036. The effect will be found
= 1 + 0.0722-
1.8327
:. Q, = 95.82(106) Btu/hr,
of changing the excess air to 16% (16.721b air/lb fuel) on the
amount of fuel to be fired while maintaining the same heat
absorption.
Ratioing Eq. (8.45) to yield the ratio of the releases at the two
conditions.
which is the heat release with 10% excess air.
With 25% excess air, Q/QZ = l/1.8327 = 0.5456,
With 10% excess air, Q/Q, = 0.5456(102.86/95.82) = 0.5857,
QfZ l+ (16.72/42OO)dm
102.86(106) = 1 + (19.0/4200)~102.86(106)/3036
which shows that approximately 7% more of the released heat is
absorbed when the excess air is cut from 25% down to 10%.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-238-320.jpg)
![220 HEAT TRANSFER AND HEAT EXCHANGERS
II I
Feed
T, = 400 F
195394 Ib/hr
H = 248 Btullb
v’ = 0.920 cfs
u = 5.08 fps, cold
8” Sched 40.
‘8
,/
Convection
b
Shield
VA 4 -
Radiant
Fuel
+ 25% excess air
Figure 8.20. Flowsketch of process of Example 8.16.
Figure 8.21. Tube and box configuration of the fired heater of
Example 8.16.
.I0
.03
.OG
.04
.02
0
TEMPERATURE T
CONVERSION, x
0 20 40 60
TUBE NUMBER
Figure 8.22. Effects of three modes of heat flux distribution on
temperature and conversion in pyrolysis of a fuel oil: (1) two levels,
12,500 and 7500; (2) linear variation between the same limits; (3)
constant at 10,000 Btu/(hr)(sqft). Obtained by method of Example
8.16.
temperature levels are in Tables 8.19-8.21. Outdoors under windy
conditions, heat losses are somewhat greater than indoors at natural
convections. Tabulations of economic thicknesses in Chemical
Engineers Handbook (McGraw-Hill, New York, 1984, 11.55-11.58)
suggest that lo-20% greater thickness of insulation is justified at
wind velocity of 7.5 miles/hr.
The optimum thickness of insulation can be established by
economic analysis when all of the cost data are available, but in
practice a rather limited range of thicknesses is employed. Table
8.22 of piping insulation practice in one instance is an example.
The procedure for optimum selection of insulation thicknesses
is exemplified by Happel and Jordan [Chem. Process Economics,
380 (1975)]. They take into account the costs of insulation and fuel,
payout time, and some minor factors. Although their costs of fuel
are off by a factor of 10 or more, their conclusions have some
validity if it is recognized that material costs likewise have gone up
by roughly the same factor. They conclude that with energy cost of
$2,5/millionBtu (adjusted by a factor of lo), a payout time of 2
years, for pipe sizes of 2-8 in., the optimum thicknesses in
0.70, . . , , , , , 1
Figure 8.23. Total emissivity of carbon dioxide and water with
pHzoIpcoz = 1 and a total pressure of 1 atm [Hadvig, J. Inst. Fuel
43, 129 (1970)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-239-320.jpg)
![TABLE 8.24. Comparative Data of Freon Refrigerants
Refrigerant Number (AM Designation) 1 1 1 2 2 2 1 1 3 1 1 4 500 502
C h e m i c a l n a m e
Chemical formula
Molecular wl
Gas constant R [(ft lb/lb R)]
Boiling point at 1 atm (“F)
Freezing point at 1 atm (“F)
Critical temperature (“F)
Critical pressure (psia)
Specific heat of liquid, 86°F
Specific heat of vapor, C, 60°F at 1 atm
Specific heat at vapor, C, 60°F at 1 atm
Ratio CJC, = K (86°F at 1 atm)
Saturation pressure (psia) at
-50°F
0°F
40°F
105°F
Net refrigerating effect (Btu/lb) 40-105°F (no
subcooling)
Cycle efficiency (% Carnot cycle) 40-105°F
Liquid circulated 40-105°F [(lb/min/ton)]
Theoretical displacement 40-105°F
(cuft/min/ton)]
Theoretical horsepower per ton 40-105°F
Coefficient at performance 40-105°F (4.71/HP
per ton)
Cost compared with R 11
trichloromono-
fluoromethane
dichlorodi-
fluoromethane
monochlorodi-
fluoromethane
trichlorotri-
fluoroethane
dichlorotetra-
fluoroethane
CCI,F CCI,F,
1 3 7 . 3 8 120.93
1 1 . 2 5 12.78
7 4 . 7 -21.62
-168 -252
3 8 8 . 0 2 3 3 . 6
6 3 5 . 0 5 9 7 . 0
0 . 2 2 0 0 . 2 3 5
a 0 . 1 4 6
a 0 . 1 3 0
1.11 1.14
C H C I F , CCI,F-CCIF, C,‘W,
8 6 . 4 8 187.39 1 7 0 . 9 3
17.87 8 . 2 5 9 . 0 4
-41.4 117.6 3 8 . 4
-256 -31 -137
2 0 4 . 8 4 1 7 . 4 2 9 4 . 3
7 1 6 . 0 4 9 5 . 0 4 7 4 . 0
0 . 3 3 5 0 . 2 1 8 0 . 2 3 8
0 . 1 4 9 a 0 . 1 5 6
0 . 1 2 7 a 0 . 1 4 5
1.18 1.12 1.09
azeotrope of
dichlorodi-
fluoromethane
a n d
difluoroethane
73.8% CCI,F,
26.2% CHsCHF,
9 9 . 2 9
15.57
-28.0
-254
221.1
6 3 1 . 0
0 . 3 0 0
0.171
0.151
1.13
azeotrope of
monochlorodi-
fluoromethane
a n d
monochloropenta-
fluoroethane
48.8% CHCLF,
51.2% CCIF,-CF,
1 1 1 . 6 4
1 3 . 8 7
-50.1
a
194.1
6 1 8 . 7
0 . 3 0 5
0.164
0.161
1 . 0 2 3
0 . 5 2 7 . 1 2 11.74 a 1.35 8.395 1 4 . 7 4
2 . 5 5 2 3 . 8 5 3 8 . 7 9 0 . 8 4 5 . 9 6 2 7 . 9 6 45.94
7 . 0 3 5 1 . 8 7 8 3 . 7 2 2 . 8 6 15.22 6 0 . 9 4 9 4 . 9 0
2 5 . 7 1 4 1 . 2 5 2 2 7 . 6 5 1 1 . 5 8 5 0 . 2 9 1 6 7 . 8 5 244.40
6 7 . 5 6 4 9 . 1 3 6 6 . 4 4 5 4 . 5 4 4 3 . 4 6 5 9 . 8 2 4 3 . 7 2
9 0 . 5 8 3 . 2 8 1 . 8 8 7 . 5 9 4 . 9 8 2 . 0 76.1
2 . 9 6 4 . 0 7 3 . 0 2 3 . 6 6 4 . 6 2 3 . 3 5 4.58
16.1 3 . 1 4 1.98 3 9 . 5 9 . 1 6 2 . 6 9 2 . 0 4
0 . 6 7 6 0 . 7 3 6 0 . 7 5 0 . 7 0 0 . 7 2 2 0 . 7 4 7 0.806
6 . 9 5 6 . 3 9 6 . 2 9 8 . 7 4 6 . 5 2 6.31 5 . 8 6
1 . o o 1.57 2.77 2.15 2.97 2 . 0 0 5 . 5 4
a Data not available or not applicable.
(Carrier Air Conditioning Co.).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-247-320.jpg)
![9.2. RATE OF DRYING 235
mture content (tMC)
Ttme
(a)
Final moisture
cOntent IFMC)
0 4 60 P'
% S A T U R A T I O N
(cl
5 - leather, sole, oak tann
1.16
Relatwe, humidity f?&
(b)
0 .02 .04 .06 .06 .10 .I2 .I. .I6 .I6 .ZP
UOlSTURE CDNTENT.LES./LB.OF DRY SAND
(4
Figure 9.3. (a) Classic drying curve of moisture content against time; a heat-up period in which no drying occurs also is usually present
(Proctor and Schwartz, Inc.; Schweitzer, p. 4.144). (b) Equilibrium moisture content as a function of relative humidity; many other data are
tabulated in Chemical Engineers Handbook (McGraw-Hill, New York, 1984, 20.12). (These data are from National Academy of Science,
copyright 1926.) (c) Rate of drying as a function of % saturation at low (subscript 1) and high (subscript 2) drying rates: (A) glass spheres,
60 pm, bed 51 mm deep; (B) silica flour, 23.5 pm, 51 mm deep; (C) silica flour, 7.5 pm, 51 mm bed; (D) silica flour, 2.5 p, 65 mm deep (data
of Newitt et al., Trans. Inst. Chem. Eng. 27, 1 (1949). (d) Moisture content, time and drying rates in the drying of a tray of sand with
superheated steam; surface 2.35 sqft, weight 27.125 lb. The scatter in the rate data is due to the rough numerical differentiation (Wenzel,
Ph.D. thesis, University of Michigan, 1949). (e) Temperature and drying rate in the drying of sand in a tray by blowing air across it. Dry bulb
76.1”C, wet bulb 36.o”C (Ceaglske and Hougen, Trans. AIChE 33, 283 (1937). (f) Drying rates of slabs of paper pulp of several thicknesses
[after McCready and McCabe, Trans. AIChE 29, 131 (1933)]. (g) Drying of asbestos pulp with air of various humidities [McCready and
McCabe, Trans. AIChE 29, 131 (1933)]. (h) Effect of temperature difference on the coefficient K of the falling rate equation -dW/dO = KW
[Sherwood and Comings, Trans. AIChE 27, 118 (1932)]. (i) Effect of air velocity on drying of clay slabs. The data are represented by
R = ~.OU’.‘~(H,,, - H). The dashed line is for evaporation in a wetted wall tower (Walker, Lewis, McAdams, and Gilliland, Principles of
Chemical Engineering, McGraw-Hill, New York, 1937).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-254-320.jpg)
![9.3. CLASSIFICATION AND GENERAL CHARACTERISTICS OF DRYERS 2%
EXAMPLE 9.4
Effects of Moist Air Recycle and Increase of Fresh Air Rate in
Belt Conveyor Drying
The conditions of Example 9.3 are taken except that recycle of
moist air is employed and the equilibrium moisture content is
assumed constant at We = 0.014. The material balance in terms of
the recycle ratio R appears on the sketch:
A = 7790 R
W=1501.4R
c!&d=FE
A = air, W = water, S = dry solid
Humidity of the air at any point is obtained from the water balance
H = 1581.4R + 97.4 + 14OO(W - 0.1)
t? 7790(R + 1) (1)
The vapor pressure is
ps = exp[11.9176 - 7173.9/(T, + 389.5)] atm.
The saturation humidity is
H, = (18/29)p,/(l -p,).
The heat capacity is
(2)
(3)
C = 0.24 + 0.45H,. (4)
With constant air temperature of 170”F, the equation of the
adiabatic saturation line is
170 - r, = ; (H, - H,) = F (H, - H.J. (5)
The drying rate equations above and below the critical moisture
content of 0.58 are
R=O
-lo!!!!
d0
134.15(R + l)Os(H, - H,), 0.58<W<1.16, ( 6 )
= 60.33(R+ l)‘.s(H,- H,)(W-0.014), W <0.58. (7)
When fresh air supply is simply increased by a factor R + 1 and no
recycle is employed, Eq. (1) is replaced by
H = 97.4(R + 1) + 1400( W - 0.1)
* 7790(R + 1)
The solution procedure is:
1. Specify the recycle ratio R (Ibs recycle/lb fresh air, dry air basis).
2. Take a number of discrete values of W between 1.16 and 0.1.
For each of these fmd the saturation temperature T, and the
drying rates by the following steps.
3. Assume a value of T,.
4. Find H,, P,, H,, and C from Eqs. (l)-(4).
5. Find the value of T, from Eq. (5) and compare with the assumed
value. Apply the Newton-Raphson method with numerical
derivatives to ultimately find the correct value of T, and the
corresponding value of H,.
6. Find the rate of drying from Eqs. (6), (7).
7. Find the drying time by integration of the reciprocal rate as in
Example 9.3, with the trapezoidal rule.
The printout shows saturation temperatures and reciprocal
rates for R = 0, 1, and 5 with recycle; and for R = 1 with only the
fresh air rate increased, using Eq. (8). The residence times for the
four cases are
R = 0, moist air, 8 = 3.667 hrs
= 1, moist air, = 2.841
= 5, moist air, = 1.442
= 1, fresh air, = 1.699.
Although recycling of moist air does reduce the drying time
because of the increased linear velocity, an equivalent amount of
fresh air is much more effective because of its lower humidity. The
points in favor of moist air recycle, however, are saving in fuel
when the fresh air is much colder than 170°F and possible avoidance
of case hardening or other undesirable phenomena resulting from
contact with very dry air.
R = 1, fresh air
Tlz 1 I Rate](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-258-320.jpg)
![Pneumatic conveying dryer
”
Ttme r
(a)
0 8 1 6 24 32 40 46 56 6 4
T i m e , s -
(b)
Y t I I
0 1 2 3 4
(cl
Figure 9.5. Residence time distribution in particle dryers. (a) Four
types of dryers (McCormick, 1979). (b) Residence time distribution
of air in a detergent spray tower; example shows that 27%
(difference between the ordinates) has a residence time between 24
and 32sec [Place et al., Trans. Inst. Chem. Eng. 37,268 (1959)]. (c)
Fluidized bed drying of two materials (Vanacek et al., Fluidized Bed
Drying, 1966).
particularly for materials that tend to degrade when they are
moved. From the point of view of drying, belt conveyors are of two
types: with solid belts and air flow across the top of the bed, called
convection drying, or with perforated belts and through circulation
of the air. The screw conveyor of Figure 9.8(f) has indirect heating.
Solid belts are used for pastes and fine powders. Through
9.5. CONTINUOUS TRAY AND CONVEYOR BELT DRYERS 245
TABLE 9.4. Examples of Products Dried in Specific Kinds of
Equipment
1. Spray dryers: rubber chemicals, sulfonates, inorganic phosphates,
ceramics, kaolin, coffee, detergents, pharmaceuticals, pigments,
inks, lignosulfonate wood waste, melamine and urea formaldehyde
resins, polyvinyl chloride, microspheres, skim milk, eggs, starch,
yeast, silica gel, urea, salts
2. Drum dryers: potatoes, cereals, buttermilk, skim milk, dextrins,
yeasts, instant oat meal, polyacylemides, sodium benzoate,
propionates, acetates, phosphates, chelates, aluminum oxide,
m-disulfuric acid, barium sulfate, calcium acetate-arsenate-
carbonate-hydrate-phosphate, caustic, ferrous sulfate, glue, lead
arsenate, sodium benzene sulfonate, and sodium chloride
3. Vacuum drum dryers: syrups, malted milk, skim milk, coffee, malt
extract, end glue
4. Vacuum rotary dryers: plastics, organic polymers, nylon chips,
chemicals of all kinds, plastic fillers, plasticizers, organic thickeners,
cellulose acetate, starch, and sulfur flakes
4. Belt conveyor dryers: yeast, charcoal briquettes, synthetic rubber,
catalysts, soap, glue, silica gel, titanium dioxide, urea formaldehyde,
clays, white lead, chrome yellow, and metallic stearates
6. Pneumatic conveyor dryers: yeast filter cake, starch, whey, sewage
sludge, gypsum, fruit pulp, copper sulfate, clay, chrome green,
synthetic casein, and potassium sulfate
7. Rotary multitray dryer: pulverized coal, pectin, penicillin, zinc
sulfide, waste slude, pyrophoric zinc powder, zinc oxide pellets,
calcium carbonate, boric acid, fragile cereal products, calcium
chloride flakes, caffein, inorganic fluorides, crystals melting near
lOO”F, prilled pitch, electronic grade phosphors, and solvent-wet
organic solids
8. Fluidized bed dryer: lactose base granules, pharmaceutical crystals,
weed killer, coal, sand, limestone, iron ore, polyvinyl chloride,
asphalt, clay granules, granular desiccant, abrasive grit, and salt
9. Freeze dryers: meat, seafood, vegetables, fruits, coffee,
concentrated beverages, pharmaceuticals, veterinary medicines,
and blood plasma
10. Dielectric drying: baked goods, breakfast cereals, furniture timber
blanks, veneers, plyboard, plasterboard, water-based foam plastic
slabs, and some textile products
11. infrared drying: sheets of textiles, paper and films, surface finishes
of paints and enamels, and surface drying of bulky nonporous
articles.
circulation belts are applied to granules more than about 3 mm in
narrowest dimension. When the feed is not in suitable granular
form, it is converted in a preformer to a size range usually of
3-15 mm. Belts are made of chain mail mesh or metal with 2 mm
perforations or slots of this width.
Several arrangements of belt dryers are shown in Figures
9.8(c)-(e). In the wet zone, air flow usually is upward, whereas in
the drier and cooling zones it is downward in order to minimize
dusting. The depth of material on the belt is l-8in. Superficial air
velocities of 5 ft/sec usually are allowable. The multizone
arrangement of Figure 9.8(e) takes advantage of the fact that the
material becomes lighter and stronger and hence can be loaded
more deeply as it dries. Each zone also can be controlled separately
for air flow and temperature. The performance data of Table 9.9
cover a range of drying times from 11 to 2OOmin, and thermal
efficiencies are about 50%.
Laboratory drying rate data of materials on trays are best
obtained with constant air conditions. Along a belt conveyor or in a
tray-truck tunnel, the moisture contents of air and stock change
with position. Example 9.3 shows how constant condition drying
tests can be adapted to belt conveyor operation. The effects of
recycling moist air and of increasing the air velocity beyond that
studied in the laboratory tests are studied in Example 9.4. Recycling
does reduce drying time because of the increased air velocity, but it](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-264-320.jpg)
![TABLE 9.6. Performance Data of Batch Tray and Tray-Truck Dryers
(a) Cross-Flow Operation
C o a t e d
Tablets
Capacity, wet charge (lb) 120 8 0 5 6 2 0 , 0 0 0 1800 3000 2800 4300
Number of trays 4 0 2 0 2 0 320 7 2 8 0 8 0 8 0
Tray area (ft’) 140 7 0 7 0 4800 1130 280 280 280
Depth of loading (in.) 0 . 5 1.0 0 . 5 2.0 2 . 0 1.0 1.0 1.5
Initial moisture (% w/w basis) 2 5 25-30 15 71 4 6 7 0 7 0 8 0
Final moisture (% w/w basis) nil 0 . 4 0 . 5 0 . 5 2 . 0 1.0 1.0 0 . 2 5
Maximum air temperature (“F) 113 284 122 200 180 300 200 200
Loading (lb/f?) 0 . 9 1.2 0 . 4 0 . 9 0.91 3 . 2 5 3 . 0 4 11.7
Drying time (hr) 12 5 . 5 1 4 2 4 4 . 5 2 2 4 5 12
Overall drying rate (Ib/hr) 2 . 6 5.3 0 . 8 4 6 2 . 5 185 9 6 . 6 4 3 . 2 so
Evaporative rate (lb/hr/ft’) 0 . 0 1 8 6 0 . 0 5 0 . 0 0 8 0 . 0 1 3 0 . 3 2 7 0.341 0 . 1 8 4 0 . 3 1 7
Total installed HP 1 1 1 4 5 6 4 2 2
P T F E C h a l k
Filter
Cake
(Williams-Gardner, 1971, p. 75, Table 12: first three columns courtesy Calmic Engineering Co.; last five columns courtesy A.P.V.-Mitchell
(Dryers) Ltd.)
(b) Vacuum Dryers with Steam Heated Shelves
Soluble Paint Ferrous Ferrous Lithium T u n g s t e n Stabilized
Aspirin P i g m e n t Glutinate Succinate H y d r o x i d e Alloy D i a z a m i n
Capacity, wet product (lb/h) 4 4
Tray area (ft*) 108
Depth of loading (in.)
Initial moisture (% w/w basis)
Final moisture (% w/w basis)
Max temp f”F)
Loading [lb charge (wet) ft*]
Drying time (hr)
Overall drying rate (lb moisture evaporated/ft*/hr)
Total installed HP
7 2 . 4
1.25
104
6.1
15
0 . 2 9 3
6
3 0 . 5 4 1 . 6 5 2 . 5 3 6 . 8 12.8 4 . 6
108 108 108 5 4 215 172
2 0 . 5 1 1 0 . 5 0 . 7 5
4 9 . 3 2 5 3 7 . 4 5 9 1.6 22.2
0 . 7 5 0 . 5 18.8 0 . 9 nil 0 . 5
158 203 203 122 239 9 5
102 2 . 3 1.94 3 . 0 8 7 . 1 6 1.22
3 6 6 4 4 . 5 12 4 . 8
0 . 1 4 0.11 0.11 0.034 0 . 0 1 3 0 . 0 0 5 8
6 6 6 3 2 5
Vacuum (in. Hg) 2 9 . 5 2 8 2 7 2 7 2 7 2 9 22-23
(Williams-Gardner, 1971, p. 88, Table 15: courtesy C a l m i c Engineering Co.)
(c) Vacuum Dryers with Steam-Heated Shelves
Material Sulfur Black
C a l c i u m C a l c i u m
C a r b o n a t e Phosphate
Loading (kg dry material/m’) 2 5 17 3 3
Steam (kPa gauge)
pressure 410 410 205
Vacuum (mm Hg) 685-710 685-710 685-7 10
Initial moisture content f%, wet basis) 5 0 5 0 . 3 3 0 . 6
Final moisture content f%, wet basis) 1 1.15 4 . 3
Drying time (hr) 8 7 6
Evaooration rates fka/sec m*) 8.9 x 1O-4 7.9 x 1om4 6.6 x 1o-4
(Chemical Engineers’ Handbook, McGraw-Hill, New York, 1984, p. 20.23, Table 20.8).
(d) Through Circulation Dryers
Kind of Material Vegetable
Capacity (kg product/hr) 122
Number of trays 1 6
Tray spacing (cm) 4 3
Tray size (cm) 91.4x 104
Depth of loading (cm) 7 . 0
Physical form of product c r u m b s
Initial moisture content (%, dry basis) 11.1
Final moisture content (%, dry basis) 0.1
Air temperature f”C) 8 8
Air velocity, superficial (m/set) 1.0
Tray loading (kg product/m2) 16.1
Drying time (hr) 2 . 0
Overall drying rate (kg water evaporated/hr m*) 0 . 8 9
Steam consumption (kg/kg water evaporated) 4 . 0
Installed (kW)
p o w e r 7 . 5
4 2 . 5 2 7 . 7
2 4 2 4
4 3 4 3
91.4x 104 85 x 98
6 4
0.6~cm diced w a s h e d
cubes s e e d s
6 6 9 . 0 1 0 0 . 0
5 . 0 9 . 9
77 dry-bulb 3 6
0.6-l .O 1.0
5 . 2 6 . 7
8 . 5 5 . 5
1 1 . 8 6 1.14
2 . 4 2 6 . 8
19 19
(Proctor and Schwartz Co.).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-267-320.jpg)
![9.6 ROTARY CYLINDRICAL DRYERS 253
TABLE 9.9. Petformance of Through-Circulation Belt Conveyor Dryers [See Figs. 9.8(c)-(e)]
(a) Data of A.P.V.-Mitchell (Dryers) Ltd.
Fertilizers Bentonite Pigment
Nickel Metallic
Hydroxide Stearate
Effective dn/er length
Effective band width
Capacity (lb productlhr)
Method of feeding
Feedstock preforming >
Initial moisture (% w/w basis)
Final moisture (% w/w basis)
Drying time (min)
Drying rate (lb evaporated/f?/hrJ
Air temperature range 1°F)
Superficial air velocity (ft/min)
Heat consumption (Btu/lb evaporated)
Method of heating
Fan installed HP
42ft6in. 60ftOin. 24ftOin.
8ft6in. 8ft6in. 4ftOin.
2290 8512 100
oscillator
30
10.0
14
6.5
-
200
-
direct oil
50
45.0
2.0 ’
16
7.0
-
200
-
direct oil
35
58.9
0.2
60
2.0
-
180
-
steam
14
24ftOin.
4ftOin.
125
extruder
75
0.5
70
7.5
180
-
steam
14
41 ft 3 in.
6ftOin.
125
extruder
75
0.2
60
1.5
-
125
-
steam
28
(Williams-Gardner, 1971).
(b) Data of Krauss-Maffei-Imperial GmbH
Aluminium Polyecrylic
Hydrate Nitrile Sulfur
Calcium Titanium
Carbonate Dioxide
Effective dryer length
Effective band width
Capacity (lb product/hr)
Method of feeding
Feedstock preforming >
Initial moisture (% w/w basis)
Final moisture I% w/w basis)
Drying time (min)
Drying rate (lb evaporated/hr/$
Air temperature range (“F)
Superficial air velocity Ift/min)
Heat consumption (lb steam/lb
evaporated)
Method of heating
Fan installed hp (approx.)
32ft9in.
6h6in.
615
grooved
drum
38.0
0.2
26
2.88
233
140
43ftOin. 28ftOin. 50ftOin. 108ftOin.
6ft6in. 6ft6in. 6ft3in. 9ft6in.
2070 660 1800 6000
extruder extruder extruder extruder
55.0 45.0 60.0 50.0
1.0 1.0 0.5 0.5
52 110 40 45
3.37 3.57 5.73 6.0
186/130 194/230 320 3141392
100/216 140 160 150
1.7-1.8 1.8-1.9 1.8-1.9
50 lb/in.’ 25 lb/in.* 90 lb/in.’
steam steam steam
25 65 20
1.7-1.8
160 lb/in
steam
35
2
1.8-1.9
260 lb/in.’
steam
80
(Williams-Gardner, 1971)
(c) Data of Proctor and Schwartz Inc.
Kind of Material
Inorganic
Pigment Cornstarch Fiber Staple
Charcoal
Briquettes Gelatin
Inorganic
Chemical
Capacity (kg dry product/hr) 712
Approximate dryer area (m’) 22.11
Depth of loading (cm) 3
Air temperature (‘X1 120
Loading (kg product/m? 18.8
Type of conveyor (mm) 1.59 by 6.35
slots
Preforming method or feed
Type and size of preformed
particle (mm)
Initial moisture content (%
bone-dry basis)
Final moisture content (% bone-
dry basis)
Drying time (min)
Drying rate [kg water
evaporated/(hr m’)]
Air velocity (superficial)(m/sec)
Heat source per kg water
evaporated [steam kg/kg gas
h3/kgll
Installed power (kW) 29.8 119.3 194.0 82.06 179.0 41.03
rolling filtered and
extruder scored
6.35-diameter scored filter
extrusions cake
120 85.2
0.5
35
38.39
1.27
gas
0.11
4536
66.42
4
115-140
27.3
1.19 by 4.76
slots
1724
Stage A Stage 6
57.04 35.12
- -
130-100 100
3.5 3.3
2.57.diameter
holes, perforated
plate
fiber feed
cut fiber
110
13.6 9
24 11
42.97 17.09
1.12 0.66
steam steam
2.0 1.73
5443 295
52.02
16
135-120
182.0
8.5
x 8.5 mesh
screen
pressed
104.05
5
32-52
9.1
4.23 x 4.23 mesh
screen
extrusion
64 x 51 x 25 2-diameter
extrusions
37.3 300
5.3
105
22.95
1.12
waste heat
11.1
192
9.91
1.27
steam
2.83
30.19
4
121-82
33
1.59 x 6.35 slot
rolling
extruder
6.35.diameter
extrusions
111.2
1.0
70
31.25
1.27
9s
0.13
(Perrys Chemical Engineers Handbook, McGraw-Hill, New York, 1984).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-272-320.jpg)
![256 D R Y E R S A N D C O O L I N G T O W E R S
EXAMPLE 9.5
Scale-Up of a Rotary Dryer
Tests on a laboratory unit come up with the stated conditions for
drying a pelleted material at the rate of 1000 lb dry/hr:
The residence time is 20min. The speed is 3-4rpm. On the
average, 7.5% of the cross section is occupied by solid. Because of
dusting problems, the linear velocity of the air is limited to
12 ft/sec. The diameter and length will be found. Since the inlet and
outlet conditions are specified and the moisture transfer is known,
the heat balance can be made. The heat capacity of the solid is 0.24:
moisture evap = 1000(0.6-0.05) = 550 lb/hr
air rate = 550/(0.0428 - 0.013) = 18,456 lb/hr
Off a psychrometric chart, the sp vol of the air is 15.9 cuft/(lb dry).
The diameter is
18,456(15.9)
>
112
D =
3600(12)(1-0.075)x/4
= 3.06 ft, say 3.0 ft.
The length is
L= 30(20/w
0.075nD2/4
= 18.9 ft.
EXAMPLE 9.6
Design Details of a Countercurrent Rotary Dryer
Pilot plants indicate that a residence time of 3 hr is needed to
accomplish a drying with the conditions indicated on the sketch.
For reasons of entrainment, the air rate is limited to 750 lbs
dry/(hr)(sqft cross section). Properties of the solid are 501b/
tuft and 0.22Btu/(lb)(“F). Symbols on the sketch are A = dry air,
S = dry solid, W = water:
136F
150 psig steam
A Ib/hr 60 F Air
4
H = 0.008
In terms of the dry air rate, A lb/hr, the average moist heat capacity
is
In the dryer, the enthalpy change of the moist air equals the sum of
the enthalpy changes of the moisture and of the solid. Add 7% for
heat losses. With steam table data,
(0.2436 + 74.93/A)A(290 - 136) = 1.07[333(1120.3) + l(228)
+ 1000(0.22)(260 - 60) - 334(28)]
= 1.07(407,936) = 43,649],
:. A = 11,633 lb/hr.
The exit humidity is
H = 0.008 + 333/11,633 = 0.0366 lb/lb,
which corresponds to an exit dewpoint of 96”F, an acceptable value.
With the allowable air rate of 750 lb/hr sqft, the diameter of
the dryer is
D = dl1,633/750n/4 =4.44ft, say 4.5 ft.
Say the solid occupies 8% of the cross section. With a solids
density of 50 lb/tuft, the dryer volume,
v = 3(1000/50)/0.08 = 750 tuft,
and the length is
L =750/(4.5)=x/4=47.2 ft.
The standard number of flights is 2-4 times the diameter, or
number = (2-4)4.5 = 9-18, say 12.
The product of rpm and diameter is 25-35
:. rpm = (25-35)/4.5 = 5.5-7.8, say 6.7.
The stm heater duty is
Q, = 11,633(0.2436)(290 - 60) = 651,733 Btu/hr,
150 psig stm,
stm = 651,733/857 = 760.5 lb/hr.
Evaporation efficiency is
7 = 333/760.5 = 0.438 lb water/lb stm.
The efficiency of the dryer itself is
qd = 407,936/651,733 = 0.626 Btu/Btu.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-275-320.jpg)
![9.8. PNEUMATIC CONVEYING DRYERS 261
TABLE 9.11. Performance Data of Drum Dryers
(a] Drum Dryers
Yeast S t o n e Starch Zirconium Brewers
Cream Slop Solutions G l a z e Silicate Yeast tlY;
Feed solids (% by weight)
Product moisture (% w/w basis)
Capacity (lb prod./hr)
Dryer type (a) single, (b) twin, (c) double
D r u m
d i a m e t e r
length
Type of feed method
Steam pressure (lb/in* gauge)
Atmospheric or vacuum
Steam consumption (lb/lb evaporated)
Average effective area (%)
Evaporation/ft*/hr
16
5.7
168
(a)
40 36
5
300-400
(a)
6 4 7 0 2 5 7 5
0 . 2 5 9
1120 146 4000
(a) (a) (a)
48 in.
120 in.
side
4 0
atmos.
1.35
6 5
8 . 4
0 . 2
420
(a)
0.2
225
(a)
4ftOin.
10ftOin.
top roller
8 0
atmos.
-
2ft6in.
5ftOin.
dip
6 0
atmos.
-
-
4
48 in. 18 in.
120 in. 36 in.
top roller side
8 0 -
atmos. atmos.
1.3 1.3
8 6 -
5 9
36in.
72 in.
dip
8 0
a t m o s .
-
28 in.
60 in.
center nip
4 0
- - -
6
6 . 5 8 . 4
(Courtesy A.P.V. Mitchell Dryers, Ltd.; Williams-Gardner, 1971).
(b) Drum Dryers in the Size Range 0.4 x 0.4-0.8 x 2.25 ma
Type of Dryer
and Feed
Size by Letter,
A, B, or C
D r u m Steam
Speed Press
(rev/min) (bar. a)
TYpe of Physical Form
Material of Feed
Solids
in Feed
(%I
WS’ output Evaporation
in of Dried Rate of
Product Product Water
w (g/see m2) Wsec m2)
Single (dip) 4 . 4 3.5b
Single (splash) 1 3 . 0
Twin (splash) A 3 3 . 0
Double 3-8 5.0
Double and twin 7-9 2-3
Double and twin 5-9 4-6
inorganic salts
alk. carbs
Mg(OW,
WOW,
Na Acetate
Na,S04
Na,HP04
- 5 0 8-12
thick slurry 3 5 0 . 5
thin slurry 2 2 3 . 0
solution 2 0 0.4-10
solution 2 4 0.15-5.5
solution 44 0.8-0.9
Twin (dip) A 5 5.5 organic salts solution 2 7 2 . 8
Twin A 3 5 . 5 organic salts solution 3 3 13.0
Twin B 2 ” 3 . 5 organic salts solution 2 0 1.0
T w i n C 5 5 . 5 organic salts solution 3 9 0 . 4
T w i n C 5; 5 . 5 organic salts solution 4 2 1.0
T w i n C 6 5 . 5 organic salts solution 3 5 5.0
Twin (splash) A 3-5 5 . 0 organic salts thin slurry 2 0 1.7-3.1
Double A 5; 6 . 0 organic salts solution 1 1 -
Double B 6; 5-6 organic salts solution 4 0 3
Twin (dip) A
Twin A
Double
Double
organic
c o m p o u n d s
thin slurry 3 0
viscous soln. 2 8
viscous soln. -
thin slurry 2 5
Twin (dip)
Twin
T w i n
5
5
2
4;
5
10
10
5 . 5
5 . 0
3 . 0
3 . 5
5 . 0
5 . 5
5 . 5
la) solution 2 5
(b) thick slurry 3 0
(c) thick slurry 3 5
1.2
10.5
6 . 0
1.0
0 . 5
2 . 5
-
Double 11 5 . 5
organic
compounds of
low surface
tension
similar
letters
f o r s a m e
c o m p o u n d
(b) thin paste 4 6
Double 1 2 5 . 5
Double 11 5 . 5
(c) thick paste 5 8
(a) solution 2 0
-
-
0 . 5
5 . 5 4 . 9
1.9 1.5
4 . 3 1.3
2.0-7.0 8-24
4.7-6.1 11-12
8.2-l 1.1 9-14
1.9 5.2
1.4 2 . 6
1.0 3 . 8
3 . 9 6.1
2.1 4 . 6
4.1 7 . 2
1.0-I .9 3.7-7.3
1.1 9
3 . 4 4 . 9
2 . 4 5 . 5
1.9 4 . 2
0.7 -
0.4-l .9 3.5-5.0
0 . 3 0 . 8
2 . 0 4 . 6
3.1 -
6 . 4 7 . 3
6 . 0 4 . 3
0 . 2 4 1.0
‘Dryer dia and width (ml: (A)
b Plus external hot air flow.
0.457 x 0.457; (B) 0.71 x 1.52; (C) 0.91 x 2.54.
‘Stainless steel drum.
(Nonhebel and Moss, 1971).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-280-320.jpg)
![9 . 9 . FLUIDIZED B E D D R Y E R S 265
‘Outlet
Igases
(a)
I. Fan
2. Rmg duct
3. Manifold
4. Injector
5. Air outlet
6. Feeder
7. Filter
8. Heoter
9. Cyclone
IO. Dwntegrotor
II. Bog filter
12. Discharge
Expansion-
bellows
Change over flap
, I D fan
Recirculated materlol
Y Dkble paddle mixer
_-.-
Combustion chamber
lb)
Figure 9.12. Examples of pneumatic conveying dryers; corresponding performance data are in Table 9.13. (a) Raymond flash dryer, with a
hammer mill for disintegrating the feed and with partial recycle of product (Raymond Division, Combustion Engineering). (b) Buttner-Rosin
pneumatic dryer with separate recycle and disintegration of large particles (Rosin Engineering Ltd.). (c) Berks ring dryer; the material
circulates through the ring-shaped path, product is withdrawn through the cyclone and bag filter (Penndt Chemical Co.).
complete drying is a recirculation scheme like that of Figure
9.13(e). In batch operation the time can be made as long as
necessary.
Stable fluidization requires a distribution of particle sizes,
preferably in the range of a few hundred microns. Normally a size
of 4mm or so is considered an upper limit, but the coal dryers of
Tables 9.15(a) and (b) accommodate sizes up to 0.5in. Large and
uniformly sized particles, such as grains, are dried successfully in
spouted beds [Fig. 9.13(f)]: H ere a high velocity gas stream entrains
the solid upward at the axis and releases it at the top for flow back
through the annulus. Some operations do without the mechanical
draft tube shown but employ a naturally formed central channel.
One way of drying solutions or pastes under fluidizing
conditions is that of Figure 9.13(g). Here the tluidized mass is of
auxiliary spheres, commonly of plastic such as polypropylene, into
which the solution is sprayed. The feed material deposits uniformly
on the spheres, dries there, and then is knocked off automatically as
it leaves the drier and leaves the auxiliary spheres behind. When a
mass of dry particles can be provided to start a fluidized bed drying
process, solutions or pastes can be dried after deposition on the
seed material as on the auxiliary spheres. Such a process is
employed, for instance, for growing fertilizer granules of desired
larger sizes, and has largely replaced rotary dryers for this purpose.
A few performance data of batch fluid dryers are in Table](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-284-320.jpg)
![266 D R Y E R S A N D C O O L I N G T O W E R S
EXAMPLE 9.8
Sizing a Pneumatic Conveying Dryer
A granular solid has a moisture content of 0.035 kg/kg dry material
which is to be reduced to 0.001 kg/kg. The charge is at the rate of
9.72 kg/set, is at 60°C and may not be heated above 90°C. Inlet air
is at 450°C and has a moisture content of 0.013 kg/kg dry air.
T;,g,-I----I-T,sw,
Specific gravity of the solid is 1.77 and its heat capacity is
0.39 Cal/g “C. The settling velocity of the largest particle present,
2.5 mmdia, is lOm/sec. Heat capacity of the air is taken as
0.25 Cal/g “C and the latent heat at 60°C as 563 Cal/g. Experimental
data for this system are reported by Nonhebel and Moss (1971, pp.
240ff) and are represented by the expressions:
Heat transfer coefficient:
hn = 0.47 cal/(kg solid)(C)
Vapor pressure:
P = exp(13.7419 - 5237.0/T), atm, K
Mass transfer coefficient:
&a = exp(-3.1811- 1.7388 In w - 0.2553(ln w)*,
where w is the moisture content of the solid (kg/kg) in the units kg
water/(kg solid)(atm)(sec).
In view of the strong dependence of the mass transfer
coefficient on moisture content and the 35-fold range of that
property, the required residence time and other conditions will be
found by analyzing the performance over small decrements of the
moisture content.
An air rate is selected on the assumption that the exit of the
solid is at 85°C and that of the air is 120°C. These temperatures
need not be realized exactly, as long as the moisture content of the
exit air is below saturation and corresponds to a partial pressure less
than the vapor pressure of the liquid on the solid. The amount of
heat transferred equals the sum of the sensible heat of the wet solid
and the latent heat of the lost moisture. The enthalpy balance is
based on water evaporating at 60°C:
iirJ(O.39 + 0.001)(85 - 60) + (0.035 - 0.001)(85 - 60 + 563)]
= fiJ(O.25 + 0.480(0.001))(450 - 120) + 0.48(0.034)(120 - 60)],
fi _ 29.77~~ _ 29.77(9.72)
3.46 kg/set,
0 83.64 83.64 7.08 m3/sec at 450°C
3.85 m3/sec at 120°C.
At a tower diameter of 0.6 m,
“=A=
0.36~14 1
25.0 m/set at 45O”C,
13.6m/sec at 120°C.
These velocities are great enough to carry the largest particles with
settling velocity of 10 m/set.
Equations are developed over intervals in which WI+ W,,
T,+ Tz, and T;+ T;.
The procedure will be:
1. Start with known WI, T,, and T{.
2. Specify a moisture content W,.
3. Assume a value T, of the solid temperature.
4. Calculate T; from the heat balance.
5. Check the correctness of T2 by noting if the times for heat and
mass transfers in the interval are equal.
Q Q
-=
eh = ha(AT),, 0.47(AT),,
Heat balance:
fis[0.391(T,- Tl) + (W, - W&T,- Tl +563)]
= &{[0.25 + 0.48(0.001](T; - T;)
+ 0.48(W, - W,)(T; - 60)).
Substitute fiJfiI, = 9.7213.46 = 2.81 and solve for T&
T;=
-0.25048T; + 28.8(W, - W,) + 2.81
x [0.39(T, - Tl) + (WI - W,)(T, - Tl + 563)]
0.48( WI - W,) - 0.25048
(1)
g, = 0.013 +;;(W, - 0.013) = 0.013 + 2.81(W, - 0.013). (2)
pl= g,
18/29 + g,
= o,62t$ + g, (partial pressure in air). (3)
g, = 0.013 + 2.81(W, - 0.013). (4)
(5)
Pa, = exp[13.7419 - 5237.9/(T, + 273.2)], vapor pressure. (6)
Pa, = exp[13.7419 - 5237.9/(T, + 273.2)]. (7)
(Pa1 - PII - (Pa, - P*)
(“)im =ln[(Pa, - P,)/(Pa, - PJ]
T;-T,-(T;-T,)
(AT)im=ln[(T; - T,)/(T;- TJ]
(8)
(9)
AQ =0.391(&- TJ + (WI - W,)(T,- Tl +563),
per kg of solid. (10)
iir = 0.5(W, + W,). (11)
k,a = exp[-3.1811- 1.7388 In W - 0.2553(ln %‘)*I. (12)
oh = AQ/ha(AT),, = AQ/O.43(AT),,, heating time. (13)
em = (WI - W,)/k,a(AP),,, mass transfer time. (14)
2 = Oh - 8, + 0 when the correct value of T2
has been selected. (15)
After the correct value of Tz has been found for a particular
interval, m a k e W,+ WI, T2+Tl, and T;+ T;. Specify a](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-285-320.jpg)
![EXAMPLE 9.8-(continued)
decremented value of W,, assume a value of TZ, and proceed. The
solution is tabulated.
w T T ’ elsd
0.035 60 450 0
0.0325 73.04 378.2 0.0402
0.03 75.66 352.2 0.0581
0.025 77.41 315.3 0.0872
0.02 77.23 286.7 0.1133
0.015 76.28 261.3 0.1396
0.01 75.15 236.4 0.1687
0.005 74.67 208.4 0.2067
0.003 75.55 192.4 0.2317
0.001 79.00 165.0 0.2841
When going directly from 0.035 to 0.001,
Tz = 80.28,
T; = 144.04,
0=0.3279sec.
The calculation could be repeated with a smaller air rate in order to
reduce its exit temperature to nearer 12O”C, thus improving thermal
efficiency.
In the vessel with diameter = 0.6 m, the air velocities are
1
25.0 m/set at 450°C inlet
” = 5.15 m/set at 165°C outlet
2 0 . 1 m/set average.
The vessel height that will provide the needed residence time is
H = ii,0 = ZO.l(O.2841) = 5.70 m.
Very fine particles with zero slip velocity will have the same
holdup time as the air. The coarsest with settling velocity of
10 m/set will have a net forward velocity of
ti, = 20.1 - 10 = 10.1 m/set,
which corresponds to a holdup time of
0 = 5.7/10.1= 0.56 set,
which is desirable since they dry more slowly.
After the assumption of Tz, other quantities are evaluated in
the order shown in this program.
1 0 ! E x a m p l e 9 . 3 . Pneuma t ic cm
verins d r y e r
2 0 ! Findinq the e x i t s o l i d s t e
rnp T2 br t r i a l , t h e n a l l dep
s n d e n t q u a n t i t i e s
3 0
::
6 0
7 0
;i
100
110
120
130
140
150
160
170
180
190
2 0 0
2 1 0
2 2 0
230
9 . 9 . FLUIDIZED B E D D R Y E R S 2 6 7
I N P U T Wl,W2,Tl,Al ! HI i s t h
e i n l e t a i r temp T l ’
I N P U T T2 ! T r i a l v a l u e
A2=~2.8lS~.391%<T2-Tl~+~Wl-W
2>S{T2-T1+563))-.25048*f11+28
8Y~Wl-W2~~~~.48t~Wl-W2~-.25
848)
G1=.013+2.8ltCWl-.013)
Pl=Gl/C.6207+Gl)
G2=.013+2.81%CW2-.013>
P2=G2/(.6207+G2)
Ql=EXPC13.7419-5237.9/(T1+27
3.2)) ! v a p o r p r e s s u r e
@2=EXPCl3.7419-5237.9,(TZ+Z7
3.2))
P3=<Ql-Pl-Q2+P2~~LOG<~Ql-P1~
/(@2-P2>> ! ChP>lm
T3=CAl-Tl-H2+T2>,LOGO
/CAZ-T2)> ! ChTjlm
Q=.39l*~T2-Tlj+~Wl-W2>~~T2-T
1+563>
Hl=U~.47/T3 ! heatin t i m e
W=.5*cwl+W2>
K=EXPC-3.1811-1.738#*LOGCW>-
.2533SLOGCW)“2)
HZ=CWl-W2j/K/P3 ! vaporizati
o n t i m e
Z=Hl-H2 ! t i m e d i f f e r e n c e s h
o u l d b e zero
D I S P z
DISP A2,Hl
GOTO 40 ! if Z is not near e
noush t o zcroj o t h e r w i s e t h e
c o r r e c t v a l u e o f T 2 h a s bee
n f o u n d
END
D a t a f o r t h e f i r s t i n t e r v a l
Ml= ,035
w2= .0325
T2= 7 3 . 0 4
T3 ’ = 3 7 8 . 1 6 9 6 9 1 1 1
Time= 4.02283660795E-2
9.14(a). This process is faster and much less labor-intensive than
tray drying and has largely replaced tray drying in the pharma-
ceutical industry which deals with small production rates. Drying
rates of 2-lOlb/(hr)(cuft) are reported in this table, with drying
times of a fraction of an hour to several hours. In the continuous
operations of Table 9.15, the residence times are at most a few minutes.
Thermal efficiency of fluidized bed dryers is superior to that of
many other types, generally less than twice the latent heat of the
water evaporated being required as heat input. Power requirements
are a major cost factor. The easily dried materials of Table 9.15(a)
show evaporation rates of 58-1031b/(hr)(HP installed) but the
more difficult materials of Table 9.15(d) show only 5-18 Ib/(hr) (HP
installed). The relatively large power requirements of fluidized bed
dryers are counterbalanced by their greater mechanical simplicity
and lower floor space requirements.
Air rates in Table 9.15 range from 13 to 793 SCFM/sqft, which
is hardly a guide to the selection of an air rate for a particular case.
A gas velocity twice the minimum fluidization velocity may be taken
as a safe prescription. None of the published correlations of
minimum fluidizing velocity is of high accuracy. The equation of
Leva (Fluidization, McGraw-Hill, New York, 1959) appears to be
as good as any of the later ones. It is
G,f = 688D;83[p,(ps - ps)]o.94/po.88,](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-286-320.jpg)
![270 DRYERS AND COOLING TOWERS
TABLE 9.14. Performance Data of Fluidized Bed Dryers: Batch and Multistage Equipment
(a) Batch Dryers
Ammonium
B r o m i d e
Lactose
Base
Granules
Pharmaceutical Liver Weed
Crystals Residue Killer
Holding capacity (lb wet product)
Bulk density, dry (lb/f?)
Initial moisture (% w/w basis)
Final moisture 1% w/w basis)
Final drying temperature 1°F)
Drying time (min)
Fan capacity (fts/min at 11 in. w.g.)
Fan HP
Evaporation rate (lb H,O/hr)
100 104 160 280 250
7 5 3 0 2 0 3 0 3 5
6 10 6 5 5 0 20-25
1 2 0 . 4 5 . 0 1.0
212 158 248 140 140
2 0 9 0 120 7 5 210
750 1500 3000 4000 3000
5 10 2 0 2 5 2 0
1 5 5 . 7 5 2 100 17
(Courtesy Calmic Engineering Co. Ltd.; Williams-Gardner, 1971).
(b) Multistage Dryers with Dual-flow Distributors [Equipment Sketch in Fig. 9.13(b)]
Function Heater Cooler D r i e r Cooler
Material
Wheat
Grains Slag
Particle size (diameter)(mm)
Material feed rate (metric tons/hr)
Column diameter (m)
Perforated trays (shelves):
Hole diameter (mm)
Proportion of active section
Number of trays
Distance between trays (mm)
Total pressure drop on fluidized bed (kgf/m*)
Hydraulic resistance of material on one tray (kgf/m’)
Inlet gas temperature (“C)
Gas inlet velocity (m/set)
Material inlet temperature (“C)
Material discharge temperature (“C)
Initial humidity (% on wet material)
Final humidity (% on wet material)
Blower conditions
Pressure (kgf/m*)
Throughput (ms/min)
5 x 3 5 x 3 0 . 9 5
1.5 1.5 7 . 0
0 . 9 0 0 . 8 3 1.60
2 0
0 . 4
1 0
2 0
113
7 . 8
265
8 . 0 2
6 8
175
2 5
2 . 8
2 0
0 . 4
6
2 0
6 4
9 . 2
3 8
3 . 2 2
175
5 4
20; 10
0.4; 0.4
1; 2
25; 40
708
20; 10
300
4 . 6 0
2 0
170
8
0 . 5
450 250 420 250
180 130 360 100
(80°C) (50°C) (70°C) (35°C)
1 . 4
4 . 0
1.70
2 0
0 . 4
2 0
15
4 0
1.8
2 0
0 . 7 4
350
2 2
-
-
Power consumption (HP) 5 0 2 0 7 5 7 . 5
a With grids and two distributor plates.
(Romankov, in Davidson and Harrison, Fluidisation, Academic, New York, 1971).
drying time is a particular advantage with heat sensitive materials.
Porosity and small size are desirable when the material sub-
sequently is to be dissolved (as foods or detergents) or dispersed
(as pigments, inks, etc.). Table 9.17 has some data on size
distributions, bulk density, and power requirements of the several
types of atomizers.
The mean residence time of the gas in a spray dryer is the ratio
of vessel volume to the volumetric flow rate. These statements are
made in the literature regarding residence times for spray drying:
/feat Exchanger Design Handbook (1983)
McCormick (1979)
Masters (1976)
Nonhebel and Moss (1971)
Peck (1983)
Wentz and Thygeson (1979)
Williams-Gardner (1971)
Time (set)
5-60
2 0
20-40 (parallel flow)
~60
5-30
~60
4-10 (<15ftdia)
lo-20(>15ftdia)
Residence times of air and particles are far from uniform; Figure
9.5(a) and (b) is a sample of such data.
Because of slip and turbulence, the average residence times of
particles are substantially greater than the mean time of the air,
definitely so in the case of countercurrent or mixed flow. Surface
moisture is removed rapidly, in less than 5 set as a rule, but falling
rate drying takes much longer. Nevertheless, the usual drying
operation is completed in 5-30 sec. The residence time distribution
of particles is dependent on the mixing behavior and on the size
distribution. The coarsest particles fall most rapidly and take
longest for complete drying. If the material is heat-sensitive, very
tall towers in parallel flow must be employed; otherwise,
countercurrent or mixed flows with high air temperatures may
suffice. In some cases it may be feasible to follow up incomplete
spray drying with a pneumatic dryer.
Drying must be essentially completed in the straight sided
zones of Figures 9.14(a) and (b). The conical section is for gather-
ing and efficient discharge of the dried product. The lateral throw
of spray wheels requires a vessel of large diameter to avoid](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-289-320.jpg)
![2 7 2 DRYERS AND COOLING TOWERS
TABLE 9.1~(continued)
(d) Data of Rosin Engineering Ltd.
S o d i u m Weed
Perborate Killer P V C Coal S a n d
Method of feed screw vibrator screw vibrator vibrator
Material size 30-200 5-l mm 60-l 20 3 mesh- 30-120
mesh flake mesh zero mesh
Product rate (lb product/hr) 1 1 , 4 0 0 5100 1 0 , 0 7 5 440,000 1 1 2 , 0 0 0
Initial moisture (% w/w basis) 3 . 5 1 4 2 . 0 8 8
Final moisture (% w/w basis) 0 . 0 0 . 2 0 . 2 1 0 . 2
Residence time (min) 1.5 1 1 3 0 0 . 3 0 . 4 5
Drier bed size (ft x ft) 22.5 x 5.5 18 x 4.5 23 x 6 16 x 6.6 12.5 x 3.2
Fluid bed height (in.) 4 3 1 8 5 6
Air inlet temperature (“F) 176 212 167 932 1202
Air outlet temperature (“F) 104 150 122 180 221
Air quantity (fta/min std) 6600 1 4 , 2 0 0 5400 6 7 , 3 3 0 8000
Material exit temperature (“F) 104 205 122 180 212
Evaporation (Ib/hr) 400 720 183 3 3 , 4 4 0 9750
Method of heating steam steam steam coke-oven oil
gas
Heat consumption (Btu/lb water evaporated) 2100 3060 4640 1970 2200
Fan installed HP 3 3 40 34 600 70
(Williams-Gardner, 1971).
EXAMPLE 9.9
Sizing a Fluidiied Bed Dryer
A wet solid at 100°F contains W = 0.3 lb water/lb dry and is to be
dried to W = 0.01. Its feed rate is 100 lb/hr dry. The air is at 350°F
and has H,,= 0.015 lb water/lb dry. The rate of drying is
represented by the equation
- $y= 6O(H, - H,), (Ib/lb)/min.
The solid has a heat capacity 0.35 Btu/(lb)(“F), density 150 Ib/cuft,
and average particle size 0.2pm (0.00787in.). The air has a
viscosity of 0.023 CP and a density of 0.048 Ib/cuft. The fluidized
bed may be taken as a uniform mixture. A suitable air rate and
dimensions of the bed will be found:
I Tg (51.
;Wa,
Hg 5’
_--___--------__
S = 100 Ib/hr
w, = 0 . 3
- - - - - - - -
T,, = 100 F (T,)
A 1 *
Hp,, = 0.015 (H,) w = 0 . 0 1
Tsc = 350 F (T,) Ts (T,)
Symbols used in the computer program are in parentheses.
Minimum fluidizing rate by Leva’s formula:
G
mf
= 688D~s3[0.048(150 - 0.048)]“-94
PS8
= 688(0.C0787)‘s3[0.048(150 - 0.048)]“.94
(0.023)oss
= 17.17 lb/(hr)(sqft).
Let G, = 2G,/ = 34.34 lb/(hr)(sqft).
Expanded bed ratio
(L/Z,,) = (G, /G,,,,)“.22 = 2°.22 = 1.16.
Take voidage at minimum fluidization as
Em, = 0.40,
:. Ef = 0.464.
Drying time:
w,-w 0.3 - 0.01
I3 = 6o(H, - H,) = 6o(H, - Hg)
(2)
Since complete mixing is assumed, H, and H, are exit
conditions of the fluidized bed.
Humidity balance:
i(H, - Hgo) = s(W, - W),
H, = 0.015 + 0.29s/A.
Average heat capacity:
Cg = $(C,, + C,) = 0.24 + 0.45[(0.015 + H,)/2]
= 0.2434 + 0.225H,.
Heat balance:
(3)
AC.&, - T,) = S[(C, + W)(T, - T,,) + nmo - WI,
(&s&(350 - Tg) = 0.36(T, - 100) + 900(0.29). (4)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-291-320.jpg)
![EXAMPLE 9.9-(continued)
Adiabatic saturation line:
T,-T,=$(H,-H,)=F(H,-II,).
g L?
Vapor pressure:
P, = exp[11.9176 - 7173.9/(T, + 389.5)]. (6)
Saturation humidity:
H-18
P,
' 291-e' (7)
Eliminate T3 between Eqs. (4) and (5):
T +,-0.36(& -la)+261
s
RCtz
=T +9WfG-W
4
c&T
, [T3= Tg, T4- T,]. (8)
Procedure: For a specified value of R = A/S, solve Eqs. (6),
(7), and (8) simultaneously.
R T. 7-a Y 4 8 (min)
5 145.14 119.84 0.0730 0.0803 0.862
6 178.11 119.74 0.0633 0.0800 0.289
8 220.09 119.60 0.0513 0.0797 0.170
10 245.72 119.52 0.0440 0.0795 0.136
12 262.98 119.47 0.0392 0.0794 0.120
Take
R = 10 lb air/lb solid,
A = lO(100) = 1000 lb/hr,
0 = 0.136 min.
Cross section:
A/G, = 1000/34.34 = 29.12 sqft, 6.09 ft dia.
Avg density:
$(1/20.96 + l/19.03) = 0.0501 lb/tuft.
Linear velocity:
u=-!?L= 34.34
p&(60) 0.0501(0.464)(60)
= 24.62 fpm.
Bed depth:
L = u8 = 24.62(0.136) = 3.35 ft.
Note: In a completely mixed fluidized bed, the drying time is
determined by the final moisture contents of the air and solid.
9.10. S P R A Y D R Y E R S 273
When drying is entirely in the falling rate period with rate equation
dW WWfJW wsw
--=
d0 WC ’ =’
the drying time will be
w,
’ = k(H, - Hg)W
where H,, H,, and W are final conditions. When the final W is
small, 0.01 in the present numerical example, the single stage drying
time will be prohibitive. In such cases, multistaging, batch drying,
or some other kind of drying equipment must be resorted to.
1e ! Example 9.9. Fluidized bed
38
48
50
68
7 8
88
99
168
110
128
130
140
150
160
170
180
290
210
22B
230
2 4 9
258
268
278
R
I N P U T I? ! =HsSj ratio of r.a?
e5 of flow of air and solid
H3=
,:1=:
015+.29/f? ! =Hq
2434+.225*H3
INPUT T4 ! Trial value o f Ts
GDSUE( 2 0 9
5’1=y
T4=1.0001tT4
GDSUB 288
‘1’2Zjj
K=, 0001*Yl/CY2-Yl>
T4=T4/1 008 1 -K
DISP T 4
IF FiE?SCK.~T42 i=. 00001 T H E N 16
:DTD 69
DISP U S I N G 17r3 i R,T3,T4>H3,
H4.TS
i‘rhtc DD>X,DDD.D,X,DDD.D>X~.
D D D D ,X, .DDDD>X> . D D D
END
! SR for T4
P=EXP{11.9176-7173.9.(T4+3S9
5 j j
H4=18fP./Z9/Cl-P> ! = Hs
TS=T4+9001iHJ-H3)/Cl ! = T9
Y=-T3+358-i.36*<T4-1@0>+261~
/R/C 1
T5=.29x’CH4-H3)JG@ ! = time
RETURN
END
T
-2L s I1s
Time
Hg-------
5 145’.1 119.84 07.X@ @8Q3 ,662
.-
t* 1 7 8 . 1 119.74 .@E;33 .@a#@ ,289
8 2 2 8 . 1 119.61 .0513 .0797 1 i 111
la 2 4 5 . 7 119.53 .0440 ,079s :136
263.8 119.47 .0392 .8794 ,128
2 8 8 . 4 1 1 9 . 4 2 .8343 .a792 .10S](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-292-320.jpg)
![276 DRYERS AND COOLING TOWERS
TABLE 9.17. Particle Diameters, Densities, and Energy
Requirements
(a) Atomizer Performance
Type Size Range (pm)
Power input
(kWh/lOOO L)
Single fluid nozzle
Pneumatic nozzle
Spray wheel
Rotatina CUD
8-800 0.3-0.5
3-250
2-550 0.8-l .O
25-950
(b) Dry Product Size Range
Product w
Skim milk 2 0 - 2 5 0
Coffee 5 0 - 6 0 0
Egga 5 - 5 0 0
Egg white l - 4 0
Color pigments l-50
Detergents 2 0 - 2 0 0 0
Ceramics 15-500
(c) Bulk Density of Sprayed Product as Affected by Air Inlet
Temperature and Solids Content of Feed”
W t 5; s o l i d s i n f e e d
0 . 8
0
d-m
100 200 300 400 500 600
A i r i n l e t , ‘C
‘The full lines are against temperature, the dashed ones against
concentration: (a) sodium silicate; (b) coffee extract, 22%; (c) water
dispersible dye, 19.5%; (d) gelatin.
[Data of Duffie and Marshall, Chem. Eng. Prog. 49, 417 480 (1953)].
accumulation of wet material on the walls; length to diameter ratios
of 0.5-1.0 are used in such cases. The downward throw of nozzles
permits small diameters but greater depths for a given residence
time; L/D ratios of 4-5 or more are used.
ATOMIZATION DESIGN
Proper atomization of feed is the key to successful spray drying.
The three devices of commercial value are pressure nozzles,
pneumatic nozzles, and rotating wheels of various designs. Usual
pressures employed in nozzles range from 300 to 4OOOpsi, and
The design of spray dryers is based on experience and pilot plant
determinations of residence time, air conditions, and air flow rate.
Example 9.10 utilizes such data for the sizing of a commercial scale
spray dryer.
orifice diameters are 0.012-0.15 in. An acceptably narrow range of
droplet sizes can be made for a feed of particular physical properties
by adjustment of pressure and diameter. Multiple nozzles are used
for atomization in large diameter towers. Because of the expense of
motive air or steam, pneumatic nozzles are used mostly in small
installations such as pilot plants, but they are most suitable for
dispersion of stringy materials such as polymers and fibers. The
droplet size increases as the motive pressure is lessened, the range
of 60-100 psi being usual. The action of a rotating wheel is
indicated in Figure 9.14(e). Many different shapes of orifices and
vanes are used for feeds of various viscosities, erosiveness, and
clogging tendencies. Operating conditions are up to 60,000 lb/hr per
atomizer, speeds up to 20,OOOrpm, and peripheral speeds of
250400 ft/sec.
The main variables in the operation of atomizers are feed
pressure, orifice diameter, flow rate and motive pressure for nozzles
and geometry and rotation speed of wheels. Enough is known about
these factors to enable prediction of size distribution and throw
of droplets in specific equipment. Effects of some atomizer
characteristics and other operating variables on spray dryer
performance are summarized in Table 9.18. A detailed survey of
theory, design and performance of atomizers is made by Masters
(1976), but the conclusion is that experience and pilot plant work
still are essential guides to selection of atomizers. A clear choice
between nozzles and spray wheels is rarely possible and may be
arbitrary. Milk dryers in the United States, for example, are
equipped with nozzles, but those in Europe usually with spray
wheels. Pneumatic nozzles may be favored for polymeric solutions,
although data for PVC emulsions in Table 9.16(a) show that spray
wheels and pressure nozzles also are used. Both pressure nozzles
and spray wheels are shown to be in use for several of the
applications of Table 9.16(a).
APPLICATIONS
For direct drying of liquids, slurries, and pastes, drum dryers are
the only competition for spray dryers, although fluidized bed dryers
sometimes can be adapted to the purpose. Spray dryers are capable
of large evaporation rates, 12,000-15,OOOlb/hr or so, whereas a
300sqft drum dryer for instance may have a capacity of only
3000 lb/hr. The spherelike sprayed particles often are preferable to
drum dryer flakes. Dust control is intrinsic to spray dryer
construction but will be an extra for drum dryers. The completely
enclosed operation of spray dryers also is an advantage when toxic
or noxious materials are handled.
THERMAL EFFICIENCY
Exit air usually is maintained far from saturated with moisture and
at a high temperature in order to prevent recondensation of moisture
in parallel current operation, with a consequent lowering of thermal
efficiency. With steam heating of air the overall efficiency is about
40%. Direct fired dryers may have efficiencies of 80-85% with inlet
temperatures of 500-550°C and outlet of 65-70°C. Steam
consumption of spray dryers may be 1.2-1.8 lb steam/lb evapor-
ated, but the small unit of Table 9.19(b) is naturally less efficient. A
10% heat loss through the walls of the dryer often is taken for
design purposes. Pressure drop in a dryer is 15-50in. of water,
depending on duct sizes and the kind of separation equipment used.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-295-320.jpg)
![Product number
278 DRYERS AND COOLING TOWERS
TABLE 9.19. Product Numbers and Performance of a 39 x
29 in. Pilot Plant Spray Dryer
Both forms of the integral are employed in the literature to define
the number of transfer units. The relation between them is
(a) Product Numbers of Selected Materials
Morerial
k,Z/G = (L/G)(NTU).
The height of a transfer unit is
(9.27)
1. COLOURS
Reactive dyes
P i g m e n t s
Dispersed dyes
2. FOODSTUFFS
Carbohydrates
M i l k
Proteins
3. PHARMACEUTICALS
Blood insoluble/soluble
Hydroxide gels
Riboflavin
Tannin
4. RESINS
Acrylics
Formaldehyde resin
Polystyrene
5. CERAMICS
Alumina
Ceramic colours
(Bowen Engineering Inc.).
5m 6
5-11
16-26
14-20
17
16-28
II--22
6-10
15
16-20
IO--II
18-28
12-15
Il.-l5
10
HTU = Z/(NTU) = L/k, = (L/G)(G/k,). (9.28)
The quantity G/k, sometimes is called the height of a transfer unit
expressed in terms of enthalpy driving force, as in Figure 9.16, for
example:
G/k, = (G/L)(HTU). (9.29)
Integration of Eq. (9.21) provides the enthalpy balance around
one end of the tower,
L(T - TJ + G(h -h,). (9.30)
Combining Eqs. (9.22) and (9.23) relates the saturation enthalpy
and temperature,
h, = h + (k,/k,)(T - T,). (9.31)
In Figure 9.15(c), Eq. (9.31) is represented by the line sloping
upwards to the left. The few data that apparently exist suggest that
the coefficient ratio is a comparatively large number. In the absence
of information to the contrary, the ratio commonly is taken infinite,
which leads to the conclusion that the liquid film resistance is
negligible and that the interface is at the bulk temperature of the
water. For a given value of T, therefore, the value of h, in Eq.
(9.25) is found from the equilibrium relation (h,, T,) of water and
the corresponding value of h from the balance Eq. (9.30). When the
coefficient ratio is finite, a more involved approach is needed to find
the integrand which will be described.
The equilibrium relation between T, and h, is represented on
the psychrometric charts Figures 9.1 and 9.2, but an analytical
representation also is convenient. From Section 9.1,
/b)b);tr$rmance of the Pilot Unit as a Function of Product
PROOUCTNUMBER(ORYINGEFFECTIVENESS)
‘Example: For a material with product number = 10 and air inlet
temperature of 500°F. the evaporation rate is 53Ib/hr, input Btu/lb
evaporated = 1930, and the air outlet temperature is 180°F.
(Bowen Engineering).
h, = 0.24T, + (18/29)(0.45T, + llOO)[p,/(l -p,)], (9.32)
where the vapor pressure is represented by
pS = exp[11.9176 - 7173.9/(T, + 389.5)]. (9.33)
Over the limited ranges of temperature that normally prevail in
cooling towers a quadratic fit to the data,
h,=a+bT,+cT;
may be adequate. Then an analytical integration becomes possible
for the case of infinite k,/k,. This is done by Foust et al. (1980) for
example.
The Cooling Tower Institute (1967) standardized their work in
terms of a Chebyshev numerical integration of Eq. (9.25). In this
method, integrands are evaluated at four temperatures in the
interval, namely,
T2 + O.l(T, - T,), corresponding integrand Z1,
q + 0.4( T2 - q), corresponding integrand Z2,
Tl - 0.4(T, - T,), corresponding integrand Z3,
(9.34)
T, - 0. l( Tz - T,), corresponding integrand 4.
Then the integral is
~ = 0.25(T, - Tl)(Il + I2 + Z3 + ZJ. (9.35)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-297-320.jpg)
![9.11. THEORY OF AIR-WATER INTERACTION IN PACKED TOWERS 279
EXAMPLE 9.10
Siziig a Spray Dryer on the Basis of Pilot Plant Data
Feed to a spray dryer contains 20% solids and is to be dried to 5%
moisture at the rate of 5OOlb/hr of product. Pilot plant data show
that a residence time of 6sec is needed with inlet air of 230”F,
H = 0.008 lb/lb, and exit at 100°F. Ambient air is at 70°F and is
heated with steam. Enthalpy loss to the surroundings is 10% of the
heat load on the steam heater. The vessel is to have a 60” cone. Air
rate and vessel dimensions will be found.
Enthalpy, humidity, and temperatures of the air are read off
the psychrometric chart and recorded on the sketch.
W 475 pph
Water 1900 pph
;’
Air
100 F
Enthalpy loss of air is
0.1(69.8 - 28.0) = 4.2 Btu/lb.
Exit enthalpy of air is
h = 69.8 - 4.2 = 65.6.
At 100°F and this enthalpy, other properties are read off the
psychrometric chart as
H = 0.0375 lb/lb,
V= 14.9 tuft/lb.
Air rate is
DW 475 pph -
Water 23 pph
Total 500 pph
A =
1900-25
0.0375 - 0.008
= 63,559 lb/hr
With a residence time of 6 set, the dryer volume is
V, = 287(6) = 1721.4 tuft.
Make the straight side four times the diameter and the cone
60”:
0.866aD3
1721.4 = 40(~-&/4) + 12 = 3.3683D3,
:_ D = 8.0 ft.
When k,/k, --* m, evaluation of the integrands is straightforward.
When the coefficient ratio is finite and known, this procedure may
be followed:
1. For each of the four values of T, find h from Eq. (9.30).
2. Eliminate h, between Eqs. (9.31) and (9.32) with the result
h + @,lk,)(~ - T,)
= 0.24T, + (18/29)(0.451; + llOO)[p,/(l -p,)]. (9.36)
Substitution of Eq. (9.33) into (9.36) will result in an equation
that has T, as the only unknown. This is solved for with the
Newton-Raphson method.
Substitution of this value of T, back into Eq. (9.31) will evaluate
h
Txe integrand l/(h, -h) now may be evaluated at each
temperature and the integration performed with Eq. (9.35).
Example 9.11 employs this method for finding the number of
transfer units as a function of liquid to gas ratio, both with finite and
infinite values of k,/k,. The computer programs for the solution of
this example are short but highly desirable. Graphical methods have
been widely used and are described for example by Foust et al.
(1980).
TOWER HEIGHT
The information that is ultimately needed about a cooling tower
design is the height of packing for a prescribed performance. This
equals the product of the number of transfer units by the height of
each one,
2 = (NTU)(HTU). (9.37)
Some HTU data for cooling tower packing have been published, for
example, those summarized on Figure 9.16. Other data appear in
the additional literature cited for this chapter. Several kinds of
tower fill made of redwood slats are illustrated in Figure 9.17. The
numbers N of such decks corresponding to particular NTLJs and
(L/G)s are given by the equation
N=[(NW -0.071(L~IG)~
a
Values of a and b are given for each type of fill with Figure 9.17.
These data are stated to be for 120°F inlet water. Although the
authors state that corrections should be estimated for other
temperatures, they do not indicate how this is to be done. For
example, with deck type C, NTU =2 and L/G = 1.2: N =
(2 - 0.07)(l.2)“.~/0.092 = 23.4 decks, or a total of 31.2 ft since the
deck spacing is 16 in. The data of Figure 9.16 are used in Example
9.11.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-298-320.jpg)
![9.12. COOLING TOWERS 281
EXAMPLE 9.11
Sizing of a Cooling Tower: Number of Transfer Units and
Height of Packing
Water is to be cooled from 110 to 75°F by contact with air that
enters countercurrently at 90°F with a dewpoint of 60°F. The data of
London et al. (1940) of Figure 9.16 for height of transfer unit are
applicable. Calculations will be made for two values of the
coefficient ratio k,/k,, namely, 25 and m Btu/(“F) (lb dry air), of
Eq. (9.31). The effect of the ratio of liquid to gas rates, L/G, will
be explored.
6 L
T,=llOF
Air Water
x-
L
To2. = 90 T,=75
H = 0.011
h =27
The maximum allowable L/G corresponds to equilibrium
between exit air and entering water at 110. The saturation enthaipy
at 110°F is 92, so that Eq. (9.30) becomes
L
0
z max
=92= 1.857,
110 - 75
The several trials will be made at L/G = (0.6, 1.0, 1.4, 1.7).
The applicable equations with numerical substitutions are listed
here and incorporated in the computer program for solution of this
problem [Eqs. (9.30)-(9.33)]:
h = 27 + (L/G)(T - 75),
h, = h + 25( T - 75),
h, = 0.24T + (18/29)(0.45T + llOO)P,/(l - P,),
P, = exp[11.9176 - 7173.9/(T, + 389.5)].
When k,,Jk,,+m, T, in Eq. (9.33) is replaced by T.
The four temperatures at which the integrands are evaluated
for the Chebyshev integration are found with Eq. (9.34) and
tabulated in the calculation summary following.
Equations (9.30) and (9.31) are solved simultaneously for h and
h, with the aid of the Newton-Raphson method as used in the
computer program; the integrands are evaluated and the integration
are completed with Eq. (9.35).
The number of transfer units is sensitive to the value of L/G,
but the effect of km/k, is more modest, at least over the high range
used; data for this ratio do not appear to be prominently recorded.
Figure 9.16 shows a wide range of heights of transfer units for the
different kinds of packings, here characterized by the surface ad
(sqft/cuft) and substantial variation with L/G. The last line of the
calculation summary shows variation of the tower height with L/G.
Data of London et al. (1940) of Figure 9.16:
(G/L)(HTU) = 5.51(G/L)0.41
or
HTU = 5.51(L/G)0.59.
Tower height:
Z = (HTU)(NTU).
For several values of L/G:
LIG 0.6 1 1.4 1.7
HTU (ft) 4.08 5.51 6.72 7.54
Evaluation of interfacial temp and the NTU for L/G = 1 with
k,/k, = 25:
T h r, l/(h, -h)
78.5 30.5 78.099 0.0864
89 41 88.517 0.0709
96 48 95.400 0.0575
106.5 58.5 105.581 0.0385
0.2533
:. NTU = (110 - 75(0.2533)/4 = 2.217.
For other values of L/G:
l/t&-h)
T h L/G=O.6 1 1.4 1.7
78.5 30.5 0.0751 0.0864 0.0943 0.1043
89 41 0.0518 0.0709 0.1167 0.2200
96 48 0.0398 0.0575 0.1089 0.3120
106.5 58.5 0.0265 0.0385 0.0724 0.1987
- - - -
0.1933 0.2533 0.3923 0.8350
NTU --f 1.691 2.217 3.433 7.306
With k,,,/k,, + 03:
l/U&-h)
T h L/G=0.6 1 1.4 1.7
78.5 30.5 0.0725 0.0807 0.90 0.1006
89 41 0.0494 0.0683 0.1107 0.2070
96 48 0.0376 0.0549 0.1020 0.2854
106.5 106.5 0.0248 0.0361 0.0663 0.1778
- - - -
0.1844 0.2400 0.3700 0.7708
NTU + 1.613 2.100 3.238 8.745
Z-, 6.58 11.57 21.76 50.86](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-300-320.jpg)
![288 MIXING AND AGITATION
Offset
=d/2
Baffle width, <
w-D,/12
Offset = w I6
0)
E
m ”
t
H/3
H/2
Draft tube
:dlB
Figure 10.1. A basic stirred tank design, not to scale, showing a
lower radial impeller and an upper axial impeller housed in a draft
tube. Four equally spaced baffles are standard. H = height of liquid
level, 0, = tank diameter, d = impeller diameter. For radial
impellers, 0.3 5 d/D, 5 0.6.
IMPELLER SPEED
With commercially available motors and speed reducers, standard
speeds are 37, 45, 56, 68, 84, 100, 125, 155, 190, and 320rpm.
Power requirements usually are not great enough to justify the use
of continously adjustable steam turbine drives. Two-speed drives
may be required when starting torques are high, as with a settled
slurry.
I M P E L L E R L O C A T I O N
Expert opinions differ somewhat on this factor. As a first
approximation, the impeller can be placed at l/6 the liquid level off
the bottom. In some cases there is provision for changing the
position of the impeller on the shaft. For off-bottom suspension of
solids, an impeller location of l/3 the impeller diameter off the
bottom may be satisfactory. Criteria developed by Dickey (1984)
are based on the viscosity of the liquid and the ratio of the liquid
depth to the tank diameter, h/D,. Whether one or two impellers are
needed and their distances above the bottom of the tank are
identified in this table:
Viscosity
[cP (Pa set)]
Maximum
level N u m b e r o f
Impeller Clearance
h/4 Impellers L o w e r Upper
<25,000 (~25) 1 . 4 1 h/3 -
<25,000 (~25) 2.1 2 Q/3 W3M
>25,000 (>25) 0 . 8 1 h/3 -
>25,000 (>25) 1.6 2 Q/3 (2/3)h
Another rule is that a second impeller is needed when the liquid
must travel more than 4 ft before deflection.
Side entering propellors are placed 18-24 in. above a flat tank
floor with the shaft horizontal and at a 10” horizontal angle with the
centerline of the tank; such mixers are used only for viscosities
below 500 CP or so.
In dispersing gases, the gas should be fed directly below the
impeller or at the periphery of the impeller. Such arrangements also
are desirable for mixing liquids.
10.2. KINDS OF IMPELLERS
A rotating impeller in a fluid imparts flow and shear to it, the shear
resulting from the flow of one portion of the fluid past another.
Limiting cases of flow are in the axial or radial directions so that
impellers are classified conveniently according to which of these
flows is dominant. By reason of reflections from vessel surfaces and
obstruction by baffles and other internals, however, flow patterns in
most cases are mixed. When a close approach to axial flow is
particularly desirable, as for suspension of the solids of a slurry, the
impeller may be housed in a draft tube; and when radial flow is
needed, a shrouded turbine consisting of a rotor and a stator may
be employed.
Because the performance of a particular shape of impeller
usually cannot be predicted quantitatively, impeller design is largely
an exercise of judgment so a considerable variety has been put forth
by various manufacturers. A few common types are illustrated on
Figure 10.2 and are described as follows:
a. The three-bladed mixing propeller is modelled on the marine
propeller but has a pitch selected for maximum turbulence. They
are used at relatively high speeds (up to 18OOrpm) with low
viscosity fluids, up to about 4OOOcP. Many versions are avail-
able: with cutout or perforated blades for shredding and breaking
up lumps, with sawtooth edges as on Figure 10.2(g) for cutting
and tearing action, and with other than three blades. The
stabilizing ring shown in the illustration sometimes is included to
minimize shaft flutter and vibration particularly at low liquid
levels.
b. The turbine with flat vertical blades extending to the shaft is
suited to the vast majority of mixing duties up to 100,000 CP or
so at high pumping capacity. The simple geometry of this design
and of the turbines of Figures 10.2(c) and (d) has inspired
extensive testing so that prediction of their performance is on a
more rational basis than that of any other kind of impeller.
c. The horizontal plate to which the impeller blades of this turbine
are attached has a stabilizing effect. Backward curved blades
may be used for the same reason as for type e.
d. Turbine with blades are inclined 45” (usually). Constructions
with two to eight blades are used, six being most common.
Combined axial and radial flow are achieved. Especially effective
for heat exchange with vessel walls or internal coils.
e. Curved blade turbines effectively disperse fibrous materials
without fouling. The swept back blades have a lower starting
torque than straight ones, which is important when starting up
settled slurries.
f. Shrouded turbines consisting of a rotor and a stator ensure a
high degree of radial flow and shearing action, and are well
adapted to emulsification and dispersion.
g. Flat plate impellers with sawtooth edges are suited to emul-
sification and dispersion. Since the shearing action is localized,
baffles are not required. Propellers and turbines also are sometimes
provided with sawtooth edges to improve shear.
II. Cage beaters impart a cutting and beating action. Usually they are
mounted on the same shaft with a standard propeller. More violent
action may be obtained with spined blades.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-306-320.jpg)
![290 M I X I N G A N D A G I T A T I O N
i.
J*
k .
I.
Anchor paddles fit the contour of the container, prevent sticking of
pasty materials, and promote good heat transfer with the wall.
Gatepaddlesareusedinwide,shallowtanksandformaterialsofhigh
viscosity when low shear is adequate. Shaft speeds are low. Some
designs include hinged scrapers to clean the sides and bottom of the
tank.
Hollow shaft and hollow impeller assemblies are operated at high tip
speeds for recirculating gases. The gas enters the shaft above the
liquid level and is expelled centrifugally at the impeller. Circulation
rates are relatively low, but satisfactory for some hydrogenations for
instance.
This arrangement of a shrouded screw impeller and heat exchange
coil for viscous liquids is perhaps representative of the many designs
that serve special applications in chemical processing.
10.3. CHARACTERIZATION OF MIXING QUALITY
Agitation and mixing may be performed with several objectives:
1. Blending of miscible liquids.
2. Dispersion of immiscible liquids.
3. Dispersion of gases in liquids.
4. Suspension of solid particles in a slurry.
5. Enhancement of heat exchange between the fluid and the
boundary of a container.
6. Enhancement of mass transfer between dispersed phases.
When the ultimate objective of these operations is the carrying out
of a chemical reaction, the achieved specific rate is a suitable
measure of the quality of the mixing. Similarly the achieved heat
transfer or mass transfer coefficients are measures of their
respective operations. These aspects of the subject are covered in
other appropriate sections of this book. Here other criteria will be
considered.
The uniformity of a multiphase mixture can be measured by
sampling of several regions in the agitated mixture. The time to
bring composition or some property within a specified range (say
within 95 or 99% of uniformity) or spread in values-which is the
blend time-may be taken as a measure of mixing performance.
Various kinds of tracer techniques may be employed, for example:
1. A dye is introduced and the time for attainment of uniform color
is noted.
2. A concentrated salt solution is added as tracer and the measured
electrical conductivity tells when the composition is uniform.
3. The color change of an indicator when neutralization is complete
when injection of an acid or base tracer is employed.
4. The residence time distribution is measured by monitoring the
outlet concentration of an inert tracer that can be analyzed for
accuracy. The shape of response curve is compared with that of a
thoroughly (ideally) mixed tank.
The last of these methods has been applied particularly to
chemical reaction vessels. It is covered in detail in Chapter 17. In
most cases, however, the RTDs have not been correlated with
impeller characteristics or other mixing parameters. Largely this
also is true of most mixing investigations, but Figure 10.3 is an
uncommon example of correlation of blend time in terms of
Reynolds number for the popular pitched blade turbine impeller.
As expected, the blend time levels off beyond a certain mixing
intensity, in this case beyond Reynolds numbers of 30,000 or so.
The acid-base indicator technique was used. Other details of the
test work and the scatter of the data are not revealed in the
published information. Another practical solution of the problem is
typified by Table 10.1 which relates blend time to power input to
10’ l(r 10’ 10”
Reynolds number. D*Nplp
Figure 10.3. Dimensionless blend time as a function of Reynolds
number for pitched turbine impellers with six blades whose
W/D = l/5.66 [Dickey and Fenic, Chem. Eng. 145, (5Jan. 1976)].
vessels of different sizes and liquids of various viscosities. A review
of the literature on blend times with turbine impellers has been
made by Brennan and Lehrer [Trans. Inst. Chem. Eng. 54, 139-152
(1975)], who also did some work in the range lo4 < NRe < lo5 but
did not achieve a particularly useable correlation.
An impeller in a tank functions as a pump that delivers a
certain volumetric rate at each rotational speed and corresponding
power input. The power input is influenced also by the geometry of
the equipment and the properties of the fluid. The flow pattern and
the degree of turbulence are key aspects of the quality of mixing.
Basic impeller actions are either axial or radial, but, as Figure 10.4
shows, radial action results in some axial movement by reason of
deflection from the vessel walls and baffles. Baffles contribute to
turbulence by preventing swirl of the contents as a whole and
elimination of vortexes; offset location of the impeller has similar
effects but on a reduced scale.
Power input and other factors are interrelated in terms of
certain dimensionless groups. The most pertinent ones are, in
common units:
NRe = 10.75Nd2S/p, Reynolds number, (10.1)
Np = 1.523(1013)P/N3d5S, Power number, (10.2)
Np = l.037(10s)Q/Nd3, Flow number, (10.3)
bN, Dimensionless blend time, (10.4)
“Motor horsepowers for various batch volumes, viscosities in cP,
blend times in minutes.
l Denotes single four-bladed, 45” axial-flow impeller (unshaded
selections).
t Denotes portable geardrive mixer with single 1.5-pitch propeller
(“shaded” selections).
(Oldshue, 1983, p. 91).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-308-320.jpg)
![10.3. CHARACTERIZATION OF MIXING QUALITY 291
a b d
Figure 10.4. Agitator flow patterns. (a) Axial or radial impellers without baffles produce vortexes. (b) Offcenter location reduces the vortex.
(c) Axial impeller with baffles. (d) Radial impeller with baffles.
NFr = 7.454(10p4)N2d, Froude number,
d = impeller diameter (in.),
D = vessel diameter (in.),
N = rpm of impeller shaft,
P = horsepower input,
Q = volumetric pumping rate (cuft/sec),
S = specific gravity,
tb = blend time (min) ,
p = viscosity (cP).
(10.5)
The Froude number is pertinent when gravitational effects are
significant, as in vortex formation; in baffled tanks its influence is
hardly detectable. The power, flow, and blend time numbers change
with Reynolds numbers in the low range, but tend to level off above
Nne= 10,ooO or so at values characteristic of the kind of impeller.
Sometimes impellers are characterized by their limiting Np, as an
Np = 1.37 of a turbine, for instance. The dependencies on Reynolds
number are shown on Figures 10.5 and 10.6 for power, in Figure
10.3 for flow and in Figure 10.7 for blend time.
Rough rules for mixing quality can be based on correlations of
power input and pumping rate when the agitation system is
otherwise properly designed with a suitable impeller (predominantly
either axial or radial depending on the process) in a correct
location, with appropriate baffling and the correct shape of vessel.
The power input per unit volume or the superficial linear velocity
can be used as measures of mixing intensity. For continuous flow
reactors, for instance, a rule of thumb is that the contents of the
vessel should be turned over in 5-10% of the residence time.
Specifications of superficial linear velocities for different kinds of
operations are stated later in this chapter. For baffled turbine
agitation of reactors, power inputs and impeller tip speeds such as
0.10
0.01
1 10 100 1000 1 0 0 0 0 100000 1000000
REYNOLDS NUMBER
(a)
Figure 10.5. Power number, N, = PgJN’D’p, against Reynolds
number, NRe = ND*p/y, for several kinds of impellers: (a) helical
shape (OUrhue, 1983); (b) anchor shape (Old&e, 1983); (c)
several shapes: (1) propeller, pitch equalling diameter, without
baffles; (2) propeller, s = d, four baffles; (3) propeller, s = 2d,
without baffles; (4) propeller, s = 2d, four baffles; (5) turbine
impeller, six straight blades, without baffles; (6) turbine impeller,
six blades, four baffles; (7) turbine impeller, six curved blades, four
baffles; (8) arrowhead turbine, four baffles; (9) turbine impeller,
inclined curved blades, four baffles; (10) two-blade paddle, four
baffles; (11) turbine impeller, six blades, four baffles; (12) turbine
impeller with stator ring; (13) paddle without baffles (data of Miller
and Mann); (14) paddle without baffles (data of White and
Summerford). All baffles are of width O.lD [after Rushton, Costich,
and Everett, Chem. Eng. Prog. 46(9), 467 (1950)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-309-320.jpg)
![292 MIXING AND AGITATION
100
80-m
40
20
8.29
6 :
s 2
8
O.B&
$ ,“I;
0 . 1
0.01
- .-_
1 1 0 100 1000 1 0 0 0 0 1 0 0 0 0 0 1000000
REYNOLDS NUMBER
Figure 10.S(continued)
M
the following may serve as rough guides:
Operation HP/1000 gal Tip Speed (ft/.sec)
Blending 0.2-0.5
Homogeneous reaction 0.5-l .5 7.5-10
Reaction with heat transfer 1.5-5.0 10-15
Liquid-liquid mixtures 5 15-20
Liquid-gas mixtures 5 - 1 0 15-20
Slurries 10
The low figure shown for blending is for operations such as
011 I I I I I
I f0 t0O’ IO” to‘ IO5 to6
Re
(c)
incorporation of TEL into gasoline where several hours may be
allowed for the operation.
Example 10.1 deals with the design and performance of an
agitation system to which the power input is specified. Some degree
of consistency is found between the several rules that have been
cited.
10.4. POWER CONSUMPTION AND PUMPING RATE
These basic characteristics of agitation systems are of paramount
importance and have been investigated extensively. The literature is
I
VERTICAL
I
D I S K t
BLADE BLADE
NRe = “D’p/p
VERTICAL CURVED
BLADE BLADE
CURVE 4 CURVE 5
Figure 10.6. Power number against Reynolds number of some turbine impellers [Bates, Fondy, and Corpstein, Ind. Eng. Chem. Process.
Des. Dev. 2(4) 311 (1963)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-310-320.jpg)
![Reynolds number. NR, = D2Np/,,,
Figure 10.7. Flow number as a function of impeller Reynolds
number for a pitched blade turbine with N, = 1.37. D/T is the ratio
of impeller and tank diameters. [Dickey, 1984, 12, 7; Chem. Eng.,
102-110 (26Apr. 1976)].
reviewed, for example, by Oldshue (1983, pp. 155-191), Uhl and
Gray (1966, Vol. l), and Nagata (1975). Among the effects studied
are those of type and dimensions and locations of impellers,
numbers and sizes of baffles, and dimensions of the vessel. A few of
the data are summarized on Figures 10.5-10.7. Often it is
convenient to characterize impeller performance by single numbers;
suitable ones are the limiting values of the power and flow numbers
at high Reynolds numbers, above lO,OOO-30,000 or so, for example:
10.4. POWER CONSUMPTION AND PUMPING RATE 2%
Type No. baffles % 42
Propeller 0 0 . 3
Propeller 3-8 0.33-0.37 0.40-0.55
Turbine, vertical blade 0 0.93-l .08 0.33-0.34
Turbine, vertical blade 4 3-5 0.70-0.85
Pitched turbine, 45” 0 0 . 7 0 . 3
Pitched turbine, 45” 4 1.30-1.40 0.60-0.87
Anchor 0 0 . 2 8
A correlation of pumping rate of pitched turbines is shown as
Figure 10.7.
Power input per unit volume as a measure of mixing intensity
or quality was cited in Section 10.3 and in Chapter 17. From the
correlations cited in this section, it is clear that power input and
Reynolds number together determine also the pumping rate of a
given design of impeller. This fact has been made the basis of a
method of agitator system design by the staff of Chemineer. The
superficial linear velocity-the volumetric pumping rate per pnit
cross section of the tank-is adopted as a measure of quality of
mixing. Table 10.2 relates the velocity to performance of three main
categories of mixing: mixing of liquids, suspension of solids in
slurries, and dispersion of gases. A specification of a superficial
velocity will enable selection of appropriate impeller size, rotation
speed, and power input with the aid of charts such as Figures 10.6
and 10.7. Examples 10.1 and 10.2 are along these lines.
The combination of HP and rpm that corresponds to a
particular superficial velocity depends on the size of the tank, the
size of the impeller, and certain characteristics of the system. Tables
10.3, 10.4, and 10.5 are abbreviated combinations of horsepower
and rpm that are suitable at particular pumping rates for the three
main categories of mixing. More complete data may be found in the
literature cited with the tables.
1. For mixing of liquids, data are shown for a viscocity of 5OOOcP,
but data also have been developed for 25,000 cP, which allow for
EXAMPLE 10.1
Impeller Size and Speed at a Specified Power Input
For a vessel containing 5000 gal of liquid with specific gravity = 0.9
and viscosity of lOOcP, find size and speed of a pitched turbine
impeller to deliver 2 HP/1000 gal. Check also the superficial linear
velocity and the blend time.
The dimensions of the liquid content are 9.5ft high by
9.5 ft dia. Take
d = 0.40 = 0.4(9.5)(12) = 45.6 in., say 46 in., impeller,
P=2V=2(5)=10HP,
N
Re
= 10.75SNd2= 10.75(0.9)(46)‘N = 20,47N
P 1000
N
P
= 1.523(1013)P= 1523(1013)(10) 821,600
N3D5S 0.9(46)5N3 = 7
Solve for N by tria: with the aid of curve 6 of Figure 10.6.
T r i a l N 4. I$ N(Eq. (211
5 6 1146 1.3 8 5 . 8
a 4 1720 1.3 8 5 . 8
Take N = 84 rpm.
According to Figure 10.7 at d/D = 0.4,
N, = 0.61,
Q = NQNd3 = 0.61(84/60)(46/12)3 = 48.1 cfs,
y = 48.1/[(~/4)(9.5)~] = 0.68 fps.
This value corresponds to moderate to high mixing intensity
according to Table 10.2.
From Figure 10.3, at NRe = 1720, blend time is given by
tbN(d/D)Z.3 = 17.0
or
17
r, = ~ - 1.67 min.
84(0.4)2.3 -
According to Table 10.1, the blend time is less than 6min,
which agrees qualitatively.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-311-320.jpg)
![294 MIXING AND AGITATION
TABLE 10.2. Agitation Results Corresponding to Specific Superficial Velocities
ft/!WC Description ftfsec Description
Liquid Systems
0.1-0.2 low degree of agitation; a velocity of 0.2 ft/sec will
a. blend miscible liquids to uniformity when specific
gravity differences are less than 0.1
b. blend miscible liquids to uniformity if the ratio of
viscosities is less than 100
c. establish liquid movement throughout the vessel
d. produce a flat but moving surface
0.3-0.6 characteristic of most agitation used in chemical
processing; a velocity of 0.6ft/sec will
e. blend miscible liquids to uniformity if the specific
gravity differences are less than 0.6
f. blend miscible liquids to uniformity if the ratio of
viscosities is less than 10,000
g. suspend trace solids (less than 2%) with settling
rates of 2-4 ft/min
h. produce surface rippling at low viscosities
0.7-l .o high degree of agitation; a velocity of 1.0 ft/sec will
i. blend miscible liquids to uniformity if the specific
gravity differences are less than 1.0
j. blend miscible liquids to uniformity if the ratio of
viscosities is less than 100,000
k. suspend trace solids (less than 2%) with settling
rates of 4-6 ft/min
I. produce surging surface at low viscosities
Solids Suspension
0.1-0.2 minimal solids suspension; a velocity of 0.1 ft/sec will
a. produce motion of all solids with the design settling
velocity
b. move fillets of solids on the tank bottom and
suspend them intermittently
0.3-0.5 characteristic of most applications of solids suspension
and dissolution; a velocity of 0.3 ft/sec will
0.6-0.8
0.9-l .o
c. suspend all solids with the design settling velocity
completely off the bottom of the vessel
d. provide slurry uniformity to at least one-third of the
liquid level
e. be suitable for slurry drawoff at low exit nozzle
locations
when uniform solids distribution must be approached; a
velocity of 0.6 ft/sec will
f. provide uniform distribution to within 95% of liquid
level
g. be suitable for slurry drawoff up to 80% of liquid
level
when the maximum feasible uniformity is needed. A
velocity of 0.9 ft/sec will
h. provide slurry uniformity to 98% of the liquid level
i. be suitable for slurry drawoff by means of overflow
Gas Dispersion
0.1-0.2
0.3-0.5
0.6-1.0
used when degree of dispersion is not critical to the
process; a velocity of 0.2 ft/sec will
a. provide nonflooded impeller conditions for coarse
dispersion
b. be typical of situations that are not mass transfer
limited
used where moderate degree of dispersion is needed; a
velocity of 0.5 ft/sec will
c. drive fine bubbles completely to the wall of the
vessel
d. provide recirculation of dispersed bubbles back into
the impeller
used where rapid mass transfer is needed; a velocity of
1 .O ft/sec will
e. maximize interfacial area and recirculation of
dispersed bubbles through the impeller
[Chemineer, Co. Staff, Chem. Eng., 102-110 (26 April 1976); 144-150 (24 May 19%); 141-148 (19 July lg76)].
Effects of the Ratios of Impeller and Tank Diameters
Power and rpm requirements will be investigated and compared
with the data of Table 10.3. The superficial velocity is 0.6ft/sec,
V = 5000 gals, Sp Gr = 1.0. Viscosities of 100 CP and 5000 CP will be
considered.
With h/D = 1, D = h = 9.47 ft,
pumping rate Q = 0.6(n/4)(9.47)’ = 42.23 cfs,
N, = l.037(105)Q/Nd3 = 4.3793/Nd3
NRC = 10.7NdzS/p = 0.00214Nd2, /A = 5000,
P = N,N3d5S/1.523(10’3),
(1)
(2)
(3)
N, from Figure 10.6.
For several choices of d/D, solve Eqs. (1) and (2)
simultaneously with Figure 10.7. With p = 5000 cP;
d/D d [E$$] (Fig20.7) % P(HP)
0 . 2 5 2 8 . 4 300 0 . 6 3 7 518 0 . 6 4 1.4 4 5 . 9
0 . 3 3 3 7 . 5 145 0 . 5 7 3 436 0 . 5 7 1 . 4 5 2 1 . 5
0 . 5 0 5 6 . 8 5 2 0 . 4 6 0 359 0 . 4 5 1.5 8.2
With p = 100 cP, turbulence is fully developed.
d/D d N nb 4. (Fig%l.7) NP P
0 . 2 5 2 8 . 4 228 0.839 1 8 , 9 9 0 0 . 8 4 1.3 18.7
0 . 3 3 3 7 . 5 112 0.742 1 6 , 8 5 0 0 . 7 4 1.3 8 . 9
0 . 5 0 5 6 . 8 40 0.597 1 3 , 8 0 0 0 . 6 0 1.3 3 . 2
Table 10.3 gives these combinations of HP/rpm as suitable: 25/125,
20/1OO, 10/56, 7.5/37. The combination lo/56 checks roughly the
last entry at 5OOOcP. Table 10.3 also has data for viscosities of
25,OOOcP, thus allowing for interpolation and possibly extra-
polation.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-312-320.jpg)
![10.5. SUSPENSION OF SOLIDS 2%
TABLE 10.3. Mixing of Liquids; Power and Im eller Speed (hp/rpm) for
Two Viscosities, as a Function oPthe Liquid Superficial
Velocity; Pitched Blade Turbine Impeller
ftfsec 1 0 0 0
5OoocP
2000
Volume (gal)
5000 1 0 0 0
25,000 CP
2000 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2/280 2/190
l/l90 l/100
21190
l/100
21125
m4
1.5184
21125 3/84
1.5184 I.5156
m4
1.5156
51125
3184
51125
3168
3/56
2/45
7.51125
5184
5/100
3168
3156
2/45
7.5/125
5/w
151155
lO/lOO
7.5184
3137
lo/84
7.5168
5145
lo/125 10168
7.5/100 7.5156
151155 15184
lo/loo lo/56
7.5184 7.5145
10164
7.5168
30/155 50/100
251125 40184
20/m 30/68
15168 25156
2/100
51125
3184
3168
2145
7.51125
5/100
5184
3156
lo/84
7.5168
5/45
3137
15/100
10/68
7.5145
251125
20/100
lo/56
7.5/37
15168
15156
10145
10137
30/100
25184
20168
15145
601155
40/100
2/125 -a34
1.5184 1.5156
3/84
2184
1.5156
51125
5184
3166
2145
7.5184
5156
5/125
3184
3168
2145
151155
7.5168
5145
3137
lo/84
7.5145
151155
lO/lOO
lo/84
7.5/68
201155
151125
25/155
15164
30/155
251125
20/100
251125
20/100
15184
IO/56
251100
15168
15156
10/45
401155
30/100
25184
20168
50/155
401125
401155
30/125
25/100
401125
30/100
751190
60/155
40/100
30/68
60/125
50/100
50/84
40184
7.51125
5/100
5/84
3156
lo/84
7.5168
5145
3137
20/100
15168
10145
7.5137
30/100
25184
20/68
1OJ37
751190
601155
40/100
15/45
40184
30168
25156
20137
751125
50184
30145
751100
60/64
50168
40/56
75184
60/68
50156
1251125
100/100
75/68
60/56
[Hicks, Morton, and Fenic, Chem. Eng., 102-110 (26 April 1976)].
interpolation and possibly extrapolation. The impeller is a
pitched-blade turbine.
2. For suspension of solids, the tables pertain to particles with
settling velocities of lOft/min, but data are available for
25 ft/min. The impeller is a pitched-blade turbine.
3. For gas dispersion the performance depends on the gas rate.
Data are shown for a superficial inlet gas rate of 0.07 ft/sec, but
data are available up to 0.2 ft/sec. Four baffles are specified and
the impeller is a vertical blade turbine.
Example 10.2 compares data of Table 10.4 with calculations
based on Figures 10.6 and 10.7 for all-liquid mixing. Power and rpm
requirements at a given superficial liquid velocity are seen to be
very sensitive to impeller diameter. When alternate combinations of
HP/rpm are shown in the table for a particular performance, the
design of the agitator shaft may be a discriminant between them.
The shaft must allow for the torque and bending moment caused by
the hydraulic forces acting on the impeller and shaft. Also, the
impeller and shaft must not rotate near their resonant frequency.
Such mechanical details are analyzed by Ramsey and Zoller [Chem.
Eng., 101-108 (30 Aug. 1976)].
10.5. SUSPENSION OF SOLIDS
Besides the dimensions of the vessel, the impeller, and baffles,
certain physical data are needed for complete description of a slurry
mixing problem, primarily:
1. Specific gravities of the solid and liquid.
2. Solids content of the slurry (wt %).
3. Settling velocity of the particles (ft/min).
The last of these may be obtained from correlations when the
mesh size or particle size distribution is known, or preferably
experimentally. Taking into account these factors in their effect on
suspension quality is at present a highly empirical process. Tables](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-313-320.jpg)
![TABLE 10.5. Dispersion of Gases; Power and Impeller Speed
(hr/r m) for Two Gas Inlet Superficial Velocities,
as a Punction of the Liquid Superficial Velocity;
Vertical Blade Turbine Impeller
Volume (gal)
0.07ftJsec 0.20 */set
R/set 1500 3000 5000 1500 3000 5000
0.1 2156 5/m
0.2 2145 7.51125
0.3 3184
3168
3J56
0.4
0.5
0.6
51125
5184
5JlOO
5J45
7.51125
7.51155
7.5/68
7.5184
lOJ84
10/100
7.5168
5145
7.5/84
5156
lo/84
1 O/l 00
1o/45
lo/56
15/l 55
15J68
15184
15145
20/l 00
20;45
0.7 lo/56
0.8 15/l 55
15184
25/l 25
25/84
25/l 00
25156
30/l 55
3OJlOO
301125
0.9
1.0
15168 3OJ68
401155
40184
7.5168
151155
IO/84
7.5145
1o/45
1O/56
15168
20/l 00
15184
20168
25/l 25
25184
25JlOO
25156
30/l 55
3OJlOO
30/l 25
30168
40/l 55
40184
40/l 00
40156
50/l 00
w@J
50184
50145
60/l 25
60/l 55
60184
60156
751190
75/100
751125
3156
3145
5/100
5184
7.51155
5156
7.51125
7.5168
7.5/84
1 O/84
10/100
lo/56
151155
f5/84
15168
7.5168
lO/lOO
151155
1O/84
7.5145
1o/45
1 O/56
15168
15184
15145
15156
20/l 00
20168
251125
25184
25/100
25156
3OJl55
30/100
30/l 25
25/l 25 40/l 55
25184 40184
1o/45 SYSTEM DESIGN
15168
20/100
251125
The impeller commonly used for gas dispersion is a radial turbine
with six vertical blades. For a liquid height to diameter ratio
hfD 11, a single impeller is adequate; in the range 1 rh/Ds1.8
two are needed, and more than two are rarely used. The lower and
upper impellers are located at distances of l/6and 2/3 of the liquid
level above the bottom. Baffling is essential, commonly with four
baffles of width l/l2 that of the tank diameter, offset from the wall
at l/6 the width of the baffle and extending from the tangent line of
the wall to the liquid level. The best position for inlet of the gas is
below and at the center of the lower impeller; an open pipe is
commonly used, but a sparger often helps. Since ungassed power is
significantly larger than gassed, a two-speed motor is desirable to
prevent overloading, the lower speed to cut in automatically when
the gas supply is interrupted and rotation still is needed.
30/l 55
20168
15145
15156
25184
25/100
25/56
30/100
30/125
30168
30145
40/l55
40184
4OJlOO
40156
5OJlOO
50168
50184
50/56
60/125
60/155
60184
60/56
751190
75JlOO
75/l 25
[Hicks and Gates, Chem. Eng., 141-148 (13 July 1976)].
MASS TRANSFER
The starting point of agitator design is properly a mass transfer
coefficient known empirically or from some correlation in terms of
parameters such as impeller size and rotation, power input, and gas
flow rate. Few such correlations are in the open literature, but
some have come from two of the industries that employ aerated
stirred tanks on a large scale, namely liquid waste treating
and fermentation processes. A favored method of studying the
absorption of oxygen is to measure the rate of oxidation of aqueous
sodium sulfite solutions. Figure 10.9 summarizes one such
investigation of the effects of power input and gas rate on the mass
transfer coefficients. A correlation for fermentation air is given by
Dickey (1984, 12-17):
k,a = rate/(concentration driving force)
= O.O64(P /V)“.7ut2,
i? l/set, (10.6)
with P,/V in HP/1000 gal and superficial gas velocity ur in ft/sec. A
general correlation of mass transfer coefficient that does not have
10.6. GAS DISPERSION 297
power input as a factor is given by Treybal (Ma.ss Transfer
Operations, McGraw-Hill, New York, 1980, 156); presumably this
is applicable only below the minimum power input here represented
by Figure 10.11.
When mass transfer coefficients are not determinable, agitator
design may be based on superficial liquid velocities with the criteria
of Table 10.2.
MINIMUM POWER
Below a critical power input the gas bubbles are not affected
laterally but move upward with their natural buoyancy. This
condition is called gas flooding of the impeller. At higher power
inputs the gas is dispersed radially, bubbles impinge on the walls
and are broken up, consequently with improvement of mass
transfer. A correlation of the critical power input is shown as Figure
10.10.
POWER CONSUMPTION OF GASSED LIQUIDS
At least partly because of its lower density and viscosity, the power
to drive a mixture of gas and liquid is less than that to drive a liquid.
Figure 10.11(a) is a correlation of this effect, and other data at low
values of the flow number Q/Nd3 are on Figure 10.11(b). The latter
data for Newtonian fluids are correlated by the equation
P,lP = 0.497(Q/Nd3)-0.38(N2d3p,/u)-o.18, (10.7)
where the last group of terms is the Weber number, pL is the
density of the liquid, and u is its surface tension.
SUPERFICIAL LIQUID VELOCITY
When mass transfer data are not known or are not strictly pertinent,
a quality of mixing may be selected by an exercise of judgment in
terms of the superficial liquid velocity on the basis of the rules of
Table 10.2. For gas dispersion, this quantity is related to the power
input, HP/1000 gal, the superficial gas velocity and the ratio d/D in
Figure 10.12.
DESIGN PROCEDURES
On the basis of the information gathered here, three methods are
possible for the design of agitated gas dispersion. In all cases the
size of the tank, the ratio of impeller and tank diameters and the
gas feed rate are specified. The data are for radial turbine impellers
with six vertical blades.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-315-320.jpg)
![298 MIXING AND AGITATION
SLURRY VOL. - m3
I;~ 7 ; 1; 172; 3p40TOqO 1;
1000 2000 4000 6000 10000 20000 30000
SLURRY VOL. - GRLLONS
(a)
S E T T L ING VELOCITY (m04IN.l
I I I I I
1.0 2.0 3.0 4.06.0 8.0 10.0 2t D
SETTLING VELOCITY (FT./MIN.l
(c)
1.0 -
0.9 -
0.8 -
0.7 -
0.6 -
0.5
0.51 I IIII I
I IIII I I
I I
0.3
0.3 0.4
0.4 0.50.60.7
0.50.60.7 0.8
0.8 1.0
1.0 1.5
1.5 2.0
2.0
Z/T
Z/T
b)
I- 100 HP
300
200 6 0
4 0
100
8 0 2 5
6 0
4 0
3 0
2 0
10.0
8.0
k8”
0..6
0.4
0.3
0.2
-._
0.10.2 0.30.4 0.6
D/T
id)
??igure 10.8. Suspension of solids. Power and ratio of diameters of impeller and tank, with four-bladed 45” impeller,
width/diameter = 0.2. [method of Oldrhue (1983)]. (a) The factor on power consumption for slurry volume, Ft. (b) The
factor on power requirement for single and dual impellers at various h/D ratios, Fa. (c) The effect of settling velocity
on power consumption, Fs. (d) Suspension factor for various horsepowers: F4 = F,F,F,.](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-316-320.jpg)
![1 0 . 6 . G A S D I S P E R S I O N 2%
Design of the Agitation System for Maintenance of a Slurry
These conditions are taken:
V = 5000 gal,
h/D = 1,
settling velocity = 10 ft/min,
solids content = 10 wt %
Reading from Figure 10.8,
F, = 4,
&=l.l,
off bottom,
uniform.
The relation between the ratio of impeller and vessel diameters,
d/D and HP is read off Figure 10.8(d).
H P
d/D Off btm Uniform
0.2 20 65
0.4 7.5 25
0.6 4 12
Comparing with readings from Tables 10.2 and 10.3,
Superficial
liq. velocity HP/rpm
0.3 (off btm) 1 O/45,1O/56
0.6 (uniform) 30/155,30/125,30/100,30/68
These results correspond roughly to those of the Oldshue
method at d/D = 0.4. The impeller sizes can be determined with
Figures 10.6 and 10.7.
Start with a known required mass transfer coefficient. From a
correlation such as Figure 10.9 or Eq. (10.6) the gassed power
per unit volume will become known, and the total gassed power
to the tank will be Pg. The ratio of gassed power to ungassed
power is represented by Figure 10.11(a) and the equations given
there; at this stage the rotation speed N is not yet known. This
value is found by trial by simultaneous solution with Figure 10.6
which relates the Reynolds and power numbers; the power here
is the ungassed power. The value of N that results in the
precalculated Pg will be the correct one. Curve 2 of Figure 10.6 is
the one applicable to gas dispersion with the data of this section.
Start with a choice of superficial liquid velocity uL made in
accordance with the criteria of Table 10.2. With the aid of the
known gas velocity U, and d/D, find P,/V from Figure 10.12.
Then proceed to find N by trial with Figures 10.11(a) and 10.6 as
in method 1.
0 . 1
I 1
I
D/T = .25-.40
LB MOLES
FT3/HR/ATM .02
0 . 3 0 . 6 1 . 0 2 . 0 4 . 0 8 . 0 1 0
HP / 1000 GAL. GASSED
FIgare 10.9. Typical data of mass transfer coefficients at various
power levels and superficial gas rates for oxidation of sodium sulfite
in aqueous solution. d/D = 0.25-0.40 (O&hue, 1983).
3. As soon as a superficial liquid velocity has been selected, a
suitable combination of HP/rpm can be taken from Table 10.5.
These procedures are applied in Example 10.4.
As general rules, levels of 5-12HP/lOOOgal are typical of
aerobic fermentation vessels. and 1-3 HP/1000 gal of aerobic waste
treatment; concentrations and oxygen requirements of the
microorganisms are different in the two kinds of processes.
Superficial gas relocity. 1 t/s
Figure 10.10. Minimum power requirement to overcome flooding as
a function of superficial gas velocity and ratio of impeller and tank
diameters, d/D. [Hicks and Gates, Chem. Eng., 141-148 (19 July
1976)].](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-317-320.jpg)
![300 MIXING AND AGITATION
( )
%
T
,
0 . 0
0.1
0.S
0 . 5 +-
0 0:02 0.64 O.&S 0.6s
(i-y
(t-4
Figure 10.11. Power consumption. (a) Ratio of power consumptions
of aerated and unaerated liquids. Q is the volumetric rate of the
gas: (0) glycol; ( x ) ethanol; (v) water. [After Calderbank, Trans.
Inst. Chem. Eng. 36, 443 (1958)]. (b) Ratio of power consumptions
of aerated and unaerated liquids at low values of Q/Nd3. Six-bladed
disk turbine: (Cl) water; (0) methanol (10%); (A) ethylene glycol
(8%); (A) glycerol (40%); P’ = gassed power input; P = ungassed
power input; Q = gas flow rate; N = agitator speed; d = agitator-
impeller diameter. [Luong and Volesky, AIChE J. 25, 893 (1979)].
10.7. IN-LINE BLENDERS AND MIXERS
When long residence time is not needed for chemical reaction or
other purposes, small highly powered tank mixers may be suitable,
with energy inputs measured in HP/gal rather than HP/lOOOgal.
They bring together several streams continuously for a short contact
time (at most a second or two) and may be used whenever the
effluent remains naturally blended for a sufficiently long time, that
is, when a true solution is formed or a stable emulsion-like mixture.
When it is essential that the mixing be immediate each stream will
1
& 0.8
5 0.6
‘;
2 0.4
>II
0 . 2
0.1
4 . 6 80.1 2 4 6 8 1 2
X = (P/V)(d/D)‘=
Figure 10.12. Relation between power input, P/VHP/lOOOgal,
superficial liquid velocity u,ft/sec, ratio of impeller and tank
diameters, d/D, and superficial gas velocity u, ft/sec. [Hicks and
Gates, Chem. Eng., 141-148 (19JuZy 1976)].
have its own feed nozzle, as in Figure 10.13(b), but usually the
streams may be combined externally near the blender and then
given the works, as in Figure 10.13(a).
One manufacturer gives these power ratings:
Tanksize (gal) 1 5 10 30
M o t o r H P 0.5 1 2 3
Another ties in the line and motor sizes:
Line size, (in.) l - 4 6-8 10-12
M o t o r H P 0.5 1 2
But above viscosities of 1OcP a body one size larger than the line
size is recommended.
Other devices utilize the energy of the flowing fluid to do the
mixing. They are inserts to the pipeline that force continual changes
of direction and mixing. Loading a section of piping with tower
packing is an example but special assemblies of greater convenience
have been developed, some of which are shown in Figure 10.14. In
each case manufacturer’s literature recommends the sizes and
pressure drops needed for particular services.
The Kenics mixer, Figure 10.14(a), for example, consists of a
succession of helical elements twisted alternately in opposite
directions. In laminar flow for instance, the flow is split in two at
each element so that after n elements the number of striations
becomes 2”. The effect of this geometrical progression is illustrated
in Figure 10.14(b) and points out how effective the mixing becomes
after only a few elements. The Reynolds number in a corresponding
empty pipe is the major discriminant for the size of mixer, one
manufacturer’s recommendations being
4, Number of Elements
Less than 10 2 4
10-2000 12-18
More than 2000 6
Besides liquid blending applications, static mixers have been
used for mixing gases, pH control, dispersion of gases into liquids,
and dispersion of dyes and solids in viscous liquids. They have the
advantages of small size, ease of operation, and relatively low cost.
The strong mixing effect enhances the rate of heat transfer from
viscous streams. Complete heat exchangers are built with such](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-318-320.jpg)
![1 0 . 8 . M I X I N G O F P O W D E R S A N D P A S T E S 301
EXAMPLE 10.4
HP and ‘pm Requirements of an Aerated Agitated Tank
A tank contains 5OOOgal of liquid with sp gr = 1.0 and viscosity
1OOcP that is aerated and agitated. The ratio of impeller to tank
diameters is d/D = 0.4. Two sets of conditions are to be examined.
a. The air rate is 972SCFM or 872ACFM at an average
submergence of 4 ft. The corresponding superficial gas velocity is
0.206ft/sec or 0.063 m/set. A mass transfer coefficient
k,a = 0.2/set is required; Dickey’s equation (10.6) applies. Find
the power and rpm needed.
b. The air rate is 296ACFM, 0.07 ft/sec, 0.0213 m/set. The
required intensity of mixing corresponds to a liquid superficial
velocity of 0.5 ft/sec. Find the power, rotation speed, and mass
transfer coefficients for sulfite oxidation and for fermentation.
a . d=0.4(9.47)=3.79ft,45.46in.,
k,a = 0.064(P,/V)“~7u~2 = 0.2,
P,/V = [0.2/0.064(0.206)“~2]“o~7 = 8.00 HP,
Pg = 5(8.0) = 40.0 HP/5000 gal,
Q/Nd3 = 872/(379)3N = 16.02/N,
NRe = 10.75Nd2S/p = 10.75(45.46)2N/100 = 222N.
Equation (10.2),
N, = 1.523(10’3)P/N3dSS = 78,442P/N3.
Curve 2 of Figure (10.6) applies. P,/P from Figure 10.10(a). Solve
by trial.
N Cl/Nd” p,/P NRs N,, P 4
100 0.160 0.324 22,200 4 51 16.5
150 0.107 0.422 33,300 4 172 72.6
127 0.1261 0.3866 28,194 4 104.5 40.4-40.0
The last entry of Pp checks the required value 40.0. Find the
corresponding superficial liquid velocity with Figure 10.12:
X = (P/V)(d/D)‘.” = 8.04(0.4)‘-85 = 1.48,
at uG = 0.206 ft/sec, Y = 2.0,
:. uL = 2/10(0.4)‘-* = 0.60 ftlsec.
From Table 10.2, a liquid velocity of 0.6-0.7 ft/sec will give
moderate to high dispersion. Table 10.5 gives possible HP/rpm
combination of 30/125, somewhat less than the value found here.
b. With liquid circulation velocity specified,
uL = 0.5 ftlsec.
Use Figure 10.12:
Y = iou,(d/D)‘.2 = 10(0.5)(0.4)‘.’ = 1.67,
X= 0.8,
P,IV = 0.8/(0.4)‘-85 = 4.36 HP/1000 gal
(this does exceed the minimum of 1.6 from Figure lO.ll),
P, = 5(4.36) = 21.8,
$ = 296/(3.79)3N = 5.437/N,
NRe = 222N (part a),
N=y (part a).
Solve by trial, using Figure 10.10(a) and curve 2 of Figure 10.6.
N O/N2 p,/P 47. q7 p 5
100 0.0544 0.5194 22,200 4 51 26.5
94 0.0576 0.5130 4 42.35 21.7-2.8
The closest reading from Table 10.5 is HP/rpm = 25/100 which is a
good check.
For sulfite oxidation, at ug = 0.07 ft/sec,
P,/V = 4.36 HP/1000 gal, from Figure 10.9,
k,a = 0.07 lb mol/(cuft)/(hr)(atm).
For fermentation, Eq. 10.6 gives
k,a = 0.064(4.36)“.7(0. 07)“.2
= o, 1o5 lb mol/(cuft)(sec)
lb mol/cuft
mixing inserts in the tubes and are then claimed to have 3-5 times
normal capability in some cases.
10.8. MIXING OF POWDERS AND PASTES
Industries such as foods, cosmetics, pharmaceuticals, plastics,
rubbers, and also some others have to do with mixing of high
viscosity liquids or pastes, of powders together and of powders with
pastes. Much of this kind of work is in batch mode. The processes
are so diverse and the criteria for uniformity of the final product are
so imprecise that the nonspecialist can do little in the way of
equipment design, or in checking on the recommendations of
equipment manufacturers. Direct experience is the main guide to
selection of the best kind of equipment, predicting how well and
quickly it will perform, and what power consumption will be. For
projects somewhat out of direct experience and where design by
analogy may not suffice, testing in pilot plant equipment is a service
provided by many equipment suppliers.
A few examples of mixers and blenders for powders and pastes
are illustrated in Figure 10.15. For descriptions of available
equipment-their construction, capacity, performance, power
consumption, etc.--the primary sources are catalogs of manufac-
turers and contact with their offices. Classified lists of manu-
facturers, and some of their catalog information, appear in the
Chemical Engineering Catalog (Reinhold, New York, annually)
and in the Chemical Engineering Equipment Buyers Guide
(McGraw-Hill, New York, annually). Brief descriptions of some
types of equipment are in Perry’s Chemical Engineers Handbook
(McGraw-Hill, New York, 1984 and earlier editions). Well-classified
descriptions, with figures, of paste mixers are in Ullmann (1972,](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-319-320.jpg)
![310 SOLID-LIQUID SEPARATION
EXAMPLE 11.1
Constants of the Filtration Equation from Test Data
Filtration tests were performed on a CaCO, slurry with these
properties:
C = 135 kg solid/m3 liquid,
y = 0.001 N set/m’.
The area of the filter leaf was 500cm2. Data were taken of the
volume of the filtrate (L) against time (set) at pressures of 0.5 and
0.8 bar. The results will be analyzed for the filtration parameters:
0 . 5 bar 0 . 8 bar
u V/A t t/(VlA) t t/(V/Al
0.5 0.01 6.8 680 4.8 480
1 0.02 19.0 950 12.6 630
1.5 0.03 36.4 1213 22.8 760
2 0.04 53.4 1335 35.6 890
2.5 0.05 76.0 1520 50.5 1010
3 0.06 102.0 1700 69.0 1150
3.5 0.07 131.2 1874 88.2 1260
4 0.08 163.0 2038 112.0 1400
4.5 0.09 - -
5 0.10 165.0 1650
The units of V/A are m3/m2. Equation (11.2) is
d(VIA) A P
-zz
dt ,u(Rr + c&V/A) ’
whose integral may be written
R, LYC v t
~-
AP/p + 2(AP/p) A = m
Intercepts and slopes are read off the linear plots. At 0.5 bar,
AP/p = 0.5(105)/0.001 = OS(lO’),
Rf = 6OOAP/P = 3.0(10”) m-i,
(Y = [18,000(2)/C]AP/~ = 36,ooO(0.5)(10*)/135
= 1.333(10i”) m/kg.
At 0.8 bar,
AP/p = 0.8(108),
Rf = 375(0.8)(10’) = 3(10i”) m-‘,
(Y= 12,750(2)(0.8)(10s)/135 = 1.511(10’“) m/kg.
Fit the data with Almy-Lewis equation, Eq. (11.24),
(Y = kp”,
ln(cr,/cu,)
n=ln(P,lP,)=
ln(1.511/1.333) = o,2664
ln(0.8/0.5)
k = 1.511(10’“)/0.80-~661 = 1.‘604(10’“),
:. (Y= 1.604(10’“)Po~2664, m/kg, P in bar.
2000
1500
t
3 1000
2
.
500
0
r
I-
l-
/
/
0
I I I I I
0.02 0.04 0.06 0.08 0.10
V / A -
Basic filtration Eq. (11.2) is solved for the amount of filtrate,
(11.10)
Equations (11.8) and (11.10) are solved simultaneously for AP and
Q at specified values of V and the results tabulated so:
V AP Q l/Q t
0 - - - 0
- - - - -
V‘i”., - - - t‘,“a,
Integration is accomplished numerically with the Simpson or
trapezoidal rules. This method is applied in Example 11.2.
When the filtrate contains dissolved substances that should not
remain in the filter cake, the occluded filtrate is blown out; then the
cake is washed by pumping water through it. Theoretically, an
amount of wash equal to the volume of the pores should be
sufficient, even without blowing with air. In practice, however, only
30-85% of the retained filtrate has been found removed by
one-displacement wash. Figure 11.3(b) is the result of one such test.
A detailed review of the washing problem has been made by
Wakeman (1981, pp. 408-451).
The equations of this section are applied in Example 11.3 to
the sizing of a continuous rotary vacuum filter that employs a
washing operation.
COMPRESSIBLE CAKES
Resistivity of filter cakes depends on the conditions of formation of
which the pressure is the major one that has been investigated at
length. The background of this tcpic is discussed in Section 11.3,
but here the pressure dependence will be incorporated in the
filtration equations. Either of two forms of pressure usually is
taken,
Lr = cu,P” (11.11)
or
(Y = a,(1 + kP)“. (11.12)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-329-320.jpg)
![11.2. THEORY OF FILTRATION 311
EXAMPLE 11.2
Filtration Process with a Centrifuyl Charge Pump
A filter press with a surface of 50m handles a slurry with these
properties:
p = 0.001 N set/m’,
C = 10 kg/m3,
a= l.l(lO’i) m/kg,
Rf= 6.5(10’“) m-i.
The feed pump is a centrifugal with a characteristic curve
represented by the equation
trapezoidal rule:
V AP 0 t (hd
0 0.1576 43.64 0
10 0.6208 39.27 0.24
20 0.9896 35.29 0.51
30 1.2771 31.71 0.81
40 1.4975 28.53 1.14
60, 5; 1.6648 , 25.72 1.;
,
AP = 2 - Q(O.OO163Q - 0.02889), bar (1)
with Q in m3 hr. Find (a) the time required to obtain 50m3 of
filtrate; (b) the volume, flow rate, and pressure profiles. Equation
(11.2) of the text solved for V becomes
V=$c *$-pRf
i >
- 6.5(107)]
>
(2)
Equations (1) and (2) are solved simultaneously to obtain the
tabulated data. The time is found by integration with the
The first of these does not extrapolate properly to resistivity at low
pressures, but often it is as adequate as the more complex one over
practical ranges of pressure.
Since the drag pressure acting on the particles of the cake
varies from zero at the face to the full hydraulic pressure at the filter
cloth, the resistivity as a function of pressure likewise varies along
the cake. A mean value is defined by
(11.13)
where AP, is the pressure drop through the cake alone. In view of
the roughness of the usual correlations, it is adequate to use the
overall pressure drop as the upper limit instead of the drop through
the cake alone.
With Eq. (11.12) the mean value becomes
c~,k(l - n)AP
’ = (1 + kAP)‘-“- 1’
The constants (Ye, k, and n are determined most simply in
compression-permeability cells as explained in Section 11.4, but
those found from filtration data may be more appropriate because
the mode of formation of a cake also affects its resistivity.
Equations (11.14) and (11.2) together become
cu,ck(l- n)AP V -*
Rf+(l+kAp)“-‘-l~
1 ’ (11.15)
which integrates at constant pressure into
(11.16)
The four unknown parameters are cro, k, n, and Rr. The left-hand
side should vary linearly with V/A. Data obtained with at least
three different pressures are needed for evaluation of the
parameters, but the solution is not direct because the first three
parameters are involved nonlinearly in the coefficient of V/A. The
analysis of constant rate data likewise is not simple.
The mean resistivity at a particular pressure difference can be
evaluated from a constant pressure run. From three such
runs-AP,, AP,, and AP3-three values of the mean resistivity-
&i, Su,, and %,-can be determined with Eq. (11.2) and used to find
the three constants of the expression for an overall mean value,
E = rro(l + kAP)“, (11.17)
which is not the same as Eq. (11.12) but often is as satisfactory a
representation of resistivity under practical filtration conditions.
Substituting Eq. (11.17) into Eq. (11.2), the result is
WI*) A P
-=
dt p[Rf + cu,c(l + kAP)“(VIA)]
Integration at constant pressure gives the result
(11.18)
(11.19)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-330-320.jpg)
![312 SOLID-LIQUID SEPARATION
I I IO
0.1 0.2 0.4 0.6 I 2 4
Time. minutes
(a)
-. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.0
L
2 DRY TIME - MIN.
B
(c)
EFFICIENCY !
0-i
I 1 I f
0.5 1.0 1.5 2.0 2.5
WASH RATIO
b)
(4
Figure 11.3. Laboratory test data with a vacuum leaf filter. (a) Rates of formation of dry cake and filtrate. (b) Washing efficiency. (c) Air flow
rate vs. drying time. (d) Correlation of moisture content with the air rate, pressure difference AP, cake amount W lb/sqft, drying time
0, min and viscosity of liquid (Dahlrtrom and Silverblatt, 1977).
EXAMPLE 11.3
Rotary Vacuum Filter Operation
A TiO, slurry has the properties
c = 200 kg solid/m’ liquid,
p, = 4270 kg/m3,
p = 0.001/3600 N hr/m’,
(Y= 1.6(E12) m/kg (item 4 of Fig. 11.2),
.s=O.6.
Cloth resistance is I$ = l(E10) m-l. Normal peripheral speed is
about 1 m/min. Filtering surface is l/3 of the drum surface and
washing surface is l/6 of the drum surface. The amount of wash
equals the pore space of the cake. The cake thickness is to be
limited to 1 cm. At suitable operating pressures, find the drum
speed in rph and the drum diameter:
c
cake thickness = 0.01 m = ~5
P# - ~1 A
200 v,
=___-
4270(0.4) A ’
If= 0.01(4270)(0.4) = o 0854 m3,m2
A 200 .
wash liquid = pore volume
= O.Ol(O.6) = 0.006 m2 m2.
With the pressure difference in bar,
W/A) lOsAP,
dt - (0.001/3600)[10’” + 160(10’“)V/A]
36AP,
=1+16OV/A’
(2)](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-331-320.jpg)
![314 SOLID-LIQUID SEPARATION
EXAMPLE 11.4 Filtering period is
Filtration and Washing of a Compressible Material
A kaolin slurry has the properties
c = 200 kg solid/m3 filtrate,
tf =0.25+ 0.0035(Vf -0.0423)+ 7O.O(V;-0.0018).
Daily production rate,
P = 0.001 N set/m*, 2.78(E - 7) N hr/m*,
ps = 200 kg/m3,
(Y = 87(ElO)(l+ P/3.45)o.7 m/kg with P in bar,
E = 1 - 0.460(1 + P/3.45)0.‘*.
R, = (no of batches/day)(filtrate/batch)
_ 245 _ wf
td + +
- 1 + rr I m3/b2)(W
The equations for & and E are taken from Table 11.8.
Filtration will proceed at a constant rate for 15 mitt, the
pressure will rise to 8 bar and filtration will continue at this pressure
until the end of the operation. Filter cloth resistance is
R, = l(lOt”) m-l. The down time per batch is 1 hr.
a. Find the maximum daily production of filtrate.
b. The filtrate will be blown and then washed with a volume of
water equal to the pore space of the cake. Find the maximum
daily production of filtrate under these conditions.
= 1.25 + O.o035(vf - 0.0423) + 7O(V; - 0.0018)
The tabulation shows that R, is a max when Vf = 0.127.
v, t %
0.12 1.3507
0.126 1.3526
0.127 1.2533 1.3527 (max)
0.128 1.3526
0.129 1.3525
0.130 1.3522
Part (a)
Basis 1 m* of filtering surface. At P = 8 bar, or 8(105) Pa Part(b)
cr = 87(101’)(1 + g/3.45)‘.‘= 2.015(10’*) m/kg,
E = 1 - 0.46(1 + 8/3.45)‘.‘* = 0.47,
PC& = (0.001/3600)(200)(2.015)(10’*) = 1.12(108) N hr/m4.
Amount of wash liquid = fi= ~~($4571) = O.O709vf,
s
The filtration equation (11.2) is wash rate = filtering rate at the conclusion of the filtration
dV A A P A P
dt = ,u(R~ + &V/A) = (0.001/3600)[1010 + 2.015(10’*)(200)V]
A P
=2780 + 1.12(108)V’
The rate when t = 0.25/r and AP = 8(105) Pa,
8( 105) 8( 105)
’ = 2780 + 1.12(108)Qt =2780 + 0.28(108)Q
= 0.1691 m3/m2 hr.
The amount of filtrate at this time is
V. = Qt = 0.1691(0.25) = 0.0423 m3.
The integral of the rate equation at constant P is
278O(vf - 0.0423) + 0.56(108)(V; - (0.00423)*]
= S(lO”)(t, - 0.25).
24V,
AP 8(105)
=p(Rf + acv,)=2780+ 1.12(108)vf’
m3/hr,
t
w
= wash time = 0.709Vf[2780 + 1.12(108)Vf]
8( 105)
= Vf(0.000246+ 9.926Vf),
R,=
245
1 + tr + t,
24Vf
= [l + O.O035(V - 0.0423) + 7OlO(Vf - 0.0018)
+ vf(O.000246 + 9.926vf)].
The optimum operation is found by trial:
Vf = 0.105,
tf = 1.0805,
t, = 0.1095,
R, = 1.1507 (max), daily production rate.
on the parameters of the correlating equation COMPRESSIBILITY-PERMEABILITY (CP) CELL
MEASUREMENTS
cr = ab(AP)“. (11.24)
The measurements were obtained with a small filter press. Clearly,
the resistivity measured at a particular rate is hardly applicable to
predicting performance at another rate or at constant pressure.
The probable success of correlation of cake resistivity in terms of all
the factors that have been mentioned has not been great enough to
have induced any serious attempts of this nature, but the effect of
pressure has been explored. Although the (Y’S can be deduced from](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-333-320.jpg)
![316 SOLID-LIQUID SEPARATION
3 3.
1 1.5 2 2.5
(a)
0.9
0.8
0,7
T
Or6
0.5
0,4
0‘3
5
Cornpresswe pressure (P, I, psia
I-Superlite C&O, (flocculated), pH = 9.8 4-~-110 grade TIO*, PH = 3.5
2-Superlite C&O,, pH = 10.3 5-Znr. Type B, PH = 9.1
3-A-1 10 grade TiO, Iflocculated), pti = 7.8 &ZnS, Type A, PH = 9.1
(b)
Compressive pressure ! P, l. Psla
(4
Figure 11.4. Data of compressibilities and porosities of filter cakes. (a) Parameters of the correlation (Y = cu,(AP)” for resistivity of CaSiOa
filter cakes at two rates and two concentrations (Rushron and Kufsoulus, 1984). (b) Resistivity as a function of pressure measured m a
compressibility-permeability (CP) cell [Grace, Chem. Eng. Prog. 49, 303, 367, 427 (1953)]. (c) P orosity as a function of pressure for the
same six materials (Grace, Zoc. cit.).](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-335-320.jpg)
![320 SOLID-LIQUID SEPARATION
(a) -+ Thick sludge discharge
W Flocculant ccntro!
valve
Cer
iUf
:cntrol
%
Baffled !eed
-,- I sander
I,1’.ti:‘.‘n’. / “-a-Clarified ggater
:ro!le:
Figure 11.6. Thickeners for preconcentration of feed to filters or for
disposal of solid wastes [see also the rake classifier of Fig. 12.2(e)].
(a) A thickener for concentrating slurries on a large scale. The
rakes rotate slowly and move settled solids towards the discharge
port at the center. Performance data are in Table 11.11 (Brown,
Unit Operations, Wiley, New York, 1950). (b) Deep cone thickener
developed for the National Coal Board (UK). In a unit about
10 ft dia the impellers rotate at about 2 ‘pm and a flow rate of
70m3/sec with a solids content of 6 wt %, concentrates to
25-35 wt % (Strarousky, 1981).
11.13(a) performs cake removal at reduced rotating speed, whereas
the design of Figure 11.13(d) accomplishes this operation without
slowing down. The clarifying centrifuge of Figure 11.13(e) is
employed for small contents of solids and is cleaned after shutdown.
The units of Figures 11.13(b) and (c) operate continuously, the
former with discharge of cake by a continuous helical screw, the
latter by a reciprocating pusher mechanism that operates at
30-70 strokes/mio and is thus substantially continuous.
Hydrocyclooes generate their own, mild centrifugal forces.
Since the acceleration drops off rapidly with diameter, hydrocy-
TABLE 11 .S. Performances of Sedimentation Equipment
(a) Thickenersa
96 solids Unit area,
sq. ft. /ton.
Feed U n d e r f l o w day
Alumina, Bayer process:
Red-mud primary settlers
R e d - m u d w a s h e r s
Red-mud final thickener
Trihydrate seed thickener
Cement, West process
Cement kiln dust
Coral
Cyanide slimes
Lime mud:
Acetylene generator
Lime-soda process
Paper industry
Magnesium hydroxide from brine
Metallurgical (flotation or gravity
concentration):
Copper concentrates
Copper tailings
Lead concentrates
Zinc concentrates
Nickel:
Leached residue
Sulfide concentrate
Potash slimes
Uranium:
Acid leached ore
Alkaline leached ore
Uranium precipitate
3-4 lo-25 20-30
6-8 15-20 10-15
6-8 20-35 10-15
2-8 30-50 12-30
16-20 60-70 15-25
9-10 45-55 3-18
12-18 45-55 15-25
16-33 40-55 5-13
12-15 30-40 15-33
9-11 35-45 15-25
8-10 32-45 14-18
8-10 25-50 60-100
14-50 40-75 2-20
10-30 45-65 4-10
20-25 60-80 7-18
10-20 50-60 3-7
2 0 6 0 8
3-5 6 5 2 5
l - 5 6-25 40-l 25
1 O-30 25-65 2-10
2 0 6 0 1 0
l-7 10-25 50-125
(b) Clarifiers
Overflow rate,
Application gal./min., sq. ft.
Detentio: time,
Primary sewage treatment
(settleable-solids removal) 0 . 4 2
Secondary sewage treatment (final
clarifiers-activated sludge and
trickling filters) 0.55-0.7 1.5-2
Water clarification (following 30-
min. flocculation) 0.4-0.55 3
Lime and lime-soda softening (high
rate-upflow units) 1.5 2
Industrial wastes Must be tested for each application
“See also Table 14.7.
(Perry’s Chemical Engineers Handbook, McGraw-Hill, New York, 1963,
pp. 19.49,19.52).
clones are made only a few inches in diameter. For larger
capacities, many units are used in parallel. The flow pattern is
shown schematically in Figure 11.13(f). The shapes suited to
different applications are indicated in Figure 11.13(g). 10 Figure
11.13(h), the centrifugal action in a hydrocyclooe is assisted by a
high speed impeller. This assistance, for example, allows handling
of 6% paper pulp slurries in comparison with only 1% in unassisted
units. Hydrocyclones are perhaps used much more widely for dust
separation than for slurries.
11.7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT
Data of commercially available sizes of filtration equipment, their
typical applications, and specific performances are available only to
a limited extent in the general literature, but more completely in](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-339-320.jpg)
![12
DISINTEGRATION, AGGLOMERATION, AND SIZE
SEPARATION OF PARTICULATE SOLIDS
F
rom the standpoint of chemical processing, size
reduction of so/ids is most often performed to make
them more reactive chemically or to permit recovery
of valuable constituents. Common examples of
comminution are of ores for separation of valuable minerals
from gangue, of limestone and shale for the manufacture of
cement, of coal for combustion and hydrogenation to liquid
fuels, of cane and beets for recovery of sugar, of grains for
recovery of oils and flour, of wood for the manufacture of
paper, of some flora for recovery of naturaal drugs, and so on.
Since the process of disintegration ordinarily is not high/y
selective with respect to size, the product usually requires
separation into size ranges that are most suitable to their
subsequent processing. Very small sizes are necessary for
some applications, but in other cases intermediate sizes are
preferred. Thus the byproduct fines from the crushing of coal
are briquetted with pitch binder into 3-44in. cubes when
there is a demand for coal in lump form. Agglomeration in
general is practiced when larger sizes are required for ease of
handling, or to reduce dust nuisances, or to densify the
product for convenient storage or shipping, or to prepare
products in final form as tablets, granules, or prills.
Comminution and size separation are characterized by
the variety of equipment devised for them. Examples of the
main types can be described here with a few case studies.
For real, it is essential to consult manufacturers’ catalogs for
details of construction, sizes, capacities, space, and power
requirements. They are properly the textbooks for these
operations, since there are few generalizations in this area for
prediction of characteristics of equipment. A list of about
90 U.S. and Canadian manufacturers of size separation
equipment is given in the Encyclopedia of Chemical
Technology 121, 137 (7983)], together with identification of
nine equipment types. The Chemical Engineering Equipment
Buyers Guide (McGraw-Hi//, New York) and Chemical
Engineering Catalog (F’enton/Reinho/d, New York) a/so
provide listings of manufacturers according to kind of
equipment.
12.1. SCREENING
Separation of mixtures of particulate solids according to size may be
accomplished with a series of screens with openings of standard
sizes. Table 12.1 compares several such sets of standards. Sizes
smaller than the 38pm in these tables are determined by
elutriation, microscopic examination, pressure drop measurements,
and other indirect means. The distribution of sizes of a given
mixture often is of importance. Some ways of recording such data
are illustrated in Figure 16.4 and discussed in Section 16.2.
The distribution of sizes of a product varies with the kind of
disintegration equipment. Typical distribution curves in normalized
form are presented in Figure 12.1, where the size is given as a
percentage of the maximum size normally made in that equipment.
The more concave the curves, the greater the proportion of fine
material. According to these correlations, for example, the
percentages of material greater than 50% of the maximum size are
50% from rolls, 15% from tumbling mills, and only 5% from closed
circuit conical ball mills. Generalization of these curves may have
led to some loss of accuracy since the RRS plots of the data shown
in Figure 12.1(c) deviate much more than normally from linearity.
In order to handle large lumps, separators are made of sturdy
parallel bars called grizzlies. Punched plates are used for
intermediate sizes and woven screens for the smallest sizes.
Screening is best performed dry, unless the feed is the product of
wet grinding or is overly dusty and an equipment cover is not
feasible. Wetting sometimes is used to prevent particles from
sticking together. Types of screens and other classifiers to cover a
range of sizes are shown in Figure 12.2. Usually some kind of
movement of the stock or equipment is employed to facilitate the
separations.
REVOLVING SCREENS OR TROMMELS
One type is shown in Figure 12.2(a). They are perforated cylinders
rotating at 15-20rpm, below the critical velocity. The different-
sized perforations may be in series as shown or they may be on
concentric surfaces. They are suitable for wet or dry separation in
the range of 60-10 mm. Vertically mounted centrifugal screens run
at 60-80 rpm and are suitable for the range of 12-0.4 mm.
Examples of performance are: (1) a screen 3 ft dia by 8 ft long
with 5-mesh screen at 2 rpm and an inclination of 2” has a capacity
of 600 cuft/hr of sand; (2) a screen 9 ft dia by 8 ft long at 10 rpm and
an inclination of 7” can handle 4000 cuft/hr of coke.
Flat screel~~ are vibrated or shaken to force circulation of the
bed of particles and to prevent binding of the openings by oversize
particles. Usually several sizes are arranged vertically as in Figures
12.2(b) and (c), but sometimes they are placed in line as in the
cylindrical screen of Figure 12.2(a). Inclined screens vibrate at
64lO-7000 strokes/min. They are applicable down to 38pm or so,
but even down to 200 mesh at greatly reduced capacity. Horizontal
screens have a vibration component in the horizintal direction to
convey the material along; they operate in the range of 300-3000
strokes/min.
Shaking or reciprocating screens are inclined slightly. Speeds
are in the range of 30-1000 strokes/min; the lower speeds are used
for coal and nonmetallic minerals down to 12mm, and higher
speeds may size down to 0.25 mm. The bouncing rubber balls of
Figure 12.2(c) prevent permanent blinding of the perforations.
Rotary sifters are of either gyratory or reciprocating types.
They operate at 500-600rpm and are used for sizes of 12mm-
50 pm, but have low capacity for fine sizes.
CAPACITY OF SCREENS
For coarse screening, the required area per unit of hourly rate may
be taken off Figure 12.3. More elaborate calculation procedures
that take into account smaller sizes and design features of the
equipment appear in the following references:
Mathews, Chem. Eng. 76 (10 July 1972) and presented in Chemical
335](https://image.slidesharecdn.com/d5nhdxnmtykvjjqzay4y-equipos-paea-controles-quimicos-220501171544/85/CHEMICAL-PROCESS-EQUIPMENT-pdf-354-320.jpg)
CHEMICAL PROCESS EQUIPMENT.pdf
- 3. BUTTERWORTH-HEINEMANN SERIES IN CHEMICAL ENGINEERING SERIES EDITOR ADVISORY EDITORS HOWARD BRENNER Massachusetts Institute of Technology ANDREAS ACRIVOS The City College of CUNY JAMES E. BAILEY California Institute of Technology MANFRED MORARI California Institute of Technology E. BRUCE NAUMAN Rensselaer Polytechnic Institute ROBERT K. PRUD’HOMME Princeton University SERIES TITLES Chemical Process Equipment Stanley M. Walas Constitutive Equations for Polymer Melts and Solutions Ronald G. Larson Gas Separation by Adsorption Processes Ralph T. Yang Heterogeneous Reactor Design Hong H. Lee Molecular Thermodynamics of Nonideal Fluids Lloyd L. Lee Phase Equilibria in Chemical Engineering Stanley M. Walas Transport Processes in Chemically Reacting Flow Systems Daniel E. Rosner Viscous Flows: The Practical Use of Theory Stuart Winston Churchill RELATED TITLES Catalyst Supports and Supported Catalysts Alvin B. Stiles Enlargement and Compaction of Particulate Solids Nayland Stanley-Wood Fundamentals of Fluidized Beds John G. Yates Liquid and Liquid Mixtures J.S. Rowlimon and F. L. Swinton Mixing in the Process Industries N. Harnby, M. F. Edwards, and A. W. Nienow Shell Process Control Workshop David M. Prett and Manfred Morari Solid Liquid Separation Ladislav Svarovsky Supercritical Fluid Extraction Mark A. McHugh and Val .I. Krukonis
- 4. Chemical Process Equipment Selection and Design Stanley M. Walas Department of Chemical and Petroleum Engineering University of Kansas
- 5. To the memory of my parents, Stanklaus and Apolonia, and to my wife, Suzy Belle Copyright 0 1990 by Butterworth-Heinemann, a division of Reed Publishing (USA) Inc. All rights reserved. The information contained in this book is based on highly regarded sources, all of which are credited herein. A wide range of references is listed. Every reasonable effort was made to give reliable and up-to-date information; neither the author nor the publisher can assume responsibility for the validity of all materials or for the consequences.of their use. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library of Congress Cataloging-in-Publication Data Walas, Stanley M. Chemical process equipment. (Butterworth-Heinemann series in chemical engineering) Includes bibliographical references and index. 1. Chemical engineering-Apparatus and supplies. I. Title. II. Series. TP157.w334 1988 660.2’83 87-26795 ISBN 0-7506-9385-l (previously ISBN o-409-90131-8) British Library Cataloguing in Publication Data Walas, Stanley M. Chemical process equipment.-(Butterworth- Heinemann series in chemical engineering). series in chemical engineering). 1. Chemical engineering-Apparatus and supplies I. Title 660.2’8 TP157 ISBN 0-7506-9385-l (previously ISBN o-409-90131-8) Butterworth-Heinemann 3 13 Washington Street Newton, MA 02158-1626 10 9 8 7 Printed in the United States of America
- 6. LIST OF EXAMPLES ix PREFACE xi RULES OF THUMB: SUMMARY CHAPTER 1 INTRODUCTION 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. 1.11. 1.12. Contents CHAPTER 5 TRANSFER OF SOLIDS 69 ... xiii 1 Process Design I Equipment 1 Vendors’ Questionnaires 1 Specification Forms 1 Categories of Engineering Practice 1 Sources of Information for Process Design 2 Codes, Standards, and Recommended Practices 2 Material and Energy Balances 3 Economic Balance 4 Safety Factors 6 Safety of Plant and Environment 7 Steam and Power Supply 9 Design Basis 12 Utilities 1 2 Laboratory and Pilot Plant Work 12 References 15 CHAPTER 2 FLOWSHEETS 19 2.1. Block Flowsheets 19 2.2. Process Flowsheets 19 2.3. Mechanical (P&I) Flowsheets 19 2.4. Utility Flowsheets 19 2.5. Drawing of Flowsheets 20 References 31 Appendix 2.1 Descriptions of Example Process Flowsheets 33 CHAPTER 3 PROCESS CONTROL 39 6.9. 3.1. 3.2. 3.3. Feedback Control 39 Symbols 39 Cascade (Reset) Control 42 Individual Process Variables 4.2 Temperature 42 Pressure 42 Level of Liquid 43 Flow Rate 43 Flow of Solids 43 Flow Ratio 43 Composition 43 Equipment Control 43 Heat Transfer Equipment 44 Distillation Equipment 47 Liquid-Liquid Extraction Towers 50 Chemical Reactors 53 Liquid Pumps 55 Solids Feeders 55 Compressors 55 References 60 CHAPTER 4 DRIVERS FOR MOVING EQUIPMENT 61 4.1. Motors 61 Induction 61 4.2. 4.3. Synchronous 61 Direct Current 61 Steam Turbines and Gas Expanders 62 Combustion Gas Turbines and Engines 65 References 68 5.1. 5.2. 5.3. 5.4. Slurry Transport 69 Pneumatic Conveying 71 Equipment 72 Operating Conditions 73 Power Consumption and Pressure Drop 74 Mechanical Conveyors and Elevators 76 Properties of Materials Handled 76 Screw Conveyors 76 Belt Conveyors 76 Bucket Elevators and Carriers 78 Continuous Flow Conveyor Elevators 82 Solids Feeders 83 References 88 CHAPTER 6 FLOW OF FLUIDS 91 6.1. 6.2. 6.3. 6.4. 6.5. 6.6. 6.7. 6.8. Properties and Units 91 Energy Balance of a Flowing Fluid 92 Liquids 94 Fittings and Valves 95 Orifices 95 Power Requirements 98 Pipeline Networks 98 Optimum Pipe Diameter 100 Non-Newtonian Liquids 100 Viscosity Behavior 100 Pipeline Design 106 Gases 109 Isentropic Flow 109 Isothermal Flow in Uniform Ducts 110 Adiabatic Flow 110 Nonideal Gases 111 Liquid-Gas Flow in Pipelines 111 Homogeneous Model 113 Separated Flow Models 114 Other Aspects 114 Granular and Packed Beds 117 Single Phase Fluids 117 Two-Phase Flow 118 6.10. Gas-Solid Transfer 119 Choking Velocity 119 Pressure Drop 119 6.11. Fluidization of Beds of Particles with Gases 120 Characteristics of Fluidization 123 Sizing Equipment 123 References 127 CHAPTER 7 FLUID TRANSPORT EQUIPMENT 129 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. Piping 129 Valves 129 Control Valves 129 Pump Theory 131 Basic Relations 131 Pumping Systems 133 Pump Characteristics 134 Criteria for Selection of Pumps 140 Equipment for Gas Transport 143 Fans 143 Compressors 145 Centrifugals 1 4 5 Axial Flow Compressors 146 Reciprocating Compressors 146 Rotary Compressors 149 Theory and Calculations of Gas Compression 153 Dimensionless Groups 153 Ideal Gases 153 Real Processes and Gases 156 Work on Nonideal Gases 156
- 7. C O N T E N T S v i 7.7. Efficiency 1.59 Temperature Rise, Compression Ratio, Volumetric E f f i c i e n c y 1 5 9 Ejector and Vacuum Systems 162 Ejector Arrangements 162 Air Leakage 164 Steam Consumption 165 Ejector Theory 166 Glossary for Chapter 7 166 References 167 CHAPTER 8 HEAT TRANSFER AND HEAT EXCHANGERS 169 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. 8.8. 8.9. 8.10 Conduction of Heat 169 Thermal Conductivity 169 Hollow Cvlinder 170 Composite Walls 170 Fluid Films 170 Mean Temperature Difference 172 Single Pass Exchanger 172 Multipass Exchangers 173 F-Method 173 O-Method 179 Selection of Shell-and-Tube Numbers of Passes 179 Example 179 Heat Transfer Coefficients 179 Overall Coefficients 180 Fouling Factors 180 Individual Film Coefficients 180 Metal Wall Resistance 18.2 Dimensionless Groups 182 Data of Heat Transfer Coefficients 182 Direct Contact of Hot and Cold Streams 185 Natural Convection 186 Forced Convection 186 Condensation 187 Boiling 187 Extended Surfaces 188 Pressure Drop in Heat Exchangers 188 Types of Heat Exchangers 188 Plate-and-Frame Exchangers 189 Spiral Heat Exchangers 194 Compact (Plate-Fin) Exchangers 194 Air Coolers 194 Double Pipes 19.5 Shell-and-Tube Heat Exchangers 195 Construction 195 Advantages 199 Tube Side or Shell Side 199 Design of a Heat Exchanger 199 Tentative Design 200 Condensers 200 Condenser Configurations 204 Desien Calculation Method 205 The Silver-Bell-Ghaly Method 206 Reboilers 206 Kettle Reboilers 207 Horizontal Shell Side Thermosiphons 207 Vertical Thermosiphons 207 Forced Circulation Reboilers 208 Calculation Procedures 208 Evaporators 208 Thermal Economy 210 Surface Requirements 211 8.11. Fired Heaters 211 Description of Eauinment 211 Heat Transfer 213 Design of Fired Heaters 214 8.12. Insulation of Equipment 219 Low Temperatures 221 Medium Temperatures 221 8.13. Refractories 221 Refrigeration 224 Compression Refrigeration 224 Refrigerants 226 Absorption Refrigeration 229 Cryogenics 229 References 229 9 DRYERS AND COOLING TOWERS 231 9.1. Interaction of Air and Water 231 9.2. Rate of Drying 234 9.3. Laboratory and Pilot Plant Testing 237 Classification and General Characteristics of 9.4. 9.5. 9.6. 9.7. 9.8. 9.9. Dryers 237 Products 240 Costs 240 Specification Forms 240 Batch Dryers 241 Continuous Tray and Conveyor Belt Dryers 242 Rotary Cylindrical Dryers 247 Drum Dryers for Solutions and Slurries 254 Pneumatic Conveying Dryers 255 Fluidized Bed Dryers 262 9.10. Spray Dryers 268 Atomization 276 Applications 276 Thermal Efficiency 276 D e s i g n 2 7 6 9.11. Theorv of Air-Water Interaction in Packed Towers 277 Tower Height 279 9.12. Cooling Towers 280 Water Factors 285 Testing and Acceptance 285 References 285 CHAPTER 10 MIXING AND AGITATION 287 10.1. A Basic Stirred Tank Design 287 The Vessel 287 Baffles 287 Draft Tubes 287 Impeller Types 287 Impeller Size 287 Impeller Speed 288 Impeller Location 288 10.2. Kinds of Impellers 288 10.3. Characterization of Mixing Quality 290 10.4. Power Consumption and Pumping Rate 292 10.5. Suspension of Solids 295 10.6. Gas Dispersion 296 Spargers 296 Mass Transfer 297 System Design 297 Minimum Power 297 Power Consumption of Gassed Liquids 297 Superficial Liquid Velocity 297 Design Procedures 297 10.7. In-Line-Blenders and Mixers 300 10.8. Mixing of Powders and Pastes 301 References 304 CHAPTER 11 SOLID-LIQUID SEPARATION 305 11.1. Processes and Equipment 305 11.2 Theory of Filtration 306 Compressible Cakes 310 11.3. Resistance to Filtration 313 Filter Medium 313 Cake Resistivity 313
- 8. Compressibility-Permeability (CP) Cell Measurements 314 Another Form of Pressure Dependence 315 Pretreatment of Slurries 315 11.4. Thickening and Clarifying 315 11.5. Laboratory Testing and Scale-Up 317 Compression-Permeability Cell 317 The SCFT Concept 317 Scale-Up 318 11.6. Illustrations of Equipment 318 11.7. Applications and Performance of Equipment 320 References 334 CHAPTER 12 DISINTEGRATION, AGGLOMERATION, AND SIZE SEPARATION OF PARTICULATE SOLIDS 335 12.1. Screening 335 Revolving Screens or Trommels 335 Capacity of Screens 335 12.2. Classification with Streams of Air or Water 337 Air Classifiers 337 Wet Classifiers 339 12.3. Size Reduction 339 12.4. Eauiument for Size Reduction 341 Crushers 3 4 1 Roll Crushers 341 12.5. Particle Size Enlargement 351 Tumblers 351 Roll Compacting and Briquetting 354 Tabletting 357 Extrusion Processes 358 Prilling 361 Fluidized and Spouted Beds 362 Sintering and Crushing 363 References 370 CHAPTER 13 DISTILLATION AND GAS ABSORPTION 371 13.1. 13.2. 13.3. 13.4. 13.5. 13.6. 13.7. Vapor-Liquid Equilibria 371 Relative Volatility 374 Binary x-y Diagrams 375 Single-Stage Flash Calculations 375 Bubblepoint Temperature and Pressure 376 Dewpoint Temperature and Pressure 377 Flash at Fixed Temnerature and Pressure 377 Flash at Fixed Enthalpy and Pressure 377 Equilibria with KS Dependent on Composition 377 Evaporation or Simple Distillation 378 Multicomponent Mixtures 379 Binary Distillation 379 Material and Energy Balances 380 Constant Molal Overflow 380 Basic Distillation Problem 382 Unequal Molal Heats of Vaporization 382 Material and Energy Balance Basis 382 Algebraic Method 382 Batch Distillation 390 Material Balances 391 Multicomponent Separation: Generali Considerations 393 Sequencing of Columns 393 Number of Free Variables 395 Estimation of Reflux and Number of Travs (Fenske- Underwood-Gilliland Method) 395 Minimum Trays 395 Distribution of Nonkeys 395 Minimum Reflux 397 Operating Reflux 397 Actual Number of Theoretical Trays 397 Feed Tray Location 397 13.8. 13.9. CONTENTS Vii Tray Efficiencies 397 Absorption Factor Shortcut Method of Edmister 398 Seoarations in Packed Towers 398 Miss Transfer Coefficients 399 Distillation 401 Absorption or Stripping 401 13.10. Basis for Computer Evaluation of Multicomponent Separations 404 Specifications 405 The MESH Equations 405 The Wang-Henke Bubblepoint Method 408 The SR (Sum-Rates) Method 409 SC (Simultaneous Correction) Method 410 13.11. Special Kinds of Distillation Processes 410 Petroleum Fractionation 411 Extractive Distillation 412 Azeotropic Distillation 420 Molecular Distillation 425 13.12. Tray Towers 426 Countercurrent Trays 426 Sieve Trays 428 Valve Trays 429 Bubblecap Trays 431 13.13. Packed Towers 433 Kinds of Packings 433 Flooding and Allowable Loads 433 Liquid Distribution 439 Liauid Holdup 439 Pressure Drop 439 13.14. Efficiencies of Trays and Packings 439 Trays 439 Packed Towers 442 References 456 CHAPTER 14 EXTRACTION AND LEACHING 459 14.1. Equilibrium Relations 459 14.2. Calculation of Stage Requirements 463 Single Staee Extraction 463 Crosscurrent Extraction 464 Immiscible Solvents 464 14.3. Countercurrent Operation 466 Minimum Solvent/Feed Ratio 468 Extract Reflux 468 Minimum Reflux 469 Minimum Stages 469 14.4. Leaching of Solids 470 14.5. Numerical Calculation of Multicomponent Extraction 473 Initial Estimates 473 Procedure 473 14.6. Equipment for Extraction’ 476 Choice of Disperse Phase 476 Mixer-Settlers’ 477 Spray Towers 478 Packed Towers 478 Sieve Tray Towers 483 Pulsed Packed and Sieve Tray Towers 483 Reciprocating Tray Towers 485 Rotating Disk Contactor (RDC) 485 Other Rotary Agitated Towers 485 Other Kinds of Extractors 487 Leaching Equipment 488 References 493 CHAPTER 15 ADSORPTION AND ION EXCHANGE 495 15.1. Adsorption Equilibria 495 15.2. Ion Exchange Equilibria 497 15.3. Adsorption Behavior in Packed Beds 500 Regeneration 504
- 9. V i i i C O N T E N T S 15.4. Adsorption Design and Operating Practices 504 15.5. Ion Exchange Design and Operating Practices 506 Electrodialysis 508 15.6. Production Scale Chromatography 510 15.7. Equipment and Processes 510 Gas Adsorption 511 Liquid Phase Adsorption 513 Ion Exchange 517 Ion Exchange Membranes and Electrodialysis 5 1 7 Chromatographic Equipment 520 References 522 CHAPTER 16 CRYSTALLIZATION FROM SOLUTIONS 18.1. Drums 611 AND MELTS 523 18.2. Fractionator Reflux Drums 6 1 2 16.1. Solubilities and Equilibria 523 Phase Diagrams 523 Enthalpy Balances 524 16.2. Crvstal Size Distribution 525 16.3. The Process of Crystallization 528 Conditions of Precipitation 528 Supersaturation 528 Growth Rates 530 16.4. The Ideal Stirred Tank 533 Multiple Stirred Tanks in Series 536 Applicability of the CSTC Model 536 16.5. Kinds of Crystallizers 537 16.6. Melt Crystallization and Purification 543 Multistage Processing 543 The Metallwerk Buchs Process 543 Purification Processes 543 References 548 18.3. Liquid-Liquid Separators 612 Coalescence 613 Other Methods 613 18.4. Gas-Liquid Separators 613 Droplet Sizes 613 Rate of Settling 614 Empty Drums 615 Wire Mesh Pad Deentrainers 6 1 5 18.5. Cyclone Separators 616 18.6. Storage Tanks 619 18.7. Mechanical Design of Process Vessels 6 2 1 Design Pressure and Temperature 623 Shells and Heads 624 Formulas for Strength Calculations 624 References 629 CHAPTER 19 OTHER TOPICS 631 CHAPTER 17 CHEMICAL REACTORS 549 17.1. 17.2. 17.3. 17.4. 17.5. 17.6. 17.7. 17.8. Design Basis and Space Velocity 549 Design Basis 549 Reaction Times 549 Rate Equations and Operating Modes 549 Material and Energy Balances of Reactors 555 Nonideal Flow Patterns 556 Residence Time Distribution 556 Conversion in Segregated and Maximum Mixed Flows 560 Conversion in Segregated Flow and CSTR Batteries 560 Dispersion Model 560 Laminar and Related Flow Patterns 5 6 1 Selection of Catalysts 562 Heterogeneous Catalysts 562 Kinds of Catalysts 563 Kinds of Catalvzed Organic Reactions 563 Physical Characteristics of Solid Catalysts 564 Catalyst Effectiveness 565 Types and Examples of Reactors 567 Stirred Tanks 567 Tubular Flow Reactors 569 Gas-Liquid Reactions 571 Fixed Bed Reactors 572 Moving Beds 574 Kilns and Hearth Furnaces 575 Fluidized Bed Reactors 579 Heat Transfer in Reactors 582 Stirred Tanks 586 Packed Bed Thermal Conductivity 587 Heat Transfer Coefficient at Walls, to Particles, and Overall 587 Fluidized Beds 589 Classes of Reaction Processes and Their Equipment 592 Homogeneous Gas Reactions 592 Homogeneous Liquid Reactions 595 Liquid-Liquid Reactions 595 Gas-Liquid Reactions 595 Noncatalytic Reactions with Solids 595 Fluidized Beds of Noncatalytic Solids 595 Circulating Gas or Solids 596 Fixed Bed Solid Catalysis 596 Fluidized Bed Catalysis 601 Gas-Liquid Reactions with Solid Catalysts 604 References 609 CHAPTER 18 PROCESS VESSELS 611 19.1. Membrane Processes 631 Membranes 632 Equipment Configurations 632 Applications 632 Gas Permeation 633 19.2. Foam Separation and Froth Flotation 635 Foam Fractionation 635 Froth Flotation 636 19.3. Sublimation and Freeze Drying 638 Equipment 639 Freeze Drying 639 19.4. Parametric Pumping 639 19.5. Seoarations bv Thermal Diffusion 642 19.6. Electrochemical Syntheses 645 Electrochemical Reactions 646 Fuel Cells 646 Cells for Synthesis of Chemicals 648 19.7. Fermentation Processing 648 Processing 650 Operating Conditions 650 Reactors 654 References 660 CHAPTER 20 COSTS OF INDIVIDUAL EQUIPMENT 663 References 669 APPENDIX A UNITS, NOTATION, AND GENERAL DATA 671 APPENDIX B EQUIPMENT SPECIFICATION FORMS 681 APPENDIX C QUESTIONNAIRES OF EQUIPMENT SUPPLIERS 727 INDEX 747
- 10. List of Examples 1.1 1.2 1.3 1.4 1.5 3.1 4.1 4.2 5.1 5.2 5.3 5.4 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 7.1 7.2 7.3 7.4 E 717 7.8 7.9 7.10 7.11 7.12 7.13 i:: 8.3 8.4 Material Balance of a Chlorination Process with Recycle 5 Data of a Steam Generator for Making 250,000 lb/hr at 450 psia and 650°F from Water Entering at 220°F 9 Steam Plant Cycle for Generation of Power and Low Pressure Process Steam 11 Pickup of Waste Heat by Generating and Superheating Steam in a Petroleum Refinery 11 Recovery of Power from a Hot Gas Stream 12 Constants of PID Controllers from Response Curves to a Step Input 42 Steam Requirement of a Turbine Operation 65 Performance of a Combustion Gas Turbine 67 Conditions of a Coal Slurry Pipeline 70 Size and Power Requirement of a Pneumatic Transfer Line 77 Sizing a Screw Conveyor 80 Sizing a Belt Conveyor 83 Comparison of Redler and Zippered Belt Conveyors 88 Density of a Nonideal Gas from Its Equation of State 91 Unsteady Flow of an Ideal Gas through a Vessel 93 Units of the Energy Balance 94 Pressure Drop in Nonisothermal Liquid Flow 97 Comparison of Pressure Drons in a Line with Several Sets of Fittings Resistances 101 A Network of Pipelines in Series, Parallel, and Branches: the Sketch, Material Balances, and Pressure Drop Equations 101 Flow of Oil in a Branched Pipeline 101 Economic Optimum Pine Size for Pumping Hot Oil with a Motor or Turbine Drive 102 Analysis of Data Obtained in a Capillary Tube Viscometer 107 Parameters of the Bingham Model from Measurements of Pressure Drops in a Line 107 Pressure Drop in Power-Law and Bingham Flow 110 Adiabatic and Isothermal Flow of a Gas in a Pipeline 112 Isothermal Flow of a Nonideal Gas 113 Pressure Drop and Void Fraction in Liquid-Gas Flow 116 Pressure Drp in Flow of Nitrogen and Powdered Coal 120 Dimensions of a Fluidized Bed Vessel 125 Application of Dimensionless Performance Curves 132 Operating Points of Single and Double Pumps in Parallel and Series 133 Check of Some Performance Curves with the Concept of Specific Speed 136 Gas Compression, Isentropic and True Final Temperatures 155 Compression Work with Variable Heat Capacity 157 Polytropic and Isentropic Efficiencies 158 Finding Work of Compression with a Thermodynamic Chart 160 Compression Work on a Nonideal Gas 160 Selection of a Centrifugal Compressor 161 Polytropic and Isentropic Temperatures 162 Three-Stage Compression with Intercooling and Pressure Loss between Stages 164 Equivalent Air Rate 165 Interstage Condensers 166 Conduction Throueh a Furnace Wall I70 Effect of Ignoring the Radius Correction of the Overall Heat Transfer Coefficient 171 A Case of a Composite Wall: Optimum Insulation Thickness for a Steam Line 171 Performance of a Heat Exchanger with the F-Method 180 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 9.1 9.2 9.3 9.4 9.5 9.6 9.1 9.8 3:Yo 9.11 10.1 10.2 10.3 10.4 11.1 11.2 11.3 11.4 12.1 12.2 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 ix Application of the Effectiveness and the 8 Method 182 Sizing an Exchanger with Radial Finned Tubes 193 Pressure Drop on the Tube Side of a Vertical Thermosiphon Reboiler 193 Pressure Drop on the Shell Side with 25% Open Segmental Baffles by Kern’s Method 194 Estimation of the Surface Requirements of an Air Cooler 199 Process Design of a Shell-and-Tube Heat Exchanger 204 Sizing a Condenser for a Mixture by the Silver-Bell-Ghatly Method 207 Comparison of Three Kinds of Reboilers for the Same Service 209 Peak Temperatures 214 Effect of Stock Temperature Variation 214 Design of a Fired Heater 217 Annlication of the Wilson-Lobo-Hottel eauation 219 Two-Stages Propylene Compression Refrigeration with Interstage Recycle 225 Conditions in an Adiabatic Dryer 234 Drying Time over Constant and Falling Rate Periods with Constant Gas Conditions 237 Drying with Changing Humidity of Air in a Tunnel Dryer 238 Effects of Moist Air Recycle and Increase of Fresh Air Rate in Belt Conveyor Drying 239 Scale-Up of a Rotary Dryer 256 Design Details of a Countercurrent Rotary Dryer 256 Description of a Drum Drying System 260 Sizing a Pneumatic Conveying Dryer 266 Sizing a Fluidized Bed Dryer 2 7 2 Sizing a Spray Dryer on the Basis of Pilot Plant Data 279 Sizine of a Cooling Tower: Number of Transfer Units and Height of Packing- 281 Impeller Size and Speed at a Specified Power Input 293 Effects of the Ratios of impeller and Tank Diameters 294 Design of the Agitation System for Maintenance of a Slurry 299 HP and rpm Requirements of an Aerated Agitated Tank 301 Constants of the Filtration Equation from Test Data 310 Filtration Process with a Centrifugal Charge Pump 311 Rotary Vacuum Filter Operation 312 Filtration and Washing of a Compressible Material 314 Sizing a Hydrocyclone 341 Power Requirement for Grinding 342 Correlation of Relative Volatility 375 Vanorization and Condensation of a Ternarv Mixture 378 Bubblepoint Temperature with the Virial add Wilson Equations 379 Batch Distillation of Chlorinated Phenols 383 Distillation of Substances with Widely Different Molal Heats of Vaporization 385 Separation of an Azeotropic Mixture by Operation at Two Pressure Levels 387 Separation of a Partially Miscible Mixture 388 Enthalpy-Concentration Lines of Saturated Vapor and Liquid of Mixtures of Methanol and Water at a Pressure of 2 aim 390 Algebraic Method for Binarv Distillation Calculation 392 Shorcut Design of Multicomponent Fractionation 396 Calculation of an Absorber by the Absorption Factor Method 399 Numbers of Theoretical Trays and of Transfer Units with Two Values of k,/k, for a Distillation Process 402
- 11. X LIST OF EXAMPLES 13.13 13.14 13.15 13.16 13.17 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 15.1 Trays and Transfer Units for an Absorption Process 403 Representation of a Petroleum Fraction by an Equivalent Number of Discrete Components 413 Comparison of Diameters of Sieve, Valve, and Bubblecap Trays for the Same Service 4 3 1 Performance of a Packed Tower by Three Methods 4 4 1 Tray Efficiency for the Separation of Acetone and Benzene 451 The Equations for Tieline Data 465 Tabulated Tieline and Distribution Data for the System A = I-Hexene, B = Tetramethylene Sulfone, C = Benzene, Represented in Figure 14.1 466 Single Stage and Cross Current Extraction of Acetic Acid from Methylisobutyl Ketone with Water 468 Extraction with an Immiscible Solvent 469 Countercurrent Extraction Represented on Triangular and Rectangular Distribution Diagrams 470 Stage Requirements for the Separation of a Type I and a Type II System 471 Countercurrent Extraction Employing Extract Reflux 472 Leaching of an Oil-Bearing Solid in a Countercurrent Battery - 472 Trial Estimates and Converged Flow Rates and Compositions in all Stages of an Extraction Batterv for a Four-Component Mixture 476 , Sizing of Spray, Packed, or Sieve Tray Towers 486 Design of a Rotating Disk Contactor 488 Application of Ion Exchange Selectivity Data 503 15.2 15.3 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 18.1 18.2 18.3 18.4 18.5 18.6 19.1 19.2 20.1 20.2 Adsorption of n-hexane from a Natural Gas with Silica Gel 505 Size of an Ion Exchanger for Hard Water 513 Design of a Crystallizing Plant 524 Using the Phase Diagrams of Figure 16.2 528 Heat Effect Accompanying the Cooling of a Solution of MgSO, 529 Deductions from a Differential Distribution Obtained at a Known Residence Time 533 Batch Crystallization with Seeded Liquor 534 Analysis of Size Distribution Data Obtained in a CSTC 537 Crystallization in a Continuous Stirred Tank with Specified Predominant Crystal Size 538 Crystallization from a Ternary Mixture 544 Separation of Oil and Water . 614 Ouantitv of Entrainment on the Basis of Sieve Trav Correlations 6 1 7 Liquid Knockout Drum (Empty) 618 Knockout Drum with Wire Mesh Deentrainer 620 Size and Capacity of Cyclone Separators 6 2 1 Dimensions and Weight of a Horizontal Pressure Drum 628 Applications of the Equation for Osmotic Pressure 633 Concentration of a Water/Ethanol Mixture by Reverse Osmosis 642 Installed Cost of a Distillation Tower 663 Purchased and Installed Cost of Some Equipment 663
- 12. This book is intended as a guide to the selection or design of the principal kinds of chemical process equipment by engineers in school and industry. The level of treatment assumes an elementary knowledge of unit operations and transport phenomena. Access to the many design and reference books listed in Chapter 1 is desirable. For coherence, brief reviews of pertinent theory are provided. Emphasis is placed on shortcuts, rules of thumb, and data for design by analogy, often as primary design processes but also for quick evaluations of detailed work. All answers to process design questions cannot be put into a book. Even at this late date in the development of the chemical industry, it is common to hear authorities on most kinds of equipment say that their equipment can be properly fitted to a particular task only on the basis of some direct laboratory and pilot plant work. Nevertheless, much guidance and reassurance are obtainable from general experience and specific examples of successful applications, which this book attempts to provide. Much of the information is supplied in numerous tables and figures, which often deserve careful study quite apart from the text. The general background of process design, flowsheets, and process control is reviewed in the introductory chapters. The major kinds of operations and equipment are treated in individual chapters. Information about peripheral and less widely employed equipment in chemical plants is concentrated in Chapter 19 with references to key works of as much practical value as possible. Because decisions often must be based on economic grounds, Chapter 20, on costs of equipment, rounds out the book. Appendixes provide examples of equipment rating forms and manufacturers’ questionnaires. Chemical process equipment is of two kinds: custom designed and built, or proprietary “off the shelf.” For example, the sizes and performance of custom equipment such as distillation towers, drums, and heat exchangers are derived by the process engineer on the basis of established principles and data, although some mechanical details remain in accordance with safe practice codes and individual fabrication practices. Much proprietary equipment (such as filters, mixers, conveyors, and so on) has been developed largely without benefit of much theory and is fitted to job requirements also without benefit of much theory. From the point of view of the process engineer, such equipment is predesigned and fabricated and made available by manufacturers in limited numbers of types, sizes, and capacities. The process design of proprietary equipment, as considered in this book, establishes its required performance and is a process of selection from the manufacturers’ offerings, often with their recommendations or on the basis of individual experience. Complete information is provided in manufacturers’ catalogs. Several classified lists of manufacturers of chemical process equipment are readily accessible, so no listings are given here. Because more than one kind of equipment often is suitable for particular applications and may be available from several manufacturers, comparisons of equipment and typical applications are cited liberally. Some features of industrial equipment are largely arbitrary and may be standardized for convenience in particular industries or individual plants. Such aspects of equipment design are noted when feasible. Shortcut methods of design provide solutions to problems in a short time and at small expense. They must be used when data are limited or when the greater expense of a thorough method is not justifiable. In particular cases they may be employed to obtain information such as: 1. an order of magnitude check of the reasonableness of a result found by another lengthier and presumably accurate computa- tion or computer run, 2. a quick check to find if existing equipment possibly can be adapted to a new situation, 3. a comparison of alternate processes, 4. a basis for a rough cost estimate of a process. Shortcut methods occupy a prominent place in such a broad survey and limited space as this book. References to sources of more accurate design procedures are cited when available. Another approach to engineering work is with rules of thumb, which are statements of equipment performance that may obviate all need for further calculations. Typical examples, for instance, are that optimum reflux ratio is 20% greater than minimum, that a suitable cold oil velocity in a fired heater is 6ft/sec, or that the efficiency of a mixer-settler extraction stage is 70%. The trust that can be placed in a rule of thumb depends on the authority of the propounder, the risk associated with its possible inaccuracy, and the economic balance between the cost of a more accurate evaluation and suitable safety factor placed on the approximation. All experienced engineers have acquired such knowledge. When applied with discrimination, rules of thumb are a valuable asset to the process design and operating engineer, and are scattered throughout this book. Design by analogy, which is based on knowledge of what has been found to work in similar areas, even though not necessarily optimally, is another valuable technique. Accordingly, specific applications often are described in this book, and many examples of specific equipment sizes and performance are cited. For much of my insight into chemical process design, I am indebted to many years’ association and friendship with the late Charles W. Nofsinger who was a prime practitioner by analogy, rule of thumb, and basic principles. Like Dr. Dolittle of Puddleby-on- the-Marsh, “he was a proper doctor and knew a whole lot.”
- 13. RULES OF THUMB: SUMMARY Although experienced engineers know where to find information and how to make accurate computations, they also keep a minimum body of information in mind on the ready, made up largely of shortcuts and rules of thumb. The present compilation may fit into such a minimum body of information, as a boost to the memory or extension in some instances into less often encountered areas. It is derived from the material in this book and is, in a sense, a digest of the book. An Engineering Rule of Thumb is an outright statement regarding suitable sizes or performance of equipment that obviates all need for extended calculations. Because any brief statements are subject to varying degrees of qualification, they are most safely applied by engineers who are substantially familiar with the topics. Nevertheless, such rules should be of value for approximate design and cost estimation, and should provide even the inexperienced engineer with perspective and a foundation whereby the reason- ableness of detailed and computer-aided results can be appraised quickly, particularly on short notice such as in conference. Everyday activities also are governed to a large extent by rules of thumb. They serve us when we wish to take a course of action but are not in a position to find the best course of action. Of interest along this line is an amusing and often useful list of some 900 such digests of everyday experience that has been compiled by Parker (Rules of Thumb, Houghton Mifflin, Boston, 1983). Much more can be stated in adequate summary fashion about some topics than about others, which accounts in part for the spottiness of the present coverage, but the spottiness also is due to ignorance and oversights on the part of the author. Accordingly, every engineer undoubtedly will supplement or modify this material in his own way. COMPRESSORS AND VACUUM PUMPS 1. Fans are used to raise the pressure about 3% (12in. water), blowers raise to less than 40 psig, and compressors to higher pressures, although the blower range commonly is included in the compressor range. 2. Vacuum pumps: reciprocating piston type decrease the pressure to 1 Torr; rotary piston down to 0.001 Torr, two-lobe rotary down to 0.0001 Torr; steam jet ejectors, one stage down to lOOTorr, three stage down to 1 Torr, five stage down to 0.05 Torr. 3. A three-stage ejector needs 1OOlb steam/lb air to maintain a pressure of 1 Torr. 4. In-leakage of air to evacuated equipment depends on the absolute pressure, Torr, and the volume of the equipment, V cuft, according to w = kVz3 lb/hr, with k = 0.2 when P is more than 90 Torr, 0.08 between 3 and 20 Torr, and 0.025 at less than 1 Torr. 5. Theoretical adiabatic horsepower (THP) = [(SCFM)T1/8130a] [(PJPJ - 11, where Tt is inlet temperature in °F+ 460 and a = (k - 1)/k, k = CJC,,. 6. Outlet temperature & = T,(P,/P,)“. 7. To compress air from lOO”F, k = 1.4, compression ratio = 3, theoretical power required = 62 HP/million tuft/day, outlet temperature 306°F. 8. Exit temperature should not exceed 350-400°F; for diatomic gases (C,/C, = 1.4) this corresponds to a compression ratio of about 4. 9. Compression ratio should be about the same in each stage of a multistage unit, ratio = (PJPi)““, with n stages. 10. Efficiencies of reciprocating compressors: 65% at compression ratio of 1.5, 75% at 2.0, and 80-85% at 3-6. 11. Efficiencies of large centrifugal compressors, 6000-100,000 ACFM at suction, are 76-78%. 12. Rotary compressors have efficiencies of 70%, except liquid liner type which have 50%. CONVEYORS FOR PARTICULATE SOLIDS 1. Screw conveyors are suited to transport of even sticky and abrasive solids up inclines of 20” or so. They are limited to distances of 150ft or so because of shaft torque strength. A 12in. dia conveyor can handle 100@3000cuft/hr, at speeds ranging from 40 to 60 ‘pm. 2. Belt conveyors are for high capacity and long distances (a mile or more, but only several hundred feet in a plant), up inclines of 30” maximum. A 24in. wide belt can carry 3OOOcuft/hr at a speed of lOOft/min, but speeds up to 6OOft/min are suited to some materials. Power consumption is relatively low. Bucker elevators are suited to vertical transport of sticky and abrasive materials. With buckets 20 x 20 in. capacity can reach 1000 cuft/hr at a speed of 100 ft/min, but speeds to 300 ft/min are used. Drug-type conveyors (Redler) are suited to short distances in any direction and are completely enclosed. Units range in size from 3 in. square to 19 in. square and may travel from 30 ft/min (fly ash) to 250 ft/min (grains). Power requirements are high. Pneumatic conveyors are for high capacity, short distance (400 ft) transport simultaneously from several sources to several destinations. Either vacuum or low pressure (6-12psig) is employed with a range of air velocities from 35 to 120ft/sec depending on the material and pressure, air requirements from 1 to 7 cuft/cuft of solid transferred. COOLING TOWERS 1. Water in contact with air under adiabatic conditions eventually cools to the wet bulb temperature. 2. In commercial units, 90% of saturation of the air is feasible. 3. Relative cooling tower size is sensitive to the difference between the exit and wet bulb temperatures: AT('F) 5 15 25 Relative volume 2.4 1.0 0.55 4. Tower fill is of a highly open structure so as to minimize pressure drop, which is in standard practice a maximum of 2 in. of water. 5. Water circulation rate is l-4gpm/sqft and air rates are 1300-1800 lb/(hr)(sqft) or 300-400 ft/min. 6. Chimney-assisted natural draft towers are of hyperboloidal shapes because they have greater strength for a given thickness; a tower 250 ft high has concrete walls 5-6 in. thick. The enlarged cross section at the top aids in dispersion of exit humid air into the atmosphere. 7. Countercurrent induced draft towers are the most common in process industries. They are able to cool water within 2°F of the wet bulb. 8. Evaporation losses are 1% of the circulation for every 10°F of cooling range. Windage or drift losses of mechanical draft towers
- 14. Xiv R U L E S O F T H U M B : S U M M A R Y are O.l-0.3%. Blowdown of 2.5-3.0% of the circulation is necessary to prevent excessive salt buildup. CRYSTALLIZATION FROM SOLUTION 1. 2. 3. 4. 5. 6. Complete recovery of dissolved solids is obtainable by evaporation, but only to the eutectic composition by chilling. Recovery by melt crystallization also is limited by the eutectic composition. Growth rates and ultimate sizes of crystals are controlled by limiting the extent of supersaturation at any time. The ratio S = C/C,,, of prevailing concentration to saturation concentration is kept near the range of 1.02-1.05. In crystallization by chilling, the temperature of the solution is kept at most l-2°F below the saturation temperature at the prevailing concentration. Growth rates of crystals under satisfactory conditions are in the range of 0.1-0.8 mm/hr. The growth rates are approximately the same in all directions. Growth rates are influenced greatly by the presence of impurities and of certain specific additives that vary from case to case. DISINTEGRATION 1. Percentages of material greater than 50% of the maximum size are about 50% from rolls, 15% from tumbling mills, and 5% from closed circuit ball mills. 2. Closed circuit grinding employs external size classification and return of oversize for regrinding. The rules of pneumatic conveying are applied to design of air classifiers. Closed circuit is most common with ball and roller mills. 3. 4. 5. 6. Jaw crushers take lumps of several feet in diameter down to 4 in. Stroke rates are 10@300/min. The average feed is subjected to 8-10 strokes before it becomes small enough to escape. Gyratory crushers are suited to slabby feeds and make a more rounded product. Roll crushers are made either smooth or with teeth. A 24in. toothed roll can accept lumps 14in. dia. Smooth rolls effect reduction ratios up to about 4. Speeds are 50-900 rpm. Capacity is about 25% of the maximum corresponding to a continuous ribbon of material passing through the rolls. Hammer mills beat the material until it is small enough to pass through the screen at the bottom of the casing. Reduction ratios of 40 are feasible. Large units operate at 900 rpm, smaller ones up to 16,OOOrpm. For fibrous materials the screen is provided with cutting edges. Rod mills are capable of taking feed as large as 50 mm and reducing it to 300 mesh, but normally the product range is 8-65 mesh. Rods are 25-150mm dia. Ratio of rod length to mill diameter is about 1.5. About 45% of the mill volume is occupied by rods. Rotation is at 50-65% of critical. 7. Ball mills are better suited than rod mills to fine grinding. The charge is of equal weights of 1.5, 2, and 3 in. balls for the finest grinding. Volume occupied by the balls is 50% of the mill volume. Rotation speed is 70-80% of critical. Ball mills have a length to diameter ratio in the range l-1.5. Tube mills have a ratio of 4-5 and are capable of very fine grinding. Pebble mills have ceramic grinding elements, used when contamination with metal is to be avoided. 8. Roller mills employ cylindrical or tapered surfaces that roll along flatter surfaces and crush nipped particles. Products of 20-200 mesh are made. DISTILLATION AND GAS ABSORPTION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Distillation usually is the most economical method of separating liquids, superior to extraction, adsorption, crystallization, or others. For ideal mixtures, relative volatility is the ratio of vapor pressures rri2 = P,/P,. Tower operating pressure is determined most often by the temperature of the available condensing medium, lOO-120°F if cooling water; or by the maximum allowable reboiler temperature, 150 psig steam, 366°F. Sequencing of columns for separating multicomponent mix- tures: (a) perform the easiest separation first, that is, the one least demanding of trays and reflux, and leave the most difficult to the last; (b) when neither relative volatility nor feed concentration vary widely, remove the components one by one as overhead products; (c) when the adjacent ordered components in the feed vary widely in relative volatility, sequence the splits in the order of decreasing volatility; (d) when the concentrations in the feed vary widely but the relative volatilities do not, remove the components in the order of decreasing concentration in the feed. Economically optimum reflux ratio is about 1.2 times the minimum reflux ratio R,. The economically optimum number of trays is near twice the minimum value N,,,. The minimum number of trays is found with the Fenske- Underwood equation Nn = W[~l(l -~)lovtdM~ - ~)ltxrns~/~~~ a. Minimum reflux for binary or pseudobinary mixtures is given by the following when separation is esentially complete (xD = 1) and D/F is the ratio of overhead product and feed rates: R,D/F = l/(cu - l), when feed is at the bubblepoint, (R, + l)D/F = a/((~ - l), when feed is at the dewpoint. A safety factor of 10% of the number of trays calculated by the best means is advisable. Reflux pumps are made at least 25% oversize. For reasons of accessibility, tray spacings are made 20-24 in. Peak efficiency of trays is at values of the vapor factor F, = ~6 in the range 1.0-1.2 (ft/sec) B. This range of F, establishes the diameter of the tower. Roughly, linear velocities are 2ft/sec at moderate pressures and 6ft/sec in vacuum. The optimum value of the Kremser-Brown absorption factor A = K(V/L) is in the range 1.25-2.0. Pressure drop per tray is of the order of 3 in. of water or 0.1 psi. Tray efficiencies for distillation of light hydrocarbons and aqueous solutions are 60-90%; for gas absorption and stripping, lo-20%. Sieve trays have holes 0.25-0.50 in. dia, hole area being 10% of the active cross section. Valve trays have holes 1.5 in. dia each provided with a liftable cap, 12-14 caps/sqft of active cross section. Valve trays usually are cheaper than sieve trays. Bubblecap trays are used only when a liquid level must be maintained at low turndown ratio; they can be designed for lower pressure drop than either sieve or valve trays. Weir heights are 2 in., weir lengths about 75% of tray diameter, liquid rate a maximum of about 8 gpm/in. of weir; multipass arrangements are used at high liquid rates.
- 15. 20. Packings of random and structured character are suited especially to towers under 3 ft dia and where low pressure drop is desirable. With proper initial distribution and periodic redistribution, volumetric efficiencies can be made greater than those of tray towers. Packed internals are used as replacements for achieving greater throughput or separation in existing tower shells. 21. For gas rates of 500 cfm, use 1 in. packing; for gas rates of 2000 cfm or more, use 2 in. 22. The ratio of diameters of tower and packing should be at least 15. 23. Because of deformability, plastic packing is limited to a lo-15 ft depth unsupported, metal to 20-25 ft. 24. Liquid redistributors are needed every 5-10 tower diameters with pall rings but at least every 20ft. The number of liquid streams should be 3-5/sqft in towers larger than 3 ft dia (some experts say 9-12/sqft), and more numerous in smaller towers. 25. Height equivalent to a theoretical plate (HETP) for vapor-liquid contacting is 1.3-1.8ft for 1 in. pall rings, 2.5-3.0 ft for 2 in. pall rings. 26. Packed towers should operate near 70% of the flooding rate given by the correlation of Sherwood, Lobo, et al. 27. Reflux drums usually are horizontal, with a liquid holdup of 5 min half full. A takeoff pot for a second liquid phase, such as water in hydrocarbon systems, is sized for a linear velocity of that phase of 0.5 ft/sec, minimum diameter of 16 in. 28. For towers about 3 ft dia, add 4ft at the top for vapor disengagement and 6 ft at the bottom for liquid level and reboiler return. 29. Limit the tower height to about 175 ft max because of wind load and foundation considerations, An additional criterion is that L/D be less than 30. DRIVERS AND POWER RECOVERY EQUIPMENT 1 . 2 . 3 . 4 . 5 . 6 . Efficiency is greater for larger machines. Motors are 85-95%; steam turbines are 42-78%; gas engines and turbines are 28-38%. For under IOOHP, electric motors are used almost exclusively. They are made for up to 20,000 HP. Induction motors are most popular. Synchronous motors are made for speeds as low as 150rpm and are thus suited for example for low speed reciprocating compressors, but are not made smaller than 50HP. A variety of enclosures is available, from weather-proof to explosion-proof. Steam turbines are competitive above 1OOHP. They are speed controllable. Frequently they are employed as spares in case of power failure. Combustion engines and turbines are restricted to mobile and remote locations. Gas expanders for power recovery may be justified at capacities of several hundred HP; otherwise any needed pressure reduction in process is effected with throttling valves. DRYING OF SOLIDS 1. Drying times range from a few seconds in spray dryers to 1 hr or less in rotary dryers and up to several hours or even several days in tunnel shelf or belt dryers. 2. Continuous tray and belt dryers for granular material of natural size or pelleted to 3-15 mm have drying times in the range of lo-200 min. 3. Rotary cylindrical dryers operate with superficial air velocities of 5-lOft/sec, sometimes up to 35 ft/sec when the material is coarse. Residence times are S-90 min. Holdup of solid is 7-8%. RULES OF THUMB: SUMMARY xv An 85% free cross section is taken for design purposes. In countercurrent flow, the exit gas is lo-20°C above the solid; in parallel flow, the temperature of the exit solid is 100°C. Rotation speeds of about 4rpm are used, but the product of rpm and diameter in feet is typically between 15 and 25. 4. Drum dryers for pastes and slurries operate with contact times of 3-12 set, produce flakes 1-3 mm thick with evaporation rates of 15-30 kg/m2 hr. Diameters are 1.5-5.Oft; the rotation rate is 2-10rpm. The greatest evaporative capacity is of the order of 3000 lb/hr in commercial units. 5. Pneumatic conveying dryers normally take particles l-3 mm dia but up to 10 mm when the moisture is mostly on the surface. Air velocities are lo-30m/sec. Single pass residence times are 0.5-3.0 set but with normal recycling the average residence time is brought up to 60 sec. Units in use range from 0.2 m dia by 1 m high to 0.3 m dia by 38 m long. Air requirement is several SCFM/lb of dry product/hr. 6. Fluidized bed dryers work best on particles of a few tenths of a mm dia, but up to 4 mm dia have been processed. Gas velocities of twice the minimum fluidization velocity are a safe prescription. In continuous operation, drying times of l-2min are enough, but batch drying of some pharmaceutical products employs drying times of 2-3 hr. 7. Spray dryers: Surface moisture is removed in about 5sec, and most drying is completed in less than 60 sec. Parallel flow of air and stock is most common. Atomizing nozzles have openings 0.012-0.15 in. and operate at pressures of 300-4OOOpsi. Atomizing spray wheels rotate at speeds to 20,000 rpm with peripheral speeds of 250-600 ft/sec. With nozzles, the length to diameter ratio of the dryer is 4-5; with spray wheels, the ratio is 0.5-1.0. For the final design, the experts say, pilot tests in a unit of 2 m dia should be made. EVAPORATORS 1. Long tube vertical evaporators with either natural or forced circulation are most popular. Tubes are 19-63 mm dia and 12-30 ft long. 2. In forced circulation, linear velocities in the tubes are 15-20 ft/sec. 3. Elevation of boiling point by dissolved solids results in differences of 3-10°F between solution and saturated vapor. 4. When the boiling point rise is appreciable, the economic number of effects in series with forward feed is 4-6. 5. When the boiling point rise is small, minimum cost is obtained with 8-10 effects in series. 6. In backward feed the more concentrated solution is heated with the highest temperature steam so that heating surface is lessened, but the solution must be pumped between stages. 7. The steam economy of an N-stage battery is approximately 0.8N lb evaporation/lb of outside steam. 8. Interstage steam pressures can be boosted with steam jet compressors of 20-30% efficiency or with mechanical compres- sors of 70-75% efficiency. EXTRACTION, LIQUID-LIQUID 1. The dispersed phase should be the one that has the higher volumetric rate except in equipment subject to backmixing where it should be the one with the smaller volumetric rate. It should be the phase that wets the material of construction less well. Since the holdup of continuous phase usually is greater, that phase should be made up of the less expensive or less hazardous material.
- 16. Xvi RULES OF THUMB: SUMMARY 2 . 3 . 4. 5. 6 . 7 . 8 . 9 . There are no known commercial applications of reflux to extraction processes, although the theory is favorable (Treybal). Mixer-settler arrangements are limited to at most five stages. Mixing is accomplished with rotating impellers or circulating pumps. Settlers are designed on the assumption that droplet sizes are about 150 pm dia. In open vessels, residence times of 30-60 min or superficial velocities of 0.5-1.5 ft/min are provided in settlers. Extraction stage efficiencies commonly are taken as 80%. Spray towers even 20-40ft high cannot be depended on to function as more than a single stage. Packed towers are employed when 5-10 stages suffice. Pall rings of l-l.5 in. size are best. Dispersed phase loadings should not exceed 25 gal/(min) (sqft). HETS of 5-10 ft may be realizable. The dispersed phase must be redistributed every 5-7 ft. Packed towers are not satisfactory when the surface tension is more than 10 dyn/cm. Sieve tray towers have holes of only 3-8 mm dia. Velocities through the holes are kept below 0.8 ft/sec to avoid formation of small drops. Redispersion of either phase at each tray can be designed for. Tray spacings are 6-24 in. Tray efficiencies are in the range of 20-30%. Pulsed packed and sieve tray towers may operate at frequencies of 90 cycles/min and amplitudes of 6-25 mm. In large diameter towers, HETS of about 1 m has been observed. Surface tensions as high as 30-40 dyn/cm have no adverse effect. Reciprocating tray towers can have holes 9/16in. dia, 50-60% open area, stroke length 0.75 in., 100-150 strokes/mitt, plate spacing normally 2 in. but in the range l-6 in. In a 30in. dia tower, HETS is 20-25 in. and throughput is 2000 gal/(hr)(sqft). Power requirements are much less than of pulsed towers. Rotating disk contactors or other rotary agitated towers realize HETS in the range 0.1-0.5 m. The especially efficient Kuhni with perforated disks of 40% free cross section has HETS 0.2 m and a capacity of 50 m3/m2 hr. FILTRATION 1. Processes are classified by their rate of cake buildup in a laboratory vacuum leaf filter: rapid, 0.1-10.0 cm/set; medium, O.l-lO.Ocm/min; slow, O.l-lO.Ocm/hr. 2. Continuous filtration should not be attempted if l/8 in. cake thickness cannot be formed in less than 5 min. 3. Rapid filtering is accomplished with belts, top feed drums, or pusher-type centrifuges. 4. Medium rate filtering is accomplished with vacuum drums or disks or peeler-type centrifuges. 5. Slow filtering slurries are handled in pressure filters or sedimenting centrifuges. 6. Clarification with negligible cake buildup is accomplished with cartridges, precoat drums, or sand filters. 7. Laboratory tests are advisable when the filtering surface is expected to be more than a few square meters, when cake washing is critical, when cake drying may be a problem, or when precoating may be needed. 8. For finely ground ores and minerals, rotary drum filtration, rates may be 1500 lb/(day)(sqft), at 20 rev/hr and 18-25in. Hg vacuum. 9. Coarse solids and crystals may be filtered at rates of 6000 lb/(day)(sqft) at 20 rev/hr, 2-6 in. Hg vacuum. FLUIDIZATION OF PARTICLES WITH GASES 1. Properties of particles that are conducive to smooth fluidization include: rounded or smooth shape, enough toughness to resist 2 . 3 . 4 . 5 . 6 . attrition, sizes in the range 50-500pm dia, a spectrum of sizes with ratio of largest to smallest in the range of 10-25. Cracking catalysts are members of a broad class characterized by diameters of 30-150 pm, density of 1.5 g/mL or so, appreciable expansion of the bed before fluidization sets in, minimum bubbling velocity greater than minimum fluidizing velocity, and rapid disengagement of bubbles. The other extreme of smoothly fluidizing particles is typified by coarse sand and glass beads both of which have been the subject of much laboratory investigation. Their sizes are in the range 150-500 pm, densities 1.5-4.0 g/mL, small bed expansion, about the same magnitudes of minimum bubbling and minimum fluidizing velocities, and also have rapidly disengaging bubbles. Cohesive particles and large particles of 1 mm or more do not lluidize well and usually are processed in other ways. Rough correlations have been made of minimum fluidization velocity, minimum bubbling velocity, bed expansion, bed level fluctuation, and disengaging height. Experts recommend, however, that any real design be based on pilot plant work. Practical operations are conducted at two or more multiples of the minimum fluidizing velocity. In reactors, the entrained material is recovered with cyclones and returned to process. In dryers, the fine particles dry most quickly so the entrained material need not be recycled. HEAT EXCHANGERS 1. Take true countercurrent flow in a shell-and-tube exchanger as a basis. 2. Standard tubes are 3/4in. OD, 1 in. triangular spacing, 16 ft long; a shell 1 ft dia accommodates 100 sqft; 2 ft dia, 400 sqft, 3 ft dia, 1100 sqft. 3. Tube side is for corrosive, fouling, scaling, and high pressure fluids. 4. Shell side is for viscous and condensing fluids. 5. Pressure drops are 1.5 psi for boiling and 3-9psi for other ‘services. 6. Minimum temperature approach is 20°F with normal coolants, 10°F or less with refrigerants. 7. Water inlet temperature is 90”F, maximum outlet 120°F. 8. Heat transfer coefficients for estimating purposes, Btu/(hr)(sqft)(“F): water to liquid, 150; condensers, 150; liquid to liquid, 50; liquid to gas, 5; gas to gas, 5; reboiler, 200. Max flux in reboilers, 10,000 Btu/(hr)(sqft). 9. Double-pipe exchanger is competitive at duties requiring 10. 11. 12. 13. 100-200 sqft. Compact (plate and fin) exchangers have 35Osqft/cuft, and about 4 times the heat transfer per tuft of shell-and-tube units. Plate and frame exchangers are suited to high sanitation services, and are 25-50% cheaper in stainless construction than shell-and-tube units. Air coolers: Tubes are 0.75-1.00 in. OD, total finned surface 15-20 sqft/sqft bare surface, U = 80-100 Btu/(hr)(sqft bare surface)( fan power input 2-5 HP/(MBtu/hr), approach 50°F or more. Fired heaters: radiant rate, 12,000 Btu/(hr)(sqft); convection rate, 4000; cold oil tube velocity, 6 ft/sec; approx equal transfers of heat in the two sections; thermal efficiency 70-75%; flue gas temperature 250-350°F above feed inlet; stack gas temperature 650-950°F. INSULATION 1. Up to 650”F, 85% magnesia is most used. 2. Up to 1600-19OO”F, a mixture of asbestos and diatomaceous earth is used.
- 17. 3. Ceramic refractories at higher temperatures. 4. Cyrogenic equipment (-200°F) employs insulants with fine pores in which air is trapped. 5. Optimum thickness varies with temperature: 0.5 in. at 2OO”F, l.Oin. at 400”F, 1.25 in. at 600°F. 6. Under windy conditions (7.5 miles/hr), lo-20% greater thickness of insulation is justified. MIXING AND AGITATION 1. 2. 3. 4. 5. 6. I. 8. Mild agitation is obtained by circulating the liquid with an impeller at superficial velocities of O.l-0.2ft/sec, and intense agitation at 0.7-1.0 ft/sec. Intensities of agitation with impellers in baffled tanks are measured by power input, HP/1000 gal, and impeller tip speeds: Operation HP/1000 gal Tip speed (ft/min) Blending 0.2-0.5 Homogeneous reaction 0.5-l .5 7.5-10 Reaction with heat transfer 1.5-5.0 10-15 Liquid-liquid mixtures 5 15-20 Liquid-gas mixtures 5-10 15-20 Slurries 1 0 Proportions of a stirred tank relative to the diameter D: liquid level = D; turbine impeller diameter = D/3; impeller level above bottom = D/3; impeller blade width = D/15; four vertical baffles with width = D/10. Propellers are made a maximum of 18 in., turbine impellers to 9ft. Gas bubbles sparged at the bottom of the vessel will result in mild agitation at a superficial gas velocity of 1 ft/min, severe agitation at 4 ft/min. Suspension of solids with a settling velocity of 0.03 ft/sec is accomplished with either turbine or propeller impellers, but when the settling velocity is above 0.15 ft/sec intense agitation with a propeller is needed. Power to drive a mixture of a gas and a liquid can be 25-50% less than the power to drive the liquid alone. In-line blenders are adequate when a second or two contact time is sufficient, with power inputs of 0.1-0.2 HP/gal. PARTICLE SIZE ENLARGEMENT 1. The chief methods of particle size enlargement are: compression into a mold, extrusion through a die followed by cutting or breaking to size, globulation of molten material followed by solidification, agglomeration under tumbling or otherwise agitated conditions with or without binding agents. 2. Rotating drum granulators have length to diameter ratios of 2-3, speeds of lo-20 rpm, pitch as much as 10”. Size is controlled by speed, residence time, and amount of binder; 2-5 mm dia is common. 3. Rotary disk granulators produce a more nearly uniform product than drum granulators. Fertilizer is made 1.5-3.5 mm; iron ore lo-25 mm dia. 4. Roll compacting and briquetting is done with rolls ranging from 130mm dia by 50mm wide to 910mm dia by 550mm wide. Extrudates are made l-10 mm thick and are broken down to size for any needed processing such as feed to tabletting machines or to dryers. Tablets are made in rotary compression machines that convert powders and granules into uniform sizes. Usual maximum diameter is about 1.5 in., but special sizes up to 4in. dia are possible. Machines operate at 1OOrpm or so and make up to 10,000 tablets/min. Extruders make pellets by forcing powders, pastes, and melts RULES OF THUMB: SUMMARY Xvii through a die followed by cutting. An 8 in. screw has a capacity of 2000 Ib/hr of molten plastic and is able to extrude tubing at 150-3OOft/min and to cut it into sizes as small as washers at 8OOO/min. Ring pellet extrusion mills have hole diameters of 1.6-32 mm. Production rates cover a range of 30-200 Ib/(hr)(HP). Prilling towers convert molten materials into droplets and allow them to solidify in contact with an air stream. Towers as high as 60m are used. Economically the process becomes competitive with other granulation processes when a capacity of 200- 409 tons/day is reached. Ammonium nitrate prills, for example, are 1.6-3.5 mm dia in the 5-95% range. Fluidized bed granulation is conducted in shallow beds 12-24 in. deep at air velocities of 0.1-2.5 m/s or 3-10 times the minimum fluidizing velocity, with evaporation rates of 0.005- 1.0 kg/m* sec. One product has a size range 0.7-2.4 mm dia. PIPING 1. Line velocities and pressure drops, with line diameter D in inches: liquid pump discharge, (5 + D/3) ft/sec, 2.0 psi/100 ft; liquid pump suction, (1.3 + D/6) ft/sec, 0.4 psi/100 ft; steam or gas, 200 ft/sec, 0.5 psi/100 ft. 2. Control valves require at least 10 psi drop for good control. 3. Globe valves are used for gases, for control and wherever tight shutoff is required. Gate valves are for most other services. 4. Screwed fittings are used only on sizes 1.5 in. and smaller, flanges or welding otherwise. 5. Flanges and fittings are rated for 150, 300, 600, 900, 1500, or 2500 psig. 6. Pipe schedule number = lOOOP/S, approximately, where P is the internal pressure psig and S is the allowable working stress (about 10,000 psi for A120 carbon steel at 500°F). Schedule 40 is most common. PUMPS 1. 2. 3. 4. 5. 6. 7. Power for pumping liquids: HP = (gpm)(psi difference)/(l714) (fractional efficiency). Normal pump suction head (NPSH) of a pump must be in excess of a certain number, depending on the kind of pumps and the conditions, if damage is to be avoided. NPSH = (pressure at the eye of the impeller - vapor pressure)/(density). Common range is 4-20 ft. Specific speed N, = (rpm)(gpm)0.5/(head in ft)‘.“. Pump may be damaged if certain limits of N, are exceeded, and efficiency is best in some ranges. Centrifugal pumps: Single stage for 15-5000gpm, 500ft max head; multistage for 20-11,000 gpm, 5500 ft max head. Efficiency 45% at 100 gpm, 70% at 500 gpm, 80% at 10,000 gpm. Axial pumps for 20-100,000 gpm, 40 ft head, 65-85% efficiency. Rotary pumps for l-5000 gpm, 50,OOOft head, 50-80% efficiency. Reciprocating pumps for lo-10,000 gpm, l,OOO,OOO ft head max. Efficiency 70% at 10 HP, 85% at 50 HP, 90% at 500 HP. REACTORS 1. The rate of reaction in every instance must be established in the laboratory, and the residence time or space velocity and product distribution eventually must be found in a pilot plant. 2. Dimensions of catalyst particles are 0.1 mm in fluidized beds, 1 mm in slurry beds, and 2-5 mm in fixed beds. 3. The optimum proportions of stirred tank reactors are with liquid level equal to the tank diameter, but at high pressures slimmer proportions are economical.
- 18. Xviii RULES OF THUMB: SUMMARY 4. Power input to a homogeneous reaction stirred tank is 0.5-1.5 HP/lOOOgal, but three times this amount when heat is to be . transferred. 5. Ideal CSTR (continuous stirred tank reactor) behavior is approached when the mean residence time is 5-10 times the length of time needed to achieve homogeneity, which is accomplished with 500-2000 revolutions of a properly designed stirrer. 6. 7. 8. 9. 10. Batch reactions are conducted in stirred tanks for small daily production rates or when the reaction times are long or when some condition such as feed rate or temperature must be programmed in some way. Relatively slow reactions of liquids and slurries are conducted in continuous stirred tanks. A battery of four or five in series is most economical. Tubular flow reactors ate suited to high production rates at short residence times (set or min) and when substantial heat transfer is needed. Embedded tubes or shell-and-tube construction then are used. In granular catalyst packed reactors, the residence time distribution often is no better than that of a five-stage CSTR battery. For conversions under about 95% of equilibrium, the performance of a five-stage CSTR battery approaches plug flow. REFRIGERATION 1. 2. 3. 4. 5. 6. 7. A ton of refrigeration is the removal of 12,000 Btu/hr of heat. At various temperature levels: O-50”F, chilled brine and glycol solutions; -50-40”F, ammonia, freons, butane; -150--5O”F, ethane or propane. Compression refrigeration with 100°F condenser requires these HP/ton at various temperature levels: 1.24 at 20°F; 1.75 at 0°F; 3.1 at -40°F; 5.2 at -80°F. Below -80”F, cascades of two or three refrigerants are used. In single stage compression, the compression ratio is limited to about 4. In multistage compression, economy is improved with interstage flashing and recycling, so-called economizer operation. Absorption refrigeration (ammonia to -3O”F, lithium bromide to +45”F) is economical when waste steam is available at 12 psig or so. SIZE SEPARATION OF PARTICLES 1. Grizzlies that are constructed of parallel bars at appropriate spacings are used to remove products larger than 5 cm dia. 2. Revolving cylindrical screens rotate at 15-20 rpm and below the critical velocity; they are suitable for wet or dry screening in the range of lo-60 mm. 3. Flat screens are vibrated or shaken or impacted with bouncing balls. Inclined screens vibrate at 600-70@0 strokes/min and are used for down to 38 pm although capacity drops off sharply below 200pm. Reciprocating screens operate in the range 30-1000 strokes/min and handle sizes down to 0.25 mm at the higher speeds. 4. Rotary sifters operate at 500-600 rpm and are suited to a range of 12 mm to 50 pm. 5. Air classification is preferred for fine sizes because screens of 150 mesh and finer are fragile and slow. 6. Wet classifiers mostly are used to make two product size ranges, oversize and undersize, with a break commonly in the range between 28 and 200 mesh. A rake classifier operates at about 9 strokes/min when making separation at 200 mesh, and 32 strokes/min at 28 mesh. Solids content is not critical, and that of the overflow may be 2-20% or more. 7. Hydrocyclones handle up to 6OOcuft/min and can remove particles in the range of 300-5 pm from dilute suspensions. In one case, a 20in. dia unit had a capacity of 1000 gpm with a pressure drop of 5 psi and a cutoff between 50 and 150 pm. UTILITIES: COMMON SPECIFICATIONS 1. 2. 3. 4. 5. 6. 7. Steam: 1.5-30 psig, 250-275°F; 150 psig, 366°F; 400 psig, 448°F; 600 psig, 488°F or with lOO-150°F superheat. Cooling water: Supply at 80-90°F from cooling tower, return at 115-125°F; return seawater at llO”F, return tempered water or steam condensate above 125°F. Cooling air supply at 85-95°F; temperature approach to process, 40°F. Compressed air at 45, 150, 300, or 450 psig levels. Instrument air at 45 psig, 0°F dewpoint. Fuels: gas of lOOOBtu/SCF at 5-lopsig, or up to 25psig for some types of burners; liquid at 6 million Btu/barrel. Heat transfer fluids: petroleum oils below 600”F, Dowtherms below 750”F, fused salts below lloo”F, direct fire or electricity above 450°F. 8. Electricity: l-100 Hp, 220-550 V; 200-2500 Hp, 2300-4000 V. VESSELS (DRUMS) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Drums are relatively small vessels to provide surge capacity or separation of entrained phases. Liquid drums usually are horizontal. Gas/liquid separators are vertical. Optimum length/diameter = 3, but a range of 2.5-5.0 is common. Holdup time is 5 min half full for reflux drums, 5-10 min for a product feeding another tower. In drums feeding a furnace, 30 min half full is allowed. Knockout drums ahead of compressors should hold no less than 10 times the liquid volume passing through per minute. Liquid/liquid separators are designed for settling velocity of 2-j in./min. Gas velocity in gas/liquid separators, V = kw ft/sec, with k = 0.35 with mesh deentrainer, k = 0.1 without mesh deentrainer. Entrainment removal of 99% is attained with mesh pads of 4-12 in. thicknesses; 6 in. thickness is popular. For vertical pads, the value of the coefficient in Step 9 is reduced by a factor of 213. Good performance can be expected at velocities of 30-100% of those calculated with the given k; 75% is popular. Disengaging spaces of 6-18in. ahead of the pad and 12in. above the pad are suitable. Cyclone separators can be designed for 95% collection of 5 pm particles, but usually only droplets greater than 50 pm need be removed. VESSELS (PRESSURE) 1. Design temperature between -20°F and 650°F is 50°F above operating temperature; higher safety margins are used outside the given temperature range. 2. The design pressure is 10% or 10-25 psi over the maximum oper- ating pressure, whichever is greater. The maximum operating pressure, in turn, is taken as 25 psi above the normal operation. 3. Design pressures of vessels operating at 0-1Opsig and 600- 1000°F are 40 psig.
- 19. RULES OF THUMB: SUMMARY Xix 4. For vacuum operation, design pressures are 15 psig and full vacuum. 5. Minimum wall thicknesses for rigidity: 0.25 in. for 42 in. dia and ‘under, 0.32 in. for 42-60 in. dia, and 0.38 in. for over 60 in. dia. 6. Corrosion allowance 0.35 in. for known corrosive conditions, 0.15 in. for non-corrosive streams, and 0.06 in. for steam drums and air receivers. 7. Allowable working stresses are one-fourth of the ultimate strength of the material. 8. Maximum allowable stress depends sharply on temperature. Temperature 1°F) - 2 0 - 6 5 0 750 850 1000 Low alloy steel SA203 (psi) 18,750 15,650 9550 2500 Type 302 stainless (psi) 18,750 18,750 15,900 6250 VESSELS (STORAGE TANKS) 1. For less than 1000 gal, use vertical tanks on legs. 2. Between 1000 and 10,OOOgal, use horizontal tanks on concrete supports. 3. Beyond 10,000 gal, use vertical tanks on concrete foundations. 4. Liquids subject to breathing losses may be stored in tanks with floating or expansion roofs for conservation. 5. Freeboard is 15% below 500 gal and 10% above 500 gal capacity. 6. Thirty days capacity often is specified for raw materials and products, but depends on connecting transportation equipment schedules. 7. Capacities of storage tanks are at least 1.5 times the size of connecting transportation equipment; for instance, 7500 gal tank trucks, 34,500 gal tank cars, and virtually unlimited barge and tanker capacities.
- 20. 1 INTRODUCTION A /though this book is devoted to the selection and performance is dependent on the others in terms of material design of individual equipment, some mention and energy balances and rate processes. This chapter will should be made of integration of a number of units discuss general background material relating to complete into a process. Each piece of equipment interacts process design, and Chapter 2 will treat briefly the basic topic - with several others in a plant, and the range of its required of flowsheets. 1.1. PROCESS DESIGN Process design establishes the sequence of chemical and physical operations; operating conditions; the duties, major specifications, and materials of construction (where critical) of all process equipment (as distinguished from utilities and building auxiliaries); the general arrangement of equipment needed to ensure proper functioning of the plant; line sizes; and principal instrumentation. The process design is summarized by a process flowsheet, a material and energy balance, and a set of individual equipment specifi- cations. Varying degrees of thoroughness of a process design may be required for different purposes. Sometimes only a preliminary design and cost estimate are needed to evaluate the advisability of further research on a new process or a proposed plant expansion or detailed design work; or a preliminary design may be needed to establish the approximate funding for a complete design and construction. A particularly valuable function of preliminary design is that it may reveal lack of certain data needed for final design. Data of costs of individual equipment are supplied in this book, but the complete economics of process design is beyond its scope. 1.2. EQUIPMENT Two main categories of process equipment are proprietary and custom-designed. Proprietary equipment is designed by the manufacturer to meet performance specifications made by the user; these specifications may be regarded as the process design of the equipment. This category includes equipment with moving parts such as pumps, compressors, and drivers as well as cooling towers, dryers, filters, mixers, agitators, piping equipment, and valves, and even the structural aspects of heat exchangers, furnaces, and other equipment. Custom design is needed for many aspects of chemical reactors, most vessels, multistage separators such as fractionators, and other special equipment not amenable to complete stan- dardization. Only those characteristics of equipment are specified by process design that are significant from the process point of view. On a pump, for instance, process design will specify the operating conditions, capacity, pressure differential, NPSH, materials of construction in contact with process liquid, and a few other items, but not such details as the wall thickness of the casing or the type of stuffing box or the nozzle sizes and the foundation dimensions- -although most of these omitted items eventually must be known before a plant is ready for construction. Standard specification forms are available for most proprietary kinds of equipment and for summarizing the details of all kinds of equipment. By providing suitable check lists, they simplify the work by ensuring that all needed data have been provided. A collection of such forms is in Appendix B. Proprietary equipment is provided “off the shelf’ in limited sizes and capacities. Special sizes that would fit particular appli- cations more closely often are more expensive than a larger standard size that incidentally may provide a worthwhile safety factor. Even largely custom-designed equipment, such as vessels, is subject to standardization such as discrete ranges of head diameters, pressure ratings of nozzles, sizes of manways, and kinds of trays and packings. Many codes and standards are established by government agencies, insurance companies, and organizations sponsored by engineering societies. Some standardizations within individual plants are arbitrary choices from comparable methods, made to simplify construction, maintenance, and repair: for example, restriction to instrumentation of a particular manufacturer or to a limited number of sizes of heat exchanger tubing or a particular method of installing liquid level gage glasses. All such restrictions must be home in mind by the process designer. VENDORS’ QUESTIONNAIRES A manufacturer’s or vendor’s inquiry form is a questionnaire whose completion will give him the information on which to base a specific recommendation of equipment and a price. General information about the process in which the proposed equipment is expected to function, amounts and appropriate properties of the streams involved, and the required performance are basic. The nature of additional information varies from case to case; for instance, being different for filters than for pneumatic conveyors. Individual suppliers have specific inquiry forms. A representative selection is in Appendix C. SPECIFICATION FORMS When completed, a specification form is a record of the salient features of the equipment, the conditions under which it is to operate, and its guaranteed performance. Usually it is the basis for a firm price quotation. Some of these forms are made up by organizations such as TEMA or API, but all large engineering contractors and many large operating companies have other forms for their own needs. A selection of specification forms is in Appendix B. 1.3. CATEGORIES OF ENGINEERING PRACTICE Although the design of a chemical process plant is initiated by chemical engineers, its complete design and construction requires the inputs of other specialists: mechanical, structural, electrical, and instrumentation engineers; vessel and piping designers; and purchasing agents who know what may be available at attractive prices. On large projects all these activities are correlated by a job engineer or project manager; on individual items of equipment or small projects, the process engineer naturally assumes this function. A key activity is the writing of specifications for soliciting bids and ultimately purchasing equipment. Specifications must be written so explicitly that the bidders are held to a uniform standard and a clear-cut choice can be made on the basis of their offerings alone. 1
- 21. 2 INTRODUCTION % of Total Project Time Figure 1.1. Progress of material commitment, engineering manhours, and construction [Matozzi, Oil Gas. J. p. 304, (23 March 1953)]. % of Total Project Time Figure 1.2. Rate of application of engineering manhours of various categories. The area between the curves represents accumulated manhours for each speciality up to a given % completion of the project [Miller, Chem. Eng., p. 188, (July 1956)]. For a typical project, Figure 1.1 shows the distributions of engineering, material commitment, and construction efforts. Of the engineering effort, the process engineering is a small part. Figure 1.2 shows that it starts immediately and finishes early. In terms of money, the cost of engineering ranges from 5 to 15% or so of the total plant cost; the lower value for large plants that are largely patterned after earlier ones, and the higher for small plants or those based on new technology or unusual codes and specifications. 1.4. SOURCES OF INFORMATION FOR PROCESS DESIGN A selection of books relating to process design methods and data is listed in the references at the end of this chapter. Items that are especially desirable in a personal library or readily accessible are identified. Specialized references are given throughout the book in connection with specific topics. The extensive chemical literature is served by the bibliographic items cited in References, Section 1.2, Part B. The book by Rasmussen and Fredenslund (1980) is addressed to chemical ~engineers and cites some literature not included in some of the other bibliographies, as well as information about proprietary data banks. The book by Leesley (References, Section 1.1, Part B) has much information about proprietary data banks and design methods. In its current and earlier editions, the book by Peters and Timmerhaus has many useful bibliographies on classified topics. For information about chemical manufacturing processes, the main encyclopedic references are Kirk-Othmer (1978-1984), McKetta and Cunningham (1976-date) and Ullmann (1972-1983) (References, Section 1.2, Part B). The last of these is in German, but an English version was started in 1984 and three volumes per year are planned; this beautifully organized reference should be most welcome. The most comprehensive compilation of physical property data is that of Landolt-Bornstein (1950-date) (References, Section 1.2, Part C). Although most of the material is in German, recent volumes have detailed tables of contents in English and some volumes are largely in English. Another large compilation, somewhat venerable but still valuable, is the International Critical Tables (1926-1933). Data and methods of estimating properties of hydrocarbons and their mixtures are in the API Data Book (1971-date) (References, Section 1.2, Part C). More general treatments of estimation of physical properties are listed in References, Section 1.1, Part C. There are many compilations of special data such as solubilities, vapor pressures, phase equilibria, transport and thermal properties, and so on. A few of them are listed in References, Section 1.2, Part D, and references to many others are in the References, Section 1.2, Part B. Information about equipment sizes and configurations, and sometimes performance, of equipment is best found in manufac- turers’ catalogs. Items 1 and 2 of References, Section 1.1, Part D, contain some advertisements with illustrations, but perhaps their principal value is in the listings of manufacturers by the kind of equipment. Thomas Register covers all manufacturers and so is less convenient at least for an initial search. The other three items of this group of books have illustrations and descriptions of all kinds of chemical process equipment. Although these books are old, one is surprised to note how many equipment designs have survived. 1.5. CODES, STANDARDS, AND RECOMMENDED PRACTICES A large body of rules has been developed over the years to ensure the safe and economical design, fabrication and testing of equipment, structures, and materials. Codification of these rules has been done by associations organized for just such purposes, by professional societies, trade groups, insurance underwriting companies, and government agencies. Engineering contractors and large manufacturing companies usually maintain individual sets of standards so as to maintain continuity of design and to simplify maintenance of plant. Table 1.1 is a representative table of contents of the mechanical standards of a large oil company. Typical of the many thousands of items that are standardized in the field of engineering are limitations on the sizes and wall th,icknesses of piping, specifications of the compositions of alloys, stipulation of the safety factors applied to strengths of construction materials, testing procedures for many kinds of materials, and so on. Although the safe design practices recommended by profes- sional and trade associations have no legal standing where they have not actually been incorporated in a body of law, many of them have the respect and confidence of the engineering profession as a whole and have been accepted by insurance underwriters so they are widely observed. Even when they are only voluntary, standards constitute a digest of experience that represents a minimum re- quirement of good practice. Two publications by Burklin (References, Section 1.1, Part B) are devoted to standards of importance to the chemical industry. Listed are about 50 organizations and 60 topics with which they are concerned. National Bureau of Standards Publication 329 contains about 25,000 titles of U.S. standards. The NBS-SIS service maintains a reference collection of 200,000 items accessible by letter or phone. Information about foreign standards is obtainable through the American National Standards Institute (ANSI). A listing of codes and standards bearing directly on process
- 22. TABLE 1.1. Internal Engineering Standards of a Large Petroleum Refinery’ ’ 1 Appropriations and mechanical orders (10) 2 Buildings-architectural (15) 3 Buildings-mechanical (10) 4 Capacities and weights (25) 5 Contracts (I 0) 6 Cooling towers (10) 7 Correspondence (5) 8 Designation and numbering rules for equipment and facilities (10) / 9 Drainage (25) 10 Electrical (10) 1 1 Excavating, grading, and paving (10) 12 Fire fighting (10) 13 Furnaces and boilers (10) 14 General instructions (20) 15 Handling equipment (5) 16 Heat exchangers (IO) 17 Instruments and controls (45) 18 Insulation (IO) 19 Machinery (35) 2 0 Material procurement and disposition (20) 2 1 Material selection (5) 22 Miscellaneous process equipment (25) 23 Personnel protective equipment (5) 24 Piping (150) 25 Piping supports (25) 26 Plant layout (20) 27 Pressure vessels (25) 28 Protective coatings (IO) 29 Roads and railroads (25) 30 Storage vessels (45) 31 Structural (35) 32 Symbols and drafting practice (15) 33 Welding (10) ‘Figures in parentheses identify the numbers of distinct standards. TABLE 1.2. Codes and Standards of Direct Bearin on Chemical Process Design (a Selection A. American Institute of Chemical Engineers, 345 E. 47th St., New York, NY 10017 1. Standard testing procedures; 21 have been published, for example on centrifuges, filters, mixers, firer heaters B. American Petroleum Institute, 2001 L St. NW, Washington, DC 20037 2. Recommended practices for refinery inspections 3. Guide for inspection of refinery equipment 4. Manual on disposal of refinery wastes 5. Recommended practice for design and construction of large, low pressure storage tanks 6. Recommended practice for design and construction of pressure relieving devices 7. Recommended practices for safety and fire protection C. American Society of Mechanical Engineers, 345 W. 47th St., New York, NY 10017 8. ASME Boiler and Pressure Vessel Code. Sec. VIII, Unfired Pressure Vessels 9. Code for pressure piping 10; Scheme for identification of piping systems D. American Society for Testing Materials, 1916 Race St., Philadelphia, PA 19103 11. ASTM Standards, 66 volumes in 16 sections, annual, with about 30% revision each year E. American National Standards Institute (ANSI), 1430 Broadway, New York, NY 10018 12. Abbreviations, letter symbols, graphical symbols, drawing and drafting room practice 1.6. MATERIAL AND ENERGY BALANCES 3 TABLE 1.2-( continued) F. Chemical Manufacturers’ Association, 2501 M St. NW, Washington, DC 20037 13. Manual of standard and recommended practices for containers, tank cars, pollution of air and water 14. Chemical safety data sheets of individual chemicals G. Cooling Tower Institute, 19827 Highway 45 N, Spring, TX 77388 15. Acceptance test procedure for water cooling towers of mechanical draft industrial type H. Hydraulic Institute, 712 Lakewood Center N, 14600 Detroit Ave., Cleveland, OH 44107 16. Standards for centrifugal, reciprocating, and rotary pumps 17. Pipe friction manual I. Instrument Society of America (ISA), 67 Alexander Dr., Research Triangle Park, NC 27709 18. Instrumentation flow plan symbols 19. Specification forms for instruments 20. Dynamic response testing of process control instrumentation J. Tubular Exchangers Manufacturers’ Association, 25 N Broadway, Tarrytown, NY 10591 21. TEMA standards K. International Standards Organization (ISO), 1430 Broadway, New York, NY 10018 22. Many standards TABLE 1.3. Codes and Standards Supplementary to Process Design (a Selection) A. American Concrete Institute, 22400 W. 7 Mile Rd., Detroit, Ml 48219 1. Reinforced concrete design handbook 2. Manual of standard practice for detailing reinforced concrete structures B. American Institute of Steel Construction, 400 N. Michigan Ave., Chicago, IL 60611 3. Manual of steel construction 4. Standard practice for steel buildings and bridges C. American Iron and Steel Institute, 1000 16th St. NW, Washington, DC 20036 5. AISI standard steel compositions D. American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRE), 1791 Tullie Circle NE, Atlanta, GA 30329 6. Refrigerating data book E. Institute of Electrical and Electronics Engineers, 345 E. 47th St., New York, NY 10017 7. Many standards F. National Bureau of Standards, Washington, DC 8. American standard building code 9. National electrical code G. National Electrical Manufacturers Association, 2101 L St. NW, Washington, DC 20037 10. NEMA standards design is in Table 1.2, and of supplementary codes and standards in Table 1.3. 1.6. MATERIAL AND ENERGY BALANCES Material and energy balances arc based on a conservation law which is stated generally in the form input + source = output + sink + accumulation. The individual terms can be plural and can be rates as well as absolute quantities. Balances of particular entities are made around a bounded region called a system. Input and output quantities of an entity cross the boundaries. A source is an increase in the amount
- 23. 4 INTRODUCTION of the entity that occurs without a crossing of the boundary; for example, an increase in the sensible enthalpy or in the amount of a substance as a consequence of chemical reaction. Analogously, sinks are decreases without a boundary crossing, as the dis- appearance of water from a fluid stream by adsorption onto a solid phase within the boundary. Accumulations are time rates of change of the amount of the entities within the boundary. For example, in the absence of sources and sinks, an accumulation occurs when the input and output rates are different. In the steady state, the accumulation is zero. Although the principle of balancing is simple, its application requires knowledge of the performance of all the kinds of equipment comprising the system and of the phase relations and physical properties of all mixtures that participate in the process. As a consequence of trying to cover a variety of equipment and processes, the books devoted to the subject of material and energy balances always run to several hundred pages. Throughout this book, material and energy balances are utilized in connection with the design of individual kinds of equipment and some processes. Cases involving individual pieces of equipment usually are relatively easy to balance, for example, the overall balance of a distillation column in Section 13.4.1 and of nonisothermal reactors of Tables 17.4-17.7. When a process is maintained isothermal, only a material balance is needed to describe the process, unless it is also required to know the net heat transfer for maintaining a constant temperature. In most plant design situations of practical interest, however, the several pieces of equipment interact with each other, the output of one unit being the input to another that in turn may recycle part of its output to the inputter. Common examples are an absorber-stripper combination in which the performance of the absorber depends on the quality of the absorbent being returned from the stripper, or a catalytic cracker-catalyst regenerator system whose two parts interact closely. Because the performance of a particular piece of equipment depends on its input, recycling of streams in a process introduces temporarily unknown, intermediate streams whose amounts, com- positions, and properties must be found by calculation. For a plant with dozens or hundreds of streams the resulting mathematical problem is formidable and has led to the development of many computer algorithms for its solution, some of them making quite rough approximations, others more nearly exact. Usually the problem is solved more easily if the performance of the equipment is specified in advance and its size is found after the balances are completed. If the equipment is existing or must be limited in size, the balancing process will require simultaneous evaluation of its performance and consequently is a much more involved operation, but one which can be handled by computer when necessary. The literature of this subject naturally is extensive. An early book (for this subject), Nagiev’s Theory of Recycle Processes in Chemical Engineering (Macmillan, New York, 1964, Russian edition, 1958) treats many practical cases by reducing them to systems of linear algebraic equations that are readily solvable. The book by Westerberg et al., Process Flows/reefing (Cambridge Univ. Press, Cambridge, 1977) describes some aspects of the subject and has an extensive bibliography. Benedek in Steady State Flowsheering of Chemical Plants (Elsevier, New York, 1980) provides a detailed description of one simulation system. Leesley in Computer-Aided Process Design (Gulf, Houston, 1982) describes the capabilities of some commercially available flowsheet simulation programs. Some of these incorporate economic balance with material and energy balances. A program MASSBAL in BASIC language is in the book of Sinnott et al., Design, Vol. 6 (Pergamon, New York, 1983); it can handle up to 20 components and 50 units when their several outputs are specified to be in fixed proportions. Figure 1.3. Notation of flow quantities in a reactor (1) and distillation column (2). Ar) designates the amount of component A in stream k proceeding from unit i to unit j. Subscripts 0 designates a source or sink beyond the boundary limits. I designates a total flow quantity. A key factor in the effective formulation of material and energy balances is a proper notation for equipment and streams. Figure 1.3, representing a reactor and a separator, utilizes a simple type. When the pieces of equipment are numbered i and j, the notation A$!‘) signifies the flow rate of substance A in stream k proceeding from unit i to unit j. The total stream is designated IF). Subscript t designates a total stream and subscript 0 designates sources or sinks outside the system. Example 1.1 adopts this notation for balancing a reactor-separator process in which the performances are specified in advance. Since this book is concerned primarily with one kind of equipment at a time, all that need be done here is to call attention to the existence of the abundant literature on these topics of recycle calculations and flowsheet simulation. 1.7. ECONOMIC BALANCE Engineering enterprises always are subject to monetary considera- tions, and a balance is sought between fixed and operating costs. In the simplest terms, fixed costs consist of depreciation of the investment plus interest on the working capital. Operating costs include labor, raw materials, utilities, maintenance, and overheads which consists in turn of administrative, sales and research costs. Usually as the capital cost of a process unit goes up, the operating cost goes down. For example, an increase in control instrumenta- tion and automation at a higher cost is accompanied by a reduction in operating labor cost. Somewhere in the summation of these factors there is a minimum which should be the design point in the absence of any contrary intangibles such as building for the future or unusual local conditions. Costs of many individual pieces of equipment are summarized in Chapter 20, but analysis of the costs of complete processes is beyond the scope of this book. References may be made, however, to several collections of economic analyses of chemical engineering interest that have been published: 1. AIChE Student Contest Problems (annual) (AIChE, New York).
- 24. 1.7. ECONOMIC BALANCE 5 EXAMPLE 1.1 Separator no. 2 returns 80% of the unreacted chlorine to the Material Balance of a Chlorination Process with Recycle A plant for the chlorination has the flowsheet shown. From pilot reactor and separator no. 3 returns 90% of the benzene. Both plant work, with a chlorine/benzene charge weight ratio of 0.82, the recycle streams are pure. Fresh chlorine is charged at such a rate that the weight ratio of chlorine to benzene in the total charge composition of the reactor effluent is remains 0.82. The amounts of other streams are-found by material A. C,H, balances and are shown in parentheses on the sketch per 100 lbs of 0 . 2 4 7 B. Cl, 0 . 1 0 0 fresh benzene to the system. C. C,H,CI 0.3174 D. C,H,CI, 0 . 1 5 5 9 E . H C I 0.1797 Fresh C,H, A 3, (68.0) Recycle C 6 H 6 A,, = 100 B,, (24.5) Recycle Cl, Fresh Cl 2 B,, (113.2) , r 1 3 HCl E,, Cl, B20 H2° %H, LO C, H5C1 .C,, C,H,C1, D, 2. Bodman, Industrial Practice of Chemical Process Engineering (MIT Press, Cambridge, MA, 1968). 3. Rase, Chemical Reactor Design for Process Plants, Vol. II, Case Studies (Wiley, New York, 1977). 4. Washington University, St. Louis, Case Studies in Chemical Engineering Design (22 cases to 1984). Somewhat broader in scope are: 5. Wei et al., The Structure of the Chemical Processing Industries (McGraw-Hill, New York, 1979). 6. Skinner et al., Manufacturing Policy in the Oil Industry (Irwin, Homewood, IL., 1970). I. Skinner et al., Manufacturing Policy in the Plastics Industry (Irwin, Homewood, Il., 1968). Many briefer studies of individual equipment appear in some books, of which a selection is as follows: l Happel and Jordan, Chemical Process Economics (Dekker, New York, 1975): 1. Absorption of ethanol from a gas containing CO, (p. 403). 2. A reactor-separator for simultaneous chemical reactions (p. 419). 3. Distillation of a binary mixture (p. 38.5). 4. A heat exchanger and cooler system (p. 370). 5. Piping of water (p. 353). 6. Rotary dryer (p. 414). l Jelen et al., Cost and Optimization Engineering (McGraw-Hill, New York, 1983): 7. Drill bit life and replacement policy (p. 223). 8. Homogeneous flow reactor (p. 229). 9. Batch reaction with negligible downtime (p. 236). l Peters and Timmerhaus, Plant Design and Economics for Chemical Engineers (McGraw-Hill, New York, 1980): 10. Shell and tube cooling of air with water (p. 688). l Rudd and Watson, Strategy of Process Engineering (Wiley, New York, 1968): 11. Optimization of a three stage refrigeration system (p. 172). l Sherwood, A Course in Process Design (MIT Press, Cambridge, MA, 1963): 12. Gas transmission line (p. 84). 13. Fresh water from sea water by evaporation (p. 138). l Ulrich, A Guide to Chemical Engineering Process Design and Economics (Wiley, New York, 1984): 14. Multiple effect evaporator for Kraft liquor (p. 347). l Walas, Reaction Kinetics for Chemical Engineers (McGraw-Hill, New York, 1959): 15. Optimum number of vessels in a CSTR battery (p. 98). Since capital, labor, and energy costs have not escalated equally over the years since these studies were made, their conclusions are subject to reinterpretation, but the patterns of study that were used should be informative. Because of the rapid escalation of energy costs in recent years,
- 25. 6 INTRODUCTION closer appraisals of energy utilizations by complete processes are being made, from the standpoints of both the conservation laws and the second law of thermodynamics. In the latter cases attention is focused on changes in entropy and in the related availability function, AB = AH - &AS, with emphasis on work as the best possible transformation of energy. In this way a second law analysis of a process will reveal where the greatest generation of entropy occurs and where possibly the most improvement can be made by appropriate changes of process or equipment. Such an analysis of a cryogenic process for air separation was made by Benedict and Gyftopolous [in Gaggioli (Ed.), Thermodynamic Second Law Analysis, ACS Symposium Series No. 122, American Chemical Society, Washington, DC, 19801; they found a pressure drop at which the combination of exchanger and compressor was most economical. A low second law efficiency is not always realistically improv- able. Thus Weber and Meissner (Thermodynamics for Chemical Engineers, John Wiley, New York, 1957) found a 6% efficiency for the separation of ethanol and water by distillation which is not substantially improvable by redesign of the distillation process. Perhaps this suggests that more efficient methods than distillation should be sought for the separation of volatile mixtures, but none has been found at competitive cost. Details of the thermodynamic basis of availability analysis are dealt with by Moran (Availability Annfysb, Prentice-Hall, Englewood Cliffs, NJ, 1982). He applies the method to a cooling tower, heat pump, a cryogenic process, coal gasification, and par- ticularly to the efficient use of fuels. An interesting conclusion reached by Linnhoff [in Seider and Mah (Eds.), Foundations of Computer-Aided Process Design, AIChE, New York, 19811 is that “chemical processes which are properly designed for energy versus capital cost tend to operate at approximately 60% efficiency.” A major aspect of his analysis is recognition of practical constraints and inevitable losses. These may include material of construction limits, plant layout, operability, the need for simplicity such as limits on the number of compressor stages or refrigeration levels, and above all the recognition that, for low grade heat, heat recovery is preferable to work recovery, the latter being justifiable only in huge installations. Unfortunately, the edge is taken off the dramatic 60% conclusion by Linnhoff’s admission that efficiency cannot be easily defined for some complexes of interrelated equipment. For example, is it economical to recover 60% of the propane or 60% of the ethane from a natural gas? 1.8. SAFETY FACTORS In all of the factors that influence the performance of equipment and plant there are elements of uncertainty and the possibility of error, including inaccuracy of physical data, basic correlations of behavior such as pipe friction or tray efficiency or gas-liquid distribution, necessary approximations of design methods and calculations, not entirely known behavior of materials of con- struction, uncertainty of future market demands, and changes in operating performance with time. The solvency of the project, the safety of the operators and the public, and the reputation and career of the design engineer are at stake. Accordingly, the experienced engineer will apply safety factors throughout the design of a plant. Just how much of a factor should be applied in a particular case cannot be stated in general terms because cir- cumstances vary widely. The inadequate performance of a particular piece of equipment may be compensated for by the superior performance of associated equipment, as insufficient trays in a fractionator may be compensated for by increases in reflux and reboiling, if that equipment can take the extra load. With regard to specific types of equipment, the safety factor practices of some 250 engineers were ascertained by a questionnaire and summarized in Table 1.4; additional figures are given by Peters and Timmerhaus (References, Section 1.1, Part B, pp. 35-37). Relatively inexpensive equipment that can conceivably serve as a bottleneck, such as pumps, always is liberally sized; perhaps as much as 50% extra for a reflux pump. In an expanding industry it is a matter of policy to deliberately oversize certain major equipment that cannot be supplemented readily or modified suitably for increased capacity; these are safety factors to account for future trends. Safety factors should not be used to mask inadequate or careless design work. The design should be the best that can be made in the time economically justifiable, and the safety factors should be estimated from a careful consideration of all factors entering into the design and the possible future deviations from the design conditions. Sometimes it is possible to evaluate the range of validity of measurements and correlations of physical properties, phase equilibrium behavior, mass and heat transfer efficiencies and similar factors, as well as the fluctuations in temperature, pressure, flow, etc., associated with practical control systems. Then the effects of such data on the uncertainty of sizing equipment can be estimated. For example, the mass of a distillation column that is related directly to its cost depends on at least these factors: 1. The vapor-liquid equilibrium data. 2. The method of calculating the reflux and number of trays. 3. The tray efficiency. 4. Allowable vapor rate and consequently the tower diameter at a given tray spacing and estimated operating surface tension and fluid densities. 5. Corrosion allowances. Also such factors as allowable tensile strengths, weld efficiencies, and possible inaccuracies of formulas used to calculate shell and head thicknesses may be pertinent. When a quantity is a function of several variables, Y =y(x,, x2, . . .>> its differential is dy=~dx,++x,+. 1 2 Some relations of importance in chemical engineering have the form y = (X,)“(XJb. . ., whose differential is rearrangable to dy 4 -= Y ax,+b%+..., X2 that is, the relative uncertainty or error in the function is related linearly to the fractional uncertainties of the independent variables. For example, take the case of a steam-heated thermosyphon reboiler on a distillation column for which the heat transfer equation is q = UAAT. The problem is to find how the heat transfer rate can vary when the other quantities change. U is an experimental value that is known
- 26. 1.9. SAFETY OF PLANT AND ENVIRONMENT 7 TABLE 1.4. Safety Factors in Equipment Design: Results of a Questionnaire Equipment Design Variable Range of Safety Factor 1 % ) Compressors, reciprocating piston displacement Conveyors, screw diameter H a m m e r m i l l s power input Filters, plate-and-frame area Filters, rotary area Heat exchangers, shell and tube for area liquids Pumps, centrifugal impeller diameter Separators, cyclone diameter Towers, packed d i a m e t e r Towers, tray d i a m e t e r Water cooling towers volume B Based on pilot plant tests. [Michelle, Beattie, and Goodgame, Chem. Eng. frog. 50,332 (1954)). 11-21 8-21 15-21” ll-218 14-20’ 11-18 7-14 7-11 11-18 lo-16 12-20 only to a certain accuracy. AT may be uncertain because of possible fluctuations in regulated steam and tower pressures. A, the effective area, may be uncertain because the submergence is affected by the liquid level controller at the bottom of the column. Accordingly, dq dU dA d(AT) -=7+x+ A T ’ 4 that is, the fractional uncertainty of q is the sum of the fractional uncertainties of the quantities on which it is dependent. In practical cases, of course, some uncertainties may be positive and others negative, so that they may cancel out in part; but the only safe viewpoint is to take the sum of the absolute values. Some further discussion of such cases is by Sherwood and Reed, in Applied Mathematics in Chemical Engineering (McGraw-Hill, New York, 1939). It is not often that proper estimates can be made of uncertainties of all the parameters that influence the performance or required size of particular equipment, but sometimes one particular parameter is dominant. All experimental data scatter to some extent, for example, heat transfer coefficients; and various cor- relations of particular phenomena disagree, for example, equations of state of liquids and gases. The sensitivity of equipment sizing to uncertainties in such data has been the subject of some published information, of which a review article is by Zudkevich [Encycl. Chem. Proc. Des. 14, 431-483 (1982)]; some of his cases are: 1. Sizing of isopentane/pentane and propylene/propane splitters. 2. Effect of volumetric properties on sizing of an ethylene compressor. 3. Effect of liquid density on metering of LNG. 4. Effect of vaporization equilibrium ratios, K, and enthalpies on cryogenic separations. 5. Effects of VLE and enthalpy data on design of plants for coal-derived liquids. Examination of such studies may lead to the conclusion that some of the safety factors of Table 1.4 may be optimistic. But long experience in certain areas does suggest to what extent various uncertainties do cancel out, and overall uncertainties often do fall in the range of lo-20% as stated there. Still, in major cases the uncertainty analysis should be made whenever possible. 1.9. SAFETY OF PLANT AND ENVIRONMENT The safe practices described in the previous section are primarily for assurance that the equipment have adequate performance over anticipated ranges of operating conditions. In addition, the design of equipment and plant must minimize potential harm to personnel and the public in case of accidents, of which the main causes are a. human failure, b. failure of equipment or control instruments, c. failure of supply of utilities or key process streams, d. environmental events (wind, water, and so on). A more nearly complete list of potential hazards is in Table 1.5, and a checklist referring particularly to chemical reactions is in Table 1.6. Examples of common safe practices are pressure relief valves, vent systems, flare stacks, snuffing steam and fire water, escape hatches in explosive areas, dikes around tanks storing hazardous materials, turbine drives as spares for electrical motors in case of power failure, and others. Safety considerations are paramount in the layout of the plant, particularly isolation of especially hazardous operations and accessibility for corrective action when necessary. Continual monitoring of equipment and plant is standard practice in chemical process plants. Equipment deteriorates and operating conditions may change. Repairs sometimes are made with “improvements” whose ultimate effects on the operation may not be taken into account. During start-up and shut-down, stream compositions and operating conditions are much different from those under normal operation, and their possible effect on safety must be taken into account. Sample checklists of safety questions for these periods are in Table 1.7. Because of the importance of safety and its complexity, safety engineering is a speciality in itself. In chemical processing plants of any significant size, loss prevention reviews are held periodically by groups that always include a representative of the safety depart- ment. Other personnel, as needed by the particular situation, are from manufacturing, maintenance, technical service, and possibly research, engineering, and medical groups. The review considers any changes made since the last review in equipment, repairs, feedstocks and products, and operating conditions. Detailed safety checklists appear in books by Fawcett and Wood (Chap. 32, Bibliography 1.1, Part E) and Wells (pp. 239-257, Bibliography 1.1, Part E). These books and the large one by Lees (Bibliography 1.1, Part E) also provide entry into the vast literature of chemical process plant safety. Lees has particularly complete bibliographies. A standard reference on the properties of dangerous materials is the book by Sax (1984) (References, Section 1.1, Part E). The handbook by Lund (1971) (References, Section 1.1, Part E) on industrial pollution control also may be consulted.
- 27. 8 INTRODUCTION TABLE 1.5. Some Potential Hazards Energy Source Process chemicals, fuels, nuclear reactors, generators, batteries Source of ignition, radio frequency energy sources, activators, radiation sources Rotating machinery, prime movers, pulverisers, grinders, conveyors, belts, cranes Pressure containers, moving objects, falling objects Release of Material Spillage, leakage, vented material Exposure effects, toxicity, burns, bruises, biological effects Flammability, reactivity, explosiveness, corrosivity and fire-promoting properties of chemicals Wetted surfaces, reduced visibility, falls, noise, damage Dust formation, mist formation, spray Fire hazard Fire, fire spread, fireballs, radiation Explosion, secondary explosion, domino effects Noise, smoke, toxic fumes, exposure effects Collapse, falling objects, fragmentation Process state High/low/changing temperature and pressure Stress concentrations, stress reversals, vibration, noise Structural damage or failure, falling objects, collapse Electrical shock and thermal effects, inadvertent activation, power source failure Radiation, internal fire, overheated vessel Failure of equipment/utility supply/flame/instrument/component Start-up and shutdown condition Maintenance, construction and inspection condition Environmental effects Effect of plant on surroundings, drainage, pollution, transport, wind and light change, source of ignition/vibration/noise/radio interference/fire spread/explosion Effect of surroundings on plant (as above) Climate, sun, wind, rain, snow, ice, grit, contaminants, humidity, ambient conditions Acts of God, earthquake, arson, flood, typhoon, force majeure Site layout factors, groups of people, transport features, space limitations, geology, geography Processes Processes subject to explosive reaction or detonation Processes which react energetically with water or common contaminants Processes subject to spontaneous polymerisation or heating Processes which are exothermic Processes containing flammables and operated at high pressure or high temperature or both Processes containing flammables and operated under refrigeration Processes in which intrinsically unstable compounds are present Processes operating in or near the explosive range of materials Processes involving highly toxic materials Processes subject to a dust or mist explosion hazard Processes with a large inventory of stored pressure energy Operations The vaporisation and diffusion of flammable or toxic liquids or gases The dusting and dispersion of combustible or toxic solids The spraying, misting or fogging of flammable combustible materials or strong oxidising agents and their mixing The separation of hazardous chemicals from inerts or diluents The temperature and pressure increase of unstable liquids (Wells, Safety in Process P/ant Design, George Godwin, London, 1980). TABLE 1.6. Safety Checklist of Questions About Chemical Reactions 1. Define potentially hazardous reactions. How are they isolated? Prevented? (See Chaps. 4,5, and 16) 2. Define process variables which could, or do, approach limiting conditions for hazard. What safeguards are provided against such variables? 3. What unwanted hazardous reactions can be developed through unlikely flow or process conditions or through contamination? 4. What combustible mixtures can occur within equipment? 5. What precautions are taken for processes operating near or within the flammable limits? (Reference: S&PP Design Guide No. 8.) (See Chap. 19) 6. What are process margins of safety for all reactants and intermediates in the process? 7. List known reaction rate data on the normal and possible abnormal reactions 8. How much heat must be removed for normal, or abnormally possible, exothermic reactions? (see Chaps. 7, 17, and 18) 9. How thoroughly is the chemistry of the process including desired and undesired reactions known? (See NFPA 491 M, Manual of Hazardous Chemical Reactions) 10. What provision is made for rapid disposal of reactants if required by emergency? 11. What provisions are made for handling impending runaways and for short-stopping an existing runaway? 12. Discuss the hazardous reactions which could develop as a result of mechanical equipment (pump, agitator, etc.) failure 13. Describe the hazardous process conditions that can result from gradual or sudden blockage in equipment including lines 14. Review provisions for blockage removal or prevention 15. What raw materials or process materials or process conditions can be adversely affected by extreme weather conditions? Protect against such conditions 16. Describe the process changes including plant operation that have been made since the previous process safety review (Fawcett and Wood, Safety and Accident Prevention in Chemical Operations, Wiley, New York, 1982, pp. 725-726. Chapter references refer to this book.) TABLE 1.7. Safety Checklist of Questions About Start-up and Shut-down Start-up Mode (54.1) Dl Can the start-up of plant be expedited safely? Check the following: (a) lb) (4 (d (e) (f) (cl) (h) (i) 0) (k) (I) Abnormal condentrations, phases, temperatures, pressures, levels, flows, densities Abnormal quantities of raw materials, intermediates and utilities (supply, handling and availability) Abnormal quantities and types of effluents and emissions (91.6.10) Different states of catalyst, regeneration, activation Instruments out of range, not in service or de-activated, incorrect readings, spurious trips Manual control, wrong routeing, sequencing errors, poor identification of valves and lines in occasional use, lock-outs, human error, improper start-up of equipment (particularly prime movers) Isolation, purging Removal of air, undesired process material, chemicals used for cleaning, inerts, water, oils, construction debris and ingress of same Recycle or disposal of off-specification process materials Means for ensuring construction/maintenance completed Any plant item failure on initial demand and during operation in this mode Lighting of flames, introduction of material, limitation of heating rate
- 28. TABLE 1.7~(continued) (m) Different modes of the start-up of plant: Initial start-up of plant Start-up of plant section when rest of plant down Start-up of plant section when other plant on-stream Start-up of plant after maintenance Preparation of plant for its start-up on demand Shut-down Mode [884.1,4.2) D2 Are the limits of operating parameters, outside which remedial action must be taken, known and measured? (Cl above) D3 To what extent should plant be shut down for any deviation beyond the operating limits? Does this require the installation of alarm and/or trip? Should the plant be partitioned differently? How is plant restarted? (59.6) D4 In an emergency, can the plant pressure and/or the inventory of process materials be reduced effectively, correctly, safely? What is the fire resistance of plant (@9.5,9.6) D5 Can the plant be shut down safely? Check the following: (a) See the relevant features mentioned under start-up mode (b) Fail-danger faults of protective equipment (c) Ingress of air, other process materials, nitrogen, steam, water, lube oil (54.3.5) (d) Disposal or inactivation of residues, regeneration of catalyst, decoking, concentration of reactants, drainage, venting (e) Chemical, catalyst, or packing replacement, blockage removal, delivery of materials prior to start-up of plant (f) Different modes of shutdown of plant: Normal shutdown of plant Partial shutdown of plant Placing of plant on hot standby Emergency shutdown of plant (Wells, Safety in Process Plant Design, George Godwin, London, 1980, pp. 243-244. Paragraph references refer to this book.) 1.10. STEAM AND POWER SUPPLY 9 1.10. STEAM AND POWER SUPPLY For smaller plants or for supplementary purposes, steam and power can be supplied by package plants which are shippable and ready to hook up to the process. Units with capacities in a range of sizes up to about 350,OOOlb/hr of steam are on the market, and are obtainable on a rental/purchase basis for emergency needs. Modem steam plants are quite elaborate structures that can recover 80% or more of the heat of combustion of the fuel. The simplified sketch of Example 1.2 identifies several zones of heat transfer in the equipment. Residual heat in the flue gas is recovered as preheat of the water in an economizer and in an air preheater. The combustion chamber is lined with tubes along the floor and walls to keep the refractory cool and usually to recover more than half the heat of combustion. The tabulations of this example are of the distribution of heat transfer surfaces and the amount of heat transfer in each zone. More realistic sketches of the cross section of a steam generator are in Figure 1.4. Part (a) of this figure illustrates the process of natural circulation of water between an upper steam drum and a lower drum provided for the accumulation and eventual blowdown of sediment. In some installations, pumped circulation of the water is advantageous. Both process steam and supplemental power are recoverable from high pressure steam which is readily generated. Example 1.3 is of such a case. The high pressure steam is charged to a turbine-generator set, process steam is extracted at the desired process pressure at an intermediate point in the turbine, and the rest of the steam expands, further and is condensed. In plants such as oil refineries that have many streams at high temperatures or high pressures, their energy can be utilized to generate steam or to recover power. The two cases of Example 1.4 E X A M P L E 1.2 Data of a Steam Generator for Making 25O,OOOIb/br at 450 psia and 650°F from Water Entering at 224lT Fuel oil of 18,500 Btu/lb is fired with 13% excess air at 80°F. Flue gas leaves at 410°F. A simplified cross section of the boiler is shown. Heat and material balances are summarized. Tube selections and arrangements for the five heat transfer zones also are summarized. The term A, is the total internal cross section of the tubes in parallel, (Steam: Its Generation and Use, 14.2, Babcock and Wilcox, Barberton, OH, 1972). (a) Cross section of the generator: (b) Heat balance: Fuel input 335.5 MBtu/hr To furnace tubes 1 6 2 . 0 To boiler tubes 6 8 . 5 To screen tubes 8.1 To superheater 3 1 . 3 To economizer 15.5 Total to water and steam 285.4 Mbtu/hr In air heater 18.0 MBtu/hr (c) Tube quantity, size, and grouping: Screen 2 rows of 2&-m. OD tubes, approx 18 ft long Rows in line and spaced on 6-in. centers 23 tubes per row spaced on 6-in. centers S = 542 sqft A, = 129 sqft
- 29. 10 INTRODUCTION EXAMPLE 1.2-(continued) Superheater 12 rows of 2$-in. OD tubes (0.165-in. thick), 17.44 ft long Rows in line and spaced on 3$in. centers 23 tubes per row spaced on 6-in. centers S = 3150 sqft A, = 133 sqft Boiler 25 rows of 2&in. OD tubes, approx 18 ft long Rows in line and spaced on 3$-in. centers 35 tubes per row spaced on 4-m. centers s = 10,308 sqft A, = 85.0 sqft Economizer 10 rows of 2-in. OD tubes (0.148-in. thick), approx 10 ft long Rows in line and spaced on 3-m. centers 47 tubes per row spaced on 3-m centers S = 2460 sqft A, = 42 sqft Air heater 53 rows of 2-in. OD tubes (0.083-in. thick), approx 13 ft long Rows in line and spaced on 2$-in. centers 41 tubes per row spaced on 3&n. centers S = 14,809 sqft A, (total internal cross section area of 2173 tubes) = 39.3 sqft A, (clear area between tubes for crossflow of air) = 70 sqft Air temperature entering air heater = 80°F (a) lb) Steam out Downcomer not Heated I (c) Gas Steam Coil Outlet Air Heater t / II II II Fire 1.4. Steam boiler and furnace arrangements. [Steam, Babcock and Wilcox, Barberton, OH, 1972, pp. 3.14, 12.2 (Fig. 2), and 25.7 (Fig. 5)]. (a) Natural circulation of water in a two-drum boiler. Upper drum is for steam disengagement; the lower one for accumulation and eventual blowdown of sediment. (b) A two-drum boiler. Preheat tubes along the Roor and walls are connected to heaters that feed into the upper drum. (c) Cross section of a Stirling-type steam boiler with provisions for superheating, air preheating, and flue gas economizing; for maximum production of 550,000 Ib/hr of steam at 1575 psia and 900°F.
- 30. 1 . 1 0 . S T E A M A N D P O W E R S U P P L Y 11 EXAMPLE 1.3 Steam Plant Cycle for Generation of Power and Low Pressure Process Steam The flow diagram is for the production of 5000 kW gross and 20,000 lb/hr of saturated process steam at 20 psia. The feed and hot well pumps make the net power production 4700 kW. Conditions at L ’ + 60,8OOw-2Op-228%-I 156h n-x ~.~00n~-400p-655%1337h O w Reducing valve (and desuperhecled ,------e ---e--m ---*---L--*-‘-q l-l Boiler 0.8eff Generator 0.95 eif.---T,+,&Okw. ; 10,000w-4 C~km.~q~lixii*:F L t ‘2opoow 1!obr 79%-slo r nr iO.000 Ib./hr. ’ 26 Ib.hq. in. obo ’ Iin Hg& dry and so?. - L.-.-,L Feed pump s : entropy, 6.1 u. /(lb.)(‘R 1 ,‘/h key points are indicated on the enthalpy-entropy diagram. The process steam is extracted from the turbine at an intermediate point, while the rest of the stream expands to 1 in. Hg and is condensed (example is corrected from Chemical Engineers Handbook, 5th ed., 9.48, McGraw-Hill, New York, 1973). 1337 EXAMPLE 1.4 Pickup of Waste Heat by Generating and Superheating Steam in a Petroleum Refinery The two examples are generation of steam with heat from a sidestream of a fractionator in a 9000 Bbl/day fluid cracking plant, and superheating steam with heat from flue gases of a furnace (4 WATER 17,300 ppl 1 STEAM I FRACTtONATOR 160 psig SIDESTREAM 98% quality 17,300 pph 580 F R E T U R N 4 2 5 F whose main function is to supply heat to crude topping and vacuum service in a 20,OOOBbl/day plant. (a) Recovery of heat from a sidestream of a fractionator in a 9000 Bbl/day fluid catalytic cracker by generating steam, Q = 15,950,OOO Btu/hr. (b) Heat recovery by superheating steam with flue gases of a 20,OOOBbl/day crude topping and vacuum furnace. lb) STEAM 50 psig sard 6910 pph w Q= 1.2 MBtulhr 640 F ATMOSPHERIC COIL 0 = 5 3 . 2 MBtulhr V A C U U M C O I L Q=9.2 MBtulhr are of steam generation in a kettle reboiler with heat from a with an expansion turbine. Recovery of power from a high pressure fractionator sidestream and of steam superheating in the convection gas is a fairly common operation. A classic example of power tubes of a furnace that provides heat to fractionators. recovery from a high pressure liquid is in a plant for the absorption Recovery of power from the thermal energy of a high of CO, by water at a pressure of about 4OOOpsig. After the temperature stream is the subject of Example 1.5. A closed circuit absorption, the CO, is releastd and power is recovered by releasing of propane is the indirect means whereby the power is recovered the rich liquor through a turbine.
- 31. 12 INTRODUCTION EXAMPLE 1.5 Recovery of Power from a Hot Gas Stream A closed circuit of propane is employed for indirect recovery of power from the thermal energy of the hot pyrolyzate of an ethylene plant. The propane is evaporated at 500 psig, and then expanded to PROPANE 34700 pph y-fFoy=TE 500 psig 195F 5600 pph 190 psig 1OOF I CONDENSER 100°F and 190 psig in a turbine where the power is recovered. Then the propane is condensed and pumped back to the evaporator to complete the cycle. Since expansion turbines are expensive machines,even in small sizes, the process is not economical on the scale of this example, but may be on a much larger scale. TURBINE _---- 75%eff 204.6 HP 1.11. DESIGN BASIS 14. Before a chemical process design can be properly embarked on, a certain body of information must be agreed upon by all concerned persons, in addition to the obvious what is to be made and what it is to be made from. Distinctions may be drawn between plant expansions and wholly independent ones, so-called grassroots types. The needed data can be classified into specific design data and basic design data, for which separate check lists will be described. Specific design data include: 15. 16. 17. 1. 2. 3. 4. Required products: their compositions, amounts, purities, toxicities, temperatures, pressures, and monetary values. Available raw materials: their compositions, amounts, toxi- cities, temperatures, pressures, monetary values, and all pertinent physical properties unless they are standard and can be established from correlations. This information about properties applies also to products of item 1. Daily and seasonal variations of any data of items 1 and 2 and subsequent items of these lists. All available laboratory and pilot plant data on reaction and phase equilibrium behaviors, catalyst degradation, and life and corrosion of equipment. 5. Any available existing plant data of similar processes. 6. Local restrictions on means of disposal of wastes. Basic engineering data include: UTILITIES 7. 8. Characteristics and values of gaseous and liquid fuels that are to be used. 9. 10. 11. 12. l3. Characteristics of raw makeup and cooling tower waters, temperatures, maximum allowable temperature, flow rates available, and unit costs. Steam and condensate: mean pressures and temperatures and their fluctuations at each level, amount available, extent of recovery of condensate, and unit costs. Electrical power: Voltages allowed for instruments, lighting and various driver sizes, transformer capacities, need for emergency generator, unit costs. Compressed air: capacities and pressures of plant and in- strument air, instrument air dryer. Plant site elevation. Soil bearing value, frost depth, ground water depth, piling requirements, available soil test data. 18. 19. 20. 21. 22. Climatic data. Winter and summer temperature extrema, cooling tower drybulb temperature, air cooler design temperature, strength and direction of prevailing winds, rain and snowfall maxima in 1 hr and in 12 hr, earthquake provision. Blowdown and flare: What may or may not be vented to the atmosphere or to ponds or to natural waters, nature of required liquid, and vapor relief systems. Drainage and sewers: rainwater, oil, sanitary. Buildings: process, pump, control instruments, special equipment. Paving types required in different areas. Pipe racks: elevations, grouping, coding. Battery limit pressures and temperatures of individual feed stocks and products. Codes: those governing pressure vessels, other equipment, buildings, electrical, safety, sanitation, and others. Miscellaneous: includes heater stacks, winterizing, insulation, steam or electrical tracing of lines, heat exchanger tubing size standardization, instrument locations. A convenient tabular questionnaire is in Table 1.8. For anything not specified, for instance, sparing of equipment, engineering standards of the designer or constructor will be used. A proper design basis at the very beginning of a project is essential to getting a project completed and on stream expeditiously. These provide motive power and heating and cooling of process streams, and include electricity, steam, fuels, and various fluids whose changes in sensible and latent heats provide the necessary energy transfers. In every plant, the conditions of the utilities are maintained at only a few specific levels, for instance, steam at certain pressures, cooling water over certain temperature ranges, and electricity at certain voltages. At some stages of some design work, the specifications of the utilities may not have been established. Then, suitable data may be selected from the commonly used values itemized in Table 1.9. 1.12. LABORATORY AND PILOT PLANT WORK The need for knowledge of basic physical properties as a factor in equipment selection or design requires no stressing. Beyond this, the state-of-the-art of design of many kinds of equipment and
- 32. TABLE 1.8. Typical Design Basis Questionnaire I.101 Pldnt Location l.ltJ? PlaruCapactty. Ibortons/yr I. 103 Operating Factor or Yearly Operating Hours (For mos: modern chemical plants. this figure is generally 8.000 hours per year). I. IO4 Provisions for Expansion 1.10s Raw Material Feed (Typical of the analyses required for a liquid) Array. WI per cent mitt Impurities. WI per cent maa Characteristic specifications Specific gravity Distillation range ‘F Initial boiling point ‘F Dry end point ‘F Viscosity. centipoises Color APHA Heat stability color Reaction rat6 with established reagent Acid number Freezing point or set point ‘F Corrosion test End-use test For a solid material chemical assay, level of impurities and its physical characteristics, such as spcciftc density, bulk density, particle size distribution and the liko are included. This physical shape inrormation is required to assure that adequate processing and material handling operations will be provided. I.1051 Source Supply conditiona at proccu plant battery limits Max M i n Normal Storage capacity (volume or day’s inventory) Rquircd delivery conditions at battery limits Pressure - - Temperature Method of transfer I .I06 Product !ipodfiEaliON Here again spcci6cationr would be similar IO that of the raw material in quivalent or some- times greater detail as often traa impurities at&t the marketability of the final product. Storage rquircmatts (volume or slays of inventory) Type of product storage For solid pro&eta. type of wntainu or method of ship- . _ 1.107 Miscellaneous Chemicals and Catalyst Supply In this section the operating group should outline how various misccllancuus chemicals and catalysts arc to be stored and handled for consumplion within the plant. 1.108 Atmospheric Conditions Barometric pressure ran*e Temperature Design dry bulb temperature (‘F) ‘/. of summer season, this temperature is exceeded. Design wet bulb temperature % of summer season. this temperature is uaedcd. Minimum design dry bulb temperature winter condition (‘F) Level of applicable pollutants that could afTcct the process. Examples of these are sulfur compounds. dust and solids, chlorides and salt water mist when the plant is at a coastal location. 2.100 Utilities 2.101 Electricity Characteristics of primary supply Voltage. phases. cyclu Preferred voltage (or motors Over 200 hp Under 200 hp Value, t/kWtt (If available and if desired. detailed clatricity pricing schedule an be included for base load and incrmnmtal additional consumption.) 2.102 Supply Water Clcmlinas coNNlv- Solids content analysis Other detaila Pressure (at grade) Huimum M i n i m u m SWPIY Return 2.103 Cooling Water Well. river. sea. cooling tower, other. Quality Value men1 and loading bcilitia sbottld be outltnat.
- 33. TABLE 1.84continued) USC for heat cxchallpf dasign Fouling properties D&in hdin# hcKor Pr&md tuba material 2.104 slwm Max Normal Min HWP=-=.tiil Tanparatur~, ‘F Hoislurc. % Value par thousand lb Medium pressure. pria lanpera~urc. ‘F Hois!urc. % Valw per thousand lb Lm~~e.psiJ Tanpcruure. ‘F MOislUrc. % Valua par thousand lb 2.105 slwmcondaut8 Diilioo Rsquircd prusura at battery limiu Valua par thousand lb or gal 2106 BoikrFccdWatu CWW H-.PP~ silica coolalt HlrQar Total solids. ppm Chk&aib cbcmiidditiva M u M i n WPb v= Tanpratmo. ‘F VJWprtbOWWdIJ 2107 buss Waut ([~~qtulityolchcprocmrrtnirditkrcntlromchcIrulc-oprrtcr~boi~ reed -ICI. separate ioformatiuo should be plovidcd.) Quali* M u Min SupplY prcplue. Pe Temperature. ’ F valwp8rtbouuadIrl 2.108 lnul Gas Mu M i n Rcssurc. psi: Dw poiot,‘F Composition h ant CO* Pet cent oxygm Rrwulco Other tmca impuritiu Quantity rvaikbk VJW per th~0d w n 2.109 Plant Air Supply Source OUsita battuy limits (OSBL) lbrlabkcomprusor Pl-OCUSlirSyrtcm spaial comprcnor WPlY Pm. prit 2.110 IllswumallAir supply loure (OSBL) Spoial compressor SUPPlY prar”rr. pris DcrpOilll.‘F Oii din md moisture rcmovrl requiremenu IO gcwrol , valua of planl mod indrumall air is usu8Ily no: given as lbe ycarIy over-all cost is bui&cant in ttktion to lbc utlur utiliriu required. 3.101 Wosta Disposal Rcqubwna~u In plrarL tbcrc UC tirea typo of wuu 10 be cunsidcrcdz liquid, solid and gaseous. The destination aud dkposal of ucb of lbcp clsuents b usually diUucn~. Typical items arc as followl: Daliwtiocl of liquid dnualu C4tolilyrrterblowdown clwnial- stormwmw HclbOdorchanialveo~fwliquid~a Pdemd matuiok dcofumdoo for cooli- rater bluwdowo ChEiCd- stcmllaawu Fxilitiol for dwmil lfatiq for liquid CtRomtr Fsilitia for trcatnxn~ uf - clnwats Solidsdispa8l (Landau, The Chemical Plant, Reinhold, New York, 1966).
- 34. REFERENCES 15 TABLE 1.9. Typical Utility Characteristics Pressure (psig) Saturation (“F) Superheat (“F) 15-30 250-275 150 366 400 448 600 488 100-150 Heat Transfer Fluids “F Fluid Below 600 Below 750 Below 1100 Above 450 petroleum oils Dowtherm and others fused salts direct firing and electrical heating Refrigerants “F Fluid 40-80 O-50 -50-40 -150--50 -350--150 -4oo--300 Below -400 chilled water chilled brine and glycol solutions ammonia, freons, butane ethane or propane methane, air, nitrogen hydrogen helium Cooling Water Supply at EO-90°F Return at 115°F. with 125°F maximum Return at 110°F (salt water) Return above 125°F (tempered water or steam condensate) Cooling Air Supply at 85-95°F Temperature approach to process, 40°F Power input, 20 HP/1000 sqft of bare surface Fuel Gas: 5-10 psig, up to 25 psig for some types of burners, pipeline gas at 1000 Btu/SCF Liquid: at 6 million Btu/barrel Compressed Air Pressure levels of 45, 150, 300, 450 psig Instrument Air 45 psig, 0°F dewpoint REFERENCES 1.1. Process Design A. Books Essential to a Private Library 1. Ludwig, Applied Process Design for Chemical and Petroleum Plants, Gulf, Houston 1977-1983, 3 ~01s. 2. Marks Standard Handbook for Mechanical Engineers, 9th ed., McGraw-Hill, New York, 1987. 3. Perry, Green, and Maloney, Perry’s Chemical Engineers Handbook, Electricity Driver HP Voltage l-100 220,440, 550 75-250 440 200-2500 2300,400O Above 2500 4000, 13,200 processes often demands more or less extensive pilot plant effort. This point is stressed by specialists and manufacturers of equipment who are asked to provide performance guaranties. For instance, answers to equipment suppliers’ questionnaires like those of Appendix C may require the potential purchaser to have performed certain tests. Some of the more obvious areas definitely requiring test work are filtration, sedimentation, spray, or fluidized bed or any other kind of solids drying, extrusion pelleting, pneumatic and slurry conveying, adsorption, and others. Even in such thoroughly researched areas as vapor-liquid and liquid-liquid separations, rates, equilibria, and efficiencies may need to be tested, particularly of complex mixtures. A great deal can be found out, for instance, by a batch distillation of a complex mixture. In some areas, suppliers make available small scale equipment that can be used to explore suitable ranges of operating conditions, or they may do the work themselves with benefit of their extensive experience. One engineer in the extrusion pelleting field claims that merely feeling the stuff between his fingers enables him to properly specify equipment because of his experience of 25 years with extrusion. Suitable test procedures often are supplied with “canned” pilot plants. In general, pilot plant experimentation is a profession in itself, and the more sophistication brought to bear on it the more efficiently can the work be done. In some areas the basic relations are known so well that experimentation suffices to evaluate a few parameters in a mathematical model. This is not the book to treat the subject of experimentation, but the literature is extensive. These books may be helpful to start: 1. R.E. Johnstone and M.W. Thring, Pilot Plants, Models and Scale-up Method in Chemical Engineering, McGraw-Hill, New York, 1957. 2. D.G. Jordan, Chemical Pilot Plant Practice, Wiley-Interscience, New York, 1955. 3. V. Kafarov, Cybernetic Metho& in Chemtitry and Chemical Engineering, Mir Publishers, Moscow, 1976. 4. E.B. Wilson, An Introduction to Scientific Research, McGraw- Hill, New York, 1952. McGraw-Hill, New York, 1984; earlier editions have not been obsolesced entirely. 4. Sinnott, Coulson, and Richardsons, Chemical Engineering, Vof. 6, Design, Pergamon, New York, 1983. B . Other B o o k s 1. Aerstin and Street, Applied Chemical Process Design, Plenum, New York, 1978. 2. Baasel, Preliminary Chemical Engineering Plant Design, Elsevier, New York, 1976.
- 35. 16 INTRODUCTION 3. Backhurst and Harker, Process Plant Design, Elsevier, New York, 1973. 4. Benedek (Ed.), Steady State Flowsheeting of Chemical Plants, Elsevier, New York, 1980. 5. Bodman, The Industrial Practice of Chemical Process Engineering, MIT Press, Cambridge, MA, 1968. 6. Branan, Process Engineers Pocket Book, Gulf, Houston, 1976, 1983, 2 vols. 7. Burklin, The Process Plant Designers Pocket Handbook of Codes and Standards, Gulf, Houston, 1979; also, Design codes standards and recommended practices, Encycl. Chem. Process. Des. 14, 416-431, Dekker, New York, 1982. 8. Cremer and Watkins, Chemical Engineering Practice, Butterworths, London, 1956-1965, 12 ~01s. 9. Crowe et al., Chemical Plant Simulation, Prentice-Hall, Englewood Cliffs, NJ, 1971. 10. F.L. Evans, Equipment Design Handbook for Refineries and Chemical Plants, Gulf, Houston, 1979, 2 ~01s. 11. Franks, Modelling and Simulation in Chemical Engineering, Wiley, New York, 1972. 12. Institut Franfaise du Petrole, Manual of Economic Analysis of Chemical Processes, McGraw-Hill, New York, 1981. W. Kafarov, Cybernetic Methods in Chemistry and Chemical Engineering, Mir Publishers, Moscow, 1976. 14. Landau (Ed.), The Chemical Plant, Reinhold, New York, 1966. 15. Leesley (Ed.), Computer-Aided Process Plant Design, Gulf, Houston, 1982. 16. Lieberman, Process Design for Reliable Operations, Gulf, Houston, 1983. 17. Noel, Petroleum Refinery Manual, Reinhold, New York, 1959. 18. Peters and Timmerhaus, Plant Design and Economics for Chemical Engineers, McGraw-Hill, New York, 1980. 19. Rase and Barrow, Project Engineering of Process Plants, Wiley, New York, 1957. 20. Resnick, Process Analysis and Design for Chemical Engineers, McGraw-Hill, New York, 1981. 21. Rudd and Watson, Strategy of Process Engineering, Wiley, New York, 1968. 22. Schweitzer (Ed.), Handbook of Separation Processes for Chemical Engineers, McGraw-Hill, New York, 1979. 23. Sherwood, A Course in Process Design, MIT Press, Cambridge, MA, 1963. 24. Uhich, A Guide to Chemical Engineering Process Design and Economics, Wiley, New York, 1984. 25. Valle-Riestra, Project Evaluation in the Chemical Process Industries, McGraw-Hill, New York, 1983. 26. Vilbrandt and Dryden, Chemical Engineering Plant Design, McGraw- Hill, New York, 1959. 27. Wells, Process Engineering with Economic Objective, Leonard Hill, London, 1973. C. Estimation of Properties 1. AIChE Manual for Predicting Chemical Process Design Data, AIChE, New York, 1984-date. 2. Bretsznajder, Prediction of Transport and Other Physical Properties of Fluids, Pergamon, New York, 1971; larger Polish edition, Warsaw, 1962. 3. Lyman, Reehl, and Rosenblatt, Handbook of Chemical Property Estimation Methods: Environmental Behavior of Organic Compounds, McGraw-Hill, New York, 1982. 4. Reid, Prausnitz, and Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, 1987. 5. Sterbacek, Biskup, and Tausk, Calculation of Properties Using Corresponding States Methods, Elsevier, New York, 1979. 6. S.M. Walas, Phase Equilibria in Chemical Engineering, Butterworths, Stoneham, MA, 1984. D. Equipment 1. Chemical Engineering Catalog, Penton/Reinhold, New York, annual. 2. Chemical Engineering Equipment Buyers’ Guide, McGraw-Hill, New York, annual. 3. Kieser, Handbuch der chemisch-technischen Apparate, Spamer-Springer, Berlin, 1934-1939. 4. Mead, The Encyclopedia of Chemical Process Equipment, Reinhold, New York, 1964. 5. Riegel, Chemical Process Machinery, Reinhold, New York, 1953. 6. Thomas Register of American Manufacturers, Thomas, Springfield IL, annual. E. Safety Aspects 1. Fawcctt and Wood (Eds.), Safety and Accident Prevention in Chemical Operations, Wiley, New York, 1982. 2. Lees, Loss Prevention in the Process Industries, Buttenvorths, London, 1980, 2 ~01s. 3. Lieberman, Troubleshooting Re@ery Processes, PennWell, Tulsa, 1981. 4. Lund, Industrial Pollution Control Handbook, McGraw-Hill, New York, 1971. 5. Rosaler and Rice, Standard Handbook of Plant Engineering, McGraw-Hill, New York, 1983. 6. Sax, Dangerous Properties of Industrial Materials, Van Nostrand/ Reinhold, New York, 1982. 7. Wells, Safety in Process Plant Design, George Godwin, Wiley, New York, 1980. 1.2. Process Equipment A. Encyclopedias 1. Considine, Chemical and Process Technology Encyclopedia, McGraw- Hill, New York, 1974. 2. Kirk-Othmer Concise Encyclopedia of Chemical Technology, Wiley, New York, 1985. 3. Kirk-Othmer Encyclopedia of Chemical Technology, Wiley, New York, 1978-1984, 26 ~01s. 4. McGraw-Hill Encyclopedia of Science and Technology, 5th ed., McGraw-Hill, New York, 1982. 5. McKetta and Cunningham (Eds.), Encyclopedia of Chemical Processing and Design, Dekker, New York, 1976-date. 6. Ullmann, Encyclopedia of Chemical Technology, Verlag Chemie, Weinheim, FRG, German edition 1972-1983; English edition 1984- 1994(?). B. Bibliographies 1. Fratzcher, Picht, and Bittrich, The acquisition, collection and tabulation of substance data on fluid systems for calculations in chemical engineering, Znt. Chem. Eng. u)(l), 19-28 (1980). 2. Maize& How to Find Chemical Information, Wiley, New York, 1978. 3. Mellon, Chemical Publications: Their Nature and Use, McGraw-Hill, New York, 1982. 4. Rasmussen and Fredenslund, Data Banks for Chemical Engineers, Kemiigeniorgruppen, Lyngby, Denmark, 1980. C. General Data Collections 1. American Petroleum Institute, Technical Data Book-Petroleum Rejining, API, Washington, DC, 1971-date. 2. Bolz and N. Tuve, Handbook of Tables for Applied Engineering Science, CRC Press, Washington, DC, 1972. 3. CRC Handbook of Chemistry and Physics, CRC Press, Washington, DC, 4. 5. 6. 7. 8. 9. 10. 11. 12. annual. Gallant, Physical Properties of Hydrocarbons, Gulf, Houston, 1968, 2 vols. International Critical Tables, McGraw-Hill, New York, 1926-1933. Landolt-BGmstein, Numerical Data and Functional Relationships in Science and Technology, Springer, New York, 1950-date. Lange’s Handbook of Chemistry, 13th ed., McGraw-Hill, New York, 1984. Maxwell, Data Book on Hydrocarbons, Van Nostrand, New York, 1950. Melnik and Melnikov, Technology of Inorganic Compounds, Israel Program for Scientific Translations, Jerusalem, 1970. National Gas Processors Association, Engineering Data Book, Tulsa, 1987. Perry’s Chemical Engineers Handbook, McGraw-HiIl, New York, 1984. Physico-Chemical Properties for Chemical Engineering, Maruzen Co., Tokyo, 1977-date.
- 36. R E F E R E N C E S 1 7 W. Raznjevic, Handbook of Thermodynamics Tables and Charts (St Units), Hemisphere, New York, 1976. 14. Vargaftik, Handbook of Physical Properties of Liquids and Gases, Hemisphere, New York, 1983. 15. Yaws et al., Physical and Thermodynamic Properties, McGraw-Hill, New York. 1976. D. Special Data Collections 1. Gmehling et al., Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt/Main, FRG, 1977-date. 2. Hirata, Ohe, and Nagahama, Computer-Aided Data Book of Vapor-Liquid Equilibria, Elsevier, New York, 1976. 3. Keenan et al., Steam Tables, Wiley, New York, English Units, 1969, SI Units, 1978. 4. Kehiaian, Selected Data on Mixtures, International Data Series A: Thermodynamic Properties of Non-reacting Binary Systems of Organic Substances, Texas A & M Thermodynamics Research Center, College Station, TX, 1977-date. 5. Kogan, Fridman, and Kafarov, Equilibria between Liquid and Vapor (in Russian), Moscow, 1966. 6. Larkin, Selected Data on Mixtures, International Data Series’ B, Thermodynamic Properties of Organic Aqueous Systems, Engineering Science Data Unit Ltd, London, 197%date. 7. Ogorodnikov, Lesteva, and Kogan, Handbook of Azeotropic Mixtures (in Russian), Moscow, 1971; data of 21,069 systems. 8. Ohe, Computer-Aided Data Book of Vapor Pressure, Data Publishing Co., Tokyo, 1976. 9. Sorensen and Arlt, Liquid-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt/Main, FRG, 1979-1980, 3 ~01s. 10. Starling, Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf, Houston, 1973. 11. Stephen, Stephen and Silcock, Solubilities of Inorganic and Organic Compounds, Pergamon, New York, 1979, 7 ~01s. l2. Stull, Westrum, and Sinke, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969. l3, Wagman et al., The NBS Tables of Chemical Thermodynamic Properties: Selected Values for Inorganic and C, and C, Organic Substances in SI Units, American Chemical Society, Washington, DC, 1982.
- 38. 2 Flowsheets A plant design is made up of words, numbers, and pictures. An engineer thinks naturally in terms of the sketches and drawings which are his “pictures. ” Thus, to solve a material balance problem, he will start with a block to represent the equipment and then will show entering and leaving streams with their amounts and properties. Or ask him to describe a process and he will begin to sketch the equipment, show how iris interconnected, and what the flows and operating conditions are. Such sketches develop into flow sheets, which are more elaborate diagrammatic representations of the equipment, the sequence of operations, and the expected performance of a proposed p/ant or the actual performance of an already operating one. For clarity and to meet the needs of the various persons engaged in design, cost estimating, purchasing, fabrication, operation, maintenance, and management, several different kinds of flowsheets are necessary. Four of the main kinds will be described and illustrated. 2.1. BLOCK FLOWSHEETS At an early stage or to provide an overview of a complex process or plant, a drawing is made with rectangular blocks to represent individual processes or groups of operations, together with quantities and other pertinent properties of key streams between the blocks and into and from the process as a whole. Such block flowsheets are made at the beginning of a process design for orientation purposes or later as a summary of the material balance of the process. For example, the coal carbonization process of Figure 2.1 starts with 1OO,OOOIb/hr of coal and some process air, involves six main process units, and makes the indicated quantities of ten different products. When it is of particular interest, amounts of utilities also may be shown; in this example the use of steam is indicated at one point. The block diagram of Figure 2.2 was prepared in connection with a study of the modification of an existing petroleum refinery. The three feed stocks are separated into more than 20 products. Another representative petroleum refinery block diagram, in Figure 13.20, identifies the various streams but not their amounts or conditions. 2.2. PROCESS FLOWSHEETS Process flowsheets embody the material and energy balances between and the sizing of the major equipment of the plant. They include all vessels such as reactors, separators, and drums; special processing equipment, heat exchangers, pumps, and so on. Numerical data include flow quantities, compositions, pressures, temperatures, and so on. Inclusion of major instrumentation that is essential to process control and to complete understanding of the flowsheet without reference to other information is required particularly during the early stages of a job, since the process flowsheet is drawn first and is for some time the only diagram representing the process. As the design develops and a mechanical flowsheet gets underway, instrumentation may be taken off the process diagram to reduce the clutter. A checklist of the information that usually is included on a process flowsheet is given in Table 2.1. Working flowsheets are necessarily elaborate and difficult to represent on the page of a book. Figure 2.3 originally was 30in. wide. In this process, ammonia is made from available hydrogen supplemented by hydrogen from the air oxidation of natural gas in a two-stage reactor F-3 and V-S. A large part of the plant is devoted to purification of the feed gases of carbon dioxide and unconverted methane before they enter the converter CV-1. Both commercial and refrigeration grade ammonia are made in this plant. Com- positions of 13 key streams are summarized in the tabulation. Characteristics of the streams such as temperature, pressure, enthalpy, volumetric flow rates, etc., sometimes are conveniently included in the tabulation. In the interest of clarity, however, in some instances it may be preferable to have a separate sheet for a voluminous material balance and related stream information. A process flowsheet of the dealkylation of toluene to benzene is in Figure 2.4; the material and enthalpy flows and temperature and pressures are tabulated conveniently, and basic instrumentation is represented. 2.3. MECHANICAL (P&l) FLOWSHEETS Mechanical flowsheets also are called piping and instrument (P&I) diagrams to emphasize two of their major characteristics. They do not show operating conditions or compositions or flow quantities, but they do show all major as well as minor equipment more realistically than on the process flowsheet. Included are sizes and specification classes of all pipe lines, all valves, and all instruments. In fact, every mechanical aspect of the plant regarding the process equipment and their interconnections is represented except for supporting structures and foundations. The equipment is shown in greater detail than on the PFS, notably with regard to external piping connections, internal details, and resemblance to the actual appearance. The mechanical flowsheet of the reaction section of a toluene dealkylation unit in Figure 2.5 shows all instrumentation, including indicators and transmitters. The clutter on the diagram is minimized by tabulating the design and operating conditions of the major equipment below the diagram. The P&I diagram of Figure 2.6 represents a gas treating plant that consists of an amine absorber and a regenerator and their immediate auxiliaries. Internals of the towers are shown with exact locations of inlet and outlet connections. The amount of instrumentation for such a comparatively simple process may be surprising. On a completely finished diagram, every line will carry a code designation identifying the size, the kind of fluid handled, the pressure rating, and material specification. Complete information about each line-its length, size, elevation, pressure drop, fittings, etc.-is recorded in a separate line summary. On Figure 2.5, which is of an early stage of construction, only the sizes of the lines are shown. Although instrumentation symbols are fairly well standard- ized, they are often tabulated on the P&I diagram as in this example. 2.4. UTILITY FLOWSHEETS These are P&I diagrams for individual utilities such as steam, steam condensate, cooling water, heat transfer media in general, 1 9
- 39. 20 FLOWSHEETS I Net Fuel Gas 7183 I SUlfLN Sulfur 1070 r Recovery Phenols 2 5 Coal 100,000 Air c I r-l r-l Steam I Net Waste Liquids 2380 Carbonizer Primary Fractionator w 22,500 * Oils 1 Light Aromatics 770 Recovery * I Middle Oils (diesel, etc.) 12575 Tar Acids 3320 Pitch Distillation I Figure 2.1. Coal carbonization block flowsheet. Quantities are in Ib/hr. Heavy Oils (creosote, etc.) 2380 Pitch 3000 C h a r 77500 compressed air, fuel, refrigerants, and inert blanketing gases, and how they are piped up to the process equipment. Connections for utility streams are shown on the mechanical flowsheet, and their conditions and flow quantities usually appear on the process flowsheet. Since every detail of a plant design must be recorded on paper, many other kinds of drawings also are required: for example, electrical flow, piping isometrics, instrument lines, plans and elevations, and individual equipment drawings in all detail. Models and three-dimensional representations by computers also are now standard practice in many design offices. 2.5. DRAWING OF FLOWSHEETS Flowsheets are intended to represent and explain processes. To make them easy to understand, they are constructed with a consistent set of symbols for equipment, piping, and operating conditions. At present there is no generally accepted industrywide body of drafting standards, although every large engineering office does have its internal standards. Some information appears in ANSI and British Standards publications, particularly of piping symbols. Much of this information is provided in the book by Austin (1979) along with symbols gleaned from the literature and some engineering firms. Useful compilations appear in some books on process design, for instance, those of Sinnott (1983) and Ulrich (1984). The many flowsheets that appear in periodicals such as Chemical Engineering or Hydrocarbon Processing employ fairly consistent sets of symbols that may be worth imitating. Equipment symbols are a compromise between a schematic representation of the equipment and simplicity and ease of drawing. A selection for the more common kinds of equipment appears in Table 2.2. Less common equipment or any with especially intricate configuration often is represented simply by a circle or rectangle. Since a symbol does not usually speak entirely for itself but also carries a name and a letter-number identification, the flowsheet can be made clear even with the roughest of equipment symbols. The TABLE 2.1. Checklist of Data Normally Included on a Process Flowsheet 1. Process lines, but including only those bypasses essential to an understanding of the process 2. All process equipment. Spares are indicated by letter symbols or notes 3. Major instrumentation essential to process control and to understanding of the flowsheet 4. Valves essential to an understanding of the flowsheet 5. Design basis, including stream factor 6. Temperatures, pressures, flow quantities 7. Weight and/or mol balance, showing compositions, amounts, and other properties of the principal streams 6. Utilities requirements summary 9. Data included for particular equipment a. Compressors: SCFM (60°F. 14.7 psia); APpsi; HHP; number of stages; details of stages if important b. Drives: type; connected HP; utilities such as kW, lb steam/hr, or Btu/hr c. Drums and tanks: ID or OD, seam to seam length, important internals d. Exchangers: Sqft, kBtu/hr, temperatures, and flow quantities in and out; shell side and tube side indicated e. Furnaces: kBtu/hr, temperatures in and out, fuel f. Pumps: GPM (6o”F), APpsi, HHP, type, drive g. Towers: Number and type of plates or height and type of packing; identification of all plates at which streams enter or leave; ID or OD; seam to seam length; skirt height h. Other equipment: Sufficient data for identification of duty and size
- 40. 2.5. DRAWING OF FLOWSHEETS 21 TABLE 2.2. Flowsheet Equipment Symbols Fluid Handling Heat Transfer HEAT TRANSFER FLUID HANDLING Centrifugal pump or blower, motor driven Shell-and-tube heat exchanger Condenser Tubeside T?Shellside Centrifugal pump or blower, d turbine -driven -a, Reboiler -B-@ Rotary pump or blower Vertical thermosiphon reboiler -42 Reciprocating pump or compressor Process + Centrifugal compressor Kettle reboiler Process 4- Fuel Centrifugal compressor, alternate symbol Air cooler with finned tubes S t m -3 Process Fired heater Steam ejector Fired heater with radiant and convective coils Coil in tank Rotary dryer or kiln Evaporator Tray dryer 22 Air Spray condenser with steam ejector Cooling tower, forced draft i Water
- 41. 22 F L O W S H E E T S TABLE 2.2~(continued) Mass Transfer V e s s e l s MASS TRANSFER Tray c o l u m n Packed c o l u m n Solvent 7F kJ Multistage spray stirred oolumn column Process Extract 4 Raffinate Mixer-settler extraction battery VESSELS Drum or tank Drum or tank Storage tank Open tank Gas holder Jacketed vessel with agitator Vessel with heat transfer coil Bin for solids rl -m-w t-l -TQ 0 letter-number designation consists of a letter or combination to designate the class of the equipment and a number to distinguish it from others of the same class, as two heat exchangers by E-112 and E-215. Table 2.4 is a typical set of letter designations. Operating conditions such as flow rate, temperature, pressure, enthalpy, heat transfer rate, and also stream numbers are identified with symbols called flags, of which Table 2.3 is a commonly used set. Particular units are identified on each flowsheet, as in Figure 2.3. Letter designations and symbols for instrumentation have been
- 42. TABLE 2.2~(continued) Convevors and Feeders 2.5. DRAWING OF FLOWSHEETS 23 S e p a r a t o r s Conveyor Belt conveyor Screw conveyor Elevator Feeder Screw feeder Weighing feeder Tank car Freight car Conical settling tank Raked thickener SEPARATORS ‘late-and-frame filter Rotary vacuum filter Sand filter Dust collector Cyclone separator Centrifuge Mesh entrainment separator Liquid-liquid separator Drum with water settling pot I I ; Screen gE -0 -% H e a v y Light tcCourse ‘- F i n e thoroughly standardized by the Instrument Society of America For clarity and for esthetic reasons, equipment should be (ISA). An abbreviated set that may be adequate for the usual represented with some indication of their relative sizes. True scale is flowsketch appears on Figure 3.4. The P&I diagram of Figure 2.6 not feasible because, for example, a flowsheet may need to depict affords many examples. both a tower 15Oft high and a drum 2ft in diameter. Logarithmic
- 43. 24 FLOWSHEETS TABLE 2.2~(continued) ’ Mixing and Comminution Drivers MIXING & COMMINUTION Liquid mixing impellers: basic, propeller,turbine, anchor Ribbon blender Double cone blender Crusher Roll crusher Pebble or rod mill DRIVERS Motor DC motor AC motor, 3-phase Turbine Turbines: steam, hydraulic, w scaling sometimes gives a pleasing effect; for example, if the 150 ft tower is drawn 6in. high and the 2ft drum 0.5 in., other sizes can be read off a straight line on log-log paper. A good draftsman will arrange his flowsheet as artistically as possible, consistent with clarity, logic, and economy of space on the drawing. A fundamental rule is that there be no large gaps. Flow is predominantly from left to right. On a process flowsheet, distillation towers, furnaces, reactors, and large vertical vessels often are arranged at one level, condenser and accumulator drums on another level, reboilers on still another level, and pumps more or less on one level but sometimes near the equipment they serve in order to minimize excessive crossing of lines. Streams enter the flowsheet from the left edge and leave at the right edge. Stream numbers are assigned to key process lines. Stream compositions and other desired properties are gathered into a table that may be on a separate sheet if it is especially elaborate. A listing of flags with the units is desirable on the flowsheet. Rather less freedom is allowed in the construction of mechanical flowsheets. The relative elevations and sizes of equip- ment are preserved as much as possible, but all pumps usually are shown at the same level near the bottom of the drawing. Tab- ulations of instrumentation symbols or of control valve sizes or of relief valve sizes also often appear on P&I diagrams. Engineering offices have elaborate checklists of information that should be included on the flowsheet, but such information is beyond the scope here. Appendix 2.1 provides the reader with material for the construction of flowsheets with the symbols of this chapter and possibly with some reference to Chapter 3.
- 44. 2.5. DRAWING OF FLOWSHEETS 25 TABLE 2.3. Flowsheet Flags of Operating Conditions in Typical Units Mass flow rate, lbslhr Molal flow rate, Ibmols/hr Temperature, “F Pressure, psig (or indicate if psia or Torr or bar) Volumetric liquid flow rate, gal!min. Volumetric liquid flow rate, bbls/day Kilo Btu/hr, at heat transfer equipment Enthalpy, Btu/lb O t h e r s > A < <TsiGi--> 0 155 psia <XT-> TABLE 2.4. Letter Designations of Equipment Equipment Lettera Equipment Lettan Agitator Air filter Bin Blender B l o w e r Centrifuge Classifying equipment Colloid mill C o m p r e s s o r C o n d e n s e r Conveyor Cooling tower C r u s h e r Crystallizer Cyclone separator (gas) Cyclone separator (liquid) D e c a n t e r Disperser D r u m Dryer (thermal) Dust collector Elevator Electrostatic separator Engine Evaporator Fan F e e d e r Filter (liquid) Furnace M FG l-r M J B FF S S R J C E C TE S R K F G F FL M D D E FG C F G PM FE J J C P B SR E M R D D G L M PM B L F G PM S R J E R G RM S FG M S R S R l-r F T V E L Grinder H e a t e x c h a n g e r H o m o g e n i z e r Kettle Kiln (rotary) Materials handling e q u i p m e n t Miscellaneous” Mixer Motor Oven Packaging machinen/ Precipitator (dust or mist) Prime mover Pulverizer Pump (liquid) Reboiler Reactor Refrigeration system R o t a m e t e r Screen Separator (entrainment) S h a k e r Spray disk Spray nozzle Tank Thickener Tower Vacuum equipment Weigh scale ‘Note: The letter L is used for unclassified equipment when only a few items are of this type; otherwise, individual letter designations are assigned.
- 45. Fii 2.2. Block flowsheet of the revamp of a 30,000 Bbl/day refinery with supplementary light stocks (The C. W. Nofsinger Co.).
- 46. 1 J t Figure 2.3. Process flowsheet of a plant making 47 tons/day of ammonia from available hydrogen and hydrogen made from natural gas (The C. W. Nofsinger Co.).
- 47. Figure 2.4. Pro- cess flowsheet of the manufacture of benzene by deal- kylation of toluene (Wells, Safety in Process Design, G e o r g e Godwin, London, 1980). Figure 2.5. Engineering (P&I) flowsheet of the reaction section of plant for dealkyla- tion of benzene (Wells, Safety in Process Design, George Godwin, London, 1980). 28
- 48. E-102 D-101 Em3 T-lo! Em4 D-ID.3 P-102b.p E-105 Ed06 REACTOR UlGH PRESSVRE BENZENL 6ENZElE OVEWMEID REFLUX REFLUX PRODUCT BENZENE EFFLVENT KNOCKOUT POT COLUMN COLUMN CouDEN.9ER COOLER REBDIWI CONDENSEI) 23MID. PR HEATER 3 7 4 ccaqn 01 GGlL,H 5 I%o”dy” r/l 0 26 GCAUU 2 07Gc444 X67M T/T 1-1 xYZ ENGINEERING LTD.
- 49. Figure 2.6. Engineering flowsheet of a gas treating plant. Note the tabulation of instrumentation flags at upper right (Fluor Engineers, by way of Ruse and Barrow, Project Engineering of Process Plants, Wiley, New York, 1957).
- 50. REFERENCES 31 REFERENCES 1. D.G. Austin, Chemical Engineering Drawing Symbols, George Godwin, London, 1979. 2. Graphical Symbols for Piping System and Plant, British Standard 1553: Part 1: 1977. 3. Graphical Symbols for Process Flow Diagrams, ASA Y32.11.1961, American Society of Mechanical Engineers, New York. 4. E.E. Ludwig, Applied Process Design for Chemical and Petrochemical Plants, Gulf, Houston, 1977, Vol. 1. 5. H.F. Rase and M.H. Barrow, Project Engineering of Process Plants, Wiley, New York, 1957. 6. R.K. Sinnott, Coulson, and Richardson, Chemical Engineering, vol. 6, Design, Pergamon, New York, 1983. 7. G.D. Ulrich, A Guide to Chemical Engineering Process Design and Economics, Wiley, New York, 1984. 8. R. Weaver, Process Piping Design, Gulf, Houston, 1973, 2 ~01s.
- 52. Appendix 2.1 Descriptions of Example Process Flowsheets These examples ask for the construction of flowsheets from the given process descriptions. Necessary auxiliaries such as drums and pumps are to be included even when they are not mentioned. Essential control instrumentation also is to be provided. Chapter 3 has examples. The processes are as follows: 1. visbreaker operation, 2. cracking of gas oil, 3. olefin production from naptha and gas oil, 4. propylene oxide synthesis, 5. phenol by the chlorobenzene process, 6. manufacture of butadiene sulfone, 7. detergent manufacture, 8. natural gas absorption, 9. tall oil distillation, 10. recovery of isoprene, 11. vacuum distillation, l2. air separation. 1. VISBREAKER OPERATION Visbreaking is a mild thermal pyrolysis of heavy petroleum fractions whose object is to reduce fuel production in a refinery and to make some gasoline. The oil of 7.2API and 700°F is supplied from beyond the battery limits to a surge drum F-l. From there it is pumped with J-lA&B to parallel furnaces B-lA&B from which it comes out at 890°F and 200 psig. Each of the split streams enters at the bottom of its own evaporator T-lA&B that has five trays. Overheads from the evaporators combine and enter at the bottom of a 30-tray fractionator T-2. A portion of the bottoms from the fractionator is fed to the top trays of T-IA&B; the remainder goes through exchanger E-5 and is pumped with J-2A&B back to the furnaces B-lA&B. The bottoms of the evaporators are pumped with JdA&B through exchangers E-5, E-3A (on crude), and E-3B (on cooling water) before proceeding to storage as the fuel product. A side stream is withdrawn at the tenth tray from the top of T-2 and proceeds to steam stripper T-3 equipped with five trays. Steam is fed below the bottom tray. The combined steam and oil vapors return to T-2 at the eighth tray. Stripper bottoms are pumped with J-6 through E-2A (on crude) and E-2B (on cooling water) and to storage as “heavy gasoline.” Overhead of the fractionator T-2 is partially condensed in E-1A (on crude) and E-1B (on cooling water). A gas product is withdrawn overhead of the reflux drum which operates at 15 psig. The “light gasoline” is pumped with J-5 to storage and as reflux. Oil feed is 122,48Opph, gas is 3370, light gasoline is 5470, heavy gasoline is 9940, and fuel oil is 103,708 pph. Include suitable control equipment for the main fractionator T-2. 2. CRACKING OF GAS OIL A gas oil cracking plant consists of two cracking furnaces, a soaker, a main fractionator, and auxiliary strippers, exchangers, pumps, and drums. The main fractionator (150 psig) consists of four zones, the bottom zone being no. 1. A light vacuum gas oil (LVGO) is charged to the top plate of zone 3, removed from the bottom tray of this zone and pumped to furnace no. 1 that operates at 1OOOpsig and 1000°F. A heavy vacuum gas oil (HVGO) is charged to the top plate of zone 2, removed at the bottom tray and charged to furnace no. 2 that operates at 500 psig and 925°F. Effluents from both furnaces are combined and enter the soaker; this is a large vertical drum designed to provide additional residence time for conversion under adiabatic conditions. Effluent at 5OOpsig and 915°F enters the bottom zone of the main frac- tionator. Bottoms from zone 1 goes to a stripping column (5 psig). Overhead from that tower is condensed, returned partly as reflux and partly to zone 3 after being cooled in the first condenser of the stripping column. This condensing train consists of the preheater for the stream being returned to the main fractionator and an air cooler. The cracked residuum from the bottom of the stripper is cooled to 170°F in a steam generator and an air cooler in series. Live steam is introduced below the bottom tray for stripping. All of the oil from the bottom of zone 3 (at 7OO”F), other than the portion that serves as feed to furnace no. 1, is withdrawn through a cooler (500°F) and pumped partly to the top tray of zone 2 and partly as spray quench to zone 1. Some of the bottoms of zone 1 likewise is pumped through a filter and an exchanger and to the same spray nozzle. Part of the liquid from the bottom tray of zone 4 (at 590°F) is pumped to a hydrogenation unit beyond the battery limits. Some light material is returned at 400°F from the hydrogenation unit to the middle of zone 4, together with some steam. Overhead from the top of the column (zone 4) goes to a partial condenser at 400°F. Part of the condensate is returned to the top tray as reflux; the rest of it is product naphtha and proceeds beyond the battery limits. The uncondensed gas also goes beyond the battery limits. Condensed water is sewered. 3. OLEFIN PRODUCTION A gaseous product rich in ethylene and propylene is made by pyrolysis of crude oil fractions according to the following description. Construct a flowsheet for the process. Use standard symbols for equipment and operating conditions. Space the symbols and proportion them in such a way that the sketch will have a pleasing appearance. Crude oil is pumped from storage through a steam heated exchanger and into an electric desalter. Dilute caustic is injected into the line just before the desalting drum. The aqueous phase collects at the bottom of this vessel and is drained away to the sewer. The oil leaves the desalter at 19O”F, and goes through heat exchanger E-2 and into a furnace coil. From the furnace, which it leaves at 600”F, the oil proceeds to a distillation tower. After serving to preheat the feed in exchanger E-2, the bottoms proceeds to storage; no bottoms pump is necessary because the tower operates with 65 psig at the top. A gas oil is taken off as a sidestream some distance above the feed plate, and naphtha is taken off overhead. Part of the overhead is returned as reflux to the tower, and the remainder proceeds to a cracking furnace. The gas oil also is charged to the same cracking furnace but into a separate coil. Superheated steam at 800°F is injected into both cracking coils at their inlets. Effluents from the naphtha and gas oil cracking coils are at 1300°F and 12OO”F, respectively. They are combined in the line just before discharge into a quench tower that operates at 5 psig and 235°F at the top. Water is sprayed into the top of this tower. The 33
- 53. 34 APPENDIX 2.1 bottoms is pumped to storage. The overhead is cooled in a water exchanger and proceeds to a separating drum. Condensed water and an aromatic oil separate out there. The water is sewered whereas the oil is sent to another part of the plant for further treating. The uncondensed gas from the separator is compressed to 3OOpsig in a reciprocating unit of three stages and then cooled to 100°F. Condensed water and more aromatic distillate separate out. Then the gas is dried in a system of two desiccant-filled vessels that are used alternately for drying and regeneration. Subsequently the gas is precooled in exchanger E-6 and charged to a low temperature fractionator. This tower has a reboiler and a top refluxing system. At the top the conditions are 280psig and -75°F. Freon refrigerant at -90°F is used in the condenser. The bottoms is recycled to the pyrolysis coil. The uncondensed vapor leaving the reflux accumulator constitutes the product of this plant. It is used to precool the feed to the fractionator in E-6 and then leaves this part of the plant for further purification. 4. PROPYLENE OXIDE SYNTHESIS Draw a process flowsheet for the manufacture of propylene oxide according to the following description. Propylene oxide in the amount of 5000 tons/yr will be made by the chlorohydrin process. The basic feed material is a hydrocarbon mixture containing 90% propylene and the balance propane which does not react. This material is diluted with spent gas from the process to provide a net feed to chlorination which contains 40mol% propylene. Chlorine gas contains 3% each of air and carbon dioxide as contaminants. Chlorination is accomplished in a packed tower in which the hydrocarbon steam is contacted with a saturated aqueous solution of chlorine. The chlorine solution is made in another packed tower. Because of the limited solubility of chlorine, chlorohydrin solution from the chlorinator is recirculated through the solution tower at a rate high enough to supplement the fresh water needed for the process. Solubility of chlorine in the chlorohydrin solution is approximately the same as in fresh water. Concentration of the effluent from the chlorinator is 81b organics/lOO lb of water. The organics have the composition Propylene chlorohydrin 75 mol % Propylene dichloride 1 9 Propionaldehyde 6 Operating pressure of the chlorinator is 3Opsig, and the temperature is 125°F. Water and the fresh gas stream are at 80°F. Heat of reaction is 2OOOBtu/lb chlorine reacted. Percentage conversion of total propylene fed to the chlorinator is 95% (including the recycled material). Overhead from the chlorinator is scrubbed to remove excess chlorine in two vessels in succession which employ water and 5% caustic solution, respectively. The water from the first scrubber is used in the chlorine solution tower. The caustic is recirculated in order to provide adequate wetting of the packing in the caustic scrubber; fresh material is charged in at the same rate as spent material is purged. Following the second scrubber, propylene dichloride is recovered from the gas by chilling it. The spent gas is recycled to the chlorinator in the required amount, and the excess is flared. Chlorohydrin solution is pumped from the chlorinator to the saponitier. It is mixed in the feed line with a 10% lime slurry and preheated by injection of live 25 psig steam to a temperature of 200°F. Stripping steam is injected at the bottom of the saponifier, which has six perforated trays without downcomers. Propylene oxide and other organic materials go overhead; the bottoms contain unreacted lime, water, and some other reaction products, all of which can be dumped. Operating pressure is substantially atmospheric. Bubblepoint of the overhead is 60°F. Separation of the oxide and the organic byproducts is ac- complished by distillation in two towers. Feed from the saponifier contains oxide, aldehyde, dichloride, and water. In the first tower, oxide and aldehyde go overhead together with only small amounts of the other substances; the dichloride and water go to the bottom and also contain small amounts of contaminants. Two phases will form in the lower section of this tower; this is taken off as a partial side stream and separated into a dichloride phase which is sent to storage and a water phase which is sent to the saponifier as recycle near the top of that vessel. The bottoms are a waste product. Tower pressure is 20psig. Live steam provides heat at the bottom of this column. Overhead from the first fractionator is condensed and charged to the second tower. There substantially pure propylene oxide is taken overhead. The bottoms is dumped. Tower pressure is 15 psig, and the overhead bubblepoint is 100°F. Reactions are Cl, + HzO+ ClOH + HCI C,H, + Cl, + HZO+ C,H,CIOH + HCI 2C,H,CIOH + Ca(OH), CA + Cl, + C,H,CI, --) 2C,H,O + CaCl, + 2H,O C,H,CIOH - C,H,CHO + HCI Show all necessary major equipment, pumps, compressors, refrigerant lines. Show the major instrumentation required to make this process continuous and automatic. 5. PHENOL BY THE CHLOROBENZENE PROCESS A, portion of a plant for the manufacture of phenol from mono- chlorbenzene and NaOH is in accordance with the following descrip- tion. a. Construct a flowsheet of the process, with operating conditions and the two control instruments mentioned. b. Prepare a material balance showing the compositions of the process streams in the portion of the plant before the brine decanter V-103. The amount of phenol in this stream is 2000 Ib/hr. Excess caustic (5%) is fed to the emulsifier. Process description: The principal reactions in the plant are C,H,Cl + 2NaOH+ C,H,ONa + NaCl + H,O 2C,H,OH C,H,ONa + HCI + C,H,OH + NaCl I + (G&),0 + Hz0 From storage, monochlorbenzene and 10% caustic are pumped together with diphenyl ether from decanter V-102 into emulsifier V-101 which is provided with intense agitation. The effluent from that vessel is pumped with a high pressure steam driven reciprocating pump P-103 at 4OOOpsig through a feed-effluent exchanger E-101 and through the tube side of a direct fired heater R-101. Here the stream is heated to 700°F and reaction 1 occurs. From the reactor, the effluent is cooled in E-101, cooled further to 1lO”F in water cooler E-102, and then enters diphenyl ether decanter V-102. The lighter DPE phase is returned with pump P-104 to the emulsifier. The other phase is pumped with P-105 to another stirred vessel R-102 called a Springer to which 5% HCl also is pumped, with P-106; here reaction 2 occurs. The mixture of two liquid phases is cooled in water cooler E-103 and then separated in brine decanter V-103. From that vessel the lighter phenol phase proceeds (P-108) to a basket type evaporator D-101 that is heated with steam. Overhead vapor from
- 54. 7. DETERGENT MANUFACTURE 35 the evaporator proceeds beyond the battery limit for further purification. Evaporator bottoms proceeds to waste disposal. The aqueous phase from decanter V-103 is pumped with P-109 through a feed-bottoms exchanger E-104 to the top tray of the brine tower D-102. The overhead is condensed in E-105, collected in accumulator V-104 and pumped beyond the battery limits for recovery of the phenol. Tower D-102 is provided with a steam heated reboiler E-106. Bottom product is a weak brine that is pumped with P-110 through the feed-bottoms exchanger and beyond the battery limits for recovery of the salt. Two important control instruments are to be shown on the flowsheet. These are a back pressure controller in the reactor effluent line beyond exchanger E-101 and a pH controller on the feed line of the 5% HCI that is fed to springer R-102. The pH instrument maintains proper conditions in the springer. Note: There is a tendency to byproduct diphenyl ether formation in reactor R-101. However, a recycle of 100 pph of DPE in the feed to the reactor prevents any further formation of this substance. 6. MANUFACTURE OF BUTADIENE SULFONE A plant is to manufacture butadiene sulfone at the rate of 1250 lb/hr from liquid sulfur dioxide and butadiene to be recovered from a crude C, mixture as starting materials. Construct a flowsheet for the process according to the following description. The crude C, mixture is charged to a 70 tray extractive distillation column T-l that employs acetonitrile as solvent. Trays are numbered from the bottom. Feed enters on tray 20, solvent enters on tray 60, and reflux is returned to the top tray. Net overhead product goes beyond the battery limits. Butadiene dissolved in acetonitrile leaves at the bottom. This stream is pumped to a 25-tray solvent recovery column T-2 which it enters on tray 20. Butadiene is recovered overhead as liquid and proceeds to the BDS reactor. Acetonitrile is the bottom product which is cooled to 100°F and returned to T-l. Both columns have the usual condensing and reboiling provisions. Butadiene from the recovery plant, liquid sulfur dioxide from storage, and a recycle stream (also liquified) are pumped through a preheater to a high temperature reactor R-l which is of shell-and-tube construction with cooling water on the shell side. Operating conditions are 100°C and 3OOpsig. The combined feed contains equimolal proportions of the reactants, and 80% conversion is attained in this vessel. The effluent is cooled to 70°C then enters a low temperature reactor R-2 (maintained at 70°C and 50psig with cooling water) where the conversion becomes 92%. The effluent is flashed at 70°C and atmospheric pressure in D-l. Vapor product is compressed, condensed and recycled to the reactor R-l. The liquid is pumped to a storage tank where 24 hr holdup at 70°C is provided to ensure chemical equilibrium between sulfur dioxide, butadiene, and butadiene sulfone. Cooling water is available at 32°C. 7. DETERGENT MANUFACTURE The process of making synthetic detergents consists of several operations that will be described consecutively. ALKYLATION Toluene and olefinic stock from storage are pumped (at 80°F) separately through individual driers and filters into the alkylation reactor. The streams combine just before they enter the reactor. The reactor is batch operated 4 hr/cycle; it is equipped with a single impeller agitator and a feed hopper for solid aluminum chloride which is charged manually from small drums. The alkylation mixture is pumped during the course of the reaction through an external heat exchanger (entering at -10°F and leaving at -15°F) which is cooled with ammonia refrigerant (at -25°F) from an absorption refrigeration system (this may be represented by a block on the FS); the exchanger is of the kettle type. HCI gas is injected into the recirculating stream just beyond the exit from the heat exchanger; it is supplied from a cylinder mounted in a weigh scale. The aluminum chloride forms an alkylation complex with the toluene. When the reaction is complete, this complex is pumped away from the reactor into a storage tank with a complex transfer pump. To a certain extent, this complex is reused; it is injected with its pump into the reactor recirculation line before the suction to the recirculation pump. There is a steam heater in the complex line, between the reactor and the complex pump. The reaction mixture is pumped away from the reactor with an alkymer transfer pump, through a steam heater and an orifice mixer into the alkymer wash and surge tank. Dilute caustic solution is recirculated from the a.w.s. tank through the orifice mixer. Makeup of caustic is from a dilute caustic storage tank. Spent caustic is intermittently drained off to the sewer. The a.w.s. tank has an internal weir. The caustic solution settles and is removed at the left of the weir; the alkymer overflows the weir and is stored in the right-hand portion of the tank until amount sufficient for charging the still has accumulated. DISTILLATION Separation of the reactor product is effected in a ten-plate batch distillation column equipped with a water-cooled condenser and a Dowtherm-heated (650”F, 53psig) still. During a portion of the distillation cycle, operation is under vacuum, which is produced by a two-stage steam jet ejector equipped with barometric condensers. The Dowtherm heating system may be represented by a block. Product receiver drums are supplied individually for a slop cut, for toluene, light alkymer, heart alkymer, and a heavy alkymer distillate. Tar is drained from the still at the end of the operation through a water cooler into a bottoms receiver drum which is supplied with a steam coil. From this receiver, the tar is loaded at intervals into 50 gal drums, which are trucked away. In addition to the drums which serve to receive the distillation products during the operation of the column, storage tanks are provided for all except the slop cut which is returned to the still by means of the still feed pump; this pump transfers the mixture from the alkymer wash and surge tank into the still. The recycle toluene is not stored with the fresh toluene but has its own storage tank. The heavy alkymer distillate tank connects to the olefinic stock feed pump and is recycled to the reactor. SULFONATION Heart alkymer from storage and 100% sulfuric acid from the sulfuric acid system (which can be represented by a block) are pumped by the reactor feed pump through the sulfonation reactor. The feed pump is a positive displacement proportioning device with a single driver but with separate heads for the two fluids. The reactor is operated continuously; it has a single shell with three stages which are partially separated from each other with horizontal doughnut shaped plates. Each zone is agitated with its individual impeller; all three impellers are mounted on a single shaft. On leaving the reactor, the sulfonation mixture goes by gravity through a water cooler (leaving at 130°F) into a centrifuge. Spent acid from the centrifuge goes to storage (in the sulfuric acid system block); the sulfonic acids go to a small surge drum or can bypass this drum and go directly to a large surge tank which is equipped with an agitator and a steam jacket. From the surge drum, the material is sent by an extraction feed pump through a water cooler, then a “flomix,” then
- 55. 36 APPENDIX 2.1 another water cooler, then another “flomix” (leaving at 150”F), and then through a centrifuge and into the sulfonic acid surge tank. Fresh water is also fed to each of the “flomixers.” Wash acid is rejected by the centrifuge and is sent to the sulfuric acid system. The “flomix” is a small vertical vessel which has two compartments and an agitator with a separate impeller for each compartment. NEUTRALIZATION Neutralization of the sulfonic acid and building up with sodium sulfate and tetrasodium pyrophosphate (TSPP) is accomplished in two batch reactors (5 hr cycle) operated alternately. The sodium sulfate is pumped in solution with its transfer pump from the sodium sulfate system (which can be represented by a block). The TSPP is supplied as a solid and is fed by means of a Redler conveyor which discharges into a weigh hopper running on a track above the two reactors. Each reactor is agitated with a propeller and a turbine blade in a single shaft. Sodium hydroxide of 50% and 1% concentrations is used for neutralization. The 50% solution discharges by gravity into the reactor; the 1% solution is injected gradually into the suction side of the reactor slurry circulating pump. As the caustic is added to the reactor, the contents are recirculated through a water-cooled external heat exchanger (exit at 160°F), which is common to both reactors. When the reaction is completed in one vessel, the product is fed gradually by means of a slurry transfer pump to two double drum dryers which are steam-heated and are supplied with individual vapor hoods. The dry material is carried away from the dryers on a belt conveyor and is taken to a flaker equipped with an air classifier. The fines are returned to the trough between the dryer drums. From the classifier, the material is taken with another belt conveyor to four storage bins. These storage bins in turn discharge onto a belt feeder which discharges into drums which are weighed automatically on a live portion of a roller conveyor. The roller conveyor takes the drums to storage and shipping. Notes: All water cooled exchangers operate with water in at 75°F and out at 100°F. All pumps are centrifugal except the complex transfer, and the sulfonation reactor feed, which are both piston type; the neutralization reactor recirculation pump and the transfer pumps are gear pumps. Show all storage tanks mentioned in the text. 8. NATURAL GAS ABSORPTION A gas mixture has the composition by volume: C o m p o n e n t N, Ct.4 C4-h ‘3, Mot fraction 0 . 0 5 0 . 6 5 0 . 2 0 0 . 1 0 It is fed to an absorber where 75% of the propane is recovered. The total amount absorbed is 50mol/hr. The absorber has four theoretical plates and operates at 135 psig and 100°F. All of the absorbed material is recovered in a steam stripper that has a large number of plates and operates at 25 psig and 230°F. Water is condensed out of the stripped gas at 100°F. After compression to 50 psig, that gas is combined with a recycle stream. The mixture is diluted with an equal volume of steam and charged to a reactor where pyrolysis of the propane occurs at a temperature of 1300°F. For present purposes the reaction may be assumed to be simply C,H,-+C,H,+ CH, with a specific rate k =0.28/set. Conversion of propane is 60%. Pressure drop in the reactor is 20 psi. Reactor effluent is cooled to remove the steam, compressed to 285 psig, passed through an activated alumina drying system to remove further amounts of water, and then fed to the first fractionator. In that vessel, 95% of the unconverted propane is recovered as a bottoms product. This stream also contains 3% ethane as an impurity. It is throttled to 50psig and recycled to the reactor. In two subsequent towers, ethylene is separated from light and heavy impurities. Those separations may be taken as complete. Construct a flow diagram of this plant. Show such auxiliary equipment as drums, heat exchangers, pumps, and compressors. Show operating conditions and flow quantities where calculable with the given data. 9. TALL OIL DISTILLATION Tall oil is a byproduct obtained from the manufacture of paper pulp from pine trees. It is separated by vacuum distillation (50mmHg) in the presence of steam into four primary products. In the order of decreasing volatility these are unsaponifiables (US), fatty acid (FA), rosin acids (RA), and pitch (P). Heat exchangers and reboilers are heated with Dowtherm condensing vapors. Some coolers operate with water and others generate steam. Live steam is charged to the inlet of every reboiler along with the process material. Trays are numbered from the bottom of each tower. Tall oil is pumped from storage through a preheater onto tray 10 of the pitch stripper T-l. Liquid is withdrawn from tray 7 and pumped through a reboiler where partial vaporization occurs in the presence of steam. The bottom 6 trays are smaller in diameter and serve as stripping trays. Steam is fed below tray 1. Pitch is pumped from the bottom through steam generator and to storage. Overhead vapors are condensed in two units E-l and E-2. From the accumulator, condensate is pumped partly as reflux to tray 15 and partly through condenser E-l where it is preheated on its way as feed to the next tower T-2. Steam is not condensed in E-2. It flows from the accumulator to a barometric condenser that is connected to a steam jet ejector. Feed enters T-2 at tray 5. There is a pump-through reboiler. Another pump withdraws material from the bottom and sends it to tower T-3. Liquid is pumped from tray 18 through a cooler and returned in part to the top tray 20 for temperature and reflux control. A portion of this pumparound is withdrawn after cooling as unsaps product. Steam leaves the top of the tower and is condensed in the barometric. Tray 5 of T-3 is the feed position. This tower has two reboilers. One of them is a pumparound from the bottom, and the other is gravity feed from the bottom tray. Another pump withdraws material from the bottom, and then sends it through a steam generator and to storage as rosin acid product. A slop cut is withdrawn from tray 20 and pumped through a cooler to storage. Fatty acid product is pumped from tray 40 through a cooler to storage. Another stream is pumped around from tray 48 to the top tray 50 through a cooler. A portion of the cooled pumparound is sent to storage as another unsaps product. A portion of the overhead steam proceeds to the barometric condenser. The rest of it is boosted in pressure with high pressure steam in a jet compressor. The boosted steam is fed to the inlets of the two reboilers associated with T-3 and also directly into the column below the bottom tray. The vapors leaving the primary barometric condenser proceed to a steam ejector that is followed by another barometric. Pressures at the tops of the towers are maintained at 50mmHg absolute. Pressure drop is 2 mm Hg per tray. Bottom temperatures of the three towers are 450, 500, and 540”F, respectively. Tower overhead temperatures are 200°F. Pitch and rosin go to storage at 350°F and the other products at 125°F. The steam generated in the pitch and rosin coolers is at 20 psig. Process steam is at 150 psig. 10. RECOVERY OF ISOPRENE Draw carefully a flowsheet for the recovery of isoprene from a mixture of C, hydrocarbons by extractive distillation with aqueous acetonitrile according to the following description.
- 56. 12. AIR SEPARATION 37 A hydrocarbon stream containing 60 mol % isoprene is charged at the rate of 10,OOOpph to the main fractionator D-l at tray 40 from the top. The solvent is acetonitrile with 10wt % water; it is charged at the rate of 70,000 pph on tray 11 of D-l. This column has a total of 70 trays, operates at 1Opsig and 100°F at the top and about 220°F at the bottom. It has the usual provisions for reboiling and top rellux. The extract is pumped from the bottom of D-l to a stripper D-2 with 35 trays. The stripped solvent is cooled with water and returned to D-l. An isoprene-acetonitrile azeotrope goes overhead, condenses, and is partly returned as top tray reflux. The net overhead proceeds to an extract wash column D-3 with 20 trays where the solvent is recovered by countercurrent washing with water. The overhead from D-3 is the finished product isoprene. The bottoms is combined with the bottoms from the raffinate wash column D-4 (20 trays) and sent to the solvent recovery column D-5 with 15 trays. Overhead from D-l is called the raffinate. It is washed countercurrently with water in D-4 for the recovery of the solvent, and then proceeds beyond the battery limits for further conversion to isoprene. Both wash columns operate at substantially atmospheric pressure and 100°F. The product streams are delivered to the battery limits at 100 psig. Solvent recovery column D-5 is operated at 50 mmHg absolute, so as to avoid the formation of an azeotrope overhead. The required overhead condensing temperature of about 55°F is provided with a propane compression refrigeration system; suction condition is 40°F and 8Opsig, and discharge condition is 2OOpsig. Vacuum is maintained on the reflux accumulator with a two-stage steam ejector, with a surface interstage condenser and a direct water spray after-condenser. The stripped bottoms of D-5 is cooled to 100°F and returned to the wash columns. Some water makeup is necessary because of leakages and losses to process streams. The solvent recovered overhead in D-5 is returned to the main column D-l. Solvent makeup of about 20 pph is needed because of losses in the system. Steam is adequate for all reboiling needs in this plant. 11. VACUUM DISTILLATION This plant is for the distillation of a heavy petroleum oil. The principal equipment is a vacuum tower with 12 trays. The top tray is numbered 1. Trays 1, 2, 10, 11, and 12 are one-half the diameter of the other trays. The tower operates at 50 mm Hg. Oil is charged with pump J-l through an exchanger E-l, through a fired heater from which it proceeds at 800°F onto tray 10 of the tower. Live steam is fed below the bottom tray. Bottoms product is removed with pump J-3 through a steam generator and a water cooled exchanger E-3 beyond the battery limits. A side stream is taken off tray 6, pumped with J-2 through E-l, and returned onto tray 3 of the tower. Another stream is removed from tray 2 with pump J-4 and cooled in water exchanger E-2; part of this stream is returned to tray 1, and the rest of it leaves the plant as product gas oil. Uncondensed vapors are removed at the top of the column with a one-stage steam jet ejector equipped with a barometric condenser. Show the principal controls required to make this plant operate automatically. 12. AIR SEPARATION Make a flowsheet of an air purification and separation plant that operates according to the following description. Atmospheric air at the rate of 6.1 million SCFD is compressed to 160 psig in a two-stage compressor JJ-1 that is provided with an intercooler and a knockout drum. Then it proceeds to a packed tower T-l where it is scrubbed with recirculating caustic soda solution. Overhead from T-l is cooled to 14°F in a refrigerated exchanger. After removal of the condensate, this stream proceeds to a dryer system that consists principally of two vessels F-l and F-2 packed with solid desiccant. After being precooled with product oxygen in exchanger E-l and with product nitrogen in E-2, the air serves as the heating medium in reboiler E-3 of column T-2. Its pressure then is reduced to 100 psig, and it is fed to the middle of column T-2. Bottoms of T-2 is fed to the middle of column T-3. This stream contains 40% oxygen. Columns T-3 and T-4 operate at 15 and 3Opsig, respectively. Column T-3 is located above T-4. Elevations and pressure differentials are maintained in such a way that no liquid pumps are needed in the distillation section of the plant. Part of the overhead from T-2 (containing 96% nitrogen) is condensed in E-4 which is the reboiler for column T-3, and the remainder is condensed in E-5 which is the reboiler for T-4. Part of the condensate from E-4 is returned as reflux to T-2 and the rest of the condensates from E-4 and E-5 serve as top reflux to T-3. Overhead from T-3 contains 99.5% nitrogen. After precooling the feed in E-2, this nitrogen proceeds to the battery limits. Bottoms of T-3 proceeds to the top of stripper T-4. Vapor overhead from T-4 is recycled to the middle of T-3. The bottoms product (containing 99.5% oxygen) is sent partly to liquid storage and the remainder to precooler E-l where it is vaporized. Then it is compressed to 150psig in a two-stage compressor JJ-2 and sent to the battery limits. Compressor JJ-2 has inter- and aftercoolers and knockout drums for condensate.
- 58. 3 PROCESS CONTROL A /I processes are subject to disturbances that tend to change operating conditions, compositions, and physical properties of the streams. In order to minimize the i/l effects that could result from such disturbances, chemical plants are implemented with substantial amounts of instrumentation and automatic control equipment. In critical cases and in especially large p/ants, moreover, the instrumentation is computer monitored for convenience, safety, and optimization. for example, a typical billion /b/yr ethylene p/ant may have 600 control loops with control valves and 400 interacting loops with a cost of about $6 million. (Skrokov, 1980, pp. 13, 49; see Sec. 3.1); the computer implementation of this control system will cost another $3 million. Figure 3.7 shows the controol system of an ethylene fractionator which has 12 input signals to the computer and four outgoing reset signals to flow controllers. In order for a process to be controllable by machine, it must represented by a mathematical mode/. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as we// as the parameters of sensing devices, control valves, and control instruments. The process as a who/e then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process mode/s; then the computer can be made to optimize the operation continua//y. For control purposes, somewhat simplified mathematical mode/s usually are adequate. In distillation, for instance, the Underwood-Fenske-Gil/i/and mode/ with constant relative volatilities and a simplified enthalpy balance may be preferred to a full-fledged tray-by-tray calculation every time there is a perturbation. In control situations, the demand for speed of response may not be realizable with an over/y elaborate mathematical system. Moreover, in practice not all disturbances are measurable, and the process characteristics are not known exactly. According/y feedforward control is supplemented in most instances with feedback. In a we//designed system (Shinskey, 1984, p. 186) typically 90% of the corrective action is provided by feed forward and 10% by feedback with the result that the integrated error is reduced by a factor of IO. A major feature of many modern control systems is composition control which has become possible with the development of fast and accurate on-line analyzers. Figure 3.2 shows that 10 analyzers are used for control of ethylene composition in this p/ant within the purities shown, High speed on-line gas chromatographs have analysis times of 30- 120 set and are capable of measuring several components simultaneously with a sensitivity in the parts/million range. Mass spectrometers are faster, more stable, and easier to maintain but are not sensitive in the ppm range. Any one instrument can be hooked up to a half-dozen or so sample ports, but, of course, at the expense of time lag for controller response. Infrared and NMR spectrometers also are feasible for on-line analysis. Less costly but also less specific analyzers are available for measuring physical properties such as refractive index and others that have been calibrated against mixture composition or product purity. The development of a mathematical model, even a simplified one that is feasible for control purposes, takes a major effort and is we// beyond the scope of the brief treatment of process control that can be attempted here. What will be given is examples of control loops for the common kinds of equipment and operations, Primarily these are feedback arrangements, but, as mentioned earlier, feedback devices usually are necessary supplements in primarily feedfonvard situations. When processes are subject on/y to slow and small perturbations, conventional feedback P/D controllers usually are adequate with set points and instrument characteristics fine-tuned in the field. As an example, two modes of control of a heat exchange process are shown in Figure 3.8 where the objective is to maintain constant out/et temperature by exchanging process heat with a heat transfer medium. Part (a) has a feedback controller which goes into action when a deviation from the preset temperature occurs and attempts to restore the set point. inevitably some oscillation of the outlet temperature will be generated that will persist for some time and may never die down if perturbations of the in/et condition occur often enough. In the operation of the feedforward control of part (6). the flow rate and temperature of the process input are continua//y signalled to a computer which then finds the flow rate of heat transfer medium required to maintain constant process outlet temperature and adjusts the flow control valve appropriate/y. Temperature oscillation amplitude and duration will be much less in this mode. 3.1. FEEDBACK CONTROL mode of action of the controller. The usual controllers provide one, two, or three of these modes of corrective action: In feedback control, after an offset of the controlled variable from a preset value has been generated, the controller acts to eliminate or 1. Proportional, in which the corrective action is proportional to reduce the offset. Usually there is produced an oscillation in the the error signal. value of the controlled variable whose amplitude, period, damping 2. Integral, in which the corrective action at time t is proportional and permanent offset depend on the nature of the system and the to the integral of the error up to that time. 39
- 59. 40 PROCESS CONTROL I I I yyyz$Jw; COLUMN OPTIMIZER i - - - - - - - - - - - - - FEED FOR WARD ALGORITHM ,= - - - - ON HEAT AND MATERIAL BALANCE +- - - - 1 fs- LI 8 -----!E+--_I .- .- _- -- -- - ._ _- - - - J RESET ._ _ _ _ _ _ _ _ _ _ _ - _ - - - - _ _ _ _ _ _ _ --------7 ” - - - 1 1 I 1 -R(c ETHYLENE p R PRODUCT 0 YT CH4 PRODUCT CzH2 C3H6 CD2 c o Figure 3.1. Optimized control of an ethylene tower (Skrokou (Ed.), Mini- and Microcomputer Control in Industrial Processes, Van Nostrand/Reinhold, New York, 1980). h FEED LINE mmEssoR - w FURNACES QuwcH PRIMARY CAUSTK; DfwER FRACTICNATOR SCRUBBER HEAT Exc+bwGER DEMETHANIZER ACETYLENES DEETHANIZER ETHYLENE SPLITTER Ethylene 99.95% weight Methane less than 500 pp” mol. % Ethane less than 500 pp” mol. % Propylene (and heaver) less than 100 pp” mol. % Acetylene less than 5 pp”mol. % Carbon dioxide less than IO pp”mol. % Total sulfur less than.5 pp” mol. % Hydrogen sulfide less than I pp” mol. % Water less than I5 pp” mol. % Oxygen less than 5 pp” mol. % Hydrogen less than 1 pp” mol. % Carbon monoxide less than 5 ppm mol. % -m -m METHYIACETY- METHYIACETY- LENES 8 PROPY- LENES 8 PROPY- LENE REMOVAL LENE REMOVAL b b PROPYLENE PROWCT DEPROPANIZER PROPYLENE SPLll-rER Figure 3.2. Plowsketch of an olefins plant and specifications of the ethylene product. AR designates a composition analyzer and controller (after Skrokov (Ed.), Mini- and Microcomputer Control in Industrial Processes, Van Nostrand/Reinhold, New York, 1980).
- 60. 3. Derivative, in which the corrective action is proportional to the rate at which the error is being generated. The relation between the change in output m -ma and input e signals accordingly is represented by Just how these modes of action are achieved in relatively inexpensive pneumatic or electrical devices is explained in books on control instruments, for example, that of Considine (Process Instruments and Controls Handbook, Sec. 17, 1974). The low prices and considerable flexibility of PID controllers make them the dominant types in use, and have discouraged the development of possibly superior types, particularly as one-shot deals which would be the usual case in process plants. Any desired mode of action can be simulated by a computer, but at a price. A capsule summary of the merits of the three kinds of corrective action can be made. The proportional action is rapid but has a permanent offset that increases as the action speeds up. The addition of integral action reduces or entirely eliminates the offset but has a more sluggish response. The further addition of derivative action speeds up the correction. The action of a three-mode PID controller can be made rapid and without offset. These effects are illustrated in Figure 3.3 for a process subjected to a unit step upset, in this case a change in the pressure of the control air. The ordinate is the ratio of the displacements of the response and upset from the set point. The reason for a permanent offset with a proportional con- troller can be explained with an example. Suppose the tempera- ture of a reactor is being controlled with a pneumatic system. At the set point, say the valve is 50% open and the flow rate 0 . 6 I 0 . 5 .- VI :, 0.4 .e P 0.3 ?I ; 0 . 2 I2 : 0 0.1 0 -0.1 0 10 20 30 40 50 60 70 80 90 100 110 120 Time, set Figure 3.3. Response of various modes of control to step input (Eckman, Automatic Process Control, Wiley, New York, 1958). 3.1. FEEDBACK CONTROL 41 of cooling water is fixed accordingly. Suppose the heat load is doubled suddenly because of an increase in the reactor contents. At steady state the valve will remain 50% open so that the water flow rate also will remain as before. Because of the greater rate of heat evolution, however, the temperature will rise to a higher but still steady value. On the other hand, the corrective action of an integral controller depends on displacement of the temperature from the original set point, so that this mode of control will restore the original temperature. The constants K,,, K,, and Kd are settings of the instrument. When the controller is hooked up to the process, the settings appropriate to a desired quality of control depend on the inertia (capacitance) and various response times of the system, and they can be determined by field tests. The method of Ziegler and Nichols used in Example 3.1 is based on step response of a damped system and provides at least approximate values of instrument settings which can be further fine-tuned in the field. The kinds of controllers suitable for the common variables may be stated briefly: Variable Controller Flow and liquid pressure PI Gas pressure P Liquid level P or PI Temperature P I D Composition P, PI, PID Derivative control is sensitive to noise that is made up of random higher frequency perturbations, such as splashing and turbulence generated by inflow in the case of liquid level control in a vessel, so that it is not satisfactory in such situations. The variety of composition controllers arises because of the variety of composition analyzers or detectors. Many corrective actions ultimately adjust a flow rate, for instance, temperature control by adjusting the flow of a heat transfer medium or pressure by regulating the flow of an effluent stream. A control unit thus consists of a detector, for example, a thermocouple, a transmitter, the control instrument itself, and a control valve. The natures, sensitivities, response speeds, and locations of these devices, together with the inertia or capacity of the process equipment, comprise the body of what is to be taken into account when designing the control system. In the following pages will be described only general characteristics of the major kinds of control systems that are being used in process plants. Details and criteria for choice between possible alternates must be sought elsewhere. The practical aspects of this subject are treated, for example, in the References at the end of this chapter. SYMBOLS On working flowsheets the detectors, transmitters, and controllers are identified individually by appropriate letters and serial numbers in circles. Control valves are identified by the letters CV- followed by a serial number. When the intent is to show only in general the kind of control system, no special symbol is used for detectors, but simply a point of contact of the signal line with the equipment or process line. Transmitters are devices that convert the measured variable into air pressure for pneumatic controllers or units appropriate for electrical controllers. Temperature, for instance, may be detected with thermocouples or electrical resistance or height of a liquid column or radiant flux, etc., but the controller can accept only pneumatic or electrical signals depending on its type. When the nature of the transmitter is clear, it may be represented by an encircled cross or left out entirely. For clarity, the flowsheet can include only the most essential information. In an actual design
- 61. 42 PROCESS CONTROL EXAMPLE 3.1 Constants of PID Controllers from Response Curves to a Step Input The method of Ziegler and Nichols [Tram ASME, (Dec. 1941)] will be used. The example is that of Tyner and May (Process Engineering Control, Ronald, New York, 1967). The response to a change of 2 psi on the diaphragm of the control valve is shown. The full range of control pressure is from 3 to 15 psi, a difference of 12psi, and the range of temperature is from 100 to 2OO”F, a difference of 100°F. Evaluate the % displacement of pressure as Am = 100(2/12) = 16.7%. From the curve, the slope at the inflection point is R = 17.5/100(7.8 - 2.4) = 3.24%/min, and the apparent time delay is the intercept on the abscissa, L = 2.40 min. The values of the constants for the several kinds of controllers are Proportional: 100/K, = % PB = lOORL/Am = 100(3.24)(2.4)/ 16.7 = 46.6%. Proportional-integral: % PB = llORL/Am = 51.2% Ki=L/0.3=8min Proportional-integral-derivative: % PB = 83RLIAm = 38.6%, Ki = 2L = 4.8 min, Kd = 0.5L = 1.2 min. These are approximate instrument settings, and may need to be adjusted in process. PB is proportional band. A recent improvement of the Ziegler-Nichols method due to Yuwana and Seborg [AZChE J. 28, 434 (1982)] is calculator programmed by Jutan and Rodriguez [Chem. Eng. 91(18), 69-73 (Sep. 3, 1984)]. 170 t Am (t) = 2 psig r----------------------------------------- Time (min) --+ case, details of detectors and transmitters as well as all other elements of a control system are summarized on instrument specification forms. The simplified coding used in this chapter is summarized on Figure 3.4. CASCADE (RESET) CONTROL Some control situations require interacting controllers. On Figure 3.19(d), for instance, a composition controller regulates the setpoint of the temperature controller of a reactor and on Figure 3.15(g) the set point of the reflux flow rate is regulated by composition or temperature control. Composite systems made up of regions that respond with varying degrees of speed or sluggishness are advantageously equipped with cascade control. In the reactor of Figure 3.19(b), the temperature T-I-1 of the vessel contents responds only slowly to changes in flow rate of the heat transfer medium, but the temperature TT-2 of the HTM leaving the cooling coil is comparatively sensitive to the flow rate. Accordingly, controller TC-2 is allowed to adjust the setpoint of the primary controller TC-1 with an overall improvement in control of the reactor temperature. The controller being reset is identified on flowsheets. 3.2. INDIVIDUAL PROCESS VARIABLES The variables that need to be controlled in chemical processing are temperature, pressure, liquid level, flow rate, flow ratio, com- position, and certain physical properties whose magnitudes may be influenced by some of the other variables, for instance, viscosity, vapor pressure, refractive index, etc. When the temperature and pressure are fixed, such properties are measures of composition which may be known exactly upon calibration. Examples of control of individual variables are shown in the rest of this chapter with the various equipment (say pumps or compressors) and processes (say distillation or refrigeration) and on the earlier flowsketches of this and the preceding chapters, but some general statements also can be made here. Most control actions ultimately depend on regulation of a flow rate with a valve. TEMPERATURE Temperature is regulated by heat exchange with a heat transfer medium (HTM). The flow rate of the HTM may be adjusted, or the condensing pressure of steam or other vapor, or the amount of heat transfer surface exposed to condensing vapor may be regulated by flooding with condensate, which always has a much lower heat transfer coefficient than that of condensing vapor. In a reacting system of appropriate vapor pressure, a boiling temperature at some desired value can be maintained by relluxing at the proper controlled pressure. Although examples of temperature control appear throughout this chapter, the main emphasis is in the section on heat exchangers. P R E S S U R E Pressure is controlled by regulating the flow of effluent from the vessel. The effluent may be the process stream itself or a non- condensable gas that is generated by the system or supplied for blanketing purposes. The system also may be made to float on the pressure of the blanketing gas supply. Control of the rate of condensation of the effluent by allowing the heat transfer surface to flood partially is a common method of regulating pressure in fractionation systems. Throttling a main effluent vapor line usually is not done because of the expense of large control valves. Figure 3.5 shows vacuum production and control with steam jet ejectors.
- 62. Analysis (composition) controller, transmitter Differential pressure controller, transmitter Flow rate controller, transmitter Liquid level controller, transmitter Pressure controller, transmitter Temperature controller, transmitter General symbol for transmitter Control valve Signal line, pneumatic or electrical Point of detection Figure 3.4. Symbols for control elements to be used on flowsheets. Instrument Society of America (ISA) publication no. S 51.5 is devoted to process instrumentation terminology. LEVEL OF LIQUID Level of liquid in a vessel often is maintained by permanent or adjustable built-in weirs for the effluent, notably on the trays of fractionators, extractors, etc., and in reactors and drums. Any desired adjustments of weir height, however, can be made only on shutdown. Control of the flow rate of effluent (sometimes of the input) is the most common other method of level control. Liquid levels often are disturbed by splashing or flow turbulence, so that rather sluggish controllers are used for this service. Conceivably, a level could be controlled by forcing effluent through an opening of fixed size with a controlled pressure, but there do not appear to be many such applications. Continual control of the weight of a vessel and its contents is another control method that is not used often. Figure 3.6 is devoted to level control. FLOW RATE A rate of flow is commonly measured by differential pressure across an orifice, but many other devices also are used on occasion. Simultaneous measurements of temperature and pressure allow the flow measurement to be known in mass units. Direct mass flow 3.3. EQUIPMENT CONTROL 43 meters also are available. The flow measurement is transmitted to a controller which then adjusts the opening of a control valve so as to maintain the desired condition. FLOW OF SOLIDS Except for continuous weighing, control of the flow of solids is less precise than that of fluids. Several devices used for control of feed rates are shown schematically in Figure 3.7. They all employ variable speed drives and are individually calibrated to relate speed and flow rate. Ordinarily these devices are in effect manually set, but if the solid material is being fed to a reactor, some property of the mixture could be used for feed back control. The continuous belt weigher is capable ordinarily of f 1% accuracy and even fO.l% when necessary. For processes such as neutralizations with lime, addition of the solid to process in slurry form is acceptable. The slurry is prepared as a batch of definite concentration and charged with a pump under flow control, often with a diaphragm pump whose stroke can be put under feedback control. For some applications it is adequate or necessary to feed weighed amounts of solids to a process on a timed basis. FLOW RATIO Flow ratio control is essential in processes such as fuel-air mixing, blending, and reactor feed systems. In a two-stream process, for example, each stream will have its own controller, but the signal from the primary controller will go to a ratio control device which adjusts the set point of the other controller. Figure 3.17(a) is an example. Construction of the ratioing device may be an adjustable mechanical linkage or may be entirely pneumatic or electronic. In other two-stream operations, the flow rate of the secondary stream may be controlled by some property of the combined stream, temperature in the case of fuel-air systems or composition or some physical property indicative of the proportions of the two streams. COMPOSITION The most common detectors of specific substances are gas chromatographs and mass spectrometers, which have been mentioned earlier in this chapter in connection with feedforward control. Also mentioned have been physical properties that have been calibrated against mixture compositions. Devices that are specific for individual substances also are sometimes available, for example pH, oxygen, and combustion products. Impregnated reactive tapes have been made as specific detectors for many substances and are useful particularly for low concentrations. Composition controllers act by adjusting some other condition of the system: for instance, the residence time in converters by adjusting the flow rate, or the temperature by adjusting the flow of HTM, or the pressure of gaseous reactants, or the circulation rate of regenerable catalysts, and so on. The taking of representative samples is an aspect of on-line analysis that slows down the responsiveness of such control. The application of continuously measuring in-line analyzers is highly desirable. Some physical properties can be measured this way, and also concentrations of hydrogen and many other ions with suitable electrodes. Composition controllers are shown for the processes of Figures 3.1 and 3.2. 3.3. EQUIPMENT CONTROL Examples are presented of some usual control methods for the more widely occurring equipment in chemical processing plants. Other methods often are possible and may be preferable because of
- 63. 44 PROCESS CONTROL (a) 1 S U M P STEAM 1 S U M P (b) (d) 1 S U M P Figure 3.5. Vacuum control with steam jet ejectors and with mechanical vacuum pumps. (a) Air bleed on PC. The steam and water rates are hand set. The air bleed can be made as small as desired. This can be used only if air is not harmful to the process. Air bleed also can be used with mechanical vacuum pumps. (b) Both the steam and water supplies are on automatic control. This achieves the minimum cost of utilities, but the valves and controls are relatively expensive. (c) Throttling of process gas flow. The valve is larger and more expensive even than the vapor valve of case (a). Butterfly valves are suitable. This method also is suitable with mechanical vacuum pumps. (d) No direct pressure control. Settings of manual control valves for the utilities with guidance from pressure indicator PI. Commonly used where the greatest vacuum attainable with the existing equipment is desired. EFFLUENT b) I VAPoR HTM- LIQUID (c) I N P U T Figure 3.6. Some modes of control of liquid level. (a) Level control by regulation of the effluent flow rate. This mode is externally adjustable. (b) Level control with built in overflow weir. The weir may be adjustable, but usually only during shutdown of the equipment. (c) Overflow weir in a horizontal kettle reboiler. The weir setting usually is permanent. greater sensitivity or lower cost. Also it should be noted that the choice of controls for particular equipment may depend on the kind of equipment it is associated with. Only a few examples are shown of feedforward control, which should always be considered when superior control is needed, the higher cost is justified, and the process simulation is known. Another relatively expensive method is composition control, which has not been emphasized here except for reactors and fractionators, but its possible utility always should be borne in mind. Only primary controllers are shown. The complete instrumentation of a plant also includes detectors and transmitters as well as indicators of various operating conditions. Such indications may be input to a computer for the record or for control, or serve as guides for manual control by operators who have not been entirely obsolesced. HEAT TRANSFER EQUIPMENT Four classes of this kind of equipment are considered: heat exchangers without phase change, steam heaters, condensers, and vaporizers or reboilers. These are grouped together with descriptions in Figures 3.8-3.11. Where applicable, comments are made about the utility of the particular method. In these heat
- 64. 3.3. EQUIPMENT CONTROL 45 Adjustable Adjustable Adjustable Collar )A{ pih id) Figure 3.7. Solids feeders with variable speed drives. (a) Rotary vane (star) feeder with variable speed drive. (b) Horizontal screw feeder. (c) Belt feeder taking material from a bin with an adjustable underflow weir. (d) Rotary plate feeder: Rate of discharge is controlled by the rotation speed, height of the collar, and the position of the plow. (e) Continuously weighing feeder with variable speed belt conveyor. Figure 3.8. Heat exchangers without phase change. PF = process fluid, HTM = heat transfer medium. (a) Feedback control of PF outlet temperature. Flow rate of HTM is adjusted as the PF outlet temperature is perturbed. The valve may be in either the input or output line. (b) Feedforward control. PF outlet setpoint T-2 and perturbations of PF input flow and temperature are fed to the monitor which adjusts the flow rate of the HTM to maintain constant PF outlet temperature T2. (c) Exchanger with bypass of process fluid with a three-way valve. The purpose of TC-2 is to conserve on that fluid or to limit its temperature. When the inherent leakage of the three-way valve is objectionable, the more expensive two two-way valves in the positions shown are operated off TC-1. (d) A two-fluid heat transfer system. The PF is heated with the HTM which is a closed circuit heated by Dowtherm or combustion gases. The Dowtherm is on flow control acting off TC-2 which is on the HTM circuit and is reset by TC-1 on the PF outlet. The HTM also is on flow control. Smoother control is achievable this way than with direct heat transfer from very high temperature Dowtherm or combustion gases. (e) Air cooler. Air flow rate is controllable with adjustable louvers or variable pitch fan or variable speed motors. The latter two methods achieve some saving of power compared with the louver design. Multispeed motors are also used for change between day and night and between winter and summer. The switching can be made automatically off the air temperature. (a) H T M P F :’ M O N I T O R 7-2 Setpoint H T M P F w THREE-WAY VALVE HTM id) Dowtherm Boiler P F 1 m & !. (e) adjustable louvers variable pitch fan variable speed motor
- 65. 46 P R O C E S S C O N T R O L P steam trap or liquid level controller (a) condensate S T M - - ___________, , I i (b) S T M D three-way valve (‘3 ’ PF bypass trap S T M - - - trap (4 Figure 3.9. Steam heaters. (a) Flow of steam is controlled off the PF outlet temperature, and condensate is removed with a steam trap or under liquid level control. Subject to difficulties when condensation pressure is below atmospheric. (b) Temperature control on the condensate removal has the effect of varying the amount of flooding of the heat transfer surface and hence the rate of condensation. Because the flow of condensate through the valve is relatively slow, this mode of control is sluggish compared with (a). However, the liquid valve is cheaper than the vapor one. (c) Bypass of process fluid around the exchanger. The condensing pressure is maintained above atmospheric so that the trap can discharge freely. (d) Cascade control. The steam pressure responds quickly to upsets in steam supply conditions. The more sluggish PF temperature is used to adjust the pressure so as to maintain the proper rate of heat transfer. (a) PF VAPOR ----------I I PF CONDENSATE PF VAPOR _---------i ,:’ Q M + PF CONDENSATE PF VAPOR __----_--- - - H T M 4 PF CONDENSATE : accumulator drum (d) PF CONDENSATE Figure 3.10. Condensers. (a) Condenser on temperature control of the PF condensate. Throttling of the flow of the HTM may make it too hot. (b) Condenser on pressure control of the HTM flow. Throttling of the flow of the HTM may make it too hot. (c) Flow rate of condensate controlled by pressure of PF vapor. If the pressure rises, the condensate flow rate increases and the amount of unllooded surface increases, thereby increasing the rate of condensation and lowering the pressure to the correct value. (d) Condenser with vapor bypass to the accumulator drum. The condenser and drum become partially flooded with subcooled condensate. When the pressure falls, the vapor valve opens, and the vapor flows directly to the drum and heats up the liquid there. The resulting increase in vapor pressure forces some of the liquid back into the condenser so that the rate of condensation is decreased and the pressure consequently is restored to the preset value. With sufficient subcooling, a difference of lo-l.5 ft in levels of drum and condenser is sufficient for good control by this method.
- 66. 3.3. EQUIPMENT CONTROL 47 (a) (cl PF VAPOR DISTILLATION EQUIPMENT PF PF LIQUID _________________ I I HOTPF _ REFRIG Q accumulator (d) COLD PF Figure 3.11. Vaporizers (reboilers). (a) Vaporizer with flow-rate of HTM controlled by temperature of the PF vapor. HTM may be liquid or vapor to start. (b) Thermosiphon reboiler. A constant rate of heat input is assured by flow control of the HTM which may be either liquid or vapor to start. (c) Cascade control of vaporizer. The flow control on the HTM supply responds rapidly to changes in the heat supply system. The more sluggish TC on the PF vapor resets the FC if need be to maintain temperature. (d) Vaporization of refrigerant and cooling of process fluid. Flow rate of the PF is the primary control. The flow rate of refrigerant vapor is controlled by the level in the drum to ensure constant condensation when the incoming PF is in vapor form. transfer processes the object is to control the final temperature of the process fluid (PF) or the pressure of its source or to ensure a constant rate of heat input. This is accomplished primarily by regulation of the flow of the heat transfer medium (HTM). Regulation of the temperature of the HTM usually is less convenient, although it is done indirectly in steam heaters by throttling of the supply which has the effect of simultaneously changing the condensing pressure and temperature of the steam side. As a minimum, a distillation assembly consists of a tower, reboiler, condenser, and overhead accumulator. The bottom of the tower serves as accumulator for the bottoms product. The assembly must be controlled as a whole. Almost invariably, the pressure at either the top or bottom is maintained constant; at the top at such a value that the necessary reflux can be condensed with the available coolant; at the bottom in order to keep the boiling temperature low enough to prevent product degradation or low enough for the available HTM, and definitely well below the critical pressure of the bottom composition. There still remain a relatively large number of variables so that care must be taken to avoid overspecifying the number and kinds of controls. For instance, it is not possible to control the flow rates of the feed and the top and bottom products under perturbed conditions without upsetting holdup in the system. Two flowsketches are shown on Figures 3.1 and 3.12 of controls on an ethylene fractionator. On Figure 3.1, which is part of the complete process of Figure 3.2, a feedforward control system with a multiplicity of composition analyzers is used to ensure the high degree of purity that is needed for this product. The simpler diagram, Figure 3.12, is more nearly typical of two-product fractionators, the only uncommon variation being the use of a feed-overhead effluent heat exchanger to recover some refrig- eration. Crude oil fractionators are an example of a more elaborate system. They make several products as side streams and usually have some pumparound reflux in addition to top reflux which serve to optimize the diameter of the tower. Figure 3.13 is of such a tower operating under vacuum in order to keep the temperature below cracking conditions. The side streams, particularly those drawn off atmospheric towers, often are steam stripped in external towers hooked up to the main tower in order to remove lighter com- ponents. These strippers each have four or five trays, operate OVHD PRODUCT FEED - I I REFLUX PUMP BTMS PRODUCT Figure 3.12. Fractionator for separating ethylene and ethane with a refrigerated condenser. FC on feed, reflux, and steam supply. LC on bottom product and refrigerant vapor. Pressure control PC on overhead vapor product.
- 67. 48 PROCESS CONTROL I R E S I D U U M H V G O O I L F E E D Figure 3.13. Crude oil vacuum tower. Pumparound reflux is provided at three lower positions as well as at the top, with the object of optimizing the diameter of the tower. Cooling of the side streams is part of the heat recovery system of the entire crude oil distillation plant. The cooling water and the steam for stripping and to the vacuum ejector are on hand control. off level control on the main tower, and return their vapors to the main tower. A variety of control schemes are shown separately in Figures 3.14 and 3.15 for the lower and upper sections of fractionators. To some extent, these sections are controllable independently but not entirely so because the flows of mass and heat are interrelated by the conservation laws. In many of the schemes shown, the top reflux rate and the flow of HTM to the reboiler are on flow controls. These quantities are not arbitrary, of course, but are found by calculation from material and energy balances. Moreover, neither the data nor the calculation method are entirely exact, so that some adjustments of these flow rates must be made in the field until the best possible performance is obtained from the equipment. In modern large or especially sensitive operations, the fine tuning is done by computer. For the lower section of the fractionator, the cases of Figure 3.14 show the heat input to be regulated in these five different ways: 1. On flow control of the heat transfer medium (HTM), 2. On temperature control of the vapor leaving the reboiler or at some point in the tower, 3. On differential pressure between key points in the tower, 4. On liquid level in the bottom section, 5. On control of composition or some physical property of the bottom product. Although only one of these methods can be shown clearly on a particular sketch, others often are usable in combination with the other controls that are necessary for completeness. In some cases the HTM shown is condensing vapor and in other cases it is hot oil, but the particular flowsketches are not necessarily restricted to one or the other HTM. The sketches are shown with and without pumps
- 68. 3.3. EQUIPMENT CONTROL 49 late location (a) PRODUCT DUCT (4 W I PRODUCT I + CONDENSATE (0 + CONDENSATE Figure 3.14. The lower ends of fractionators. (a) Kettle reboiler. The heat source may be on TC of either of the two locations shown or on flow control, or on difference of pressure between key locations in the tower. Because of the built-in weir, no LC is needed. Less head room is needed than with the thermosiphon reboiler. (b) Tbermosiphon reboiler. Compared with the kettle, the heat transfer coefficient is greater, the shorter residence time may prevent overheating of thermally sensitive materials, surface fouling will be less, and the smaller holdup of hot liquid is a safety precaution. (c) Forced circulation reboiler. High rate of heat transfer and a short residence time which is desirable with thermally sensitive materials are achieved. (d) Rate of supply of heat transfer medium is controlled by the difference in pressure between two key locations in the tower. (e) With the control valve in the condensate line, the rate of heat transfer is controlled by the amount of unflooded heat transfer surface present at any time. (f) Withdrawal on TC ensures that the product has the correct boiling point and presumably the correct composition. The LC on the steam supply ensures that the specified heat input is being maintained. (g) Cascade control: The set point of the FC on the steam supply is adjusted by the TC to ensure constant temperature in the column. (h) Steam flow rate is controlled to ensure specified composition of the PF effluent. The composition may be measured directly or indirectly by measurement of some physical property such as vapor pressure. (i) The three-way valve in the hot oil heating supply prevents buildup of excessive pressure in case the flow to the reboiler is throttled substantially. (j) The three-way valve of case (i) is replaced by a two-way valve and a differential pressure controller. This method is more expensive but avoids use of the possibly troublesome three-way valve.
- 69. 50 PROCESS CONTROL 4 CONDENSATE (i) HOT OIL Figure 3.1~(conh4 for withdrawal of bottom product. When the tower pressure is sufficient for transfer of the product to the following equipment, a pump is not needed. Upper section control methods are shown on Figure 3.15. They all incorporate control of the pressure on the tower, either by throttling some vapor flow rate or by controlling a rate of condensation. In the latter case this can be done by regulating the flow or temperature of the HTM or by regulating the amount of heat transfer surface exposed to contact with condensing vapor. Flow control of reflux is most common. It is desirable in at least these situations: 1. When the temperature on a possible control tray is insensitive to the composition, which is particularly the case when high purity overhead is being made, 2. When the expense of composition control is not justifiable, 3. When noncondensables are present, 4. With tall and wide columns that have large holdup and consequently large lags in interchange of heat and mass between phases, 5. When the process coupling of the top and bottom temperature controllers makes their individual adjustments difficult, 6. When the critical product is at the bottom. In all these cases the reflux rate is simply set at a safe value, enough to nullify the effects of any possible perturbations in operation. There rarely is any harm in obtaining greater purity than actually is necessary. The cases that are not on direct control of reflux flow rate are: (g) is on cascade temperature (or composition) and flow control, (h) is on differential temperature control, and (i) is on temperature control of the HTM flow rate. CONDENSATE (j) HOT OIL LIQUID-LIQUID EXTRACTION TOWERS The internals of extraction towers can be packing, sieve trays, empty with spray feeds or rotating disks. The same kinds of controls are suitable in all cases, and consist basically of level and flow controls. Figure 3.16 shows some variations of such arrangements. If the solvent is lighter than the material being extracted, the two inputs indicated are of course interchanged. Both inputs are on flow control. The light phase is removed from the tower on LC or at the top or on level maintained with an internal weir. The bottom stream is removed on interfacial level control (ILC). A common type of this kind of control employs a hollow float that is weighted to have a density intermediate between those of the two phases. As indicated by Figures 3.16(a) and 3.16(d), the interface can be maintained in either the upper or lower sections of the tower. Some extractions are performed with two solvents that are fed separately to the tower, ordinarily on separate flow controls that may be, however, linked by flow ratio control. The relative elevations of feed and solvents input nozzles depend on the nature of the extraction process. Controls other than those of flow and level also may be needed in some cases, of which examples are on Figure 3.17. The scheme of part (a) maintains the flow rate of solvent in constant ratio with the main feed stream, whatever the reasons for variation in flow rate of the latter stream. When there are fluctuations in the composition of the feed, it may be essential to adjust the flow rate of the solvent to maintain constancy of some property of one or the other of the effluent streams. Figure 3.17(b) shows reset of the solvent flow rate by the composition of the raffinate. The temperature of an extraction process ordinarily is controlled by regulating the temperatures of the feed streams. Figure 3.17(c) shows the
- 70. 3.3. EQUIPMENT CONTROL 51 temperature of one of the streams to be controlled by TC-2 acting on the flow rate of the HTM, with reset by the temperature of a control point in the tower acting through TC-1. When the effluents are unusually sensitive to variation of input conditions, it may be inadvisable to wait for feedback from an upset of output performance, but to institute feedforward control instead. In this P F (a) P F w (cl kind of system, the input conditions are noted, and calculations are made and implemented by on-line computer of other changes that are needed in order to maintain satisfactory operation. Mixer-settler assemblies for extraction purposes often are preferable to differential contact towers in order to obtain very high extraction yields or to handle large flow rates or when phase b) (4 Flgure 3.15. Control modes for the upper sections of fractionators. (a) Pressure control by throttling of the overhead vapor flow. The drawbacks of this method are the cost of the large control valve and the fact that the reflux pump operates with a variable suction head. The flow of HTM is hand set. (b) Applicable when the overhead product is taken off as vapor and only the reflux portion need be condensed. Two two-way valves can replace the single three-way valve. The flow of HTM is hand set. (c) Flow rate of the HTM is regulated to keep the pressure constant. One precaution is to make sure that the HTM, for example water, does not overheat and cause scaling. The HTM flow control valve is small compared with the vapor valve of case (a). (d) Pressure control is maintained by throttling uncondensed vapors. Clearly only systems with uncondensables can be handled this way. The flow of the HTM is manually set. (e) Bypass of vapor to the drum on PC: The bypassed vapor heats up the liquid there, thereby causing the pressure to rise. When the bypass is closed, the pressure falls. Sufficient heat transfer surface is provided to subcool the condensate. (f) Vapor bypass between the condenser and the accumulator, with the condenser near ground level for the ease of maintenance: When the pressure in the tower falls, the bypass valve opens, and the subcooled liquid in the drum heats up and is forced by its vapor pressure back into the condenser. Because of the smaller surface now exposed to the vapor, the rate of condensation is decreased and consequently the tower pressure increases to the preset value. With normal subcooling, obtained with some excess surface, a difference of lo-15 ft in levels of drum and condenser is sufficient for good control. (g) Cascade control: The same system as case (a), but with addition of a TC (or composition controller) that resets the reflux flow rate. (h) Reflux rate on a differential temperature controller. Ensures constant internal reflux rate even when the performance of the condenser fluctuates. (i) Reflux is provided by a separate partial condenser on TC. It may be mounted on top of the column as shown or inside the column or installed with its own accumulator and reflux pump in the usual way. The overhead product is handled by an after condenser which can be operated with refrigerant if required to handle low boiling components.
- 71. PROCESS CONTROL (e) P C T-9 I- P F L - (9 v-0 P C H T M -Y-M7 D T C P F Figure 3.lS(continued)
- 72. 3.3. EQUIPMENT CONTROL 53 I I F C GL Solvent F C a Feed Extract (a) (b) (cl Fiaffinate (d) Figure 3.16. Extraction tower control. (a) Operation with heavy solvent, interface in the upper section, top liquid level on LC. (b) Same as part (a) but with overflow weir for the light phase. (c) Same as part (a) but with completely full tower and light phase out at the top. (d) Operation with interface on ILC in the lower section, removal of the light phase from the upper section by any of the methods of (a), (b), or (c). separation is slow and much time is needed. Often, also, relatively simple equipment is adequate for small capacities and easy separations. Several designs of varying degrees of sophistication are available commercially, some of which are described by Lo, Baird, Hanson (Handbook of Solvent Extraction, Wiley, New York, 1983). The basic concept, however, is illustrated on Figure 3.18. The solvent and feed are thoroughly mixed in one chamber and overflow into another, partitioned chamber where separation into light and heavy phases occurs by gravity. Ordinarily the settling chamber is much the larger. The heavy phase is removed on interfacial level control and the light one on level control. The takeoffs also can be controlled with internal weirs or manually. Several centrifugal contactors of proprietary nature are on the market. Their controls are invariably built in. CHEMICAL REACTORS The progress of a given reaction depends on the temperature, pressure, flow rates, and residence times. Usually these variables are controlled directly, but since the major feature of a chemical reaction is composition change, the analysis of composition and the resetting of the other variables by its means is an often used means of control. The possible occurrence of multiple steady states and the onset of instabilities also are factors in deciding on the nature and precision of a control system. Because of the sensitivity of reaction rates to temperature, control of that variable often dominates the design of a reactor so that it becomes rather a heat exchanger in which a reaction occurs almost incidentally. Accordingly, besides the examples of reactor controls of this section, those of heat exchangers in that section may be consulted profitably. Heat transfer and holding time may be provided in separate equipment, but the complete assembly is properly regarded as a reactor. An extreme example, perhaps, is the two-stage heater-reactor system of Figure 3.19(f); three or more such stages are used for endothermic catalytic reforming of naphthas, and similar arrangements exist with intercoolers for exothermic processes. Although the bulk of chemical manufacture is done on a continuous basis, there are sectors of the industry in which batch reactors are essential, notably for fermentations and polymeriza- tions. Such plants may employ as many as 100 batch reactors. The basic processing steps include the charging of several streams, ’ bringing up to reaction temperature, the reaction proper, maintenance of reaction temperature, discharge of the product, and preparation for the next batch. Moreover, the quality of the product depends on the accuracy of the timing and the closeness of the control. Small installations are operated adequately and economically by human control, but the opening and closing of many valves and the setting of conditions at precise times clearly call for computer control of multiple batch installations. Computers actually have taken over in modern synthetic rubber and other polymerization industries. Interested readers will find a description, complete with
- 73. 54 PROCESS CONTROL Flow Ratio Control Feed (a) Solvent Raffinate --&-- 1 H T M 1 I I Figure 3.17. Some other controls on extraction towers. (a) Solvent flow rate maintained in constant ratio with the feed rate. (b) Solvent flow rate reset by controlled composition of raffinate. (c) Temperature of solvent or feed reset by the temperature at a control point in the tower. logic diagrams for normal and emergency operations, of the tasks involved in generating a computer system for a group of batch reactors in the book of Liptak (1973, pp. 536-565). Control of discontinuous processes in general is treated in the book of Skrokov (1980, pp. 128-163). In the present discussion, emphasis will be placed on the control of continuous reactors, concentrating on the several examples of Figure 3.19 in the order of the letter designations of individual figures used there. (a) Stirred tanks are used either as batch or continuous flow reactors. Heat transfer may be provided with an external heat exchanger, as shown on this figure, or through internal surface or a jacket. Alternate modes of control may be used with the controls shown: (i) When the HTM is on temperature control, the pumparound will be on flow control; (ii) when the pumparound is on temperature control, the HTM will be on flow control; (iii) for continuous overflow of product, the control point for temperature may be on that line or in the vessel; (iv) for batch operation, the control point for temperature clearly must be in the vessel. Although level control is shown to be maintained with an internal weir, the product can be taken off with the pump on level control. (b) This shows either direct or cascade control of the temperature of a reactor with internal heat transfer surface and an internal weir. The sluggishly responding temperature of the vessel is used to reset the temperature controller of the HTM. For direct control, the TC-2 is omitted and the control point can be on the HTM outlet or the product line or in the vessel. (c) Quite a uniform temperature can be maintained in a reactor if the contents are boiling. The sketch shows temperature maintenance by refluxing evolved vapors. A drum is shown from which uncondensed gases are drawn off on pressure control, but the construction of the condenser may permit these gases to be drawn off directly, thus eliminating need for the drum. The HTM of the condenser is on TC which resets the PC if necessary in order to maintain the correct boiling temperature in the reactor. Other modes of pressure control are shown with the fractionator sketches of Figure 3.15 and on Figure 3.5 dealing with vacuum control. (d) Flow reactors without mechanical agitation are of many configurations, tanks or tubes, empty or containing fixed beds of particles or moving particles. When the thermal effects of reaction are substantial, multiple small tubes in parallel are used to provide adequate heat transfer surface. The sketch shows a single tube provided with a jacket for heat transfer. Feed to the reactor is on flow control, the effluent on pressure control, and the flow of the HTM on temperature control of the effluent with the possibility of reset by the composition of the effluent. (e) Heat transfer to high temperature reactions, above 300°C or so, may be accomplished by direct contact with combustion gases. The reaction tubes are in the combustion zone but safely away from contact with the flame. The control mode is essentially similar to that for case (d), except that fuel-air mixture takes the place of the HTM. The supply of fuel is on either temperature or composition control off the effluent stream, and the air is maintained in constant ratio with the fuel with the flow ratio controller FRC. (f) High temperature endothermic processes may need several reaction vessels with intermediate heat input. For example, the inlet temperature to each stage of a catalytic reformer is about 975°F and the temperature drop ranges from about 100°F in the first stage to about 15°F in the last one. In the two-stage assembly of this figure, the input is on FC, the outlet of the last reactor on PC, and the fuel supply to each furnace is on TC of its effluent, with the air supply on flow ratio control, as shown for example (e). (g) Very effective heat transfer is accomplished by mixing of streams at different temperatures. The cumene process shown here employs injection of cold reacting mixture and cold inert propane and water to prevent temperature escalation; by this scheme, the inlet and outlet temperature are made essentially the same, about 500°F. Although not shown here, the main feed is, as usual for reactors, on FC and the outlet on PC. The
- 74. 3.3. EQUIPMENT CONTROL 55 Mixing Chamber 1 - ! ----I Light Phase m Heavy Phase Separating Chamber Figure 3.18. Functioning and controls of a mixer-settler assembly for liquid-liquid extraction. sidestreams are regulated with hand-set valves by experienced operators in this particular plant, but they could be put on automatic control if necessary. Other processes that employ injection of cold process gas at intermediate points are some cases of ammonia synthesis and sulfur dioxide oxidation. (h) In catalytic cracking of petroleum fractions, an influential side reaction is the formation of carbon which deposits on the catalyst and deactivates it. Unacceptable deactivation occurs in about lOmin, so that in practice continuous reactivation of a portion of the catalyst in process must be performed. As shown on this sketch, spent catalyst is transferred from the reactor to the regenerator on level control, and returns after regeneration under TC off the reactor temperature. Level in the regenerator is maintained with an overflow standpipe. Smooth transfer of catalyst between vessels is assisted by the differential pressure control DPC, but in some plants transfer is improved by injection of steam at high velocity into the lines as shown on this sketch for the input of charge to the reactor. Feed to the system as a whole is on flow control. Process effluent from the reactor is on pressure control, and of the regenerator gases on the DPC. Fuel to regeneration air preheater is on TC off the preheat air and the combustion air is on flow ratio control as in part (e). LIQUID PUMPS Process pumps are three types: centrifugal, rotary positive displacement, and reciprocating. The outputs of all of them are controllable by regulation of the speed of the driver. Controllability of centrifugal pumps depends on their pressure- flow characteristics, of which Figure 3.20 has two examples. With the upper curve, two flow rates are possible above a head of about 65 ft so that the flow is not reliably controllable above this pressure. The pump with the lower curve is stable at all pressures within its range. Throttling of the discharge is the usual control method for smaller centrifugals, variable speed drives for larger ones. Suction throttling may induce flashing and vapor binding of the pump. Figures 3.21(a) and (b) are examples. Rotary pumps deliver a nearly constant flow at a given speed, regardless of the pressure. Bypass control is the usual method, with speed control in larger sizes. Reciprocating pumps also may be controlled on bypass if a pulsation damper is provided in the circuit to smooth out pressure fluctuations; Figure 3.21(c) shows this mode. Reciprocating positive displacement pumps may have adjust- ment of the length or frequency of the stroke as another control feature. These may be solenoid or pneumatic devices that can be operated off a flow controller, as shown on Figure 3.21(d). S O L I D S F E E D E R S Several of the more common methods of controlling the rate of supply of granular, free-flowing solids are represented in Figure 3.7. COMPRESSORS Three main classes of gas compressors are centrifugal and axial, rotary continuous positive displacement, and reciprocating positive
- 75. 56 P R O C E S S C O N T R O L Feed Recycle ‘1’ Feed (c) ‘i Product FC FL J--w Feed Product PC fl (4 Figure 3.19. Chemical reactor control examples. (a) Temperature control of a stirred tank reactor with pumparound through an external heat exchanger, operable either in batch or continuously: Some alternate control modes are discussed in the text. Cascade control as in (b) can be implemented with external heat transfer surface. (b) Either cascade or direct control of temperature: For direct control, controller TC-2 is omitted, and the control point can be taken on the effluent line or in the vessel or on the HTM effluent line. A similar scheme is feasible with an external heat exchanger. (c) Reactor temperature control by regulation of the boiling pressure: The HTM is on TC off the reactor and resets the PC on the vent gases when necessary to maintain the correct boiling temperature. Although shown for batch operation, the method is entirely feasible for continuous flow. (d) Basic controls on a flow reactor: Feed on flow control, effluent on pressure control, and heat transfer medium flow rate on process effluent temperature or reset by its composition. (e) A fired heater as a tubular flow reactor: Feed is on FC, the product is on PC, the fuel is on TC or AC off the product, and the air is on flow ratio control. (f) A two-stage fired heater-reactor assembly: Details of the fuel-air supply control are in (e). (g) Control of the temperature of the exothermic synthesis of cumene by splitting the feed and by injection of cold propane and water into several zones. The water also serves to maintain activity of the phosphoric acid catalyst. (h) The main controls of a fluidized bed reactor-regenerator: Flow of spent catalyst is on level control, and that of regenerated catalyst is on TC off the reactor; these flows are assisted by maintenance of a differential pressure between the vessels. Details of the fuel-air control for the preheater are in (e).
- 76. 3.3. EQUIPMENT CONTROL 57 (e) w Product Propylene and Benzene (9) Figure 3.1%(contbmed) C u m e n e Water Quench Propane Quench
- 77. 58 PROCESS CONTROL Separator -m Liquid II I-I Steam I I A f t Reactor Air Preheater Regenerator Air Figure 3.19-(continued) ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 1 0 60 120 Flow Rate, gpm Figure 3.20. Characteristics curves of two centrifugal pumps. displacement. The usual or feasible modes of control of pressure and flow may be tabulated: Control Mode Centrifugal Rotary Reciprocating and Axial PD P D Suction throttling x Discharge throttling x Bypass x x x Speed x x x Guide vanes x Suction valves x Cylinder clearance x Steam Controlled Temperature (a) G--T b) Figure 3.21. Control of centrifugal, rotary, and reciprocating pumps. (a) Throttling of the discharge of a centrifugal pump. (b) Control of the flow rate of any kind of pump by regulation of the speed of the driver. Although a turbine is shown, engine drive or speed control with gears, magnetic clutch, or hydraulic coupling may be feasible. (c) On the left, bypass control of rotary positive displacement pump; on the right, the reciprocating pump circuit has a pulsation dampener to smooth out pressure fluctuations. (d) Adjustment of the length or frequency of the stroke of a constant speed reciprocating pump with a servomechanism which is a feed- back method whose action is control of mechanical position.
- 78. 3.3. EQUIPMENT CONTROL 59 pressor must be maintained above the magnitude at the peak in pressure. Figure 3.23(c) shows an automatic bypass for surge protection which opens when the principal flow falls to the critical minimum; recycle brings the total flow above the critical. Smaller rotary positive displacement compressors are con- trolled with external bypass. Such equipment usually has a built-in relief valve that opens at a pressure short of damaging the lflw equipment, but the external bypass still is necessary for smooth control. Large units may be equipped with turbine or gas engine drives which are speed adjustable. Variable speed gear boxes or belt drives are not satisfactory. Variable speed dc motors also are c o u p l i n g s a r e u s e d . not useful as compressor drives. Magnetic clutches and hydraulic (c) Reciprocating compressors may be controlled in the same way as rotary units. The normal turndown with gasoline or diesel engines is 50% of maximum in order that torque remains within m (4 Figure 3.21-(continued) Throttling of the suction of centrifugal and axial compressors wastes less power than throttling the discharge. Even less power is wasted by adjustment of built-in inlet guide vanes with a servomechanism which is a feedback control system in which the controlled variable is mechanical position. Speed control is a particularly effective control mode, applicable to large units that can utilize turbine or internal combustion drives; control is by throttling of the supply of motive fluids, steam or fuel. Characteristic curves-pressure against flowrate-of centrifugal and axial compressors usually have a peak. Figure 3.22 is an example. In order to avoid surging, the flow through the com- I OO I I I I I I I I I I 5 10 Flow Rate, M Ib/hr Figure 3.22. Characteristic curves of a centrifugal compressor at different speeds, showing surge limits. - P C v M --D Figure 3.23. Control of centrifugal compressors with turbine or motor drives. (a) Pressure control with turbine or motor drives. (b) Flow control with turbine or motor drives. SC is a servomechanism that adjusts the guide vanes in the suction of the compressor. (c) Surge and pressure control with either turbine or motor drive. The bypass valve opens only when the flow reaches the minimum calculated for surge protection.
- 79. 60 PROCESS CONTROL * W Figure 3.24. Control of positive displacement compressors, rotary and reciprocating. (a) Flow control with variable speed drives. (b) Pressure control with bypass to the suction of the compressor. (c) Reciprocating compressor. SC is a servomechanism that opens some of suction valves during discharge, thus permitting stepwise internal bypass. The clearance unloader is controllable similarly. These built-in devices may be supplemented with external bypass to smooth out pressure fluctuations. acceptable limits. Two other aids are available to control of recip- rocating units. 1. Valve unloading, a process whereby some of the suction valves remain open during discharge. Solenoid or pneumatic unloaders can be operated from the output of a control instrument. The stepwise controlled flow rate may need to be supplemented with controlled external bypass to smooth out pressure fluctuations. 2. Clearance unloaders are small pockets into which the gas is forced on the compression stroke and expands into the cylinder on the return stroke, thus preventing compression of additional gas. Figure 3.24 shows control schemes for rotary and reciprocating compressors. Vacuum pumps are compressors operating between a low suction pressure and a fixed discharge pressure, usually REFERENCES 1. Chemical Engineering Magazine, Practical Process Instrumentation and Control, McGraw-Hill, New York, 1980. 2. D.M. Considine, Process Instruments and Controls Handbook, McGraw- Hill, New York, 1985. atmospheric. Mechanical pumps are used for small capacities, steam jet ejectors for larger ones. Ejectors also are used as ther- mocompressors to boost the pressure of low pressure steam to an intermediate value. Control of suction pressure with either mech- anical or jet pumps is by either air bleed [Fig. 3.5(a)] or suction line throttling [Fig. 3.5(c)]; air bleed is the more economical process. Up to five jets in series are used to produce high vacua. The steam from each stage is condensed by direct contact with water in baro- metric condensers or in surface condensers; condensation of steam from the final stage is not essential to performance but only to avoid atmospheric pollution. In a single stage ejector, motive steam flow cannot be reduced below critical flow in the diffuser, and water to the barometric condenser must not be throttled below 30-50% of the maximum if proper contacting is to be maintained. Control by throttling of steam and water supply, as on Figure 3.5(b), is subject to these limitations. 3. B. Liptak, Instrumentation in the Process Industries, Chilton, New York, 1973. 4. F.G. Shinskey, Process Control Systems, McGraw-Hill, New York, 1979. 5. F.G. Shinskey, Distillation Control, McGraw-Hill, New York, 1984. 6. M.R. Skrokov (Ed.), Mini- and Microcomputer Control in Industrial Processes, Van Nostrand Reinhold, New York, 1980.
- 80. 4 DRIVERS FOR MOVING EQUIPMENT P owered chemical processing equipment includes pumps, compressors, agitators and mixers, crushers and grinders, and conveyors. Drivers are electric motors, steam or gas turbines, and internal combustion engines. For loads under 150 HP or so electric motors are almost invariably the choice. Several criteria are applicable. For example, when a pump and a spare are provided, for flexibility one of them may be driven by motor and the other by turbine. Centrifugal and axial blowers and compressors are advantageously driven by turbines because the high operating speeds of 4000- 10,000 rpm are readily attainable whereas electric motors must operate through a speed increasing gear at extra expense. When fuel is relatively cheap or accessible, as in the field, gas turbines and internal combustion engines are preferred drivers. Turbines, internal combustion engines, and direct current motors are capable of continuous speed adjustment over a wide range. Energy efficiencies vary widely with the size and type of driver as shown in this table. Efficiency (%I D r i v e r 10kW 100kW 7OOOkW 10,OOOkW Gas turbine andinternal 28 34 38 combustion engine Steam turbine 42 63 76 Motor 8.5 92 96 97 Since the unit energy costs are correspondingly different, the economics of the several drive modes often are more nearly comparable. 4.1. MOTORS Although each has several subclasses, the three main classes of motors are induction, synchronous, and direct current. Higher voltages are more efficient, but only in the larger sizes is the housing ample enough to accomodate the extra insulation that is necessary. The voltages commonly used are H o r s e p o w e r Voltage l-100 220.440.550 75-250 440 200-2500 2300,400O Above 2500 4000, 13,200 Direct current voltages are 11.5, 230, and 600. The torque-speed characteristic of the motor must be matched against that of the equipment, for instance, a pump. As the pump comes up to speed, the torque exerted by the driver always should remain 5% or so above that demanded by the pump. The main characteristics of the three types of motors that bear on their process applicability are summarized following. INDUCTION Induction motors are the most frequent in use because of their simple and rugged construction, and simple installation and control. They are constant speed devices available as 3600 (two-pole), 1800, 1200, and 900rpm (eight-pole). Two speed models with special windings with 2: 1 speed ratios are sometimes used with agitators, centrifugal pumps and compressors and fans for air coolers and cooling towers. Capacities up to 20,OOOHP are made. With speed increasing gears, the basic 1800 rpm model is the economical choice as drive for centrifugal compressors at high speeds. SYNCHRONOUS Synchronous motors are made in speeds from 1800 (two-pole) to 150 rpm (48-pole). They operate at constant speed without slip, an important characteristic in some applications. Their efficiencies are l-2.5% higher than that of induction motors, the higher value at the lower speeds. They are the obvious choice to drive large low speed reciprocating compressors requiring speeds below 600 rpm. They are not suitable when severe fluctuations in torque are encountered. Direct current excitation must be provided, and the costs of control equipment are higher than for the induction types. Consequently, synchronous motors are not used under 50 HP or so. DIRECT CURRENT Direct current motors are used for continuous operation at constant load when fine speed adjustment and high starting torque are needed. A wide range of speed control is possible. They have some process applications with centrifugal and plunger pumps, conveyors, hoists, etc. Enclosures. In chemical plants and refineries, motors may need to be resistant to the weather or to corrosive and hazardous locations. The kind of housing that must be provided in particular situations is laid out in detail in the National Electrical Code, Article 500. Some of the classes of protection recognized there are in this table of differential costs. Type Drip proof Weather protected, I and II Totally enclosed fan cooled, TEFC, below 250 HP Totally enclosed, water cooled, above 500 HP Explosion proof, below 3000 HP 96 Cost above Drip Proof 10-50 25-100 25-100 110-140 Protection Against Dripping liquids and falling particles Rain, dirt, snow Explosive and nonexplosive a t m o s p h e r e s S a m e a s T E F C Flammable and volatile liquids 61
- 81. * 62 DRIVERS FOR MOVING EQUIPMENT TABLE 4.1. Selection of Motors for Process Equipment TABLE 4.2. Checklist for Selection of Motors Motor Type’ Motor Data Application A.C. D.C. Agitator la, lb, 2b 5a Ball mill lc, 2b. 3a 5b B l o w e r 1a.1b.2b.3a.4 5 a C o m p r e s s o r la,lb,lc,3a,4 5b. 7 Conveyor la,lc,2b,3a 5b, 7 Crusher la, lc, Id 5a. 5b Dough mixer la, lb, lc.2b 5a. 5b Fan, centrifugal and propeller la, lb,2c,3a,4 5a. 7 H a m m e r m i l l lc 5 a Hoist Id, 2a, 3b 6 Pulverizer lc 5b Pump, centrifugal 1a.1b.2b.3a.4 5b Pump, positive displacement lc, 2b. 3a 5b General Type of motor (cage, wound-rotor, synchronous, or de). . . . . . . . Quantity . . . . . . . . Hp . . . . . . . . Rpm . . . . . . . . . Phase . . . . . . . . . Cycles. . . . . . . . Voltage. . . . . . . . Time rating (continuous, abort-time, intermittent). . . . . . . . . . . . Overload (if any) . . . . . . % for . . . . . . Service factor . . . . . . % Ambient temperature. . . . . . . . . . C Temperature rise. . . . . . . . . . C Class of insulation: Armature. . . Field. . . Rotor of w-r motor. . . Horizontal or vertical . . . . . . . . . . . . Plugging duty . . . . . . . . . . . . Full- or reduced-voltage or part-winding rtarting (ac) . . . . . . . . If reduced voltage-by autotransformer or reactor . . . . . . . . . . Locked-rotor starting current limitations . . . . . . . . . . . . . . . . . . . . . Special characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Induction Motora Locked-rotor torque. . . . . . . . . % Breakdown torque. . . . . . . . . % or for general-purpose cage motor: NEMA Design (A, B, C, D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rock crusher 3 a 5b. 6 a Code: 1. Squirrel-cage, constant speed a. normal torque, normal starting current b. normal torque, low starting current c. high torque, low starting current d. high torque, high slip 2. Squirrel-cage, multispeed a. constant horsepower b. constant torque c. variable torque 3. Wound rotor a. general purpose b. crane and hoist 4. Synchronous 5. Direct current, constant speed a. shunt wound b. compound wound 6. Direct current, variable speed series wound 7. Direct current, adjustable speed (After Allis-Chalmers Mfg. Co., Motor and Generator Reference Book, Colorado Springs, CO). Standard NEMA ratings for induction motors: General purpose: i, a, 1, 1;. 2, 3, 5, 7;. 10. 15, 20, 25, 30, 40, 50, 60, 75, 100, 125, 150, 200, 250, 300, 350, 400, 450, 500. Large motors: 250, 300,350,400, 450, 500, 600, 700,800, 900, 1000, 1250, 1500, 1750,2000, 2250,2500, 3000,3500,4000,4600,5000 and up to 30,000. Clearly the cost increments beyond the basic drip-proof motor enclosures are severe, and may need to be balanced in large sizes against the cost of isolating the equipment in pressurized buildings away from the hazardous locations. Applications. The kinds of motors that are being used successfully with particular kinds of chemical process equipment are identified in Table 4.1. As many as five kinds of AC motors are shown in some instances. The choice may be influenced by economic considerations or local experience or personal preference. In this area, the process engineer is well advised to enlist help from electrical experts. A checklist of basic data that a supplier of a motor must know is in Table 4.2. The kind of enclosure may be specified on the last line, operating conditions. Load Data Typeofload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . If compressor drive, give NEMA application number. . . . . . . . . . . . . Direct-connected, geared, chain, V-belt, or flat-belt drive. . . . . . . . . . Wk’ (inertia) for high inertia drives. . . . . . . . . . . . . . . . . . . .Ib-ft’ Starting with full load, or unloaded . . . . . . . . . . . . . . . . . . . . . . . . . . . If unloaded, by what means?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . For variable-speed or multi-speed drives, is load variable torque, constant torque, or constant horsepower?. . . . . . . . . . . . . . . . . . . . . . Operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (By permission, Allis Chalmers Motor and Generator Reference Book, Bul. 51R7933, and ES. Lincoln (Ed.), Electrical Reference Book, Electrical Modernization Bureau, Colorado Springs, CO. 4.2. STEAM TURBINES AND GAS EXPANDERS 4. simple controls, Turbines utilize the expansion of steam or a gas to deliver power to 5. low first cost and maintenance, and a rotating shaft. Salient features of such equipment are 6. flexibility with regard to inlet and outlet pressures. 1. high speed rotation, Single stage units are most commonly used as drivers, but above 2. adjustable speed operation, 5OOHP or so multistage units become preferable. Inlet steam 3. nonsparking and consequently nonhazardous operation, pressures may be any value up to the critical and with several Synchronous Motors Power factor . . . . . . Torques: Locked-rotor. . . . . % Pull-in. . . . . % Pull-out . . . . . . % Excitation . . . . . .volta dc Type of exciter. . . . . . If m-g exciter set, what are motor characteristier?. . . . . . . . . . . . Motor field rheostat. . . . . . . . Motor field discharge resistor . . . . . . . Direct-current Motors Shunt, stabilized shunt, compound, or series wound . . . . . . . . . . . . . Speed range. . . . . . . . . . Non-roversing or reversing. . . . . . . . . . . . . Continuous or tapered-rated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Featured Protection or enclosure. . . . . . . . . . . . . . Stator shift . . . . . . . . . . . . . Mechanical Featww (cont.) Nudm of bearings . . . . . . . . . . . . . Type of bearings . . . . . . . . . . . . Shaft extension: Flanged . . . . . . . Standard or special length . . . . . . Press on half-coupling . . . . . . . . Terminal box . . . . . . . . . . . . . . . . . . NEMA C or D flange . . . . . . . . Round-frame or with feet . . . . . . . . Vertical: External thrust load . . . . . Ibs.Typeofthrustbearing.. . . . Base ring type. . . . . . . . . . . . . . . . Sole plates . . . . . . . . . . . . . . . . . Accessories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 82. 4.2. STEAM TURBINES A N D G A S E X P A N D E R S 63 60 K O”“Kll,J@““~ r^--r’ --^^ RPM 6OOPSI. t.8oOl R P M GEARED TURBINE (INCL. GEAR LOSS) 15OPSI. 3.600RPM x)OPSI, 3,600RPM 60OPSI, 3,600RPM I IIll z z 40 0 z k 30 %J 2 w s 20 10 I III IIlllll I I II lllllll RPM RPM RPM OJ ’ ” 1 IllIll I Ill Ilrllll 20 30 40 50607080 1 0 0 200 300 400500 RATED BHP Average efficiency of single-stage turbinw (noncondensing, dry, and saturated steam) (a) Figure 4.1. Efficiencies of (a) single-stage and (b) multistage turbines (Gartmann, De Lava1 Engineering Handbook, McGraw-Hill, New York, 1970, pp. 5.8-S. 9, Figs. 5.2 and 5.3).
- 83. 64 DRIVERS FOR MOVING EQUIPMENT hundred degrees of superheat. In larger sixes turbines may be convenient sources of low pressure exhaust steam in the plant. From multistage units, steam may be bled at several reduced pressures. When the expansion is to subatmospheric conditions, the operation is called condensing because the exhaust steam must be condensed before removal from the equipment. Although the efficiency of condensing turbines is less, there is an overall reduction of energy consumption because of the wider expansion range. Several parameters affect the efficiency of steam turbines, as shown partially on Figure 4.1. Closer examination will need to take into account specific mechanical details which usually are left to the manufacturer. Geared turbines [the dashed line of Fig. 4.1(b)] have higher efficiencies, even with reduction gear losses, because they operate with especially high bucket speeds. For example, for a service of SOOHP with 3OOpsig steam, a geared turbine has an efficiency of 49.5% and one with a direct drive at 1800 rpm has an efficiency of 24%. The flow rate of steam per unit of power produced is represented by 2545 m=-q(H2-Hl) lb/HP hr 3412 = - Wz - 4) lb/kWh with the enthalpies in Btu/lb. The efficiency is 9, off Figure 4.1, for example. The enthalpy change is that of an isentropic process. It may be calculated with the aid of the steam tables or a Mollier diagram for steam. For convenience, however, special tables have been derived which give the theoretical steam rates for typical combinations of inlet and outlet conditions. Table 4.3 is an abbreviated version. Example 4.1 illustrates this kind of calculation and compares the result with that obtained by taking the steam to behave as an ideal gas. For nonideal gases with known PVT equations of state and low pressure heat capacities, the method of calculation is the same as for compressors which is described in that section of the book. On a Mollier diagram like that with Example 4.1, it is clear that expansion to a low pressure may lead to partial condensation if insufficient preheat is supplied to the inlet steam. The final condition after application of the efficiency correction is the pertinent one, even though the isentropic point may be in the two-phase region. Condensation on the blades is harmful to them and must be avoided. Similarly, when carbon dioxide is expanded, possible formation of solid must be guarded against. When gases other than steam are employed as motive fluids, the equipment is called a gas expander. The name gas turbine usually is restricted to equipment that recovers power from hot TABLE 4.3. Theoretical Steam Rates for Typical Steam Conditions (Ib/kWh)” IC(I 25(1 410 6llO 600 Xi0 X50 000 Yoo 1,200 l,?jO 1,250 1,450 I ,ijO I ,x00 2 , 4 0 0 Initid tamp, “F Z6C.Y ioo hi0 ii0 x25 x25 YOO x25 9oll x25 Y00 Y50 X25 YjO I000 I000 E:haut Initial cnth:alpv, I3tu/lh prc5t,re 1,IYj.i 1 , 2 6 1 . X 1,114.Y 1,379.hI,-t!t.4 I.4tO.6I,-Ijj.j t,-WX.-l 1.451.61,jY-i.T 1.43X.4 I,-KX.I1,2X2.7I,-Ml.ll,GW.Il,Mt.-t inf fg ill) 2 . 0 I O . 5 2 o.oio 7.X31 7.0X3 6.761 6,.5x0 6.2X2 6 .i j 5 6.256 (,.-l.il h.l!? 5.Y-H 6.40X 5.YCO 5.6fa 5,633 2 . 5 IO.XX Y. 343 x . 0 3 ; 7.251 6.Yl6 h.i?l h.-tl5 6.6Y6 6.3xX 6.5X-l 6 . 2 5 6 6.061 6.536 6.01-t S.77? 5.i33 i.396 i.052 6.XJi 6.ilO fi.XIY 6..iO? 6.G.v 6 . 3 6 2 6.162 6.64x 6.112 5.w j.XIY 3 . 0 t 1.20 4.0 I I . 7 6 IlJill’g,lgc i 21.6Y I O ?!.Yi 20 2 X . 6 1 30 31.6Y 40 3Y.!Y 50 -Ki.(Hl 60 5 3 . 9 0 l6.5i I7.YO !O.+t !?.Yj 2 5 . 5 2 2 X . 2 1 31.07 13.01 13.X3 lj.13 16.73 18.0X 19.42 2 0 . 7 6 i.frH 7.2x2 I .Oj t0.42 I.# I O . 9 5 2.6X II.‘)0 3.61 12.75 +.31 13.5-t 5 . 3 6 l-I.30 6. IX 15.05 I ’ 7.05x Y.H.38 I O . 1 0 I I . 1 0 Il.XO 12.46 1 3 . 0 ; 1 3 . 6 6 6.iX i.026 6.X9-l 6.541 6.332 6.27i 6.OIZ j.Y6? Y.?XX Y.iOj IO.43 I I.OX I I .h6 I ? . ? ! t2.i-t Y.i55 IO.202 t O.YX? II.67 lZ.!c-+ 12.00 13.47 6.W Y. ?IW Y.flli I O . 3 2 7 IO.YC? Il.i? 1 2 . 0 6 12.57 Y.!Yi Y. xi IO.-Km I I.OYS II.fi-wJ 12.16 I2.64 X.X20 0.1X0 Y.XOI IO.341 10.x31 II.2X-t Il.71 x.+Yl x.x10 0.415 9.Y22 10.1Xu lO.XOt-+ I I . 2 0 Y.2IX Y.jY? IO.240 Io.xoI II.?W I l . 7 7 9 I?.?-! X.351 X.673 Y.227 ‘).7(L) IO.11-t lO..i31 lO.YO 7.x7-t X.ISX X.&l2 Y.057 9.427 Y.767 IO.OX i.il3 7.97j X.-121 x . 7 9 9 Y.136 Y.-t-t! 9 . 7 2 7 i5 69.-t 3i.7; ??.XI I;.40 I6.l6 I-1.50 Il.51 I-t.?X 11.30 13.1-t 1 2 . 3 2 X0 i5.Y 37.47 23.51 17.x0 In.54 I-t.78 1 3 . 7 7 l-I.55 13.55 1 3 . 5 6 12.52 IO0 -ti.?l 26.46 IY.43 IX.05 IJ.Xfi I-t.77 I5.iY I-t.50 l-t.42 l!.2i I25 j7.XX 30.59 21.56 20.03 17.22 I6.04 16.X7 IS.70 15.46 I-t.Ii Ii0 76.5 35.40 2 3 . 8 3 22.1-t I X . 6 1 I i . 3 3 IX.IX Ih.Yl l&-t7 IC.06 I60 X6.X 3i.j; 2 4 . 7 9 23.03 19.17 17.X5 I X . 7 1 17.41 Ih.XX l.i.41 Ii5 41.16 2 6 . 2 9 24.43 20.04 I X . 6 6 l9.j? I X . 1 6 17.4X Ij.Yi 200 4x.24 29.w 2 6 . 9 5 21.53 20.05 20.9I 19.45 IX.-tX 1fi.X-l 2 5 0 6 Y . l 35.40 32.x9 24.7X 23.0x 23.YO 22.2-t 20.57 1X.6X XX) 4 2 . 7 2 GO.62 2X. 50 2 6 . 5 3 2 7 . 2 7 25.37 22.iY 20.62 wo 7 2 . 2 6 7 . 0 3X.05 ?5.43 3 5 . 7 1 3 2 . 2 2 2 7 . 8 2 2 4 . 9 9 -tLj x-t.2 7X.3 41.0x 3 X . 2 6 3X.33 3 5 . 6 5 29.2-t 2 6 . 2 1 6c4) i x . 5 73.1 6 X . 1 1 63.-t 4 2 . 1 0 37.03 ‘From Theoretical Steam Rate Table-Compatible with the 1967 ASME Steam Tables, ASME, 1969. I I . 7 7 I I . 9 5 1 2 . 6 5 13.51 I-k.35 l-t.69 lj.20 16.05 17.x1 19.66 23.X2 ?-l.YX 35.?0 12.X5 t 3.05 13.X3 l-l.76 15.65 tr5.00 16.j2 Ii.?9 19.11 2 0 . 8 9 24.7-I 2 5 . 7 X ?-l.jO Il.-I? IO.53 t o . 1 2 I I . 6 0 Io.6; I O . 2 5 12.2-t I I . 2 1 10.73 1 3 . 0 1 11.x-t II.?X 1 3 . 7 5 12.44 I l.XO I4.0j 12.6X 12.00 I-+.-tY 13.03 1 2 . 2 9 IS.23 1 3 . 6 2 Il.77 16.73 1-1.7x 1 3 . 6 9 IX.?X t5.95 l4..i9 21.64 I X . 3 9 16.41 2 2 . 5 5 19.03 16.X7 30. I6 24.06 2 0 . 2 9
- 84. 4.3. COMBUSTION GAS TURBINES AND ENGINES 65 EXAMPLE 4.1 Steam Requirement of a Turbine Operation Steam is fed to a turbine at 614.7 psia and 825°F and is discharged at 64.7 psia. (a) Find the theoretical steam rate, Ib/kWh, by using the steam tables. (b) If the isentropic efficiency is 70%, find the outlet temperature. (c) Find the theoretical steam rate if the behavior is ideal, with C,/C, = 1.33. (a) The expansion is isentropic. The initial and terminal conditions are identified in the following table and on the graph. The data are read off a large Mollier diagram (Keenan et al., Steam Tables, Wiley, New York, 1969). Point P fF H S 1 614.7 825 1421.4 1.642 2 64.7 315 1183.0 1.642 3 64.7 445 1254.5 1.730 AH, = H2 - HI = -238.4 Btu/lb Theoretical steam rate = 3412/238.4 = 14.31 lb/kWh. This value is checked exactly with the data of Table 4.3. (b) H3 - HI = 0.7(H, - HI) = -166.9 Btu/lb H3 = 1421.4 - 166.9 = 1254.5 Btu/lb The corresponding values of T3 and S, are read off the Mollier diagram, as tabulated. (c) The isentropic relation for ideal gases is AH= & RTl[(P2/Pl)(k~‘)~k - l] = 1’9;f5285) [(64.7/614.7)“-25 - l] = -4396 Btu/lbmol, -244 Btu/lb. f F 1 ?@ v 1.64 1.73 ENTROPY , BTU/(LB)(F) combustion gases. The name turboexpander is applied to machines whose objective is to reduce the energy content (and temperature) of the stream, as for cryogenic purposes. Gas expanders are used to recover energy from high pressure process gas streams in a plant when the lower pressure is adequate for further processing. Power calculations are made in the same way as those for compressors. Usually several hundred horsepower must be involved for economic justification of an expander. In smaller plants, pressures are simply let down with throttling valves (Joule-Thomson) without attempt at recovery of energy. The specification sheet of Table 4.4 has room for the process conditions and some of the many mechanical details of steam turbines. 4.3. COMBUSTION GAS TURBINES AND ENGINES When a low cost fuel is available, internal combustion drivers surpass all others in compactness and low cost of installation and operation. For example, gas compression on a large scale has long been done with integral engine compressors. Reciprocating engines also are widely used with centrifugal compressors in low pressure applications, but speed increasing gears are needed to up the 300-6OOrpm of the engines to the 3000-10,OOOrpm or so of the compressor. Process applications of combustion gas turbines are chiefly to driving pumps and compressors, particularly on gas and oil transmission lines where the low thermal efficiency is counter- balanced by the convenience and economy of having the fuel on hand. Offshore drilling rigs also employ gas turbines. Any hot process gas at elevated pressure is a candidate for work recovery in a turbine. Offgases of catalytic cracker regenerators, commonly at 45 psig and as high as 1250”F, are often charged to turbines for partial recovery of their energy contents. Plants for the manufacture of nitric acid by oxidation of ammonia at pressures of 100 psig or so utilize expanders on the offgases from the absorption towers, and the recovered energy is used to compress the process air to the reactors. Combustion gas turbine processes are diagrammed on Figure 4.2 and in Example 4.2. In the basic process, a mixture of air and fuel (or air alone) is compressed to 5-10 atm, and then ignited and burned and finally expanded through a turbine from which power is recovered. The process follows essentially a Brayton cycle which is shown in Figure 4.2 in idealized forms on TS and PV diagrams. The ideal process consists of an isentropic compression, then heating at constant pressure followed by an isentropic expansion and finally cooling at the starting pressure. In practice, efficiencies of the individual steps are high: Compressor isentropic efficiency, 85% Expander isentropic efficiency, 85-90% Combustion efficiency, 98%
- 85. TABLE 4.4. Data Sheet for General Purpose Steam Turbines, Sheet 1 of 2’ GENERAL-PURPOSE STEAM TURBINE DATA SHEET ;-E;;;;T NO REV. NO. DATE CUSTOMARY UNITS BY REVIEWED SHEET 1 O F 2 P O N O NOTE: 0 Indicmm Information Completed q vPurchaser 0 OPERATING CONDITIONS POWOI, SL*ed. ODer~tln0 Point B”P RPY Normal R*ted Cl fl” M~mlfacNrw 0 PERFORMANCE Operating Point/ NO. “end Valver stum Rrn. Steam Condition OP.” (3.4.1 41 LbJHP H r . NormaIINormd RmtmdlNOrmd 0 STEAM CONDITIONS M A X . N O R M A L M I N . In1.t Prw, PSIG Inlet T.m,,, OF Exheust Pran IPSIGI iIn. Hgl Unusual Conditions i2.12.2.6) Duty 0 COnti”Uou* 0 Standby 0 Auto Start Ewl. Stsam Cost. S/1000 Lb8 u CONSTRUCTION Turbln. T y p . 0 Horlz. 0 “.Rk.I N O . Stsq.3 Whrl OIL. Ir;. PayOUt Pwiod. Y.W. Hr./Y, TURBINE DATA - u Mlnimum Allowable Speed. RPM 0 Maximum Continuous Spud. RPM 0 Trip Soeti. RPM 0 First Critical Sp..d. RPM 0 Turbine Consnuction Safe For Runaway Speed (2.11.11 0 Exh. T.mP. OF N0rm.l 0 Pot*nrial Max. POww. SUP 13 M.x. Nozrl.St..m F l o w . Lbs/Hr !, Max. Allow~bl. Sp..d. RPM Rotor’ l-l Built Up u Solid Etading 0 2 R O W 0 3 Row 0 Re Entry Cming Split 0 Axial 0 Radial Casing Support 0 cent*r1inm 0 F o o t ,, N E M A “ P ” 9.” Trlf, “al”. Cl lnngrd 0 Sw~r~t* I nt.r*tag. .s*mts 0 Labyrinth 0 Carbon End S*all 0 Crbon Ring. No/Box 0 Labyrinth Type Radial Sawin Type Thrust Buring (2.9.21 Thrmt Collar (2.9.8) 0 Replunbk 0 Intqwl 0 N o n . N O Load L”b. 011 Viscosity (2.10.2) s u s 0 1 0 0 % S”S a 210°F Lubrication 0 Ring Oiled 0 PrwBUr* 0 Purge Oil Mist 0 Pur* Oil Milt 0 shaft ~raas Suitable For Obuwinp By N~n-C~nta~tinp TVP4
- 86. Compressor Expander 4.3. COMBUSTION GAS TURBINES AND ENGINES 67 Exhaust G Air P (a) 2 3 L 1 4 V T 4 3 4 2 1 S lb) Figure 4.2. Combustion gas turbine arrangements and their thermodynamic diagrams. (a) Basic unit with PV and TS diagrams. (b) Unit with an air preheater and TS diagram. Performance of a Combustion Gas Turbine Atmospheric air at 80°F (305K) is compressed to 5 atm, combined with fuel at the rate of 1 kg/s, then expanded to 1 atm in a power 5 atm 1200 K Compressor Expander 4 Water turbine. Metallurgical considerations limit the temperature to 1700°F (1200K). The heat capacities of air and combustion products are C, = 0.95 + 0.00021T (K) kJ/kg, the heat of combustion is 42,000 kJ/kg, the furnace efficiency is 0.975, the isentropic efficiency of the compressor is 0.84, and that of the expander is 0.89. Find a. the required air rate, b. the power loads of the compressor and expander, and c. the overall efficiency as a function of the temperature of the exhaust leaving a steam generator. Point P < T 1 1 305 2 5 483 517 3 5 1200 4 1 802 846 5 1 400 Compression: k = 1.4, k/(k - 1) = 3.5, T2 = Tl(P2/Pl)1’3.s = 305(5)“3-5 = 483K, 483 - 305 T,=305+0.84=517K. Combustion: rn: = flow rate of air, kg/kg fuel 0.975(42000) = Ir Cp dT + rn: ly C, dT = 991682 + 771985 rn: mi=51.8 Expansion: k = 1.33, k/(k - 1) = 4.0 T& = T3(P4/Pl)o~2s = 1200(0.2)“.25 = 802°K T4 = 1200 - 0.89( 1200 - 802) = 846°K Power calculations: I 517 Compressor: w: = -mAAH = -51.8 C, dT 305 = -51.8(216.98) = -11.240 kJ/s I 517 Expander: w: = -52.8 C, dT = 52.8(412.35) = 21,772 kJ/s ,200 I 846 Steam generator: Q’ = 52.8 C, dT T qt = overall efficiency = 21772 - 11380 + Q' 42000 The tabulation shows efficiency with three different values of the exhaust temperature. T 0' 'It 846 0 0.247 600 14311 0.588 500 19937 0.722
- 87. 68 DRIVERS FOR MOVING EQUIPMENT Other inefficiencies are due to pressure drops of 2-5%, loss of l-3% of the enthalpy in the expander, and 1% or so loss of the air for cooling the turbine blades. The greatest loss of energy is due to the necessarily high temperature of the exhaust gas from the turbine, so that the overall efficiency becomes of the order of 20% or so. Some improvements are effected with air preheating as on Figure 4.2(b) and with waste heat steam generators as in Example 4.2. In many instances, however, boilers on 1OOO’F waste gas are economically marginal. Efficiencies are improved at higher pressure and temperature but at greater equipment cost. Inlet temperature to the expander is controlled by the amount of excess air. The air/fuel ratio to make 1700°F is in the range of 50 lb/lb. Metallurgical considerations usually limit the temperature to this value. Special materials are available for temperatures up to 2200°F but may be too expensive for process applications. REFERENCES 1. M.P. Boyce, G~J Turbine Engineering Handbook, Gulf, Houston, 1982. 2. F.L. Evans, Equipment Design Handbook for Rt$neries and Chemical Plants, Gulf, Houston, 1979, vol. 1. 3. H. Gadmann, De Lava1 Engineering Handbook, McGraw-Hill, New York, 1970. 4. R.T.C. Harman, Gas Turbine Engineering, Macmillan, New York, 1981. 5. E.E. Ludwig, Applied Process Design for Chemical and Process Plants, Gulf, Houston, 1983, vol. 3. 6. Marks’ Standard Handbook for Mechanical Engineers, McGraw-Hill, New York, 1987.
- 88. 5 TRANSFER OF SOLIDS I n contrast to fluids which are transferred almost equipment. Most commonly, solids are carried on or pushed exclusively through pipelines with pumps or blowers, a along by some kind of conveyor. So/ids in granular form also greater variety of equipment is employed for moving are transported in pipelines as slurries in inert liquids or as so/ids to and from storage and between process suspensions in air or other gases. 5.1. SLURRY TRANSPORT Aude, Seiter, and Thompson (1971), In short process lines slurries are readily handled by centrifugal pumps with large clearances. When there is a distribution of sizes, the fine particles effectively form a homogeneous mixture of high density in which the settling velocities of larger particles are less than in clear liquid. Turbulence in the line also helps to keep particles in suspension. It is essential, however, to avoid dead spaces in which solids could accumulate and also to make provisions for periodic cleaning of the line. A coal-oil slurry used as fuel and acid waste neutralization with lime slurry are two examples of process applications. z = exp(-2.55u,/ku@, 0 where C = concentration of a particular size at a level 92% of the vertical diameter, Co = concentration at the center of the pipe, assumed to be the same as the average in the pipe, f = Fanning friction factor for pipe flow Many of the studies of slurry transfer have been made in connection with long distance movement of coal, limestone, ores, and others. A few dozen such installations .have been made, in length from several miles to several hundred miles. Coal-water slurry transport has been most thoroughly investigated and implemented. One of the earliest lines was 108 miles long, 10 in. dia, 50-60 wt % solids up to 14 mesh, at velocities of 4.5-5.25ft/sec, with positive displacement pumps at 30-mile intervals. The longest line in the United States is 273 miles, 18in. dia and handles 4.8-6.0 million tons/yr of coal; it is described in detail by Jacques and Montfort (1977). Other slurry pipeline literature is by Wasp, Thompson, and Snoek (1971), Bain and Bonnington (1970) Ewing (1978) and Zandi (1971). Principally, investigations have been conducted of suitable linear velocities and power requirements. Slurries of 40-50~01% solids can be handled satisfactorily, with particle sizes less than 24-48 mesh or so (0.7-0.3 mm). At low line velocities, particles settle out and impede the flow of the slurry, and at high velocities the frictional drag likewise increases. An intermediate condition exists at which the pressure drop per unit distance is a minimum. The velocity at this condition is called a critical velocity of which one correlation is =0.25!?!? LUZ P I D %c At high Reynolds numbers, for example, Blasius’ equation is f = o.o791/h$n:5, NRe 2 lo5 (5.4) k in Eq. (5.2) is a constant whose value is given in this paper as 0.35, but the value 0.85 is shown in a computer output in a paper by Wasp, Thompson, and Snoek (1971, Fig. 9). With the latter value, Eq. (5.2) becomes C/C, = exp(-3.OOu,/uVjj. (5.5) The latter paper also states that satisfactory flow conditions prevail when C/C, ~0.7 for the largest particle size. On this basis, the minimum line velocity becomes ’ = lTln~ud,,/C) = 8.41u,/fl where u, is the settling velocity of the largest particle present. u: = 34.6C, Dutw, consistent units, (5.1) As Example 5.1 shows, the velocities predicted by Eqs. (5.1) and (5.6) do not agree closely. Possibly an argument in favor of Eq. (5.6) is that it is proposed by the organization that designed the successful 18 in., 273 mi Black Mesa coal slurry line. where u, = critical flow velocity, u, = terminal settling velocity of the particle, given by Figure 5.1, Pressure drop in flow of aqueous suspensions sometimes has been approximated by multiplying the pressure drop of clear liquid at the same velocity by the specific gravity of the slurry. This is not borne out by experiment, however, and the multiplier has been correlated by other relations of which Eq. (5.7) is typical: C, = volume fraction of solids, D = pipe diameter, d = particle diameter, s = ratio of densities of solid and liquid, g = acceleration of gravity, 32.2 ft/sec’, or consistent units. The numerical coefficient is due to Hayden and Stelson (1971). Another criterion for selection of a flow rate is based on considerations of the extent of sedimentation of particles of various sizes under flow conditions. This relation is developed by Wasp, This equation is a modification by Hayden and Stelson (1971) of a series of earlier ones. The meanings of the symbols are Cv = volume fraction occupied by the solids in the slurry, d = particle diameter, D = pipe diameter, s = ratio of specific gravities of solid and liquid. (5.2) (5.3) (5.7)
- 89. 70 T R A N S F E R O F S O L I D S EXAMPLE 5.1 Conditions of a Coal Slurry Pipeline Data of a pulverized coal slurry are c, = 0.4, D = 0.333 ft, f= 0.0045 (Blasius’ eq. at N, = 105), s = 1.5. Mesh size 24 48 100 Mixture dhn) 0.707 0.297 0.125 0.321 Weight fraction 0.1 0.8 0.1 1 u, Wsec) 0.164 0.050 0.010 0.0574 The terminal velocities are read off Figure 5.1, and the values of the mixture are weight averages. The following results are found with the indicated equations: item Eq. 24 48 1 0 0 M i x t u r e “C 5.1 7.94 5.45 3.02 k 5.6 5.8 20.6 1.36 6.27 2.89 9.38 1.25 3.39 WIAPL 5.11 1.539 ApStAp, 5.13 1.296 Eq. (5.1): u;= 34.6(0.4)(0.333)dm =3232, Eq. (5.6): u=8.41u,=125u qcjYom5 ” 4 32.2(1.5 - 1) d,, _ O.O704d,, = 1.5391, Eq. (5.13): s= 1 + 0.272(0.4) 0.0045(0.333)32.2(0.5) ’ 3 L (0.0574)2(3.39) 1 = 1.296. 100 6Ll 4 0 10 6 fii 4 ” E 0 2 i 5 0 1 5 F 0 6 0 4 c u-l 0 2 01 0 06 0 0 4 0 0 2 0 0 1 0 006 0 0 0 4 0 0 0 2 0 001 01 Sphere diameter, cm Figure 5.1. Settling velocities of spheres as a function of the ratio ot densities of the two phases. Stokes law applies at diameters below approximately 0.01 cm (based 011 a chart of La&e et al., Chemical Engineering Handbook, McGraw-Hill, New York, 1984, p. 5.67). With coal of sp gr = 1.5, a slurry of 40 ~01% has a sp gr = 1.2. Accordingly the rule, AP,/AP, = sp gr, is not confirmed accurately by these results. For particles of one size, Eqs. (5.7) and (5.8) combine to APs/APr = 1 + ~OOC,[(U,D/U~)~~‘~~, consistent units. (5.10) The drag coefficient is The pressure drop relation at the critical velocity given by Eq. (5.1) is found by substitution into Eq. (5.7) with the result CD = 1.333gd(s - 1)/u:. (5.8) A&/APL = 1 + $$[(l/uJvgd(s - 1)/C,]‘.3. I, (5.11) For mixtures, a number of rules has been proposed for evaluating the drag coefficient, of which a weighted average seems to be favored, With Eq. (5.10) the result is APJAP, = 1 + 1/Co,.3. (5.12) lG=cw*vG (5.9) With the velocity from Eq. (5.6), Eq. (5.7) becomes where the wi are the weight fractions of particles with diameters di. A&/APL = 1 + 0.272C,[fgD(s - 1)/~:6]‘.~ (5.13)
- 90. 5.2. PNEUMATIC CONVEYING 71 IO’ IO0 fii 07 a” >: IO -1 .E g ii .- > 10-Z 10-3 I F 0-2 I I I r I 1 I r slope = - 0.51 Shear rate, I/set (a) IO’ IO2 Shear rate, I/set (b) IO3 Figure 5.2. Non-Newtonian behavior of suspensions: (a) viscosity as a function of shear rate, 0.4 wt % polyacrylamide in water at room temperature; (b) shear stress as a function of shear rate for suspensions of TiO, at the indicated ~01% in a 47.1 wt % sucrose solution whose viscosity is 0.017 Pa set (Denn, Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1980). and, for one-sized particles, 5.2. PNEUMATIC CONVEYING APs/APL = 1+ 0.394Cu[cfD/u,)~&7j72]‘~3. (5.14) These several pressure drop relations hardly appear consistent, and the numerical results of Example 5.1 based on them are only roughly in agreement. From statements in the literature, it appears that existing slurry lines were designed on the basis of some direct pilot plant studies. Nonsettling slurries are formed with fine particles or plastics or fibers. Although their essentially homogeneous nature would appear to make their flow behavior simpler than that of settling slurries, they often possess non-Newtonian characteristics which complicate their flow patterns. In Newtonian flow, the shear stress is proportional to the shear strain, Granular solids of free-flowing natures may be conveyed through ducts in any direction with high velocity air streams. In the normal plant, such lines may be several hundred feet long, but dusty materials such as fly ash and cement have been moved over a mile in this way. Materials that are being air-veyed include chemicals, plastic pellets, grains, and powders of all kinds. The transfer of catalysts between regenerator and reactor under fluidized conditions is a common operation. Stoess (1983) has a list of recommendations for about 150 different materials, of which Table 5.1 is a selection. Basic equipment arrangements are represented in Figure 5.3. The performance of pneumatic conveyors is sensitive to several characteristics of the solids, of which the most pertinent ones are stress = ~(strain), 1. bulk density, as poured and as aerated, 2. true density, but in other cases the relation between these two quantities is more complex. Several classes of non-Newtonian behavior are recognized for suspensions. Pseudoplastic or power-law behavior is represented by stress = k(strain)“, n<l, where k is called the consistency index. Plastic or Bingham behavior is represented by 3. coefficient of sliding friction ( = tangent of the angle of repose), 4. particle size distribution, 5. particle roughness and shape, 6. moisture content and hygroscopicity, and 7. characteristics such as friability, abrasiveness, flammability, etc. Sulfur, for example, builds up an electrostatic charge and may introduce explosive risks. stress = k, + ~(strain), where n is called the plastic viscosity. Data for some suspensions are given on Figure 5.2. The constants of such equations must be found experimentally over a range of conditions for each particular case, and related to the friction factor with which pressure drops and power requirements can be evaluated. The topic of nonsettling slurries is treated by Bain and Bonnington (1970) and Clift (1980). Friction factors of power-law systems are treated by Dodge and Metzner (1959) and of fiber suspensions by Bobkowitz and Gauvin (1967). In comparison with mechanical conveyors, pneumatic types must be designed with greater care. They demand more power input per unit weight transferred, but their cost may be less for complicated paths, when exposure to the atmosphere is undesirable and when operator safety is a problem. Although in the final analysis the design and operation of pneumatic conveyors demands the attention of experienced engineers, a design for orientation purposes can be made by the inexpert on the basis of general knowledge and rules of thumb that appear in the literature. An article by Solt (1980) is devoted entirely to preventive trouble- shooting. Some basic design features are the avoidance of sharp bends, a minimum of line fittings, provision for cleanout, and possibly electrical grounding. In many cases equipment suppliers may wish to do pilot plant work before making final recommendations. Figure
- 91. 72 TRANSFER OF SOLIDS TABLE 5.1. Flow Rates and Power Requirements of Vacuum and Low Pressure Pneumatic Conveying System?? Vacuum SystemCB-9 via) Low Pressure System(6-12 psid Slaterial Collve)ing Ihtallce vt iuo ft ii0 ft 250 ft 400 ft per - ‘clocit CU f t S a t . tl,,/i’ Sat. 11,,{,11’ Sdt. hplf- SJt h,3~1‘ rtjsec Comeying Distance 100 ft 250 ft 400 ft +ssure ‘elocit! t:actor S a t . bp/r S a t . bpll‘ S a t bplr (ft/sec) Alum 50 3.6 4.5 3.9 5.0 4.3 5 7 4.7 6.3 Alumina 60 2.4 4.0 2.8 4.7 3.4 5.7 4.0 6.4 Carbonate, 25-30 3.1 -1 2 3.t 5.0 3.9 5.5 4.2 6 U calcium Cellulose acetate 22 3.2 4.7 3.5 5.1 3.8 5.7 4.1 6.U Clay. air floated 30 3.3 4.5 3.5 5.0 3.9 5.5 4.2 6.0 Clay, water 40-50 3.5 5.0 3.8 5.6 4.2 6.5 4.5 7.2 washed Clay. spray dried 60 3.4 4.7 3.6 5.2 4.0 6.2 4.4 7.1 Coffee beans Corn, shelled Flour. wheat Grits, corn Lime, pebble Lime, hydrated hlalt Oats Phosphate, trisodium Polyethylene pellets Rubber pellets Salt cake Soda ash, hght Soft feeds Starch. pulverized Sugar, granulated Wheat Wood flour 4 2 1.2 2.0 1.6 3.0 2.1 3.5 2.4 4.2 4 5 1 9 2.5 2.1 2.9 2.4 3.6 2.8 4.3 4 0 1.5 3 0 17 3.3 2 0 3.7 2.5 4 4 3 3 1.7 2 5 2.2 3U 2.9 4.0 3.5 4.8 5 6 2.b 3 8 3.0 4.0 3.4 4.7 3.9 5.4 30 2.1 3.3 2.4 3.9 2.8 4.7 3.4 60 2 8 1.8 2.5 2.0 2.8 2.3 3.4 2.8 4.2 2 5 2.3 3.0 2.6 3.5 3.0 4.4 3.4 5.2 65 3.1 4.2 3.6 5.0 3.9 5.5 4.2 6.0 3 0 I.2 2.0 1.6 i.0 2.1 3.5 2.4 -I2 -10 2.9 4.2 3.5 5.0 4.0 6.0 4.5 7.2 90 4.0 6.5 4.2 6.8 4.6 i.5 5.0 8.5 35 3.1 4.2 3.6 5 0 3.9 5.5 4.2 60 20-40 3.0 4.2 3 1 4.5 3.7 5.0 4.2 j 5 40 1.7 3.0 2.0 3.4 2.6 4.0 3.4 5 U 50 3.0 3.7 3 2 4.0 i i 5.2 3 9 6.U 4 8 1.9 2.5 2.1 2.9 2.4 3.6 2.8 4.3 12-20 2.5 3 5 2 8 4.0 3.4 4.9 4.4 6.5 4.0 50 3.5 3.0 3 4.3 5.0 5.0 2.5 3.5 0.X 1.5 1.3 2.4 1.6 2.9 5.0 1.3 2.3 I.6 2.8 1.8 3.3 40 0.6 1.x 0.8 2.2 0.9 2.6 5.0 0.x 15 1.1 2.0 1.3 2.5 5.0 1.0 1.8. I.4 2.6 I.6 3.1 4 5 l.4 2.5 1.8 3.3 1.9 3.6 5 0 0.55 I.2 0.9 2.1 1.1 2.5 7 0 5.0 2.9 3.9 3.5 4.5 4.0 5.1 b3 5.0 1.4 2.5 1.4 3.3 1.9 3.6 65 3.8 I.3 2.5 1.7 3.1 1.9 3.7 7 0 3 0 0.s I.’ 1.1 2.4 l.5 3.0 5 5 5.0 5 0 1.6 2.7 2.0 3.4 2.2 3.8 65 1.1 2.4 I.6 3.4 1.9 3.9 6 0 I.4 2.5 1.8 3.3 2.0 3.6 6 5 1.4 2.8 1.7 3.4 1.9 3.6 I.5 2.7 1.8 3.3 1.9 3.6 1.6 3.0 1.9 3.9 2.1 4.4 1.5 2.8 1.8 3.7 2.0 4.3 0.6 l.,? 0.9 2.1 1.1 2.5 0.9 1.5 1.1 2.2 1.3 2.6 0.7 I 8 0.9 2 2 1.1 2.7 14 2.2 I.6 3.1 1.7 3.6 60 0.9 1.5 1.1 2.1 1.3 2.6 5 5 5 5 E 5 5 4 5 5 5 3 5 7 0 7 0 4 0 5 5 5 5 7 5 “HP/ton = (pressure factor)(hp/T)(sat.). The units of sat. are standard tuft of air/lb of solid transferred), and those of hp/T are horsepower/(tons/hr of solid transferred). (Stoess, 1983). 5.4 shows a typical pilot plant arrangement. A preliminary design procedure is given by Raymus (1984). Many details of design and operation are given in books by Stoess (1983) and Kraus (1980) and in articles by Gerchow (1980), and Perkins and Wood (1974). Some of that information will be restated here. Pressure drop and power requirements can be figured largely on the basis of general knowledge. E Q U I P M E N T The basic equipment consists of a solids feeding device, the transfer line proper, a receiver, a solid-air separator, and either a blower at the inlet or a vacuum pump at the receiver. Four common kinds of arrangements are shown on Figure 5.3. Vacuum systems are favored for shorter distances and when conveying from several sources to one destination. Appropriate switching valves make it possible to service several sources and destinations with either a vacuum or pressure system. Normally the vacuum system is favored for single destinations and the pressure for several destinations or over long distances. Figure 5.3(b) shows a rotary valve feeder and Figure 5.3(c) a Venturi feeder which has a particularly gentle action suitable for friable materials. Figure 5.3(d) utilizes a fan to suck the solids from a source and to deliver them under positive pressure. Friable materials also may be handled effectively by the equipment of Figure 5.5 in which alternate pulses of granular material and air are transported. Typical auxiliary equipment is shown on Figure 5.6. The most used blower in pneumatic conveying is the rotary positive dis- placement type; they can achieve vacua 6-8psi below atmos- pheric or positive pressures up to 15psig at efficiencies of about 65%. Axial positive displacement blowers also are used, as well as centrifugals for large capacities. Rotary feeders of many proprietary designs are available; Stoess (1983) and Kraus (1980) illustrate several types. Receivers may be equipped with fabric filters to prevent escape of fine particles; a dacron fabric suitable for up to 275°F is popular. Cyclone receivers are used primarily for entirely nondusting services or ahead of a filter. A two-stage design is shown in Figure 5.6(d). Typical dimensions are cited by Stoess (1983), for example: line diameter (in.) 3 5 8 primary diameter Wt) 3.5 4.5 6.75 secondary diameter (ft) 2.75 3.5 5.0
- 92. 5.2. PNEUMATIC CONVEYING 73 & Pickup (a) Vent MateJial In Filter Receiver LJI”“Y~l and Motor Rotary Valve yq-p) L , itch Rotary Valve Collector ifi3 Venturi I c Process Machine Collector 3 3 Figure 5.3. Basic equipment arrangements of pneumatic conveying systems. (a) Vacuum system with several sources and one destination, multiple pickup; (b) pressure system with rotary valve feeder, one source and several destinations, multiple discharge; (c) pressure system with Venturi feed for friable materials; (d) pull-push system in which the fan both picks up the solids and delivers them [ufier F. J. Gerchow, Chem. Eng. (17 Feb. 1975, p. Ss)]. Piping usually is standard steel, Schedule 40 for 3-7 in. IPS and Schedule 30 for 8-12 in. IPS. In order to minimize pressure loss and abrasion, bends are made long radius, usually with radii equal to 12 times the nominal pipe size, with a maximum of 8ft. Special reinforcing may be needed for abrasive conditions. feeders, positive pressure systems are limited to about 12 psig. Other feeding arrangements may be made for long distance transfer with 90-125psig air. The dense phase pulse system of Figure 5.4 may operate at lo-30 psig. Linear velocities, carrying capacity as tuft of free air per lb of solid and power input as HP/tons per hour (tph) are listed in Table OPERATING CONDITIONS 5.1 as a general guide for a number of substances. These data are for 4-, S-, and 6-in. lines; for 8-in. lines, both Sat. and HP/tph are Vacuum systems usually operate with at most a 6 psi differential; at reduced by 15%, and for lo-in. by 25%. Roughly, air velocities in lower pressures the carrying power suffers. With rotary air lock low positive pressure systems are 2OOOft/min for light materials,
- 93. TRANSFER OF SOLIDS Hose Connec Inns W!th Qwck Couplings - Medium L o o p - - - Long LOOP ll Figure 5.4. Sketch of pilot plant arrangement for testing pneumatic conveying under positive pressure (Kruu.s, Pneumatic Conveying of Bulk Materials, McGraw-Hill, New York, 1980). 3000-4000 ft/min for medium densities such as those of grains, and XJOOft/min and above for dense materials such as fly ash and cement; all of these velocities are of free air, at atmospheric pressure. Another set of rules for air velocity as a function of line length Material inlet To receiving hopper Figure 5.5. Concept of dense phase transfer of friable materials, by intermittent injection of material and air pulses, air pressures normally lo-30 psig and up to 90 psig (Sturteuant Engineering Co., Boston, MA). and bulk density is due to Gerchow (1980) and is ft/min Line length w 55 Ib/cuft 55-85 85-115 200 4000 5000 6000 500 5000 6000 7000 1000 6000 7000 8000 Conveying capacity expressed as ~01% of solids in the stream usually is well under 5 ~01%. From Table 5.1, for example, it is about 1.5% for alumina and 6.0% for polystyrene pellets, figured at atmospheric pressure; at 12psig these percentages will be roughly doubled, and at subatmospheric pressures they will be lower. POWER CONSUMPTION AND PRESSURE DROP The power consumption is made up of the work of compression of the air and the frictional losses due to the flows of air and solid through the line. The work of compression of air at a flow rate ML and C,/C, = 1.4 is given by WC = 3.5(53.3)(7- + 460)m:[(Pz/q)0~2”57 - l] (ft lbf/sec) (5.15) with the flow rate in lb/set. Frictional losses are evaluated separately for the air and the solid. To each of these, contributions are made by the line itself, the elbows and other fittings, and the receiving equipment. It is conservative to assume that the linear velocities of the air and solid are the same. Since the air flow normally is at a high Reynolds number, the friction factor may be taken constant at f, = 0.015. Accordingly the frictional power loss of the air is given by w,=~P,m:/p,=(u2/2g)[1+2n,+4n,+(0.015/D)(L+~Li)]m: (ft lbf/sec). (5.16) The unity in the bracket accounts for the entrance loss, n, is the number of cyclones, nr is the number of filters, L is the line length, and Li is the equivalent length of an elbow or fitting. For long radius bends one rule is that the equivalent length is 1.6 times the actual length of the bend. Another rule is that the long bend radius is 12 times the nominal size of the pipe. Accordingly, Li = 1.6(nRi/2) = 2.5R, = 2.5D;ft, with 0:’ in inches. (5.17) The value of g is 32.2 ft lb m/(lbf sec2). The work being done on the solid at the rate of ml lb/set is made up of the kinetic gain at the entrance (w2), the lift (ws) through an elevation AZ, friction in the line (wJ, and friction in the elbow (ws). Accordingly, w, = $ ml (ft lbf/sec) . (5.18) The lift work is 8 w,=Az-mmj=Azmj 8, (ft lbf/sec). (5.19) The coefficient of sliding friction f, of the solid equals the tangent of the angle of repose. For most substances this angle is 30-45” and
- 94. 5.2. PNEUMATIC CONVEYING 75 Air Thimble t Secondary cyclone Air and material - Inner skirt Primary cyclone S e c o n d a r y discharge lock Primary discharge lock Y 1 I Dust t Material Figure 5.6. Components of pneumatic conveying systems. (a) Rotary positive displacement blower for pressure or vacuum. (b) A rotary airlock feeder for fine materials (Detroit Stoker Co.). (c) A four-compartment receiver-filter (Fuller Co., Bethlehem, PA). (d) A two-stage cyclone receiver. (e) The Fuller-Kinyon pump for cement and other fine powders. Powder is fed into the aeration chamber with a screw and is fluidized with compressed air (Fuller Co., Bethlehem, PA).
- 95. 76 TRANSFER OF SOLIDS the value off, is 0.58-1.00. The sliding friction in the line is w, = f, Lrni (ft lbf/sec) , (5.20) where L is the line length. Friction in the curved elbows is enhanced because of centrifugal force so that w, =h$ (y)m: = O.O488f,u*mi (ft lbf/sec) (5.21) The total frictional power is wf=w1+w*+w3+wq+wg, and the total power consumption is (5.22) w = 5$;.$) W/(ton/hr)l, (5.23) where 17 is the blower efficiency. Pressure drop in the line is obtained from the frictional power, the total flow rate, and the density of the mixture: AP= Wf 144(mA + ml) pm (Psi). (5.24) The specific air rate, or saturation, is saturation = 0.7854(60)0* (cuft/min of air)/(lb/min of solid)], (5.25) where the velocity of the air is evaluated at atmospheric pressure. Example 5.2 makes the calculations described here for power and pressure drop, and compares the result with the guidelines of Table 5.1. 5.3. MECHANICAL CONVEYORS AND ELEVATORS Granular solids are transported mechanically by being pushed along or dragged along or carried. Movement may be horizontal or vertical or both. In the process plant distances may be under a hundred feet or several hundred feet. Distances of several miles may be covered by belts servicing construction sites or mines or power plants. Capacities range up to several hundred tons/hr. The principal kinds of mechanical conveyors are illustrated in Figures 5.7-5.13 and will be described. Many construction features of these machines are arbitrary. Thus manufacturers’ catalogs are the ultimate source of information about suitability for particular services, sizes, capacities, power requirements and auxiliaries, Much of the equipment has been made in essentially the present form for about 100 years by a number of manufacturers so that a body of standard practice has developed. PROPERTIES OF MATERIALS HANDLED BELT CONVEYORS The physical properties of granular materials that bear particularly on their conveying characteristics include size distribution, true and bulk densities, and angle of repose or coefficient of sliding friction, but other less precisely measured or described properties are also of concern. A list of pertinent properties appears in Table 5.2. The elaborate classification given there is applied to about 500 materials in the FMC Corporation Catalog 100 (1983, pp. B.27-B.35) but is too extensive for reproduction here. For each material the table also identifies the most suitable design of screw conveyor of this These are high capacity, relatively low power units for primarily horizontal travel and small inclines. The maximum allowable inclination usually is 5-15” less than the angle of repose; it is shown as “recommended maximum inclination” in Table 5.3 for some substances, and is the effective angle of repose under moving conditions. The majority of conveyor belts are constructed of fabric, rubber, and wire beads similarly to automobile tires, but they are made also of wire screen or even sheet metal for high temperature company’s manufacture and a factor for determining the power requirement. An abbreviated table of about 150 substances appears in the Chemical Engineers Handbook (1984, p. 7.5). Hudson (1954, pp. 6-9), describes the characteristics of about 100 substances in relation to their behavior in conveyors. Table 5.3 lists bulk densities, angles of respose at rest, and allowable angles of inclination which are angles of repose when a conveyor is in motion; references to more extensive listings of such data are given in this table. The angle of repose is a measure of the incline at which conveyors such as screws or belts can carry the material. The tangent of the angle of repose is the coefficient of sliding friction. This property is a factor in the power needed to transfer the material by pushing or dragging as in pneumatic, screw, flight, and Redler equipment. Special provisions need to be made for materials that tend to form bridges; Figure 5.13(a) is an example of a method of breaking up bridges in a storage bin so as to ensure smooth flow out. Materials that tend to pack need to be fluffed up as they are pushed along by a screw; adjustable paddles as in Figure 5.7(d) may be sufficient. SCREW CONVEYORS These were invented by Archimedes and assumed essentially their present commercial form a hundred years or so ago. Although the equipment is simple in concept and relatively inexpensive, a body of experience has accumulated whereby the loading, speed, diameter, and length can be tailored to the characteristics of the materials to be handled. Table 5.4, for example, recognizes four classes of materials, ranging from light, freeflowing, and nonabrasive materials such as grains, to those that are abrasive and have poor flowability such as bauxite, cinders, and sand. Only a portion of the available data are reproduced in this table. Lengths of screw conveyors usually are limited to less than about 150 ft; when the conveying distance is greater than this, a belt or some other kind of machine should be chosen. The limitation of length is due to structural strength of the shaft and coupling. It is expressed in terms of the maximum torque that is allowable. Formulas for torque and power of screw conveyors are given in Table 5.4 and are applied to selection of a conveyor in Example 5.3. Several designs of screws are shown in Figure 5.7. The basic design is one in which the pitch equals the diameter. Closer spacing is needed for carrying up steep inclines, and in fact very fine pitch screws operating at the relatively high speeds of 350 rpm are used to convey vertically. The capacity of a standard pitch screws drops off sharply with the inclination, for example: Angle (degrees) Percent of capacity <8 20 30 45 100 55 30 0 Allowable loadings as a percentage of the vertical cross section depend on the kind of material being processed; examples are shown in Table 5.4.
- 96. 5.3. MECHANICAL CONVEYORS AND ELEVATORS 77 EXAMPLE 5.2 Size aud Power Requirement of a Pneumatic Transfer Line A pneumatic transfer line has 300 ft of straight pipe, two long radius elbows, and a lift of 5Oft. A two-stage cyclone is at the receiving end. Solid with a density of 125 Ib/cuft is at the rate of 10 tons/hr and the free air is at 5000 ft/min. Inlet condition is 27 psia and 100°F. Investigate the relation btween line diameter and power requirement. On a first pass, the effect of pressure loss on the density of the air will be neglected. Mass flow rate of solid: ml = 20,000/3600 = 5.56 Ib/sec. Mass flow rate of air: rn: = ~~(0.075)0’ = 4.91D*Ib/sec. Density of air: on = 0.075 & = 0.138 Ib/cuft. ( .> Density of mixture: Pm = (4 + 4) mLlp, + dl~, (mi + 5.56) =mL/0.138 + 5.56’125 Linear velocity of air at inlet: u =z + =45.37fps. ( > Assume air and solid velocities equal. Elbow radius = 120. Elbow equivalent length, L, = 1.6(n’2)(120) = 30.20 Power for compression from 14.7 psia and 560 R to 27 psia, k/(/c - 1) = 3.5, w, = 3.5RT,[(P,/P,)“~2857 - l]mi = 3.5(53.3)(560)[(27/14.7)“~2857 - 1]4.910’ = 973050’ ft lbf/sec. Frictional contribution of air w1 =$ [5 + (0.015/0)(300 + 2(30.2)D]mi = [(45.4)2’64.4][5.9 + (4.5’D)](4.91DZ) = 157.102(5.9 + 4.5’0) For the solid, take the coefficient of sliding friction to be f, = 1. Power loss is made up of four contributions. Assume no slip velocity; w,=w*+w,+w,+w, = [u2/2g + AZ +f,L + 2(0.0488)f,u2]mj = 5.56[45.4”64.4 + 50 + 300 + 2(0.0488)45.4’] = 3242.5ft lbf/sec. Total friction power: wf = 3242.5 + 157.10’(5.9 + 4.5/D). Pressure drop: AP- Wf I Pm psi 144(m: + m,) Fan power at 9 = 0.5: p = 550;.$0) = sHP/tph, saturation = 5000(n’4)D2 20, ooo/60 = 11.78D2SCFM/(lb/min). 1 PS D (RI In: pm w, w, 3 0.2557 0.3210 2.4808 6362 3484 4 0.3356 0.5530 1.5087 10,959 3584 5 0.4206 0.8686 1.0142 17,214 3704 6 0.5054 1.2542 0.7461 24,855 3837 3 10.2 3.58 0.77 4 6.1 5.29 1.33 5 4.1 7.60 2.08 6 2.9 1 0 . 4 4 3.00 From Table 5.1, data for pebble lime are sat = 1.7 SCFM/(lb/min) power = 3.0 HP/TPH and for soda ash: sat = 1.9 SCFM/(lb/min) power = 3.4 HP/TPH. The calculated values for a 4in. line are closest to the recom- mendations of the table. services. A related design is the apron conveyor with overlapping For bulk materials, belts are troughed at angles of 20-45”. Loading pans of various shapes and sizes (Fig. 5.8), used primarily for short of a belt may be accomplished by shovelling or directly from travel at elevated temperatures. With pivoted deep pans they are overhead storage or by one of the methods shown on Figure 5.9. also effective elevators. Discharge is by throwing over the end of the run or at intermediate Flat belts are used chiefly for moving large objects and cartons. points with plows.
- 97. 78 TRANSFER OF SOLIDS TABLE 5.2. Codes for Characteristics of Granular Materialsa Sm Flowablkty Abrasweness MlSCdl~“~OUS Properties O r Hazards Material Characteristics Included Bulk Derwty, Loose No. 200 Sieve (.W29”) And Under Very Fme No 100 Slew? 1.0059”) And Under No. 40 Sewf.016”) And Under Fine NO 6 Slew 1.132”) And Under Granular %“A”d Under Granular 3”And Under I’)Lump~ Over 3”To Se Special X=Actual Maximum Sue Irregular Stringy, Fibrous. Cylmdncal. Slabs. etc. Very Free Flowing-Flow Funchon > to t Free Flowmg- Flow Funchon _‘4 But x 10 2 AverageFlowablllhl-FlowFunctlo” 2 But~.4 3 Sluggish-Flow Funchon < 2 4 Mildly Abrasive -Index 1-17 5 Moderately Abraswe-Index 1667 6 Extremely Abraswe- Index 66-416 7 coda Desipnstion ACUil lbslft’ Builds Up and Hardens F Generates Stabc Electruty G Decomposes- Deteriorates m Storage H Flammablltty J Becomes Plasbc or Tends to Soften K Very Dusty L Aerates and Becomes Fluid M Explosiveness Stickmess-Adhesion PI Contamlnable. Alfectmg Use Degradable, Affecting Use i Gwes Off Harmful or TOXIC Gas or Fumes I7 Highly Corrosive S f&Idly Corrosive T Hygroscopic U Interlocks. Mats or Agglomerates V 011% Present W Packs Under Pressure X Very Light and Fluffy-May Be Windswept Y Elevated Temperature z ‘Example: A fine 100 mesh material with an average density of 50 Ib/cuft that has average flowability and is moderately abrasive would have a code designation 50A,,036; if it were dusty and mildly corrosive, it would be 50A,,,36LT. (FMC Corp., Materials Handling Division, Homer City, PA, 1963). Power is required to run the empty conveyor and to carry the load horizontally and vertically. Table 5.5 gives the equations, and they are applied in Example 5.4. Squirrel-cage ac induction motors are commonly used as drives. Two- and four-speed motors are available. Mechanical efficiencies of speed reducing couplings between motor and conveyor range from 95 to 50%. Details of idlers, belt trippers, cleaners, tension maintaining devices, struc- tures, etc. must be consulted in manufacturers’ catalogs. The selec- tion of belt for strength and resistance to abrasion, temperature, and the weather also is a topic for specialists. BUCKET ELEVATORS AND CARRIERS Bucket elevators and carriers are endless chains to which are attached buckets for transporting granular materials along vertical, inclined or horizontal paths. Figure 5.10 shows two basic types: spaced buckets that are far apart and continuous which overlap. Spaced buckets self-load by digging the material out of the boot and are operated at speeds of 20&300fpm; they are discharged centrifugally. Continuous buckets operate at lower speeds, and are used for friable materials and those that would be difficult to pick up in the boot; they are fed directly from a loading chute and are discharged by gravity. Bucket carriers are essentially forms of pan conveyors; they may be used instead of belt conveyors for shorter distances and when they can be made of materials that are Alum, fine Alumina Aluminum sulfate Ammonium chloride Ammonium nitrate Ammonium sulfate Asbestos shred Ashes, coal, dry, fin. max Ashes, coal, wet, 4 in. max Ashes, fly Asphalt, i in. max Baking powder Barium carbonate Bauxite, ground Bentonite, 100 mesh max Bicarbonate of soda Borax, ; in. Borax, fine Boric acid, fine Calcium acetate Carbon, activated, dry, fine Carbon black, pelleted Casein Cement, Portland Cement, Portland, aerated Cement clinker Charcoal Chips, paper mill Clay, calcined Clay, dry, fine Clay, dry, lumpy Coal, anthracite, i in. max Coal, bituminous, 50 mesh max Coal, bituminous ’ in. max ,* Coal, lignite Coke breeze ’ in. max C o p p e r sulfZ Cottonseed, dry, delinted Cottonseed, dry, not delinted Cottonseed meal Cryolite dust Diatomaceous earth Dicalcium phosphate Disodium phosphate Earth, as excavated, dry Earth, wet, containing clay Epsom salts Feldspar, 1 in. screenings Ferrous sulfate Flour, wheat Fullers earth, dry Fullers earth, oily Grain, distillery, spen, dry Graphite, flake Grass seed Gravel, bank run Gravel, dry, sharp Gravel, pebbles Gypsum dust, aerated Gypsum, i in. screenings Iron oxide pigment Kaolin talc, 100 mesh Lactose Lead arsenate 45-50 50-65 5 4 45-52 4 5 45-58 20-25 35-40 45-50 40-45 45 40-55 7 2 6 8 50-60 40-50 55-60 45-55 5 5 125 8-20 20-25 3 6 8 4 60-75 75-95 18-25 20-25 80-100 100-120 60-75 6 0 50-54 43-50 40-45 25-35 75-85 3 5 18-25 35-40 75-90 11-14 40-50 25-31 70-80 100-110 40-50 70-85 60-75 35-40 30-35 60-65 3 0 4 0 10-12 go- 100 go-100 go-100 60-70 70-80 2 5 42-56 3 2 7 2 TABLE 5.3. Bulk Densities, Angles of Repose, and Allowable Angles of Inclination Material Recom- Average Angle of m e n d e d R e p o s e Maximum ,E:%, (degrees) Inclination 30-45 2 2 32 10-12 1 7 4 0 20-25 5 0 23-27 4 2 20-25 3 5 18 2 0 20-22 3 9 20-23 30-40 18-20 3 5 20-25 35 20-22 3 5 18-20 3 5 18 4 5 2 4 4 0 2 2 3 8 2 2 30-45 20-22 31 17 2 9 1 6 3 5 19 3 5 2 2 3 5 2 0 4 5 2 3 3 8 18 2 3 3 8 3 0 4 2 4 0 4 0 4 5 2 0 15-17 12 2 3 21 2 5 2 3
- 98. TABLE 5.3-(continued) Lead oxides 60-l 50 Lime, A in. max 60-65 Lime, hydrated, i in. max 4 0 Lime, hydrated, pulverized 32-40 Limestone, crushed 85-90 Limestone dust 80-85 Lithopone 45-50 Magnesium chloride 3 3 Magnesium sulfate 7 0 Milk, dry powder 3 6 Phosphate, triple super, fertilizer 50-55 Phosphate rock, pulverized 6 0 Polystyrene beads 4 0 Potassium nitrate 7 6 Rubber, pelletized 50-55 Salt, common, coarse 40-55 Salt, dry, fine 70-80 Salt cake, dry, coarse 8 5 Salt cake, dry, pulverized 60-85 Saltpeter 8 0 Sand, bank, damp 100-130 Sand, bank, dry 90-l 10 Sawdust 10-13 Shale, crushed 85-90 Soap chips 15-2’=. Soap powder 20-2!, Soda ash briquetts 5 0 Soda ash, heavy 55-65 Soda ash, light 20-35 Sodium bicarbonate 41 Sodium nitrate 70-80 Starch 25-50 Sugar, granulated 50-55 Sugar, powdered 50-60 Trisodium phosphate, pulverized 5 0 Wood chips 1 O-30 Zinc oxide, heavy 30-35 43 40 4 2 3 8 2 3 21 2 2 18 2 0 4 5 3 0 4 0 2 5 3 5 2 2 2 5 1 1 3 6 21 45 20-22 3 5 16-18 3 6 2 2 3 9 2 2 3 0 1 8 2 2 7 3 2 1 9 3 7 2 2 4 2 2 3 2 4 1 1 2 4 12 4 0 2 5 2 7 Zinc oxide, light 10-15 Other tables of these properties appear in these publications: 1. Conveyor Equipment Manufacturers Association, Belt Conveyors for Bulk Materials, 1966, 25-33. pp. 2. Stephens-Adamson Mfg. Co. Catalog 66, 1964, pp. 634-636. 3. FMC Corporation Material Handling Equipment Division Catalog 100, 1983, pp. B.27-B.35. 4. Perry’s Chemical Engineers Handbook, 1984, p. 7.5. TABLE 5.4. Sizing Data for Screw Conveyors’ (a) Diameter (rpm and cuft/hr) Maximum Capadtia. Cubic M~Xirnum Cspaitia. Cubic Feet Per Hour Recommended Feet Per Hour “I+ R .M. ‘Example 5.3 utilizes these data. (Stephens-Adamson Co. Catalog, 1954, p. 66). 5.3. MECHANICAL CONVEYORS AND ELEVATORS 79 TABLE 5.4(a)-(continued) (b) Characteristics of Some Materials (A Selection From the Original Table) Yaeriala Ahlfn meal.. . . . . . . . . . . . . . . . . . . . . . . Alum. lumpy . . . . . . . . . . . . . . . . . . . . . . . Alum, pulverized. *Alumma. ............................................ Alumln~m. hydrate ~rngta~~b$a. .................................................. lAshea.dry . . . . . . . . . . . . . . . . . . . . . . . . . Ap& wlmlm~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bd¶&+der . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tBaux.te. crushed . . . . . . . . . . . . . . . . . . . . Fkans. eutor . . . . . . . . . . . . . . . . . . . . . . . Bans. navy, dry . . . . . . . . . . . . . . . . . . . Bentonite. . . . . . . . . . . . . . . . . . . . . . . . . . ‘Bones. crudled . . . . . . . . . . . . . . . . . . . . . *Bon en, 2rantited or wound. . . . . . . . . *Bone black. . . . . . . . . . . . . . . . . . . . . . . . . Bonechpr . . . . . . . . . . . . . . . . . . . . . . . . . . amemed......................... Borax, powdered. .................. Boric add powder. . . . . . . . . . . . . . . . . . B= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (c) Factor Sin the Formula for Power P SEALfhU,STER Bearing :: I% II ‘x.1’ XIX :: ‘I I:’ 1:x :::: 11x 11x 11x ;I Babbitt. Bronze or Oil-Impreg- nsted Wood 2 1 ii ti 15.5 1 8 6 240 285 390 33 ir", 114 171 255 336 i%l 690 Hard Ir0n (d) Limits of Horsepower and Torque
- 99. 80 TRANSFER OF SOLIDS Shear (a) pin (d) (e) Figure 5.7. A screw conveyor assembly and some of the many kinds of screws in use. (a) Screw conveyor assembly with feed hopper and discharge chute. (b) Standard shape with pitch equal to the diameter, the paddles retard the forward movement and promote mixing. (c) Short pitch suited to transfer of material up inclines of as much as 20”. (d) Cut flight screws combine a moderate mixing action with forward movement, used for light, fine, granular or flaky materials. (e) Ribbon flights are suited to sticky, gummy or viscous substances. EXAMPLE 5.3 Sizing a Screw Conveyor Dense soda ash with bulk density 6Olb/cuft is to be conveyed a distance of 100 ft and elevated 12 ft. The material is class II-X with a factor F = 0.7. The bearings are self-lubricated bronze and the drive is V-belt with 7) = 0.93. The size, speed, and power will be selected for a rate of 15 tons/hr. Q = 15(2000)/60 = 500 cuft/hr. According to Table 5.4(a) this capacity can be accommodated by a 12 in. conveyor operating at o = (500/665)(50) = 37.6 rpm, say 40 rpm From Table 5.4(c) the bearing factor is s = 171. Accordingly, 1; = [171(40) + 0.7(500)(60)]100 + 0.51(12)(30,000)/106 = 2.97 HP motor HP = G@/q = 1.25(2.97)/0.93 = 3.99, torque = 63,000(2.97)/40 = 4678 in. lb. From Table 5.4(d) the limits for a 12 in. conveyor are 10.0 HP and 6300 in. lb so that the selection is adequate for the required service. A conveyor 137 ft long would have a shaft power of 4.00 HP and a torque of 6300 in. Ibs, which is the limit with a 2 in. coupling; a sturdier construction would be needed at greater lengths. For comparison, data of Table 5.5 show that a 14 in. troughed belt has an allowable speed of 267fpm at allowable inclination of 19” (from Table 5.3), and the capacity is 2.67(0.6)(38.4) = 61.5 tons/hr, far more than that of the screw conveyor.
- 100. 5.3. MECHANICAL CONVEYORS AND ELEVATORS 81 TABLE 5.5. Belt Conveyor Data” (a) Capacity (tons/hr) at lOOft/min, 100 Ib/cuft, and Indicated Slope Angle 45"Troughed Belt 33.OC 45.6C 6000 76.2C (a) 114.9 187.5 277.8 385.8 511.5 654.6 815.4 994.2 1190.1 Flat Belt loo ! zoo! 3o” 14 2.85 -t 669 14.01 21.42 16 387 9.18 19 05 29.1E 18 5.07 I I.88 2 4 . 9 0 38.1C 20 6.39 1506 31.50 48.24 24 9.57 22.47 47.10 72.Of 30 13.51 t-t 3645 76.32 116.8 36 122.86 53.73 112.6 172.3 74.37 155.9 2385 90.15 196.2 300.0 d-t 1257 263.4 4032 156.5 327.9 501.9 1 9 0 5 399.6 6111 2330 471.9 731 1 42 3165 48 39.84 t 54 53 49 60 6660 66 81.12 12 96 99 ‘Example 5.4 utilizes these data. Power = PhDrilOnta, + PV,,i,,, + P O.%%W (HP). w h e r e Phorirontel = (0.4 + L/300)( W/100), P,.,icaI = and P obtained from part (c), with H= lift (ft), L = horikntal trav:lm, and W = tons/hr. (a) From Conveyor Equipment Manufacturers Association, 1979; (b) from Stephens-Adamson Catalog 66, 1954; (c) from Hudson, 19541. (b) fHrH;irn Recommended Belt Speeds for Nondusting T I?clt Width. Inches Belt Speed in Feet per Minute I Gravel I ump Frr;;; stone t ih’ t w- 300 250 350 350 300 400 400 350 450 Slack t WOOd Coal t Sand p;y; - - - 4":"o 350 400 400 600 480 450 600 i.llmp stone or ore 250 .300 350 (e) Figure 5.8. Flight conveyors in which the material is scraped along, and apron conveyors in which the material is carried along in a closed path of interconnected pans. (a) Flight conveyor, in which the material is scraped along a trough with flights attached to a continuous chain. (b) Scraper-type of flight. (c) Roller flights. (d) Apron conveyor, in which the material is carried along in moving, overlapping pans. (e) Shallow and deep types of overlapping pans. -I-I- 400 450 500 I 500 600 700 650 550 800 600 600 800 - - - 650 600 A00 700 600 800 700 600 300 550 550 550 550 550 48 ii 66 72
- 101. 82 TRANSFER OF SOLIDS TABLE 5.5-(continued) (c) Power to Drive Empty Conveyor 18 16 I I Ml#lt,nlv Chnrt 60” or-1 1 ’ ’ I I I I I I 0 400 800 1200 1600 2000 2400 Length of Conveyor in Feet particularly suited to a process. Capacity and power data for bucket machines are given in Table 5.6. Flight and apron conveyors are illustrated in Figure 5.11. CONTINUOUS FLOW CONVEYOR ELEVATORS One design of a drag-type of machine is the Redler shown on Figure 5.12. They function because the friction against the flight is greater than that against the wall. Clearly they are versatile in being able to transfer material in any direction and have the often important merit of being entirely covered. Circular cross sections are available but usually they are square, from 3 to 30 in. on a side, and operate at speeds of 30-250 ft/min, depending on the material handled and the construction. Some data are shown in Table 5.7. Most dry granular materials such as wood chips, sugar, salt, and soda ash are handled very well in this kind of conveyor. More difficult to handle are very fine materials such as cement or those that tend to pack such as hot grains or abrasive materials such as sand or crushed stone. Power requirement is dependent on the coefficient of sliding friction. Factors for power calculations of a few substances are shown in Table 5.7. The closed-belt (zipper) conveyor of Figure 5.13 is a carrier that is not limited by fineness or packing properties or abrasiveness. Of course, it goes in any direction. It is made in a nominal 4-in. size, with a capacity rating by the manufacturer of O.O7cuft/ft of travel. The power requirement compares favorably with that of open belt conveyors, so that it is appreciably less than that of other types. The formula is HP = O.OOl[(L,/30 + 5)~ + (L,/16 + 2L,)T], (5.26) where u = ft/min, T = tons/hr, L, = total belt length (ft), L, = length of loaded horizontal section (ft), L, = length of loaded vertical section (ft). Speeds of 2OOft/min or more are attainable. Example 5.5 shows that the power requirement is much less than that of the Redler conveyor. (a) Figure 5.9. Some arrangements of belt conveyors (Stephens-Adamson Co.) and types of idlers (FMC Corp.). (a) Horizontal conveyor with discharge at an intermediate point as well as at the end. (b) Inclined conveyor, satisfactory up to 20” with some materials. (c) Inclined or retarding conveyor for lowering materials gently down slopes. (d) A flat belt idler, rubber cushion type. (e) Troughed belt idler for high loadings; usually available in 20”, 35”, and 45” side inclinations.
- 102. 5.4. SOLID FEEDERS 83 --/2./L (4 Figure S.~(continued) Closing Comments. Most kinds of conveyors and elevators are obtainable from several manufacturers, each of whom builds equipment to individual standards of sturdiness, materials of construction, mechanical details, performance, and price. These differences may be decisive in individual cases. Accordingly, a selection usually must be made from a manufacturer’s catalog, and ultimately with the advice of the manufacturer. 5.4. SOLIDS FEEDERS Several types are illustrated in Figures 5.9 and 3.7. Rates are controlled by adjusting gates or rotation speeds or translation (e) speeds. All of these methods require free flow from a storage bin which may be inhibited by bridging or arching. The device of Figure 5.9(a) provides motion to break up such tendencies. For the most part the devices shown provide only rough feed rate control. More precise control is achieved by continuous weighing. The equipment of Figure 3.16(l) employs measurements of belt speed and the weight impressed on one or several of the belt idlers to compute and control the weight rate of feed; precision better than 0.5% is achievable. For some batch processes, the feeder discharges into an overhead weighing hopper for accurate measurement of the charge. Similar systems are used to batch feed liquids when integrating flow meters are not sufficiently accurate. EXAMPLE~.~ Sizing a Belt Conveyor Soda ash of bulk density hOlb/cuft is to be transported at 400 tons/hr a horizontal distance of 1200 ft up an incline of 5”. The running angle of repose of this material is 19”. The conveyor will be sized with the data of Table 5.5. Consider a 24 in. belt. From Table 5.5(a) the required speed is conveyor length = 12OO/cos 5” = 1205 ft, rise = 1200 tan 5” = 105 ft. With the formulas and graph (c) of Table 5.5, the power requirement becomes Power = Phorizonta~ + Pvertical + Pempty = (0.4 + 1200/300)(400/100) u = (400/132)100 = 303 ft/min. + 0.001(105)(400) + 303(3.1)/100 = 69.0 HP. Since the recommended maximum speed in Table 5.5(b) is Perhaps 10 to 20% more should be added to compensate for losses 350 fpm, this size is acceptable: in the drive gear and motor.
- 103. 84 T R A N S F E R O F S O L I D S T&E -UP PULLEY (a) (b) (c) Figure 5.10. Closed belt (zipper) for conveying in any direction (Stephens-Adumson Co.). (a) Arrangement of pulley, feed hopper and open and closed belt regions. (b) The tubular belt conveyor for horizontal and vertical transport; a section of the zippered closed belt is shown. (c) Showing how the zipper closes (on downward movement of the belt in this sketch) or opens (on upward movement of the belt).
- 104. TABLE 5.6. Capacities and Power Requirements of Bucket Elevator Conveyors (a) Gravity Discharge Elevators Used Primarily For Coal”,” Size of I Capacity. tons!hr. at loo ft./mm. Hp.? with material at 50 Ib./cu. ft. L.._,.-1 I PP~ loft.. vertical I Per IOO-ft. horizontal 1 1.21 1 16.30 1 . . . 1 8 40 (b) Capacities and Maximum Size of Lumps of Centrifugal Discharge EIevatorsb*C Capacity, tons/hr. (c) Centrifugal Discharge of Continuous Belt and Bucket Elevators’ I 8 16x8 298 lumps material material material ~~~ s Drive Sprocket L of Material (a) “Buckets 80% full. “Buckets 75% full. L Horsepower = 0.002 (tons/hrWt in feet). (Link Belt Co.) Knob Operates fake+p (d) Figure 5.11. Drag-type enclosed conveyor-elevator (Redler Design) for transfer in any direction (Stephens-Adamon Mfg. Co.). (a) Head and discharge end of elevator. (b) Carrying and return runs. (c) Loading end. (d) Some shapes of flights; some are made close-fitting and edged with rubber or plastics to serve as cleanouts. 85
- 105. (d) Figure 5.12. Bucket elevators and conveyors. (a) Spaced bucket elevator. (b) Bucket conveyor for vertical and horizontal travel. (c) Discharge of pivoted buckets on horizontal path. (d) Spaced buckets receive part of their load directly and part by scooping the bottom. (e) Continuous buckets are filled as they pass through the loading leg with a feed spout above the tail wheel. (f) Centrifugal discharge of spaced buckets. (g) Discharge mode of continuous buckets. TABLE 5.7. Speed and Horsepower of Drag-Type Conveyors of Redler Design’ (b) Factors F, G, and Kfor Use in the Power Equation for Three Sizes of Units (a) Typical Speeds (ft/min)b Weight 3 ” u n i t s 19” Units MATERIAL 1000 1000 2000 3000 HANDLED COIW. EIW. CWW. COIW. CC4 125 125 8 0 150 Coke 4 0 4 0 4 0 4 0 Flyash 3 0 3 0 3 0 3 0 Grain (Whole) 1 2 5 1 2 5 6 0 2 5 0 (Processed) 126 1 0 0 8 0 1 5 0 Salt 1 2 5 1 0 0 8 0 1 5 0 Wood (Chips) 100 8 0 8 0 1 5 0 ( S a w d u s t , 1 0 0 1 0 0 8 0 I50 ‘HP = 0.001 (FL + GH + K) (tons/hr), where H = r&e (ft), L = horizontal run (ft), F, G, and Kare factors from Table (b); factor E is not used in this formula. bSeries 1000,2000, and 3000 differ in the shapes and sturdiness of the flights. (Stephens-Adamson Mfg. Co.). Ce;lhecetate dry. co- Cement. dry Portland Clay. dry lumpy Clay. pulverized Coal. minus Y” alack dry with I’8 ‘s pmportlO” “en Coal minus X”aback moderate1 .-A Coal. minus %” alack very wet Cosl. minus 1%” &ck dry or Salt. br; sranulakd Salt rock Sand silica coame dry Rand’very fine. dry Sawdust. dry Soda ash. bsht soybean meal Starch. lump Starch ulverired sumr. 2N sraaulati .%gar. bmvn Wheat. dry fairly clean Wood chips. dry E F G ---mm 54 100 1 . 5 2 . 9 4 . ii 0 0 3.0 4.1 8.33. 6.98. CL% so 0 8.015.94 2.9 7.46 ;FF 80 0 3 6017.76 1 5.94 uh30 4 0 2 . 4 4 . 6 4 ‘!iL% 40 20 33 2.5 6.15 5.45 :EE ii: 2 . 2 1 . 1 3 25 2 0 3 . 0 6 . 1 3 :; 20 0 2.4 3.8 4.83 7.92 “co 80 0 3.2 3.1 7.13 6.97 5 0 2 0 0 3 . 7 5 . 0 7 120 3 0 0 ::: Lo; 011.*35.:,7 8 ” I.9 3 . 8 5 76 100 I.9 3 . 5 6 90-100 *Go 2 . 1 4 . 2 7 EU$, 25-35 I200 2 6.2 4 14.64 5.27 2 0 4.5 Il.46 4 0 20 2 . 2 4 . 8 4 2 5 % 80 0 2.1 5.4 15.86 3.93 40% IM 40 4.4 2.7 8.57 5.89 ,320 40 40 3.5 I.7 3.35 6 62 E F ff - - - I.1 2.02.6 2 . 2 4 6 4 . 9 2 . 6 5 . 0 2 . 4 2 3 4 2 3 . 1 I . 8 3 . 6 3 . 2 I8 3 3 2 . 6 1 . 5 2 8 2 . 4 I Q 3.72.1 1 . 5 3.02.1 2 . 1 4.31.7 2 2.: :::::i 2 . 0 3.53.8 2 . 5 4 . 9 3 . 6 3 4 6:: I?! 3:: I.5 2 . 8 3 . 2 1 . 6 2 . 6 3 . 6 I.7 3.23.8 I . 9 3.84.0 3:‘s ;:;2:; 2 3 I.6 3 . 1 2 . 8 1 . 4 2 . 5 2 . 4 3 . 4 8.93.4 2 3:: :::4:: 1 . 2 2 . 2 3 . 0 2 . 0 3 . 7 1 . 9 86
- 106. 5 . 4 . S O L I D F E E D E R S 87 (a) lb) Storage bin GUM~LER f4oD ( O P T I O N A L ) (e) (f) ) (i) (k) Figure 5.13. Types of feeders for granular solids; also suitable are conveyors such as closed belt, Redler, and bucket types. (a) Bin discharge feeder. (b) Rotary plate feeder with adjustable collar and speed. (c) Flow controlled by an adjustable gate. (d) Rotary drum feeder, regulated by gate and speed. (e) Rotary vane feeder, can be equipped with air lock for fine powders. (f) Vane or pocket feeder. (g) Screw feeder. (h) Apron conveyor feeder. (i) Belt conveyor feeder. (j) Undercut gate feeder. (k) Reciprocating plate feeder. (1) Vibrating feeder, can transfer uphill, downhill, or on the level. (m) “Air-slide” feeder for powders that can be aerated. (n) Weighing belt feeder; unbalance of the weigh beam causes the material flow rate onto the belt to change in the direction of restoring balance.
- 107. 88 TRANSFER OF SOLIDS h-d Feed hopper r Screw conveyer Belt dwe in) Figure 5X%-(continued) Fabric C h a m b e r ’ Comparison of Redler and Zippered Belt Conveyors Soda ash of bulk density 30 lb/tuft is to be moved 120ft horizontally and 30 ft vertically at the rate of 350 cuft/hr. Compare power requirements of Redler and zippered belt conveyors for this service. A 3-in Redler is adequate: HP = $$ [X4(120) + 6.5(30) + 201 = 8.31. For a closed belt, 350 u=-=83.3fpm, 0.07(60) 350 u = 60(n,4)(3,12)2 = 118.8 fpm, which is well under the 200 fpm that could be used, which is within the range of Table 5.7(a), L, = 300, L, = 120, L, = 30. Use Eq. (5.26): tons/hr = 350(30)/2000 = 5.25 HP = 0.001{(300/30 + 5)83.3 + [120/16 + 2(30)]5.25} Take constants from Table 5.7(b) for a Redler. = 1.60. R E F E R E N C E S 1. T.H. Allegri, Materials Handling Principles and Practice, Van Nostrand Reinhold, New York, 1984. 2. A.G. Bain and S.T. Bonnington, The Hydraulic Transport of Solids by Pipeline, Pergamon, New York, 1970. 3. M.V. Bhatic and P.N. Cheremisinoff, Solid and Liquid Conveying System, Technomic, Lancaster, PA, 1982. 4. A.J. Bobkowicz and W.G. Gauvin, The effects of turbulence in the flow characteristics of model tibre suspensions, Chem. Eng. Sci. 22, 229-247 (1967). 5. R. Clift, Conveyors, hydraulic, Encycl. Chem. Process. Des. 11, 262-278 (1980). 6. H. Colijn, Mechanical Conveyors for Bulk Solidz, Elsevier, New York, 1985. 7. Conveyor Equipment Manufacturers Association, Belt Conveyors for Bulk Materials, Van Nostrand Reinhold, New York, 1979. 8. D.W. Dodge and A.B. Metzner, Turbulent flow of non-newtonian systems, AIChE .I. 5, 189 (1959). 9. G.H. Ewing, Pipeline transmission, in Marks’ Mechanical Engineers Handbook, McGraw-Hill, New York, 1978, pp. 11.134-11.135. 10. FMC Corp. Material Handling Equipment Division, Catalog 100, Homer City, PA, 1983. 11. F.J. Gerchow, Conveyors, pneumatic, in Encycl. Chem. Process. Des. l&278-319 (1980); Chem. Eng., (17 Feb. 1975, 31 Mar. 1975). 12. H.V. Hawkins, Pneumatic conveyors, in Marks’ Mechanical Engineers Handbook, McGraw-Hill, New York, 1978, pp. 10.50-10.63. l3. J.W. Hayden and T.E. Stelson, Hydraulic conveyance of solids in pipes, in Zandi, Ref. 27, 1971, pp. 149-163. 14. W.G. Hudson, Conveyors and Related Equipment, Wiley, New York, 1954. 15. E. Jacques and J.G. Montfort, Coal transportation by slurry pipeline, in Considine (Ed.), Energy Technology Handbook, McGraw-Hill, New York, 1977, pp. 1.178-1.187.
- 108. REFERENCES 89 16. M. Kraus, Pneumatic Conveying of Bulk Materials, McGraw-Hill, New York, 1980. 17. R.A. Kulwiec (Ed.), Material Handling Handbook, Wiley, New York, 1985. 18. D.E. Perkins, and J.E. Wood, Design and Select Pneumatic Conveying Systems, Hydrocarbon Processing 75-78 (March 1974). 19. G.J. Raymus, Pneumatic conveyors, in Perry’s Chemical Engineers Handbook, McGraw-Hill, New York, 1984, pp. 7.11-1.25. 20. P.E. Solt, Conveying, pneumatic troubleshooting, Encycl. Cbem. Process. Des. 11, 214-226 (1980). 21. Stephens-Adamson Mfg. Co., General Catalog 66, Aurora, IL, 1954, and updated sections. 22. H.A. Stoess, Pneumatic Conveying, Wiley, New York, 1983. 23. E.J. Wasp, T.C. Aude, R.H. Seiter, and T.L. Thompson, in Zandi, Ref. 27, 1971, pp. 199-210. 24. E.J. Wasp, J.P. Kenny, and R.L. Gandhi, Solid-Liquid Flow in Slurry Pipeline Transportation, Trans. Tech. Publ., 1917, Gulf, Houston, 1979. 25. E.J. Wasp, T.L. Thompson, and P.E. Snoek, The era of slurry pipelines, Chem. Technol., 552-562 (Sep. 1971). 26. O.A. Williams, Pneumatic and Hydraulic Conveying of Soli&, Dekker, New York, 1983. 27. I. Zandi (Ed.), Advances in Solid-Liquid Flow in Pipes and Its Applications, Pergamon, New York, 1971.
- 110. 6 FLOW OF FLUIDS T he transfer of fluids through piping and equipment is rates. In this chapter, the concepts and theory of fluid accompanied by friction and may result in changes mechanics bearing on these topics will be reviewed briefly in pressure, velocity, and elevation. These effects and practical and empirical methods of sizing lines and require input of energy to maintain flow at desired auxiliary equipment will be emphasized. 6.1. PROPERTIES AND UNITS The basis of flow relations is Newton’s relation between force, mass, and acceleration, which is F = (m /gJa. (6.1) When F and m are in lb units, the numerical value of the coefficient is g= = 32.174 lb ft/lbf se?. In some other units, EL = 1 kg== cE!z!?cg 806 kg m/sec2 N dyn ’ kg, Since the common engineering units for both mass and force are 1 lb, it is essential to retain g, in all force-mass relations. The interconversions may be illustrated with the example of viscosity whose basic definition is force/(velocity)(distance). Accordingly the viscosity in various units relative to that in SI units is 1 Ns/m’ = &kg, s/m2 = 10 g/(cm)(s) = 10 P = 0.0672 lb/(ft)(sec) 0.0672 = 32.174 lbf sec/ft2 = 0.002089 lbf sec/ft*. In data books, viscosity may be recorded either in force or mass units. The particular merit of SI units (kg, m, s, N) is that g, = 1 and much confusion can be avoided by consistent use of that system. Some numbers of frequent use in fluid flow problems are Viscosity: 1 cPoise = 0.001 N s/m2 = 0.4134 lb/(ft)(hr). Density: 1 g m/cm3 = 1000 kg/m3 = 62.43 lb/f?. Specific weight: 62.43 Ibf/cuft = 1000 kg,/m3. Pressure: 1 atm = 0.10125 MPa = 0.10125(106) N/m2 = 1.0125 bar. Data of densities of liquids are empirical in nature, but the effects of temperature, pressure, and composition can be estimated; suitable methods are described by Reid et al. (Properties of Gases and Liquids, McGraw Hill, New York, 1977), the API Refining Data Book (American Petroleum Institute, Washington, DC, 1983), and the AZChE Data Prediction Manual (1984-date). The densities of gases are represented by equations of state of which the simplest is that of ideal gases; from this the density is given by: p = l/V = MP/RT, mass/volume (6.2) where M is the molecular weight. For air, for example, with P in atm and Tin “R, 29P ’ =0.73T’ - lb/tuft. For nonideal gases a general relation is p = MPIzRT, (6.4) where the compressibility factor z is correlated empirically in terms of reduced properties T/T, and P/PC and the acentric factor. This subject is treated for example by Reid et al. (1977, p. 26) and Walas (1985, pp. 17, 70). Many PVT equations of state are available. That of Redlich and Kwong may be written in the form V = b + RT/(P + a/fiV’), (6.5) which is suitable for solution by direct iteration as used in Example 6.1. Flow rates are expressible as linear velocities or in volumetric, mass, or weight units. Symbols for and relations between the several modes are summarized in Table 6.1. The several variables on which fluid flow depends may be gathered into a smaller number of dimensionless groups, of which the Reynolds number and friction factor are of particular importance. They are defined and written in the common kinds of units also in Table 6.1. Other dimensionless groups occur less frequently and will be mentioned as they occur in this chapter; a long list is given in Perry’s Chemical Engineers Handbook (McGraw-Hill, New York, 1984, p. 5.62). EXAMPLE 6.1 Density of a Nonideal Gas from Its Equation of State The Redlich-Kwong equation of carbon dioxide is (P + 63.72(106)/fiV2)(V - 29.664) = 82.05T with P in atm, V in mL/g mol and Tin K. The density will be found at P = 20 and T = 400. Rearrange the equation to V = 29.664 + (82.05)(400)/(20 + 63.72(106)/$i% V2). Substitute the ideal gas volume on the right, V = 1641; then find V on the left; substitute that value on the right, and continue. The successive values of V are V = 1641, 1579, 1572.1, 1571.3, 1571.2, . . . mL/gmol and converge at 1571.2. Therefore, the density is p = l/V = 111571.2, or 0.6365gmol/L or 28.OOg/L. 91
- 111. 92 FLOW OF FLUIDS TABLE 6.1. Flow Quantities, Reynolds Number, and Friction Factor F l o w Quantity S y m b o l a n d Equivalent Typical Units C o m m o n SI Linear Volumetric Mass W e i g h t Mass/area Weight/area 0 ft/sec m/set Q=uA=nD=u/4 cuft/sec m3/sec rh=pQ=pAu Ib/sec kg/set ti==yQ=yAu Ibf/sec N/set G=pu IWsqfNsec) kg/m* set G,, = yu Ibf/(sqft)(sec) N/m2 set Reynolds Number (with A= rcD’/4) Dup Do DG 4Qp 4ri, &l=T=y=l =-=- nDp nDp (1) Friction Factor =2gcDAPILpu2=1.6364 * (2) (Round’s equation) AP L u2 8LQ2 -=--ff= * gf= ELrh* LG’ P D2gc gc= D gcn2p2D5 f = 2gcDp2 f (3) In the units D = in., rh = Ib/hr Q = cuft/sec, p = CP p = specific gravity 6.314rh 1.418(106)pQ Re=-= DM DU (4) A P 3.663(10-9)rh2 L pD5 f , atm/ft (5) 5.385(10m8)~* z PD’ f , psi/ft (6) 0.6979pQ’ =v f psi/ft D ’ Laminar Flow (7) Re < 2300 f = 64/Re APIL= 32fiulD2 (2a) 1.841(1 OK$rb = 4 OD ’ atm/ft (5a) 2.707(10-a)~rh = 4 PD ’ psi/ft (6a) 35.083~0 = D4 ’ psi/ft Va) Gravitation Constant gc = 1 kg m/N sec2 = 1 g cm/dyn sec2 = 9.806 kg m/kgf set* = 32.174 Ibm ft/lbf set* = 1 slug ft/lbf sec2 = 1 Ibm ft/ooundal set’ 6.2. ENERGY BALANCE OF A FLOWING FLUID The energy terms associated with the flow of a fluid are 1. Elevation potential (g/g&, 2. Kinetic energy, u2/2g,, 3. Internal energy, U, 4. Work done in crossing the boundary, PV, 5. Work transfer across the boundary, W,, 6. Heat transfer across the boundary, Q. Figure 6.1 represents the two limiting kinds of regions over which energy balances are of interest: one with uniform conditions throughout (completely mixed), or one in plug flow in which gradients are present. With single inlet and outlet streams of a uniform region, the change in internal energy within the boundary is d(mU) = m dU + Udm = m dU + U(dm, - dm,) = dQ - dW, + WI + u$k, + k/g&,1 dm, - [HZ + u%gc + (glgJz21 dm2. (6.6) One kind of application of this equation is to the filling and emptying of vessels, of which Example 6.2 is an instance. Under steady state conditions, d(mU) = 0 and dm, = dm, = dm, so that Eq. (6.6) becomes AH + Au2/2g, + (g/g,)Az = (Q - W/m, (6.7) AU + A(PV) + Au2/2gC + (g/g,)Az = (Q - W,)/m, (6.8) or AU + W/P) + Au2/%, + (g/g,)Az = (Q - Wm. (6.9) For the plug Row condition of Figure 6.1(b), the balance is made in terms of the differential changes across a differential length dL of the vessel. which is dH + (l/g,)u du + (g/g,) dz = dQ - dW,, (6.10) where all terms are per unit mass. (a) dQ dW, k----- dL --+i (b) dCl dW, Figure 6.1. Energy balances on fluids in completely mixed and plug flow vessels. (a) Energy balance on a bounded space with uniform conditions throughout, with differential flow quantities dm, and dm,. (b) Differential energy balance on a fluid in plug flow in a tube of unit cross section.
- 112. 6.2. ENERGY BALANCE OF A FLOWING FLUID 93 EXAMPLE 6.2 Unsteady Flow of an Ideal Gas through a Vessel An ideal gas at 350 K is pumped into a 1000 L vessel at the rate of 6 g mol/min and leaves it at the rate of 4 g mol/min. Initially the vessel is at 310K and 1 atm. Changes in velocity and elevation are negligible. The contents of the vessel are uniform. There is no work transfer. Thermodynamic data: U=C,T=5T, H=C,T=7T. Heat transfer: dQ = h(300 - T) df3 = 15(300 - T) de. The temperature will be found as a function of time 6 with both h = 15 and h = 0. dn, = 6d0, dn, = 4 do, dn=dn,-dn,=2dtI, n, = P,V/RT, = 1000/(0.08205)(310) = 39.32 gmol, n=n,+2f3, v= 10001 T, = 350 To=310 *c P,= 1 T2 = 7 n, = 6 t n2 = 4 dQ d,=O Energy balance d(nCJ) = n dU + U dn = nC, dT + C, T(2 do) =H,dn,-H,dn,+dQ-dw, = C,(6T, - 4T) do + h(300 - T) d0. This rearranges into dT + 300h - (4Cp + 2C, + h)T h = 15, h =O. The integrals are rearranged to find T, 362.26 - TZ = 52.26 ( 1 + o ;509e 5.3 , h = 15, > 3.8 , h - 0 . Some numerical values are tl 0 0.2 0.5 1 5 10 cc h P h=15 h = O h=15 h = O 310 310 1 1 312.7 312.9 1.02 1.02 316.5 317.0 322.1 323.2 346.5 354.4 356.4 370.8 1.73 1.80 362.26 386.84 m m The pressures are calculated from p =&T= (39.32 + 28)(0.08205)T V 1000 Friction is introduced into the energy balance by noting that it is a mechanical process, dWf, whose effect is the same as that of an equivalent amount of heat transfer dQ,. Moreover, the total effective heat transfer results in a change in entropy of the flowing liquid given by TdS=dQ+dW? When the thermodynamic equivalent (6.11) dH=VdP-t TdS (6.12) and Eq. (6.11) are substituted into Eq. (6.10), the net result is VdP + (l/g& du + (g/g,) dz = -(dW, + dWf), (6.13) which is known as the mechanical energy balance. With the expression for friction of Eq. (6.18) cited in the next section, the mechanical energy balance becomes VdP + (l/g& du + (g/g,) dz + & dL = -dW,. (6.13’) c For an incompressible fluid, integration may be performed term by term with the result AP/p + Au2/2g, + (g/g,)Az = -(W, + W,). (6.14) The apparent number of variables in Eq. (6.13) is reduced by the substitution u = V/A for unit flow rate of mass, where A is the cross-sectional area, so that VdP + (l/g,A’)VdV + (g/g,) dz = -(dW, + dWf). (6.15) Integration of these energy balances for compressible fluids under several conditions is covered in Section 6.7. The frictional work loss W, depends on the geometry of the system and the flow conditions and is an empirical function that will be explained later. When it is known, Eq. (6.13) may be used to find a net work effect W, for otherwise specified conditions. The first three terms on the left of Eq. (6.14) may be grouped into a single stored energy terms as AE = APlp + Au2/2g, + (g/g,)Az, (6.16)
- 113. 94 FLOW OF FLUIDS EXAMPLE 6.3 Units of the Energy Balance In a certain process the changes in stored energy and the friction are AE = - 135 ft lbf/lb = 3 6 4 . 6 2 , 364.66, w =364.6=kgf=37.19-. m kgf s kg 9.806N kg rvf = 13 ft lbf/lb. The net work will be found in several kinds of units: At sea level, numerically lbf = lb and kgf = kg. Accordingly, w, = -(AE + wr) = 122 ft Ibf/lb, ft lbf 4.448N2.204 lb m w, = 122~~~~ lbf k g 3.28ft w = ,,,!+f&~fm= 37,19- kgf m s lb lbf kg 3.28ft kg ’ as before. and the simpler form of the energy balance becomes AE + W, = -W,. (6.17) The units of every term in these energy alternately: balances are ft Ib,/lb with g, = 32.174 and g in ft/sec* (32.174 at sea level). N m/kg = J/kg with g, = 1 and g in m/se? (1.000 at sea level). kg, m/kg with g, = 9.806 and g in m/se? (9.806 at sea level). Example 6.3 is an exercise in conversion of units of the energy balances. The sign convention is that work input is a negative quantity and consequently results in an increase of the terms on the left of Eq. (6.17). Similarly, work is produced by the flowing fluid only if the stored energy AE is reduced. 6.3. LIQUIDS Velocities in pipe lines are limited in practice because of 1. the occurrence of erosion. 2. economic balance between cost of piping and equipment and the cost of power loss because of friction which increases sharply with velocity. Although erosion is not serious in some cases at velocities as high as lo-15ft/sec, conservative practice in the absence of specific knowledge limits velocities to 5-6 ft/sec. Economic optimum design of piping will be touched on later, but the rules of Table 6.2 of typical linear velocities and pressure drops provide a rough guide for many situations. The correlations of friction in lines that will be presented are for new and clean pipes. Usually a factor of safety of 20-40% is advisable because pitting or deposits may develop over the years. There are no recommended fouling factors for friction as there are for heat transfer, but instances are known of pressure drops to double in water lines over a period of 10 years or so. In lines of circular cross section, the pressure drop is represented by D,, = 4(cross section)/wetted perimeter. For an annular space, D,, = Dz - D,. In laminar flow the friction is given by the theoretical Poiseuille equation f = WN,,, Nne < 2100, approximately. (6.19) At higher Reynolds numbers, the friction factor is affected by the roughness of the surface, measured as the ratio e/D of projections on the surface to the diameter of the pipe. Values of E are as follows; glass and plastic pipe essentially have E = 0. E (R) E (mm) Riveted steel Concrete Wood stave Cast iron Galvanized iron Asphalted cast iron Commercial steel or wrought iron Drawn tubing 0.003-0.03 0.9-9.0 0.001-0.01 0.3-3.0 0.0006-0.003 0.18-0.9 0.00085 0 . 2 5 0.0005 0 . 1 5 0.0004 0 . 1 2 0 . 0 0 0 1 5 0.046 0.000005 0 . 0 0 1 5 The equation of Colebrook [J. Inst. Civ. Eng. London, 11, pp. 133-156 (1938-1939)] is based on experimental data of Nikuradze [Veer. Dtsch. Zng. Forschungsh. 356 (1932)]. Nae > 2100. (6.20) Other equations equivalent to this one but explicit in f have been devised. A literature review and comparison with more recent experimental data are made by Olujic [Chem. Eng., 91-94, (14 Dec. 1981)]. Two of the simpler but adequate equations are f =1.6364 ln H ?+:)I-’ Re [Round, Can. J. C&m. Eng. 58, 122 (1980)], I=(-. [ - 2 0 86861n &-2.18021n &+!$ III (6.22) Re For other shapes and annular spaces, D is replaced by the hydraulic [Schacham, Ind. Eng. Chem. Fundam. 19(5), 228 (198O)J. These
- 114. 6.3. LIQUIDS 95 TABLE 6.2. Typical Velocities and Pressure Drops in Pipelines Liquids (psi/lOOft) LiquidzPwrhin Bubble Point Light Oils and Water “%p,” Pump suction Pump discharge Gravity flow to or from tankage, maximum Thermosyphon reboiler inlet and outlet 0 . 1 5 2 . 0 (or 5-7 fps) 0 . 0 5 0 . 2 0 . 2 5 0 . 2 5 2.0 2.0 (or 5-7 fps) (or 3-4fps) 0 . 0 5 0 . 0 5 Gases (psi/lOOft) Pressure (psig) o-300ft 300-600ft Equivalent Length Equivalent Length -13.7(28 in.Vac) 0 . 0 6 0 . 0 3 -12.2(25 in.Vac) 0 . 1 0 0 . 0 5 -7.5(15 in.Vac) 0 . 1 5 0 . 0 8 0 0 . 2 5 0 . 1 3 5 0 0 . 3 5 0 . 1 8 100 0 . 5 0 0 . 2 5 150 0 . 6 0 0 . 3 0 200 0 . 7 0 0 . 3 5 500 2 . 0 0 1.00 Steam psi/lOOft Maximumft/min Under 50 psig 0 . 4 1 0 , 0 0 0 Over 50 psig 1.0 7000 Steam Condensate To traps, 0.2 psi/l 00 ft. From bucket traps, size on the basis of 2-3 times normal flow, according to pressure drop available. From continuous drainers, size on basis of design flow for 2.0 psi/100 ft Control Valves Require a pressure drop of at least 10 psi for good control, but values as low as 5 psi may be used with some loss in control quality Particular Equipment Lines (R/see) Reboiler, downcomer (liquid) Reboiler, riser (liquid and vapor) Overhead condenser Two-phase flow Compressor, suction Compressor, discharge Inlet, steam turbine Inlet, gas turbine Relief valve, discharge Relief valve, entry point at silencer 3-7 35-45 25-100 35-75 75-200 loo-250 120-320 150-350 0.5v," KS a v, is sonic velocity. three equations agree with each other within 1% or so. The Colebrook equation predicts values l-3% higher than some more recent measurements of Murin (1948), cited by Olujic (Chemical Engineering, 91-93, Dec. 14, 1981). For orientation purposes, the pressure drop in steel pipes may be found by the rapid method of Table 6.3, which is applicable to highly turbulent flow for which the friction factor is given by von Karman’s equation f = 1.3251[ln(D/e) + 1.3123)]-*. (6.23) Under some conditions it is necessary to employ Eq. (6.18) in differential form. In terms of mass flow rate, (6.24) Example 6.4 is of a case in which the density and viscosity vary along the length of the line, and consequently the Reynolds number and the friction factor also vary. FITTINGS AND VALVES Friction due to fittings, valves and other disturbances of flow in pipe lines is accounted for by the concepts of either their equivalent lengths of pipe or multiples of the velocity head. Accordingly, the pressure drop equation assumes either of the forms AP = f(L + c Li)pu2/2gJ, (6.25) AP = [f(L/D) + c K]w2/2gc. (6.26) Values of equivalent lengths Li and coefficients K, are given in Tables 6.4 and 6.5. Another well-documented table of Ki is in the Chemical Engineering Handbook (McGraw-Hill, New York, 1984 p. 5.38). Comparing the two kinds of parameters, K, = fLJD (6.27) so that one or the other or both of these factors depend on the friction factor and consequently on the Reynolds number and possibly E. Such a dependence was developed by Hooper [Chem. Eng., 96-100, (24 Aug. 1981)] in the equation K = KJNRe + K,(l + l/D), (6.28) where D is in inches and values of K, and K, are in Table 6.6. Hooper states that the results are applicable to both laminar and turbulent regions and for a wide range of pipe diameters. Example 6.5 compares the several systems of pipe fittings resistances. The K, method usually is regarded as more accurate. O R I F I C E S In pipe lines, orifices are used primarily for measuring flow rates but sometimes as mixing devices. The volumetric flow rate through a thin plate orifice is A, = cross sectional area of the orifice, /3 = d/D, ratio of the diameters of orifice and pipe. For corner taps the coefficient is given by cd = 0.5959 + 0.0312/12.’ - 0.184@ + (0.0029~2s)(106/Re,)0~7s (6.30) (International Organization for Standards Report DIS 5167, Geneva, 1976). Similar equations are given for other kinds of orifice taps and for nozzles and Venturi meters.
- 115. 96 FLOW OF FLUIDS TABLE 6.3. Approximate Computation of Pressure Drop of Liquids and Gases in Highly Turbulent Flow in Steel Pipesa w c, 10 9 8 I.l .09 .08 -07 .06 7 1.5-= -= .002 _-- .0015 1.0-= .OOl -= .0009 .g - - .OOOB - - .0007 *a .-- .oooli .I5 - - .5 .6 6 d-25 .7--_ z .8- cij .9 30 -it 1.0 > le5 - - 4 0 21: z-60 4y- 5-S-70 6-y -- 80 7--_ 8x----90 1: 100 w (‘1 I- 80 I- 70 250-- 60 -r 50 aoo-z-40 30 25 150-z ---m _-- 15 100 - - 10 4 0 5 80 x 160 . . . x x :ooz 160 . . . x x 4 0 5 80 x 160 . . . x x 4 0 5 8 0 x 160 ..*xx 4 0 5 8 0 x 160 . . . x x 4 0 s 8 0 x 160 . . . x x E 160 . . . x x “81 l “8: i :E . . . x x 4 0 5 8 0 x :z . . . x x 4 0 s 8 0 x :2 .a. xx :z 140 . . . x x 160 :i i8; 8 0 it 160 7.920.000 26.200.000 93,500 186.100 4.300.000 11.180,OOO %i 100:100 627,000 E% 22:500 114.100 627 904 1.656 4.630 169 236 Iti! 66.7 91.8 146.3 380.0 10.0 13.2 5.11 6.75 8.94 :81::: 1.59 2.04 :-t; 4193 0.610 xt 1:376 1.861 1 4 1 6 1 8 20 24 :i . . . 5 40 . . . x 60 1:: ::i 160 :i :i= . . . x 60 1:: ::I 160 1 0 :is 40 x 60 ;iJ 140 160 :i 5 . . x :: 60 80 ;g 160 E%; 0:01046 EE o:ol244 i-8:::: ;3;;;8 0:0252 0.00463 0.00298 E%:i 0:00435 i-E:;:: 0:00669 O.Wl41 0.000835 Note: The letters I. x. and xx in the columns of Schedule Num- bers indicate Standard, Extra Strong, and Double Extra Strong pipe. respectively. sAP,,,= C,C,/p psi/100 ft, with p in lb/&t. (Crane Co. Flow of Nuids through Fittings, Valves and Pipes, Crane Co., New York, 1982).
- 116. 6.3. LIQUIDS 97 EXAMPLE~.~ Pressure Drop in Nonisothennai Liquid Flow Oil is oumoed at the rate of 6000 lb/hr through a reactor made of commercial steel pipe 1.278in. ID and 2000ft long. The inlet condition is 400°F and 750psia. The temperature of the outlet is 930°F and the pressure is to be found. The temperature varies with the distance, L ft, along the reactor according to the equation T = 1500 - 1100 exp(-0.0003287L) (“F) The viscosity and density vary with temperature according to the equations ~ - 6.1076 , cP, p = 0.936 - O.O0036T, g/mL. Round’s equation applies for the friction factor: &,2L 4(6000) 29,641 =- nDp n(1.278/12)2.42~ /I ’ E/D = o.m15(12) = 0 00141 1.278 ’ ’ 1 0 2 0 .3 gl 40 50 FE 98: 100 110 :s: 140 150 160 170 180 130 200 2 1 0 2 2 0 2 3 0 240 ! Exams 1 e 6 4 .: P re55u t-e cl t-op i n nonisothermal flow R E H D L.#P..D ! CD = l e n g t h inns remen t DHTH 0>750,280 GOSue lB0 Il=l GDSClB 1 5 0 Il=l L=L+D GDSU8 1 8 0 P=P-.s*D*<Il+I) GDSUB 1 5 0 I F L>1800 T H E N 1 4 0 GDTD 7 0 END DISP llSING 1 6 0 i L,T,R1/1000 ,100SF,P IMAGE DDDD,2X>DDD.D,2X,DDD.D >ZX,D.DD>2X>DDD.D RETURN T=1500-1100SEXP~-~.0003287%L >> M=EXPC7445.3/CT+459.6>-6.187 61 R=.936-.00036tT R1=29641/M F=1.6364,‘LOG<.135t.00141+6.5 /El ‘1,2 , I= ~S.~*:FS’R RETURN The differential pressure is given by - d P = &fdl-= 8(6000/3600)* 32.2~r*62.4p(1.278/12)~(144) fdL OS68f =-dL, psi, P P = 750 - I dL. The pressure profile is found by integration with the trapezoidal rule over 200 ft increments. The computer program and the printout are shown. The outlet pressure is 700.1 psia. For comparison, taking an average temperature of 665”F, p =1.670, p =0.697 NRe = 17,700, f = 0.00291, P,,, = 102.5. L 0 280 400 600 880 1000 1200 1400 1600 1300 2 0 0 0 N T Re 1000 1OOf P 4 0 0 . 0 2 . 3 4.85- 750. kl 4 7 0 . 0 4 . 4 3 . 9 9 743,6 5 3 5 . 5 7 . 5 3.49 7 3 7 ‘g 5 9 6 . 9 1 1 . 6 3 . 1 6 732.S 6 5 4 . 4 1 6 . 7 2 . 9 5 7 2 7 . 9 7 0 8 . 2 2 2 . 7 2 . 8 0 7 2 3 . 2 7 5 8 . 5 2 9 . 5 2 . 6 9 7 1 8 . 5 8 0 5 . 7 3 7 . 1 2 . 6 1 7 1 3 . 9 3 4 9 . 9 4 5 . 2 2 . 5 5 7 0 9 . 3 8 9 1 . 3 5 3 . 8 2 . 5 1 7 0 4 . 7 9 3 0 . 0 6 2 . 7 2 . 4 7 7 0 0 . 1
- 117. 98 FLOW OF FLUIDS TABLE 6.4. Equivalent Lengths of Pipe Fitting9 P i p e size, in. 1 2.7 2.3 1.7 1.3 5.8 0.6 27 6.7 2 5.5 4.6 3.5 2.5 11.0 1.2 57 13 3 8.1 6.8 5.1 3.8 17.0 1.7 85 20 4 11.0 9.1 7.0 5.0 22 2.3 110 27 5 14.0 12.0 8.9 6.1 27 2.9 140 33 6 16.0 14.0 11.0 7.7 33 3.5 160 40 8 21 18.0 14.0 1 0 . 0 43 4.5 220 53 10 26 22 17.0 1 3 . 0 56 5.7 290 67 12 32 26 20.0 15.0 66 6.7 340 80 14 36 31 23 17.0 76 8.0 390 93 16 42 35 27 19.0 87 9.0 430 107 18 46 40 30 21 100 10.2 500 120 20 52 43 34 23 110 12.0 560 134 24 63 53 40 28 140 14.0 680 160 36 94 79 60 43 200 20.0 1,000 240 ul Standard ell I I L Medium Long- radius radius ell ell 45-deg ell Tee Gate Globe Swing valve, valve, check, open 0Den 0Den ! Length of straight pipe (ft) giving equivalent resistance. (Hicks and Edwards, Pump Application Engineering, McGraw-Hill, New York, 1971). POWER REQUIREMENTS A convenient formula in common engineering units for power consumption in the transfer of liquids is p = (volumetric flow rate)(pressure difference) (equipment efficiency) (gals/min)(lb/sq in.) = 1714(fractional pump eff)(fractional driver eff) horsepower. (6.30a) Efficiency data of drivers are in Chapter 4 and of pumps in Chapter 7. For example, with 500 gpm, a pressure difference of 7.5 psi, pump efficiency of 0.7, and driver efficiency of 0.9, the power requirement is 32.9 HP or 24.5 kw. 6.4. PIPELINE NETWORKS A system for distribution of fluids such as cooling water in a process plant consists of many interconnecting pipes in series, parallel, or branches. For purposes of analysis, a point at which several lines meet is called a node and each is assigned a number as on the figure of Example 6.6. A flow rate from node i to node j is designated as Q,; the same subscript notation is used for other characteristics of the line such as f, L, D, and NRe. Three principles are applicable to establishing flow rates, pressures, and dimensions throughout the network: 1. Each node i is characterized by a unique pressure P,. 2. A material balance is preserved at each node: total flow in equals total flow out, or net flow equals zero. 3. The friction equation & - 4 = (8p/gCnZ)hjLijQ$/Ds applies to the line connecting node i with j. In the usual network problem, the terminal pressures, line lengths, and line diameters are specified and the flow rates through- out are required to be found. The solution can be generalized, however, to determine other unknown quantities equal in number to the number of independent friction equations that describe the network. The procedure is illustrated with the network of Example 6.6. The three lines in parallel between nodes 2 and 5 have the same pressure drop PZ - PS. In series lines such as 37 and 76 the flow rate is the same and a single equation represents friction in the series: The number of flow rates involved is the same as the number of lines in the network, which is 9, plus the number of supply and destination lines, which is 5, for a total of 14. The number of material balances equals the number of nodes plus one for the overall balance, making a total of 7. The solution of the problem requires 14 - 7 = 7 more relations to be established. These are any set of 7 friction equations that involve the pressures at all the nodes. The material balances and pressure drop equations for this example are tabulated. From Eqs. (4)-(10) of Example 6.6, any combination of seven quantities Q, and/or L, and/or 0, can be found. Assuming that the Q, are to be found, estimates of all seven are made to start, and the corresponding Reynolds numbers and friction factors are found from Eqs. (2) and (3). Improved values of the Q, then are found
- 118. 6 . 4 . P I P E L I N E N E T W O R K S 99 TABLE 6.5. Velocity Head Factors of Pipe Fittingsa REGULAR SCREWED 45’ ELL. 2 .6 REGULAR FLANGED ’ 1 :: 9O”ELL. mtttit~ * j D .6,3 .5 I 2 47 :-2 D’151 2 4 6 .4!?sskh k!d!& ’ = u .3 FLANGED .3 LONG RETURN K 2 BEND fymED K 2 J 90’ELL. ,, D n - LINE 1 FLOW K 8 .6 c, S C R E W E D r-rrrm- SCREWED I TEE B R A N C H GATE VALVE SCREWED GLOBE VALVE I IIll llI!IIl~ D.4, 3 rn 3, SWING CHECK VALVE ‘h = Ku*/2g,, ft of fluid. (Hydraulic Institute, Cleveland, OH, 1957).
- 119. 100 FLOW OF FLUIDS TABLE 6.6. Velocity Head Factors of Pipe Fittings’ 6.5. OPTIMUM PIPE DIAMETER Elbows ValWS Fitting type K1 Kc.2 - - Standard (RID = 1 I, screwed 800 0.40 Standard (RID = 1). flanged/welded 800 0.25 Long-radius (RID = 1.5). all types 800 0.20 30” 1 Weld (90” angle) 1,000 1 . 1 5 Mitered 2 Weld (45” angles) 800 0.35 elbows 3 Weld (30’ angles) 800 0.30 (RID-1.5) 4 Weld (22X” angles) 800 0.27 5 Weld (18” angles) 800 0.25 Standard (R/D = 1). all types 500 0.20 15O Long-radius (RID = 1.5). all types 500 0.15 Mitered, 1 weld, 45’ angle 500 0.25 Mitered, 2 weld, 22X” angles 500 0.15 Standard (R/D = 1). screwed 1,000 0.60 180” Standard (RID = 1). flanged/welded 1,000 0.35 Long radius (RID = 1.5). all types 1,000 0.30 Jsed Standard, screwed 500 0.70 Long-radius, screwed 800 0.40 as Standard, flanged or welded 800 0.80 !Ibow Stub-in-type branch 1,000 1 .oo +Jn- Screwed 200 0.10 -hrough Flanged or welded 150 0.50 ee Stub-in-type branch 100 0.00 Sate, Full line size, p = 1 .O 300 0.10 Iall, Reduced trim, p = 0.9 500 0.15 1lug Reduced trim, p = 0.8 1,000 0.25 Globe, standard 1,500 4.00 Globe, angle or Y-type 1,000 2.00 diaphragm, dam type 1,000 2.00 3utterflv 800 0.25 Lift 2,000 10.00 :heck Swing 1,500 1.50 Tilting-disk 1,000 0.50 Note: Use R/D = 1.5 values for R/D = 5 pipe bends, 45’ to 180’. Use appropriate tee values for flow through crossas. a Inlet, flush, K = 160/N,, + 0.5. Inlet, intruding, K = 160/N,, = 1.0. Exit, K = 1 .O. K = K,/NRe + K,(l + l/D), with D in inches. [Hooper, Chem. Eng. 96-100 (24 Aug. 1981)]. from Eqs. (4)-(10) with the aid of the Newton-Raphson method for simultaneous nonlinear equations. Some simplification is permissible for water distribution systems in metallic pipes. Then the Hazen-Williams formula is adequate, namely Ah = AP/p = 4.727L(Q/130)‘-852/D4~87w (6.31) with linear dimensions in ft and Q in cuft/sec. The iterative solution method for flowrate distribution of Hardy Cross is popular. Examples of that procedure are presented in many books on fluid mechanics, for example, those of Bober and Kenyon (Fluid Mechanics, Wiley, New York, 1980) and Streeter and Wylie (Fluid Mechanics, McGraw-Hill, New York, 1979). With particularly simple networks, some rearrangement of equations sometimes can be made to simplify the solution. Example 6.7 is of such a case. In a chemical plant the capital investment in process piping is in the range of 25-40% of the total plant investment, and the power consumption for pumping, which depends on the line size, is a substantial fraction of the total cost of utilities. Accordingly, economic optimization of pipe size is a necessary aspect of plant design. As the diameter of a line increases, its cost goes up but is accompanied by decreases in consumption of utilities and costs of pumps and drivers because of reduced friction. Somewhere there is an optimum balance between operating cost and annual capital cost. For small capacities and short lines, near optimum line sizes may be obtained on the basis of typical velocities or pressure drops such as those of Table 6.2. When large capacities are involved and lines are long and expensive materials of construction are needed, the selection of line diameters may need to be subjected to complete economic analysis. Still another kind of factor may need to be taken into account with highly viscous materials: the possibility that heating the fluid may pay off by reducing the viscosity and consequently the power requirement. Adequate information must be available for installed costs of piping and pumping equipment. Although suppliers quotations are desirable, published correlations may be adequate. Some data and references to other published sources are given in Chapter 20. A simplification in locating the optimum usually is permissible by ignoring the costs of pumps and drivers since they are essentially insensitive to pipe diameter near the optimum value. This fact is clear in Example 6.8 for instance and in the examples worked out by Happel and Jordan (Chemical Process Economics, Dekker, New York, 1975). Two shortcut rules have been derived by Peters and Timmerhaus (1980; listed in Chapter 1 References) for optimum diameters of steel pipes of l-in. size or greater, for turbulent and laminar flow: D = 3.9Q”.45po.‘3, turbulent flow, (6.32) D = 3.0Q”.36po.18, laminar flow. (6.33) D is in inches, Q in cuft/sec, p in lb/tuft, and p in cP. The factors involved in the derivation are: power cost = O.O55/kWh, friction loss due to fittings is 35% that of the straight length, annual fixed charges are 20% of installation cost, pump efficiency is 50%, and cost of l-in. IPS schedule 40 pipe is $0.45/ft. Formulas that take additional factors into account also are developed in that book. Other detailed studies of line optimization are made by Happel and Jordan (Chemical Process Economics, Dekker, New York, 1975) and by Skelland (1967). The latter works out a problem in simultaneous optimization of pipe diameter and pumping tem- perature in laminar flow. Example 6.8 takes into account pump costs, alternate kinds of drivers, and alloy construction. 6.6. NON-NEWTONIAN LIQUIDS Not all classes of fluids conform to the frictional behavior described in Section 6.3. This section will describe the commonly recognized types of liquids, from the point of view of flow behavior, and will summarize the data and techniques that are used for analyzing friction in such lines. VISCOSITY BEHAVIOR The distinction in question between different fluids is in their viscosity behavior, or relation between shear stress r (force per unit area) and the rate of deformation expressed as a lateral velocity
- 120. 6.6. NON-NEWTONIAN LIQUIDS 101 EXAMPLE 6.5 Comparison of Pressure Drops in a Line with Several Sets of Fittings Resistances The flow considered is in a 12-inch steel line at a Reynolds number of 6000. With E = 0.00015, Round’s equation gives f = 0.0353. The line composition and values of fittings resistances are: Table 6.6 Table 6.4 Table 6.5 L K K, 4 K Line 1000 6 LR ells 0.25 ii0 075 0.246 4 tees, branched fi 0.5 150 0 . 1 5 0 . 5 6 7 2 gate valves, open 1 globe valve 3470 0.05 300 0 . 1 0 0 . 1 5 8 5.4 1500 4 . 0 0 4 . 5 8 1738 9.00 8.64 Table 6.4, &=;(1738)=61.3, Table 6.5, A P 0 =f+ K, = 0~035w~) + gJ0 = 44 1 3 . , Table 6.6, A P 0 = 35.3 + 8.64 = 43.9. The value K = 0.05 for gate valve from Table 6.5 appears to be low: Chemical Engineering Handbook, for example, gives 0.17, more nearly in line with that from Table 6.6. The equivalent length method of Table 6.4 gives high pressure drops; although convenient, it is not widely used. EXAMPLE 6.6 Friction factor: A Network of Pipelines in Series, Parallel, and Branches: the Sketch, Material Balances, and Pressure Drop Equations Pressure drop: Jj = 1.6364/[1n(c/D, + 6.5/(NnJij)]‘. Pressure drops in key lines: hei = (8plg,n2)f;iLijQ;/D, = k&L,Q;/D;. Q, ” * 3 7 6 Reynolds number: (Ge)ij = JQ,jPlnDijP. (4 App12 = PI - f’z - &L,,Q:,lD:, = 0, Apa3 = P2 - P3 - kf,,L,,Q$JD& = 0, Ap,, = P2 - Ps = kf~~)L~~)(Q~))‘/(D~))5 = kf~~~L~~~(Q~~~)2/(D~~)5 = kf~~)L~)(Q~~))2/(D~))5 App4s = P4 - P5 - kfd5 L,, Q&/L& = 0, Ap,, = Ps - Ps - kf,&L!:dD:, = 0 N o d e Material Balance at Node: 1 c&,-cl,,-Q,,=O 2 Q,,-Q,,-Q~~-Q~~-Q~~=O 3 Q,,+Q,,-OS,=0 4 Q,4-Q40-Q45=0 5 Q + Ql” + Q’2’ + Q’3’ 2s - Qs, - Qss = 0 6 Q;;+Q:,“-Q;;=O Overall Q,,+Q,,-Q,,-Q,,-Q,,=O (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (1‘3 (17) EXAMPLE 6.7 Flow of Oil in a Branched Pipeline The pipeline handles an oil with sp gr = 0.92 and kinematic viscosity of 5centistokes(cS) at a total rate of 12,00Ocuft/hr. All three pumps have the same output pressure. At point 5 the elevation is 100 ft and the pressure is 2 atm gage. Elevations at the other points are zero. Line dimensions are tabulated following. The flow rates in each of the lines and the total power requirement will be found. Line L (ft) D (ft) 14 1000 0.4 24 2000 0.5 = 34 1500 0.3 4 5 4000 0.75 Q, + Q, + Q3 = Q., = 12,000/3600 = 3.333 cfs N -3L- 4Q 23,657Q zz- Re nDV nD(5/92,900) D 59,142&r 47,313(2,, 78,556Q2,, 31,542Q2,, (1) (2)
- 121. 102 FLOW OF FLUIDS EXAMPLE 6.7-(continued) E = 0.00015 ft, h = 8fL2Q: = 0.0251fLQ2,DS ft, f gcn D Q,[ 1 + 1.2352 fi (,,I” + 0.3977($1’2] = Q4 = 3.333, (3) (4) (5) (6) (7) (8) 1.6364 ’ = [ln(2.03(10-‘)/D + 6.5/NRJ2. For line 45, (N& = 31542 (3.333) = 105,140, f4 = 0.01881, @f 145 = 0.02517(0.01881)(4000)(3.333)2 = 88,65 ft, (o.75)5 Procedure: 1. 2. 3. 4. 5. As a first trial assume fi = f2 =f3, and find fJ, = 1.266 from Eq. (8). Find Q, and Q3 from Eqs. (6) and (7). With these values of the Qi, find improved values of the f; and hence improved values of Q2 and Q3 frog Eqs. (6) and (7). Check how closely Q, + Q2 + Q3 - 3.333 = 0. If check is not close enough, adjust the value of Q, and repeat the calculations. The two trials shown following prove to be adequate. Q, 0, Q, 0.3 10/3-a, f, 1.2660 1.5757 0.4739 3.3156 0.0023 0.02069 1.2707 1.5554 0.5073 3.3334 0.0001 0.02068 Summary : Line &#. f a 4 I 14 75,152 0.02068 1.2707 82.08 24 60,121 0.02106 1.5554 82.08 34 99,821 0.02053 0.5073 82.08 45 105,140 0.01881 3.3333 88.65 hf14 = kf24 = 5 34 = 0.02517(0.02068)(1000)(1.2707)2 = 82.08 ft. (o.4)5 Velocity head at discharge: s=&&$=O.SSft. Total head at pumps: 2(2117) hp = 0.92(62.4) + loo + 0.88 + 82.08 + 88.65 = 345.36 ft. 0.92(62.4)(10/3)345.36 = 66,088 ft lb/set 120.2 HP, 89.6 kW. 1 0 ! ExarilF-le 6 7 ; t 1 ow in a ts t-at-, chcd PIPeline 20 REAU Dl,D2>D3,Ll>L2,L3 30 DATA .4,.5,.3>1000>2000>1500 48 INFIJT Ql 50 Q2=1.2352$Ql 60 Q3=.397i*Ql 70 R1=59142561 8 0 R2=47313*Ql 90 R3=78556*Ql 100 Fl=1.6364/L#G~.135f.00015~Dl +6.51Rl>^2 110 F2=1.6364/LOGC.l35*.00015~D2 +6.5.‘R2)*2 120 F3=1.6364iLOGC.135Y.00015~D3 +6.5/R3)*2 1 3 0 Q2=1,2352SQl*CFl~F2>^.5 ! i m p r o v e d v a l u e 1 4 0 Q3=.3977%Ql%CFl/F3>‘.5 ! imp r o v e d v a l u e 1 5 0 X=10/3-G!l-Q2-Q3 ! s h o u l d b e l e s s t h a n 0 . 0 0 0 1 1 6 0 DISF XpQl>G!2,Q3 1 7 0 GOTO 4 0 ! c h o o s e a n o t h e r val UQ o f 121 i f condi?icln o f s t e P 1 5 0 i s n o t s a t i s f i e d 180 END. Characteristics of the alternate pump drives are: Economic Optimum Pipe Size for Pumping Hot Oil with a Motor or Turbine Drive A centrifugal pump and its spare handle 1OOOgpm of an oil at 500°F. Its specific gravity is 0.81 and its viscosity is 3.OcP. The length of the line is 600 ft and its equivalent length with valves and other fittings is 9OOft. There are 12 gate valves, two check valves, a. Turbines are 36OOrpm, exhaust pressure is 0.75 bar, inlet pressure is 20 bar, turbine efficiency is 45%. Value of the high pressure steam is $5.25/10OOlbs; that of the exhaust is $0.75/1000 lbs. h. Motors have efficiency of 90%, cost of electricity is $O.O65/kWh. and one control valve. Cost data are: Suction pressure at the pumps is atmospheric; the pump head exclusive of line friction is 120 psi. Pump efficiency is 71%. Material of construction of line and pumps is 316 SS. Operation is 8000 hr/yr. 1. Installed cost of pipe is 7.50 $/ft and that of valves is 600D”.7 $ each, where D is the nominal pipe size in inches.
- 122. EXAMPLE 6.8-(continued) 2. Purchase costs of pumps, motors and drives are taken from Manual of Economic Analysis of Chemical Processes, Institut Francais du Petrole (McGraw-Hill, New York, 1976). 3. All prices are as of mid-1975. Escalation to the end of 1984 requires a factor of 1.8. However, the location of the optimum will be approximately independent of the escalation if it is assumed that equipment and utility prices escalate approximately uniformly; so the analysis is made in terms of the 1975 prices. Annual capital cost is 50% of the installed price/year. The summary shows that a 6-in. line is optimum with motor drive, and an B-in. line with turbine drive. Both optima are insensitive to line sizes in the range of 6-10 in. Q = 1000/(7.48)(60) = 2.2282 cfs, 227.2 m3/hr, N -4Qp -4(2.2282)(0.81)(62.4)-71,128 Re nDp n(O.O00672)(3)D D ’ 0.135(0.00015) 6 . 5 0 2 D +71,128 1 Pump head: h = 120(144) 8fLQ’ p O.gl(62.4) +$$ = 341.88 + 124.98f /Ds ft. Motor power: p =C?P~ = 2.22fWO.W h WI 17,vm p 550(0.71(0.90)) p = 0.3204h,, HP Turbine power: p = 2’2282(50’54) h r 550(0.71) p = 0, 2883h ,,, HP. Steam 6.6. NON-NEWTONIAN LIQUIDS 103 = 10.14 kg/HP (from the “manual”) = 10.14(0.2883)(2.204)h,/1000 = 0.006443hp, 1000 lh/hr. Power cost: O.O65(8000)(kw), $/yr, Steam cost: 4.5(8000)(lOOOlb/hr), $/yr. Installed pump cost factors for alloy, temperature, etc (data in the “manual”) = 2[2.5(1.8)(1.3)(0.71)] = 8.2. Summary: IPS 4 6 6 10 D (ft) 0.3355 0.5054 0.6651 0.8350 1OOf 1 a9 1.67 1.89 1.93 hp (it) 898 413 360 348 Pump efficiency 0.71 0.71 0.71 0.71 motor (kW) 214.6 98.7 86.0 83.2 Steam, 1000 Ib/hr 5.97 2.66 2.32 2.25 Pump cost, 2 installed 50,000 28,000 28,000 28,000 Motor cost, 2 installed 36,000 16,000 14,000 14,000 Turbine cost, 2 installed 56,000 32,000 28,000 28,000 Pipe cost 18,000 27,000 36,000 45,000 Valve cost 2 3 , 7 5 0 3 1 , 5 4 6 3 8 , 5 8 4 4 5 , 1 0 7 Equip cost, motor drive 1 2 7 , 7 5 0 9 3 , 5 4 6 1 0 7 , 5 8 4 1 2 3 , 1 0 7 Equip cost, turbine drive 1 4 7 , 7 5 0 1 0 9 , 5 4 6 1 2 1 , 5 8 4 1 3 7 , 1 0 7 Power cost ($/yr) 1 1 1 , 5 9 2 5 1 , 3 2 4 4 4 , 7 2 0 4 3 , 2 6 4 Steam cost ($/yr) 2 0 8 , 4 4 0 9 5 , 7 6 0 8 3 , 5 2 0 8 0 , 8 3 4 Annual cost, motor drive 1 7 5 , 4 6 7 9 8 , 0 9 7 9 8 , 5 1 2 1 0 4 , 8 1 7 Annual cost, turbine drive 2 8 2 , 3 1 5 1 5 0 , 5 3 3 1 4 4 , 3 1 2 1 4 9 , 3 8 7 gradient, f = du/dx. The concept is represented on Figure 6.2(a): one of the planes is subjected to a shear stress and is translated parallel to a fixed plane at a constant velocity but a velocity gradient is developed between the planes. The relation between the variables may be written r = F/A = p(du/dx) = pLj, (6.34) where, by definition, p is the viscosity. In the simplest case, the viscosity is constant, and the fluid is called Newtonian. In the other cases, more complex relations between z and y involving more than one constant are needed, and dependence on time also may be present. Classifications of non-Newtonian fluids are made according to the relation between r and + by formula or shape of plot, or according to the mechanism of the resistance of the fluid to deformation. The concept of an apparent viscosity CL, = r/P (6.35) is useful. In the Newtonian case it is constant, but in general it can be a function of t, 9, and time 0. Non-Newtonian behavior occurs in solutions or melts of polymers and in suspensions of solids in liquids. Some t-p plots are shown in Figure 6.2, and the main classes are described following. 1. Pseudoplastic liquids have a z-9 plot that is concave downward. The simplest mathematical representation of such relations is a power law r=Kp”, n<l (6.36) with n < 1. This equation has two constants; others with many more than two constants also have been proposed. The apparent viscosity is pa = z/p = K/j+‘. (6.37) Since n is less than unity, the apparent viscosity decreases with the deformation rate. Examples of such materials are some polymeric solutions or melts such as rubbers, cellulose acetate and napalm; suspensions such as paints, mayonnaise, paper pulp, or detergent slurries; and dilute suspensions of inert solids. Pseudoplastic properties of wallpaper paste account for good spreading and adhesion, and those of printing inks prevent their running at low speeds yet allow them to spread easily in high speed machines. 2. Dilatant liquids have rheological behavior essentially
- 123. 104 F L O W O F F L U I D S Deformation rate [du/dy lb) (a) Shearmg stress - (e) Figure 6.2. Relations between shear stress, deformation rate, and viscosity of several classes of fluids. (a) Distribution of velocities of a fluid between two layers of areas A which are moving relatively to each other at a distance x under influence of a force F. In the simplest case, F/A = p(du/&) with p constant. (b) Linear plot of shear stress against deformation. (c) Logarithmic plot of shear stress against deformation rate. (d) Viscosity as a function of shear stress. (e) Time-dependent viscosity behavior of a rheopectic fluid (thixotropic behavior is shown by the dashed line). (f) Hysteresis loops of time-dependent fluids (arrows show the chronology of imposed shear stress). r--Bingham plastic
- 124. opposite those of pseudoplastics insofar as viscosity behavior is concerned. The t--P plots are concave upward and the power law applies t=Kf”, n>l, (6.38) but with n greater than unity; other mathematical relations also have been proposed. The apparent viscosity, ,u. = KY-l, increases with deformation rate. Examples of dilatant materials are pigment-vehicle suspensions such as paints and printing inks of high concentrations; starch, potassium silicate, and gum arabic in water; quicksand or beach sand in water. Dilatant properties of wet cement aggregates permit tamping operations in which small impulses produce more complete settling. Vinyl resin plastisols exhibit pseudoplastic behavior at low deformation rates and dilatant behavior at higher ones. 3. Bingham plastics require a finite amount of shear stress before deformation begins, then the deformation rate is linear. Mathematically, r = to + /&(dU/dx) = to + ,uBj, (6.39) where pL8 is called the coefficient of plastic viscosity. Examples of materials that approximate Bingham behavior are drilling muds; suspensions of chalk, grains, and thoria; and sewage sludge. Bingham characteristics allow toothpaste to stay on the brush. 4. Generalized Bingham or yield-power law fluids are represented by the equation t=t,+Kf”. (6.40) Yield-dilatant (n > 1) materials are rare but several cases of 0.50 0.45 0 . 4 0 0.35 ‘, 0 . 3 0 I g 0.25 . b l/l- 0.20 z 6 0.15 b al 0.10 6 I - 1 I I I I I I Shear Rate , sec.’ 8267 1377 c ” 918 0 20 4 0 60 80 100 120 140 160 Duration of Shear, min Figure 6.3. Time-dependent rheological behavior of a rheopectic fluid, a 2000 molecular weight polyester [after Steg and Katz, J. Appl. Polym. Sci. 9, 3177 (1965)]. 6.6. NON-NEWTONIAN LIQUIDS 105 yield-pseudoplastics exist. For instance, data from the literature of a 20% clay in water suspension are represented by the numbers to = 7.3 dyn/cm*, K = 1.296 dyn(sec)“/cm’ and n = 0.483 (Govier and Aziz, 1972, p. 40). Solutions of OS-5.0% carboxypolymethylene also exhibit this kind of behavior, but at lower concentrations the yield stress is zero. 5. Rheopecticfluids have apparent viscosities that increase with time, particularly at high rates of shear as shown on Figure 6.3. Figure 6.2(f) indicates typical hysteresis effects for such materials. Some examples are suspensions of gypsum in water, bentonite sols, vanadium pentoxide sols, and the polyester of Figure 6.3. 6. Z’hixotropic fiuio!.s have a time-dependent rheological behavior in which the shear stress diminishes with time at a constant deformation rate, and exhibits hysteresis [Fig. 6.2(f)]. Among the substances that behave this way are some paints, ketchup, gelatine solutions, mayonnaise, margarine, mustard, honey, and shaving cream. Nondrip paints, for example, are thick in the can but thin on the brush. The time-effect in the case of the thixotropic crude of Figure 6.4(a) diminishes at high rates of deformation. For the same crude, Figure 6.4(b) represents the variation of pressure gradient in a pipe line with time and axial position; the gradient varies fivefold over a distance of about 2 miles after 200 min. A relatively simple relation involving five constants to represent thixotropic behavior is cited by Govier and Aziz (1972, p. 43): 7J = (PO + cd)?, (6.41) M/d0 = a - (a + by)A. (6.42) The constants pO, a, b, and c and the structural parameter I are obtained from rheological measurements in a straightforward manner. 7. Viscoelastic fluids have the ability of partially recovering their original states after stress is removed. Essentially all molten polymers are viscoelastic as are solutions of long chain molecules such as polyethylene oxide, polyacrylamides, sodium carboxy- methylcellulose, and others. More homely examples are egg whites, dough, jello, and puddings, as well as bitumen and napalm. This property enables eggwhites to entrap air, molten polymers to form threads, and such fluids to climb up rotating shafts whereas purely viscous materials are depressed by the centrifugal force. Two concepts of deformability that normally are applied only to solids, but appear to have examples of gradation between solids and liquids, are those of shear modulus E, which is E = shear stress/deformation, (6.43) and relaxation time 0*, which is defined in the relation between the residual stress and the time after release of an imposed shear stress, namely, T= roexp(-8/O*). (6.44) A range of values of the shear modulus (in kgf/cm’) is Gelatine 0.5% solution 4 x lo-lo 10% solution (jelly) 5 x lo-* Raw rubber 1.7 x lo2 Lead 4.8x 10” Wood (oak) 8~10~ Steel 8~10~
- 125. 106 FLOW OF FLUIDS E 5 i?! 4 iz 3 Duration of Pkmbino Crude Oil, Temperature 44.5;F lO-2 I ,I I I,l,, IOI I lo 20 30 50 70 100 200 300 500 (a) 0.0032 0.0028 T z 0 0.0024 21; ; 0.0020 z d ; 0.0016 e 7 z OL: 0.0012 O.OOOE 0.0004 b) Rate of Shear, s+ IO ,sec-’ Figure 6.4. Shear and pipeline flow data of a thixotropic Pembina crude oil at 44.5”F. (a) Rheograms relating shear stress and rate of shear at several constant durations of shear (Ritter and Govier, Can. J. Chem. Eng. 48, 505 (1970)]. (b) Decay of pressure gradient of the fluid flowing from a condition of rest at 15,000 barrels/day in a 12 in. line [Ritter and B&y&y, SPE Journal 7, 369 (1967)]. and that of relaxation time (set) is Water 3 x 1o-6 Castor oil 2 x 1o-3 Copal varnish 2x 10 Colophony (at 55°C) 5x 10 Gelatine, 0.5% solution 8~10~ Colophony (at 12°C) 4x 10s Ideal solids cc Examples thus appear to exist of gradations between the properties of normally recognized true liquids (water) and true solids. Elastic properties usually have a negligible effect on resistance to flow in straight pipes, but examples have been noted that the resistances of fittings may be as much as 10 times as great for viscoelastic liquids as for Newtonian ones. PIPELINE DESIGN The sizing of pipelines for non-Newtonian liquids may be based on scaleup of tests made under the conditions at which the proposed line is to operate, without prior determination and correlation of rheological properties. A body of theory and some correlations are available for design with four mathematical models: rw = Kp”, power law, (6.45) rw = zy + PBY1 Bingham plastic, (6.46) r,=q,+Kjf’, Generalized Bingham or yield-power law, (6.47) z, = K’@/D)“’ Generalized power law (Metzner-Reed) (AZChE J. 1,434, 1955). (6.48) In the last model, the parameters may be somewhat dependent on the shear stress and deformation rate, and should be determined at magnitudes of those quantities near those to be applied in the plant. The shear stress r,,, at the wall is independent of the model and is derived from pressure drop measurements as z, = DAPI4L. (6.49) Friction Factor. In rheological literature the friction factor is defined as (6.50) This value is one-fourth of the friction factor used in Section 6.3. For the sake of consistency with the literature, the definition of Eq. (6.50) will be used with non-Newtonian fluids in the present section. Table 6.2 lists theoretical equations for friction factors in laminar flows. In terms of the generalized power law, Eq. (6.48), f=+= K’(SV/D)“’ PV I% PV2/2tTc 16 = D”‘V2-“‘p/g,K’8”‘-l~ By analogy with the Newtonian relation, f = 16/Re, the denominator of Eq. (6.52) is designated as a modified Reynolds number, Re,, = D”‘V2-“‘p,gcK’8”‘-l~ (6.53) The subscript MR designates Metzner-Reed, who introduced this form. Scale Up. The design of pipelines and other equipment for handling non-Newtonian fluids may be based on model equations with parameters obtained on the basis of measurements with viscometers or with pipelines of substantial diameter. The shapes of plots of t, against p or W/D may reveal the appropriate model. Examples 6.9 and 6.10 are such analyses. In critical cases of substantial economic importance, it may be advisable to perform flow tests-Q against BP-in lines of moderate size and to scale up the results to plant size, without necessarily trying to fit one of the accepted models. Among the effects that may not be accounted for by such models are time
- 126. 6.6. NON-NEWTONIAN LIQUIDS 107 EXAMPLE 6.9 Analysis of Data Obtained in a Capillary Tube Viscometer Data were obtained on a paper pulp with specific gravity 1.3, and are given as the first four columns of the table. Shear stress t, and deformation rate 7 are derived by the equations applying to this kind of viscometer (Skelland, 1967, p. 31; Van Wazer et al., 1963, p. 197): r, = D API4L, . 3n’+l 8 - - '= 4n' D (7 d 144 n”d ln(8V/D) The plot of log r, against log (8V/D) shows some scatter but is approximated by a straight line with equation rw = 1.329(8V/D)“.5*. Since f = (2.53/2.08)(8V/D), the relation between shear stress and deformation is given by the equation t, = 1.203i,“.51 0.15 14 0.20 3200 464 8.57 0.15 14 0.02 1200 46.4 3.21 0.30 28 0.46 1950 133.5 5.22 0.30 28 0.10 860 29.0 2.30 0.40 28 1.20 1410 146.9 5.04 Parameters of the Bingham Model from Measurements of Pressure Drops in a Line Data of pressure drop in the flow of a 60% limestone slurry of density 1.607g/ml were taken by Thomas [Znd. Eng. Chem. 55, 18-29 (1963)]. They were converted into data of wall shear stress r, = DAP/4L against the shear rate 8V/D and are plotted on the figure for three line sizes. The Buckingham equation for Bingham flow in the laminar region is The second expression is obtained by neglecting the fourth-power term. The Bingham viscosity ,ur, is the slope of the plot in the laminar region and is found from the terminal points as pB = (73-50)/(347-O) = 0.067 dyn set/cm’. From the reduced Buckingham equation, ra = 0.75t, (at 8V/D = 0) = 37.5. Accordingly, the Bingham model is represented by rw = 37.5 +0.067(81/‘/D), dyn/cm’ with time in seconds. Transitions from laminar to turbulent flow may be identified off a 4.04 cm dia _ 2 ,, 7.75 cm dia 3 0 0 200 400 600 -, 800 SHEAR RATE Ev/D, SAC the plots: D = 2.06 cm, 8V/D = 465, V = 120 cm/set 4.04 215, 109 7.75 (critical not reached). The transition points also can be estimated from Hanks’ correlation [AZChE .I. 9, 45, 306 (1963)] which involves these expressions: xc = (%/LL He = D*q,p/&, x,/(1 - x,)~ = He/16,800, Re,, = (1 - $x, + fxd)He&,. The critical linear velocity finally is evaluated from the critical Reynolds number of the last equation with the following results;
- 127. 108 FLOW OF FLUIDS EXAMPLES 6.1~(continued) D (cm) 1O-4 H e 2 . 0 6 5 . 7 4.04 2 2 . 0 7 . 7 5 81 .O xc %, v, 0.479 5 6 3 5 114(120) 0.635 8945 93 (109) 0.750 14,272 77 The numbers in parentheses correspond to the break points on the figure and agree roughly with the calculated values. The solution of this problem is based on that of Wasp et al. (1977). dependence, pipe roughness, pipe fitting resistance, wall slippage, and viscoelastic behavior. Although some effort has been devoted to them, none of these particular effects has been well correlated. Viscoelasticity has been found to have little effect on friction in straight lines but does have a substantial effect on the resistance of pipe fittings. Pipe roughness often is accounted for by assuming that the relative effects of different roughness ratios E/D are represented by the Colebrook equation (Eq. 6.20) for Newtonian fluids. Wall slippage due to trace amounts of some polymers in solution is an active field of research (Hoyt, 1972) and is not well predictable. The scant literature on pipeline scaleup is reviewed by Heywood (1980). Some investigators have assumed a relation of the form z, = DAPI4L = kV”/Db and determined the three constants K, a, and b from measurements on several diameters of pipe. The exponent a on the velocity appears to be independent of the diameter if the roughness ratio E/D is held constant. The exponent b on the diameter has been found to range from 0.2 to 0.25. How much better this kind of analysis is than assuming that a = b, as in Eq. (6.48) has not been established. If it can be assumed that the effect of differences in E/D is small for the data of Examples 6.9 and 6.10, the measurements should plot as separate lines for each diameter, but such a distinction is not obvious on those plots in the laminar region, although it definitely is in the turbulent region of the limestone slurry data. Observations of the performance of existing large lines, as in the case of Figure 6.4, clearly yields information of value in analyzing the effects of some changes in operating conditions or for the design of new lines for the same system. Laminar Flow. Theoretically derived equations for volumetric flow rate and friction factor are included for several models in Table 6.7. Each model employs a specially defined Reynolds number, and the Bingham models also involve the Hedstrom number, He = z,pD’/& (6.54) These dimensionless groups also appear in empirical correlations of the turbulent flow region. Although even in the approximate Eq. (9) of Table 6.7, group He appears to affect the friction factor, empirical correlations such as Figure 6.5(b) and the data analysis of Example 6.10 indicate that the friction factor is determined by the Reynolds number alone, in every case by an equation of the form, f = 16/Re, but with Re defined differently for each model. Table 6.7 collects several relations for laminar flows of fluids. Transitional Flow. Reynolds numbers and friction factors at which the flow changes from laminar to turbulent are indicated by the breaks in the plots of Figures 6.4(a) and (b). For Bingham models, data are shown directly on Figure 6.6. For power-law liquids an equation for the critical Reynolds number is due to Mishra and Triparthi [Z’runs. ZChE 51, T141 (1973)], Re, = 1400(2n + 1)(5n + 3) c (3n + 1)2 . (6.55) The Bingham data of Figure 6.6 are represented by the equations of Hanks [AZChE J. 9, 306 (1963)], (Re,),=e(l-i*,+fxf), H e - - - (1 -x;,)” - 16,800. (6.56) (6.57) They are employed in Example 6.10. Turbulent Flow. Correlations have been achieved for all four models, Eqs. (6.45)-(6.48). For power-law flow the correlation of Dodge and Metzner (1959) is shown in Figure 6.5(a) and is represented by the equation $= ,n:$,, log,,[Re,.f(‘~“‘“)] -s. These authors and others have demonstrated that these results can represent liquids with a variety of behavior over limited ranges by TABLE 6.7. Laminar Flow: Volumetric Flow Rate, Friction Factor, Reynolds Number, and Hedstrom Number Newtonian f = 16/Re, Fie = DVply Power Law [Eq. (6.491 (1) Q+p-)(g” f = 16lRe’ Bingham Plastic [Eq. (6.4611 iTD3t Q=L 32~~ Re, = DVple, He = toD2pl& 1 fHe 4 -=---+J& (solveforfl R% 1 6 SRe, f= 96Rei 6Re, + He [neglecting (s,/rw14 in Eq. (91 (5) (6) (7) (8) (9) &neralized Bingham (Yield-Power Law) [Eq. (6.4711 Qua& (y(l-5) x[l*[l+$y)(l+ny] (10) f=g(l-gJ 111 (11) IRe’ bv Ea. (4) and He by Eq. (7)I
- 128. 10,000 R E Y N O L D S N U M B E R , Re,, (a) 6.7. GASES 109 IO’ IO’ IO’ IO’ B i n g h a m R e y n o l d s N u m b e r . Re, lb) Figure 6.5. Friction factors in laminar and turbulent flows of power-law and Bingham liquids. (a) r, = K’(8V/D)“‘, with K’ and n’ constant or dependent on T,: l/$= [4.0/(n;)“.‘5~log,o[Re,.f( For pseudoplastic liquids represented by n *)I - 0.40/(n')'.', [Dodge and Metzner, AIChE J. 5, 189 (1959)]. (b) For Bingham plastics, Re, - - DVplp,, He = t,D p/p* [Hanks and Dadia, AIChE J. 17,554 (1971)]. evaluating K’ and n’ in the range of shear stress z,,, = DAP/4L that will prevail in the required situation. Bingham flow is represented by Figure 6.5(b) in terms of Reynolds and Hedstrom numbers. Theoretical relations for generalized Bingham flow [Eq. (6.47)] have been devised by Torrance [S. Afr. Me&. Eng. 13, 89 (1963)]. They are 2.69 n-2.95 +Fln(l-x) > + F In(Re~~1-“‘2) + y (%I - 8) (6.59) with the Reynolds number Re, = D”V2-“p/8”m’K and where (6.60) x = ro/5,. (6.61) In some ranges of operation, materials may be represented approximately equally well by several models, as in Example 6.11 where the power-law and Bingham models are applied. 6.7. GASES The differential energy balances of Eqs. (6.10) and (6.15) with the friction term of Eq. (6.18) can be integrated for compressible fluid flow under certain restrictions. Three cases of particular importance are of isentropic or isothermal or adiabatic flows. Equations will be developed for them for ideal gases, and the procedure for nonideal gases also will be indicated. I S E N T R O P I C F L O W In short lines, nozzles, and orifices, friction and heat transfer may be neglected, which makes the flow essentially isentropic. Work transfer also is negligible in such equipment. The resulting theory is a basis of design of nozzles that will generate high velocity gases for Figure 6.6. Critical Reynolds number for transition from laminar to turbulent flow of Bingham fluids. The data also are represented by Eqs. (6.56) and (6.57): (0) cement rock slurry; (A) river mud slurries; (0) clay slurry; (P) sewage sludge; (A) ThO, slurries; (m) lime slurry. [Hanks and Pratt, SPE Journal, 342-346 (Dec. 1967)]. power production with turbines. With the assumptions indicated, Eq. (6.10) becomes simply dH + (l/g& du = 0, (6.62) which integrates into HZ-HI++-u;)=O. (6.63) c One of these velocities may be eliminated with the mass balance, +I = u,A,/V, = u,A,/V, (6.64) so that u; - u: = (rizV,/A,)*[l - (A2VI/A,V2)*]. For ideal gases substitutions may be made from H2 - HI = C,( T, - TI) (6.65) (6.66)
- 129. 110 FLOW OF FLUIDS and T*/T, = (P2/Pl)‘k-“‘k = (VJV,)“. (6.67) After these substitutions are made into Eq. (6.63), the results may be solved for the mass rate of flow as At specified mass flow rate and inlet conditions Pr and VI, Eq. (6.68) predicts a relation between the area ratio AZ/Al and the pressure ratio P,/P, when isentropic flow prevails. It turns out that, as the pressure falls, the cross section at first narrows, reaches a minimum at which the velocity becomes sonic; then the cross section increases and the velocity becomes supersonic. In a duct of constant cross section, the velocity remains sonic at and below a critical pressure ratio given by p, 2 -4 1 kl(k+ 1) 4 k+l . (6.69) The sonic velocity is given by u,=vamms+.> (6.70) where the last result applies to ideal gases and M, is the molecular weight. ISOTHERMAL FLOW IN UNIFORM DUCTS When elevation head and work transfer are neglected, the mechanical energy balance equation (6.13) with the friction term of Eq. (6.18) become fu2 VdP + (l/g& du + ~ dL = 0. W’ (6.71) Make the substitutions u=GJp=GV (6.72) and the ideal gas relation V = PIVl/P and dV/V = -dP/P so that Eq. (6.71) becomes (6.73) (6.74) This is integrated term-by-term between the inlet and outlet conditions, and may be rearranged into p2=p23V,G2 fL 2 1 g,[20+4~)1 (6.76) (6.75) In terms of a density, pm, at the average pressure in the line, (6.77) The average density may be found with the aid of an approximate evaluation of P2 based on the inlet density; a second trial is never justified. Eqs. (6.76) and (6.77) and the approximation of Eq. (6.76) obtained by neglecting the logarithmic term are compared in Example 6.12. The restriction to ideal gases is removed in Section 6.7.4. ADIABATIC FLOW The starting point for development of the integrated adiabatic flow energy balance is Eq. (6.71) and again ideal gas behavior will be assumed. The equation of condition of a static adiabatic process, PVk = const, is not applicable to the flow process; the appropriate EXAMPLE 6.11 Pressure Drop in Power-Law and Bingham Plow A limestone slurry of density 1.693 g/mL is pumped through a 4-in. (152 mm) line at the rate of 4 ft/sec (1.22 m/set). The pressure drop (psi/mile) will be calculated. The slurry behavior is represented by a. The power-law with n = 0.165 and K = 34.3 dyn sec”.165/cm2 (3.43 Pa sec0.r6’). h. Bingham model with to= 53 dyn/cm2 (5.3 Pa) and pa = 22cP (0.022 Pa set). Power law: Re’ = D”V2-“p/8”-1K = (0.152)“~165(1.22)1~835(1693)(8)o.835/3.43 =2957, f = 0.0058 [Fig. 6.6(a)] A P 4fpV= 4(0.0058)(1693)(1.22)= -=-= L 2gcD 2(0.152) = 192.3 N/(m’)(m) [gC = kgm/sec=/N], + 192.3(14.7/101,250)1610 = 45.0 psi/mile. Bingham: Re I3 = Dvp = 0.152(1.22)(1693) = 14 270 0.022 7 3 UR He = tbD2p/pi = 5.3(0.152)2(1693)/(0.022)2 = 428,000, critical Re, = 12,000 (Fig. 6.5), f = 0.007 [Fig. 6.6(b)], AP 0.007 L = 0.0058 45.0 = 54.3 psi/mile.
- 130. 6.8. LIQUID-GAS FLOW IN PIPELINES 111 one is obtained as follows. Begin with =C,dT=& dT = & d(PV), from which d(PV) = (y)g VdV, (6.78) (6.79) (6.80) and the integral is PV = PIVl - ( > 7 g (V”- v:>. c (6.81) Also VdP = d(PV) - (PV) $ (6.82) Substitutions into Eq. (6.71) result in d(PV)-PV$+f%dV+$$dL=O. c c (6.83) Further substitutions from Eqs. (6.80) and (6.81) and multiplying through by 2kg,/G2V2 result in 2 dv _ %cP, V, V 7+(k-1)V; G 1 $+(k-l)y+;dL=O. (6.84) Integrating from VI to V, and L = 0 to L gives or (k+I)ln$+i[v+(k-I)Vf]($--$)+%=O 1 2 1 (6.85) (6.86) In terms of the inlet Mach number, M, = u,/~g~kRTIM, = GV,/~g~kRTJM,, the result becomes (6.87) l- v (:)‘I +Tln(z)‘. ( 6 . 8 8 ) When everything else is specified, Eqs. (6.86) or (6.88) may be solved for the exit specific volume V,. Then P2 may be found from Eq. (6.81) or in the rearrangement !g+l+(~M~)[l-(!5)2], 11 1 from which the outlet temperature likewise may be found. (6.89) Although the key equations are transcendental, they are readily solvable with hand calculators, particularly those with root-solving provisions. Several charts to ease the solutions before the age of calculators have been devised: M.B. Powley, Can. J. Chem. Eng., 241-245 (Dec. 1958); C.E. Lapple, reproduced in Perry’s Chemical Engineers’ Handbook, McGraw-Hill, New York, 1973, p. 5.27; 0. Levenspiel, reproduced in Perry’s Chemical Engineers’ Handbook, McGraw-Hill, New York, 1984, p. 5.31; Hougen, Watson, and Ragatz, Thermodynamics, Wiley, New York, 1959, pp. 710-711. In all compressible fluid pressure drop calculations it is usually justifiable to evaluate the friction factor at the inlet conditions and to assume it constant. The variation because of the effect of temperature change on the viscosity and hence on the Reynolds number, at the usual high Reynolds numbers, is rarely appreciable. NONIDEAL GASES Without the assumption of gas ideality, Eq. (6.71) is dP+~dV+fcZdL=O V gc V 20 ’ (6.90) In the isothermal case, any appropriate PVT equation of state may be used to eliminate either P or V from this equation and thus permit integration. Since most of the useful equations of state are pressure-explicit, it is simpler to eliminate P. Take the example of one of the simplest of the non-ideal equations, that of van der Waals P=&-$, of which the differential is Substituting into Eq. (6.90), (6.91) (6.92) (6.93) Although integration is possible in closed form, it may be more convenient to perform the integration numerically. With more accurate and necessarily more complicated equations of state, numerical integration will be mandatory. Example 6.13 employs the van der Waals equation of steam, although this is not a particularly. suitable one; the results show a substantial difference between the ideal and the nonideal pressure drops. At the inlet condition, the compressibility factor of steam is z = PV/RT = 0.88, a substantial deviation from ideality. 6.6. LIQUID-GAS FLOW IN PIPELINES In flow of mixtures of the two phases in pipelines, the liquid tends to wet the wall and the gas to concentrate in the center of the channel, but various degrees of dispersion of each phase in the other may exist, depending on operating conditions, particularly the individual flow rates. The main patterns of flow that have been recognized are indicated on Figures 6.7(a) and (b). The ranges of conditions over which individual patterns exist are represented on maps like those of Figures 6.7(c) and (d). Since the concept of a
- 131. 112 FLOW OF FLUIDS EXAMPLE 6.12 Adiabatic and Isothermal Flow of a Gas in a Pipeline Steam at the rate of 7000 kg/hr with an inlet pressure of 23.2 barabs and temperature of 220°C flows in a line that is 77.7mm dia and 30.5 m long. Viscosity is 28.5(10e6)N set/m’ and specific heat ratio is k = 1.31. For the pipe, E/D = 0.0006. The pressure drop wih be found in (a) isothermal flow; (b) adiabatic flow. Also, (c) the line diameter for sonic flow will be found. VI = 0.0862 m3/kg, G=7000/(3600)(~~/4)(0.0777)*=410.07 kg/m*sec, Re 1 -DG-0.0777(410.07)=l,12(106) P 28.5(10-6) f = 1.6364/[1n(0.13.5)(0.0006) + 6..5/l.2(106)J2 = 0.0187. Inlet sonic velocity: us1 = vg=kRT,/M,,, = Vl(l.31)(8314)493.2/18.02 = 546 m/set M,=u,/u,,= GV,/u,,= 410.07(0.0862)/546=0.0647. As a preliminary calculation, the pressure drop will be found by neglecting any changes in density: :. P2 = 23.2 - 5.32 = 17.88 bar. (a) Isothermal fIow. Use Eq. (6.76): F = 2(23.2)(10’)(0.0862)(410.07)* = 6.726(10”), p;-?!p(g+&)]l’z 2 = 10’ 23.2(10’) 0.0187(305)/2(0.0777)+ Inp 2 = 17.13(10’) N/m*, and AP = 23.2 - 17.13 = 5.07 bar. When the logarithmic term is neglected, P2= 17.07(10)5N/m2. (b) Adiabatic flow. Use Eq. (6.88): 0.0187(305) 0.0777 > 73.4 =182.47 l- Equation (6.89) for the pressure: = 1 + o’31(20;y)2 [l - (1.2962)‘] AP=23.2- 17.89=5.31 bar. (c) Line diameter for sonic flow. The critical pressure ratio is kl(k-I) = 0.5439, with k = 1.31, G=7000/3600-2.4757 (n/4)oZ D2 ’ M =~=2.4757(0.0862)=3.909(10-4) l us, 546D* D* ’ (4 Equation (6.89) becomes 0.5439(V2/Vl) = 1 + O.l183M:[l- (V,/V,)*], fL/D =0.0187(305)/D = 5.703510 = rhs of Eq. (6.88). Procedure (3) (4) 1. Assume D. 2. Find Ml [Eq. (2)]. 3. Find VJV, from Eq. (6.89) [Eq. (3)]. 4. Find rhs of Eq. (6.88) [Eq. (l)]. 5. Find D = 5.7035/[rhs of Eq. (6.88)] [Eq. (4)]. 6. Continue until steps 1 and 5 agree. Some trials are: Eq.(6.69) Eq.(6.66) D 4 WV, rhs D 0.06 0.1086 0.5457 44.482 0.1282 0.07 0.0798 0.5449 83.344 0.06843 0.0697 0.08046 0.5449 81.908 0.06963 :. D = 0.0697 m. 1 0 ! Example 6. 12. Line dia for sonic f l o w 2 0 K=1.31 3 0 I N P U T D ! ( T r i a l v a l u e > 4 0 M=.0003909/ll~~2 ! CEq 2) 5 0 I N P U T ‘J ! C=Vl/VZ> $9” 8 0 1:: 110 GOSIJP 1 3 0 I F ABS~X1~>=.0001 F=l/Z/KX<K-1+2fM*2 CK+l)x’2/KtLOG{V’Z) Ol=S . 7 0 3 5 / F OISP D>Dl THEN 50 zJ*:(l-v*2)+ ! (Es 11 GOTO 3 0 ! (For ano t h e r t r i a l value of D if it i s n o t cl0 s e enough t o c a l c u latcd Dl> 120 END 1 3 0 Xl=- < 5439~V~+l+~K-l>~Z~K*N* 2%Cl-l/V^2) 1 4 0 DISP X l 150 RETURN
- 132. particular flow pattern is subjective and all the pertinent variables apparently have not yet been correlated, boundaries between regions are fuzzy, as in (d). It is to be expected that the kind of phase distribution will affect such phenomena as heat transfer and friction in pipelines. For the most part, however, these operations have not been correlated yet with flow patterns, and the majority of calculations of two-phase flow are made without reference to them. A partial exception is annular flow which tends to exist at high gas flow rates and has been studied in some detail from the point of view of friction and heat transfer. The usual procedure for evaluating two-phase pressure drop is to combine pressure drops of individual phases in some way. To this end, multipliers $+ are defined by In the following table, subscript L refers to the liquid phase, G to the gas phase, and LO to the total flow but with properties of the liquid phase; x is the weight fraction of the vapor phase. Subscript R e AP/L e2 G DGxIPL, f,G2x2/2g Dp, (APILV(APIL), L DG(1 - x)lpL tG2(1 -x~J$P, (APILMAPIL), LO DGh, h,G=l2g&, W/U/W/L),, In view of the many other uncertainties of two phase flow correlations, the friction factors are adequately represented by 64/Re, Re < 2000, Poiseuille equation, f = {0.32/Re0.“, Re > 2000, Blasius equation. (6.95) (6.96) HOMOGENEOUS MODEL The simplest way to compute line friction in two-phase flow is to adopt some kinds of mean properties of the mixtures and to employ the single phase friction equation. The main problem is the assignment of a two-phase viscosity. Of the number of definitions that have been proposed, that of McAdams et al. [Trans. ASME 6.8. LIQUID-GAS FLOW IN PIPELINES 113 64, 193-200 (1942)] is popular: 1 lkVo-ph~S~ = X/k + (1 -x)//k. The specific volumes are weight fraction additive, (6.97) VtWO-phW = xv, + (1 - x)V, (6.98) so that 11Ptwo+3se =x/p, + (1 - X)IPL, (6.99) where x is the weight fraction of the gas. Pressure drops by this method tend to be underestimated, but are more nearly accurate at higher pressures and higher flow rates. With the Blasius equation (6.96), the friction factor and the pressure gradient become, with this model, (6.100) A P fG2 -r = 2g,D[xlp, + (1 - X)lPJ (6.101) A particularly simple expression is obtained for the multiplier in terms of the Blasius equation: APlL 1 - x + XPJP, -= “‘= (AP/L),, (1 -x + xpJno)“.25. Some values of $“,a from this equation for steam are x P = 0.669 bar P = 10.3 bar 0.01 3.40 1.10 0.10 12.16 1.95 0.50 80.2 4.36 High values of multipliers are not uncommon. (6.102) EXAMPLE 6.13 Isothermal Flow of a Nonideal Gas The case of Example 6.12 will be solved with a van der Waals equation of steam. From the CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1979), a = 5.464 atm(m3/kg mol)* = 1703.7 Pa(m3/kg)2, b = 0.03049 m3/kg mol = 0.001692 m3/kg, RT = 8314(493.2)/18.02 = 2.276(105) N m/kg. Equation (6.93) becomes +0.0187(410.07)2(305)=o 2(0.0777) ’ qb =f+62 [(v ~o,,~l~9)2+5'52$-4)+0.0272]~+ l-0 The integration is performed with Simpson’s rule with 20 intervals. Values of V, are assumed until one is found that makes 4 = 0. Then the pressure is found from the v dW equation: 2.276(10') 1703.7 - - ‘=(V,- 0.00169) V; Two trials and, a linear interpolation are shown. The value P2 = 18.44 bar compares with the ideal gas 17.13. v, cp s 0.120 -0.0540 0.117 +0.0054 0.1173 0 18.44bar
- 133. 114 FLOW OF FLUIDS Bubble Plug Stratified Dispersed Wavy (a) Bubbly I k g rn-*s-‘1 Churn (b) Annular Dispersed Dispersed flow IDBI StratIfled flow(SSJ (4 Figure 6.7. Flow patterns and correlations of flow regimes of liquid-gas mixtures in pipelines. (a) Patterns in horizontal liquid-gas flow. (b) Patterns in vertical liquid-gas flow. (c) Correlations of ranges of flow patterns according to Baker [Oil Gas J. 53(U), 185 (1954)], as replotted by Bell et al. [Chem. Eng. Prog. Symp. Ser. 66, 159 (1969)]; u is surface tension of the liquid, and u, that of water. (d) Flow regimes of water/air at 25°C and 1 atm [Tuirel and Dukler, AIChE J. 22, 47 (1976)]; the fuzzy boundaries are due to Mandhane et al. [Int. J. Two-Phase Flow 1, 537 (1974)]. SEPARATED FLOW MODELS Pressure drop in two-phase flow is found in terms of pressure drops of the individual phases with empirical multipliers. The basic relation is The last term is the pressure drop calculated on the assumption that the total mass flow has the properties of the liquid phase. Some correlations of multipliers are listed in Table 6.8. Lockhart and Martinelli distinguish between the various combina- tions of turbulent and laminar (viscous) flows of the individual phases; in this work the transition Reynolds number is taken as 1000 instead of the usual 2000 or so because the phases are recognized to disturb each other. Item 1 of Table 6.8 is a guide to the applicability of the Lockhart-Martinelli method, which is the oldest, and two more recent methods. An indication of the attention that has been devoted to experimentation with two phase flow is the fact that Friedel (1979) based his correlation on some 25,000 data points. Example 6.14 compares the homogeneous and Lockhart- Martinelli models for the flow of a mixture of oil and hydrogen. O T H E R A S P E C T S The pattern of annular flow tends to form at higher gas velocities; the substantial amount of work done on this topic is reviewed by
- 134. 6.8. LIQUID-GAS FLOW IN PIPELINES 115 TABLE 6.8. Two-Phase Flow Correlations of Pressure Drop 1. Recommendations R /PG G (kg/m* set) Correlation ilOO0 >lOOO >lOOO all Friedel >I00 C h i s h o l m - B a r o c z y <IO0 Lockhart-Martinelli 2. Lockhart-Martinelli Correlation 8 1oc 10 ’ 0.01 0 10 1.00 1 0 100 PARAMETER X $J:=r+CIX+lIX= $&=l +cx+xz X2 = WIU,I(APIL), Liquid Gas Subscript C Turbulent Turbulent tt 2 0 Viscous T u r b u l e n t vt 12 Turbulent Viscous tv 10 Viscous Viscous w 5 3. Chisholm-Baroczy Correlation & = 1 + (y’- ,)[Bx’2-““z(1 -x)(*-“)‘* + x*~“] = (AP/L)/(AP/L), n = 0.25 v’= (AP/L),,/(APIL),, B = 55/G0.=, 0 < Y < 9.5 = 5201 YG”‘5, 9.5 < Y < 28 = 15,000/Y2G0.5, Y > 28 Fr = G’/g,Dp$ We = G2Dlp,a x= weight fraction gas 4. Friedel Correlation &=E+ 3.24FH Fr0’045We0’035 ’ E=(, -.&+x2pLfGo P&o’ FE xo.78(1 - x)‘--, ,q= (~)o~9’(~)o~“(t -zr”, x= weight fraction gas 1. (P.B. Whalley, cited by G.F. Hewitt, 1982). 2. [Lockhart and Martinelli, Chem. Eng. Prog. 45, 39-48 (1949); Chisholm, Int. J. Heat Mass Transfer 10, 1767-1778 (1967)]. 3. [Chisholm, ht. J. Heat Mass Transfer 16, 347-348 (1973); Baroczy, Chem. Eng. Prog. Symp. Ser. 62, 217-225 (1965)]. 4. (Friedel, European Two Phase Flow Group Meeting, Ispra, Italy, Paper E2, 1979, cited by G.F. Hewitt, 1982).
- 135. 116 FLOW OF FLUIDS EXAMPLE 6.14 Pressure Drop and Void Fraction in Liquid-Gas Flow A mixture of an oil and hydrogen at 500psia and 200°F enters a 3 in. Schedule 40 steel line. Data are: Oil: 140,000 Ib/hr, 51.85 Ib/cuft, 2700 cfh, viscosity 15 cP. Hydrogen: 800 Ib/hr, 0.142 Ib/cuft, 5619 cfh, 2.5(10p7) lbf sec/sqft. viscosity The pressure drop in 1OOft of line will be found, and also the voidage at the inlet condition. ReG = n(0.2557)(32.2)(2.5)(10-7) = 137’500J ; = 0.00059. Round equations: 1.6434 f= [ln(O.l35s/D + 6.5/Re]‘= 0.0272, liquid, 0.0204, gas, (AI’lL), = 8friz 8(0.0272)(38.89)* jt2g,pD5 = ~r’(32.2)(51.85)(0.2557)~ = 18.27 psf/ft, 8(0.0204)(0.222)’ (AP~‘)G = K~(32.2)(o.142)(o.2557)5 = 0.1663 P*f/fta X2 = 18.27/0.1633 = 111.8. Lockhart-Martinelli-Chisholm: c = 20 for TI regime (Table 6.8), +:=1+;++=2.90, :. (AP/L) two phase = &AP/L), = 2.90(18.27) = 53.0 psf/ft, 36.8 psi/100 ft. Check with the homogeneous model: x = 140 or+ 8oo = 0.0057 wt fraction gas, 4(39.11) Re =n(32.2)(0.2557)3.85(10-j) = 157’100 f = 0.0202, BP 8(0.0202)(39.11)2 7 = ~~‘(32.2)(16.86)(0.2557)’ = 42’2 psf’ft’ compared with 53.0 by the LMC method. Void fraction by Eq. (6.104): EC = 1 - l/h = 1 - l/Vz% = 0.413, compared with input flow condition of QG 5619 ’ = m = 5619 + 2700 = oh75’ Method of Premoli [Eqs. (6.105) and (6.106)]: Surface tension u = 20 dyn/cm, 0.00137 lbf/ft, We=DG2= 16ti* &PLO n2gcD3tw 16(38.89)* = n2(32.2)(0.2557)3(51.85)(0.00137) = 64’118’ Re = 19,196, E, = 1.578(19196)-“~‘9(51.85/0.142)o~22 = 0.8872, E, = 0.0273(6411.8)(19196)-“~5*(51.85/0.142)-o~o* = 7.140, y = 5619/2700 = 2.081, yE, = 2.081(7.140) = 14.86. Clearly, this term must be less than unity if Eq. (6.105a) for S is to be valid, so that equation is not applicable to this problem as it stands. If yE, is replaced by y/E, = 0.2914, then S=1+0.8872 E- (. 0.5 0.2914 = 2.02, and the voidage is 5619 ’ = 5619 + 2.02(2700) = o’51J which is a plausible result. However, Eqs. (6.105) and (6.105a) are quoted correctly from the original paper; no numerical examples are given there. Hewitt (1982). A procedure for stratified flow is given by Cheremisinoff and Davis [AZChE J. 25, 1 (1979)]. Voidage of the holdup in the line is different from that given by the proportions of the incoming volumetric flows of the two phases, but is of course related to it. Lockhart and Martinelli’s work indicates that the fractional gas volume is &=1-l/&, (6.104) where #L is defined in Table 6.8. This relation has been found to give high values. A correlation of Premoli et al. [Termotecnica 25, 17-26 (1971); cited by Hewitt, 19821 gives the void fraction in terms of the incoming volumetric flow rates by the equation EC = Q,/(Q, + SQ3, (6.105) where S is given by the series of equations S = 1 + E,[y/(l + YE,) - yE,]‘“, E, = 1.578 Re-0.‘9(p,/p,)0.22, (6.105’) E, = 0.0273 We Re-“~51(p,/p,)-o~08, Y = QclQu Re = DG/pL, We = DG*/up,.
- 136. 6.9. GRANULAR AND PACKED BEDS 117 Direct application of these equations in Example 6.14 is not successful, but if E, is taken as the reciprocal of the given expression, a plausible result is obtained. 6.9. GRANULAR AND PACKED BEDS Flow through granular and packed beds occurs in reactors with solid catalysts, adsorbers, ion exchangers, filters, and mass transfer equipment. The particles may be more or less rounded or may be shaped into rings, saddles, or other structures that provide a desirable ratio of surface and void volume. Natural porous media may be consolidated (solids with holes in them), or they may consist of unconsolidated, discrete particles. Passages through the beds may be characterized by the properties of porosity, permeability, tortuosity, and connectivity. The flow of underground water and the production of natural gas and crude oil, for example, are affected by these characteristics. The theory and properties of such structures is described, for instance, in the book of Dullien (Porous Media, Fluid Transport and Pore Structure, Academic, New York, 1979). A few examples of porosity and permeability are in Table 6.9. Permeability is the proportionality constant k in the flow equation u = (k/p) dP/dL. Although consolidated porous media are of importance in chemical engineering, only unconsolidated porous media are incorporated in process equipment, so that further attention will be restricted to them. Granular beds may consist of mixtures of particles of several sizes. In flow problems, the mean surface diameter is the appropriate mean, given in terms of the weight fraction distribution, xi, by When a particle is not spherical, its characteristic diameter is taken as that of a sphere with the same volume, so that D, = (6V,/n)‘“. (6.107) SINGLE PHASE FLUIDS Extensive measurements of flow in and other properties of beds of particles of various shapes, sizes and compositions are reported by TABLE 6.9. Porosity and Permeability of Several Unconsolidated and Consolidated Porous Media Media p”l%ty 0 Perme;.jility Bed saddles 68-83 1.3 x 1om3-3.9 x 1o-3 W i r e c r i m p s 68-76 3.8 x 1O-5-1.Ox lo+ Black slate powder 57-66 4.9 x 10-‘“-1.2 x 10-S Silica powder 37-49 1.3 x 10-‘“-5.1 x lo-l0 Sand (loose beds) 37-50 2.0 x 1O-7-1.8~ lo-’ Soil 43-54 2.9x1o-9-1.4x1o-7 Sandstone (oil sand) 8-38 5.0 x lo-‘*-3.o x 1oe Limestone, dolomite 4-10 2.0 x 10-“-4.5x 1o-‘O Brick 12-34 4.8 x lo-“-2.2 x 1O-9 Concrete 2-7 1.0 x 1O-9-2.3 x IO-’ Leather 56-59 9.5 x 10-‘“-1.2 x 1o-9 Cork board - 3.3 x 1o-6-1.5x w5 Hair felt - 8.3 x IO-‘-l.2 x 1O-5 Fiberglass 88-93 2.4 x 10-7-5.1 x lo-’ Cigarette filters 17-49 1.1 x 1o-5 Agar-agar - 2.0 x 10-‘“-4.4 x 1o-9 fA.E. Scheidegger, Physics of Flow through Porous Media, University of Toronto Press, Toronto, Canada, 1974). Leva et al. (1951). Differences in voidage are pronounced as Figure 6.8(c) shows. A long-established correlation of the friction factor is that of Ergun (Chem. Eng. Prog. 48, 89-94, 1952). The average deviation from his line is said to be f20%. The friction factor is = 150/Re, + 1.75 with ReP = D,G/p(l- E). (6.108) (6.109) (6.110) l PRESENT WORK A WENTZ & THODOS”) 0.9 0.0 i5 5 05 ‘Z :: t Smooth, mixed -h Fused olundum ‘f g’ / I h i 1 a I I II h I1 -0.75 rJn -L.” -1.0 -3.0 - 1.5 -4.0 -2.0 -6.0 -3’o -0.0 -4.0 Ratio of porhcle to tube diameter, 2 /I. b) Figure 6.8. Friction factors and void fractions in flow of single phase fluids in granular beds. (a) Correlation of the friction factor, Re = D,G/(l - 8)~ and f, = [g,D,E3/pu’(l - &)J(AP/L = 150/Re + 4.2/(Re)1’6 [Sato et al., J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (b) Void fraction in granular beds as a function of the ratio of particle and tube diameters [Leva, Weintraub, Grummer, Pollchik, and Starch, U.S. Bur. Mines Bull. 504 (1951)].
- 137. 118 FLOW OF FLUIDS The pressure gradient accordingly is given by AP -= L 1 (6.111) For example, w h e n D =O.O05m, G = SOkg/m*sec, g, = 1 kgm/N set’, p = 800 kg/m’, p = 0.010 N set/m’, and E = 0.4, the gradient is AP/L = 0.31(105) Pa/m. An improved correlation is that of Sato (1973) and Tallmadge (AZChE J. 16, 1092 (1970)] shown on Figure 6.8(a). The friction factor is f, = 150/Re, + 4.2/ReF (6.112) with the definitions of Eqs. (6.108) and (6.110). A comparison of Eqs. (6.109) and (6.112) is 9 5 50 500 5000 $ Ergun) 31.8 4.80 2.05 1.78 $, (Sate) 33.2 5.19 1.79 1.05 In the highly turbulent range the disagreement is substantial. TWO-PHASE FLOW Operation of packed trickle-bed catalytic reactors is with liquid and gas flow downward together, and of packed mass transfer equipment with gas flow upward and liquid flow down. Concurrent flow of liquid and gas can be simulated by the homogeneous model of Section 6.8.1 and Eqs. 6.109 or 6.112, but several adequate correlations of separated flows in terms of Lockhart-Martinelli parameters of pipeline flow type are available. A number of them is cited by Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, New York, 1979, p. 184). The correlation of Sato (1973) is shown on Figure 6.9 and is represented by either 4 = (APLo/AP,)o.5 = 1.30+ 1.85(X)-‘.*‘, 0.1 <X(20, (6.113) or log10 APL, 0.70 AP, + APc = [log*o(x/1.2)]* + 1.00 ’ where X = ~@PIL),I(APIL), The pressure gradients for the liquid and vapor phases are calculated on the assumption of their individual flows through the bed, with the correlations of Eqs. (6.108)-(6.112). The fraction h, of the void space occupied by liquid also is of interest. In Sato’s work this is given by h, = 0.40(a,)“3x0.22, where the specific surface is (6.116) a, = 6(1 - &)/Dp. (6.117) Additional data are included in the friction correlation of Specchia and Baldi [Chem. Eng. Sci. 32, 515-523 (1977)], which is represented by fm = ’ (6.118) X (a) X b) Figure 6.9. Pressure drop gradient and liquid holdup in liquid-gas concurrent flow in granular beds. [Sato, Hirose, Takuhashi, and Toda, J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (a) Correlation of the two phase pressure drop gradient AP/L, 4 = 1.30 + 1.85X-o.85. (b) Correlation of frictional holdup h, of liquid in the bed; a, is the specific surface, l/mm, d is particle diameter, and D is tube diameter. h, = 0.4~~‘~~~~. Inf,, = 7.82 - 1.30 ln(Z/~‘~‘) - 0.0573[ln(Z/@‘)]‘. (6.119) The parameters in Eq. (6.119) are Z = (Re,)1.‘67/(Re,)0-767, (6.120) w=z [z pg”‘. (6.121) Liquid holdup was correlated in this work for both nonfoaming and foaming liquids. Nonfoaming, h, = 0. 125(Z/~‘~‘)~0~3*2(u~D~/~)o-65, (6.122) Foaming, h, = 0.06(Z/~‘~1)-o~‘72(u,D,/~)o~65. (6.123) The subscript w in Eq. (6.121) refers to water. Countercurrent flow data in towers with shaped packings are represented by Figure 13.37. The pressure drop depends on the viscosity of the liquid and on the flow rates and densities of the liquid and gas, as well as on characteristics of the packing which are represented here by the packing factor P. Nominally, the packing factor is a function of the specific surface a, and the voidage E, as F = as/e3, (6.124) but calculated values are lower than the experimental values shown in the table by factors of 2-5 or so. Clearly the liquid holdup reduces the effective voidage to different extents with different packings. The voidages of the packings in the table range from 70 to
- 138. 6 . 1 0 . G A S - S O L I D T R A N S F E R 119 95%, whereas voidages obtained with small spherical or cylindrical packings normally used as catalysts are less than 40% or so, which makes them impractical for countercurrent operation. However, catalysts are made in the forms of rings or saddles when very low pressure drop or countercurrent operation is desirable. Even when they are nominally the same type and size, packings made by different manufacturers may differ substantially in their pressure drop and mass transfer behavior, so that manufacturers data should be obtained for final design. Many data on individual packings are given by Billet (Distillation Engineering, Chemical Pub. Co., New York), in Chemical Engineers Handbook (McGraw-Hill, New York, 1984, p. 18.23) and with Figure 13.37. The uppermost line of Figure 13.37(a) marks the onset of flooding which is the point at which sharp increase of pressure drop obtains on a plot against liquid rate. Flooding limits also are represented on Figure 13.36; in practice, it is customary to operate at a gas rate that is 70% of that given by the line, although there are many data points below this limit in this correlation. Mesh or other open structures as vessel packing have attractive pressure drop and other characteristics, but each type has quite individual behavior so that it is best to consult their manufacturer’s data. 6.10. GAS-SOLID TRANSFER Equipment for pneumatic conveying is described in Section 5.2 along with some rules for calculating power requirements. Here the latter topic will be supplemented from a more fundamental point of view. CHOKING VELOCITY Although the phenomena are not clearcut, partial settling out of solids from the gas stream and other instabilities may develop below certain linear velocities of the gas called choking velocities. Normal pneumatic transport of solids accordingly is conducted above such a calculated rate by a factor of 2 or more because the best correlations are not more accurate. Above choking velocities the process is called dilute phase transport and, below, dense phase transport. What appears to be the best correlation of choking velocities is due to Yang [AZChE J. 21, 1013-1015 (1975)], supplemented by Punwani et al. and Yang (cited by Teo and Leung, 1984, pp. 520-521). The choking velocity Or,, and voidage E, are found by simultaneous solution of the equations G,/P, = (us, - u,)(l- &c) (6.125) or E, = 1 - WP,(% - ‘A) (6.126) and gD(er4-‘- 1) = 3.41(10’)(p,/p,)2.“(u,, - U,)2, where G, is the mass rate of flow of solid per unit cross section and the other terms are defined in Table 6.10. When E, from Eq. (6.126) is substituted into Eq. (6.127), the single unknown in that equation is readily found with a root solving routine. For the case of Example 6.15, G, = 29.6 kg/m2 set, U, = 0.45 m/set, p, = 1282 kg/m3, and pg = 1.14 kg/m3. Accordingly, Ug,, = 1.215 m/set and E, = 0.9698. TABLE 6.10. Equations for the Calculation of Pressure Drop in Gas-Solid Transport Solid Friction Factor c According to Various Investigators investigator Stemerding (1962) Reddy and Pei (1969) Van Swaaij, Buurman, and van Breugel (1970) Capes and Nakamura (1973) Konno and Saito (1969) f 0.003 (1) O.O46U,’ c-3 O.O8OlJ,’ (3) 0.048U;z (4) 0.0285vgD U,’ (5) Yang (1978). vertical Yang (1976). horizontal Free Setting Velocity 63) UrL%okes~ = SaJP-Pf), K<3,3 Ki3.3 (9) 1 Gr Utiintemediete) = 0,,53g0.7’D’.‘4(p -p )O.” P P f 9 4.3 PP kc , 3.3<K<43.6 (10) U 43.6 < K < 2360 (11) Particle Velocity Investigator 0, Hinkle (1953) u, - 4 (12) IGT (1978) UJl - 0.68D~&5p;0-zD-o’M) (13) Yang (1976) (14) Voidage E = 1 - 4lfl,lnD~(p, - p,,u, (15) Notation: U, is a fluid velocity, U, is particle velocity, U, is particle free settling velocity, f& is mass rate offlow of solid, D = pipe diameter, 0, is particle diameter, g = 9.806 m/set at sea level. (Klinzing, Gas-So/id Transport, McGraw-Hill, New York, 1981). PRESSURE DROP The relatively sparse data on dense phase transport is described by Klinzing (1981) and Teo and Leung (1984). Here only the more important category of dilute phase transport will be treated. The pressure drop in simultaneous flow of gas and solid particles is made up of contributions from each of the phases. When the particles do not interact significantly, as in dilute transport, the overall pressure drop is represented by AP = p,(l - .z)Lg + p&g + 2fgP&L + %P,(l - +q D D (6.128) for vertical transport; in horizontal transport only the two frictional terms will be present. The friction factor f, for gas flow is the normal one for pipe flow; except for a factor of 4, it is given by Eq. (6.19) for laminar flow and by the Round equation (6.21) for turbulent flow. For the solid friction factor f,, many equations of
- 139. 120 FLOW OF FLUIDS EXAMPLE 6.15 Eq. (6.128), Pressure Drop in Flow of Nitrogen and Powdered Coal Powdered coal of 100 ym dia and 1.28 specific gravity is transported vertically through a l-in. smooth line at the rate of 15g/sec. The carrying gas is nitrogen at 1 atm and 25°C at a linear velocity of 6.1 m/set. The density of the gas is 1.14 kg/m3 and its viscosity is 1.7( lo-‘) N set/m’. The equations of Table 6.10 will be used for the various parameters and ultimately the pressure gradient AP/L will be found: AP/L = 9.806[1282(1- 0.9959) + 1.14(0.9959)] +(2/0.0254)[0.0076(1.14)(6.1)2 +0.0031(1282)(0.0041)(5.608)2] = 51.54 + 11.13 + 25.38 + 40.35 = 128.4 Pa/m. With Eqs. (5) and (13), no trial calculations are needed. Eq. @h K = 1O-4 9.806(1.14)(1282- 1.14) [1.7(10-y 1/3=3,67 Eq. (lo) u =0.153(9.806)"~71(0.0001)1~14(1282- l.l4)'.'l ) f 1.14°.Z9[1.7(10--5)]0.43 = 0.37 m/set (0.41 m/set by Stokes’ law), Eq. (15), E = l- 0.015 (~/4)(0.0254)~(1282- l.l4)U, =l-0.0231 Up ' E q . (14), U, =6.1-0.45~l+f,U;/2(9.806)(0.0254) = 6.1- 0.4561+ 2.007fU; (1) (11) Eq, (7), f, = 0.003y - El [ “,-,“‘2;“]-“‘79 (III) P Equations (I), (II), and (III) are solved simultaneously with the results: E = 0.9959 and Up = 5.608, For the calculation of the pressure drop, f, = 0.0031 (Yang equation), Ref- orrp,- 0.0254(6.1)(1.14) = 1o 390, Pf 1.7(10-5) ’ Therefore, Round’s Eq. (6.21) applies: fr = $fRound=0.0076, Eq. (13), Up = 6.1[1 - 0.68(0.0001)“~92(1282)o~5 x (1.14)-“~2(0.0254)-o~54] = 5.88 m/set, Eq. (15), E = 1 - 0.0231/5.78 = 0.9960, Eq. (5), f, = 0.0285~9.806(0.0254)/5.88 = 0.00242. Therefore, the solid frictional gradient is obtained from the calculated value 40.35 in the ratio of the friction factors. (AP/L)so,idfriction = 40.35(0.00242/0.0031) = 31.5 Pa/m. 10 ZT: 4 0 5 0 6 0 ifi 3 0 ! E x a m p l e 6 . 1 5 . P r e s s u r e dt-o P i n flow o f nitroscn a n d P O wdered c o a l INPUT U E=l-.0231/U ! (Es I) F=.003251*~1-E~/E”3*(.45t(l- E)~‘<6.1-Ujj*-. 9 7 3 ! (Es 111) G=-U+6.1-.45*<1+2.007*F#U*2> *.S ! (should = 0> PRINT “U=“j U PRINT “G=” j G GOTrJ 20 ! (if G is not suffi c i e n t l r c l o s e to zero) END u = 5 . 6 0 8 - - L--. 0 0 0 0 5 9 3 4 8 0 6 1 varying complexity have been proposed, of which some important ones are listed in Table 6.10. These equations involve the free settling velocity Cl,, for which separate equations also are shown in the table. At lower velocities Stokes’ law applies, but corrections must be made at higher ones. The particle velocity U, is related to other quantities by Eqs. (12)-(14) of the table, and the voidage in turn is represented by Eq. (15). In a review of about 20 correlations, Modi et al. (Proceedings, Powder and Bulk Solids Handling and Processing Conference, Powder Advisory Center, Chicago, 1978, cited by Klinzing, 1981) concluded that the correlations of Konno and Saito (1969) and of Yang (1976, 1978) gave adequate representation of pneumatic conveying of coal. They are applied in Example 6.15 and give similar results there. 6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES As the flow of fluid through a bed of solid particles increases, it eventually reaches a condition at which the particles are lifted out of permanent contact with each other. The onset of that condition is called minimum fluidization. Beyond this point the solid-fluid mass exhibits flow characteristics of ordinary fluids such as definite viscosity and tlow through lines under the influence of hydrostatic head difference. The rapid movement of particles at immersed surfaces results in improved rates of heat transfer. Moreover, although heat transfer rate between particles and fluid is only moderate, l-4 Btu/(hr)(sqft)(“F), the amount of surface is so great, lO,OOO-150,000 sqft/cuft, that temperature equilibration between phases is attained within a distance of a few particle diameters. Uniformity of temperature, rapid mass transfer, and rapid mixing of solids account for the great utility of fluidized beds in process applications. As the gas flow rate increases beyond that at minimum fluidization, the bed may continue to expand and remain homo- geneous for a time. At a fairly definite velocity, however, bubbles begin to form. Further increases in flow rate distribute themselves between the dense and bubble phases in some ways that are not well correlated. Extensive bubbling is undesirable when intimate contacting between phases is desired, as in drying processes or solid catalytic reactions. In order to permit bubble formation, the
- 140. 6 . 1 1 . FLUIDIZATION O F B E D S O F P A R T I C L E S W I T H G A S E S 121 0.5 Gas velocity. m/s (a) Fluldizing rate. U/U,, bl I*= pvr’(G~-Gn~)/Gm/ I Figure 6.10. Characteristics of gas-solid fluidization. (a) Schematic of the progress of pressure drop and bed height with increasing velocity, for “normal” and “abnormal” behavior. For normal systems, the rates at minimum fluidization and minimum bubbling are the same. (b) Behavior of heat transfer coefficient with gas flow rate analogous to part (a). The peak depends on the density and diameter of the particles (Botteril, Fluid Bed Heat Transfer, Academic, New York, 1975). (c) Bed expansion ratio as a function of reduced flow rate and particle size. The dashed line is recommended for narrow size range mixtures (Leva, 1959, p. 102). (d) Correlation of fluctuations in level, the ratio of the maximum level of disturbed surface to average level (Leva, 1959, p. 105). (e) Bed voidage at minimum fluidization (Leua, 1959). Agarwal and Storrow: (a) soft brick; (b) absorption carbon; (c) broken Raschig rings; (d) coal and glass powder; (e) Carborundum; (f) sand. U.S. Bureau of Mines: (g) round sand, $+ = 0.86; (h) sharp sand, Gs = 0.67; (i) Fischer-Tropsch catalyst, & =0.58; (j) anthracite coal, & = 0.63; (k) mixed round sand, Gs = 0.86. Van Heerden et al.: (I) coke; (m) Carborundum. rate at minimum fluidization (Leva, 1959): G,, (&ZoetIicient C in the equation for mass flow = CDzg,p,(p, - pF)/p and C = 0.0007 Re- (g) Minimum bubbling and fluidization velocities of cracking catalysts (Hurriott and Simone, in Cheremisinoff and Gupta, Eds., Handbook of Fluids in Motion, Ann Arbor Science, Ann Arbor, MI, 1983, p. 656). (h) Minimum fluidization and bubbling velocities with air as functions of particle diameter and density [Geldart, Powder Technol. 7, 285 (1973)]. (i) Transport disengagement height, TDH, as a function of vessel diameter and superficial linear velocity [Zenz and Weil, AIChE J. 4, 472 (1958)]. (j) Good fluidization conditions (W.V. Battcock and K.K. Pillai, “Particle size in Pressurised Combustors,” Proc. Fifth International Conference on Fluidised Bed Combustion, Mitre Corp., Washington D.C., 1977).
- 141. (4 20 15 - 10 - 6- p 6- E 5 b 4 zE 3- Rd. VA-Y- 2 0 7 1.5 I /I 06 Cl 0 1119 11 I I ,I I j/,,,,, I I I I I 'II'll 1 0 1 5 2” 2 5 3 0 40 60 60 1 0 0 1 5 0 200 300 4 0 0 600 1000 (9) d,,. pm I I I I 1 2 5 10 20 50 (h) Velocity, U,, or Urn, mm/s 0.01 50 100 1000 10000 Good fluidization Minimum fluidization (iI Figure 6.1@---(continued) (j) Particle diameter, pm 122
- 142. 6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES 123 particles appear to interlock to form a skin around the bubble and thus prevent free particles from raining through those spaces. Bubble sizes become large at high rates of flow and may eventually reach the diameter of the vessel, at which time slugging and severe entrainment will occur. Onset of fluidization commonly is detected by noting a break in the plot of flow against pressure drop. For a range beyond the minimum fluidizing velocity, the pressure drop remains constant and equal to the weight of the bed but the bed level rises gradually and bubbles are generated at an increasing rate. Not in all cases, however, is the fluidization behavior entirely smooth. Figure 6.10(a) compares “normal” with a case of “abnormal” behavior. Among the reasons for abnormality are aggregation of particles because of stickiness or attractive forces between small particles and interlocking of rough surfaces. It is even possible for bubbling to occur before the onset of fluidization by formation of channels in the bed. CHARACTERISTICS OF FLUIDIZATION Six different regimes of fluidization are identified in Figure 6.11 and its legend. Particulate fluidization, class (b) of the figure, is desirable for most processing since it affords intimate contacting of phases. Fluidization depends primarily on the sizes and densities of the particles, but also on their roughness and the temperature, pressure, and humidity of the gas. Especially small particles are subject to electrostatic and interparticle forces. Four main classes characterized by diameters and differences in densities of the phases are identified in Figure 6.12 and its legend. Groups A and B are most frequently encountered; the boundary between them is defined by the equation given in the legend. Group A particles are relatively small, 30-150 pm dia, with densities below 1.5 g/cc. Their bed behavior is “abnormal” in that the bed expands appreciably before bubbling sets in, and the minimum bubbling velocity always is greater than the minimum fluidization velocity. The bubbles disengage quickly. Cracking catalysts that have been studied extensively for their fluidization behavior are in this class. Group B materials have dp = 150-500ym and are 1.5--4.0g/mL. The bed expansion is small, and minimum bubbling and fluidization velocities are nearly the same. The bubbles also disengage rapidly. Coarse sand and glass beads that have been favorite study materials fall in this group. Group C comprises small cohesive particles whose behavior is influenced by electrostatic and van der Waals forces. Their beds are difficult to fluidize and subject to channelling. Group D particles are large, 1 mm or more, such as lead shot and grains. They do not fluidize well and are usually handled in spouted beds, such as Figure 9.13(f). Among the properties of particles most conducive to smooth fluidization are the following: 1 . 2. 3. 4. rounded and smooth shape, in the range of 50-500 pm diameter, a broad spectrum of particle sizes, with ratios of largest to smallest sizes in the range of 10 to 25, enough toughness to resist attrition. Such tailoring of properties is feasible for many catalyst-carrier formulations, but drying processes, for instance, may be restricted by other considerations. Fluidization of difficult materials can be maintained by mechanical or ultrasonic vibration of the vessel, or pulsation of the supply of the fluid, or mechanical agitation of the contents of the vessel, or by addition of fluidization aids such as fine foreign solids. Ill :, : ..:: ,: ,. .: :‘:.‘,.:’ I._., ti: ::: : .: .: ‘.‘, ;.,.. .. . 0 p A:’ :I.-:.., ..: ‘. ‘. ‘y ., :.,: ..... o 9. (0) (11) (cl (4 (e) m Figure 6.11. Six regimes of fluidization identified with increasing gas superficial velocity (Grace, 198.2). Velocity Appearance and R a n g e R e g i m e Principal Features (a) OSu<u,, fixed particles are quiescent; gas flows bed through interstices (b) q,,,cu<q,,b P articulate bed expands smoothly in a homoge- fluid- ization (c) u,,,~ c u < u,, bubbling fluid- ization neoub manner; top surface is well defined; some small-scale particle motion; little tendency for particles to aggregate; very little fluctuation void regions form near the distributor, grow mostly by coalescence, and rise to the surface; top surface is well defined with bubbles breaking through periodically; irregular pres- sure fluctuations of appreciable amplitude (d) u,,,, 5 u < u, slugging r e g i m e (e) u, _c u < utr turbulent r e g i m e (0 ut, 5 JJ fast fluid- ization voids fill most of the column cross section; top surface rises and col- lapses with reasonably regular fre- quency; large and regular pressure fluctuations small voids and particle clusters dart to and fro; top surface difficult to distinguish; small-amplitude pressure fluctuations only no upper surface to bed; particles are transported out the top and must be replaced by adding solids at or near the bottom; clusters or strands of particles move downward, mostly near the wall, while gas, containing widely dispersed particles, moves upward; at fixed solid feed rate, increasingly dilute as u is increased SIZING EQUIPMENT Various aspects of the hydrodynamics of gas-solid fluidization have been studied extensively with conclusions that afford guidance to the interpretation and extension of pilot plant data. Some of the leading results bearing on the sizing of vessels will be discussed here. Heat transfer performance is covered in Chapter 17. Example 6.16 applies to some of the cited data.
- 143. 124 FLOW OF FLUIDS Mean particle diameter d, (urn) Figure 6.12. Characteristics of four kinds of groups of particles classified by Geldart [Powder Technol. 6, 201-205 (1972); 7, 285-292 (1973)]. The boundary between A and B is represented by the equation d, = 44,000p~‘&9/g(p, - pF) and that between B and D by (pS - pF) 2: = lo- kg/m. Feature Group C Group A Group B G r o u p D Distinguishing word or phrase E x a m p l e Particle size for ps = 2.5 g/cm3 Channeling Spouting Collapse rate Expansion Bubble shape Rheological character of dense phase Solids mixing Gas back mixing Slugging mode Effect of ds (within group) on hydrodynamics Effect of particle size distribution Cohesive Flour 520pm Severe little N o n e n o n e - s l o w Low because high; initially of channeling bubble-free channels, no flat base, bubbles spherical cap high yield stress very low very low flat raining plugs unknown unknown aeratable fluid cracking catalyst 2O<ds a90ym apparent viscosity of order 1 poise high high a x i s y m m e t r i c appreciable appreciable bubble readilv spoutable SO<& s650pm negligible shallow beds only rapid m e d i u m rounded with small indentation apparent viscosity of order 5 poise m e d i u m m e d i u m mostly axi- symmetric m i n o r negligible >650 pm negligible readily rapid m e d i u m rounded a p p a r e n t viscosity of order 10 poise l o w l o w mostly wall slugs u n k n o w n can cause segregation Solids of practical interest often are mixtures of a range of particle diameters, but, for convenience, correlations are expressed in terms of a single size which is almost invariably taken as the surface average diameter given by d, = l/c xidi, (6.129) where xi is the weight fraction of the material having a diameter di measured by screen analysis. Particles that deviate substantially from a spherical shape are characterized as having the diameter of a sphere with the same volume as the particle. The sphericity is defined as the ratio + = (surface of a sphere)/(surface of the particle with the same volume) (6.130) and is always less than unity. Accordingly, the relation between the effective particle size dp and that found by screen analysis is dp = Wscreen. (6.131)
- 144. 6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES 125 EXAMPLE 6.16 Dimensions of B Fluidiied Bed Vessel A fluidized bed is to hold 10,000 kg of a mixture of particles whose true density is 1700 kg/m3. The fluidizing gas is at 0.3 m3/sec, has a viscosity of 0.017cP or 1.7(E - 5) Nsec/m* and a density of 1.2 kg/m3. The size distribution of the particles is d (rm) 252 178 126 89 70 50 30 10 x(wtfrac- 0.088 0.178 0.293 0.194 0.113 0.078 0.042 0.014 tion) IJ, (m/se4 3.45 1.72 0.86 0.43 0.27 0.14 0.049 0.0054 The terminal velocities are found with Stokes’ equation u, = dPD - .Q) d2 = 18/J p 9.81(~$~2)~lp 12) [dp (pm)]‘. (a) The average particle size is d, = 1 / x (xJdJ = 84.5 ym. (b) With d,, = 84.5 and density difference of 1699 kg/m3, the material appears to be in Group A of Figure 6.12. (c) Minimum fluidization velocity with Eq. (6.133) %zf = O.O093[84S(E - 6)]‘.82(1700 - l.2)“.94 [1.7(E - 5)]0.*8(1.2)0.~ = 0.0061 m/set, and with Eqs. (6.134) and (6.135), - - Ar = 1.2(1700 1.2)(9.81)[84.5(E 6)J3 = 41 75 [1.7(E - 5)]’ . 7 R e , = V(27.2)*+ 0.0408(41.75) - 27.2 = 0.0313, u,b _ P Remf- l.7(E - 5)(0.0313) dPP 84.5(E - 6)(1.2) = o’0052 m’sec’ Use the larger value, umf = 0.0061, as the conservative one. (d) Minimum bubbling velocity, with Eq. (6.136) u,,,* = 33(84.5)(E - 6)[1.2/1.7(E - 5)]“.’ = 0.0085 m/set, :. U,b lhzf = 0.0085/0.0061= 1.39. From Eq. (6.139) c,,- 82[1.7(E - 5)]“.6(l.2)o.06 u,,,~ - 9.81[84.5(E - 6)]‘.3(170fI - 1.2) = 1’35’ which is in rough agreement. (e) Voidage at minimum bubbling from Eq. (6.138): [1.7(E - 5)]2 0.5 9.81[84.5(E - 6)]3(1700)2 = 0.1948, :. E,,,~ = 0.469. It is not certain how nearly consistent this value is with those at minimum fluidization read off Figure 6.10(e). Only a limited number of characteristics of the solids are accounted for in Eq. (6.138). (f) Operating gas velocity. The ratios of entraining and minimum fluidizing velocities for the two smallest particle sizes present are 0.049/0.0061= 8.03, for 30 pm, 0.0054/0.0061= 0.89, for 10 pm. Entrainment of the smallest particles cannot be avoided, but an appreciable multiple of the minimum fluidizing velocity can be used for operation; say the ratio is 5, so that Uf =5u mf = 5(0.0061) = 0.0305 m/set. (g) Bed expansion ratio. From Figure 6.10(c) with d, = 84.5 pm or 0.0033 in. and Gf /G,,,f = 5, R = I 1.16, by interpolation between the full lines, 1.22, off the dashed line. Take R = 1.22 as more conservative. From Eq. (6.140) the ratio of voidages is E,,,~/E,,,~ = 5’.** = 1.42. From part (e), E,~ =0.469 so that cmf =0.469/1.42 = 0.330. Accordingly, the ratio of bed levels is L,,/L, = (1 - ~,,,~)/(l- E,,,~) = 0.67/0.531= 1.262. Although the value of E,,,~ appears somewhat low, the value of R checks roughly the one from Figure 6.10(c). (h) Fluctuations in level. From Figure 6.10(d), with d, = 0.0033 in., the value of m’ = 0.02, so that r = exp[0.02(5 - 1)] = 1.083. (i) TDH from Figure 6.10(i). At ur = u,~ - 4(0.0061) = 0.0244 m/set, the abscissa is off the plot, but a rough extrapolation and interpolation indicates about 1.5 m for TDH. (j) Dimensions of the bed and vessel. With a volumetric flow rate of 0.3 m3/sec, the required diameter is D = dO.3/(0.305)(n/4) = 3.54 m. With a charge of 10,000 kg of solids and a voidage at minimum bubbling of 0.469, the height of the minimum bubbling bed is loo00 L = 1700(1- 0.469)(n/4)D2 = “13 m’ This value includes the expansion factor which was calculated separately in item (g) but not the fluctuation parameter; with this correction the bed height is Lb = 1.13(1.083) = 1.22 m. The vessel height is made up of this number plus the TDH of 1.5 m or vessel height = 1.22 + 1.5 = 2.72 m.
- 145. 126 FLOW OF FLUIDS Minimum Fluidizafion. The fundamental nature of this phenomenon has led to many correlations for its prediction. That of Leva (1959) applies to Reynolds numbers Re, = dPG,,,f/p < 5, and is Gmf = 688D’.8* [PAPS - PF)1°.94 P Po.88 (6.132) in the common units G,,,f in lb/(hr)(sqft), DP in inches, densities in lb/tuft, and viscosity in cP. In SI units it is LI mf = 0.0093d~“(p, - pf)o.94 ~"~88pfo.M (6.133) The degree of confidence that can be placed in the correlation is indicated by the plot of data on which it is based in Figure 6.10(f). An equation more recently recommended by Grace (1982) covers Reynolds numbers up to 1000: Re,f = d+,,,plp = 4(27.2)‘+ O.O408(Ar) = 27.2, (6.134) where Ar = P(P, - p)&ld Here also the data show much scatter, so that pilot plant determinations of minimum fluidization rates usually are advisable. Minimum Bubbling Conditions. Minimum bubbling velocities for Group B substances are about the same as the minimum fluidization velocities, but those of Group A substances are substantially greater. For Group A materials the correlation of Geldart and Abrahamsen [Powder Technol 19, 133 (1978)] for minimum bubbling velocity is u,,,~ = 33dP(p/p)Po.‘. For air at STP this reduces to (6.136) umb = lOOd,. (6.137) For cracking catalysts represented on Figure 6.10(g), Harriott and Simone (1983) present an equation for the ratio of the two kinds of velocities as (6.138) The units of this equation are SI; the coefficient given by Cheremisinoff and Cheremisinoff (1984, p. 161) is incorrect. Figures 6.10(g) and (h) compare the two kinds of velocities over a range of particle diameters. Voidage at minimum bubbling is correlated by an equation of Cheremisinoff and Cheremisinoff (1984, p. 163): &,/(l - E,,,~) = 47.4(gd;p;/p2)-o? Bed Expansion and Fluctuation. The change of bed level with increasing gas rate is represented schematically in Figure 6.10(a). The height remains constant until the condition of minimum fluidization is reached, and the pressure drop tends to level off. Then the bed continues to expand smoothly until some of the gas begins to disengage from the homogeneous dense phase and forms bubbles. The point of onset of bubbling corresponds to a local maximum in level which then collapses and attains a minimum. With increasing gas rate, the bed again continues to expand until entrainment develops and no distinct bed level exists. Beyond the minimum bubbling point, some fraction of the excess gas continues through the dense phase but that behavior cannot be predicted with any accuracy. Some smoothed data of expansion ratio appear in Figure 6.10(c) as a function of particle size and ratio of flow rates at minimum bubbling and fluidization. The rather arbitrarily drawn dashed line appears to be a conservative estimate for particles in the range of 100 pm. Ordinarily under practical conditions the flow rate is at most a few multiples of the minimum fluidizing velocity so the local maximum bed level at the minimum bubbling velocity is the one that determines the required vessel size. The simplest adequate equation that has been proposed for the ratio of voidages at minimum bubbling and fluidization is h,b lG?f = (G,,,,/G,,f)o’2* (6.140) = 2. 64cc~.89po.5~/go.22d~06(pp _ p)0.22 (6.141) The last equation results from substitution of Eq. (6.138) into (6.140). Then the relative bed level is found from LmbIL, = (1 - %,f)/(l - &,,,b). (6.142) Either E,,,~ or E,,,~ must be known independently before Eq. (6.141) can be applied, either by application of Eq. (6.139) for .smb or by reading off a value of E,~ from Figure 6.8(c) or Figure 6.10(e). These values are not necessarily consistent. At high gas velocities the bed level fluctuates. The ratio of maximum disturbed level to the average level is correlated in terms of Gf/Gmf and the particle diameter by the equation r = expb’(Gf - G,,fYGmfl, (6.143) where the coefficient m’ is given in Figure 6.10(d) as a function of particle diameter. Freeboard. Under normal operating conditions gas rates somewhat in excess of those for minimum fluidization are employed. As a result particles are thrown into the space above the bed. Many of them fall back, but beyond a certain height called the transport disengaging height (TDH), the entrainment remains essentially constant. Recovery of that entrainment must be accomplished in auxiliary equipment. The TDH is shown as a function of excess velocity and the diameter of the vessel in Figure 6,10(i). This correlation was developed for cracking catalyst particles up to 400 pm dia but tends to be somewhat conservative at the larger sizes and for other materials. Viscosity. Dense phase solid-gas mixtures may be required to flow in transfer line catalytic crackers, between reactors and regenerators and to circulate in dryers such as Figures 9.13(e), (f). In dilute phase pneumatic transport the effective viscosity is nearly that of the fluid, but that of dense phase mixtures is very much greater. Some data are given by Schiigerl (in Davidson and Harrison, 1971, p. 261) and by Yates (1983). Apparent viscosities with particles of 50-550 pm range from 700 to 1300 cP, compared with air viscosity of 0.017 CP at room temperature. Such high values of the viscosity place the flow definitely in the laminar flow range. However, information about friction in flow of fluidized mixtures through pipelines is not easy to find in the open literature. Someone must know since many successful transfer lines are in operation.
- 146. REFERENCES General M.M. Denn, Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1980. 0. Levenspiel, Engineering Flow and Heat Exchange, Plenum, New York, 1984. M. Model1 and R.C. Reid, Thermodynamics and Its Applications, Prentice-Hall, Englewood Cliffs, NJ, 1983. V.L. Streeter and E.B. Wylie, Fluid Mechanics, McGraw-Hill, New York, 1979. Non-Newtonian Fluids 5. G.W. Govier and K. Aziz, Flow of Complex Mixtures in Pipes, Van Nostrand Reinhold, New York, 1972. 6. N.I. Heywood, Pipeline design for non-Newtonian fluids, ht. Chem. Eng. Symp. Ser. No. 60, 33-52 (1980). 7. J.W. Hoyt, The effect of additives on fluid friction, Trans. ASME J. Basic Eng., 258 (June 1972). 8. P.A. Longwell, Mechanics of Fluid Flow, McGraw-Hill, New York, 1966. 9. R.D. Patel, Non-Newtonian flow, in Handbook of Fluids in Motion, (Cheremisinoff and Gupta, Eds.), Ann Arbor Science, Ann Arbor, MI, 1983, pp. 135-177. 10. A.H.P. Skelland, Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967. 11. J.R. Van Wazer, J.W. Lyons, K.Y. Kim, and R.E. Colwell, Viscosity and Flow Measurement, Wiley-Interscience, New York, 1963. 12. E.J. Wasp, J.P. Kenny, and R.L. Gandhi, Solid Liquid Flow Slurry Pipeline Transportation, Trans. Tech. Publications, Clausthal, Germany, 1977. Two-phase Flow l3. D. Chisholm, Gas-liquid flow in pipeline systems, in Handbook of Fluids 14. 15. 16. REFERENCES 127 in Motion, (Cheremisinoff and Gupta, Eds.) Ann Arbor Science, Ann Arbor, MI, 1983, pp. 483-513. D. Chishohu, Two-Phase Flow in Pipelines and Heat Exchangers, George Godwin, London, 1983. G.W. Govier and K. Aziz, The Flow of Complex Mixtures in Pipes, Van Nostrand Reinhold, New York, 1972. G.F. Hewitt, Liquid-gas systems, in Handbook of Multiphase Systems, (G. Hetsroni, Ed.), Hemisphere, New York, 1982, pp. 2.1-2.94. Gas-Solid (Pneumatic) Transport 17. G. Klinzing, Gas-Solid Transport, McGraw-Hill, New York, 1981. 18. N.P. Cheremisinoff, and R. Gupta (Eds.), Gas-solid flows, in Handbook of Fluids in Motion, Ann Arbor Science, Ann Arbor, MI, 1983, pp. 623-860. 19. C.S. Teo and L.S. Leung, Vertical flow of particulate solids in standpipes and risers, in Hydrodynamics of Gas-Solids Fluidization, (N.P. Cheremisinoff and P.N. Cheremisinoff, Eds.), Gulf, Houston, 1984, pp. 471-542. Fluidization 20. J.S.M. Botteril, Fluid-Bed Heat Transfer, Academic, New York, 1975. 21. N.P. Cheremisinoff and P.N. Cheremisinoff, Hydrodynamics of Gas-Solid Fluidization, Gulf, Houston, 1984. 22. J.F. Davidson and D. Harrison, Eds., Fluidization, Academic, New York, 1971. 23. J.R. Grace, Fluidization, Section 8 of G. Hetsroni, 1982. 24. G. Hetsroni (Ed.), Handbook of Multiphase Systems, McGraw-Hill, New York, 1982. 25. M. Leva, Fluidization, McGraw-Hill, New York, 1959. 26. J.C. Yates, Fundamentals of Fluidized-Bed Chemical Processes, Butterworths, London, 1983.
- 148. 7 FLUID TRANSPORT EQUIPMENT A /though Gquids particularly can be transported by operators carrying buckets, the usual mode of transport of fluids is through pipelines with pumps, blowers, compressors, or ejectors. Those categories of equipment will be considered in this chapter. A few statements will be made at the start about piping, fittings, and valves, although for the most part this is information best gleaned from manufacturers’ catalogs. Special problems such as mechanical flexibility of piping at elevated temperatures are beyond the scope here, and special problems associated with sizing of piping for thermosyphon reboilers and the suction side of pumps for handling volatile liquids are deferred to elsewhere in this book. 7.1. PIPING Standard pipe is made in a discrete number of sizes that are designated by nominal diameters in inches, as “inches IPS (iron pipe size).” Table A5 lists some of these sizes with dimensions in inches. Depending on the size, up to 14 different wall thicknesses are made with the same outside diameter. They are identified by schedule numbers, of which the most common is Schedule 40. Approximately, Schedule number = 1000 P/S, where P = internal pressure, psig S = allowable working stress in psi. Tubing for heat exchangers, refrigeration, and general service is made with outside diameters measured in increments of l/16 or l/8 in. Standard size pipe is made of various metals, ceramics, glass, and plastics. Dimensional standards, materials of construction, and pressure ratings of piping for chemical plants and petroleum refineries are covered by ANSI Piping Code B31.3 which is published by the ASME, latest issue 1980. Many details also are given in such sources as Cracker and King, Piping Handbook (McGraw-Hill, New York, 1967), Perry’s Chemical Engineers Handbook (1984), and Marks Standard Handbook for Mechanical Engineers (1987). In sizes 2in. and less screwed fittings may be used. Larger joints commonly are welded. Connections to equipment and in lines whenever need for disassembly is anticipated utilize flanges. Steel flanges, flanged fittings, and valves are made in pressure ratings of 150,300,600,900, 1500, and 2500 psig. Valves also are made in 125 and 25Opsig cast iron. Pressure and temperature ratings of this equipment in various materials of construction are specified in the piping code, and are shown in Chem. Eng. Handbook 1984, pp. 6.75-6.78. V A L V E S Control of flow in lines and provision for isolation of equipment when needed are accomplished with valves. The basic types are relatively few, some of which are illustrated in Figure 7.1. In gate valves the flow is straight through and is regulated by raising or lowering the gate. The majority of valves in the plant are of this type. In the wide open position they cause little pressure drop. In globe valves the flow changes direction and results in appreci- able friction even in the wide open position. This kind of valve is essential when tight shutoff is needed, particularly of gas flow. Multi- pass plug cocks, butterfly valves, slide valves, check valves, various quick-opening arrangements, etc. have limited and often indispens- able applications, but will not be described here. The spring in the relief valve of Figure 7.1(c) is adjusted to open when the pressure in the line exceeds a certain value, at which time the plug is raised and overpressure is relieved; the design shown is suitable for pressures of several hundred psig. More than 100 manufacturers in the United States make valves that may differ substantially from each other even for the same line size and pressure rating. There are, however, independent publications that list essentially equivalent valves of the several manufacturers, for example the books of Zappe (1981) and Lyons (1975). CONTROL VALVES Control valves have orifices that can be adjusted to regulate the flow of fluids through them. Four features important to their use are capacity, characteristic, rangeability and recovery. Capacity is represented by a coefficient Cd = C, /d2, where d is the diameter of the valve and C,, is the orifice coefficient in equations such as the following Q = Cud(PI - P,)/p,, gal/min of liquid, Q = 22.7C,d(P, - P,)P,/p,T, SCFM of gas when P,lP, > 0.5, Q=11.3C,P,/m, SCFMofgaswhenP,/P,<O.S, where Pi is pressure in psi, p, is specific gravity relative to water, pa is specific gravity relative to air, and T is temperature “R. Values of C, of commercial valves range from 12 for double-seated globe valves to 32 for open butterflies, and vary somewhat from manufacturer to manufacturer. Chalfin (1980) has a list. Characteristic is the relation between the valve opening and the flow rate. Figure 7.1(h) represents the three most common forms. The shapes of plugs and ports can be designed to obtain any desired mathematical relation between the pressure on the diaphragm, the travel of the valve stem, and the rate of flow through the port. Linear behavior is represented mathematically by Q = kx and equal percentage by Q = k, exp(k,x), where x is the valve opening. Quick-opening is a characteristic of a bevel-seated or flat disk type of plug; over a limited range of lo-25% of the maximum stem travel is approximately linear. Over a threefold load change, the performances of linear and equal percentage valves are almost identical. When the pressure drop across the valve is less than 25% of the system drop, the equal 129
- 149. 130 FLUID TRANSPORT EQUIPMENT percentage type is preferred. In fact, a majority of characterized valves currently are equal percentage. Rangeability is the ratio of maximum to minimum flows over which the valve can give good control. This concept is difficult to quantify and is not used much for valve selection. A valve generally can be designed properly for a suitably wide flow range. Recovery is a measure of the degree of pressure recovery at the valve outlet from the low pressure at the vena contracta. When flashing occurs at the vena contracta and the pressure recovery is high, the bubbles co!lapse with resulting cavitation and noise. The more streamlined the valve, the more complete the pressure recovery; thus, from this point of view streamlining seems to be an undesirable quality. A table of recovery factors of a number of valve types is given by Chalfin (1980); such data usually are provided by manufacturers. Homwbeel Neck Seat (a) These characteristics and other properties of 15 kinds of valves are described by Chalfin (1980). Pressure drop. Good control requires a substantial pressure drop through the valve. For pumped systems, the drop through the valve should be at least l/3 of the pressure drop in the system, with a minimum of 15 psi. When the expected variation in flow is small, this rule can be relaxed. In long liquid transportation lines, for instance, a fully open cqntrol valve may absorb less than 1% of the system pressure drop. In systems with centrifugal pumps, the variation of head with capacity must be taken into account when sizing the valve. Example 7.2, for instance, illustrates how the valve drop may vary with flow in such a system. Types of valves. Most flow control valves are operated with adjustable air pressure on a diaphragm, as in Figure 7.1(d), since this arrangement is more rapid, more sensitive and cheaper than (e) Figure 7.1. Some kinds of manual and automatically controlled valves. (a) Gate valve, for the majority of applications. (b) Globe valve, when tight shutoff is needed. (c) Swing check valve to ensure flow in one direction only. (d) A pressure relief valve, in which the plug is raised on overpressure. (e) A control valve with a single port. (f) A double-port, reverse-acting control valve. (g) A control valve with a double port, in which the correct opening is maintained by air pressure above the diaphragm. (A) valve body; (B) removable seat; (C) discs; (D) valve-stem guide; (E) guide bushing; (F) valve bonnet; (G) supporting ring; (H) supporting arms; (J) diaphragm; (K) coupling between diaphragm and valve stem; (L) spring-retaining rod; (44) spring; (N) spring seat; (0) pressure connection. (Fischer.) (h) Relation between fractional opening and fractional flow of three modes of valve openings.
- 150. 7.2. PUMP THEORY 131 electrical motor control. Double-ported valve (d) gives better control at large flow rates; the pressures on the upper and lower plugs are balanced so that less force is needed to move the stem. The single port (e) is less expensive but gives a tighter shutoff and is generally satisfactory for noncritical service. The reverse acting valve (f) closes on air failure and is desirable for reasons of safety in some circumstances. 7.2. PUMP THEORY Pumps are of two main classes: centrifugal and the others. These others mostly have positive displacement action in which the discharge rate is largely independent of the pressure against which they work. Centrifugal pumps have rotating elements that impart ie / r - J or’ ’ ’ ’ ’ ’ ’ ’ ’ 0 0.2 0.4 0.6 iii3 1.0 (h) Figure 7.1-(conthued) high velocity initially and high pressure head ultimately to the liquid. Elements of their theory will be discussed here. A glossary of pump terms and terms relating primarily to centrifugal pumps are defined in the Glossary at the end of this chapter. The chief variables involved in pump theory are listed here with typical units: D, diameter of impeller (ft or m), H, output head (ft or m), n, rotational speed (l/set), i, output power (HP or kW), Q, volumetric discharge rate (cfs or m3/sec), p, viscosity (Ib/ft set or N sec/m2), p, density (Ib/cuft or kg/m3), E, surface roughness (ft or m). BASIC RELATIONS A dimensional analysis with these variables reveals that the functional relations of Eqs. (7.1) and (7.2) must exist: gWn2D2 = 9dQlnD3, D=npl~, &ID)> PJpn3D5 = &(QlnD3, D’npJp, E/D). The group D2nplp is roughness ratio. Three named the Reynolds number and E/D is the new groups also have arisen which are capacity coefficient, C, = Q/no’, head coefficient, C, = gHln2D2, power coefficient, Ck = i/pn3D5. (7.1) (7.2) (7.3) (7.4) (7.5) The hydraulic efficiency is expressed by these coefficients as 17 = gHpQ/P = C,C,/C,. (7.6) Although this equation states that the efficiency is independent of the diameter, in practice this is not quite true. An empirical relation is due to Moody [ASCE Trans. 89, 628 (1926)]: q2 = 1 - (1 - ~,)(D,/D,)“-25. (7.7) Geometrically similar pumps are those that have all the dimensionless groups numerically the same. In such cases, two different sets of operations are related as follows: QJQ, = (n2/4(4/Dd3J H,IH, = (n24/nlDl)z, . . P,lP, = (p21pl)(nzlnl)3(4/Dl)5. (7.8) (7.9) (7.10) The performances of geometrically similar pumps also can be represented in terms of the coefficients C,, C,, C,, and 7. For instance, the data of the pump of Figure 7.2(a) are transformed into the plots of Figure 7.2(b). An application of such generalized curves is made in Example 7.1. Another dimensionless parameter that is independent of diameter is obtained by eliminating D between C, and C, with the result, N, = nQ”.5/(gH)o.‘5. (7.11) This concept is called the specific speed. It is commonly used in the
- 151. 132 FLUID TRANSPORT EQUIPMENT EXAMPLE 7.1 Application of Dimensionless Performance Curves Model and prototypes are represented by the performance curves of Figure 7.2. Comparisons are to be made at the peak efficiency, assumed to be the same for each. Data off Figure 7.2(b) are: 7j = 0.93, C, = gH/n2D2 = 5.2, C, = &pn3D5 = 0.69, CQ = Q/no3 = 0.12. (a) The prototype is to develop a head of 76 m: Q = nD3C, = 32.27(0.371)3(0.12) = 0.198 m3/sec, P = pn3D5C, = 1000(32.27)“(0.371)‘(0.69) = 0.163(106) W, 163 kW. (b) The prototype is to have a diameter of 2 m and to rotate at 400 rpm: Q = nD3Ca = (400/60)(2)3(0. 12) = 6.4 m”/sec, H = n2D2C,/g = (400/60)2(2)2(5.2)/9.81 = 94.2 m, k= pn3D5C, = 1000(400/60)3(2)5(0.69) = 6.54(106) kgm2/sec3, 6.54(106) N m/set, 6540 kW. (c) Moody’s formula for the effect of diameter on efficiency gives q2 = 1 - (1 - ~1)(D1/D2)o~25 = 1 - 0.07(0.371/2)“.25 = 0.954 at 2 m, compared with 0.93 at 0.371 m. (d) The results of (a) and (b) also are obtainable directly from Figure 7.2(a) with the aid of Eqs. (7.7), (7.8), and (7.9). Off the figure at maximum efficiency, q =0.93, Q =0.22, H=97, a n d P=218. When the new value of H is to be 76m and the diameter is to remain the same, n2 = 35.6(HJH,)“’ = 35.6(76/97)‘-’ = 31.5 rps, Q, = Ql(n2/nl) = 0.22(H,/HJ”.’ = 0.195 m’/sec, f+, = ~l(p2/pl)(nJnl)3(D2/D,)5 = 218(H2/Hl)‘~5 = 151.2 kw. These values agree with the results of (a) within the accuracy of reading the graphs. CQ b) Figure 7.2. Performance curves in dimensional and dimensionless forms: (a) Data of a pump with a specific diameter and rotation speed. (b) Dimensionless performance curves of all pumps geometrically similar to (a). The dashed lines identify the condition of peak efficiency. (After Daugherv and Franrini, Fluid Mechanics with Engineering Applications, McGraw-Hill, New York, 1957).
- 152. 7.2. PUMP THEORY 133 EXAMPLE~.~ Some values are Operating Points of Single and Double Pumps in Parallel and Series The head loss in a piping system is represented by the equation H, =50+6.0(Q/100)2+ H,,, where & is the head loss in the control valve. The pump to be used has the characteristic curve of the pump of Figure 7.7(b) with an 8 in. impeller; that curve is represented closely by the equation O/100 0.8 1.0 1.2 1.286 H" 10.88 7.00 2.28 0 4 59.92 (b) In parallel each pump has half the total flow and the same head H,: HP = 68 - OS(Q/lOO) - 4.5(Q/100)2. The following will be found (see Figure 7.17): (a) The values of H, corresponding to various flow rates Q gpm. (b) The flow rate and head on the pumps when two pumps are connected in parallel and the valve is wide open (H, = 0). (c) The same as (b) but with the pumps in series. (d) The required speed of the pump at 80gpm when no control valve is used in the line. 5O+6.O(Q/1OO)2=68-(O.5/2)(Q/1OO)-(4.5/4)(Q/1OO)2, :. Q = 157.2 gpm, H, = 64.83 ft. (c) In series each pump has the same flow and one-half the total head loss: ~(50+6.0(Q/100)2]=68-0.5(Q/100)-4.5(Q/100)2, :. Q = 236.1 gpm, H, = 83.44 ft. Series flow allows 50% greater gpm than parallel. (a) The operating point is found by equating e, and HP from which H, = 68 - 0.5(Q/lOO) - 4.5(Q/lOO)* - [50 + 6.O(Q/lOO)‘]. (d) H,=50+4.8=54.8, H,=(68-0.4- 2.88)(n/1750)2, :. n = 175Odm = 1610 rpm. mixed units N, = (rpm)(gpm)“.“/(ft)“~“. (7.12) For double suction pumps, Q is one half the pump output. The net head at the suction of the pump impeller must exceed a certain value in order to prevent formation of vapor and resulting cavitation of the metal. This minimum head is called the net positive suction head and is evaluated as NPSH = (pressure head at the source) + (static suction head) - (friction head in the suction line) - (vapor pressure of the liquid). (7.13) Usually each manufacturer supplies this value for his equipment. (Some data are in Figure 7.7.) A suction specific speed is defined as S = (rpm)(gpm)“~“/(NPSH)” “. (7.14) Standards for upper limits of specific speeds have been established, like those shown in Figure 7.6 for four kinds of pumps. When these values are exceeded, cavitation and resultant damage to the pump may occur. Characteristic curves correspond- ing to widely different values of iV, are shown in Figure 7.3 for several kinds of pumps handling clear water. The concept of specific speed is utilized in Example 7.3. Further data are in Figure 7.6. Recommendations also are made by the Hydraulic Institute of suction specific speeds for multistage boiler feed pumps, with S = 7900 for single suction and S = 6660 for double suction. Thus the required NPSH can be found by rearrangement of Eq. (7.14) as NPSH = [(rpm)(gpm)0.5/S]4’3. (7.15) For example, at 35OOrpm, lOOOgpm, and S = 7900, the required NPSH is 34 ft. For common fluids other than water, the required NPSH usually is lower than for cold water; some data are shown in Figure 7.16. PUMPINGSYSTEMS The relation between the flow rate and the head developed by a centrifugal pump is a result of its mechanical design. Typical curves are shown in Figure 7.7. When a pump is connected to a piping system, its head must match the head loss in the piping system at the prevailing flow rate. The plot of the flow rate against the head loss in a line is called the system curve. The head loss is given by the mechanical energy balance, (7.16) where H, is the head loss of a control valve in the line. The operating point may be found as the intersection of plots of the pump and system heads as functions of the flow rate. Or an equation may be fitted to the pump characteristic and then solved simultaneously with Eq. (7.16). Figure 7.17 has such plots, and Example 7.2 employs the algebraic method. In the normal situation, the flow rate is the specified quantity. With a particular pump curve, the head loss of the system may need to be adjusted with a control valve in the line to make the system and pump heads the same. Alternately, the speed of the pump can be adjusted to make the pump head equal to that of the system. From Eq. (7.9) the relation between speeds and pump heads at two
- 153. 134 FLUID TRANSPORT EQUIPMENT Figure 7.3. Performance curves of single-suction impellers corresponding to two values of the specific speed. (a) N, = 1550, centrifugal pump. (b) N, = 10,000, mixed and axial flow pumps. conditions is n2 = n,(H2/H,)0.5. (7.17) Example 7.2 is of cases with control valve throttling and pump speed control. In large systems, the value of power saved can easily overbalance the extra cost of variable speed drives, either motor or steam turbine. When needed, greater head or greater capacity may be obtained by operating several pumps in series or parallel. In parallel operation, each pump develops the same head (equal to the system head), and the flow is the sum of the flows that each pump delivers at the common head. In series operation, each pump has the same flow rate and the total head is the sum of the heads developed by the individual pumps at the prevailing flow rate, and equal to the system head. Example 7.1 deals with a pair of identical pumps, and corresponding system and head curves are shown in Figure 7.17. 7.3. PUMP CHARACTERISTICS A centrifugal pump is defined in the glossary at the end of this chapter as a machine in which a rotor in a casing acts on a liquid to give it a high velocity head that is in turn converted to pressure head by the time the liquid leaves the pump. Other common nomenclature relating to the construction and performance of centrifugal and related kinds of pumps also is in that table. 880 rpm Gallons per Mmule (t-4 Figure 7.4. Performance of several kinds of pumps. (a) Comparison of small centrifugal and turbine pumps (Kristul and Anne& 1940). (b) An axial flow pump operating at 880rpm (Chem. Eng. Handbook, 1973). (c) An external gear pump like that of Figure 7.12(e) (Viking Pump Co.). (d) A screw-type positive displacement pump. (e) NPSH of reciprocating positive displacement pumps.
- 154. 6 0 4 0 L 8 0 GO 3 0 b ; t k-F : 2 g 4 0 9 2 0 ” 2 0 I O 0 0 0 6 0 I20 160 2 4 0 300 Discharge pressure, PSI P L U N G E R Figure 7.4-(continued) (e) r (a) Efficiencies as % of those with direct piston drive: Stroke, in 5 8 10 2 0 3 0 4 0 5 0 Crank-and-flywheel pump 8 7 8 8 9 0 9 2 Piston p u m p 6 0 7 0 7 4 8 4 8 6 8 8 9 0 High-pressure pump 5 5 6 4 6 7 7 6 7 8 8 0 81 (b) Efficiencies of crankshaft-driven pumps of various sizes: Water HP 3 5 10 2 0 3 0 5 0 7 5 100 200 Efficiency (%) 55 65 7 2 7 7 8 0 8 3 8 5 8 6 8 8 (c) % of flow above and below the mean; curve is shown for triplex double-acting: p-- Cyhnder h.’ I 4 L Cyhder No. 3 L Cylinder No. .? 4 N u m b e r o f % above % below Plunger Twe Plungers Mean Mean P h a s e Duplex (double) 2 2 4 2 2 180” Triplex 3 6 17 120” Quaduplex 4 1 1 2 2 9 0 ” Quintaplex 5 2 5 7 2 ” Sextuplex 6 5 9 6 0 ” (d) Efficiency as a function of % reduced pressure or % reduced speed: % Full-Load Mechanical Mechanical Developed Pressure Efficiency % Speed Efficiency 2 0 8 2 44 9 3 . 3 4 0 8 8 5 0 9 2 . 5 6 0 9 0 . 5 7 3 9 2 . 5 8 0 9 2 100 9 2 . 5 100 9 2 . 5 (e) Approximate steam consumption of reciprocating pumps (Hydraulic Institute, Cleveland, OH, 1957). Example: A pump with a 10 x 10 cylinder and developing 33 HP at 90 ft/min needs 73 lb steam/water HP. The 50 fpm line is a reference line. Figure 7.5. Data relating to the performance of piston and plunger pumps. 135
- 155. 136 FLUID TRANSPORT EQUIPMENT EXAMPLE 7.3 Check of Some Performance Curves with the Concept of Specific Speed (a) The performance of the pump of Figure 7.7(b) with an 8in. impeller will be checked by finding its specific speed and comparing with the recommended upper limit from Figure 7.6(b). Use Eq. (7.12) for N, Clearly the performance curves are well within the recom- mended upper limits of specific speed. (b) The manufacturer’s recommended NPSH of the pump of Figure 7.7(c) with an 8 in. impeller will be checked against values from Eq. (7.15) with S = 7900: 0 kwm) 100 150 200 H Vt) 490 440 300 NPSH (mfgr) 1 0 18 35 NPSH [Eq. (7.15)j 7.4 9.7 11.8 The manufacturer’s recommended NPSHs are conservative. Q (gpm) 100 200 300 H (fi) 268 255 225 IV, (calcd) 528 776 1044 Ns [Fig. 7.10(a)] 2050 2150 2500 NPSH 5 7 13 1 / I VtZeroft I H = total head(,a’; (first stage) H= total head,ft (f!rst stage) (b) H= totaiheod,ft (first stage) H= total head, ft (first stage) (cl (d) Figure 7.6. Upper specific-speed limits for (a) double-suction pumps (shaft through impeller eye) handling clear water at 85°F at sea level, (b) single-suction pumps (shaft through impeller eye) handling clear water at 85°F at sea level, (c) single-suction pumps (overhung-impeller type) handling clear water at 85°F at sea level, (d) single-suction mixed- and axial-flow pumps (overhung-impeller type) handling clear water at 85°F at sea level. (Hydraulic Institute, Cleveland, OH, 1957).
- 156. 7 . 3 P U M P C H A R A C T E R I S T I C S 137 I! ! ! ! ! ! ! !.! mo- cum E-6994-2 rm3X2XBk m( CSO u P-1757-1 -OIL 8k’ U. L GALLONS PER MINLITE (a) U. S. GALLONS PER MINUTE b) (c) Figure 7.7. Characteristic curves of centrifugal pumps when operating on water at 85°F (Allis Chalmers Co.). (a) Single suction, 1750 rpm. (b) The pump of (a) operated at 3500 ‘pm. (c) Multistage, single suction, 3550 rpm. The basic types of centrifugals are illustrated in Figure 7.9. A centrifugal vane action; the propeller confers high rates of flow but volute is a gradually expanding passage in which velocity is partially the developed pressure is low. Figure 7.3(b) represents a typical converted to pressure head at the outlet. The diffuser vanes of axial pump performance. Figures 7.9(b) and 7.10(d) direct the flow smoothly to the periphery. The turbine impeller of Figure 7.10(h) rotates in a case of The volute design is less expensive, more amenable to use with uniform diameter, as in Figure 7.12(j). As Figure 7.4(a) demon- impellers of different sizes in the same case, and, as a consequence, strates, turbine pump performance resembles that of positive dis- by far the most popular construction. Diffuser construction is used placement types. Like them, turbines are essentially self-priming, to a limited extent in some high pressure, multistage machines. The that is, they will not vapor bind. double suction arrangement of Figure 7.9(d) has balanced axial All rotating devices handling fluids require seals to prevent thrust and is favored particularly for severe duty and where the leakage. Figure 7.13 shows the two common methods that are used: lowered NPSH is an advantage. Multistage pumps, however, are stuffing boxes or mechanical seals. Stuffing boxes employ a soft exclusively single suction. packing that is compressed and may be lubricated with the pump Some of the many kinds of impellers are shown in Figure 7.10. liquid or with an independent source. In mechanical seals, smooth For clear liquids, some form of closed impeller [Figure 7.10(c)] is metal surfaces slide on each other, and are lubricated with a very favored. They may differ in width and number and curvature of the small leakage rate of the pump liquid or with an independent liquid. vanes, and of course in the primary dimension, the diameter. Performance capability of a pump is represented on diagrams Various extents of openness of impellers, [Figs. 7.10(a) and (b)] are like those of Figure 7.7. A single point characterization often is desirable when there is a possibility of clogging as with slurries or made by stating the performance at the peak efficiency. For pulps. The impeller of Figure 7.10(e) has both axial propeller and example, the pump of Figure 7.7(c) with a 9 in. impeller is called a
- 157. 138 FLUID TRANSPORT EQUIPMENT (a) Single-suction, 1800 rpm standard pumps: (b) Single-suction, 3600 rpm standard pumps: = 6 0 0 ; 4 0 U.S. G. P. M. K e y N o . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Suction and Discharge 4 x 3 6 x 4 4 x 3 5 x 4 2x1; 2$x2 4 x 3 5 x 4 5 x 4 (1200 rpm) 1iXlf 2 x 2 3x2; (1200 rpm) 4 x 3 (1200 rpm) 5 x 4 (1200 rpm) 2fx2f 3 x 3 Approximate cost $1200 1350 1200 1500 750 1050 1200 1350 1500 700 750 1050 1200 2-5 1350 2-5 500 i-1; 600 l-2 H o r s e p o w e r Range at 1.0 S p Gr 7;-25 20-30 15-25 15-30 2-7; 3-10 5-15 7f-20 3-7; l-2 l&3 Ii-3 100 6 0 6 0 K e y N o . 1 2 3 4 5 6 7 8 9 Suction and Approximate Discharge cost 5 x 4 4 x 3 3x2; 4 x 4 5 x 5 2x1; 2;x2 3x2; 4 x 3 $2250 1950 1650 1800 1950 1200 1350 1500 1650 U.S. G. P. M. H o r s e p o w e r Range at 1.0 Sp. Gr. 40-60 20-40 7;-20 3-20 5-30 3 4-2 l-3 2-7l 2-7; (c) Single-suction 1800 and 3600rpm refinery pumps for elevated temperatures and pressures: Key No. 1 2 3 4 5 6 7 8 9 10 11 u. s. Suction and Discharge 2x 1; 3 x 2 (3600 rpm) 4 x 3 6 x 4 3 x 2 4 x 3 (1800 rpm) 6 x 4 2x1; 3~2(1800rpm) 4 x 3 6 x 4 G. P. M Approximate cost $3400 3700 4300 4800 4200 4500 5400 3400 3700 4300 H o r s e p o w e r Range at 1.0 Sp Gr 7;-30 15-50 20-75 40-125 5-15 7;-20 15-40 l-5 2-7; 3-10 5-15 Figure 7.8. Typical capacity-head ranges of some centrifugal pumps, their 1978 costs and power requirements. Suction and discharge are in inches (Evans, 1979, Vol. 1).
- 158. 7.3 PUMP CHARACTERISTICS 139 (a) tion ,.-Discharge ----lmpefler - - - - - - V&&e channe/ 0.4 id) ---C,,a.qne ,--- -- ____ -_ (e) (4 Figure 7.9. Some types of centrifugal pumps. (a) Single-stage, single suction volute pump. (b) Flow path in a volute pump. (c) Double suction for minimizing axial thrust. (d) Horizontally split casing for ease of maintenance. (e) Diffuser pump: vanes V are fixed, impellers P rotate. (f) A related type, the turbine pump.
- 159. 140 FLUID TRANSPORT EQUIPMENT (a) (4 (b) (c) (e) Figure 7.10. Some types of impellers for centrifugal pumps. (a) Open impeller. (b) Semiopen impeller. (c) Shrouded impeller. (d) Axial flow (propeller) type. (e) Combined axial and radial flow, open type. (f) Shrouded mixed-flow impeller. (g) Shrouded impeller (P) in a case with diffuser vanes (V). (h) Turbine impeller. 175 gpm and 56Oft head pump at a peak efficiency of 57%; it requires a 15 ft suction lift, an 18 ft NPSH and 43 BHP. Operating ranges and costs of commercial pumps are given in Figure 7.8. General operating data are in Figure 7.4. Although centrifugal pumps are the major kinds in use, a great variety of other kinds exist and have limited and sometimes unique applications. Several kinds of positive displacement types are sketched in Figure 7.12. They are essentially self-priming and have a high tolerance for entrained gases but not usually for solids unless they may be crushed. Their characteristics and applications are discussed in the next section. 7.4. CRITERIA FOR SELECTION OF PUMPS The kind of information needed for the specification of centrifugal, reciprocating and rotary pumps is shown on forms in Appendix B. General characteristics of classes of pumps are listed in Table 7.1 and their ranges of performance in Table 7.2. Figure 7.14 shows recommended kinds of pumps in various ranges of pressure and flow rate. Suitable sizes of particular styles of a manufacturer’s pumps are commonly represented on diagrams like those of Figure 7.8. Here pumps are identified partly by the sizes of suction and discharge nozzles in inches and the rpm; the key number also
- 160. 0.8 0.7 0.4 0.3 200, 20 100 200 300 HEAD, FEET OF LIQUID Figure 7.11. Approximate efficiencies of centrifugal pumps in terms of GPM and head in feet of liquid. Valve open on forward stroke Valve open on reverse stroke (a) j/j-- i (cl 7.4. CRITERIA FOR SELECTION OF PUMPS 141 identifies impeller and case size and other details which are stated in a catalog. Each combination of head and capacity will have an efficiency near the maximum of that style. Although centrifugal pumps function over a wide range of pressure and flow rates, as represented by characteristic curves like those of Figures 7.2 and 7.7, they are often characterized by their performance at the peak efficiency, as stated in the previous section. Approximate efficiencies of centrifugal pumps as functions of head and capacity are on Figure 7.11 and elsewhere here. Centrifugal pumps have a number of good qualities: 1. They are simple in construction, are inexpensive, are available in a large variety of materials, and have low maintenance cost. 2. They operate at high speed so that they can be driven directly by electrical motors. 3. They give steady delivery, can handle slurries and take up little floor space. Some of their drawbacks are 4. Single stage pumps cannot develop high pressures except at very high speeds (10,000 rpm for instance). Multistage pumps for high T i m e (b) k-- Cyfinder No.’ f kylinder N o . 3 L Cylinder No. 2 -4 hi) D I S C H A R G E S U C T I O N ’ OISCHARGE 4 ION S C R E W S C R E W Figure 7.12. Some types of positive displacement pumps. (a) Valve action of a double acting reciprocating piston pump. (b) Discharge curve of a single acting piston pump operated by a crank; half-sine wave. (c) Discharge curve of a simplex double acting pump as in (a). (d) Discharge curve of a duplex, double acting pump. (e) An external gear pump; characteristics are in Figure 7.8(c). (f) Internal gear pump; the outer gear is driven, the inner one follows. (g) A double screw pump. (h) Peristaltic pump in which fluid is squeezed through a flexible tube by the follower. (i) Double diaphragm pump shown in discharge position (BIF unit of General Signal). (j) A turbine pump with essentially positive displacement characteristics (data on Fig. Z 4(a)].
- 161. Eccentric Drive _-_, D i scharge Open- U-t) Figure 7.~(continued) (i) SEALINQ LIOIJID I BOTTOMING RING PICKING ANNULAR COOLING AREA AROUND PACKING- Discharge p r e s s u r e (DP) “-*Suet ion COOLING WATER OUTLET CORED PASSAGE INTO PRECOOLING ANNULAR SPACE PRECOOLING OF LEAKAGE PUMP lNTERlol7 COOLING WATER INLET-P TATING E L E M E N T S ATMOSPHERIC ( c ) (4 Figure 7.W. Types of seals for pump shafts. (a) Packed stuffing box; the sealing liquid may be from the pump discharge or from an independent source. (b) Water cooled stuffing box. (c) Internal assembly mechanical seal; the rotating and fixed surfaces are held together by the pressure of the pump liquid which also serves as lubricant; a slight leakage occurs. (d) Double mechanical seal with independent sealing liquid for handling toxic or inflammable liquids. 142
- 162. 7 . 5 . E Q U I P M E N T F O R G A S T R A N S P O R T 143 Head in feet o 2 5 I50 I75 ~i00~150~200~250 300~400~500~Above 500 20 .. Single sucfion Either double sucfion 40 -. I or mu/tistoge Fi 75 .- 200-- i’ (r 2 Either 400-. single or daub/e suction - Mu/C- ,s 600-- sfoge 2 lOOO-- ‘: 2000 -. g 2500 -. ‘> 4000 -- 6000 -. Double s&ion 8000 -. l0,000 (a) of 50-1OOOatm or more. Some performance data are shown in Figure 7.5. Diaphragm pumps [Fig. 7.12(i)] also produce pulsating flow. They are applied for small flow rates, less than 100 gpm or so, often for metering service. Their utility in such applications overbalances the drawback of their intrinsic low efficiencies, of the order of 20%. Screw pumps [Fig. 7.12(g)] are suited for example to high viscosity polymers and dirty liquids at capacities up to 2000 gpm and pressures of 200 atm at speeds up to 3000 rpm. They are compact, quiet, and efficient. Figure 7.4(d) shows typical performance data. Gear pumps [Figs. 7.12(e) and (f)] are best suited to handling clear liquids at a maximum of about 1OOOgpm at 150atm. Typical performance curves are shown in Figure 7.4(c). Peristaltic pumps [Fig. 7.12(h)] move the liquid by squeezing a tube behind it with a rotor. Primarily they are used as metering pumps at low capacities and pressures in corrosive and sanitary services when resistant flexible tubes such as those of teflon can be used, and in laboratories. Turbine pumps [Figs. 7.9(f), 7.12(i), and 7.4(a)] also are called regenerative or peripheral. They are primarily for small capacity and high pressure service. In some ranges they are more efficient than centrifugals. Because of their high suction lifts they are suited to handling volatile liquids. They arc not suited to viscous liquids or abrasive slurries. 7.5. EQUIPMENT FOR GAS TRANSPORT Gas handling equipment is used to transfer materials through pipe lines, during which just enough pressure or head is generated to overcome line friction, or to raise or lower the pressure to some required operating level in connected process equipment. The main classes of this kind of equipment are illustrated in Figures 7.18 and 7.19 and are described as follows. u.s.gallonsperrmnute (b) Figure 7.14. Range of applications of various kinds of pumps. (a) Range of applications of single and double suction pumps (Allis-Chalmers Co.). (b) Recommended kinds of pumps for various kinds of head and flow rate (Fairbanks, Morse, and Co.). pressures are expensive, particularly in corrosion-resistant mate- rials 5. Efficiencies drop off rapidly at flow rates much different from those at peak efficiency. 6. They are not self-priming and their performance drops off rapidly with increasing viscosity. Figure 7.15 illustrates this ef- feet On balance, centrifugal pumps always should be considered first in comparison with reciprocating or rotary positive displacement types, but those do have their places. Range of applications of various kinds of pumps are identified by Figure 7.14. Pumps with reciprocating pistons or plungers are operated with steam, motor or gas engine drives, directly or through gears or belts. Their mode of action is indicated on Figure 7.12(a). They are always used with several cylinders in parallel with staggered action to smooth out fluctuations in flow and pressure. Figure 7.5(c) shows that with five cylinders in parallel the fluctuation is reduced to a maximum of 7%. External fluctuation dampers also are used. Although they are self-priming, they do deteriorate as a result of cavitation caused by release of vapors in the cylinders. Figure 7.4(e) shows the NPSH needed to repress cavitation. Application of reciprocating pumps usually is to low capacities and high pressures 1. 2 . 3 . 4 . 5 . 6 . Fans accept gases at near atmospheric pressure and raise the pressure by approximately 3% (12in. of water), usually on air for ventilating or circulating purposes. Blowers is a term applied to machines that raise the pressure to an intermediate level, usually to less than 40 psig, but more than accomplished by fans. Compressors are any machines that raise the pressure above the levels for which fans are used. Thus, in modern terminology they include blowers. Jet compressors utilize a high pressure gas to raise other gases at low pressure to some intermediate value by mixing with them. Vacuum pumps produce subatmospheric pressures in process equipment. Often they are compressors operating in reverse but other devices also are employed. Operating ranges of some commercial equipment are stated in Table 7.3. Steam jet ejectors are used primarily to evacuate equipment but also as pumps or compressors. They are discussed in Section 7.7. Application ranges of fans and compressors are indicated on Figures 7.20 and 7.21. Some of these categories of equipment now will be discussed in some detail. F A N S Fans are made either with axial propellers or with a variety of radial vanes. The merits of different directions of curvature of the vanes are stated in Figure 7.24 where the effect of flow rate of pressure, power, and efficiency also are illustrated. Backward curved vanes are preferable in most respects. The kinds of controls used have a marked effect on fan performance as Figure 7.23 shows. Table 7.4 shows capacity ranges and other characteristics of various kinds of
- 163. 144 FLUID TRANSPORT EQUIPMENT TABLE 7.1. Characteristics of Various Kinds of Pumps Pump Type Construction Style Construction Characteristics Notes Centrifugal (horizontal) Centrifugal (vertical) Axial Turbine Reciprocating R o t a r y single-stage overhung, process type two-stage overhung single-stage impeller between bearings chemical slurry canned multistage, horizontally split casing multistage, barrel type single-stage, process type multistage inline high speed slump multistage, deep well propeller regenerative piston, plunger metering diaphragm screw gear impeller cantilevered beyond bearings capacity varies with head two impellers cantilevered beyond used for heads above single-stage bearings capability impeller between bearings; casing radially or axially split casting patterns designed with thin sections for high-cost alloys designed with large flow passages used for high flows to 1083f-i (330 ml head have low pressure and temperature ratings no stuffing box; pump and motor enclosed in a pressure shell nozzles located in bottom half of casing low speed and adjustable axial clearance; has erosion control features low head capacity limits when used in chemical services have moderate temperature-pressure ranges outer casing contains inner stack of diaphragms used for high temperature-pressure ratings vertical orientation many stages with low head per stage inline installation, similar to a valve speeds to 380 rps, heads to 5800 R (1770 m) used to exploit low net positive section head (NPSH) requirements low-cost installation low-cost installation high head/low flow; moderate costs casing immersed in sump for easy priming and installation long shafts propeller-shaped impeller fluted impeller. Flow path resembles low cost screw around periphery slow speeds consists of small units with precision used for water well service vertical orientation capacity independent of head; low flow/high head performance driven by steam engine cylinders or motors through crankcases diaphragm and packed plunger types flow control system no stuffing box I, 2, or 3 screw rotors intermeshing gear wheels used for chemical slurries; can be pneumatically or hydraulically actuated for high-viscosity, high-flow high-pressure s e r v i c e s for high-viscosity, moderate- pressure/moderate-flow services (Cheremisinoff, 1981). TABLE 7.2. Typical Performances of Various Kinds of Pumpsa Tvpe Style Centrifugal (horizontal) Centrifugal (vertical) Axial Turbine Reciprocating R o t a r y single-stage overhung two-stage overhung single-stage impeller between bearings chemical slurry canned multistage horizontal split multistage, barrel type single stage multistage inline high speed sump multistage deep well propeller regenerative piston, plunger metering diaphragm screw gear 15-5,000 15-l ,200 15-40.000 1000 1000 1-20.000 20-l 1,000 20-9.000 20-10.000 20-80.000 20-l 2,000 5-400 1 O-700 5-400 20-100.000 l-2000 1 o-1 0,OcJil O-10 4-100 l-2000 l-5000 Max Max Head P (ft) (psi) 492 600 1394 600 NPSH M a x T (fd (OF) 8.56-19.7 851 6.56-22.0 851 1099 980 6.56-24.9 239 200 3.94-19.7 394 600 4.92-24.9 4921 1 0 , 0 0 0 6.56-19.7 5495 3000 6.56-19.7 5495 6000 6.56-19.7 804 600 0.98-19.7 6004 700 0.98-19.7 705 500 6.56-19.7 5807 2000 7.87-39.4 197 200 0.98-22.0 6004 2000 0.98-19.7 3 9 150 6 . 5 6 2493 1500 6.56-8.20 1.13x IO6 >50,000 12.1 1.70x lo5 5 0 , 0 0 0 15.1 1.13x IO5 3500 12.1 6.79 x IO4 3000 9 . 8 4 11,155 500 9 . 8 4 401-851 401 851 1004 401-500 851 653 500 500 500 401 149 248 554 572 500 500 653 20-80 20-75 30-90 20-75 20-80 20-70 65-90 40-75 20-85 25-90 20-80 10-50 45-75 30-75 65-85 55-85 65-85 2 0 2 0 50-80 50-80 8I m3/min = 264 gpm, 1 m = 3.281% I bar = 14.5 psi, “C = (OF - 32)/I.8.
- 164. 7 . 5 . E Q U I P M E N T F O R G A S T R A N S P O R T 145 Figure 7.7(c). To the left the developed head increases with flow, but to the right the head decreases with increasing flow rate. At the peak the flow pulsates and the machine vibrates. This operating point is called the surge limit and is always identified by the manufacturer of the equipment, as shown on Figure 7.25 for those centrifugal and axial machines. Stable operation exists anywhere right of the surge limit. Another kind of tlow limitation occurs when the velocity of the gas somewhere in the compressor approaches sonic velocity. The resulting shock waves restrict the flow; a slight increase in flow then causes a sharp decline in the developed pressure. Table 7.6 shows as many as 12 stages in a single case. These machines are rated at either 10K or 12Kft/stage. The higher value corresponds to about 850 ft/sec impeller tip speed which is near the limit for structural reasons. The limitation of head/stage depends on TABLE 7.3. Operating Ranges of Some Commercial Vacuum Producing Equipment Type of Pump Operaaizg$nge Reciprocating piston l-stage 760-10 2-stage 760-l Rotary piston oil-sealed l-stage 760-lo-* 2-stage 760-W3 Centrifugal multistage (dry) liquid jet 760-200 Mercury Sprengel 760-10-3 Water aspirator (18%) 760-15 Two-lobe rotary blower (Roots n/pe) 20-1om4 Turbomolecular lo-‘-lo-‘0 Zeolite sorption (liquid nitrogen cooled) 760-10m3 Vapor jet pumps Steam ejector l-stage 760-100 2-stage 760-10 3-stage 760-l 4-stage 760-3x10-l 5-stage 760-5x lo-* Oil ejector (l-stage) 2-lo-* Diffusion-ejector 2-10-4 Mercury diffusion with trap 1 -stage lo-‘- < 10-6 P-stage I-<10-s 3-stage lo-< 1om6 Oil diffusion l-stage 10-‘-5x 10-s 4-stage fractionating (untrapped) 5x1o-'-1o-9 Cstage fractionating (trapped) 5 x lo~‘-lo~‘* Getter-ion (sputter-ion) lo-S-lo-” Sublimation (titanium) lo-a-lo-” Cn/opumps (20 K) lo-Z-lo-‘0 Cryosorption (15 K) lo-*-lo-‘2 (Encyclopedia of Chemical Technology, Wiley-Interscience, New York, 1978-1984). , fans. Figure 7.24 allows exploration of the effects of changes in specific speed or diameter on the efficiencies and other characteristics of fans. The mutual effects of changes in flow rate, pressure, speed, impeller diameter, and density are related by the “fan laws” of Table 7.5, which apply to all rotating propelling equipment. COMPRESSORS The several kinds of commercial compressors are identified in this classification: 1. Rotodynamic a. Centrifugal (radial flow) b. Axial llow 2. Positive displacement a. Reciprocating piston b. Rotary (screws, blades, lobes, etc.). Sketches of these several types are shown in Figures 7.19 and 7.20 and their application ranges in Figures 7.20 and 7.21. CENTRIFUGALS The head-flow rate curve of a centrifugal compressor often has a maximum as shown on Figure 3.21, similar to the pump curve of 1 15 2 3 4 5678910 15 CAPACITY, 100 GPM Figure 7.15. Effects of viscosity on performance of centrifugal pumps: (a) Hydraulic Institute correction chart for pumping liquids. (b) Typical performances of pumps when handling viscous liquids. The dashed lines on the chart on the left refer to a water pump that has a peak efficiency at 750 gpm and 100 ft head; on a liquid with viscosity 1OOOSSU (220CS) the factors relative to water are efficiency 64%, capacity 95% and head 89% that of water at 120% normal capacity (1.2QH).
- 165. 146 FLUID TRANSPORT EQUIPMENT 25 qnl ! ! ! !-4 ! ! !” ! I 0 20 40 60 80 100 120 140 160 180 200 220 Capdclty. gpm b) Figure 7.lS(confinued) the nature of the gas and the temperature, as indicated on Figure 7.26. Maximum compression ratios of 3-4.5 per stage with a maximum of 8-12 per machine are commonly used. Discharge pressures as high as 3000-5000 psia can be developed by centrifugal compressors. A specification form is included in Appendix B and as Table 4.4. Efficiency data are discussed in Section 7.6, Theory and Calculations of Gas Compression: Efficiency. AXIAL FLOW COMPRESSORS Figure 7.18(b) shows the axial flow compressor to possess a large number of blades attached to a rotating drum with stationary but adjustable blades mounted on the case. Typical operating characteristics are shown on Figure 7.22(a). These machines are suited particularly to large gas flow rates at maximum discharge pressures of 80-130 psia. Compression ratios commonly are 1.2-1.5 per stage and 5-6.5 per machine. Other details of range of applications are stated on Figure 7.20. According to Figure 7.21, (a) TEMPERATURE,‘F Figure 7.16. Recommended values of net positive suction head (NPSH) at various temperatures or vapor pressures: (a) NPSH of several types of pumps for handling water at various temperatures. (b) Correction of the cold water NPSH for vapor pressure. The maximum recommended correction is one-half of the cold water value. The line with arrows shows that for a liquid with 30psia vapor pressure at 100”F, the reduction in NPSH is 2.3ft (data of Worthington International Inc.). specific speeds of axial compressors are in the range of 1000-3000 or so. Efficiencies are 8-10% higher than those of comparable cen- trifugal compressors. RECIPROCATING COMPRESSORS Reciprocating compressors are relatively low flow rate, high pressure machines. Pressures as high as 35,000-50,OOOpsi are
- 166. I I Flow 100% ia) r One Pump I . I I I 5 0 % A 100% Flow b) A 100% Flow (cl Figure 7.17. Operating points of centrifugal pumps under a variety of conditions. (a) Operating points with a particular pump characteristic and system curves corresponding to various amounts of flow throttling with a control valve. (b) Operating point with two identical pumps in parallel; each pump delivers one-half the flow and each has the same head. (c) Operating point with two identical pumps in series; each pump delivers one-half the head and each has the same flow. Second-Stage Impeller, Return Guide Vanes haft Nut ACarbon Rings L -.. (a) T- Stator b l a d e s ‘Ia d e s b) Figure 7.18. Heavy-duty centrifugal, axial, and reciprocating compressors. (a) Section of a three-stage compressor provided with steam-sealed packing boxes (DeLaval Steam Turbine Co.). (b) An axial compressor (Clark Brothers Co.). (c) Double-acting, two-stage reciprocating compressor with water-cooled jacket and intercooler (IngersoN-Rand Co.). 147
- 167. 148 FLUID TRANSPORT EQUIPMENT Figure 7.18--(continued) / D i s c h a r g e p o r t 1 4 0 D r i v e s h a f t (a) Figure 7.19. Some rotary positive displacement compressors Gas ir) (cl 20 r-’ , 1 2 0 = 3 80 t - 4 0 Pressure Rise ,% (t.4 8 80 2 70 .: 60 i; 5 50 $4 40 2 Ji 30 20 1000 2000 3000 4000 5000 6000 7000 Viscosity in Seconds,Soybolt Universal (d) (a) A two-lobe blower. (b) Performance of a two-lobe blower ,.~ _ _ _.. (Roots-Connersville Co.). (c) A screw pump with one power and two idle rotors (K&al and Annett, 1940). (d) Performance ot 3.5” screw pump handling oils at 1150 rpm against 325 psig (Kr.ktal and Annett, 1940). (e) Principle of the liquid ring seal compressor (Nash Engineering Co.). (f) A sliding vane blower (Beach-Russ Co.).
- 168. 7 . 5 . E Q U I P M E N T F O R G A S T R A N S P O R T 149 (e) Figure 7.19.-(continued) Capmty, cubic n per ml” (a) D i 10’ 10‘ Capmty. c u b i c f t p e r mm U-4 Figure 7.20. Applications ranges of compressors and fans (Worthington): (a) Pressure-capacity ranges for air at 1 atm, 60”F, 0.075 Ib/cuft. (b) Head-capacity ranges for all gases. Similar charts are given by Ludwig (1983, Vol. 1, p. 251) and Chemical Engineers Handbook (1984, p. 6.21). developed with maximum compression ratios of lo/stage and any desired number of stages provided with intercoolers. Other data of application ranges are in Figure 7.20. The limitation on compression ratio sometimes is due to the limitations on discharge temperature which normally is kept below 300°F to prevent ignition of machine lubrications when oxidizing gases are being compressed, and to the fact that power requirements are proportional to the absolute temperature of the suction gas. A two-stage double-acting compressor with water cooled cylinder jackets and intercooler is shown in Figure 7.18(c). Selected dimensional and performance data are in Table 7.7. Drives may be with steam cylinders, turbines, gas engines or electrical motors. A specification form is included in Appendix B. Efficiency data are discussed in Section 7.6, Theory and Calculations of Gas Compression: Temperature Rise, Compression Ratio, Volumetric Efficiency. ROTARY COMPRESSORS Four of the many varieties of these units are illustrated in Figure 7.19. Performances and comparisons of five types are given in Tables 7.8-7.9. All of these types also are commonly used as vacuum pumps when suction and discharge are interchanged. Lobe type units operate at compression ratios up to 2 with efficiencies in the range of 80-95%. Typical relations between volumetric rate, power, speed, and pressure boost are shown in Figure 7.19(b). Spiral screws usually run at 1800-3600rpm. Their capacity ranges up to 12,OOOCFM or more. Normal pressure boost is 3-2Opsi, but special units can boost pressures by 60-lOOpsi. In vacuum service they can produce pressures as low as 2psia. Some other performance data are shown with Figure 7.19(d). The sliding vane compressor can deliver pressures of 50 psig or
- 169. 150 FLUID TRANSPORT EQUIPMENT 6t ~istbn o;mb 1 0.6 sN,=Nfi,/H’ 0.3 I)* = IHI k 3fl$ N = sneed. mm - 8 = fi0w ft3& H = head. ft D = Impeller diameter, ft dh 0.1 I c 0.1 0.3 0.6 1 3 6 10 30 60 100 300 6001000 3OGO 10,003 Specific speed, N, Figure 7.21. Operating ranges of single-stage pumps and compressors [Balje, Trans. ASME, J. Eng. Power. 84, 103 (1962)]. Example: atmospheric air at the rate of 100,000 SCFM is compressed to 80,000 ft Ibf/ft (41.7 psig) at 12,000 rpm; calculated N, = 103; in the radial flow region with about 80% efficiency, D, = 1.2-1.6, so that D = 2.9-3.9 ft. 150 0 140 2 130 a 6 120 53 110 E 100 s 90 “u 80 5 7 0 a 6 0 D 50 g 40 330 g 20 10 40 50 60 70 80 90 100 1 1 0 120 1 3 0 PERCENT DESIGN VOLUME (a) 160 ’ 140 I I III1 .. ?? 99 PERCENT, PEAK EFFICIENCY w”46 m 60 4 0 60 60 100 120 140 160 PERCENT. INLET VOLUME Figure 7.22. Performances of dynamic compressors: (a) Axial compressor. (b) Centrifugal compressor. All quantities are expressed as percentages of those at the design condition which also is the condition of maximum efficiency (De Lava1 Engineering Handbook, McGraw-Hill, New York, 1970).
- 170. l- 500 - ,400 - f f 3Od 7 d 200 - L 100 4 / OL 0 TABLE 7.4. Performance Characteristics of Fans” Description Quantity (1000 acfm) Min Max Head Inches Water OF. Max (fps) Q,j Diameter (in.) Min Max NS Axial propeller 8 2 0 10 410 0 . 1 3 2 3 2 7 470 0 . 6 3 7 7 Axial propeller 2 0 9 0 8 360 0 . 1 2 2 7 7 2 500 0 . 6 0 8 0 Axial propeller 6 120 2 . 5 315 0 . 1 0 2 7 8 4 560 0 . 5 0 8 4 Radial air foil 6 100 2 2 250 0 . 4 5 1 8 9 0 190 0 . 8 5 8 8 Radial BC 3 3 5 1 8 260 0 . 6 3 1 8 9 0 100 1.35 7 8 Radial MH o p e n 2 2 7 1 8 275 0 . 5 5 1 8 6 6 9 7 1.45 5 6 Radial MH 2 2 7 18 250 0 . 5 5 18 6 6 8 6 1.53 71 Radial IS Vane 81 fIL 2 2 7 18 250 0 . 5 5 18 6 6 8 6 1.53 6 6 1 10 12 250 0 . 4 3 10 3 0 210 0.81 7 0 Vane FC 1 10 2 6 5 1.15 IO 3 0 166 0 . 6 5 6 6 a %d = 32.2&, ,,,, = NQ0.5J “- (specific speed), 0, = D~‘25/00’5 (specific diameter), where D = diameter (ft), H = head (ft). Q = suction flow rate kfs), V = impeller tip speed (fps), and N = rotation speed bpm). (Evans. 1979). I I I I I I Head-Capacity at EHP a t 900 rpn, ‘BHP w i t h h y d r a u l i c cuupl inq . I I I I I I 25 50 75 100 125 150 C a p a c i t y . KCFM Control Control Required Power Advantages (A), and Twe cost Input Disadvantages (D) a l o w high (A) simplicity; (D) high power input b m o d e r a t e m o d e r a t e (A) lower input power; (D) higher cost C l o w m o d e r a t e (A) simplicity; (D) fan erosion d m o d e r a t e m o d e r a t e (0) complex; also needs dampers e high l o w (A) simple; no dampers n e e d e d Figure 7.23. Performances of fans with several kinds of controls (American Standard Co. Inc.). (a) A damper in the duct with constant-speed fan drive, (b) two-speed fan driver, (c) inlet vanes or inlet louvers with a constant-speed fan drive, (d) multiple-step variable-speed fan drive, and (e) hydraulic or electric coupling with constant-speed driver giving wide control over fan speed. TABLE 7.5. Fan Laws’ Fan Law Number Ratio of - Variables Ratio X Ratio Ratio 1 a b c 2 a b c 3 a b C 4 a b c 5 a b C 6 a b c 7 a b C 8 a b C 9 a b C 10 a b C c f m size3 press - size* H P size5 c f m size* rpm - l/size H P size’ wm 1/size3 press - l/size4 H P l/size4 c f m size ‘m press - 1/sizeU3 rpm l/sizeY3 size cfm”2 rpm - l/cfm”’ H P c f m size cfm’” press - cfmz3 H P cfmY3 size press”’ cfm - pressW2 H P press=* size 1/HP”4 rpm - HPW4 press H P size HP’” rpm - l/HP”* c f m H P size HP”5 ^.- c f m - HP”’ press HPz5 X wm X rpm* x rpm3 x p r e s s ” ’ x press”’ x pressW2 x c f m x cfm’ X cfm3 x HP”3 x HPz3 x HP”3 x l/press”4 x pressW4 X p r e s s x llrpm’” x x rpml: vm x Vrpm x l/rpm’ x l/rpm* x cfmz4 x l/cfmY4 X l/cfm X 1fpressW4 X pres? X l/press X l/rpmv5 X l/rpm4/3 X rpma5 X x X X x X X X X X “S=plg, For example, the pressure P varies as D’N’plg, line l(b). Q2(p/?c)/D4 line 3(b), Pu3(,/gc)“3/D4/3 line 4(b), Qz3N”3plgc line 6(b), P/Q line 8(c), and P2/5N”5(plgc)3/5 line 10(c). (R.D. Madison, 1949). 151
- 171. 152 FLUID TRANSPORT EQUIPMENT Static Pressure C u r v e B l a d e VI I I I I I, I I,, , I I, I I I Oo IO I’ 20 30 4 0 50 60 70 60 90 I Wide Open Volume,% (a) Wbds OpenVolume,% (cl (d) Backwardly Curved EE Fog+rye;l~ First Cost*. . . . . . . . . . . H i g h Medium Low Efficiency. . . . . . . . . . . H i g h Medium Low Stability of Operation. . G o o d Good Poor Space Required. . . . . . . Medium Medium Small Tip Speed.. . . . . . . . H i g h Medium Low Resistance to Abrasion.. Medium Good Poor Ability to Handle Sticky Materials. . . . Medium G o o d Poor Figure 7.24. Performances of fans with various-shaped blades (Green Fuel Economizer Co.): (a) Backward curved blades. (b) Straight radial blades. (c) Forward curved blades. (d) Comparison of characteristics of the several blade types (Sturtevant). TABLE 7.6. Specifications of Centrifugal Compressors Frame Normal Inlet Flow Rangea (f+/min) Nominal Polytropjc Head pee $tage P Nominal Polytropic Nominal Maximum Efficiency No. of h,) Stagesc xx%t; Polytropic Head/Stage 29M 30M 46M 60M 70M 88M 103M 1lOM 25MB(H)(HH) 32MB(H)(HH) 38MEI(H) 46MB 60MB 70MB 500-8000 1 0 , 0 0 0 0.76 10 11500 6000-23.000 10,000/12,000 0.77 9 8100 20,000-35,000 10,000/12,000 0.77 9 6400 30.000-58.000 10,000/12,000 0.77 8 5000 50.000-85.000 10,000/12,000 0.78 8 4100 75.000-130.000 10,000/12,000 0.78 8 3300 110,000-160,000 10,000 0.78 7 2800 140.000-190.000 10,000 0.78 7 2600 500-5000 12,000 0.76 12 11500 5000-10.000 12,000 0.78 10 10200 8000-23.000 10,000/12,000 0.78 9 8100 20,000-35,000 10,000/12,000 0.78 9 6400 30.000-58.000 10,000/12,000 0.78 8 5000 50,000-85,000 10,000/12,000 0.78 8 4100 75.000-130.000 10.000/12.000 0.78 8 3300 a Maximum flow capacity is reduced in direct proportion to speed reduction. bUse either 10,000 or 12,OOOfl for each impeller where this option is mentioned ‘At reduced speed, impellers can be added. (Elliott Co.).
- 172. 7.6. T H E O R Y A N D C A L C U L A T I O N S O F G A S C O M P R E S S I O N 153 3 . 0 2 . 5 5 2 0 t; ?: 13 i5 2 IO 3 06 g 0 6 - 05 0’ 04 Theoretical methods allow making such calculations for ideal and real gases and gas mixtures under isothermal and frictionless adiabatic (isentropic) conditions. In order that results for actual operation can be found it is neecessary to know the efficiency of the equipment. That depends on the construction of the machine, the mode of operation, and the nature of the gas being processed. In the last analysis such information comes from test work and its correlation by manufacturers and other authorities. Some data are cited in this section. DIMENSIONLESS GROUPS 20 304050 75IW 200300 scQ76OlcOo zow 4wo N,,SRCIFIC SPEEDICFS) Figure 7.25. Efficiency and head coefficient qad as functions of specific speeds and specific diameters of various kinds of impellers (Evans, 1979). Example: An axial propeller has an efficiency of 70% at N, = 200 and D, = 1.5; and 85% at N, = 400 and 0, = 0.8. See Table 7.4 for definitions of gad, N,, and 0,. The theory of dimensionless groups of Section 7.2, Basic Relations, also applies to fans and compressors with rotating elements, for example, Eqs. (7.8)-(7.10) which relate flow rate, head, power, speed, density, and diameter. Equivalent information is embodied in Table 7.5. The concept of specific speed, Eqs. (7.11) and (7.12), also is pertinent. In Figures 7.21 and 7.25 it is the basis for identifying suitable operating ranges of various types of compressors. IDEAL GASES The ideal gas or a gas with an equation of state pull a vacuum of 28in. of mercury. A two-stage unit can deliver 250psig. A generous supply of lubricant is needed for the sliding vanes. Table 7.9 shows that power requirements are favorable in comparison with other rotaries. Liquid-her compressors produce an oil-free discharge of up to 125psig. The efficiency is relatively low, 50% or so, but high enough to make them superior to steam jet ejectors for vacuum service. The liquid absorbs the considerable heat of compression and must be circulated and cooled; a 200HP compressor requires 1OOgpm of cooling water with a 10°F rise. When water vapor is objectionable in the compressed gas, other sealing liquids are used; for example, sulfuric acid for the compression of chlorine. Figure 7.19(e) shows the principle and Table 7.10 gives specifications of some commercial units. PV = zRT (7.18) is a convenient basis of comparison of work requirements for real gases and sometimes yields an adequate approximation of these work requirements. Two limiting processes are isothermal and isentropic (frictionless adiabatic) flows. Changes in elevation and velocity heads are considered negligible here. With constant compressibility z the isothermal work is I 9 w = V dP = zRT ln(PJP,). 4 (7.19) 7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION The main concern of this section is how to determine the work requirement and the effluent conditions of a compressor for which the inlet conditions and the outlet pressure are specified. Under isentropic conditions and with constant heat capacities, the pressure-volume relation is PVk = P,Vf = const, (7.20) where k = CJC, (7.21) TABLE 7.7. Some Sizes of One- and Two-Stage Reciprocating Compressors (a) Horizontal, One-Stage, Belt-Driven Diameter Brake Openings (in.) Cy(l.;;n;ler Stroke Displacement Air Pressure HP at Rated (in.) (cuft/min.) wm (Ib/sq in.) Pressure Inlet Outlet 71 8; 6 106 310 80-100-125 15.9-17-18 2; 2; 9 170 300 80-100-125 25-27-29 3 3 10 10 250 285 80-100-125 36-38.5-41 3; 3; 11 12 350 270 80-100-125 51-57-60 - 4 8; 6 138 350 40-60 15-18.5 - 3 10 9 245 300 40-75 27-34 3; 3; 11 10 312 285 40-75 34-43 4 4 13 12 495 270 40-75 54-70 5 5 12 9 350 300 20-45 30-42 4 4 13 10 435 285 30-45 42-52 6 6 15 12 660 270 30-50 59-74 7 7 (Worthington Corp.).
- 173. 154 FLUID TRANSPORT EQUIPMENT TABLE 7.7-4continued) (b) Horizontal, One-Stage, Steam-Driven= D i a m e t e r , D i a m e t e r , Steam Air Cylinder (in.) Cylinder, (in.) Stroke (in.) Displacement, (cuftfmin) wm Air Pressure, (Ib/sq in.) 7 a 9 10 7 a 9 10 a 9 10 7; a; 10 1 1 8: 10 1 1 13 12 13 15 6 9 10 12 6 9 10 12 9 10 12 106 350 170 300 250 285 350 270 136 350 245 300 312 285 495 270 350 300 435 285 660 270 ao-loo-125 80-100-125 80-100-125 80-100-125 40-60 40-75 b 40-75 b 40-75 b 20-45’ 20-45’ 20-50’ “,A11 machines have piston-type steam valves. llO-lb steam necessary for maximum air pressure. c 125-lb steam necessary for maximum air pressure. (Worthington Corp.). (c) Horizontal, Two-Stage, Belt-Driven Diameter Cylinder (in.) Low Pressure High Pressure 4 2; 6 2; a 3: 10 4; Stroke (in.) wm 4 500 6 350 a 300 10 275 Piston Displacement (tuft free air/min) 2 8 6 5 133 241 (Ingersoll-Rand Co.). TABLE 7.8. Summary of Rotary Compressor Performance Data Helical Screw Sliding Liquid Vanes Liner Configuration, features (male x female) Max displacement (cfm) Max diameter (in.) Min diameter (in.) Limiting tip speed (Mach) Normal tip speed (Mach) Max L/d, low pressure Normal L/d, high pressure Vfactor for volumetric efficiency Xfactor for displacement Normal overall efficiency Normal mech. eff. at +I00 HP (%) Normal compression ratio R, Normal blank-off R, 4 x 6 2 0 , 0 0 0 2 5 4 0 . 3 0 0 . 2 4 1.62 1 .oo 7 0 . 0 6 1 2 7 5 9 0 2/W 6 Displacement form-factor Ae 0 . 4 6 2 2 x 4 2 x 2 1 3 , 0 0 0 3 0 , 0 0 0 1 6 la 6 10 0 . 1 2 0 . 0 5 0 . 0 9 0 . 0 4 2 . 5 0 2 . 5 0 1.50 1.50 3 5 0 . 1 3 3 0 . 2 7 7 0 6 8 9 3 9 5 3 1.7 5 5 1.00 2 . 0 0 8 1 6 Blades Sprockets 6 , 0 0 0 1 3 , 0 0 0 3 3 4 8 5 12 0 . 0 5 0 . 0 6 0 . 0 4 0 . 0 5 3 . 0 0 1.1 2 . 0 0 1 .oo 3 3 0 . 0 4 6 0.071 7 2 5 0 9 4 9 0 2/W 5 7 9 0 . 3 4 5 0 . 5 3 5 (Evans, 1979).
- 174. 7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 1% TABLE 7.9. Five Rotary Compressors for a Common Service Liquid Liner Suction loss 6, 9 . 3 5 1.32 Discharge loss 6, 7 . 3 5 1.04 Intrinsic corr. S 1 . 1 8 5 1 . 0 2 3 Adiabatic eff. qsd 8 5 . 6 9 7 . 7 Slippage W, (%) 2 8 . 5 18.6 Slip eff. vs (%) 7 1 . 5 8 3 . 4 Thermal eff. (%) qt 8 9 . 2 9 3 . 7 Volumetric eff. E,, 8 8 . 0 8 5 . 7 Displacement (cfm) 1 4 , 7 0 0 1 1 , 6 5 0 Rotor dia. (in.) 2 6 . 6 2 6 . 2 Commercial size, d x L 25 x 25 22x33 Speed (rpm) 3 , 5 0 0 1 , 2 5 0 Motor (HP) 1,100 800 Service factor 1.09 1.11 Discharge temp “F 309 270 ‘Twin 32.5 x 65 or triplet 2 6 . 5 x 3 3 ( 6 6 7 rpm) are more realistic. bTwin 32 x 32 (613 rpm) alternate where L= d. (Evans, 1979). is the ratio of heat capacities at constant pressure and constant volume and C”=R-C,. A related expression of some utility is T,/T, = (P2/P,)‘k-“‘k. (7.22) (7.23) Since k ordinarily is a fairly strong function of the temperature, a suitable average value must be used in Eq. (7.20) and related ones. Under adiabatic conditions the flow work may be written as W=H,-H,= I 9 V dP. (7.24) 4 Upon substitution of Eq. (7.20) into Eq. (7.24) and integration, the isentropic work becomes (7.25) TABLE 7.10. Specifications of Liquid Liner Compressors Pressure Capacity Motor tpsi) (cuftfmin) 0-W 5 1020 4 0 K - 6 10 990 6 0 1 5 870 7 5 2 0 650 100 621 2 6 1251 120 1256 i 3 5 440 621 1251 8 0 1256 2 3 110 410 7; 4 0 100 1 0 5 0 i 570 3500 1750 1750 3500 1750 1750 0 . 8 9 0 . 9 0 1.40 0 . 7 0 0 . 7 0 1.10 1 . 0 1 6 1 . 0 1 6 1 . 0 2 5 9 8 . 5 9 8 . 5 9 7 . 9 11.8 11.8 3 . 0 8 8 . 2 8 8 . 2 9 7 . 0 9 5 . 8 9 5 . 5 4 2 . 5 89.1 8 9 . 9 9 6 . 6 1 1 , 2 2 0 1 1 , 1 2 0 1 0 , 3 7 0 2 7 . 0 6 5 . 0 4 5 . 5 22 x 33 46 x 92a 43~48~ 593 284 378 750 750 1,400 1.10 1.12 1.10 262 263 120 In multistage centrifugal compression it is justifiable to take the average of the inlet and outlet compressibilities so that the work becomes ~=H*-Hl=(~)(~)RT,[(~)‘k-l”k-I]. ( 7 . 2 6 ) When friction is present, the problem is handled with empirical eficiency factors. The isentropic compression efficiency is defined as 17s = isentropic work or enthalpy change actually required work or enthalpy change (7.27) Accordingly, W = AH = WJs = (AH),/n,. (7.28) When no other information is available about the process gas, it is justifiable to find the temperature rise from AT = (AT),/rl, so that (7.29) T, = T,(l + (l/q,)[(P2/PI)‘k-“‘k - 11. (7.30) A case with variable heat capacity is worked out in Example 7.5. For mixtures, the heat capacity to use is the sum of the mol Gas Compression, Isentropic and True Final Temperatures With k = 1.4, PJPI = 3 and 9, = 0.71; the final temperatures are (T2)S = 1.369Tt and G= 1.519T, with Eqs. (7.24) and (7.31). (Nash Engineering Co.).
- 175. 156 FLUID TRANSPORT EQUIPMENT fraction weighted heat capacities of the pure components, c, = &Cpi. (7.31) REAL PROCESSES AND GASES Compression in reciprocating and centrifugal compressors is essentially adiabatic but it is not frictionless. The pressure-volume behavior in such equipment often conforms closely to the equation PV” = P, V; = const . (7.32) Such a process is called polytropic. The equation is analogous to the isentropic equation (7.20) but the polytropic exponent n is different from the heat capacity ratio k. Polytropic exponents are deduced from PV measurements on the machine in question. With reciprocating machines, the PV data are recorded directly with engine indicators. With rotary machines other kinds of instruments are used. Such test measurements usually are made with air. Work in polytropic compression of a gas with equation of state PV = zRT is entirely analogous to Eq. (7.26). The hydrodynamic work or the work absorbed by the gas during the compression is w,, = f vdP = (-&IRTl[ (;)“I’” - I]. (7.33) Manufacturers usually characterize their compressors by their polytropic efficiencies which are defined by (7.34) The polytropic work done on the gas is the ratio of Eqs. (7.33) and (7.34) and comprises the actual mechanical work done on the gas: W, = W,,,q, = (&)zIRTl[ ($‘n-l”n - I] (7.35) Losses in seals and bearings of the compressor are in addition to Wp; they may amount to l-3% of the polytropic work, depending on the machine. The value of the polytropic exponent is deduced from Eq. (7.34) as (7.36) The isentropic efficiency is 77 = isentropic work [Eq. (7.25)] s actual work [Eq. (7.35)] = (P*/PJ’k-“‘k - 1 (P*/P,)(“-‘1’” - 1 (P*/P#-“‘k - 1 = (pz/pl)‘~-“‘% - 1 (7.37) (7.38) (7.39) The last version is obtained with the aid of Eq. (7.34) and relates the isentropic and polytropic efficiencies directly. Figure 7.27(b) is a plot of Eq. (7.39). Example 7.6 is an exercise in the relations between the two kinds of efficiencies. MAXIMUM HEAD PER STAGE (FT-LB/LB) @ 00 4 00 60 00 + 00 00 00” 00 d’ 96 8. ,%P is-’ 3 0 4 0 5 0 6 0 7 0 80 9 0 t o o t4OLECULAR YEIGH, (a) 10 3 0 4 0 so 60 7 0 80 Head, It-lb/lb (multiply by 1000) (b) H = 5 ft/stage K= 0.50-0.65, empirical coefficient u = 600-900 ft / set, impeller peripheral speed H = 10,000 with average values K = 0.55 and u = 765 fl ! set (cl Figure 7.26. Several ways of estimating allowable polytropic head per stage of a multistage centrifugal compressor. (a) Single-stage head as a function of k, molecular weight, and temperature (Elliott Co.). (b) Single-stage head as a function of the nature of the gas (NGPSA Handbook, Gas Processors Assn, Tub, OK, 1972), obtained by dividing the total head of the compressor by number of stages. H = Ku*/32.2 ft/stage, K = 0.50-0.65, empirical coefficient, u = 600-900 ft/sec, impeller peripheral speed, and H = 10,000 with average values K = 0.55 and u = 765 ft/sec. (c) An equation and parameters for estimation of head.
- 176. 7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 157 EXAMPLE 7.5 The isentropic enthalpy change becomes Compression Work with Variable Heat Capacity Hydrogen sulfide heat capacity is given by C, = 7.629 + 3.431(E - 4)T + 5809(E - 6)T’ - 2.81(E - 9)T3, Cal/g mol, with 7’ in K. The gas is to be compressed from 100°F (310.9 K) and 14.7 psia to 64.7 psia. I 441.1 AH, = C, dT = 1098.1 Cal/g mol 310.1 + 1098.1(1.8)/34.08 = 58.0 Btu/lb, Assuming the heat capacity to be independent of pressure in this low range, the isentropic condition is compared with 59.0 from Example 7.7. The integration is performed with Simpson’s rule on a calculator. The actual final temperature will vary with the isentropic efficiency. It is found by trial from the equation AS = I Tz (CJT) dT - R ln(Z’,/P,) Tl I 5 = (C,/T) dT - 1.987 ln(64.7/14.7) = 0. 310.9 1098.1/r), = I E C, dT. 1098.1 Some values are By trial, with a root-solving program, lls 1.0 0.75 0.50 0.25 G 441.1 462.93 564.29 791.72 G = 441.1 K, 334.4”F (compared with 345°F from Example 7.7). WORK ON NONIDEAL GASES The methods discussed thus far neglect the effect of pressure on enthalpy, entropy, and heat capacity. Although efficiencies often are not known well enough to justify highly refined calculations, they may be worth doing in order to isolate the uncertainties of a design. Compressibility factors are given for example by Figure 7.29. Efficiencies must be known or estimated. Thermodynamic Diagram Method. When a thermodynamic diagram is available for the substance or mixture in question, the flow work can be found from the enthalpy change, W=AH. (7.40) The procedure is illustrated in Example 7.7 and consists of these steps: 1. Proceed along the line of constant entropy from the initial condition to the final pressure P2 and enthalpy (HJs. 2. Evaluate the isentropic enthalpy change (AH), = (H& - HI. 3. Find the actual enthalpy change as AH = (W,/v, and the final enthalpy as (7.41) H, = 4 + (AH),lvs. (7.42) 4. At the final condition (P2, HJ read off any other desired properties such as temperature, entropy or specific volume. Thermodynamic diagrams are known for light hydrocarbons, refrigerants, natural gas mixtures, air, and a few other common substances. Unless a substance or mixture has very many applications, it is not worthwhile to construct a thermodynamic diagram for compression calculations but to use other equivalent methods. General Method. The effects of composition of mixtures and of pressure on key properties such as enthalpy and entropy are deduced from PVT equations of state. This process is described in books on thermodynamics, for example, Reid, Prausnitz, and Sherwood (Properties of Liquids and Gases, McGraw-Hill, New York, 1977) and Walas (Phase Equilibria in Chemical Engineering, Butterworths, Stoneham, MA, 1985). Only the simplest correlations of these effects will be utilized here for illustration. For ideal gases with heat capacities dependent on temperature, the procedure requires the isentropic final temperature to be found by trial from AS= I rti(Cp/T) dT - R ln(Pz/Pr)+O, 7-l (7.43) and then the isentropic enthalpy change from AH= I T2 C, dT. (7.44) TI The final temperature T2 is found by trial after applying a known isentropic efficiency, (AH),/% = lT;Cp dT. (7.45) The fact that heat capacities usually are represented by empirical polynomials of the third or fourth degree in temperature accounts for the necessity of solutions of equations by trial. Example 7.5 applies this method and checks roughly the calculations of Example 7.7 with the thermodynamic diagram of this substance. The pressures are relatively low and are not expected to generate any appreciable nonideality. This method of calculation is applied to mixtures by taking a mol fraction weighted heat capacity of the mixture, c, = 2 xicpi. (7.46) When the pressure range is high or the behavior of the gas is
- 177. 158 FLUID TRANSPORT EQUIPMENT Suction Volume CFM “0 ‘“a TABLE OF CORRECTION FACTORS DUE TO COMPRESSION RATIO .. 0 Compression Inlet Volume in CFM 60,000 2 R a t i o 1 5 0 0 2000 3000 4000 5000 7500 15,000 30,000 & over a 1.35 1.0 1 .o 1.0 1.0 1.0 1 .o 1 .o 1 .o 1 .o 1.75 .9B3 .990 .990 .994 .996 .996 .996 .996 1.0 2.25 .976 .977 .9B6 ,905 .991 .995 .995 .995 1.0 2.80 - ,969 .9BO .9BO .9B9 .992 .993 .994 1.0 5.00 - - .965 .970 .972 .9B5 .991 .996 .997 10.00 - - - .944* .955* .960* .905* .9B9* .995 15.00 - - - - .935* .957* .971* .9%6’ .993 Notes: Asterisk indicates figures applying only to high molecular weight hydrocarbons. Factors apply on one compressor body with six or less impellers. (a) (b) %oo+j--,IL,NECYLINDERS --+-H-l l I I I GENERAL PURPOSE CYLINDERS 1 I I I I ,~I”“““““““““““““““” 1 0 15 2.0 2.5 3.0 3.5 4.0 4 5 PRESSURE RATIO Pg/ Ps 0.98 0.96 / / i i I I 16 p, = Inlet pressure, psia p2 = Discharge pressure, psi0 k = Ratio of specific CPI heats, cy I I I I I I 60 70 00 90 1 0 0 Polytropic Efficiency Efficiencies Compression Ratio (Engine-driven*) 1.1 50-60 1.2 60-70 1.3 65-80 1.5 70-85 2.0 75-88 2.5 80-89 3.0 82-90 4.0 85-90 ‘Multiply by 0.95 for motor-driven compressors. Figure 7.27. Efficiencies of centrifugal and reciprocating compressors. (a) Polytropic efficiencies of centrifugal compressors as a function of suction volume and compression ratio (Clark Brothers Co.). (b) Relation between isentropic and polytropic efficiencies, Eqs. (7.22) (7.23). (c) Isentropic efficiencies of reciprocating compressors (De Lava1 Handbook, McGraw-Hill, New York, 1970). Multiply by 0.95 for motor drive. Gas engines require 7000-8000 Btu/HP. nonideal for any other reason, the isentropic condition becomes EXAMPLE 7.6 Polytropic and Isentropic Efficiencies Take np = 0.75, k = 1.4, and Pa/P, = 3. From Eq. (7.39), n = 1.6154 and nS = 0.7095. With Figure 7.27(b), 4 = 3’.‘*s7 = 1.3687, nS = 0.945~ = 0.709. The agreement is close. I T3.T AS= (CL/T) dT -R In(P,/P,) + A.9; - AS;-+ 0. (7.47) fi After the final isentropic temperature T, has been found by trial, the isentropic enthalpy change is obtained from rr7. (AH), = j -C; dT + AH; - AH&. fi (7.48)
- 178. 7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 1% 4.0 I I I I I I I I I i 1’ 5 / g I / E saturation / CUrYe -y g 3.0 / / z b /’ i2 / / e 3 / /, .i4 % 1.0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -.--0s 0.9 1.0 In terms of a known isentropic efficiency the final temperature TZ then is found by trial from (Aff)slv, = j--y CL dT + AH; - AH;. (7.49) In these equations the heat capacity CL is that of the ideal gas state or that of the real gas near zero or atmospheric pressure. The residual properties AS; and AH; are evaluated at (5, Ti) and AS; and AH; at (Pa, Tz). Figure 7.28 gives them as functions of reduced temperature T/T, and reduced pressure P/P,. More accurate methods and charts for finding residual properties from appropriate equations of state are presented in the cited books of Reid et al. (1977) and Walas (1985). For mixtures, pseudocritical properties are used for the evaluation of the reduced properties. For use with Figure 7.28, Kay’s rules are applicable, namely, (7.50) (7.51) but many equations of state employ particular combining rules. Example 7.8 compares a solution by this method with the assumption of ideal behavior. (a) EFFICIENCY The efficiencies of fluid handling equipment such as fans and compressors are empirically derived quantities. Each manufacturer will supply either an efficiency or a statement of power requirement for a specified performance. Some general rules have been devised for ranges in which efficiencies of some classes equipment usually fall. Figure 7.27 gives such estimates for reciprocating compressors. Fan efficiencies can be deduced from the power-head curves of Figure 7.24. Power consumption or efficiencies of rotary and reciprocating machines are shown in Tables 7.7, 7.8, and 7.9. Polytropic efficiencies are obtained from measurements of power consumption of test equipment. They are essentially independent of the nature of the gas. As the data of Figure 7.27 indicate, however, they are somewhat dependent on the suction volumetric rate, particularly at low values, and on the compression ratio. Polytropic efficiencies of some large centrifugal compressors are listed in Table 7.6. These data are used in Example 7.9 in the selection of a machine for a specified duty. The most nearly correct methods of Section 7.6.4 require knowledge of isentropic efficiencies which are obtainable from the polytropic values. For a given polytropic efficiency, which is independent of the nature of the gas, the isentropic value is obtained with Eq. (7.39) or Figure 7.27(b). Since the heat capacity is involved in this transformation, the isentropic efficiency depends on the nature of the substance and to some extent on the temperature also. TEMPERATURE RISE, COMPRESSION RATIO, VOLUMETRIC EFFICIENCY lb) Figure 7.28. Residual entropy and enthalpy as functions of reduced properties. (a) Residual entropy. (b) Residual enthalpy. Drawn by Smith and Vun Ness (Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1959) from data of Lydersen et al. For illustrative purposes primarily; see text for other sources.] The isentropic temperature for ideal gases by For by (T& = T,(P2/Pl)‘k-“‘k. polytropic compression (7.52) the final temperature is given directly & = T,(P,/P,)‘“-“‘” (7.53) in terms of compression ratio is given
- 179. 160 FLUID TRANSPORT EQUIPMENT EXAMPLE~.~ Finding Work of Compression with a Thermodynamic Chart Hydrogen sulfide is to be compressed from 100°F and atmospheric nressure to SOnsig. The isentropic efficiency is 0.70. A pressure-enthalpy- chart is taken from Starling <Fluid Thermo- dynamic Properties for Light Petroleum Systems, Gulf, Houston, TX, 1973). The work and the complete thermodynamic conditions for the process will be found. The path followed by the calculation is l-2-3 on the sketch. The initial enthalpy is -86Btu/lb. Proceed along the isentrop S = 1.453 to the final pressure, 64.7 psia, and enthalpy Hz = -27. The isentropic enthalpy change is AH, = -27 - (-86) = 59 Btu/lb. The true enthalpy change is AH = 5910.70 = 84.3. The final enthalpy is H,=-86+84.3=-1.7. Other conditions at points 2 and 3 are shown on the sketch. The work is ti = AH = 84.3 Btu/lb +84.3/2.545 = 33.1 HP hr/(lOOO lb). -27 Enthalpy, Btu/lb -1.7 EXAMPLE~.~ Compression Work on a Nonideal Gas When the residual properties are neglected, Hydrogen sulfide at 450K and 15 atm is to be compressed to 66 atm. The isentropic final temperature and the isentropic enthalpy change will be found with the aid of Figure 7.28 for the residual properties. The critical properties are T, = 373.2 K and P, = 88.2 atm. The heat capacity is stated in Example 7.5: T,, = 4501373.2 = 1.21, P,l = 15/88.2 = 0.17, P,2 = 66/88.2 = 0.75, T2 = 623.33 K (compared with 626.6 real), AH, = 1569.5 (compared with 1487.7 real). Real temperature rise: With n, = 0.75, the enthalpy change is 1487.7/0.75 and the enthalpy balance is rearranged to A= -!$??+,” Cp* dT + 75-AH; 2 0 450 :. AS; = 0.15, AH; = 0.2(373.2) = 75.0, AS= I T* cp 450 ~dT-1.987ln~+0.15-AS~~O, AH, = Cp dT + 75.0 - AH;. 1. Assume a value of T,. 2. Evaluate T,z and AS;. 3. Integrate Eq. (1) numerically and note the righthand side. 4. Continue with trial values of T2 until AS = 0. 5. Find AH; and finally evaluate AH,. (1) (2) Trial T2 680 670.79 670.80 r, AH; rhs 1.82 109 +91.7 1.80 112 -0.021 1.80 +0.075 :. T, = 670.79 K. For ideal gas Two trials are shown. By trial: T2 Tr, AS; AS AH; A& T, = 670.49 K 600 1.61 0.2 -0.047 626.6 1.68 0.2 +0.00009 187 1487.7 Nonideality is slight in this example.
- 180. 7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 161 EXAMPLE 7.9 Selection of a Centrifugal Compressor A hydrocarbon mixture wtth molecular weight 44.23 is raised from 41°F and 20.1 psia to 100.5psia at the rate of 24001bmol/hr. Its specific heat ratio is k = 1.135 and its inlet and outlet compressibilities are estimated as z1 = 0.97 and z, = 0.93. A size of compressor will be selected from Table 7.6 and its expected performance will be calculated: 2400 lb mol/hr = 1769 lb/min, 10,260 cfm From Table 7.6, the smallest compressor for this gas rate is # 38M. Its characteristics are &= 8100 rpm at lo-12 K ft/stage 11,=0.77 rfg::;f5 z: = 0.97 1769 Ib/min 10260 cfm Accordingly, n - l k - l 0.135 -=-= k% 1.135(0.77) = 0.1545. n Using Eq. (7.35) for the polytropic head, HP = (zg(&)RTl[ (g-“‘“- l] = 0.95(g3(+3(501,[5~~~545 - 11 =39430 ft. From Figure 7.26(a), the max head per stage is 9700, and from Figure 7.26(b) the min number of stages is about 4.5. Accordingly, use five stages with standard 10,000 ft/stage impellers. The required speed with the data of Table 7.6 is speed = 8100~39430/10,000(5) = 7190 rpm. Power absorbed by the gas is Pgas = kH, 33,OOOQ = 1W3%4W = 2745 HP, 33,000(0.77) Friction losses ~3% max; :. total power input = 2745/0.97 = 2830 HP max. or alternately in terms of the isentropic efficiency by stages, accordingly, the compression ratio of each stage is (A ZLua, = T2 - T = WLntropiclvs (7.54) so that P. /E = (P /P)"". ,+1 , " 1 (7.56) Example 7.11 works out a case involving a nonideal gas and interstage pressure losses. T2 = Tl + (AT),/q, = T,{l + (1/11,)[(P2/P~)(‘-‘)‘~ - l]}. (7.55) The final temperature is read off directly from a thermo- dynamic diagram when that method is used for the compression calculation, as in Example 7.7. A temperature calculation is made in Example 7.10. Such determinations also are made by the general method for nonideal gases and mixtures as in Example 7.8 and for ideal gases in Example 7.4. In centrifugal compressors with all stages in the same shell, the allowable head rise per stage is stated in Table 7.6 or correlated in Figure 7.26. Example 7.9 utilizes these data. Volumetric Eficieuq. For practical reasons, the gas is not completely discharged from a cylinder at each stroke of a reciprocating machine. The clearance of a cylinder is filled with compressed gas which reexpands isentropically on the return stroke. Accordingly, the gas handling capacity of the cylinder is less than the product of the cross section by the length of the stroke. The volumetric efficiency is Compression Ratio. In order to save on equipment cost, it is desirable to use as few stages of compression as possible. As a rule, the compression ratio is limited by a practical desirability to keep outlet temperatures below 300°F or so to minimize the possibility of ignition of machine lubricants, as well as the effect that power requirement goes up as outlet temperature goes up. Typical compression ratios of reciprocating equipment are: Large pipeline compressors 1 Z-2.0 Process compressors 1.5-4.0 Small units up to 6.0 For minimum equipment cost, the work requirement should be the same for each stage. For ideal gases with no friction losses between stages, this implies equal compression ratios. With it n, = suction gas volume cylinder displacement = 1 -f,[(WPYk - 11, where (7.57) L= clearance volume cyhnder displacement volume ’ For a required volumetric suction rate Q (cfm), the required product of cross section A, (sqft), stroke length L, (ft), and speed N (rpm) is given by A,L,N = Q/v,. (7.58)
- 181. 162 FLUID TRANSPORT EQUIPMENT EXAMPLE 7.10 Polytropic and Isentropic Temperatures Take k = 1.4, (PJS) = 3, and 5 = 0.75. From Eq. (7.34), (n - 1)/n = (k - l)//qp = 0.3810 so that from Eq. (7.53), TJT, = 3°.3R’o = 1.5198, isentropic, and from Eq. (7.39) 30.2857 - 1 n =--0.7094 s 30.3810 _ 1 and from Eq. (7.54), ‘&IT, = I + (1/o.7094)(3°.zs57 - 1) = 1.5197, polytropic. 7.7. EJECTOR AND VACUUM SYSTEMS EJECTOR ARRANGEMENTS Application ranges of the various kinds of devices for maintenance of subatmospheric pressures in process equipment are shown in Table 7.3. The use of mechanical pumps--compressors in reverse- for such purposes is mentioned earlier in this chapter. Pressures also can be reduced by the action of flowing fluids. For instance, water jets at 40psig will sustain pressures of 0.5-2.0psia. For intermediate pressure ranges, down to 0.1 Torr or so, steam jet ejectors are widely favored. They have no moving parts, are quiet, easily installed, simple, and moderately economical to operate, and readily adaptable to handling corrosive vapor mixtures. A specification form is in Appendix B. Several ejectors are used in parallel when the load is variable or because the process system gradually loses tightness between maintenance shutdowns-then some of the units in parallel are cut in or out as needed. Multistage units in series are needed for low pressures. Sketches are shown in Figure 7.30 of several series arrangements. In Figure 7,30(a), the first stage drives the process vapors, and the second stage drives the mixture of those vapors with the motive steam of the first stage. The other two arrangements employ interstage condensers for the sake of steam economy in subsequent stages. In contact (barometric) condensers the steam and other : 094 1 “A 02y.y ,’ ;< ; z 093 I I ‘WC 4 : 8092 3. ‘ I , 050 ‘ 091 ‘ 0900 0.0, 0.02 003 0 0 4 0 . 0 5 006 0 0 7 0 0 8 009 OIO 1 1 1 1 “‘J. “/ I o.4o r I I REDUCED PRESSURE. Pa 1 I I I I 1 I I I I ‘ , 09 1.0 0 0 0.1 0.2 0 3 0 4 05 0.6 07 0 8 REDUCED PRESSURE, PR Figure 7.29. Compressibility factors, z = PV/RT, of gases. Used for the solution of Example 7.11. PR = P/P,, TR = TIT,, and V,. = P,V/RT,.
- 182. J 2nd stage suction head High-pressure steam inlet y e 1st stage combining throat Suction -+’ - - 1st stage steam nozzle Steam Nozzle I (a) Nozzle Second S/age Discharge lnfercandenser Water Discharqe b) lnfercondenser (cl Figure 7.30. Arrangements of two-stage ejectors with condensers. (a) Identification of the parts of a two-stage ejector (Croll-Reynolds Co.). (b) A two-stage ejector with interstage barometric condenser (Elliot Co.). (c) A two-stage ejector with surface condensers interstage and terminal (Elliot Co.). Steam Nozzle Aftercondenser 163
- 183. 164 FLUID TRANSPORT EQUIPMENT condensables are removed with a cold water spray. The tail pipes of the condensers are sealed with a 34ft leg into a sump, or with a condensate pump operating under vacuum. Surface condensers permit recovery of valuable or contaminating condensates or steam condensate for return as boiler feed. They are more expensive than barometries, and their design is more complex than that of other kinds of condensers because of the large amounts of nonconden- sables that are present. As many as six stages are represented on Figure 7.30, combined with interstage condensers in several ways. Barometric condensers are feasible only if the temperature of the water is below its bubblepoint at the prevailing pressure in a particular stage. Common practice requires the temperature to be about 5°F below the bubblepoint. Example 7.13 examines the feasibility of installing intercondensers in that process. AIR LEAKAGE The size of ejector and its steam consumption depend on the rate at which gases must be removed from the process. A basic portion of such gases is the air leakage from the atmosphere into the system. Theoretically, the leakage rate of air through small openings, if they can be regarded as orifices or short nozzles, is constant at vessel pressures below about 53% of atmospheric pressure. However, the openings appear to behave more nearly as conduits with relatively large ratios of lengths to diameters. Accordingly sonic flow is approached only at the low pressure end, and the air mass inleakage rate is determined by that linear velocity and the low density prevailing at the vessel pressure. The content of other gases in the evacuated vessel is determined by each individual process. The content of condensables can be reduced by interposing a refrigerated condenser between process and vacuum pump. Standards have been developed by the Heat Exchange Institute for rates of air leakage into commercially tight systems. Their chart is represented by the equation m = kVU3 (7.59) where m is in lb/hr, V is the volume of the system in tuft, and the EXAMPLE 7.11 Three-Stage Compression with Intercooling and Pressure Loss between Stages Ethylene is to be compressed from 5 to 75atm in three stages. Temperature to the first stage is 60”F, those to the other stages are 100°F. Pressure loss between stages is 0.34 atm (5 psi). Isentropic efficiency of each stage is 0.87. Compressihilities at the inlets to the stages are estimated from Figure 7.29 under the assumption of equal compression ratios as z, = 0.98, zr = 0.93, and z, = 0.83. The interstage pressures will be determined on the basis of equal power load in each stage. The estimated compressibilities can be corrected after the pressures have been found, but usually this is not found necessary. k = C,lC, = 1.228 and (k - 1)/k = 0.1857. Z,,=O.98 t P,=75 With equal power in each stage Tota1 ‘Ower = 0.1857(2545)0.87 3(0.98)(1.987)(520) [ (l225)” ls5’- 1] “s3L[(;)“‘857-‘] = 1.34 HP/(lb mol/hr). = 0.98(520)[(PI/5)o-'857- 11 I I =0.93(560){((p,_P;34))o~lP57- 1) 32- = 0,83(560){(75/(P, - 0.34)]".'857- 1) CL x ‘ Values of PI will be assumed until the value of P2 calculated by equating the first two terms equals that calculated from the last two t “I ;i 3 0 terms. The last entries in the table are the interpolated values. A a” pr 1+2 2+3 12 27.50 28.31 12.5 29.85 28.94 13.0 32.29 29.56 12.25 -28.6+ 27 12 I I 12.5 13 p, -
- 184. 7.7. EJECTOR AND VACUUM SYSTEMS 165 TABLE 7.11. Estimated Air Leakages Through Connections, Valves, Stuffing Boxes Etc. of Process Equipmenta Type Fitting Estimated Average Air Leakage W/W Screwed connections in sizes up to 2 in. Screwed connections in sizes above 2 in. Flanged connections in sizes up to 6 in. Flanged connections in sizes 6 in. to 24 in. including m a n h o l e s 0.1 0 . 2 0 . 5 0 . 8 Flanged connections in sizes 24 in. to 6 ft Flanged connections in sizes above 6ft Packed valves up to i in. stem diameter Packed valves above f in. stem diameter Lubricated plug valves Petcocks Sight glasses Gage glasses including gage cocks Liquid sealed stuffing box for shaft of agitators, pumps, etc. (per in. shaft diameter) 1.1 2.0 0 . 5 1.0 0.1 0 . 2 1.0 2.0 0 . 3 Ordinary stuffing box (per in. of diameter) Safety valves and vacuum breakers (per in. of nominal size 1.5 1.0 ‘For conservative practice, these leakages may be taken as sup- plementary to those from Eq. (7.59). Other practices allow 5lb/hr for each agitator stuffing box of standard design; special high vacuum mechanical seals with good maintenance can reduce this rate to l-2 Ib/hr. [From C.D. Jackson, Chem. Eng. Prog. 44, 347 (194811. coefficient is a function of the process pressure as follows: Pressure (Torr) >90 20-90 3-20 l - 3 <l k 0.194 0 . 1 4 6 0 . 0 8 2 5 0 . 0 5 0 8 0 . 0 2 5 4 For each agitator with a standard stuffing box, 5 lb/hr of air leakage is added. Use of special vacuum mechanical seals can reduce this allowance to l-2 lb/hr. For a conservative design, the rate from Eq. (7.59) may be supplemented with values based on Table 7.11. Common practice is to provide oversize ejectors, capable of handling perhaps twice the standard rates of the Heat Exchange Institute. Other Gases. The gas leakage rate correlations cited are based on air at 70°F. For other conditions, corrections are applied to evaluate an effective air rate. The factor for molecular weight M is fM = 0.375 ln(M/2) (7.60) EXAMPLE 7.12 Equivalent Au Rate Suction gases are at the rate of 120lb/hr at 300°F and have a molecular weight of 90. The temperature factor is not known as a function of molecular weight so the value for air will be used. Using Eqs. (7.61) and (7.62), m = 120(0.375) ln(90/2)[1- 0.00024(300-70)] = 161.8 Ib/hr equivalent air. STEAM CONSUMPTION The most commonly used steam is 1OOpsig with 10-15” superheat, the latter characteristic in order to avoid the erosive effect of liquids on the throats of the ejectors. In Figure 7.31 the steam consumptions are given as lb of motive steam per lb of equivalent air to the first stage. Corrections are shown for steam pressures other than 100 psig. When some portion of the initial suction gas is condensable, downward corrections to these rates are to be made for those ejector assemblies that have intercondensers. Such corrections and also the distribution of motive steam to the individual stages are problems best passed on to ejector manufacturers who have experience and a body of test data. and those for temperature T in “F of predominantly air or predominantly steam are fA = 1 - O.O0024(T - 70), for air, (7.61) fs = 1 - O.O0033(T - 70), for steam. (7.62) An effective or equivalent air rate is found in Example 7.12. Figure 7.31. Steam requirements of ejectors at various pressure levels with appropriate numbers of stages and contact interconden- sers. Steam pressure lOOpsig, water temperature 85°F. Factor for 65 psig steam is 1.2 and for 200 psig steam it is 0.80 (Worthington Corp).
- 185. 166 FLUID TRANSPORT EQUIPMEN EXAMPLE 7.13 Interstage Condensers A four-stage ejector is to evacuate a system to 0.3 Torr. The compression ratio in each stage will be (P4/Po)“4 = (760/0.3)1’4 = 7.09. The individual stage pressures and corresponding water bubblepoint temperatures from the steam tables are Discharge of stage 0 1 2 3 4 T o r r 0.3 2.1 15.1 107 760 “F 1 4 6 3 . 7 1 2 7 . 4 The bubblepoint temperature in the second stage is marginal with normal cooling tower water, particularly with the practical restriction to 5°F below the bubblepoint. At the discharge of the third stage, however, either a surface or barometric condenser is quite feasible. At somewhat higher process pressure, two interstage condensers may be practical with a four-stage ejector, as indicated on Figure 7.31. Chffuser Figure 7.32. Progress of pressures, velocities, enthalpies and entropies in an ejector (Co&on and Richardson, Chemical Engineering, Pergamon, 1977, New York, Vol. I). GLOSSARY FOR CHAPTER 7 PUMP TERMS Head has the dimensions [F][L]/[M]; for example, ft lbf/lb or ft; or N m/kg or m: a. pressure head = APIp; b. velocity head = Au2/2g,; c. elevation head = Az(g/g,), or commonly AZ; d. friction head in line, Hr = f (L./D)u2/2gc; e. system head H, is made up of the preceding four items; f. pump head equals system head, H, = H,, under operating conditions; When barometric condensers are used, the effluent water temperature should be at least 5°F below the bubblepoint at the prevailing pressure. A few bubblepoint temperatures at low pressures are: Absolute (in. H g ) 0 . 2 0 . 5 1.0 2.0 Bubblepoint “F 3 4 . 6 5 8 . 8 7 9 . 0 101.1 Interstage pressures can be estimated on the assumption that compression ratios will be the same in each stage, with the suction to the first stage at the system pressure and the discharge of the last stage at atmospheric pressure. Example 7.13 examines at what stages it is feasible to employ condensers so as to minimize steam usage in subsequent stages. E J E C T O R T H E O R Y The progress of pressure, velocity, and energy along an ejector is illustrated in Figure 7.32. The initial expansion of the steam to point C and recompression of the mixture beyond point E proceed adiabatically with isentropic efficiencies of the order of 0.8. Mixing in the region from C to E proceeds with approximate conservation of momenta of the two streams, with an efficiency of the order of 0.65. In an example worked out by Dodge (1944, pp. 289-293) the compounding of these three efficiencies leads to a steam rate five times theoretical. Other studies of single-stage ejectors have been made by Work and Haedrich (1939) and DeFrate and Hoer1 (1959) where other references to theory and data are made. The theory is in principle amenable to the prediction of steam distribution to individual stages of a series, but no detailed procedures are readily available. Manufacturers charts such as Figure 7.31 state only the consumption of all the stages together. g. static suction head equals the difference in levels of suction liquid and the centerline of the pump; h. static suction lift is the static suction head when the suction level is below the centerline of the pump; numerically a negative number. NPSH (net positive suction head) = (pressure head of source) + (static suction head) - (friction head of the suction line) - (vapor pressure of the flowing liquid). Hydraulic horsepower is obtained by multiplying the weight rate of flow by the head difference across the pump and converting horsepower. For ;ipm)(sp gr)(ft)/3960. example, HHP = (gpm)(psi)/l714 =
- 186. REFERENCES 167 Brake horsepower is the driver power output needed to operate the pump. BHP = HHP/(pump efficiency). Driver horsepower, HP = BHP/(driver efficiency) = HHP/(pump efficiency)(driver efficiency). TERMS CONCERNING CENTRIFUGAL AND RELATED PUMPS Axial flow is flow developed by axial thrust of a propeller blade, practically limited to heads under 50 ft or so. Centrifugal pump consists of a rotor (impeller) in a casing in which a liquid is given a high velocity head that is largely converted to pressure head by the time the liquid reaches the outlet. Characteristic curves are plots or equations relating the volumetric flow rate through a pump to the developed head or efficiency or power or NPSH. Diffuser type: the impeller is surrounded by gradually expanding passages formed by stationary guide vanes [Figs. 7.2(b) and 7.3(d)]. Double suction: two incoming streams enter at the eye of the impeller on opposite sides, minimizing axial thrust and worthwhile for large, high head pumps [Fig. 7.2(b)]. Double volute: the liquid leaving the impeller is collected in two similar volutes displaced 180” with a common outlet; radial thrust is counterbalanced and shaft deflection is minimized, resulting in lower maintenance and repair, used in high speed pumps producing above 500 ft per stage. Impeller: the rotor that accelerates the liquid. a. Open impellers consist of vanes attached to a shaft without any REFERENCES Compressors 1. Compressors in Encyclopedia of Chemical Processing and Design, Dekker, New York, 1979, Vol. 10, pp. 157-409. 2. F.L. Evans, Compressors and fans, in Equipment Design Handbook for Refineries and Chemical Plants, Gulf, Houston, 1979, Vol. 1, pp. 54-104. 3. H. Gartmann, DeLaval Engineering Handbook, McGraw-Hill, New York, 1970, pp. 6.61-6.93. 4. R. James, Compressor calculation procedures, in Encyclopedia of Chemical Processing and Design, Dekker, New York, Vol. 10, pp. 264-313. 5. E.E. Ludwig, Compressors, in Applied Process Design for Chemical and Petrochemical Plants, Gulf, Houston, 1983, Vol. 3, pp. 251-396. 6. R.D. Madison, Fan Engineering, Buffalo Forge Co., Buffalo, NY, 1949. I. H.F. Rase and M.H. Barrow, Project Engineering of Process Plants, Wiley, New York, pp. 297-347. Ejectors 1. L.A. DeFrate and V. W. Haedrich, Chem. Eng. Prog. Symp. Ser. 21, 43-51 (1959). 2. B.F. Dodge, Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1944, pp. 289-293. 3. F.I. Evans, Equipment Design Handbook for Refineries and Chemical Plants, Gulf, Houston, 1979, Vol. 1, pp. 105-117. 4. E.E. Ludwig, lot. cit., Vol. 1, pp. 206-239. 5. R.E. Richenberg and J.J. Bawden, Ejectors, steam jet, in Encyclopedia of Chemical Processing and Design, Dekker, New York, Vol. 17, pp. 167-194. 6. L.T. Work and V.W. Haedrich, Ind. Eng. Chem. 31,464-477 (1939). Piping 1. ANSI Pioine Code. ASME. New York, 1980. form of supporting sidewall and are suited to handling slurries without clogging [Fig. 7.2(a)]. b. Semienclosed impellers have a complete shroud on one side [Fig. 7.3(c)]; they are essentially nonclogging, used primarily in small size pumps; clearance of the open face to the wall is typically 0.02 in. for 10 in. diameters. c. Closed impellers have shrouds on both sides of the vanes from the eye to the periphery, used for clear liquids [Fig. 7.3(b)]. Mechanical seals prevent leakage at the rotating shaft by sliding metal on metal lubricated by a slight flow of pump liquid or an independent liquid [Figs. 7.4(c) and (d)]. Miied flow: develops head by combined centrifugal action and propeller action in the axial direction, suited to high flow rates at moderate heads [Fig. 7.3(e)]. Multistage: several pumps in series in a single casing with the objective of developing high heads. Figure 7.6(c) is of characteristic curves. Performance curves (see characteristic curves). Single suction: the liquid enters on one side at the eye of the impeller; most pumps are of this lower cost style [Fig. 7.2(c)]. Split case: constructed so that the internals can be accessed without disconnecting the piping [Fig. 7.2(a)]. Stuffmg box: prevent leakage at the rotating shaft with compressed soft packing that may be wetted with the pump liquid or from an independent source [Figs. 7.4(a) and (b)]. Volute type: the impeller discharges the liquid into a progressively expanding spiral [Fig. 7.2(a)]. 2. 3. 4. 5. 6. 7. 8. 9. 10. S. Chalfin, Control valves, Encyclopedia of Chemical Processing and Design, Dekker, New York, 1980, Vol. 11, pp. 187-213. F.L. Evans, Equipment Design Handbook for Refineries and Chemical Plants, Gulf, Houston, 1979, Vol. 2; piping, pp. 188-304; valves, pp. 315-332. J.W. Hutchinson, ISA Handbook of Control Valves, Inst. Sot. America, Research Triangle Park, NC, 1976. R.C. King, Piping Handbook, McGraw-Hill, New York, 1967. J.L. Lyons, Encyclopedia of Values, Van Nostrand Reinhold, New York, 1975. Marks’ Standard Handbook for Mechanical Engineers, McGraw-Hill, New York, 1987. Perry’s Chemical Engineers’ Handbook, McGraw-Hill, New York, 1984. R. Weaver, Process Piping Design, Gulf, Houston, 1973, 2 Vols. P. Wing, Control valves, in Process Instruments and Controls Handbook, (D.M. Considine, Ed.), McGraw-Hill, New York, 1974. .^ 11. R.W. Zappe, Value Selection Handbook, tiulf, Houston, pp. IY.~-19.60, 1981. Pumps 1. D. Azbel and N.P. Cheremisinoff, Fluid Mechanics and Fluid Operations, Ann Arbor Science, Ann Arbor, MI, 1983. 2. N.P. Cheremisinoff, Fluid Flow: Pumps, Pipes and Channels, Ann Arbor Science, Ann Arbor, MI, 1981. 3. F.L. Evans, lot. cit., Vol. 1, pp. 118-171. 4. H. Gartmann, DeLnval Engineering Handbook, McGraw-Hill, New York, 1970, pp. 6.1-6.60. 5. I.J. Karassik and R. Carter, Centrifugal Pump Selection Operation and Maintenance, F.W. Dodge Corp., New York, 1960. 6. I.J. Karassik, W.C. Krutsch, W.H. Fraser, and Y.J.P. Messina, Pump Handbook, McGraw-Hill, New York, 1976. 7. F.A. Kristal and F.A. Annett, Pumps, McGraw-Hill, New York, 1940. 8. E.E. Ludwig, lot. cit., Vol. 1, pp. 104-143. 9. S. Yedidiah, Centrifugal Pump Problems, Petroleum Publishing, Tulsa. OK. 1980.
- 188. 8 HEAT TRANSFER AND HEAT EXCHANGERS B asic concepts of heat transfer are reviewed in this chapter and applied primarily to heat exchangers, which are equipment for the transfer of heat between two fluids through a separating wall. Heat transfer a/so is a key process in other specialized equipment, some of which are treated in the next and other chapters. The three recognized modes of heat transfer are by conduction, convection, and radiation, and may occur simultaneously in some equipment. 8.1. CONDUCTION OF HEAT In a solid wall such as Figure 8.1(a), the variation of temperature with time and position is represented by the one-dimensional Fourier equation For the most part, only the steady state condition will be of concern here, in which the case the partial integral of Eq. (8.1) becomes assuming the thermal conductivity k to be independent of temperature. Furthermore, when both k and A are independent of position, Q=-Kay=+,-7”), (8.3) in the notation of Figure 8.1(a). Equation (8.3) is the basic form into which more complex situations often are cast. For example, Q =%,,,, y when the area is variable and (8.4) Q =WA%,,, (8.5) in certain kinds of heat exchangers with variable temperature difference. THERMAL CONDUCTIVITY Thermal conductivity is a fundamental property of substances that basically is obtained experimentally although some estimation methods also are available. It varies somewhat with temperature. In many heat transfer situations an average value over the prevailing temperature range often is adequate. When the variation is linear with k = k,(l + CUT), the integral of Eq. (8.2) becomes Q&/A) = k,[T, - 7” + OSa(T: - T;)] = k,(T, - T,)[l + OSa(T, + T&l, (8.6) (8.7) which demonstrates that use of a value at the average temperature gives an exact result. Thermal conductivity data at several temperatures of some metals used in heat exchangers are in Table 8.1. The order of magnitude of the temperature effect on k is illustrated in Example 8.1. (a) lb) (4 (0 Figure 8.1. Temperature profiles in one-dimensional conduction of heat. (a) Constant cross section. (b) Hollow cylinder. (c) Composite flat wall. (d) Composite hollow cylindrical wall. (e) From fluid A to fluid F through a wall and fouling resistance in the presence of eddies. (f) Through equivalent fluid films, fouling resistances, and metal wall. 169
- 189. 170 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.1. Thermal Conductivities of Some Metals Commonly Used in Heat Exchangers is the logarithmic mean radius of the hollow cylinder. This concept tkBtu/(hr)(sqft)(“F/ft)l is not particularly useful here, but logarithmic means also occur in other more important heat transfer situations. Temperature (“F) Metal or Alloy -100 7 0 200 1000 Steels Carbon ICriMo 410 304 316 Monel400 Nickel 200 lnconel 600 Hastelloy C Aluminum Titanium Tantalum C o p p e r Yellow brass Admiralty - 3 0 . 0 2 7 . 6 22.2 - 19.2 19.1 18.0 - 13.0 14.4 - - 9 . 4 10.0 13.7 8.1 9 . 4 - 13.0 11.6 12.6 13.8 2 2 . 0 - 3 2 . 5 3 1 . 9 3 0 . 6 - 8 . 6 9.1 14.3 - 7 . 3 5.6 10.2 - 131 133 - 11.8 11.5 10.9 12.1 - 3 1 . 8 - - 225 225 222 209 5 6 6 9 - - 5 5 6 4 - - HOLLOW CYLINDER As it appears on Figure 81(b), as the heat flows from the inside to the outside the area changes constantly. Accordingly the equivalent of Eq. (8.2) becomes, for a cylinder of length N, dT Q = -kN(2~r)-, d r of which the integral is Q = 2~kNT, - G) WJr,) (8.8) This may be written in the standard form of Eq. (8.4) by taking A,,, = 2nLNr,, (8.10) and L=r,-r,, (8.11) where r,, = (5 - rdlW21rd (8.12) EXAMPLE 8.1 Conduction through a Furnace Wall A furnace wall made of fire clay has an inside temperature of 1500°F and an outside one of 300°F. The equation of the thermal conductivity is k = 0.48[1 + 5.15(E - 4)T] Btu/(hr)(sqft)(“F/ft). Accordingly, Q(L/A) = 0.48(1500 - 300)[1+ 5.15(E - 4)(900)] = 0.703. If the conductivity at 300°F had been used, Q(L/A) = 0.554. COMPOSITE WALLS The flow rate of heat is the same through each wall of Figure 8.1(c). In terms of the overall temperature difference, Q = uA(T, - T,), where I/ is the overall heat transfer coefficient and is given by 1 1 1 1 i?==k,lL,+m+k,/L; (8.14) The reciprocals in Eq. (8.14) may be interpreted as resistances to heat transfer, and so it appears that thermal resistances in series are additive. For the composite hollow cylinder of Figure 8.1(d), with length N, 2nN( Tl - T4) ’ = In(r,/r,)/k, + ln(r,/r,)/k, + ln(r,/r,)/k, ’ (8.15) With an overall coefficient Ui based on the inside area, for example, Q = 2zNrJJ,(T, - T4) = 2x~~~,~ T4) . I I On comparison of Eqs. (8.15) and (8.16), an expression for the inside overall coefficient appears to be 1nWd 1nWJ ln(r4/r3) -+-+ k, kb kc 1 (8.17) In terms of the logarithmic mean radii of the individual cylinders, 1 jj = I; [ 1 1 1 karmo/(r2 - 4 + kbrmb/(r3 - 3) + kcrmc/(rd - 4 I ’ which is similar to Eq. (8.14) for flat walls, but includes a ratio of radii as a correction for each cylinder. FLUID FILMS Heat transfer between a fluid and a solid wall can be represented by conduction equations. It is assumed that the difference in temperature between fluid and wall is due entirely to a stagnant film of liquid adhering to the wall and in which the temperature profile is linear. Figure 8.1(e) is a somewhat realistic representation of a temperature profile in the transfer of heat from one fluid to another through a wall and fouling scale, whereas the more nearly ideal Figure 8.1(f) concentrates the temperature drops in stagnant fluid and fouling films. Since the film thicknesses are not definite quantities, they are best combined with the conductivities into single coefficients h=k/L (8.18) so that the rate of heat transfer through the film becomes Q = hA A T. (8.19) Through the five resistances of Figure 8.1(f), the overall heat
- 190. 8.1. CONDUCTION OF HEAT 171 EXAMPLE 8.2 Effect of Ignoring the Radius Correction of the Overall Heat Transfer Coefticit%t The two film coefficients are 100 each, the two fouling coefficients are 2000 each, the tube outside diameter is 0.1 ft, wall thickness is 0.01 ft, and thermal conductivity of the metal is 30: Basing on the inside area, ui = [l/100 + l/2000 + [(30/0.01)(0.0448/0.04)1-’ + 0.8/100 + 0.8/2000]-’ = 52.0898. rr/ro = 0.04/0.05 = 0.8, r,,, = (0.05 -0.04)/m 1.25 = 0.0448, r,,,/ro = 0.8963, U, = [l/100(0.8) + l/2000(0.8) + l/(30/0.01)(0.8963) + l/100 + l/2000]-’ = 41.6721. Ignoring the corrections, U = (2/100 + 2/2000 + l/30/0.01)-’ = 46.8750. The last value is very nearly the average of the other two. transfer coefficient is given by L=L+L+- 1 1 1 U h, h, k,/L,+h,+h,’ (8.20) where r,,, is the mean radius of the cylinder, given by Eq. (8.12). Since wall thicknesses of heat exchangers are relatively small and the accuracy of heat transfer coefficients may not be great, the ratio of radii in Eq. (8.21) often is ignored, so that the equation for the overall coefficient becomes simply where L, is the thickness of the metal. If the wall is that of hollow cylinder with radii r, and r,, the !=L+L+- 1 1 1 (8.22) overall heat transfer coefficient based on the outside surface is U h, h, k,/L,+h,+h,’ The results of the typical case of Example 8.2, however, indicate 1 1 1 1 1 1 -=-+-+ U, hl(ri/r,) hz(ri/ro) (k3/L3)(rm/d ’ h,+h, ’ (8.21) that the correction may be significant. A case with two films and two solid cylindrical walls is examined in Example 8.3. EXAMPLE 8.3 A Case of a Composite WaII: Optimum Insulation Thickness for a Steam Line A 3 in. IPS Sched 40 steel line carries steam at 500°F. Ambient air is at 70°F. Steam side coefficient is 1000 and air side is 3 Btu/(hr)(sqft)(“F). Conductivity of the metal is 30 and that of insulation is 0.05 Btu/(hr)(sqft)(“F/ft). Value of the steam is $5,00/MBtu. cost of the insulation is $1.5/(yr)(cuft). Operation is 8760 hr/yr. The optimum diameter d of insulation thickness will be found. Pipe: do = 0.2917 ft, d, = 0.2557 ft, ln(d,/d,) = 0.1317. Insulation: In(d,/dJ = ln(d/0.2917). (1) Heat transfer coefficient based on inside area: 1 -’ +52 ’ 1 Steam cost: C, = 5(10@)(876O)Q/A, = 0.0438Q/Ai, $ (yr)(sqft inside). (2) (3) la 2@ 3 8 48 59 ! Example 8 . 5 . Drt imum incul a? ion ?hickness R E A D Dl..D2 DHTH .2317,.2557 INPUT I3 Ul=.@@l,D2+. 1307/3a+LOG<D..‘Dl j~.a5+1/3d IJ=lfUl~trE 8=430SU cl=.a438*C; C2=1 .5XCD^2-UlA2),D2’2 C=Cl+C2 ! Creq’d t o he m i n i m urn) P R I N T U S I N G 120 i D,UzC1,C2.. ff0 128 hIAGE .UDD,X.~ .DDU,X,DrJ.DD..X.. DD.DD,X,DD.DDDD 138 r,oTo 48 148 E N D h h =3 T T = 70 F
- 191. 172 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.3-(continued) D u 3 c2 3 + c2 - - ,490 .354- 6 . 6 6 3 . 5 6 1 0 . 2 1 4 7 ,494 ,349 6.57 3 . 6 5 1 0 . 2 1 1 8 ,495 ,347 6 . 5 4 3 . 6 7 10.2117 -w ,496 .346 6 . 5 2 3 . 6 9 1 0 . 2 1 1 8 .500 ,341 6 . 4 3 .3.78 1 0 . 2 1 4 8 Insulation cost: C, = 1.5K.lA; ...I I - = 1.5(d2 - 0.2917a) (0.2557)’ ’ $/(yr)(sqft inside). Total cost: C = C, + C2* minimum. (5) Substitute Eqs. (2)-(4) into Eq. (5). The outside diameter is the key unknown. The cost curve is fairly flat, with a minimum at d = 0.50 ft, corresponding to 1.25 in. thickness of insulation. Some trials are shown with the computer program. A more detailed analysis of insulation optima is made by Happel and Jordan [C/rem. Process &on., 380 (1975)], although their prices are dated. Section 8.12 also discusses insulation. Heat transfer coefficients are empirical data and derived correlations. They are in the form of overall coefficients U for frequently occurring operations, or as individual film coefficients and fouling factors. 8.2. MEAN TEMPERATURE DIFFERENCE In a heat exchanger, heat is transferred between hot and cold fluids through a solid wall. The fluids may be process streams or independent sources of heat such as the fluids of Table 8.2 or sources of refrigeration. Figure 8.2 shows such a process with inlet and outlet streams, but with the internal flow pattern unidentified because it varies from case to case. At any cross section, the differential rate of heat transfer is dQ = U(T - T’) dA = -mcdT = m’c’ dT’. The overall heat transfer rate is represented formally by (8.23) Q = UA(AT),. (8.24) The mean temperature difference (AT), depends on the terminal temperatures, the thermal properties of the two fluids and on the flow pattern through the exchanger. TABLE 8.2. Properties of Heat Transfer Media Figure 8.2. Terminal temperatures and temperature differences of a heat exchanger, with unidentified internal flow pattern. SINGLE PASS EXCHANGER The simplest flow patterns are single pass of each fluid, in either the same or opposite directions. Temperature profiles of the main kinds of thermal behavior are indicated on Figure 8.3(a). When the unbroken lines [cases (a)-(e)] are substantially straight, the mean temperature is expressed in terms of the terminal differences by (8.25) This is called the logarithmic mean temperature difference. The temperature profiles are straight when the heat capacities are Medium Trade Name Phase “F atm, gag= Remarks Electricity Water Water Flue gas Diphenyl-diphenyl oxide eutectic - - - Dowtherm A Di + triaryl cpds Ethylene glycol, inhibited Dimethyl silicones Mixed silanes Aromatic mineral oil Chlorinated biphenyls Molten nitrites and nitrates of K and Na Sodium-potassium eutectic Mercury Dowtherm G Dow SR-1 Dow Syltherm 800 H y d r o t h e r m Mobiltherm, Mobil Therminol, M o n s a n t o Hi-Tee, DuPont vapor liquid gas liquid or vapor liquid liquid liquid 100-4500 - 200-I 100 O-300 300-400 6-15 100-2000 o-7 450-750 o-9 - - - - nontoxic, carbonizes at high temp 20-700 o-3 sensitive to oxygen -4O--250 0 acceptable in food industry -40-750 0 low toxicity liquid -50-675 0 liquid 100-600 0 liquid 50-600 0 liquid liquid vapor 3 0 0 - 1 1 0 0 0 1 0 0 - 1 4 0 0 0 600-1000 O-12 react with oxygen and moisture not used with copper based materials toxic decomposition products resistant alloys needed above 850°F stainless steel needed above 1000°F low pressure vapor, toxic, and expensive
- 192. 01 BOTH FLUIDS CHANGING PnASE CONDENSING bl ONE CLUID CHANGING PtiASE c) ONE fLUI CHANGING PHASE 6) PARALLEL FLOW, NO PHASE CHANGE I I aI COUNTERFLOW , NO PHASE CHANGE SUBCOOLING I) ONE FLUID CHANGING PHASE I I ONE FLUID CMANGING PYASE CONDENSABLE AN0 NON - CONDE t,SA.BLE COMPONENTS 8.2. MEAN TEMPERATURE DIFFERENCE 173 r Shell fluid . . . lshell . -. L, / . -T- Tube fluid Figure 8.3. Temperature profiles in heat exchangers. (a) In parallel or countercurrent flow, with one or two phases. (b) One shell pass, two tube passes. (c) Two shell passes, four tube passes. substantially independent of temperature over the range of the process, or when a phase change occurs at constant temperature. When the profiles consist of linear sections, as in cases (f) and (g), the exchanger can be treated as a three-section assembly, each characterized by its own log mean temperature difference, for which intermediate temperatures may be found by direct calculation or by trial. Heat transfer for a case such as (h) with continuously curved profile must be evaluated by integration of Eq. (8.23). MULTIPASS EXCHANGERS For reasons of compactness of equipment, the paths of both fluids may require several reversals of direction. Two of the simpler cases of Figure 8.3 are (b) one pass on the shell side and two passes on the tube side and (c) two passes on the shell side and four on the tube side. On a baffled shell side, as on Figure 8.4(c), the dominant flow is in the axial direction, so this pattern still is regarded as single pass on the shell side. In the cross flow pattern of Figure 8.5(c), each stream flows without lateral mixing, for instance in equipment like Figure 8.6(h). In Figure 8.6(i) considerable lateral mixing would occur on the gas side. Lateral mixing could occur on both sides of the plate exchanger of Figure 8.6(h) if the fins were absent. Mean temperature differences in such flow patterns are obtained by solving the differential equation. Analytical solutions have been found for the simpler cases, and numerical ones for many impor- tant complex patterns, whose results sometimes are available in generalized graphical form. f-METHOD When all of the terminal temperatures are known, the mean temperature difference is found directly from (A% = W%gmean, (8.26) where the correction factor F depends on the flow pattern and is
- 193. 174 HEAT TRANSFER AND HEAT EXCHANGERS Fhd A Inlet I Iflu/d A outlet (a) Hot Fluid Cold Fluid Inlet , Shell Tubes aear End Head .uid b) Steam Condensate L/qwd Tube Hot l/qud outlet feed supper ts outlet (4 Figure 8.4. Example of tubular heat exchangers (see also Fig. 8.14). (a) Double-pipe exchanger. (b) Scraped inner surface of a double-pipe exchanger. (c) Shell-and-tube exchanger with fixed tube sheets. (d) Kettle-type reboiler. (e) Horizontal shell side thermosiphon reboiler. (f) Vertical tube side thermosiphon reboiler. (g) Internal reboiler in a tower. (h) Air cooler with induced draft fan above the tube hank. (i) Air cooler with forced draft fan below the tube bank.
- 194. 8.2. MEAN TEMPERATURE DIFFERENCE 175 Vapor Level control ‘i Liquid Bottoms (e) support Level I IlFeed t L a-x 4 Bottoms if) ?.--_ ax 1 Bottoms (9) Hot fluld out - Sectm - wppwt / channels ,Tuk supports support (h) (i) Figure 8.4.-(continued) (a) Figure 8.5. Correction factor F, effectiveness and number of transfer units in multipass and cross flow heat exchangers (Bowman et al., Trans ASME 283, 1940; Kays and London, 1984): ,J-TO T - T; ’ R = TI - T:, r--T, ’ T on the tubeside, T’ on the shellside. i = input, o = output. (a) One pass on shellside, any multiple of two passes on tubeside. (b) TWO passes on shell side, any multiple of four on tubeside. (c) Cross flow, both streams unmixed laterally. (d) Cross flow, one stream mixed laterally. (e) Cross flow, both streams mixed laterally. (f) Effectiveness and number of transfer units in parallel and countercurrent flows. (g) Three shell passes, multiples of six on tubeside. (h) Four shell passes, multiples of eight on tubeside. (i) Five shell passes, multiples of ten on tubeside. (j) Six shell passes, multiples of 12 on tubeside.
- 195. 176 HEAT TRANSFER AND HEAT EXCHANGERS 1.0 4 0.9 80.6 L .g 1 0.7 8 0.6 0.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 P 04 - ----. (cl 1.0 0.9 k, i. 0.8 3 $ 8 0.7 5 0.6 0 . 2 0 . 2 Yi i i i 1 I / 0 I I I 0 1.0 2 . 0 3.0 10 10 6 . 0 6 . 0 NTU 1001 I I , , , , , 0.9 4 g 0.8 s '5 0.7 0.6 (e) 80 6 0 48 (4 0 . 8 0 . 2 0 0 1 2 3 4 5 NW Figure 8.5-(continued)
- 196. 8.2. MEAN TEMPERATURE DIFFERENCE 177 Y I OO I I I I I I I I I 1.0 2.0 NTU 3o 40 5.0 e I5 0.6 0.5' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 K (i) Figure I.S(continued) expressed in terms of these functions of the terminal temperatures: P = w;.= actual heat transfer Ti - K maximum possible heat transfer ’ (8.27) R = T-To = mc (8.28) Some analytical expressions for Fare shown in Table 8.3, and more graphical solutions in Figure 8.5. u 0.2 0 0 1.0 2.0 3.0 4.0 5.0 h?lv if) h) e, --0.8 0 a $j 0.7 5 0.6 K (j) This method is especially easy to apply when the terminal temperatures are all known, because then F and (AT)logmean are immediately determinable for a particular flow pattern. Then in the heat transfer equation Q = UAF(AT),, (8.29) any one of the quantities Q, U, or A may be found in terms of the others. A solution by trial is needed when one of the terminal temperatures is unknown, as shown in Example 8.4. The next
- 197. 178 HEAT TRANSFER AND HEAT EXCHANGERS (a) (4 (e) (f) Liquid flow Gas flow (i) Figure 8.6. Examples of extended surfaces on one or both sides. (a) Radial fins. (b) Serrated radial fins. (c) Studded surface. (d) Joint between tubesheet and low fin tube with three times bare surface. (e) External axial fins. (f) Internal axial fins. (g) Finned surface with internal spiral to promote turbulence. (h) Plate fins on both sides. (i) Tubes and plate fins.
- 198. TABLE 8.3. Formulas for Mean Temperature Difference and Effectiveness in Heat Exchangers T --r B-METHOD 1. Parallel or countercurrent flow, (AT), = (A T),,,g,,,san = (AT, - AT,)/ln(AT,/AT,). 2. In general, o r (AT), = fl(J - T), where Fand @ depend on the actual flow paths on the shell and tube sides and are expressed in terms of these quantities: P= (T, - 7;)/(T;‘- T) = actual heat transfer/ (maximum possible heat transfer), R=(T - 7-J/(7-:, - 6’) = m’c’/mc. 3. Number of transfer units, N or NTU, is N = UAIC,,, = P/S, where Cr,,i, is the smaller of the two values mc or m’c’ of the products of mass rate of flow times the heat capacity. In parallel flow, P= NO = {I - expl-N(1 + C)]}/(l + C). In countercurrent flow, P = NO = (1 - expl-N/l - C)]]/{ 1 - C exp [-NC1 - C)l). One shell pass and any multiple of two tube passes, Two shell passes and any multiple of four tube passes, Rfl, 2(R-1) I-PR I/ In 2/P - 1 - R + (2/P)d(l - P)(l - PR) f fi I 2/P-I-R+(2/P)v(l-P)(l-PR)-fi 8. Cross flow, (a) Both streams laterally unmixed, P= 1 - exp{[exp( - NCn) - l]/Cn), where n = Nmo.*‘. (b) t$z)th;mams mixed, P= {I/]1 -exp(-N)] + C/[l - exp(-NC)]- (c) Gna, mixed, Crni, unmixed, P= (l/C){1 -exp[-C(1 - eeN)]}, Id) &, mixed, C,,,,, unmixed, P= 1 - exp{-(l/C)[l - exp(-NC)]}. 9. For more complicated patterns only numerical solutions have been made. Graphs of these appear in sources such as Heat Exchanaer Design Handbook (HEOH, j983) and Kays and London (1984). - 8.3. HEAT TRANSFER COEFFICIENTS 179 method to be described, however, may be more convenient in such a case. One measure of the size of heat transfer equipment is the number of transfer units N defined by N = UAIC,,, (8.30) where Cmin is the smaller of the two products of mass how rate and heat capacity, mc or m’c’. N is so named because of a loose analogy with the corresponding measure of the size of mass transfer equipment. A useful combination of P and N is their ratio N UA(T; - ?J - UA(T; - TJ (T; - 7J’ (8.31) where (T, - T) is the temperature change of the stream with the smaller value of mc. Thus 0 is a factor for obtaining the mean temperature difference by the formula: (AT),,, = O(T; - I;) when the two inlet temperatures are known. (8.32) The term P often is called the exchanger effectiveness. Equations and graphs are in Table 8.3 and Figure 8.4. Many graphs for 0, like those of Figure 8.7, may be found in the Heat Exchanger Design Handbook (HEDH, 1983). When sufficient other data are known about a heat exchange process, an unknown outlet temperature can be found by this method directly without requiring trial calculations as with the F-method. Example 8.5 solves such a problem. SELECTION OF SHELL-AND-TUBE NUMBERS OF PASSES A low value of F means, of course, a large surface requirement for a given heat load. Performance is improved in such cases by using several shells in series, or by increasing the numbers of passes in the same shell. Thus, two l-2 exchangers in series are equivalent to one large 2-4 exchanger, with two passes on the shell side and four passes on the tube side. Usually the single shell arrangement is more economical, even with the more complex internals. For economy, F usually should be greater than 0.7. E X A M P L E A shell side fluid is required to go from 200 to 140°F and the tube side from 80 to 158°F. The charts of Figure 8.5 will be used: P = (200 - 140)/(200 - 80) = 0.5, R = (158 - 80)/(200 - 140) = 1.30. For a l-2 exchanger, F = 0.485: 2-4 0.92 4-8 0.98 The 1-2 exchanger is not acceptable, but the 2-4 is acceptable. If the tube side outlet were at 160 instead of 158, F would be zero for the l-2 exchanger but substantially unchanged for the others. 8.3. HEAT TRANSFER COEFFlClENTS Data are available as overall coefficients, individual film coefficients, fouling factors, and correlations of film coefficients in terms of
- 199. 180 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.4 Performance of a Heat Exchanger with the F-Method Operation of an exchanger is represented by the sketch and the equation Q/UA = 50 = F(AT),, JZE- T 200 120 The outlet temperature of the hot fluid is unknown and designated by T. These quantities are formulated as follows: p = 200 - T 200-80 R = 200 - T 120-80’ T - 80 - (200 - 120) (AThm =ln[(T - 80)/(200 - 120)] F is represented by the equation of Item 6 of Table 8.3, or by Figure 8.4(a). Values of T are tried until one is found that satisfies G - 50 - F(A?fT),, = 0. The printout shows that T = 145.197. The sensitivity of the calculation is shown in the following tabulation: T P R (AT),, F G 145.0 0.458 1.375 72.24 0.679 0.94 145.197 0.457 1.370 72.35 0.691 0.00061 145.5 0.454 1.363 72.51 0.708 -1.34 10 ! ExamPle 8 .4. T h e F - m e t h o d 20 SHORT F..R>F>Tl 30 INFIJT T ;)-’ (‘=(200-T>,120 58 R=<289-T2/48 68 Tl=(T-169>.~LOG((T-802,88r 70 E=<RA2+1:>*.5 80 F=E,~(R-lI*LOG((l-Fj,~l-F*R~~ 9 0 F=F~LOG~~2-F%~R+l-Ejj~<2-P~< R+l+Ej)j 95 G=5Gj-F$Tl 100 P R I N T “T=“;T 110 P R I N T “G=“jG 120 P R I N T “F=“;F 130 P R I N T “R=“;R 140 P R I N T “F=“;F 150 P R I N T “Tl=“iTl 160 GOTO 3 0 170 E N D ZZ 145.197 .88240286 EZ i.5701 45669 physical properties and operating conditions. The reliabilities of these classes of data increase in the order of this listing, but also the ease of use of the data diminishes in the same sequence. O V E R A L L C O E F F I C I E N T S The range of overall heat transfer coefficients is approximately lo-200 Btu/(hr)(sqft)(“F). Several compilations of data are available, notably in the Chemical Engineers Handbook (McGraw- Hill, New York, 1984, pp. 10.41-10.46) and in Ludwig (1983, pp. 70-73). Table 8.4 qualifies each listing to some extent, with respect to the kind of heat transfer, the kind of equipment, kind of process stream, and temperature range. Even so, the range of values of U usually is two- to three-fold, and consequently only a rough measure of equipment size can be obtained in many cases with such data. Ranges of the coefficients in various kinds of equipment are compared in Table 8.5. FOULING FACTORS Heat transfer may be degraded in time by corrosion, deposits of reaction products, organic growths, etc. These effects are accounted for quantitatively by fouling resistances, l/hf. They are listed separately in Tables 8.4 and 8.6, but the listed values of coefficients include these resistances. For instance, with a clean surface the first listed value of U in Table 8.4 would correspond to a clean value of U= l/(1/12-0.04) =23.1. How long a clean value could be maintained in a particular plant is not certain. Sometimes fouling develops slowly; in other cases it develops quickly as a result of process upset and may level off. A high coefficient often is desirable, but sometimes is harmful in that excessive subcooling may occur or film boiling may develop. The most complete list of fouling factors with some degree of general acceptance is in the TEMA (1978) standards. The applicability of these data to any particular situation, however, is questionable and the values probably not better than f50%. Moreover, the magnitudes and uncertainties of arbitrary fouling factors may take the edge off the importance of precise calculations of heat transfer coefficients. A brief discussion of fouling is by Walker (1982). A symposium on this important topic is edited by Somerscales and Knudsen (1981). INDIVIDUAL FILM COEFFICIENTS Combining individual film coefficients into an overall coefficient of heat transfer allows taking into account a greater variety and range of conditions, and should provide a better estimate. Such individual coefficients are listed in Tables 8.6 and 8.7. The first of these is a very cautious compilation with a value range of 1.5- to 2-fold. Values of the fouling factors are included in the coeflicient listings of both tables but are not identified in Table 8.7. For clean service, for example, involving sensible heat transfer from a medium organic to heating a heavy organic, U = 10,000/(57 - 16 + 50 - 34) = 175
- 200. 8.3. HEAT TRANSFER COEFFICIENTS 181 B NTU, = AU/C, 1. 0 1.0 a 6 -; 0.5 I- F - G I a 4 c- 0 . 3 4. 0 ,I 5. 0 a 0. 2 0. I R = % = 0 1)i - (Tq Jo T; (T2)” m(T2)i 0. 0 0. 0 0 . I 0 . 2 0. 3 0 . 4 0 . 5 8. 6 0. 7 0 . 0 0. 9 1.0 (a) e NTU, = AU/C, F-c- s-4 $7 Q A - t - 1.0 0 . 2 0 . 3 0 . 4 0. 5 a 0 0. 8 I.0 as 1.2 0. e I. 4 0 . 7 1.6 0. e 1. a 0.5 0 . 4 a 3 0 . 2 al a0 a 0 1. 1 a 2 a 3 a.4 a 5 0.0 a 7 a e a s 1.0 C2 (T,)i-(T,)o R= c, = (T,)o-(T,)i B P . Thermal Effectiveness = CT2 j. - (T, )i (T1 ), _ (TzJ, b) Figure 8.7. 8 correction charts for mean temperature difference: (a) One shell pass and any multiple of two tube passes. (b) Two shell passes and any multiple of four tube passes. [(HEDH, 1983); after Mueller in Rohsenow and Hartnett, Handbook of Heat Transfer, Section 18, McGraw-Hill, New York, 1973. Other cases also are covered in these references.]
- 201. 182 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.5 Application of the Effectiveness and the tl Method Operating data of an exchanger are shown on the sketch. These data include UA = 2000, m’c’ = 1000, mc = 800, C = Cmin/Cmax = 0.8. The equation for effectiveness P is given by item 6 of Table 8.3 or it can be read off Figure 8.4(a). Both P and 19 also can be read off Figure 8.4(a) at known N and R = CJC, = 0.8. The number of transfer units is N = lJA/C,,, = 2000/800 = 2.5, C = Cmin/Cmax = 0.8, D=m=1.2806, 2 ‘=l+ C + D[l + exp(-ND)]/1 - exp(-ND) = 0.6271, 0 = P/N = 0.2508, AT, = 0(200 - 80) = 30.1, Q = UA(AT), = 2000(30.1) = 60,200, = 800(200 - T2) = lOOO( T; - 80), :. T2 = 124.75, T; = 140.2. T, also may be found from the definition of P: P = actual AT = ?!k% = 0.6271 max possible AT 200 - 80 ’ :. T2 = 124.78. With this method, unknown terminal temperatures are found without trial calculations. compared with a normal value of CJ = 10,000/(57 + 50) = 93, where the averages of the listed numbers in Table 8.6 are taken in each case. METAL WALL RESISTANCE With the usual materials of construction of heat transfer surfaces, the magnitudes of their thermal resistances may be comparable with the other prevailing resistances. For example, heat exchanger tubing of 1/16in. wall thickness has these values of l/h, = L/k for several common materials: Carbon steel l/h,=1.76~10-~ Stainless steel 5.54 x w4 Aluminum 0.40 x 1o-4 Glass 79.0 x 1o-4 which are in the range of the given film and fouling resistances, and should not be neglected in evaluating the overall coefficient. For example, with the data of this list a coefficient of 93 with carbon steel tubing is reduced to 88.9 when stainless steel tubing is substituted. DIMENSIONLESS GROUPS The effects of the many variables that bear on the magnitudes of individual heat transfer coefficients are represented most logically and compactly in terms of dimensionless groups. The ones most pertinent to heat transfer are listed in Table 8.8. Some groups have ready physical interpretations that may assist in selecting the ones appropriate to particular heat transfer processes. Such interpreta- tions are discussed for example by Grober et al. (1961, pp. 193-198). A few are given here. The Reynolds number, Dup/p = pu*/(pu/D), is a measure of the ratio of inertial to viscous forces. The Nusselt number, hL/k = h/(k/L), is the ratio of effective heat transfer to that which would take place by conduction through a film of thickness L. The Peclet number, DGC/k = GC/(k/D) and its modification, the Graetz number wC/kL, are ratios of sensible heat change of the flowing fluid to the rate of heat conduction through a film of thickness D or L. The Prandtl number, Cp/k = (p/p)/(k/pC), compares the rate of momentum transfer through friction to the thermal diffusivity or the transport of heat by conduction. The Grashof number is interpreted as the ratio of the product of the buoyancy and inertial forces to the square of the viscous forces. The Stanton number is a ratio of the temperature change of a fluid to the temperature drop between fluid and wall. Also, St = (Nu)/(Re)(Pr). An analogy exists between the transfers of heat and mass in moving fluids, such that correlations of heat transfer involving the Prandtl number are valid for mass transfer when the Prandtl number Cp/k is replaced by the Schmidt number ,u/pkd. This is of particular value in correlating heat transfer from small particles to fluids where particle temperatures are hard to measure but measurement of mass transfer may be feasible, for example, in vaporization of naphthalene. 8.4. DATA OF HEAT TRANSFER COEFFICIENTS Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces; free or forced convection; laminar or turbulent flow; liquids, gases, liquid metals, non- Newtonian fluids; pure substances or mixtures; completely or partially condensable; air, water, refrigerants, or other specific substances; fluidized or fixed particles; combined convection and radiation; and others. In spite of such qualifications, it should be
- 202. TABLE 8.4. Overall Heat Transfer Coefficients in Some Petrochemical Applications, U Btu/(hr)(sqft)(“F)” In Tubes Outside Tubes Type Equipment Velocities wsed Tube Shell Overall Coefficient Estimated Fouling Tube Shell Overall A. Heating-cooling Butadiene mix. (Super-heating) Solvent Solvent C, unsaturates Solvent Oil Ethylene-vapor Ethylene vapor Condensate Chilled water Calcium brine-25% Ethylene liquid Propane vapor Lights and chlor. HC Unsat. light HC, CO, CO,, H, Ethonolamine Steam Steam Chilled water Wate? Water Water Water Water Water Water Water Water Water Water B. Condensing C, unsat. HC unsat. lights Butadiene Hydrogen chloride steam solvent propylene (vaporization) propylene (vaporization) chilled water oil condensate and vapor chilled water propylene (refrigerant) transformer oil chlorinated C, ethylene vapor propane liquid steam steam steam air mixture styrene and tars freon-12 lean copper solvent treated water C,-chlor. HC, lights hydrogen chloride heavy C,-chlor. perchlorethylene air and water vapor engine jacket water absorption oil air-chlorine treated water propylene refrig. propylene refrig. propylene refrig. propylene refrig. H H K K H H K H K - U H H K - U H U H H U U (in tank) H H H H H H H H H H U H K K K H 25-35 - l - 2 20-40 - - - - - - l - 2 - - - - - - - 4-7 4-5 3-5 2-3 - - - - - - 4-7 5-7 V V V - - 1.0-l .a - - - - - - - - 0.5-l .o - - - - - - - - - l - 2 - - - - - - - - - - - - - 12 400-100 35-40 110-30 30-40 40-O 13-18 100-35 35-75 115-40 60-85 150-100 go-125 600-200 50-80 270-100 60-135 60-30 40-75 75-50 40-60 -2o-+10 IO-20 -170-(-!OO) 6-15 -25-100 12-30 -30-260 IO-2 400-I 00 15-25 400-40 10-20 -30-220 50-60 190-230 100-130 90-25 100-120 180-90 loo-125 90-l 10 6-10 360-100 7-15 230-90 45-30 300-90 55-35 150-90 20-35 370-90 230-160 175-90 80-115 130-90 8-18 250-90 170-225 200-90 58-68 60-35 50-60 45-3 65-80 20-35 11 O-60 O-15 - - - 0.003 0 . 0 0 1 5 0 . 0 0 2 0.001 0.001 0.001 0 . 0 0 2 - 0.001 - 0.001 0.0005 0.001 0.001 - - 0 . 0 0 2 0 . 0 0 2 0.001 0.001 0 . 0 0 1 5 0.0015 0 . 0 0 1 5 - 0.001 - - - 0 . 0 1 2 - - - - 0.001 0 . 0 0 1 5 0.001 0.001 0.001 0.001 0 . 0 0 5 - - 0.001 - 0.001 0 . 0 0 1 5 0 . 0 0 2 0.001 - - 0.001 0.001 0.001 0.001 0 . 0 0 1 5 0.001 0.001 - 0.001 - - - 0.001 0 . 0 4 0.0065 0 . 0 0 6 0 . 0 0 5 - - - - - - - 0 . 0 0 2 0 . 0 0 2 - 0 . 3 - - - - 0.004 0 . 0 0 5 - - - - - - - 0 . 0 0 5 - 0 . 0 0 5 0.0055 0 . 0 0 4 - (continued)
- 203. TABLE 8.44continued) In Tubes Outside Tubes Type Equipment Velocities (R/se4 Tube Shell Overall Temp. Coefficient Range (“F) Estimated Fouling Tube Shell Overall Lights and chloro-ethanes Ethylene Unsat. chloro HC Unsat. chloro HC Unsat. chloro HC Chloro-HC Solvent and non cond. Water Water Water Water Treated water Oil Water Chilled water Water Water Water Air-water vapor C. Reboiling Solvent, Copper-NH, C, unsat. Chloro. HC Chloro. unsat. HC Chloro. ethane Chloro. ethane Solvent (heavy) Mono-di-ethanolamines Organics, acid, water Amines and water Steam Propylene c,, c,- Propylene-butadiene butadiene, unsat. propylene refrig. propylene refrig. water water water water water propylene vapor propylene steam steam steam (exhaust) steam propylene cooling and cond. air-chlorine (part and cond.) light HC, cool and cond. a m m o n i a a m m o n i a freon steam steam steam steam steam steam steam steam steam steam naphtha frac. K U K U H H H K U H H H H H H H H U H H U K U H H v-r v-r VT U H VT v-r VT Annulus Long. F.N. K U H - - 7-a 3-8 6 - - 2-3 - - - - - - - - - - 7-6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15-25 60-90 go-120 180-140 15-25 20-30 25-15 130-150 60-100 225-110 190-235 20-30 70-l 10 25-50 110-150 8-15 20-30 35-90 140-165 280-300 130-(-20) 120-(-10) 145-90 11 O-90 130-(-20) IIO-(-10) 260-90 200-90 130-90 300-90 230-130 220-I 30 375-130 30-45 (C) 15-20 (Co) 8-15 (C) 10-15 (Co) > 270-90 120-90 11 O-90 60-10 130-150 180-160 95-l 15 95-l 50 35-25 300-350 100-140 230-130 90-I 35 300-350 50-70 30-I 90 70-115 375-300 210-155 450-350 60-100 450-300 120-140 360-250 15-20 270-220 120-140 150-40 400-100 25-35 15-18 0 . 0 0 2 0.001 0 . 0 0 2 0.001 0 . 0 0 2 0.001 0 . 0 0 1 5 - 0.0015 0 . 0 0 2 0.0015 0.0001 0 . 0 0 3 0 . 0 0 1 5 0 . 0 0 1 5 0.0015 0.001 0.001 - - - 0.001 0.001 0.001 0 . 0 0 2 0.004 0 . 0 0 2 0 . 0 0 3 0 . 0 0 2 0.0035 0.001 - 0.001 0.001 0.001 0.001 0.001 0.001 0 . 0 0 4 - 0.001 0.0001 0.001 0.0001 0.001 0.001 0 . 0 0 5 0 . 0 0 3 0.001 0.001 - - - 0.001 0.001 0.001 0.001 0 . 0 0 0 5 0.001 0 . 0 0 0 5 0 . 0 0 1 5 0 . 0 0 0 5 0.001 - - - - - - - - 0 . 0 0 3 - - - - - - - - - - 0.01 0 . 0 0 5 0.0065 - - - - - - - - - - 0 . 0 2 LFouling resistances are included in the listed values of U. UnkSS specified, all water is untreated, brackish, bay or sea. Notes: H = horizontal, fixed or floating tuba sheet, U = U-tuba horizontal bundle, K = kettle type, v = vertical, P = reboiler, T = thermosiphon, v = variable, HC = hydrocarbon, (C) = cooling range At, (Co) = condensing range At. (Ludwig, 1983).
- 204. 8.4. DATA OF HEAT TRANSFER COEFFICIENTS 185 TABLE 8.5. Ranges of Overall Heat Transfer Coefficients in Various Types of Exchangers [U Btu/(hr)(sqft)(“F)]’ Equipment Process u Shell-and-tube exchanger IFig. 8.4c)l Double-pipe exchanger [Fig. 8.4(a)] gas (I atm)-gas (1 atm) Irrigated tube bank Plate exchanger [Fig. 8.8(a)] Spiral exchanger [Fig. 8.8fc)l Compact [Fig. 8.6(h)] Stirred tank, jacketed Stirred tank, coil inside a 1 Btu/(hr)(sqft)(“F) = 5.6745 W/m’ K. Data from (HEDH, 1983). gas (1 atm)-gas (1 atm) gas (250 atm)-gas (250 atm) liquid-gas (1 atm) liquid-gas (250 atm) liquid-liquid liquid-condensing vapor gas (250 atm)-gas (250 atm) liquid-gas (250 atm) liquid-liquid water-gas (1 atm) 3-10 water-gas 1250 atm) 25-60 water-liquid 50-160 water-condensing vapor 50-200 water-gas (1 atm) 3-10 water-liquid 60-200 liquid-liquid 120-440 liquid-condensing steam 160-600 gas (1 atm)-gas (1 atm) 2-6 gas (1 atm)-liquid 3-10 liquid-condensing steam 90-260 boiling liquid-condensing steam 120-300 water-liquid 25-60 liquid-condensing steam water-liquid l - 6 25-50 2-12 35-70 25-200 50-200 2-6 25-90 35-l 00 50-250 120-440 go-210 borne in mind that very few proposed correlations are more accurate than f20% or so. Along with rate of heat transfer, the economics of practical exchanger design requires that pumping costs for overcoming friction be taken into account. DIRECT CONTACT OF HOT AND COLD STREAMS Transfer of heat by direct contact is accomplished in spray towers, in towers with a multiplicity of segmented baffles or plates (called shower decks), and in a variety of packed towers. In some processes heat and mass transfer occur simultaneously between phases; for example, in water cooling towers, in gas quenching with water, and in spray or rotary dryers. Quenching of pyrolysis gases in transfer lines or towers and contacting on some trays in fractionators may involve primarily heat transfer. One or the other, heat or mass transfer, may be the dominant process in particular cases. Data of direct contact heat transfer are not abundant. The literature has been reviewed by Fair (1972) from whom specific data will be cited. One rational measure of a heat exchange process is the number of transfer units. In terms of gas temperatures this is defined by Tg,in - T,,out Ng = (Tg - Unean (8.33) The logarithmic mean temperature difference usually is applicable. For example, if the gas goes from 1200 to 150°F and the liquid countercurrently from 120 to 400”F, the mean temperature difference is 234.5 and Ng = 4.48. The height of a contact zone then is obtained as the product of the number of transfer units and the height H, of a transfer unit. Several correlations have been made of the latter quantity, for example, by Cornell, Knapp, and Fair (1960) and modified in the Chemical Engineers Handbook (1973, pp. 18.33, 18.37). A table by McAdams (1954, p. 361) shows that in spray towers the range of H, may be 2.5-10 ft and in various kinds of packed towers, 0.4-4 ft or so. Heat transfer coefficients also have been measured on a volumetric or cross section basis. In heavy hydrocarbon fraction- ators, Neeld and O’Bara (1970) found overall coefficients of 1360- 3480 Btu/(hr)(“F)(sqft of tower cross section). Much higher values have been found in less viscous systems. Data on small packed columns were correlated by Fair (1972) in the form Ua = CG”L”, Btu/(hr)(cuft)(OF), (8.34) where the constants depend on the kind of packing and the natures of the fluids. For example, with air-oil, 1 in. Raschig rings, in an 8 in. column L/a = 0.083G0~94L0~25. (8.35) When G and L are both 5000 lb/(hr)(sqft), for instance, this formula gives Ua = 2093 Btu/(hr)(cuft)(a). In spray towers, one correlation by Fair (1972) is h,a = 0.043G0.8L0-4/Z0.5 Btu/(hr)(cuft)(“F). (8.36)
- 205. 186 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.6. Typical Ranges of Individual Film and Fouling Coefficients [h Btu/(hr)(sqft)(OF)] Fluid and Process Conditions P (atm) (AT),,,,, (“F) 104h lo44 Sensible Water Ammonia Light organics Medium organics Heavy organics Heavy organics Very heavy organics Very heavy organics G a s G a s G a s liquid liquid liquid liquid liquid heating liquid cooling liquid heating liquid cooling l - 2 10 100 7.6-11.4 6-14 7.1-9.5 O-6 28-38 6-11 38-76 9-23 23-76 11-57 142-378 11-57 189-568 23-170 378-946 23-170 450-700 O-6 140-230 O-6 57-113 O-6 Condensing transfer Steam ammonia Steam ammonia Steam ammonia Steam ammonia Steam ammonia Light organics Light organics Light organics Medium organics Heavy organics Light condensable mixes Medium condensable mixes Heavy condensable mixes all condensable 1% noncondensable 4% noncondensable all condensable all condensable p u r e 4% noncondensable p u r e narrow range narrow range narrow range narrow range m e d i u m r a n g e 0.1 0.1 0.1 1 10 0.1 0.1 IO 1 4.7-7.1 O-6 9.5-14.2 O-6 19-28 O-6 3.8-5.7 O-6 2.3-3.8 O-6 28-38 O-6 57-76 O-6 8-19 O-6 14-38 6-30 28-95 II-28 23-57 O - I I 38-95 6-23 95-190 11-45 Vaporizing transfer Water Water Ammonia Light organics Light organics Medium organics Medium organics Heavy organics Heavy organics Very heavy organics p u r e narrow range p u r e narrow range p u r e narrow range narrow range 4 5 5.7-19 3 6 3.8-14 3 6 11-19 36 14-57 2 7 19-76 3 6 16-57 2 7 23-95 3 6 23-95 2 7 38-142 6-12 6-12 6-12 6-12 6-17 6-17 6-17 11-28 II-45 II-57 2 0 2 7 57-189 Light organics have viscosity il cP, typically similar to octane and lighter hydrocarbons. Medium organics have viscosities in the range l-5cP. like kerosene, hot gas oil, light crudes, etc. Heavy organics have viscosities in the range 5-100 cP, cold gas oil, lube oils, heavy and reduced crudes, etc. Very heavy organics have viscosities above 100 cP, asphalts, molten polymers, greases, etc. Gases are all noncondensables except hydrogen and helium which have higher coefficients. Conversion factor: 1 Btu/(hr)(sqft)(“F) = 5.6745 W/m* K. (After HEDH, 1983, 3.1.4-4). In a tower with height Z = 30ft and with both G and L at 5000 lb/(hr)(cuft), for example, this formula gives h,n = 21.5. In liquid-liquid contacting towers, data cited by Fair (1972) range from KK-12,000 Btu/(hr)(cuft)(“F) and heights of transfer units in the range of 5 ft or so. In pipeline contactors, transfer rates of 6000-60,00OBtu/(hr)(cuft)(“F) have been found, in some cases as high as 200,000. In some kinds of equipment, data only on mass transfer rates may be known. From these, on the basis of the Chilton-Colburn analogy, corresponding values of heat transfer rates can be estimated. NATURAL CONVECTION Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the most usual situations, of which heat losses to ambient air are the most common process. Simplified equations are shown for air. Transfer of heat by radiation is appreciable even at modest temperatures; such data are presented in combination with convective coefficients in item 16 of this table. FORCED CONVECTION Since the rate of heat transfer is enhanced by rapid movement of fluid past the surface, heat transfer processes are conducted under such conditions whenever possible. A selection from the many available correlations of forced convective heat transfer involving single phase fluids, including flow inside and outside bare and extended surfaces, is presented in Table 8.10. Heat transfer resulting in phase change, as in condensation and vaporization, also is covered in this table. Some special problems that arise in interpreting phase change behavior will be mentioned following.
- 206. 8.4. DATA OF HEAT TRANSFER COEFFICIENTS 187 TABLE 8.7. Individual Film Resistances (l/h) Including Fouling Effects, with h in Btu/(hr)bqft)(OF) Kind of Heat Transfer Fluid Sensible Boiling Condensing Aromatic liquids Benzene, toluene, ethylbenzene, stvrene Dowtherm Inorganic solutions CaCI, Brine (25%) Heavy acids NaCl Brine (20%) Misc. dilute solutions Light hydrocarbon liquids c,, c,. c, Chlorinated hydrocarbons Miscellaneous organic liquids Acetone Amine solutions Saturated diethanolamine and mono- ethanolamine (CO, and H,S) Lean amine solutions Oils Crude oil Diesel oil Fuel oil (bunker C) Gas oil Light Heavy (typical of cat. cracker feed) Gasoline (400” EP) Heating oil (domestic 30”API) H y d r o f o r m a t e Kerosine Lube oil stock N a p h t h a s Absorption Light virgin Light catalvtic H e a v y P o l y m e r (Ca’s) Reduced crude Slurry oil (fluid cat. cracker) Steam (no noncondensables) Water Boiler water Cooling tower (untreated) Condensate (flashed) River and well Sea water (clean and below 125°F) Gases in turbulent flow Air, CO, CO,, and N, 0 . 0 0 7 0 . 0 0 7 0 . 0 0 4 0 . 0 1 3 0 . 0 0 3 5 0.005 0 . 0 0 4 0.004 0 . 0 0 7 0 . 0 0 7 0.005 0 . 0 1 5 0.011 0 . 0 1 8 0 . 0 1 2 5 0 . 0 1 4 0 . 0 0 8 0 . 0 1 0 0 . 0 0 6 0.009 0 . 0 1 8 0 . 0 0 8 0 . 0 0 7 0 . 0 0 6 0 . 0 0 8 0 . 0 0 8 0 . 0 1 8 0 . 0 1 5 0 . 0 0 3 0 . 0 0 7 0 . 0 0 2 0 . 0 0 7 0.004 0 . 0 4 5 0.011 - - - - - 0 . 0 0 7 0 . 0 0 9 - - - - - - - - 0 . 0 1 0 - - - - 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0.011 0 . 0 1 0 - - - - - - - 0 . 0 0 7 - - - - - 0.004 0 . 0 0 7 - - - - - - 0 . 0 1 5 0 . 0 1 8 0 . 0 0 8 - - 0 . 0 1 3 - 0 . 0 0 6 0 . 0 0 7 0 . 0 0 7 0 . 0 0 8 5 0 . 0 0 8 - - 0.001 - - - - - Hydrocarbons (light through naphthas) 0 . 0 3 5 (Fair and Rase, Pet Refiner 33t7). 121, 1854; Rase and Barrow, Project Engineering of Process Plants; 224, Wiley, 1957.) CONDENSATION Depending largely on the nature of the surface, condensate may form either a continuous film or droplets. Since a fluid film is a partial insulator, dropwise condensation results in higher rates of condensation. Promoters are substances that make surfaces nonwetting, and may be effective as additives in trace amounts to the vapor. Special shapes of condensing surfaces also are effective in developing dropwise condensation. None of these effects has been generally correlated, but many examples are cited in HEDH and elsewhere. Condensation rates of mixtures are influenced by both heat and mass transfer rates; techniques for making such calculations have been developed and are a favorite problem for implementation on computers. Condensation rates of mixtures that form immiscible liquids also are reported on in HEDH. Generally, mixtures have lower heat transfer coefficients in condensation than do pure substances. BOILING This process can be nuclear or film type. In nuclear boiling, bubbles detach themselves quickly from the heat transfer surface. In film boiling the rate of heat transfer is retarded by an adherent vapor film through which heat supply must be by conduction. Either mode
- 207. 188 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.8. Dimensionless Groups and Units of Quantities Pertaining to Heat Transfer S y m b o l N u m b e r G r o u p realized heat transfer to the heat transfer that would be obtained if the fin were at the bare tube temperature throughout. The total heat transfer is the sum of the heat transfers through the bare and the extended surfaces: B i Biot F o Fourier GZ Graetz G r Grashof N U Nusselt P e Peclet P r Prandtl R e Reynolds S C S c h m i d t St Stanton hL/k ke/pCL’ wC/kL D3p2gPAT/p2 hD/k DGC/k = (Re)(Pr) Wk DGIP, DUPIY d& hC/G = (Nu)/(Re)(Pr) Notation Name and Typical Units C heat capacity ]Btu/flb)(“F), cal/(g)(“C)] D diameter (ft, m) 9 acceleration of gravity [ft/(hr)‘, m/set’] G mass velocity [lb/(hr)(ft)2, kg/set)(m)‘] h heat transfer coefficient [Btu/(hr)(sqft)(“F), W/(m)2(sec)l k thermal conductivity [Btu/(hr)(sqft)(‘F/R), cal/(sec)(cm2)(C/cm)] 4, diffusivity (volumetric) [ft*/hr, cm*/sec] L length (f-t, cm) T, AT temperature, temperature difference (“F or “R, “C or K) ” linear velocity (ft/hr, cm/set) IJ overall heat coefficient (same as units of h) B” mass rate of flow (Ib/hr, g/set) Thermal expansion coefficient (l/“F, l/C) 8 time (hr. set) P viscosity [lb/(ft)(hr), g/(cm)(sec)] P density [lb/(f$, g/(cm)3] can exist in any particular case. Transition between modes corresponds to a maximum heat flux and the associated critical temperature difference. A table of such data by McAdams (Heat Trunsmission, McGraw-Hill, New York, 1954, p. 386) shows the critical temperature differences to range from 42-90°F and the maximum fluxes from 42-126 KBtu/(hr)(sqft) for organic sub- stances and up to 410KBtu/(hr)(sqft) for water; the nature of the surface and any promoters are identified. Equations (40) and (41) of Table 8.10 are for critical heat fluxes in kettle and thermosyphon reboilers. Beyond the maximum rate, film boiling develops and the rate of heat transfer drops off very sharply. Evaluation of the boiling heat transfer coefficient in vertical tubes, as in thermosyphon reboilers, is based on a group of equations, (42)-(48), of Table 8.10. A suitable procedure is listed following these equations in that table. EXTENDED SURFACES When a film coefficient is low as in the cases of low pressure gases and viscous liquids, heat transfer can be improved economically by employing extended surfaces. Figure 8.6 illustrates a variety of extended surfaces. Since the temperature of a fin necessarily averages less than that of the bare surface, the effectiveness likewise is less than that of bare surface. For many designs, the extended surface may be taken to be 60% as effective as bare surface, but this factor depends on the heat transfer coefficient and thermal conductivity of the fin as well as its geometry. Equations and corresponding charts have been developed for the common geometries and are shown, for example, in HEDH (1983, Sec. 2.5.3) and elsewhere. One chart is given with Example 8.6. The efficiency n of the extended surface is defined as the ratio of a A, is the tube surface that is not occupied by fins. Example 8.6 performs an analysis of this kind of problem. 8.5. PRESSURE DROP IN HEAT EXCHANGERS Although the rate of heat transfer to or from fluids is improved by increase of linear velocity, such improvements are limited by the economic balance between value of equipment saving and cost of pumping. A practical rule is that pressure drop in vacuum condensers be limited to OS-l.0 psi (25-50 Torr) or less, depending on the required upstream process pressure. In liquid service, pressure drops of 5-10 psi are employed as a minimum, and up to 15% or so of the upstream pressure. Calculation of tube-side pressure drop is straightforward, even of vapor-liquid mixtures when their proportions can be estimated. Example 8.7 employs the methods of Chapter 6 for pressure drop in a thermosiphon reboiler. The shell side with a number of segmental baffles presents more of a problem. It may be treated as a series of ideal tube banks connected by window zones, but also accompanied by some bypassing of the tube bundles and leakage through the baffles. A hand calculation based on this mechanism (ascribed to K.J. Bell) is illustrated by Ganapathy (1982, pp. 292-302), but the calculation usually is made with proprietary computer programs, that of HTRI for instance. A simpler method due to Kern (1950, pp. 147-152) nominally considers only the drop across the tube banks, but actually takes account of the added pressure drop through baffle windows by employing a higher than normal friction factor to evaluate pressure drop across the tube banks. Example 8.8 employs this procedure. According to Taborek (HEDH, 1983, 3.3.2), the Kern predictions usually are high, and therefore considered safe, by a factor as high as 2, except in laminar flow where the results are uncertain. In the case worked out by Ganapathy (1982, pp. 292-302), however, the Bell and Kern results are essentially the same. 8.8. TYPES OF HEAT EXCHANGERS Heat exchangers are equipment primarily for transferring heat between hot and cold streams. They have separate passages for the two streams and operate continuously. They also are called recuperators to distinguish them from regenerators, in which hot and cold streams pass alternately through the same passages and exchange heat with the mass of the equipment, which is in- tentionally made with large heat capacity. Recuperators are used mostly in cryogenic services, and at the other extreme of tem- perature, as high temperature air preheaters. They will not be discussed here; a detailed treatment of their theory is by Hausen (1983). Being the most widely used kind of process equipment is a claim that is made easily for heat exchangers. A classified directory of manufacturers of heat exchangers by Walker (1982) has several hundred items, including about 200 manufacturers of shell-and-tube equipment. The most versatile and widely used exchangers are the shell-and-tube types, but various plate and other types are valuable and economically competitive or superior in some applications. These other types will be discussed briefly, but most of the space following will be devoted to the shell-and-tube types, primarily
- 208. 8.6. TYPES OF HEAT EXCHANGERS 189 TABLE 8.9. Equations for Heat Transfer Coefficients of Natural Convection Vertical plates and cylinders, length L XL = (Gr)(Pr) = hLlk= O.13X:‘3, turbulent, 109<XL < 10” h = 0.19(At)“3, for air, At in “F, h in Btu/(hr)(sqft)(“F) hL/k=0.59X:‘4, laminar, 104<XL< 10’ h = 0.29(At/L)“4, for air, L in fl Single horizontal cylinder, diameter D, h&/k= 0.53Xy, 103< X, < 10’ h=0.18(At)“3, forair, 109<XD<10’* h=0.27(At/D,,)“4, 104<Xo<109 Horizontal plates, rectangular, L the smaller dimension Heated plates facing up or cooled facing down hLlk= 0.14X;‘3, 2(10’) <XL <3(10”), turbulent h = 0.22(At)“3, for air hL/k = 0.54X;14, 105<XL<2(107), laminar h = 0.27(At/L)“4 Heated plates facing down, or cooled facing up hL/k = 0.27X;“, 3(105) <XL < 3(10”), laminar h= 0.12(At/L)“4, for air Combined convection and radiation coefficients, h, + h,, for horizontal steel or insulated pipes in a room at 80°F (1) (2) (3) (4) (5) 6) (7) (8) (9) (10) (11) (12) (131 (14) (15) (1’3 N o m i n a l Pipe Dia (in.) 1 z 1 2 4 8 12 2 4 5 0 100 2.12 2 . 4 8 2 . 0 3 2 . 3 8 1.93 2 . 2 7 1.a4 2 . 1 6 1.76 2 . 0 6 1.71 2.01 1.64 1.93 (At),, Temperature Difference (‘F) from Surface to Room 150 200 250 2 . 7 6 3 . 1 0 3.41 2 . 6 5 2 . 9 8 3 . 2 9 2 . 5 2 2 . 8 5 3 . 1 4 2.41 2 . 7 2 3.01 2 . 2 9 2 . 6 0 2 . 8 9 2 . 2 4 2 . 5 4 2 . 8 2 2 . 1 5 2 . 4 5 2.72 3 . 7 5 4 . 4 7 5 . 3 0 6.21 7 . 2 5 8 . 4 0 9 . 7 3 1 1 . 2 0 12.81 1 4 . 6 5 3 . 6 2 4 . 3 3 5 . 1 6 6 . 0 7 7.11 8 . 2 5 9 . 5 7 1 1 . 0 4 1 2 . 6 5 1 4 . 4 8 3 . 4 7 4 . 1 8 4 . 9 9 5 . 8 9 6 . 9 2 8 . 0 7 9 . 3 8 1 0 . 8 5 1 2 . 4 6 1 4 . 2 8 3 . 3 3 4 . 0 2 4 . 8 3 5 . 7 2 6 . 7 5 7 . 8 9 9.21 1 0 . 6 6 12.27 1 4 . 0 9 3 . 2 0 3 . 8 8 4 . 6 8 5 . 5 7 6 . 6 0 7 . 7 3 9 . 0 5 1 0 . 5 0 1 2 . 1 0 1 3 . 9 3 3 . 1 3 3 . 8 3 4.61 5 . 5 0 6 . 5 2 7 . 6 5 8 . 9 6 1 0 . 4 2 1 2 . 0 3 1 3 . 8 4 3 . 0 3 3 . 7 0 4 . 4 8 5 . 3 7 6 . 3 9 7 . 5 2 8 . 8 3 1 0 . 2 8 1 1 . 9 0 1 3 . 7 0 400 500 600 700 600 9 0 0 1000 1100 1200 (McAdams, Heat Transmission, McGraw-Hill, New York, 1954). because of their importance, but also because they are most completely documented in the literature. Thus they can be designed with a degree of confidence to fit into a process. The other types are largely proprietary and for the most part must be process designed by their manufacturers. PLATE-AND-FRAME EXCHANGERS Plate-and-frame exchangers are assemblies of pressed corrugated plates on a frame, as shown on Figure 8.8(a). Gaskets in grooves around the periphery contain the fluids and direct the flows into and out of the spaces between the plates. Hot and cold flows are on opposite sides of the plates. Figure 8.8(b) shows a few of the many combinations of parallel and countercurrent flows that can be maintained. Close spacing and the presence of the corrugations result in high coefficients on both sides-several times those of shell-and-tube equipment-and fouling factors are low, of the order of l-5 x 10-s Btu/(hr)(sqft)(“F). The accessibility of the heat exchange surface for cleaning makes them particularly suitable for fouling services and where a high degree of sanitation is required, as in food and pharmaceutical processing. Operating pressures and temperatures are limited by the natures of the available gasketing materials, with usual maxima of 300 psig and 400°F. Since plate-and-frame exchangers are made by comparatively few concerns, most process design information about them is proprietary but may be made available to serious enquirers. Friction factors and heat transfer coefficients vary with the plate spacing and the kinds of corrugations; a few data are cited in HEDH (1983, 3.7.4-3.7.5). Pumping costs per unit of heat transfer are said to be lower than for shell-and-tube equipment. In stainless steel
- 209. 190 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.10. Recommended Individual Heat Transfer Coefficient Correlations’ A. Single Phase Streams a. Laminar Flow, Re c 2300 Inside tubes Nu, = $3.663 + 1.61a Pe(d/L), 0.1 < Pe(d/L) i IO4 Between parallel plates of length L and separation distance s Nu, = 3.7% + 0.0156(Pe(s/L)]‘.‘4 1 + 0.058[Pe(s/L)]0.M Pr”.17 ’ 0.1 < Pe(s/L) < IO3 (2) In concentric annuli with d inside, d, outside, and hydraulic diameter d,, = d, - di. I, heat transfer at inside wall; II, at outside wall; Ill, at both walls at equal temperatures’ 0.19[Pe(d,,/L)]0~8 1 +0.117[Pe(d,,/L)]0.467 (3) (4) (5) 6) (7) Casell: Case Ill: b. Turbulent Flow, Re > 2300 Inside tubes Nu = 0.012(Re0-87 - 280) Prc4 (8) (9) (IO) (11) Concentric annuli: Use d,, for both Re and Nu. Nurub. from Eqs. (IO] or (11) Case I: Case II: (13) Case III: 1 + qJd, (14) Across one row of long tubes: d = diameter, s = center-to-center distance, a = s/d, R%.L = wL/qv Wvow = 0.3 + ~Nu:.,,m + Nu:turb Nu~,,am = 0.664GPr’” ‘%tur,, = 0.037 Re$ Pr/[l + 2.443 Re;ci’(Pr2’3 - I)] Nu~,ra,., = ~Llh (15) (161 (17) (18) (‘9) “Special notation used in this table: (Y = heat transfer coefficient (W/m* K) (instead of h), Q = viscosity (instead of ,n), and (Y = thermal conductivity (instead of k). (Based on HEDH, 1983).
- 210. 8 . 6 . T Y P E S O F H E A T E X C H A N G E R S 191 TABLE 8.1~(continued) Across a bank of n tubes deep: IN-LINE 0 99 O - f 0 OS’0 04 T T T T T a =5/d b=,l,d2 w y,=l-n/4a ifbzl (20) y,=l-n/4ab i f b<l (21) N%b3”k = cuLlI = b Nu,,,,,/K, n L 10 N%,bank = [l + (n - l)f,l Nu,,,,,/Kn, n < 10 [Nuo,,ow from Eq. (16)I Pa (23) b,i,.,i,e = 1 + (0.7/q’.5)[(b/a - 0.3)/(b/a + 0.7)‘1 f~..,a~ = 1 + 2/3b K = (Pr/Pr,)0.25, for liquid heating K = (Pr/Pr I’.“, for liquid cooling K= (T/T,+, for gases (24) (25) (26) (27) (28) STAGGERED 0-g -+I Subscript w designates wall condition Banks of radial high-fin tubes: E = (bare tube surface)/(total surface of finned tube) In line: Nu = 0.30 Re0..sX-0.375 pro.333 , 5~~~12, 5000<Re<105 (29) Staggered: a = s,/d, b = s2/d, s = spacing of fins Nu = 0.19(a/b)02(s/d)0~‘8(h/d)0-‘4 Re0.65Pr0.33, 100 < Re < 20,000 (30) Banks of radial low-fin tubes: D = diameter of finned tube, s =distance between fins, h = height of fin; following correlation for D = 22.2 mm, s = 1.25 mm, and h = 1.4 mm Nu = 0.0729 Re0.74 Pr”.36, 5000 < Re < 35,000 (31) Nu = 0.137 Re’.‘s Pr”.35, 35,000 < Re < 235,000 132) Nu = 0.0511 Re0.76 Pro.36 , 235,000 < Re < 10s (33) B. Condensation of Pure Vapors On vertical tubes and other surfaces; r = condensation rate per unit of periphery On a single horizontal tube: r = condensation rate per unit length of tube (34) (35) (continued)
- 211. 192 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.1~(continued) On a bank of N horizontal tubes: r = condensation rate per unit length from the bottom tube (36) C. Boiling Sing/e immersed tube: o heat flux (W/m*), oc = critical pressure, bars. or = P/P, (Y = 0.1000~“~7po~69[1 .8pF-17 + 4p:.’ + 10p:“l, W/m* K (37) Kettle and horizontal thermosiphon reboilers (Y = 0.27 exp(-0.027BR)4°.7p~69p~.‘7 + onu,, (38) BR = difference between dew and bubblepoints (“K); if more than 85, use 85 I 250 W/m’ K, for hydrocarbons a”, = 1000 W/m K, for water Critical heat flux in ketr/e and horizontal thermosiphon reboilers q,., = 80,700~ p”?l - p c r r )‘.!+# bl W/m2 pr, = (external peripheral surface of tube bundle)/ (total tube area); if >0.45, use 0.45 (39) (40) Boiling in vertical tubes: thermosiphon reboilers Critical heat flux: pc critical pressure, bars; 0; tube ID, m; L tube length, m 4 = 393,000(D~/L)a~35p~6’p~~*5(1 - p,), W/m2 Heat transfer coefficient with Eqs. (42)-(48) and following procedure (41) (43) (44) F= 1 for l/X, d 0.1 (45) F= 2.35(1/X, + 0.213)“.736 for l/X, > 0.1 (46) S=l/(l +2.53x 10m6Re:p”) (47) x, = If1 - x~/xl~-~~P,/P,~“~5~fl,/~g~o~’ (48) Procedure for finding the heat transfer coefficient and required temperature difference when the heat flux 4, mass rate of flow ri, and fraction vapor x are specified 1. Find X,, Eq. (48) 2. Evaluate Ffrom Eqs. (45). (46) 3. Calculate ru,, Eq. (43) 4. Calculate Re, = rhF’~25(1 - x)D/n, 5. Evaluate S from Eq. (47) 6. Calculate ‘ynb for a range of values of AT,,, 7. Calculate ‘ytP from Eq. (42) for this range of AT,,, values 6. On a plot of calculated q= qPATs,, against nrP, find the values of a;n and ATsat corresponding to the specified q
- 212. 8 . 6 . T Y P E S O F H E A T E X C H A N G E R S 193 EXAMPLE 8.6 Sizing an Exchanger with Radial Finned Tubes A liquid is heated from 150 to 190°F with a gas that goes from 250 to 200°F. The duty is 1.25 MBtu/hr. The inside film coefficient is 200, the bare tube outside coefficient is h, = 20 Btu/(hr)(sqft)(“F). The tubes are 1 in. OD, the fins are 5 in. high, 0.038 in. thick, and number 72/ft. The total tube length will be found with fins of steel, brass, or aluminum: LMTD = (60 - 50)/1n(60/50) = 54.8, u, = (l/20 + l/200))’ = 18.18. Fin surface: A, = 72(2)@/4)[(2.25* - 1)/144] = 3.191 sqft/ft. Uncovered tube surface: A, = (n/12)[1 - 72(0.038/12)] = 0.2021 sqft/ft, AJA, = 3.191/0.2021= 15.79, yh = half-fin thickness = 0.038/2(12) = 0.00158 ft. Abscissa of the chart: n = (re - r,)e = [(2.25 - 1)/24]~20/0.00158k =5.86/G, rJrb = 2.25, A, = QlWT(l+ vL/A,) = 1.25(10”)/18.18(54.8)(1+ 15.7917) sq ft. Find 9 from the chart. Tube length, L = AJO. ft. k x q A,, L Steel 26 1.149 0.59 121.6 602 Brass 6 0 0 . 7 5 6 0 . 7 6 9 6 . 5 4 7 7 Al 120 0.535 0.86 86.1 426 EXAMPLE 8.7 Pressure Drop on the Tube Side of a Vertical Thermosiphon Reboiler Liquid with the properties of water at 5 atm and 307°F is reboiled at a feed rate of 28OOIb/(hr)(tube) with 30wt % vaporization. The tubes are 0.1 ft ID and 12 ft long. The pressure drop will be figured at an average vaporization of 15%. The Lockhart-Martinelli, method will be used, following Example 6.14, and the formulas of Tables 6.1 and 6.8: Liquid V a p o r rh (Ib/hr) 2 3 8 0 4 2 0 F Ob/ft hr) 0.45 0.036 P Wcufi) 5 7 . 0 0 . 1 7 2 R e 6 7 3 4 0 1 4 8 5 4 4 f 0.0220 0.0203 Af/L (psi/ft) 0.00295 0.0281 X2 = 0.00295/0.0281= 0.1051, c=20, & = 1 + 20/X + l/X’ = 72.21, (AP/L) two phase = 72.21(0.00295) = 0.2130, AP = 0.2130(12) = 2.56 psi, 5.90 ft water. --- D T T i 4 Average density in reboiler tubes is 2800 pm = 2380157 + 420/O. 172 = 1.13 Ib/cuft. Required height of liquid in tower above bottom of tube sheet p,h = 2.56(144) + 1.13(12), h = 382.2157 = 6.7 ft.
- 213. 1% HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.8 Pressure Drop on the Shell Side with 25% Open Segmental Batlles, by Kern’s Method (1950, p. 147) Nomenclature and formulas: hydraulic diameter Dh = l.l028P~/D,-D,, triangular pitch, 1.2732P:/D, - D,, square pitch, D, = shell diameter, B = distance between baffles, N = number of baffles, A, = flow area = D,BC/P,, G,=h/A,, lb/(W(sqft), Re = &G/P, f= 0.0121Re-0-1g, 300 < Re < 106, 25% segmental baffles, up =~‘GSD,(N + 1) =fGSD,(N + 1) 2wD, 5.22(10'")sD,, ' psi ' s = specific gravity. Numerical example: tit = 43,800 lb/hr, s = 0.73 sp gr, p = 0.097 Ib/ft hr, D,= 1 in., P,= 1.25in., triangular pitch, C=1.25-1.00=0.25in., D,=21.25in., 1.77ft., D,, = 0.723 in., 0.0603 ft., B=5in., N = 38 baffles, A, = 21.25(0.25)(5)/1.25(144) = 0.1476 sqft, G, =43,800/O. 1476 = 296,810 lb/(hr)(sqft), Re = 0.0603(296,810)/0.97 = 18,450, f= 0.0121(18,450)-“~‘g = 0.00187, construction, the plate-and-frame construction cost is 50-70% that of shell-and-tube, according to Marriott (Chem. Eng., April 5, 1971). A process design of a plate-and-frame exchanger is worked out by Ganapathy (1982, p. 368). SPIRAL HEAT EXCHANGERS As appears on Figure 8.8(c), the hot fluid enters at the center of the spiral element and flows to the periphery; flow of the cold fluid is countercurrent, entering at the periphery and leaving at the center. Heat transfer coefficients are high on both sides, and there is no correction to the log mean temperature difference because of the true countercurrent action. These factors may lead to surface requirements 20% or so less than those of shell-and-tube ex- changers. Spiral types generally may be superior with highly viscous fluids at moderate pressures. Design procedures for spiral plate and the related spiral tube exchangers are presented by Minton (1970). Walker (1982) lists 24 manufacturers of this kind of equipment. COMPACT (PLATE-FIN) EXCHANGERS Units like Figure 8.6(h), with similar kinds of passages for the hot and cold fluids, are used primarily for gas service. Typically they have surfaces of the order of 1200m2/m3 (353 sqft/cuft), corrugation height 3.8-11.8 mm, corrugation thickness 0.2-0.6 mm, and fin density 230-700 fins/m. The large extended surface permits about four times the heat transfer rate per unit volume that can be achieved with shell-and-tube construction. Units have been de- signed for pressures up to 80 atm or so. The close spacings militate against fouling service. Commercially, compact exchangers are used in cryogenic services, and also for heat recovery at high temperatures in connection with gas turbines. For mobile units, as in motor vehicles, the designs of Figures 8.6(h) and (i) have the great merits of compactness. and light weight. Any kind of arrangement of cross and countercurrent flows is feasible, and three or more different streams can be accommodated in the same equipment. Pressure drop, heat transfer relations, and other aspects of design are well documented, particularly by Kays and London (1984) and in HEDH (1983, Sec. 3.9). AIR COOLERS In such equipment the process fluid flows through finned tubes and cooling air is blown across them with fans. Figures 8.4(g) and (h) show the two possible arrangements. The economics of application of air coolers favors services that allow 25-40°F temperature difference between ambient air and process outlet. In the range above lOMBtu/(hr), air coolers can be economically competitive with water coolers when water of adequate quality is available in sufficient amount. Tubes are 0.75-l.OOin. OD, with 7-11 fins/in. and 0.5- 0.625in. high, with a total surface 15-20 times bare surface of the tube. Fans are 4-12ft/dia, develop pressures of 0.5-1.5in. water, and require power inputs of 2-5HP/MBtu/hr or about 7SHP/ 1OOsqft of exchanger cross section. Spacings of fans along the length of the equipment do not exceed 1.8 times the width of the cooler. Face velocities are about IO ft/sec at a depth of three rows and 8 ft/sec at a depth of six rows. Standard air coolers come in widths of 8, 10, 12, 16, or 2Oft, lengths of 4-4Oft, and stacks of 3-6 rows of tubes. Example 8.8 employs typical spacings. Three modes of control of air flow are shown in Figure 3.3(e). Precautions may need to be taken against subcooling to the freezing point in winter.
- 214. 8.7. SHELL-AND-TUBE HEAT EXCHANGERS 1% (a) (i) Parallel and counter flows d-- -r- -r-‘f--: I I I m I4 f I f : I 1 I ---*L--r-- - (ii) Countercurrent flows jgTJTJQ--> -------- -- (iii) Parallel flows throughout (b) (cl L I Figure 8.8. Plate and spiral compact exchangers. (a) Plate heat exchanger with corrugated plates, gaskets, frame, and corner portals to control flow paths. (b) Flow patterns in plate exchangers, (i) parallel-counter flows; (ii) countercurrent flows; (iii) parallel flows throughout. (c) Spiral exchanger, vertical, and horizontal cross sections. Forced draft arrangement, from below the tubes, Figure 8.4(h), develops high turbulence and consequently high heat transfer coefficients. Escape velocities, however, are low, 3 m/set or so, and as a result poor distribution, backmixing and sensitivity to cross currents can occur. With induced draft from above the tubes, Figure 8.4(g), escape velocities may be of the order of 10 m/set and better flow distribution results. This kind of installation is more expensive, the pressure drops are higher, and the equipment is bathed in hot air which can be deteriorating. The less solid mounting also can result in noisier operation. Correlations for friction factors and heat transfer coefficients are cited in HEDH. Some overall coefficients based on external bare tube surfaces are in Tables 8.11 and 8.12. For single passes in cross flow, temperature correction factors are represented by Figure 8.5(c) for example; charts for multipass flow on the tube side are given in HEDH and by Kays and London (1984), for example. Preliminary estimates of air cooler surface requirements can be made with the aid of Figures 8.9 and 8.10, which are applied in Example 8.9. DOUBLE-PIPES This kind of exchanger consists of a central pipe supported within a larger one by packing glands [Fig. 8.4(a)]. The straight length is limited to a maximum of about 20 ft; otherwise the center pipe will sag and cause poor distribution in the annulus. It is customary to operate with the high pressure, high temperature, high density, and corrosive fluid in the inner pipe and the less demanding one in the annulus. The inner surface can be provided with scrapers [Fig. 8.4(b)] as in dewaxing of oils or crystallization from solutions. External longitudinal fins in the annular space can be used to improve heat transfer with gases or viscous fluids. When greater heat transfer surfaces are needed, several double-pipes can be stacked in any combination of series or parallel. Double-pipe exchangers have largely lost out to shell-and-tube units in recent years, although Walker (1982) lists 70 manufacturers of them. They may be worth considering in these situations: 1. When the shell-side coefficient is less than half that of the tube side; the annular side coefficient can be made comparable to the tube side. 2. Temperature crosses that require multishell shell-and-tube units can be avoided by the inherent true countercurrent flow in double pipes. 3. High pressures can be accommodated more economically in the annulus than they can in a larger diameter shell. 4. At duties requiring only 100-200 sqft of surface the double-pipe may be more economical, even in comparison with off-the-shelf units. The process design of double-pipe exchangers is practically the simplest heat exchanger problem. Pressure drop calculation is straightforward. Heat transfer coefficients in annular spaces have been investigated and equations are cited in Table 8.10. A chapter is devoted to this equipment by Kern (1950). 8.7. SHELL-AND-TUBE HEAT EXCHANGERS Such exchangers are made up of a number of tubes in parallel and series through which one fluid travels and enclosed in a shell through which the other fluid is conducted. CONSTRUCTION The shell side is provided with a number of baffles to promote high velocities and largely more efficient cross flow on the outsides of the
- 215. 196 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.11. Overall Heat Transfer Coefficients in Air Coolers [U Btu/(hr)(“F)(sqft of outside bare tube sutface)] Material Liquid Coolers Condensers Heat-Transfer Heat-Transfer Heat-Transfer Coefficient, [Btu/(hr) Vt%Wl Coefficient, Coefficient, Material (Btu/(hr)(ft?(“F)l Material [Btu/(hr)(rt2WF)l Oils, 20” API IO-16 200°F avg. temp lo-16 300°F avg. temp 13-22 400°F avg. temp 30-40 Oils, 30” API 150°F avg. temp 200°F avg. temp 300°F avg. temp 400°F avg. temp 12-23 25-35 45-55 50-60 Oils, 40” API 150°F avg. temp 200°F avg. temp 300°F avg. temp 400°F avg. temp 25-35 50-60 55-65 60-70 Heavy oils, 8-14”API 300°F avg. temp 400°F avg. temp Diesel oil K e r o s e n e Heavy naphtha Light naphtha Gasoline Light hydrocarbons Alcohols and most organic solvents Ammonia Brine, 75% water Water 50% ethylene glycol and water 6-10 lo-16 45-55 55-60 60-65 65-70 70-75 75-80 70-75 100-120 go-110 120-140 100-120 Vapor Coolers Steam Steam 10% noncondensibles 20% noncondensibles 40% noncondensibles Pure light hydrocarbons Mixed light hydrocarbons Gasoline Gasoline-steam mixtures Medium hydrocarbons Medium hydrocarbons w/steam Pure organic solvents Ammonia 140-150 100-110 95-100 70-75 80-85 65-75 60-75 70-75 45-50 55-60 75-80 100-110 Heat-Transfer Coefficient [Btu/(hr)(f?)(“F)] Material Light hydrocarbons Medium hydrocarbons and organic solvents Light inorganic vapors Air Ammonia Steam H y d r o g e n 100% 75% vol 50% vol 25% vol [Brown, Chem. Eng. (27 Mar. 1978)]. 10 psig 50 psig 100 psig 300 psig 500 psig 15-20 30-35 45-50 65-70 70-75 15-20 35-40 45-50 65-70 70-75 IO-15 15-20 30-35 45-50 50-55 8-10 15-20 25-30 40-45 45-50 IO-15 15-20 30-35 45-50 50-55 10-15 15-20 25-30 45-50 55-60 20-30 45-50 65-70 85-95 95-100 17-28 40-45 60-65 80-85 85-90 15-25 35-40 55-60 75-80 85-90 12-23 30-35 45-50 65-70 80-85 TABLE 8.12. Overall Heat Transfer Coefficients in Condensers, Btu/(hr)(sqft)(OF)a V a p o r Liquid Coolants Coolant Btu/(hrkqfWF) Alcohol Dowtherm Dowtherm Hydrocarbons high boiling under vacuum low boiling intermediate kerosene k e r o s e n e naphtha naphtha Organic solvents Steam Steam-organic azeotrope Vegetable oils water 100-200 tall oil 60-80 Dowtherm 80-120 water 18-50 water 80-200 oil 25-40 water 30-65 oil 20-30 water 50-75 oil 20-40 water 100-200 water 400-1000 water 40-80 water 20-50 Air Coolers V a p o r Btu/(hr) (bare sqft)(“F) Ammonia 100-120 Freons 60-80 Hydrocarbons, light 80-100 Naphtha, heavy 60-70 Naphtha, light 70-80 Steam 130-140 “Air cooler data are based on 50mm tubes with aluminum fins 16-18 mm high spaced 2.5-3 mm apart; coefficients based on bare tube surface. Excerpted from HEDH, 1983.
- 216. a00 ,000 I II I I I BROWS.u:IZO I I WOO 3mo I I I 3 ROWS.U=l00 2om 8 I M II I‘hl I. 40 I II II II l--d?-+ (b) 10 (a) :x4, , ( ( , , , , , , , , , ( , Figure 8.9. Required surfaces of air coolers with three rows of tubes. (a) CJ = 140. (b) U = 120. (c) CJ = 100. (d) CJ= 80. (e) CJ = 60. [Lerner, Hyd. Proc., 93-100 (Fed. 1972)]. ” ” “I I I ” 3 ROWS.U:60 I ! ! ! ! ! ! ! N-U_U II I I I I IIIU . 40 40 II il II III 11% 3 0 1 al 30 2 0 10 I 5 I) I lel (4
- 218. 8.7. SHELL-AND-TUBE HEAT EXCHANGERS 1% EXAMPLE 8.9 Estimation of the Surface Requirements of an Au Cooler An oil is to be cooled from 300 to 150°F with ambient air at 90”F, with a total duty of 20 MBtu/hr. The tubes have 5/8 in. fins on 1 in. OD and 2-5/16 in. triangular spacing. The tube surface is given by A = 1.33NwL, sqft of bare tube surface, N = number of rows of tubes, from 3 to 6, W = width of tube bank, ft, L = length of tubes, ft. According to the data of Table 8.12, the overall coefficient may be taken as U = 60 Btu/(hr)(oF)(sqft of bare tube surface). Exchangers with 3 rows and with 6 rows will be examined. Approach = 150 - 90 = 60”F, Cooling range = 300 - 150 = 15O”F, From Figure 8.9(f), 3 rows, A = 160 sqft/MBtu/hr) + 160(20) = 3200 sqft = 1.33(3)WL. tubes. Figure 8.4(c) shows a typical construction and flow paths. The versatility and widespread use of this equipment has given rise to the development of industrywide standards of which the most widely observed are the TEMA standards. Classifications of equipment and terminology of these standards are summarized on Figure 8.11. Baffle pitch, or distance between baffles, normally is 0.2-1.0 times the inside diameter of the shell. Both the heat transfer coefficient and the pressure drop depend on the baffle pitch, so that its selection is part of the optimization of the heat exchanger. The window of segmental baffles commonly is about 25%, but it also is a parameter in the thermal-hydraulic design of the equipment. In order to simplify external piping, exchangers mostly are built with even numbers of tube passes. Figure 8.12(c) shows some possible arrangements, where the full lines represent partitions in one head of the exchanger and the dashed lines partitions in the opposite head. Partitioning reduces the number of tubes that can be accommodated in a shell of a given size. Table 8.12 is of such data. Square tube pitch in comparison with triangular pitch accommo- dates fewer tubes but is preferable when the shell side must be cleaned by brushing. Two shell passes are obtained with a longitudinal baffle, type F in Figures 8.11(a) or 8.3(c). More than two shell passes normally are not provided in a single shell, but a 4-8 arrangement is thermally equivalent to two 2-4 shells in series, and higher combinations are obtained with more shells in series. ADVANTAGES A wide range of design alternates and operating conditions is obtainable with shell-and-tube exchangers, in particular: l Single phases, condensation or boiling can be accommodated in either the tubes or the shell, in vertical or horizontal positions. l Pressure range and pressure drop are virtually unlimited, and can be adjusted independently for the two fluids. When W = 16 ft, L = 50 ft. Two fans will make the ratio of section length to width, 25/16= 1.56 which is less than the max allowable of 1.8. At 7.5 HP/100 sqft, Power=F7.5=60HP. From Figure 8.10(c), 6 rows, A = 185 sqft/(MBtu/hr) + 185(20) = 3700 sqft. = 1.33(6)WL. When W = 16 ft, L = 29 ft. Since L/W = 1.81, one fan is marginal and two should be used: Power = [16(29)/100]7.5 = 34.8 HP. The 6-row construction has more tube surface but takes less power and less space. Thermal stresses can be accommodated inexpensively. A great variety of materials of construction can be used and may be different for the shell and tubes. Extended surfaces for improved heat transfer can be used on either side. A great range of thermal capacities is obtainable. The equipment is readily dismantled for cleaning or repair. TUBE SIDE OR SHELL SIDE Several considerations may influence which fluid goes on the tube side or the shell side. The tube side is preferable for the fluid that has the higher pressure, or the higher temperature or is more corrosive. The tube side is less likely to leak expensive or hazardous fluids and is more easily cleaned. Both pressure drop and laminar heat transfer can be predicted more accurately for the tube side. Accordingly, when these factors are critical, the tube side should be selected for that fluid. Turbulent flow is obtained at lower Reynolds numbers on the shell side, so that the fluid with the lower mass tlow preferably goes on that side. High Reynolds numbers are obtained by multipassing the tube side, but at a price. DESIGN OF A HEAT EXCHANGER A substantial number of parameters is involved in the design of a shell-and-tube heat exchanger for specified thermal and hydraulic conditions and desired economics, including: tube diameter, thickness, length, number of passes, pitch, square or triangular; size of shell, number of shell baffles, baffle type, baffle windows, baffle spacing, and so on. For even a modest sized design program, Bell (in HEDH, 1983, 3.1.3) estimates that 40 separate logical designs may need to be made which lead to 240 = 1.10 x 10” different paths through the logic. Since such a number is entirely too large for normal computer processing, the problem must be simplified with
- 219. 200 HEAT TRANSFER AND HEAT EXCHANGERS i - - E - F G - n - J - K - X - I (a) Figure 8.11, Tubular Exchanger Manufacturers Association classification and terminology for heat exchangers. (a) TEMA terminology for shells and heads of heat exchangers. (b) Terminology for parts of a TEMA type AES heat exchanger. The three letters A, E, and S come from part (a). some arbitrary decisions based on as much current practice as possible. A logic diagram of a heat exchanger design procedure appears in Figure 8.13. The key elements are: 1. Selection of a tentative set of design parameters, Box 3 of Figure 8.13(a). 2. Rating of the tentative design, Figure 8.13(b), which means evaluating the performance with the best correlations and calculation methods that are feasible. 3. Modification of some design parameters, Figure 8.13(c), then rerating the design to meet thermal and hydraulic specifications and economic requirements. A procedure for a tentative selection of exchanger will be described following. With the exercise of some judgement, it is feasible to perform simpler exchanger ratings by hand, but the present state of the art utilizes computer rating, with in-house programs, or those of HTRI or HTFS, or those of commercial services. More than 50 detailed numerical by hand rating examples are in the book of Kern (1950) and several comprehensive ones in the book of Ganapathy (1982). TENTATIVE DESIGN The stepwise procedure includes statements of some rules based on common practice. 1. Specify the flow rates, terminal temperatures and physical properties. 2. Calculate the LMTD and the temperature correction factor F from Table 8.3 or Figure 8.5. 3. Choose the simplest combination of shell and tube passes or number of shells in series that will have a value of F above 0.8 or so. The basic shell is 1-2, one shell pass and two tube passes. 4. Make an estimate of the overall heat transfer coefficient from Tables 8.4-8.7. 5. Choose a tube length, normally 8, 12, 16, or 20 ft. The 8 ft long exchanger costs about 1.4 times as much as the 20 ft one per unit of surface. 6. Standard exchanger tube diameters are 0.75 or 1 in. OD, with pitches shown in Table 8.13. 7. Find a shell diameter from Table 8.13 corresponding to the selections of tube diameter, length, pitch, and number of passes made thus far for the required surface. As a guide, many heat exchangers have length to shell diameter ratios between 6 and 8. 8. Select the kinds and number of baffles on the shell side. The tentative exchanger design now is ready for detailed evaluation with the best feasible heat transfer and pressure drop data. The results of such a rating will suggest what changes may be needed to satisfy the thermal, hydraulic, and economic require- ments for the equipment. Example 8.10 goes through the main part of such a design. 8.8. CONDENSERS Condensation may be performed inside or outside tubes, in horizontal or vertical positions. In addition to the statements made in the previous section about the merits of tube side or shell side: When freezing can occur, shell side is preferable because it is less likely to clog. When condensing mixtures whose lighter components are soluble in the condensate, tube side should be adopted since drainage is less complete and allows condensation (and dissolution) to occur at higher temperatures. Venting of noncondensables is more positive from tube side.
- 220. Segmental baffle detail Shell 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0000 0000 Strip baffle Shell _..-..coo000 0 0 c 0” 0 0 00 0 0 ““E got Doughnut doughnut Disc and doughnut baffle (a) Detail (b) Baffle Orifice baffle (a) 2 Q 1 Pass rib Two Pass 4 3 0 - - - a - l 4 @ 3 12 1 4 3 CD --- 1 2 Four Pass (cl !- Skid Bar Six Pass b) Eight Pass Figure 8.12. Arrangements of cross baffles and tube-side passes. (a) Types of cross baffles. (b) Rod baffles for minimizing tube vibrations; each tube is supported by four rods. (c) Tube-side multipass arrangements. 201
- 221. 202 H E A T TRANSFER AND HEAT EXCHANGERS THE ELEMENTS WITHIN THIS OUTLINE MAY BE DONE BY HAND OR BY COMPUTER. PARAMETERS MECHANICAL DESIGN. COSTING. ETC IYES IN PARALLEL DECREASE SHELL DIAMETER *DENOTES THE LARGEST V OF THAT PARAMETER PERMITTED IN THE FINAL DESIGN. Figure 8.13. A procedure for the design of a heat exchanger, comprising a tentative selection of design parameters, rating of the performance, modification of this design if necessary, and re-rating to meet specifications (see aLso Bell, in Heat Exchanger Design Handbook, Section 3.1.3, Hemisphere Publishing Company, 1983).
- 222. 8.8. CONDENSERS 203 TABLE 8.13. Tube Counts of Shell-and-Tube Heat Exchangers” )Icat Eschangcr Tube Sheet Layout Count Tak 37 35 33 31 2’) 27 25 235/( 21% 19% 17% 15’h 13% 12 IO 8 I.D. of Shell (In.) 1x9 1143 1019 S‘s1 783 GO.3 553 481 391 307 247 193 y; 105 F9 33 I 1127 1007 8S9 x5 fiG7 577 493 423 343 x’ o n ‘::+I’ A 277 217 157 5 7 33 %‘on 1 ’ A 5z I 9B5 8G5 X5 IX5 RS7 405 419 3 5 5 2R7 2 3 5 183 139 101 :5 33 x’on 1’U sf? I G99 G.73 551 481 427 361 307 247 2 0 5 IF3 133 103 73 57 3”; 15 l’onl%‘A 16 I 595 545 477 41.7 359 303 2 5 5 2 1 5 179 139 111 83 G5 45 33 17 l’on 1’4’ 0 --~=I=----- --_ - - - - w-- - - _ _ == ==c =r--- 1242 IOSS X3-4 8.113 734 626 528 452 3 7 0 3 0 0 2 2 8 166 124 94 5 % 1%~ M’on ‘><,‘A - - lOS8 972 858 ‘i4r, G4G 55G 4GS 3 9 8 32G 2G4 2 0 8 154 110 no St, 2 8 N’on 1’ A 5s 946 840 i4G I344 5fiO 4% 405 340 250 222 172 120 94 78 48 26 ~“Olll”O -H GCSX GO8 530 4G2 ‘=o 410 3‘10 292 2 4 4 204 1 G2 126 92 62 52 3 2 16 l ’ o n 1%’ A ZP’ 58.4 523 4GO 402 R-48 298 248 2 1 8 Ii2 136 10G 7G 56 40 2G 12 1”on 1%’ 0 t P-.----_---------- ----~ 1120 1008 -8 882 ifs 048 5:,8 4GO 3 9 8 304 234 180 134 94 64 3 4 10no 8 %’ on ‘%a”A as2 c ; ii2 874 5GG 484 406 33G 270 212 15% 108 6 0 26 8 M”onl’A 884 77% fx3.s AS6 50G 4:iG 3G2 3 0 4 242 l&t? 142 100 ;2” 52 30 1 2 X’qnl’O 2 ’ 810 532 4(X 39G 340 284 234 192 154 120 H X X l ’ o n 1 % ’ A 5X 404 ii ii:: lx iz z 400 350 304 266 214 180 134 100 1 2 x x l’on 1 % ’ 0 o”, - - --__--- C_----v-,---- - - - = = 1Ii2 1 0 2 4 901 i88 GE0 576 484 412 332 266 19G 154 108 4 8 X X %‘on ‘k{s’ A 102.4 913 SO2 GO2 506 50% 424 3G0 292 2 3 2 180 134 ;; 4 4 X X x’on 1’A 92 ES0 i i 8 GM 590 510 440 36G 3 0 8 242 192 142 12G % 72 4 8 x x K’on 1’0 ;r$ 638 5dO 4SG 422 368 308 258 212 17G 138 104 GO 44 534 47ti 2 4 X X 1’onlx.A 2~: -41-l 3G0 310 2G0 214 185 142 110 84 ;: 48 40 2 4 X X l’onl%‘O ------.-.--Ir-- ---m-p 1093 97G S52 i40 G22 534 438 378 - 2SG 2 1 8 1GG 122 5G 28 SS %‘on ‘>is’A c ; sz,s 852 744 G-IS 542 4G2 3SG 31s 25-k 198 140 ES2 ;: 52 2 0 SS x’on 1 ’ A i‘s GO0 5GO 482 414 343 2SG 2x 174 130 xi G4 2.4 SS %‘on 1’0 2 .: 5% 50s 444 37G 3”” 2GG 215 1iS 142 110 it SS SS I”onl%‘A g 500 440 3s-4 3x 2% 238 19s 1GG 122 90 2 zz %I 1G XX SX l’onl%‘lJ v: w--v -m ==-~=w-==_--- - - IlOci 064 -__- s4-l i33 fx” 532 440 3i2 29-l 2 3 0 Ii4 904 s!z 11G 8 0 SS SS SS %‘on ‘$<e’ A 544 G-IO 5;s 4G-4 3s 323 25s 202 15G 10.) GG SS SS SS K’on 1’A Yz SIS 224 (X3.4 53G 4GO 394 324 5SG 2GG 212 15s 11G 58 5 4 SS SS SS xron 1’0 514 442 3S2 335 2i4 22G 182 150 112 454 34 XS XS SS 1’011 1%’ A ga i 430 3GS 315 2GS 226 lY4 154 11G 85 t5 ‘, :: X X XS SX SS l’on l>h’ I3 - - - - - - - - - - - - - - - I : 105s 944 83G 716 596 510 416 35s 2i2 2 0 6 156 110 r. -I r 940 8%G 74 XX XX SX g” on ;I@ 151 * A i20 62G 515 440 3GG 3 0 0 2 3 8 184 134 5 G X X X S SX N’on 1’A c k 820 718 G42 634 458 392 322 268 2 1 0 IGO 118 ii 5 6 X X X X X S %‘onl’Cl. 2 562 488 4% 356 304 252 206 168 130 478 100 4 2 30 XX XX XX l”on lfd’ A g 420 362 316 2G8 224 182 152 110 80 :: 42 xx xx xs xx 1’ 0” l!B’ q v: -m-v -= ---‘v-w - %20 W-B 902 i90 FS2 576 484 398 332 2 5 8 :Ei 140 X X XS X X X X M’on ‘s:e’ A 598 694 588 496 422 344 28G 2 2 4 124 ii X X X X X X SS s’on 1’A 2” iD0 GG2 576 490 414 352 2SB 2 2 8 174 132 - XX XX SS XS $$‘on 1’0 542 4GG 400 342 298 240 190 154 120 ii $2 X X X X SS SS l’onl%‘A g&i e?i , 438 3S8 334 2S0 230 192 150 128 94 ;: XX XX XX XX XX SS 1’ on 1%:’ Cl ------____--------- : 1032 916 796 G88 5i8 490 398 342 254 190 142 102 ! 68 XS XX SX x’on 1::s’ A c El 796 692 600 498 422 350 2 8 6 692 226 170 122 82 608 512 438 374 306 254 5 2 X X X X X X x’on 1’A 194 146 106 4 8 X X X X X X x’on 1’0 2 E 464 404 340 290 238 190 Ei 396 118 90 58 2 344 300 254 206 170 2 4 XXXXXX 1’onlx’A $ :ii 98 70 50 34 X X X X X X X X l ’ o n 1%’ 0 cd, 37 3s I I 33 131 129 127 1, 25 123% 1211/r 1191/r 1171/, 1151/r 1131/r 112 110 1 (I 1I.D. of Shell (in.) ’ Allowance made for Tie Rods. ’ R.O.B. = 2: x Tube Dia. Actual Number of “U” Tubes is one-half the above figures. ‘A 3/4 in. tube has 0.1963 sqft/ft, a 1 in. OD has 0.2618 sqft/ft. Allowance made for tie rods. b R.O.B. = 2: x tube dia. Actual number of “U” tubes is one-half the above figures.
- 223. 204 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.10 Use 16 ft tubes on la in. square pitch, two pass, 33 in. shell Process Design of a Shell-and-Tube Heat Exchanger An oil at the rate of 490,000 lb/hr is to be heated from 100 to 170°F with 145,000 Ib/hr of kerosene initially at 390°F. Physical properties L/D = 16/(33/12) = 5.82, are Oil 0.85spgr.3.5cP at 135°F. 0.49spht Kerosene 0.82 sp gr, 0.4 CP at 2Oo"F, 0.61 sp ht oil, 100 F 490000 pph 170F * kerosene 2WF 145000 pph Kerosene outlet: T = 390 - (490,000/145,000)(0.49/0.61)(170 - 100) = 2OO”F, LMTD = (220 - lOO)/ln 2.2 = 152.2, P = (170 - 100)/(390 - 100) = 0.241, R = (390 - 200)/(170 - 100) = 2.71. From Figure 8.5(a), F = 0.88, so a 1-2 exchanger is satisfactory: AT = 152.2(0.88) = 133.9. From Table 8.6, with average values for medium and heavy organics, U = 104/(57 + 16 + 50 + 34) = 63.7, Q = 490,000(0.49)(170 - 100) = 1.681(10’) Btu 1 hr, A = Q/lJAT = 1.681(10’)/63.7(133.9) = 197Osqft, 1970/0.2618 = 7524.8 ft of 1 in. OD tubing. Use 1: in. pitch, two tube pass. From Table 8.13, D,he,, (number of tubes) Required L (ft) N o . T u b e s Triangular S q u a r e a 940 12 627 35(608) 37E4) :: 470 376 which is near standard practice. The 20 ft length also is acceptable but will not be taken. The pressure drops on the tube and shell sides are to be calculated. Tube side: 0.875in. ID, 230 tubes, 32ft long: Take one velocity head per inlet or outlet, for a total of 4, in addition to friction in the tubes. The oil is the larger flow so it will be placed in the tubes. ti = 490,000/230 = 2130.4 lb/(hr)(tube). Use formulas from Table 6.1 Re = 6.314(2130.4)/0.875(3.5) = 4392, f = 1.6364/[ln(5(10-‘)/0.875 + 6.5/4392)]’ = 0.0385, APf= 5.385(10-8)(2130)‘(32)(0.0385)/0.85(0.875)s = 0.691 psi. Expansion and contraction: AP, = 4p(u2/2q,) = 4(53.04)(3.26)‘/(64.4)(144) = 0.243 psi, :. APtube = 0.691 + 0.243 = 0.934 psi. Shellside. Follow Example 8.8: D,, = 1.2732(1.25/12)‘/(1/12) - l/12 = 0.0824 ft, B = 1.25 ft between baffles, E = 0.25/12 ft between tubes, D, = 33/12 = 2.75 ft shell diameter, A, = 2.75(1.25)(0.25/12)/(1.25/12) = 0.6875 sqft, G, = 145,000/0.6875 = 210,909 lb/(hr)(sqft), Re = 0.0824(210,909)/0.4(2.42) = 17,952, f = 0.0121(17,952)-“.‘9 = 0.00188, AP,,,,, - - O.oO188(21O,9O9)‘(2.75)(13)/5.22(1O’o)(O.82)(O.O824) = 0.85 psi. The pressure drops on each side are acceptable. Now it remains to check the heat transfer with the equations of Table 8.10 and the fouling factors of Table 8.6. CONDENSER CONFIGURATIONS The several possible condenser configurations will be described. They are shown on Figure 8.14. Condensation Inside Tubes: Vertical DownJlow. Tube dia- meters normally are 19-25 mm, and up to 50 mm to minimize critical pressure drops. The tubes remain wetted with condensate which assists in retaining light soluble components of the vapor. Venting of noncondensables is positive. At low operating pressures, larger tubes may be required to minimize pressure drop; this may have the effect of substantially increasing the required heat transfer surface. A disadvantage exists with this configuration when the coolant is fouling since the shell side is more difficult to clean. Condensation Inside Tubes: Vertical Upflow. This mode is used primarily for refluxing purposes when return of a hot condensate is required. Such units usually function as partial condensers, with the lighter components passing on through. Reflux condensers usually are no more than 6-loft long with tube diameters of 25 mm or more. A possible disadvantage is the likelihood of flooding with condensate at the lower ends of the tubes. Condensation Outside Vertical Tubes. This arrangement requires careful distribution of coolant to each tube, and requires a sump and a pump for return to a cooling tower or other source of coolant. Advantages are the high coolant side heat transfer
- 224. 8.8. CONDENSERS 205 Tubesheet “ent 1 Water in Packed head vapor vent T Pl % b. r cl vapor ---) 1 Baffle plate -reparator Packed head x Slip-on flange with split rinq Condensate 1 Special water Alternate head Condensate Condenwtc (a) (b) vapor vapor vent plate Water distributor I designs Irain hole Water in Baffle rotated 90” (d) Condensate Split ring Figure 8.14. Some arrangements of shell-and-tube condensers. (a) Condensate inside tubes, vertical upflow. (b) Inside tubes, vertical downflow. (c) Outside tubes, vertical downflow. (d) Condensate outside horizontal tubes. (HEDH, 1983, 3.4.3). coefficient and the ease of cleaning. The free draining of condensate is a disadvantage with wide range mixtures. Condensation Inside Horizontal Tubes. This mode is employed chiefly in air coolers where it is the only feasible mode. As condensation proceeds, liquid tends to build up in the tubes, then slugging and oscillating flow can occur. Condensation Outside Horizontal Tubes. Figure 8.14(d) shows a condenser with two tube passes and a shell side provided with vertically cut baffles that promote side to side flow of vapor. The tubes may be controlled partially flooded to ensure desired subcooling of the condensate or for control of upstream pressure by regulating the rate of condensation. Low-fin tubes often are advantageous, except when the surface tension of the condensates exceeds about 40dyn/cm in which event the fins fill up with stagnant liquid. The free draining characteristic of the outsides of the tubes is a disadvantage with wide condensing range mixtures, as mentioned. Other disadvantages are those generally associated with shell side fluids, namely at high pressures or high temperatures or corrosiveness. To counteract such factors, there is ease of cleaning if the coolant is corrosive or fouling. Many cooling waters are scale forming; thus they are preferably placed on the tube side. On balance, the advantages often outweigh the disadvantages and this type of condenser is the most widely used. DESIGN CALCULATION METHOD Data for condensation are described in Section 8.4 and given in Tables 8.4-8.7, and a few additional overall coefficients are in Table
- 225. 206 HEAT TRANSFER AND HEAT EXCHANGERS Interface PI 9T, E = 3 d - Figure 8.15. Model for partial condensation in the presence of uncondensed material: U( ?; - FL) = hg( T, - T) + n/c&, - p,). [A.P. Colburn and O.A. Hougen, Ind. Eng. Chem. 26, 1178-1182 (1934)J 8.12. The calculation of condensation of pure vapors is straight- forward. That of mixtures occurs over a range of temperatures and involves mass transfer resistance through a gas film as well as heat transfer resistance by liquid and fouling films. A model due to Colburn and Hougen (1934) is represented by Figure 8.15. The overall rate of heat transfer is regarded as the sum of the sensible heat transfer through a gas film and the heat of condensation of the material transferred by diffusion from the gas phase to the interface. The equation of this heat balance is, in terms of the notation of Figure 8.15, U(T - TJ =h,(T, - I;) + Ik,(p, -p,). The temperature I” of the coolant is related to the heat transfer Q by dQ = r&C, dT, or the integrated form TL = TLO + AQ/ti,C,. (8.38) A procedure will be described for taking the vapor from its initial dewpoint T,,, to its final dewpoint corresponding to the required amount of condensation. Gas temperatures are specified at intermediate points and the heat balance is applied over one interval at a time. 1. Prepare the condensing curve, a plot of the vapor temperature T, against the amount of heat removed Q, by a series of isothermal flashes and enthalpy balances. 2. Starting at the inlet temperature T,,, specify a temperature Tg a few degrees less, and note the heat transfer AQ corresponding to this temperature difference from the condensing curve. 3. Find the temperature T, of the coolant with Eq. (8.38). 4. Assume an interfacial temperature K, then find the correspond- ing vapor pressure pi and latent heat 1. 5. From available correlations, find values of the coefficients h,, kg, and U which are temperature- and composition-dependent, although they sometimes may be taken as constant over some ranges. The basis of the method was stated by Silver (1947). A numerical solution of a condenser for mixed hydrocarbons was carried out by Webb and McNaught (in Chisholm, 1980, p. 98); comparison of the Silver-Bell-Ghaly result with a Colburn- Hougen calculation showed close agreement in this case. Bell and Ghaly (1973) claim only that their method predicts values from 0 to 100% over the correct values, always conservative. A solution with constant heat transfer coefficients is made in Example 8.11: A recent review of the subject has been presented by McNaught (in Taborek et al., 1983, p. 35). 8.9. REBOILERS 6. Check if these values satisfy the heat balance of Eq. (8.37). If Reboilers are heat exchangers that are used primarily to provide not, repeat the process with other estimates of T until one is boilup for distillation and similar towers. All types perform partial found that does satisfy the heat balance. vaporization of a stream flowing under natural or forced circulation 7. Continue with other specifications of the vapor temperature q, one interval at a time, until the required outlet temperature is reached. 8. The heat transfer area will be found by numerical integration of (8.39) Examples of numerical applications of this method are in the original paper of Colburn and Hougen (1934), in the book of Kern (1950, p. 346) and in the book of Ludwig (1983, Vol. 3, p. 116). The Silver-Bell-Ghaly Method This method takes advantage of the rough proportionality between heat and mass transfer coefficients according to the Chilton- Colburn analogy, and employs only heat transfer coefficients for the process of condensation from a mixture. The sensible heat Q, of the vapor is transferred through the gas film dQ, = h& - ZJ dA. (8.40) In terms of an overall heat transfer coefficient U that does not include the gas film, the total heat transfer QT that is made up of the latent heat and the sensible heats of both vapor and liquid is represented by dQ7 = U(I; - TL) dA. (8.41) When the unknown interfacial temperature K is eliminated and the ratio Z of sensible and total heat transfers Z = dQ, IdQ, is introduced, the result is (8.42) which is solved for the heat transfer area as (8.44) Since the heat ratio Z, the temperatures and the heat transfer coefficients vary with the amount of heat transfer QT up to a position in the condenser, integration must be done numerically. The coolant temperature is evaluated from Eq. (8.38). Bell and Ghaly (1973) examine cases with multiple tube passes.
- 226. 8 . 9 . REBOILERS 2 0 7 EXAMPLE 8.11 Sizing a Condenser for a Mixture by the Silver-Bell-Ghatly Method shown the average gas temperature, the value of Z, and the value of the integrand of Eq. (8.44). The integrand is plotted following. A mixture with initial dewpoint 139.9”C and final bubblepoint Interval 1 2 3 4 5 48.4”C is to be condensed with coolant at a constant temperature of 27°C. The gas film heat transfer coefficient is 40 W/m’ K and the (T,)m 130.75 112.45 94.15 75.85 57.4 z 0.1708 0.1613 0.1303 0.0814 0.0261 overall coefficient is 450. Results of the calculation of the lntegrandx (lo? 6.26 7.32 8.31 8.71 9.41 condensing curve are The heat transfer surface is the area under the stepped curve, which T("C) 139.9 121.6 103.3 85.0 66.7 48.4 is a = 0.454 m2. A solution that takes into account the substantial Q (W) 0 2154 3403 4325 5153 5995 variation of the heat transfer coefficients along the condenser gives the result A = 0.385 mz (Webb and McNaught, in Chisholm, 1980, In the following tabulation, over each temperature interval are p. 98). 10 / / / / / 6 I I I 0 2000 4000 6000 C l - conditions. Sketches of a kettle and two types of thermosiphon reboilers are in Figure 8.4. Internal reboilers, with a tube bundle built into the tower bottom, also have some application. Flow through a vertical unit like that of Figure 8.4(f) may be forced with a pump in order to improve heat transfer of viscous or fouling materials, or when the vaporization is too low to provide enough static head difference, or when the tower skirt height is too low. A summary guide to the several types of reboilers is in Table 8.14. KElTLE REBOILERS Kettle reboilers consist of a bundle of tubes in an oversize shell. Submergence of the tubes is assured by an overflow weir, typically 5-15cm higher than the topmost tubes. An open tube bundle is preferred, with pitch to diameter ratios in the range of 1.5-2. Temperature in the kettle is substantially uniform. Residence time is high so that kettles are not favored for thermally sensitive materials. The large shell diameters make kettles uneconomic for high pressure operation. Deentraining mesh pads often are incorporated. Tube bundles installed directly in the tower bottom are inexpensive but the amount of surface that can be installed is limited. HORIZONTAL SHELL SIDE THERMOSIPHONS The fraction vaporized in thermosiphon reboilers usually can be made less than in kettles, and the holdup is much less. Less static head difference is needed as driving force for recirculation in comparison with vertical units. Circulation rate can be controlled by throttling the inlet line. Because of the forced flow, there is a temperature gradient, from the inlet bubblepoint to the exit bubblepoint, whereas in a kettle the boiling temperature is more nearly uniform, at the exit bubblepoint. Consequently, for the same percentage vaporization, the mean temperature difference between shell and tube sides will be greater for thermosiphons than for kettles. Or for the same mean temperature difference, the per- centage vaporization can be made less. Large surface require- ments favor horizontal over vertical thermosiphons. Horizontal tube bundles are easier to maintain. The usual arguments for tube side versus shell side also are applicable. VERTICAL THERMOSIPHONS Circulation is promoted by the difference in static heads of supply liquid and the column of partially vaporized material. The exit
- 227. 208 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.14. A Guide to the Selection of Reboilers Reboiler Type Process Conditions Kettle or Internal Horizontal Vertical Shell-Side Tube-Side T h e r m o s i p h o n T h e r m o s i p h o n Forcad F l o w Operating pressure Moderate Near critical Deep vacuum Design AT Moderate Large Small (mixture) Very small (pure component) Fouling Clean Moderate H e a v y Very heavy Mixture boiling range Pure component N a r r o w W i d e Very wide, with viscous liquid E B-E B G Rd P P G G F G R R G R F F G G Rd P G G G B Rd Rd B G - R d Rd P G B B Rd G B B E E E F-P G - R d P B a Category abbreviations: B, best; G, good operation; F, fair operation, but better choice is possible; Rd. risky unless carefully designed, but could be best choice in some cases; R, risky because of insufficient data; P, poor operation; E, operable but unnecessarily expensive. (HEDH, 1983, 3.6.1). weight fraction vaporized should be in the range of 0.1-0.35 for hydrocarbons and 0.02-0.10 for aqueous solutions. Circulation may be controlled with a valve in the supply line. The top tube sheet often is placed at the level of the liquid in the tower. The flow area of the outlet piping commonly is made the same as that of all the tubes. Tube diameters of 19-25 mm diameter are used, lengths up to 12ft or so, but some 20ft tubes are used. Greater tube lengths make for less ground space but necessitate taller tower skirts. Maximum heat fluxes are lower than in kettle reboilers. Because of boiling point elevations imposed by static head, vertical thermosiphons are not suitable for low temperature difference serv- ices. Shell side vertical thermosiphons sometimes are applied when the heating medium cannot be placed on the shell side. FORCED CIRCULATION REBOILERS Forced circulation reboilers may be either horizontal or vertical. Since the feed liquid is at its bubblepoint, adequate NPSH must be assured for the pump if it is a centrifugal type. Linear velocities in the tubes of 1%20ft/sec usually are adequate. The main disadvantages are the costs of pump and power, and possibly severe maintenance. This mode of operation is a last resort with viscous or fouling materials, or when the fraction vaporized must be kept low. CALCULATION PROCEDURES Equations for boiling heat transfer coefficients and maximum heat fluxes are Eqs. (37) through (48) of Table 8.10. Estimating values are in Tables 8.4-8.7. Roughly, boiling coefficients for organics are 300 Btu/(hr)(sqft)(“F), or 1700 W/m2 K; and for aqueous solutions, 1000 Btu/(hr)(sqft)(“F), or 5700 W/m2 K. Similarly, maximum fluxes are of the order of 20,000 Btu/(hr)(sqft), or 63,000 W/m*, for organics; and 35,000 Btu/(hr)(sqft) or 110,000 W/m*, for aqueous systems. The design procedure must start with a specific geometry and heat transfer surface and a specific percentage vaporization. Then the heat transfer coefficient is found, and finally the required area is calculated. When the agreement between the assumed and calculated surfaces is not close enough, the procedure is repeated with another assumed design. The calculations are long and tedious and nowadays are done by computer. Example 8.12 summarizes the results of such calculations made on the basis of data in Heat Exchanger Design Handbook (1983). Procedures for the design of kettle, thermosiphon and forced circulation reboilers also are outlined by Polley (in Chisholm, 1980, Chap. 3). 8.10. EVAPORATORS Evaporators employ heat to concentrate solutions or to recover dissolved solids by precipitating them from saturated solutions. They are reboilers with special provisions for separating liquid and vapor phases and for removal of solids when they are precipitated or crystallized out. Simple kettle-type reboilers [Fig. 8.4(d)] may be adequate in some applications, especially if enough freeboard is provided. Some of the many specialized types of evaporators that are in use are represented on Figure 8.16. The tubes may be horizontal or vertical, long or short; the liquid may be outside or inside the tubes, circulation may be natural or forced with pumps or propellers. Natural circulation evaporators [Figs. 18.16(a)-(e)] are the most popular. The forced circulation type of Figure 18.16(f) is most versatile, for viscous and fouling services especially, but also the most expensive to buy and maintain. In the long tube vertical design, Figure 816(d), because of vaporization the liquid is in annular or film flow for a substantial portion of the tube length, and accordingly is called a rising film evaporator. In falling film
- 228. 8 . 1 0 . E V A P O R A T O R S 209 EXAMPLE 8.12 Comparison of Three Kinds of Reboilers for the Same Service The service is reboiling a medium boiling range hydrocarbon mixture at 10 atm with a duty of 14,600 kW. The designs are calculated in HEDH (1983, 3.65) and are summarized here. In each case a specific geometry and surface are assumed; then the heat transfer coefficients are evaluated, and the area is checked. When agreement between assumed and calculated areas is not close, another design is assumed and checked. Of the three sets of calculations summarized here, only that for the kettle need not be repeated. Both the others should be repeated since the assumed designs are too conservative to be economical. 160 C, 30% vap. 19oc 64 19oc 1 4 o c 165C Quantity Rated area (rn’) Tube length (m) T u b e O D (mm) Tube ID (mm) Vaporization (%) U (W/m2 K) (AT),,, Calculated area (rn’) Calculated 4 (W/m’) ilme, W/mZ) 15oc 25% vap -+- 190 c 19oc 1 4 o c Kettle reboiler Horizontal Vertical thermosiphon thermosiphon evaporators, liquid is distributed to the tops of the individual tubes and flows down as a film. The hydrostatic head is eliminated, the pressure drop is little more than the friction of the vapor flow, and heat transfer is excellent. Since the contact time is short and separation of liquid and vapor is virtually complete, falling film evaporation is suitable for thermally sensitive materials. Long tube vertical evaporators, with either natural or forced circulation are the most widely used. Tubes range from 19 to 63 mm (a) Kettle Horizontal TS Vertical TS 930 930 480 6.1 6.1 4 . 9 19 19 - - - 2 1 . 2 3 0 2 5 2 5 874 674 928 2 5 4 4 . 8 4 4 . 8 866 483 350 1 6 , 8 5 9 30,227 41,174 - - 67,760 150 c diameter, and 12-30ft in length. The calandria of Figure 8.16(b) has tubes 3-5 ft long, and the central downtake has an area about equal to the cross section of the tubes. Sometimes circulation in calandrias is forced with built in propellors. In some types of evaporators, the solids are recirculated until they reach a desired size. In Figure 8.16(f), fresh feed is mixed with the circulating slurry. In Figure 8.16(g) only the clear liquid is recirculated, and small more nearly uniform crystals are formed. kd Mot/k stem77 Figure 8.16. Some types of evaporators. (a) Horizontal tube. (b) Calandria type. (c) Thermocompressor evaporator. (d) Long tube vertical. (e) Falling film. (f) Forced circulation evaporator-crystallizer. (g) Three types of “Oslo/Krystal” circulating liquid evaporator-crystallizers.
- 229. 210 HEAT TRANSFER AND HEAT EXCHANGERS Noncondensoble qm outlet Feed id) J L 1 Product (e) P’Pe P--&CL- Body Swrl breaker Feed Inlet Mother llqua Cnculatlon I Evqmotor crystallmr Va‘“um ‘lxhg crystal llzer (9) Figure 8.1~(continued) THERMAL ECONOMY Thermal economy is a major consideration in the design and operation of evaporators. This is improved by operating several vessels in series at successively lower pressures and utilizing vapors from upstream units to reboil the contents of downstream units. Figure 8.17 shows such arrangements. Thermal economy is ex- pressed as a ratio of the amount of water evaporated in the complete unit to the amount of external steam that is supplied. For a single effect, the thermal economy is about 0.8, for two effects it is 1.6, for three effects it is 2.4, and so on. Minimum cost usually is obtained with eight or more effects. When high pressure steam is available, the pressure of the vapor can be boosted with a steam jet compressor [Fig. 8.16(c)] to a usable value; in this way savings of one-half to two-thirds in the amount of external steam can be achieved. Jet compressor thermal efficiencies are 20-30%. A possible drawback is the contamination of condensate with entrainment from the evaporator. When electricity is affordable, the pressure of the vapor can be boosted mechanically, in compressors with efficiencies of 70-75%. Because of the elevation of boiling point by dissolved solids, the difference in temperatures of saturated vapor and boiling solution may be 3-10°F which reduces the driving force available for heat transfer. In backward feed [Fig. 8.17(b)] the more concentrated solution is heated with steam at higher pressure which makes for lesser heating surface requirements. Forward feed under the influence of pressure differences in the several vessels requires more surface but avoids the complications of operating pumps under severe conditions. Several comprehensive examples of heat balances and surface
- 230. (a) (b) Figure 8.17. Forward and backward of liquid flow with respect to steam flow in triple-effect evaporators. (a) Forward flow of liquid by action of pressure differences in the vessels. (b) Backward-pumped flow of liquid through the vessels. requirements of multiple effect evaporation are worked out by Kern (1950). SURFACE REQUIREMENTS 0.4 ; 2 0 0 P $ 1 0 0 F 1 0 0 1 2 0 140 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 0 Boiling temperature. OF The data of Tables 8.4-8.7 and particularly 8.10 for boiling liquids are applicable to evaporators when due regard is given the more severe fouling that can occur. For example, cases have been cited in which fouling presents fully half the resistance to heat transfer in evaporators. Some heat transfer data specifically for evaporators are in Figure 8.18. Forced circulation and falling film evaporators have the higher coefficients, and the popular long tube vertical, some- what poorer performance. Figure 8.18. Overall heat transfer coefficients in some types of evaporations. (a) Water and sugar juice evaporators; (b) Sea water evaporators. [F.C. Standiford, Chem. Eng., 157-176 (9 Dec. 1963)J With such data, an estimate can be made of a possible evaporator configuration for a required duty, that is, the diameter, length, and number of tubes can be specified. Then heat transfer correlations can be applied for this geometry and the surface recalculated. Comparison of the estimated and calculated surfaces will establish if another geometry must be estimated and checked. This procedure is described in Example 8.12. about 3500°F. Specific data are cited by Hougen, Watson, and Ragatz (Chemical Process Principles, Vol. I, Wiley, New York, 1954, p. 409) and in Marks Mechanicat Engineers Handbook, (1978, p. 4.57). With excess air to ensure complete combustion the temperatures are lower, but still adequate for the attainment of process temperatures above 2000°F when necessary. Lower temper- atures are obtained with heat transfer media such as those of Table 8.2 which are in turn serviced in direct-fired heaters. 8.11. FIRED HEATERS DESCRIPTION OF EQUIPMENT High process temperatures are obtained by direct transfer of heat from the products of combustion of fuels. Maximum Aame temperatures of hydrocarbons burned with stoichiometric air are In fired heaters and furnaces, heat is released by combustion of fuels into an open space and transferred to fluids inside tubes which are ranged along the walls and roof of the combustion chamber. 8.11. FIRED HEATERS 211 I r I Water at 20’:. AT - - - S u g a r juice evoporotors under comparable I, / ,, (a) 120 140 160 180 200 2 2 0 2 4 0 Boilhng temperature, “F
- 231. 212 HEAT TRANSFER AND HEAT EXCHANGERS The heat is transferred by direct radiation and convection and also by reflection from refractory walls lining the chamber. Three zones are identified in a typical heater such as that of Figure 8.19(a). In the radiant zone, heat transfer is predominantly (about 90%) by radiation. The convecfion zone is “out of sight” of the burners; although some transfer occurs by radiation because the temperature still is high enough, most of the transfer here is by convection. The application of extended surfaces permits attainment of heat fluxes per unit of bare surface comparable to those in the radiant zone. Shield section is the name given to the first two rows or so leading into the convection section. On balance these tubes receive approximately the same heat flux as the radiant 5 0 0 0 0 0 0 0 0 0 0 0 0 - Radiant tubes z I0 0 0 Firebox 0 0 Radiant section (a) tubes because the higher convection transfer counteracts the lesser radiation due to lack of refractory wall backing. Accordingly, shield tubes are never finned. The usual temperature of flue gas entering the shield section is 1300-1650°F and should be 200-300°F above the process temperature at this point. The proportions of heat transferred in the radiant and convection zones can be regulated by recirculation of hot flue gases into the radiant zone, as sketched on Figure 8.19(b). Such an operation is desirable in the thermal cracking of hydrocarbons, for instance, to maintain a proper temperature profile; a negative gradient may cause condensation of polymeric products that make coke on the tubes. Multiple chambers as in M Figure 8.19. Some types of process fired heaters (See also Fig. 17.16 for a radiation panel heater). (a) Radiant, shield, and convection sections of a box-type heater. (b) Heater with a split convection section for preheating before and soaking after the radiant section (Lobe and Evans, 1939). (c) Vertical radiant tubes in a cylindrical shell. (d) Two radiant chambers with a common convection section.
- 232. Figure 8.19(d) also provide some flexibility. In many operations, about 75% of the heat is absorbed in the radiant zone of a fired heater. Horizontal tube supports are made of refractory steel to withstand the high temperatures. Hangers for vertical tubes make for a less expensive construction per unit of tube surface. Furnaces are lined with shaped light weight refractory brick 5-8 in. thick. A 1 in. layer of insulating brick is placed between the lining and the metal shell. Differences of opinion exist among designers with respect to housing shapes and tube arrangements. Nelson (Petroleum Refinery Engineering, McGraw-Hill, New York, 1958, p. 587), for example, describes a dozen types. The most common are cylindrical shells with vertical tubes and cabin or box types with horizontal tubes. Figures 8.19 and 17.16 are of typical constructions. Convection zones are most commonly at the top. Process fluid goes first through the convection section and usually leaves the radiant tubes at the top, particularly when vaporization occurs in them. In the more complex flow pattern of Figure 8.19(b), some of the convection tubes are used for preheat and the remainder to maintain the process fluid at a suitable reaction temperature that was attained in the radiant tubes. Some of the convection zone also may be used for steam generation or superheating or for other heat recovery services in the plant. Capacities of lo-200 MBtu/hr can be accommodated in heaters with single radiant chambers, and three to four chambers with a common convection section are feasible. Stoichiometric combustion air requirements of typical fuels are tabulated: Fuel Methane Propane Light fuel oil Heavy fuel oil Anthracite L H V (Btu/lb) 2 1 , 5 0 0 1 9 , 9 2 0 1 7 , 6 8 0 1 7 , 4 2 0 1 2 , 5 0 0 Combustion Air lb/lb lb/1000 Btu 17.2 0 . 8 0 0 15.2 0 . 7 6 3 14.0 0 . 7 9 2 13.8 0 . 7 9 2 4 . 5 0 . 3 6 0 Burners may be located in the floor or on the ends of the heaters. Liquid fuels are atomized with steam or air or mechanically. A particularly effective heater design is equipped with radiant panel (surface combustion) burners, illustrated in Figure 17.16(a), (b). The incandescent walls are located 2-3ft from the tubes. The furnace side of the panel may reach 2200°F whereas the outer side remains at 120°F because of continual cooling by the air-gas mixture. Radiant panel burners require only 2-S% excess 8.11. FIRED HEATERS 213 air compared with lo-20% for conventional burners. Heaters equipped with radiant panels cost more but provide better control of temperatures of reactions such as pyrolysis of hydrocarbons to ethylene for instance. Distances between tube banks are of the order of 20 ft or so. A rough guide to box size is about 4cuft/sqft of radiant transfer surface, but the ultimate criterion is sufficient space to avoid impingement of flames on the tubes. Some additional notes on dimensions are stated with the design procedure of Table 8.18. Tubes are mounted approximately one tube diameter from the refractory walls. Usual center-to-center spacing is twice the outside tube diameter. Wider spacings may be employed to lower the ratio of peak flux at the front of the tube to the average flux. For single rows of tubes, some values of these ratios are Center-to-center/diameter 1 1.5 2 2.5 3 Max flux/avg flux 3.1 2.2 1.8 1.5 1.2 Less is gained by extending the ratio beyond 2.0. Excessive fluxes may damage the metal or result in skin temperatures that are harmful to the process fluid. A second row of tubes on triangular spacing contributes only about 25% of the heat transfer of the front row. Accordingly, new furnaces employ only the more economical one-row construction. Second rows sometimes are justifiable on revamp of existing equipment to marginally greater duty. HEAT TRANSFER Performance of a heater is characterized by the average heat flux in the radiant zone and the overall thermal efficiency. Heat fluxes of representative processes are listed in Table 8.15. Higher fluxes make for a less expensive heater but can generate high skin temperatures inside and out. Thermal sensitivity of the process fluid, the strength of the metal and its resistance to corrosion at elevated temperatures are factors to be taken into account in limiting the peak flux. Because of the refractory nature of water, however, allowable fluxes in steam boilers may reach 130,OOOBtu/ (hr)(sqft), in comparison with a maximum of about 20,000 in hydro- carbon service. Example 8.13 is a study of the effect of tube spacing on inside film peak temperatures. A certain amount of excess air is needed to ensure complete combustion. Typical minimum excess requirements are 10% for gaseous fuels and 15-20% for liquids. Radiant panel burners may get by with 2-5% excess air. Efficiency is the ratio of total heat absorbed in radiant, TABLE 8.15. Typical Radiant Fluxes and Process Temperatures Service Avera a Radiant Rate (&u/hr/ftz) (Based on OD) Temyegture 0 Atmospheric crude heaters 10.000-14.000 Reboilers 10,000-12,000 Circulating oil heaters 8000-l 1,000 Catalytic reformer change and reheat 7500-l 2,000 Delayed coking heater 10.000-11,000 Visbreaker heaters-heating section 9000-l 0,000 Soaking section 6000-7000 Lube vacuum heaters 7500-8500 Hydrotreater and hydrocracker charge heaters 1 0 , 0 0 0 Catalytic-cracker feed heaters 10,000-11,000 Steam superheaters 9000-l 3,000 Natural gasoline plant heaters 1 o,ooo- 12,000 Ethylene and propylene synthesis 10,000-15,000 400-700 400-550 600 800-1000 925 700-950 950 850 700-850 900-1050 700-l 500 - 1300-1650
- 233. 214 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE&W Peak Temperatures tube spacings the peak temperatures are: An average flux rate is 12,OOOBtu/(hr)(sqft) and the inside film Center-to-center/diameter 1 1.5 2 2.5 3 coefficient is 2OOBtu/(hr)(sqft)(“F). At the position where the Peak (“F) 1036 982 9 5 8 9 4 8 9.22 average process temperature is 850”F, the peak inside film For heavy liquid hydrocarbons the upper limit of 950°F often is temperature is given by T = 850+ 12,000”R/200. At the several adopted. convection, and heat recovery sections of the heater to the heat released by combustion. The released heat is based on the lower heating value of the fuel and ambient temperature. With standard burners, efficiencies may be in the range 6t-80%; with radiant panels, 80-82%. Within broad limits, any specified efficiency can be attained by controlling excess air and the extent of recovery of waste heat. An economical apportionment of heat absorption between the radiant and convection zones is about 75% in the radiant zone. This can be controlled in part by recirculation of flue gases into the radiant chamber, as shown in Figure 8.19(b). Because of practical limitations on numbers and possible locations of burners and because of variations in process temperatures, the distribution of radiant flux in a combustion chamber is not uniform. In many cases, the effect of such nonuniformity is not important, but for sensitive and chemically reacting systems it may need to be taken into account. A method of estimating quickly a flux distribution in a heater of known configuration is illustrated by Nelson (1958, p. 610). A desired pattern can be achieved best in a long narrow heater with a multiplicity of burners, as on Figure 17.16 for instance, or with a multiplicity of chambers. A procedure for design of a plug flow heater is outlined in the Heat Exchanger Design Handbook (1983, 3.11.5). For most practical purposes, however, it is adequate to assume that the gas temperature and the heat flux are constant throughout the radiant chamber. Since the heat transfer is predominantly radiative and varies with the fourth power of the absolute temperature, the effect of even substantial variation in stock temperature on flux distribution is not significant. Example 8.14 studies this problem. DESIGN OF FIRED HEATERS The design and rating of a fired heater is a moderately complex operation. Here only the completely mixed model will be treated. For this reason and because of other generalizations, the method to be described affords only an approximation of equipment size and performance. Just what the accuracy is, it is hard to say. Even the relatively elaborate method of Lobo and Evans (1939) is able to predict actual performance only within a maximum deviation of 16%. EXAMPLE 8.14 Effect of Stock Temperature Variation A combustion chamber is at 2260”R. a stock enters at 106O”R and leaves at 136O”R. Accordingly, the heat fluxes at the inlet and outlet are approximately in the ratio (2.264 - 1.064)/2.264 - 1.364) = 1.095. The small effect of even greater variation in flux on a mild cracking operation is illustrated in Figure 8.22. Pertinent equations and other relations are summarized in Table 8.16, and a detailed stepwise procedure is listed in Table 8.17. A specific case is worked out in detail in Example 8.15. Basically, a heater configuration and size and some aspects of the performance are assumed in advance. Then calculations are made of the heat transfer that can be realized in such equipment. Adjustments to the design are made as needed and the process calculations repeated. Details are given in the introduction to Example 8.16. Figures 8.20, 8.21, and 8.22 pertain to this example. Some of the approximations used here were developed by Wimpress (1963); his graphs were converted to equation form for convenience. Background and more accurate methods are treated notably by Lobo and Evans (1939) and more briefly by Kern (1950) and Ganapathy (1982). Charts of gas emissivity more elaborate than Figure 8.23 appear in these references. An early relation between the heat absorption Q in a radiant zone of a heater, the heat release Q,, the effective surface A, and the air/fuel ratio R lb/lb is due to Wilson, Lobo, and Hottel [Znd. Eng. Chem. 24, 486, (1932)]: Q,/Q = l+ (R/Q~)~. (8.45) Although it is a great simplification, this equation has some utility in appraising directional effects of changes in the variables. Example 8.16 considers changes in performance with changes in excess air. Heat transfer in the radiant zone of a fired heater occurs largely by radiation from the flue gas (90% or so) but also significantly by convection. The combined effect is represented by Q/A = W’; - T:) + h,(T, - T,), (8.46) where Tg and T, are absolute temperatures of the gas and the receiving surface. The radiative properties of a gas depend on its chemical nature, its concentration, and the temperature. In the thermal range, radiation of flue gas is significant only from the triatomic molecules H,O, CO,, and SO,, although the amount of the last is small and usually neglected. With fuels having the composition C,H,, the ratio of partial pressures is p&pco, = 1. In Figure 8.23, the emissivity of such a gas is represented as a function of temperature and the product PL of the partial pressures of water and carbon dioxide and the path of travel defined by the mean beam length. Item 8 of Table 8.16 is a curve fit of such data. When other pertinent factors are included and an approxima- tion is introduced for the relatively minor convection term, the heat transfer equation may be written Q/aA,F = 1730[(T,/1000)4 - (T,/1000)4] + 7(T, - T,). (8.47) Here the absorptivity depends on the spacing of the tubes and is given by item 5 of Table 8.16. The cold plane area A, is the product of the number of tubes by their lengths and by the center-to-center spacing. The combination cuA, is equal to the area of an ideal black plane that has the same absorptivity as the tube
- 234. 3 . 1 1 . F I R E D H E A T E R S 215 TABLE 8.16. Equations and Other Relations for Fired Heater Design 1. Radiant zone heat transfer 2. Radiant zone heat balance $F=!&F ,+s+---A i 4 QL Q R R 4 4 4 4 1 Q, is the enthalpy absorbed in the radiant zone, 0, is the enthalpy of the entering air, Qr that of the entering fuel, Q, is the enthalpy loss to the surroundings, Q, is the enthalpy of the gas leaving the radiant zone; Qa and Q, are neglected if there is no preheat, and 0,/Q” is about 0.02-0.03; Q,, is the total enthalpy released in the furnace 3. Enthalpy 4, of the stack gas, given by the overall heat balance Qs/Qn = 1 + (l/Qn)(Qe + a, - 0, - 0, - QCO”“ectio” ) 4. Enthalpy Q,, of the flue gas as a function of temperature, “F 0,/Q” = [a+ b(T/lOOO-0.1)1(T/1000-0.1) z= fraction excess air a = 0.22048 - 0.350272 + 0.92344z’ b = 0.016086 + 0.293932 - 048139z* 5. Absorptivity, (Y, of the tube surface with a single row of tubes (Y = 1 - (0.0277 + 0.0927(x - 1)1(x - 1) x= (center-to-center spacing)/(outside tube diameter) 6. Partial pressure of CO, + H,O P = 0.288 -0.229x + 0.090x2 x= fraction excess air 7. Mean beam lengths L of radiant chambers Dimensional Ratios Rectangular Furnaces Mean Length L (ft) 1. l-l-l to l-l-3 2/3 qfurnace volume, (ft3) l-2-1 to l-2-4 2. l-l-4 to l-l-co 1.0 x smallest dimension 3. l-2-5 to l-2-8 1.3 x smallest dimension 4. l-3-3 to 1-m-m 1.8 x smallest dimension Cylindrical Furnaces 5.dxd 2/3 diameter 6. dx2dtodxmd 1 x diameter s Length, width, height in any order. 8. Emissivity # of the gas (see also Fig. 8.20). @= a + b(N)+ c(PL)* PL = product of the partial pressure (6) and the mean beam length (7) z= (7-- +460)/1000 a = 0.47916 - 0.198472 + 0.022569z2 b=0.047029+0.0699z-0.01528z' c= 0.000803 - 0.00726~ + 0.001597z’ 9. Exchange factor F F=a+b$+c@' $ = gas emissivity, (8) z=AJmAR a=0.00064+0.059lz +0.0010lz* b= 1.0256+ 0.4908z- 0.058~~ c= -0.144 - 0.552.~ + 0.0402’
- 235. 216 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.184continued) 10. Overall heat transfer coefficient U, in the convection zone UC = (a + bG + ~G*)(4.5/dI~‘*~ G= flue gas flow rate, Ib/(sec)(sqft open cross section) d= tube outside diameter, (in.) z= Tr/lOOO, average outside film temperature a = 2.461 - 0.7592 + 1.6252’ b= 0.7655 + 21.3732 - 9.66252’ c = 9.7938 - 30.8092 + 14.3332* 11. Flue gas mass rate G, 106G,- 640 + 8.0x, with fuel oil 4 822 +7.78x, with fuel gas 1 Ib/MBtu heat release x= fraction excess air TABLE 8.17. Procedure for the Rating of a Fired Heater, Utilizing the Equations of Table 8.18 1. Choose a tube diameter corresponding to a cold oil velocity of 5-6 ft/sec 2. Find the ratio of center-to-center spacing to the outside tube diameter. Usually this is determined by the dimensions of available return bends, either short or long radius 3. Specify the desired thermal efficiency. This number may need modification after the corresponding numbers of tubes have been found 4. Specify the excess combustion air 5. Calculate the total heat absorbed, given the enthalpies of the inlet and outlet process streams and the heat of reaction 6. Calculate the corresponding heat release, (heat absorbed)/efficiency 7. Assume that 75% of the heat absorption occurs in the radiant zone. This may need to be modified later if the design is not entirely satisfactory 8. Specify the average radiant heat flux, which may be in the range of 8000- 20,00OBtu/(hr)(sqft). This value may need modification after the calculation of Step 28 h a s b e e n m a d e 9. Find the needed tube surface area from the heat absorbed and the radiant flux. When a process-side calculation has been made, the required number of tubes will be known and will not be recalculated as stated here 10. Take a distance of about 20ft between tube banks. A rough guide to furnace dimensions is a requirement of about 4cuft/sqft of radiant transfer surface, but the ultimate criterion is sufficient space to avoid flame impingement 11. Choose a tube length between 30 and 60ft or so, so as to make the box dimensions roughly comparable. The exposed length of the tube, and the inside length of the furnace shell, is 1.5 h shorter than the actual length 12. Select the number of shield tubes between the radiant and convection zones so that the mass velocity of the flue gas will be about 0.3-0.4 Ib/(sec)(sqft free cross section). Usually this will be also the number of convection tubes per row 13. The convection tubes usually are finned 14. The cold olane area is Am = (exposed tube length)(center-to-center spacing) (number of tubes exclusive of the shield tubes) 16. The refractory area 4, is the inside surface of the shell minus the cold plane area Acp of Step 14 &=2[W(H+L)+HxL)I-A,, where W, H, and L are the inside dimensions of the shell 16. The absorptivity n is obtained from Eq. (5) when only single rows of tubes are used. For the shield tubes, (Y = 1 17. The sum of the products of the areas and the absorptivities in the radiant zone is 4~ = 41ie1d + 4p 18. For the box-shaped shell, the mean beam length L is approximated by L = $(furnace volume)“3
- 236. 8.11. FIRED HEATERS 217 TABLE 8.17--(continued) 19. The partial pressure P of CO, + H,O is given in terms of the excess air by Eq. (6) 20. The product PL is found with the results of Steps 18 and 19 21. The mean tube wall temperature T in the radiant zone is given in terms of the inlet and outlet process stream temperatures by J = 100 + 0.5(T, + T2) 22. The temperature Tg of the gas leaving the radiant zone is found by combining the equations of the radiant zone heat transfer [Eq. (111 and the radiant zone heat balance IEq. (211. With the approximation usualty satisfactory, the equality is The solution of this equation involves other functions of T,, namely, the emissivity &J by Eq. (8). the exchange factor F by Eq. (9) and the exit enthalpy ratio C&/Q, by Eq. (4) 23. The four relations cited in Step 22 are solved simultaneously by trial to find the temperature of the gas. Usually it is in the range 1500-1800°F. The Newton-Raphson method is used in the program of Table 8.18. Alternately, the result can be obtained by interpolation of a series of hand calculations 24. After 7, has been found, calculate the heat absorbed Q, by Eq. (1) 25. Find the heat flux Q/A = Q~l4actiant and compare wit!1 value specified in Step 8. If there is too much disagreement, repeat the calculations with an adjusted radiant surface area 26. By heat balance over the convection zone, find the inlet and outlet temperatures of the process stream 27. The enthalpy of the flue gas is given as a function of temperature by Eq. (4). The temperature of the inlet to the convection zone was found in Step 23. The enthalpy of the stack gas is given by the heat balance [Eq. (3)], where all the terms on the right-hand side are known. 4/Q” is given as a function of the stack temperature T, by Eq. (4). That temperature is found from this equation by trial 28. The average temperature of the gas film in the convection zone is given in terms of the inlet and outlet temperatures of the process stream and the flue gas approximately by T=05 T +T + (T,,-T,,)-(T,-LA [ f . L1 LO Inl(T,, - TL,V(7i- TLoH 1 The flow is countercurrent 29. Choose the spacing of the convection tubes so that the mass velocity is G = 0.3-0.4 Ib/(sec)(sqft free cross section). Usually this spacing is the same as that of the shield tubes, but the value of G will not be the same if the tubes are finned 30. The overall heat transfer coefficient is found with Eq. (10) 31. The convection tube surface area is found by A, = QJU, (LMTD) and the total length of bare of finned tubes, as desired, by dividing A,by the effective area per foot 32. Procedures for finding the pressure drop on the flue gas side, the draft requirements and other aspects of stack design are presented briefly by Wimpress. [Based partly on the graphs of Wimpress, Hydrocarbon Process. 42(10), 115-126 (196311. EX A M P L E 8.15 Design of a Fiied Heater The fuel side of a heater used for mild pyrolysis of a fuel oil will be analyzed. The flowsketch of the process is shown in Figure 8.20, and the tube arrangement finally decided upon is in Figure 8.21. Only the temperatures and enthalpies of the process fluid are pertinent to this aspect of the design, but the effect of variation of heat flux along the length of the tubes on the process temperature and conversion is shown in Figure 8.22. In this case, the substantial differences in heat flux have only a minor effect on the process performance. Basic specifications on the process are the total heat release (102.86 MBtu/hr), overall thermal efficiency (75%), excess air (25%), the fraction of the heat release that is absorbed in the radiant section (75%), and the heat flux (10,000 Btu/(hr)(sqft). In the present example, the estimated split of 75% and a
- 237. 218 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE t.lS-(continued) radiant rate of 10,000 lead to an initial specification of 87 tubes, but 90 were taken. The final results are quite close to the estimates, being 77.1% to the radiant zone and 99OOBtu/(hr)(sqft) with 90 tubes. If the radiant rate comes out much different from the desired value, the number of tubes is changed accordingly. Because of the changing temperature of the process stream, the heat flux also deviates from the average value. This variation is estimated roughly from the variation of the quantity p = 1730(7-i - T;) + 7.0( Tg - TL), where the gas temperature T,, in the radiant zone is constant and TL is the temperature of the process stream, both in “R. In comparison with the average flux, the effect is a slightly increased preheat rate and a reduced flux in the reaction zone. The inside skin temperature also can be estimated on the reasonable assumptions of heat transfer film coefficients of more than 100 before cracking starts and more than 200 at the outlet. For the conditions of this example, with Q/A = 9900 and Tg = 2011”R, these results are obtained: T,(“Fl Wm h ‘LJF) 547 1.093 >lOO <655 724 1 >lOO ~823 900 1.878 >200 <943 The equation numbers cited following are from Table 8.16. The step numbers used following are the same as those in Table 8.17: 1. 2. 3. 4. 5. Flow rate = 195,394/3600(0.9455)(62.4) = 0.9200 cfs, velocity = 5.08 fps in 6-S/8 in. OD Schedule 80 pipe. Short radius return bends have 12 in. center-to-center. ?j = 0.75. Fraction excess air = 0.25. From the API data book and a heat of cracking of 332 Btu/(lb gas + gasoline): &,a = 0.9(590) + 0.08(770) + 0.02(855) = 609.6 Btu/lb, Q fOfa, = 195,394(609.6 - 248) + 19,539(332) = 77.14(E6). 6. Heat released: Q, = 77.14/0.75 = 102.86(E6) Btu/lb. 7. Radiant heat absorption: QR = 0.75(77.14)(E6) = 57.86(E6). 8. (Q/A) rad = 10,000 Btu/(hr)(sqft), average. 9. Radiant surface: A = 57.86(E6)/10,000 = 5786 sqft. 11. Tube length = 5786/1.7344 = 3336 ft; 40 foot tubes have an exposed length of 38.5ft; N =3336/38.5 =86.6, say 92 radiant tubes. 12. From Eq. (11) the flue gas rate is G, = 102.85(1020) = 104,907 Ib/hr. With four shield tubes, equilateral spacing and 3 in. distance to walls, 104,907(12) ' =3600(38.5)(27.98) = 0.325 Ib/sec sqft. 13. The 90 radiant tubes are arranged as shown on Figure 8.22: 4 shields, 14 at the ceiling, and 36 on each wall. Dimensions of the shell are shown. 14. A, = (38.5)(1)(90 - 4) = 3311 sqft. 15. Inside surface of the shell is A, = 2[20(37 + 38.5) + 37(38.5)] = 5869 sqft. Refractory surface, A, = 5869 - 3311 = 2558 sqft. 16. (Center-to-center)/OD = 12/6.625 = 1.81, (Y = 0.917, single rows of tubes [Eq. (5)]. 17. Effective absorptivity: aA, =4(38.5)(l) + 0.917(3311) = 3190 sqft, A,/cxA, = 255813190 = 0.8018. 18. Mean beam length: L=(2/3)(20 x 37 x38.5)"3=20.36. 19. From Eq. (6), with 25% excess air, P = 0.23. 20. PL = 0.23(20.36) = 4.68 atm ft. 21. Mean tube wall temp: The stream entering the radiant section has absorbed 25% of the total heat. H, = 248 + 0.25(77.14)(E6)/195,394 = 346.7, Tl = 565”F, T, = 100 + (565 + 900)/2 = 832.5. 22-X Input data are summarized as: PL = 4.68, D, = 0.8018, Dz = 0.25, T, = 832.5, Q, = QJaA, = 102.86(E6)/3190 = 32,245. From program “FRN-l”, T, = 1553.7, F= 0.6496 [Eq. (9)], + 7(T, - T,)) = 3190(0.6496)(28,679) = 59.43(E6). Compared with estimated 57.86(E6) at 75% heat absorption
- 238. 8.12. INSULATION OF EQUIPMENT 219 EXAMPLE 8.1s(continued) in the radiant section. Repeat the calculation with an estimate of 60(E6) HI = 248 + (77.14 - 60)(E6)/195,394 = 335.7, T, = 542, T, = 100 + OS(542 + 900) = 821, Tg = 1550.5, From (Eq. (4), T, = 920°F. 28-31. LMTD = 735.6 mean gas film temp is F = 0.6498, QR = 3190(0.6498)(28,727) = 5955(E6). Interpolating, 0 auumad T, ‘i T. Qe.,cd Q/A q = 0.5(400 + 547 + 735.6) = 841.3. Since G = 0.325 lb/(sec)(sqft), V, = 5.6 Btu/(hr)(sqft)(“F) [(Eq. (lo)], 57.88 565 832.5 1553.7 59.43 A = 1764(E6) = 4282 60.00 542 821 1550.5 59.55 conv 735.6(5.6) SqfL Interpolation [547 1551.2 59.50 99001 4282 = 64.1 bare tubes 26-21. 1.7344(38.5) QcOnv = (77.14 - 59.50)(E6) = 17.64(E6). Fraction lost in stack gas or 16 rows of 4 tubes each. Spacing the same as of the shield tubes. Beyond the first two rows, extended surfaces can be installed. Q,/Q, = 1 - 0.02 - 0.75 = 0.23. Total rows = 2 + 14/2 = 9. bank, and is called the equivalent cold plane area. Evaluation of the exchange factor F is explained in item 9 of Table 8.16. It depends on the emissivity of the gas and the ratio of refractory area A, to the equivalent cold plane area aA,. In turn, A,,, = A -A,, where A is the area of the inside walls, roof, and floor that are covered by refractory. In the convection zone of the heater, some heat also is trans- ferred by direct radiation and reflection. The several contribu- tions to overall heat transfer specifically in the convection zone of fired heaters were correlated by Monrad [Znd. Eng. Chem. 24,505 (1932)]. The combined effects are approximated by item 10 of Table 8.16, which is adequate for estimating purposes. The relation depends on the temperature of the gas film which is taken to be the sum of the average process temperature and one-half of the log mean temperature difference between process and flue gas over the entire tube bank. The temperature of the gas entering the convection zone is found with the trial calculation described in Steps 22-23 of Table 8.17 and may utilize the computer program of Table 8.18. 8.12. INSULATION OF EQUIPMENT Equipment at high or low temperatures is insulated to conserve energy, to keep process conditions from fluctuating with ambient conditions, and to protect personnel who have occasion to approach the equipment. A measure of protection of the equipment metal against atmospheric corrosion also may be a benefit. Application of insulation is a skilled trade. Its cost runs to 8-9% of purchased equipment cost. In figuring heat transfer between equipment and surroundings, it is adequate to take account of the resistances of only the insulation and the outside film. Coefficients of natural convection are in Table 8.9 and properties of insulating materials at several EXAMPLE 8.16 Application of the Wilson-Lobo-Hottel Equation In the case of Example 8.15, 25% excess air was employed, corresponding to 19.0lb/air/lb fuel, the heat release was Qr = 102.86(106) Btu/hr, and aA, = 3036. The effect will be found = 1 + 0.0722- 1.8327 :. Q, = 95.82(106) Btu/hr, of changing the excess air to 16% (16.721b air/lb fuel) on the amount of fuel to be fired while maintaining the same heat absorption. Ratioing Eq. (8.45) to yield the ratio of the releases at the two conditions. which is the heat release with 10% excess air. With 25% excess air, Q/QZ = l/1.8327 = 0.5456, With 10% excess air, Q/Q, = 0.5456(102.86/95.82) = 0.5857, QfZ l+ (16.72/42OO)dm 102.86(106) = 1 + (19.0/4200)~102.86(106)/3036 which shows that approximately 7% more of the released heat is absorbed when the excess air is cut from 25% down to 10%.
- 239. 220 HEAT TRANSFER AND HEAT EXCHANGERS II I Feed T, = 400 F 195394 Ib/hr H = 248 Btullb v’ = 0.920 cfs u = 5.08 fps, cold 8” Sched 40. ‘8 ,/ Convection b Shield VA 4 - Radiant Fuel + 25% excess air Figure 8.20. Flowsketch of process of Example 8.16. Figure 8.21. Tube and box configuration of the fired heater of Example 8.16. .I0 .03 .OG .04 .02 0 TEMPERATURE T CONVERSION, x 0 20 40 60 TUBE NUMBER Figure 8.22. Effects of three modes of heat flux distribution on temperature and conversion in pyrolysis of a fuel oil: (1) two levels, 12,500 and 7500; (2) linear variation between the same limits; (3) constant at 10,000 Btu/(hr)(sqft). Obtained by method of Example 8.16. temperature levels are in Tables 8.19-8.21. Outdoors under windy conditions, heat losses are somewhat greater than indoors at natural convections. Tabulations of economic thicknesses in Chemical Engineers Handbook (McGraw-Hill, New York, 1984, 11.55-11.58) suggest that lo-20% greater thickness of insulation is justified at wind velocity of 7.5 miles/hr. The optimum thickness of insulation can be established by economic analysis when all of the cost data are available, but in practice a rather limited range of thicknesses is employed. Table 8.22 of piping insulation practice in one instance is an example. The procedure for optimum selection of insulation thicknesses is exemplified by Happel and Jordan [Chem. Process Economics, 380 (1975)]. They take into account the costs of insulation and fuel, payout time, and some minor factors. Although their costs of fuel are off by a factor of 10 or more, their conclusions have some validity if it is recognized that material costs likewise have gone up by roughly the same factor. They conclude that with energy cost of $2,5/millionBtu (adjusted by a factor of lo), a payout time of 2 years, for pipe sizes of 2-8 in., the optimum thicknesses in 0.70, . . , , , , , 1 Figure 8.23. Total emissivity of carbon dioxide and water with pHzoIpcoz = 1 and a total pressure of 1 atm [Hadvig, J. Inst. Fuel 43, 129 (1970)].
- 240. TABLE 8.18. Program for Finding the Radiant Gas Temperature by Steps 22 and 23 of Table 8.17 insulation depend on the process temperature according to: T (“F) 2 0 0 400 6 0 0 Thickness (in.) 0.5 1.0 1.25 The data of Table 8.22 are roughly in agreement with these 8.12. INSULATION OF EQUIPMENT 221 calculations. Optimum thicknesses of pipe insulation also are tabulated in Chemical Engineers Handbook (1984, 11.56); they cover both indoor and outdoor conditions, temperature ranges of 150-1200°F and energy costs of l-8 dollars/million Btu. For very large tanks storing volatile liquids and subject to pressure buildup and breathing losses, it is advisable to find eco- nomic thickness of insulation by economic analysis. The influence of solar radiation should be taken into account; a brief treatment of this topic is in the book of Threlkeld (Thermal Environmental Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1970). In at least one application, rigid urethane foam sprayed onto storage tanks in 2in. thickness and covered with a 4mil thickness of neoprene rubber for weather proofing was economically attractive. Although resistance to heat transfer goes up as the thickness of pipe insulation is increased, the external surface also increases; a thickness may be reached at which the heat transfer becomes a minimum and then becomes larger. In accordance with this kind of behavior, heat pickup by insulated refrigerated lines of small diameters can be greater than that of bare lines. In another instance, electrical transmission lines often are lagged to increase the rate of heat loss. An example worked out by Kreith (Principles of Heat Transfer, Intext, New York, 1973, p. 44) reveals that an insulated 0.5 in. OD cable has a 45% greater heat loss than a bare one. LOW TEMPERATURES Insulants suited to cryogenic equipment are characterized by multiple small spaces or pores that occlude more or less stagnant air of comparatively low thermal conductivity. Table 8.19 lists the most common of these materials. In application, vapor barriers are provided in the insulating structure to prevent inward diffusion of atmospheric moisture and freezing on the cold surface with resulting increase in thermal conductivity and deterioration of the insulation. Sealing compounds of an asphalt base are applied to the surface of the insulation which then is covered with a weatherproof jacket or cement coating. For truly cryogenic operations such as air liquefaction and rectification in which temperatures as low as -300°F are encountered, all of the equipment is enclosed in a box, and then the interstices are filled with ground cork. MEDIUM TEMPERATURES Up to about 6OO”F, 85% magnesia has been the most popular material. It is a mixture of magnesia and asbestos fibers so constructed that about 90% of the total volume is dead air space. Equivalents are available for situations where asbestos is undesirable. Such insulants are applied to the equipment in the form of slabs or blankets which are held in place with supports and clips spotwelded to the equipment. They are covered with cement to seal gaps and finished off with a canvas cover that is treated for resistance to the weather. A galvanized metal outer cover may be preferred because of its resistance to mechanical damage of the insulation. A mixture of diatomaceous earth and an asbestos binder is suitable for temperatures up to the range of 1600-1900°F. Johns-Manville “Superex” is one brand. Since this material is more expensive than 85% magnesia, a composite may be used to save money: sufficient thickness of the high temperature resistant mate- rial to bring its external surface to below 6OO”F, finished off with 85% magnesia in appropriate thickness. Table 8.22(c) is one standard speci- fication of this type. REFRACTORIES Equipment made of metal and subject to high temperatures or abrasive or corrosive conditions often is lined with ceramic material.
- 241. 222 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.19. Thermal Conductivities of Insulating Materials for Low Temperatures [k Btu/(hrb$tlW/ft)1 Material Bulk/ B u l k Density, (lb/c&) ‘;;p Density, Temp h Material (lb/c&) (“F) h Fibreglas with asphalt coating (board) Glass blocks, expanded, “ F o a m g l a s ” Mineral wool board, “Rockcork” 6.9 100 0 . 0 2 2 Rubber board, -100 0 . 0 1 8 expanded, -300 0 . 0 1 0 “ R u b a t e x ” 11.0 100 0 . 0 2 3 Silica aerogel, -100 0.014 p o w d e r -300 0 . 0 0 7 “Santocel” 10.6 100 0 . 0 3 6 Vegetable fiber- -100 0 . 0 3 3 board, asphalt -300 0 . 0 1 8 coating 0.024 Foams: 0 . 0 1 7 Polystyrene’ 0 . 0 0 8 Polvurethaneb 4.9 100 -100 -300 5 . 3 100 0 -100 1 4 . 4 100 -100 -300 2 . 9 -100 5 . 0 -100 0 . 0 1 8 0 . 0 1 5 0 . 0 0 4 0 . 0 1 3 0 . 0 1 2 0 . 0 1 0 0 . 0 2 8 0.021 0 . 0 1 3 0 . 0 1 5 0 . 0 1 9 ‘Test space pressure, 1.0 atm; k = 0.0047 at 10m3 mm Hg. bTest space pressure, 1.0 atm; k= 0.007 at 10-s mm Hg. (Marks Mechanical Engineers Handbook, 1978, p. 4.64). When the pressure is moderate and no condensation is likely, brick lining. For instance, a catalytic reformer 4ft OD designed for construction is satisfactory. Some of the materials suited to this 650 psig and 1100°F has a shell 1.5 in. thick, a light weight castable purpose are listed in Table 8.21. Bricks are available to withstand lining 4-5/8in. thick and an inner shell of metal 1/8in. thick. A 3000°F. Composites of insulating brick next to the wall and stronger catalytic cracker 10 ft dia designed for 75 psig and 1100°F has a 3 in. brick inside are practical. Continuous coats of insulants are formed monolithic concrete liner and 3in. of blanket insulation on the by plastering the walls with a several inch thickness of concretes of outside. Ammonia synthesis reactors that operate at 250atm and various compositions. “Gunite” for instance is a mixture of 1 part 1ooo”F are insulated on the inside to keep the wall below about cement and 3 parts sand that is sprayed onto walls and even 7OO”F, the temperature at which steels begin to decline in strength, irregular surfaces. Castable refractories of lower density and greater and also to prevent access of hydrogen to the shell since that causes insulating powers also are common. With both brickwork and embrittlement. An air gap of about 0.75 in. between the outer shell castables, an inner shell of thin metal may be provided to guard and the insulating liner contributes significantly to the overall in- against leakage through cracks that can develop in the refractory sulating quality. TABLE 8.20. Thermal Conductivities of Insulating Materials for High Temperatures [k Btu/(hr)(sqftl”F/ftll Material Bulk Densi 2 Ib/cu Max Temp (“F) 100°F 300°F 5OO’F 1000°F 1500°F 2000°F Asbestos laminated paper, Asbestos corrugated paper, Diatomaceous earth, silica, powder Diatomaceous earth, asbestos and bonding material Fiberglas block, PF612 Fiberglas block, PF614 Fiberglas block, PF617 Fiberglas, metal mesh blanket, #900 Glass blocks, values average Hydrous calcium silicate, “Kaylo” 85% magnesia Micro-quartz fiber, blanket Potassium titanate, fibers Rock wool, loose Zirconia grain 2 2 400 0 . 0 3 8 0 . 0 4 2 1 6 300 0.031 0 . 0 4 2 18.7 1500 0 . 0 3 7 0 . 0 4 5 0 . 0 5 3 0.074 1 8 1600 0 . 0 4 5 0 . 0 4 9 0 . 0 5 3 0.065 2 . 5 500 0 . 0 2 3 0 . 0 3 9 4 . 2 5 500 0.021 0 . 0 3 3 9 500 0 . 0 2 0 0 . 0 3 3 - 1000 0 . 0 2 0 0 . 0 3 0 0 . 0 4 0 14-24 1600 - 0 . 0 4 6 0 . 0 5 3 0 . 0 7 4 1 1 1200 0 . 0 3 2 0 . 0 3 8 0 . 0 4 5 12 600 0 . 0 2 9 0 . 0 3 5 3 3000 0.021 0 . 0 2 8 0 . 0 4 2 0 . 0 7 5 0 . 1 0 8 0 . 1 4 2 7 1 . 5 - - 0 . 0 2 2 0 . 0 2 4 0 . 0 3 0 8-12 - 0 . 0 2 7 0 . 0 3 8 0 . 0 4 9 0 . 0 7 8 113 3000 - - 0 . 1 0 8 0 . 1 2 9 0 . 1 6 3 0 . 2 1 7 /Marks, Mechanical Engineers Handbook, 1978, p. 4.65).
- 242. TABLE 8.21. Properties of Refractories and Insulating Ceramics” (a) Chemical Composition of Typical Refractories Resistance to N o . Refractory Type SiO, AW, FeA TiO2 CaO MgO SIC Alkalies Siliceous High-lime Fused Coal-Ash Steel-Slag Steel-Slag Mill-Scale S l a g 1 Alumina (fused) 8-10 85-90 l - l . 5 1.5-2.2 - - - 0.8-l .3= E G F G 2 C h r o m e 6 2 3 lcib - 17 3 8 - - G E E G 3 Chrome (unburned) 5 1 8 l2b - - 3 2 3 0 - - G E E G 4 Fire clay (high-heat duty) 50-57 36-42 1.5-2.5 1.5-2.5 - - - - l-3.5= F P P F 5 Fire clay (super-duty) 5 2 43 1 2 - - - 2c F P F F 6 Forsterite 3 4 . 6 0 . 9 7 . 0 - 1.3 5 5 . 4 7 High-alumina 22-26 68-72 l - l . 5 3 . 5 - - - - l-1.5= G F F F 8 Kaolin 5 2 45.4 0 . 6 1.7 0.1 0.2 - - - F P Gd F 9 Magnesite 3 2 6 - 3 8 6 - - - P E E E 10 Magnesite (unburned) 5 7 . 5 8 . 5 - 2 6 4 10 - P E E E 1 1 Magnesite (fused) - - - - - - - - - F E E E 12 Refractory porcelain 25-70 25-60 - - - - - - l - 5 G F F F 1 3 Silica 9 6 1 1 - 2 - - - - E P F P 1 4 Silicon carbide (clay bonded) 7-9 2-4 0.3-I 1 - - - 85-90 E G F E 1 5 Sillimanite (mullite) 3 5 6 2 0 . 5 1.5 - - - - o.5c G F F F 1 6 Insulating fire-brick (2600°F) 57.7 3 6 . 8 2 . 4 1.5 0 . 6 0.5 - - P P G* P (b) Physical Properties of Typical Refractoriesa R e f r a c t o r y N o . Fusion Point wt. of Deformation under Pyrometric Load (% at “F Spalling Resistance’ Repea;a~~;rkage St2ht T Cone and lb/in.) (96 “F) B r i c k ilb) 1 3390+ 2 3580+ 3 3580+ 4 3060-3170 5 3170-3200 6 3430 7 3290 8 3200 9 3580+ 10 3580+ 1 1 3580+ 12 2640-3000 1 3 3060-3090 1 4 3390 1 5 331 O-3340 1 6 2980-3000 39+ 41+ 41+ 31-33 33-34 4 0 3 6 3 4 41+ 41+ 41+ 16+30 31-32 3 9 37-38 29-30 1 at 2730 and 50 shears 2740 and 28 shears 2955 and 28 2.5-10 at 2460 and 25 2-4 at 2640 and 25 10 at 2950 l-4 at 2640 and 25 0.5 at 2640 and 25 shears 2765 and 28 shear 2940 and 28 shears 2900 and 25 O-l at 2730 and 50 O-O.5 at 2640 and 25 0.3 at 2200 and 10 G P F G E F E E P F F G P E E G +0.5 (2910) -0.5-1.0 (3000) -0.5-1.0 (3000) fO-1.5 (2550) *o-1.5 (2910) - -2-4 (2910) -0.7-1.0 (2910) -1-2 (3000) -0.5-1.5 (3000) - +0.5-0.8 (2640) 6 . 5 +2 (2910) 8-9.3 -0-0.8 (2910) 8 . 5 -0.2 (2600) 2 . 2 5 9-10.6 11.0 11.3 7 . 5 8 . 5 9 . 0 7 . 5 7 . 7 10.0 10.7 10.5 a Divide by 12 to obtain the units k Btu/(hr)(sqft)(“F/ft). bAs FeO. clncludes lime and magnesia. d Excellent if left above 1200°F. eOxidizing atmosphere. ‘E = Excellent. G = Good. F = Fair. P = Poor. ‘[Some data from Trostel, Chem. Met. Eng. (Nov. 193811. Marks, Mechanical Engineers Handbook, McGraw-Hill, New York, 1978, pp. 6.172-6.173.
- 243. 224 HEAT TRANSFER AND HEAT EXCHANGERS TABLE 8.22. Specifications of Thicknesses of Pipe Insulation for Moderate and High Tern or Double Strength as May b eratures, in Single e Needed (a) Insulation of 85% Magnesia or Equivalent up to 600°F Pify$e Stand;;dlThick Double Standard Thick (in.) l-1/2 or less 718 l-15116 2 l-1132 2-5132 2-112 l-1132 2-5132 3 l-1132 2-5132 4 l-118 2-l/4 5 l-118 2-5116 6 l-118 2-5116 8 l-114 2-l/2 10 l-114 2-l/2 12-33 l-112 3 (b) Molded Diatomaceous Earth Base Insulation, to WOOoF, Single or Double Thickness as Needed Pipe Size (in.) Thickness (in.) 1-l/2 2 2 l-114 2-l/2 l-5/16 3 l-9116 4 l-9116 5 l-112 6 l-112 8 l-112 10 l-9116 12 l-9116 14-33 l-1/2 2 2-l/8 l-13116 2-l/16 2-l/16 2 2-l/16 2 2-l/8 2-l/8 2 (c) Combination Insulation, Inner Layer of Diatomaceous Earth Base, and Outer of 85% Magnesia or Equivalent, for High Level Insulation to 19OO’F Inner Layer Outer Layer Pipe Size (in.) Thickness (in.) Nominal Pipe Size (in.) T h i c k n e s s (in.) l-112 or less 2 no outer layer 2 l-114 4-l/2 2-l/2 l-5116 5 3 l-9/16 6 4 l-9116 7 5 l-112 8 6 l-112 9 8 l-112 11 10 l-9116 14 12 l-9116 16 14-33 l-112 17-36 l-112 l-112 l-112 l-112 2 2 2 2 2 2 Data of an engineering contractor. 8.13. REFRIGERATION Process temperatures below those attainable with cooling water or air are attained through refrigerants whose low temperatures are obtained by several means: 1. Vapor compression refrigeration in which a vapor is compressed, then condensed with water or air, and expanded to a low pressure and correspondingly low temperature through a valve or an engine with power takeoff. 2. Absorption refrigeration in which condensation is effected by absorption of vapor in a liquid at high pressure, then cooling and expanding to a low pressure at which the solution becomes cold and flashed. 3. Steam jet action in which water is chilled by evaporation in a chamber maintained at low pressure by means of a steam jet ejector. A temperature is 55°F or so is commonly attained, but down to 40°F may be feasible. Brines also can be chilled by evaporation to below 32°F. The unit of refrigeration is the ton which is approximately the removal of the heat of fusion of a ton of ice in one day, or 288,000 Btu/day, 12,000 Btu/hr, 200 Btu/min. The reciprocal of the efficiency, called the coefficient of performance (COP) is the term employed to characterize the performances of refrigerating processes: COP = energy absorbed by the refrigerant at the low temperature energy input to the refrigerant A commonly used unit of COP is (tons of refrigeration)/ (horsepower input). Some of the refrigerants suited to particular temperature ranges are listed in Tables 1.10, 8.23, and 8.24. COMPRESSION REFRIGERATION A basic circuit of vapor compression refrigeration is in Figure 8.24(a). After compression, vapor is condensed with water cooling and then expanded to a low temperature through a valve in which the process is essentially at constant enthalpy. In large scale installations or when the objective is liquefaction of the “permanent” gases, expansion to lower temperatures is achieved in turboexpanders from which power is recovered; such expansions are approximately isentropic. The process with expansion through a valve is represented on a pressure-enthalpy diagram in Figure 8.24(b). A process employing a circulating brine is illustrated in Figure 8.24(c); it is employed when cooling is required at several points distant from the refrigeration unit because of the lower cost of circulation of the brine, and when leakage between refrigerant and process fluids is harmful. For an overall compression ratio much in excess of four or so, multistage compression is more economic. Figure 8.24(d) shows two stages with intercooling to improve the capacity and efficiency of the process. Many variations of the simple circuits are employed in the interest of better performance. The case of Example 8.17 has two stages of compression but also two stages of expansion, a scheme due originally to Windhausen (in 1901). The flashed vapor of the intermediate stage is recycled to the high pressure compressor. The numerical example shows that an improved COP is attained with the modified circuit. In the circuit with a centrifugal compressor of Figure 8.25, the functions of several intermediate expansion valves and flash drums are combined in a single vessel with appropriate internals called an economizer. This refrigeration unit is used with a fractionating unit for recovering ethane and ethylene from a mixture with lighter substances. Low temperatures with the possibility of still using water for final condensation are attained with cascade systems employing coupled circuits with different refrigerants. Refrigerants with higher vapor pressures effect condensation of those with lower vapor pressures. Figure 8.26 employs ethylene and propylene in a cascade for servicing the condenser of a demethanizer which must be cooled to -145°F. A similar process is represented on a flowsketch in the book of Ludwig (1983, Vol. 1, p. 249). A three element cascade with methane, ethylene and propylene refrigerants is calculated by
- 244. 8 . 1 3 . REFRIGERATJON 225 Critical point_ Saturated liquid line 2 Load Compressor s @ (a’ Refrigerant m Brine Saturated vapor line Enthalpy, h (Btu/lb) (b) Load Brine pump (cl stage (4 Second stage Figure 8.24. Simpler circuits of compression refrigeration (see also Example 8.17). (a) Basic circuit consisting of a compressor, condenser, expansion valve and evaporator (load). (b) Conditions of the basic circuit as they appear on a pressure-enthalpy diagram; the primed points are on the vapor-liquid boundary curve. (c) Circuit with circulation of refrigerated brine to process loads. (d) Circuit with two-stage compression and intercooling. EXAMPLE 8.17 Two-Stage Propylene stage Recycle Compression Refrigeration with Inter- A propylene refrigeration cycle operates with pressures of 2.56, 64, and 16psia. Upon expansion to 64psia, the flashed vapor is recycled to the suction of the high pressure stage while the liquid is expanded to 16psia to provide the needed refrigeration at -9°F. The ratios of refrigeration to power input will be compared without and with interstage recycle. Basis: 1 lb of propylene to the high pressure stage. Conditions 256 psia 256 psia 1 .O lb 1 .O lb High pressure High pressure stage stage 7 7 L L 0.2477 0.2477 l b l b -m -m Flash Flash 64 psia 64 psia d r u m d r u m 0.7523 0.7523 l b l b $ 1 6 p s i a ,-.$ I Load Low pressure stage 25641 160 Enthalpy
- 245. 226 HEAT TRANSFER AND HEAT EXCHANGERS EXAMPLE 8.17-(continued) are shown on the pressure-enthalpy and flow diagrams. Isentropic compression and isenthalpic expansion are taken. Without recycle, refrigeration = 452-347 = 105 Btu/lb, work = 512-452 = 60 Btu/lb, COP = 105/60 = 1.75. With recycle, interstage vapor = (347-305)/(468-305) = 0.2577 lb/lb, refrigeration = (452-305)0.7423 = 109.1 Btu/lb, work = (495-46QO.2577 + (512-452)0.7423 = 51.5 Btu/lb, COP = 109.1/51.5 = 2.12, which points out the improvement in coefficient of performance by the interstage recycle. Evaporator Economizer 1.2 MBtu/hr 30” dia. by 6 560 IbmoVhr -45F 270 psia -90 F 2 psia I 98 F rrrC I I I-- l I -75 F Condenser Bogart (1981, pp. 44-47); it attains -240°F with a maximum pressure of 527 psia. Q 145 F %- Centrifugal Desuperheater Reciprocating compressor compressors 450 HP 450 HP Figure 8.25. A refrigeration system for the overhead condenser of a fractionator for recovering ethane and ethylene. Freon-12 is the refrigerant. The economizer combines the functions of several expansion valves and flash drums for intermediate recycle of flashed vapors. REFRIGERANTS Several refrigerants commonly used above -80°F or so are compared in Table 8.23. Ethylene and butane also are in use, particularly in refineries where they are recoverable from the process streams. Properties of the freons (also known by the trade name genetrons) are listed in Table 8.24. Freon 12 is listed in both tables so some comparisons of all of these refrigerants is possible. The refrigerants of Table 8.23 have similar performance. When ammonia or some hydrocarbons are made in the plant, their election as refrigerants is logical. Usually it is preferred to operate at suction pressures above atmospheric to avoid inleakage of air. The nonflammability and nontoxicity of the freons is an attractive quality. Relatively dense vapors such as Ref-12, -22, and -500 are preferred with reciprocating compressors which then may have smaller cylinders. For most equipment sizes, Ref-12 or -114 can be adopted for greater capacity with the same equipment. Ref-22 and -500 are used with specially built centrifugals to obtain highest capacities. Ammonia absorption refrigeration is particularly applicable when low level heat is available for operation of the stripper reboiler and power costs are high. Steam jet refrigeration is the large scale system of choice when chilled water is cold enough, that is above 40°F or so. Process Ethylene 3-stage compressor Process Ethylene condenser -93 FI t AM; ; -68F 70 F ,,,?‘I t”:3:F 12 psia 2 7 psia -127 F, 80 psia -9 F, 16 psia 128 F 88 psja Propylene I 116 F -9 F 71 psia Propylene 2-stage compressor water Processes Figure 8.26. A cascade refrigeration system employing ethylene and propylene for condensing the overhead of a demethanizer at -145°F. The diagram is somewhat simplified.
- 246. TABLE 8.23. Comparative Data of Refrigerant9 - 8 0 - 6 0 -40 - 2 0 0 2 0 40 6 0 Evaporator ammonia 5 . 5 5 10.4 18.3 3 0 . 4 4 9 . 0 7 3 . 0 1 0 7 . 5 pressure propylene 7 . 2 0 12.5 20.7 32.1 4 9 . 0 7 0 . 0 9 6 . 0 131 (psia) propane 5 . 5 5 9 . 7 8 16.2 2 5 . 5 38.1 5 6 . 0 8 0 . 0 110 ired” 12 2 . 8 8 5 . 3 6 9 . 3 15.3 2 3 . 8 3 5 . 7 51.7 7 2 . 4 Condensed Liquid Temperature 95°F; Condenser Pressure in psia: Ammonia 197; Propylene 212; Propane 177; 12 123 lb refrigerant/ ammonia 0 . 4 5 4 0 . 4 4 6 0 . 4 3 8 0 . 4 3 2 0 . 4 2 6 0 . 4 2 2 0 . 4 1 8 min/ton propylene 2.07 1.96 1.a7 1.79 1.72 1.66 1.60 1 . 5 4 refrigeration propane 2 . 1 8 2 . 0 4 1.93 1.a3 1.74 1.67 1.59 1.53 freon 12 5 . 1 8 4.89 4 . 6 5 4 . 4 2 4 . 2 2 4 . 0 5 3 . 8 8 3 . 7 4 CMF of ammonia 2 0 . 4 11.1 6 . 4 5 3 . 9 6 2 . 5 2 1.69 1.14 refrigerant/ propylene 27.1 15.7 9 . 1 8 5 . 8 5 3 . 8 4 2 . 5 3 1.80 1.28 min/ton propane 3 7 . 4 2 0 . 0 12.0 7 . 2 9 4 . 7 7 3 . 1 2 2 . 1 3 1.50 refrigeration freon 12 5 9 . 9 3 1 . 7 18.0 1 0 . 8 6 . 7 9 4.44 3 . 0 0 2 . 0 9 B r a k e ammonia 4.31 3 . 2 3 2.41 1.78 1.26 0 . 8 3 5 0 . 4 8 3 horsepower/ propylene 5 . 0 0 3 . 9 6 3 . 1 0 2 . 3 5 1.74 1.20 0 . 8 3 0 0 . 4 8 5 ton refrigeration propane 4 . 9 8 3 . 8 7 3 . 0 3 2 . 3 2 1.75 1 . 2 4 0 . 8 0 0 0 . 4 5 8 freon 12 5 . 7 0 4 . 3 3 3.31 2 . 4 7 1.a3 1.30 0.848 0 . 4 9 0 Condensed Liquid Temperature 125’F; Condenser Pressure in psia: Ammonia 303; Propylene 314; Propane 260; Freon 12 lS4 lb refrigerant ammonia 0 . 4 9 2 0 . 4 8 3 0 . 4 7 4 0.466 0 . 4 6 0 0.454 0 . 4 5 0 mirjton propylene 2 . 6 7 2 . 5 0 2 . 3 5 2 . 2 2 2.11 2.01 1.93 1.86 refrigeration propane 2 . 8 6 2 . 6 3 2 . 4 4 2 . 2 9 2 . 1 6 2 . 0 4 1.94 1.84 freon 12 6 . 4 2 5 . 9 8 5.61 5 . 2 8 5 . 0 0 4 . 7 5 4 . 5 3 4 . 3 3 CFM of ammonia 2 2 . 0 12.0 6 . 9 7 4 . 2 6 refrigerant/ propylene 3 5 . 2 2 0 . 0 11.5 7 . 3 2 4 . 7 2 ton/ propane 5 0 . 0 2 5 . 8 15.4 9 . 1 6 5 . 9 4 refrigeration freon 12 7 4 . 0 3 8 . 8 2 1 . 7 12.9 8 . 0 5 B r a k e ammonia 5 . 6 8 4 . 3 8 3 . 3 3 2 . 5 4 horsepower/ propylene 7 . 4 9 5 . 9 6 4.71 3 . 6 6 2 . 7 9 ton refrigeration propane 7 . 4 7 5 . 8 5 4 . 6 0 3 . 5 9 2.81 freon 12 8 . 0 9 6 . 2 5 4 . 7 8 3 . 6 7 2.7% “The horsepowers are based on centrifugal compressor efficiencies without economizers. 2 . 7 2 1.82 1.23 3 . 0 8 2 . 1 8 1.56 3 . 7 9 2 . 6 3 1.80 5.21 3 . 5 0 2.42 1.so 1.38 0 . 9 5 2 2 . 0 3 1.55 1.10 2 . 0 7 1.50 1.03 2 . 0 7 1.49 1.02 Condenser 0.92 MBtu/hr 99.5% NH, 1 0 0 F 210 psia x 3 0 F 45 psia Absorber @ 45 psia 95% equilibrium 0.96 MBWhr Intercooler ,~n F 0.65 MBtulhr Stripper @ 210 psia 20% NH, Load Pump 600,000 Btulhr 1.1 H P Reboiler 1.28 MBtulhr Figure 8.27. An ammonia absorption refrigeration process for a load of 50 tons at 30°F. The conditions were established by Hougen, Watson, and Ragatz (Thermo- dynamics, Wiley, New York, 1959, pp. 83.5-842). 227
- 247. TABLE 8.24. Comparative Data of Freon Refrigerants Refrigerant Number (AM Designation) 1 1 1 2 2 2 1 1 3 1 1 4 500 502 C h e m i c a l n a m e Chemical formula Molecular wl Gas constant R [(ft lb/lb R)] Boiling point at 1 atm (“F) Freezing point at 1 atm (“F) Critical temperature (“F) Critical pressure (psia) Specific heat of liquid, 86°F Specific heat of vapor, C, 60°F at 1 atm Specific heat at vapor, C, 60°F at 1 atm Ratio CJC, = K (86°F at 1 atm) Saturation pressure (psia) at -50°F 0°F 40°F 105°F Net refrigerating effect (Btu/lb) 40-105°F (no subcooling) Cycle efficiency (% Carnot cycle) 40-105°F Liquid circulated 40-105°F [(lb/min/ton)] Theoretical displacement 40-105°F (cuft/min/ton)] Theoretical horsepower per ton 40-105°F Coefficient at performance 40-105°F (4.71/HP per ton) Cost compared with R 11 trichloromono- fluoromethane dichlorodi- fluoromethane monochlorodi- fluoromethane trichlorotri- fluoroethane dichlorotetra- fluoroethane CCI,F CCI,F, 1 3 7 . 3 8 120.93 1 1 . 2 5 12.78 7 4 . 7 -21.62 -168 -252 3 8 8 . 0 2 3 3 . 6 6 3 5 . 0 5 9 7 . 0 0 . 2 2 0 0 . 2 3 5 a 0 . 1 4 6 a 0 . 1 3 0 1.11 1.14 C H C I F , CCI,F-CCIF, C,‘W, 8 6 . 4 8 187.39 1 7 0 . 9 3 17.87 8 . 2 5 9 . 0 4 -41.4 117.6 3 8 . 4 -256 -31 -137 2 0 4 . 8 4 1 7 . 4 2 9 4 . 3 7 1 6 . 0 4 9 5 . 0 4 7 4 . 0 0 . 3 3 5 0 . 2 1 8 0 . 2 3 8 0 . 1 4 9 a 0 . 1 5 6 0 . 1 2 7 a 0 . 1 4 5 1.18 1.12 1.09 azeotrope of dichlorodi- fluoromethane a n d difluoroethane 73.8% CCI,F, 26.2% CHsCHF, 9 9 . 2 9 15.57 -28.0 -254 221.1 6 3 1 . 0 0 . 3 0 0 0.171 0.151 1.13 azeotrope of monochlorodi- fluoromethane a n d monochloropenta- fluoroethane 48.8% CHCLF, 51.2% CCIF,-CF, 1 1 1 . 6 4 1 3 . 8 7 -50.1 a 194.1 6 1 8 . 7 0 . 3 0 5 0.164 0.161 1 . 0 2 3 0 . 5 2 7 . 1 2 11.74 a 1.35 8.395 1 4 . 7 4 2 . 5 5 2 3 . 8 5 3 8 . 7 9 0 . 8 4 5 . 9 6 2 7 . 9 6 45.94 7 . 0 3 5 1 . 8 7 8 3 . 7 2 2 . 8 6 15.22 6 0 . 9 4 9 4 . 9 0 2 5 . 7 1 4 1 . 2 5 2 2 7 . 6 5 1 1 . 5 8 5 0 . 2 9 1 6 7 . 8 5 244.40 6 7 . 5 6 4 9 . 1 3 6 6 . 4 4 5 4 . 5 4 4 3 . 4 6 5 9 . 8 2 4 3 . 7 2 9 0 . 5 8 3 . 2 8 1 . 8 8 7 . 5 9 4 . 9 8 2 . 0 76.1 2 . 9 6 4 . 0 7 3 . 0 2 3 . 6 6 4 . 6 2 3 . 3 5 4.58 16.1 3 . 1 4 1.98 3 9 . 5 9 . 1 6 2 . 6 9 2 . 0 4 0 . 6 7 6 0 . 7 3 6 0 . 7 5 0 . 7 0 0 . 7 2 2 0 . 7 4 7 0.806 6 . 9 5 6 . 3 9 6 . 2 9 8 . 7 4 6 . 5 2 6.31 5 . 8 6 1 . o o 1.57 2.77 2.15 2.97 2 . 0 0 5 . 5 4 a Data not available or not applicable. (Carrier Air Conditioning Co.).
- 248. R E F E R E N C E S 229 ABSORPTION REFRIGERATION The most widely used is ammonia absorption in water. A flowsketch of the process is in Figure 8.27. Liquid ammonia at a high pressure is obtained overhead in a stripper, and then is expanded through a valve and becomes the low temperature vapor-liquid mixture that functions as the refrigerant. The low pressure vapor is absorbed in weak liquor from the bottom of the stripper. Energy input to the refrigeration system is primarily that of the steam to the stripper reboiler and a minor amount of power to the pump and the cooling water circulation. This kind of system has a useful range down to the atmospheric boiling point of ammonia, -28°F or -33”C, or even lower. Two or three stage units are proposed for down to -94°F. Sizing of equipment is treated by Bogart (1981). REFERENCES Fired Heaters (see also Ganapathy, HEDH, and Kern above) 1. 2. 3. 4. 5. 6. I. 8. 9. 10. 11. l2. 13. 14. 15. 16. K.J. Bell and M.A. Ghaly, An approximate generalized design method for multicomponent partial condensers, Chem. Eng. Prog. Symp. Ser. Wl, 72-79 (1973). V. Cavaseno et al. (Ed%), Process Heat Exchange, McGraw-Hill, New York, 1979. D. Chisholm (Ed.), Developments in Heat Exchange Technology I, Applied Science, London, 1980. J.R. Fair, Process heat transfer by direct fluid-phase contact, Chem. Eng. Pro& Symp. Ser. 118, l-11 (1972); Chem. Eng., (12 June 1972). V. Ganapathy, Applied Heat Transfer, PennWell Books, Tulsa, OK, 1982. H. GrGber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer, McGraw-Hill, New York, 1961. H. Hausen, Heat Transfer in Counterflow, Parallel Flow and Cross Flow, McGraw-Hill, New York, 1983. HEDH, Heat Exchanger Design Handbook (E.U. Schliinder et al., Eds.), Hemisphere, New York, 1983-date, 5 ~01s. M. Jakob, Heat Transfer, Wiley, New York, 1957, Vol. 2. S. Kakac, A.E. Bergles, and F. Mayinger (Ed%), Heat Exchangers: Thermal-Hydraulic Fundamentals and Design, Hemisphere, New York, 1981. W.M. Kays and A.L. London, Compact Heat Exchangers, McGraw-Hill, New York, 1984. D.Q. Kern, Process Heat Transfer, McGraw-Hill, New York, 1950. SK. Kutateladze and V.M. Borishanskii, Concise Encyclopedia of Heat Transfer, Pergamon, New York, 1966. E.E. Ludwig, Applied Process Design for Chemical and Petrochemical Plants, Gulf, Houston, 1983, Vol. 3, pp. l-200. P.E. Minton, Designing spiral plate and spiral tube exchangers, Chem. Eng., (4 May 1970); (18 May 1970). R.K. Neeld and J.T. O’Bara, Jet trays in heat transfer service, Chem. Eng. Prog. 66(7), 53 1970. 17. P.A. Schweitzer (Ed.), Handbook of Separation Techniques for Chemical Engineers, McGraw-Hill, New York, 1979, Sec. 2.3, Evaporators, Sec. 2.4, Crystallizers. 18. L. Silver, Gas cooling with aqueous condensation, Tram. ht. Chem. Eng. 25, 30-42 (1947). 19. E.F.C. Somerscales and J.G. Knudsen (Ed%), Fouling of Heat Transfer Equipment, Hemisphere, New York, 1981. ZQ. J. Taborek, G.F. Hewitt, and N. Afgan (Eds.), Heat Exchangers Theory and Practice, Hemisphere, New York, 1983. 21. TEMA Standards, Tubular Exchanger Manufacturers Association, Tarrytown, NY, 1978. 22. G. Walker, Industrial Heat Exchangers, Hemisphere, New York, 1982.* * The book by Walker (Appendix D, 1982) has a guide to the literature of heat transfer in book form and describes the proprietary services HTFS (Heat Transfer and Fluid Services) and HTRI (Heat Transfer Research Inc.). Another kind of absorption refrigerant system employs aqueous lithium bromide as absorbent and circulating water as the refrigerant. It is used widely for air conditioning systems, in units of 600-700 tons producing water at 45°F. CRYOGENICS This term is applied to the production and utilization of temperatures in the range of liquid air, -200°F and lower. A great deal of information is available on this subject of special interest, for instance in Chemical Engineers Handbook (1984, 12.47-12.58) and in the book of Arkhanov et al. (1981). 23. F.A. Holland, R.M. Moores, F.A. Watson, and J.K. Wilkinson, Heat Transfer, Heinemann, London, 1970. 24. H.C. Hottel, in McAdams Heat Transmiwion, McGraw-Hill, New York, 1954. 25. W.E. Lobo and J.E. Evans, Heat transfer in the radiant section of petroleum heaters, Trans. AIChE 35, 743 (1939). 26. C.C. Monrad, Heat transmission in the convection section of pipe stills, Ind. Eng. Chem. 24, 505 (1932). 27. D.W. Wilson, W.E. Lobe, and H.C. Hottel, Heat transmission in the radiant section of tube stills, Ind. Eng. Chem. 24, 486 (1932). 28. R.N. Wimpress, Rating fired heaters, Hydrocarbon Process. 42(10), 115-126 (1963); Generalized method predicts fired-heater performance, Chem. Eng., 95-102 (22 May 1978). p$ted American Petroleum Institute Standards (API, Washington, . . 29. Std. 660, Shell-and-Tube Heat Exchangers for General Refinery Services, 1982. 30. Std. 661, Air-Cooled Heat Exchangers for General Refinery Services, 1978. 31. Std. 665, API Fired Heater Data Sheet, 1966, 1973. Insulation 32. Marks Mechanical Engineers Handbook, McGraw-Hill, New York, 1978, pp. 6.169-6.177. 33. H.F. Rase and M.H. Barrow, Project Engineering of Process Plants, Wiley, New York, 1957, Chap. 19. 34. G.B. Wilkes, Heat Insulation, Wiley, New York, 1950. Refrigeration 35. A. Arkhanov, I. Marfenina, Ye. Mikulin, Theory and Design of Cryogenic Systems, Mir Publishers, Moscow, 1981. 36. ASHRE, Thermophysical Properties of Refrigerants, American Society of Heating, Refrigeration and Air-Conditioning Engineers, Atlanta, GA, 1976. 31. M. Bogart, Ammonia Absorption Refrigeration in Industrial Processes, Gulf, Houston, 1981. 38. Carrier System Design Manual, Carrier Air Conditioning Co., Syracuse, NY, 1964, Part 4, Refrigerants, brines and oils. 39. F.L. Evans, Equipment Design Handbook for Refineries and Chemicil Plants, Gulf, Houston, 1979, Vol. 1, pp. 172-196. 40. T.M. Flynn and K.D. Timmerhaus, Cryogenic processes, in Chemical Engineers Handbook, 1984, pp. 12.46-12.58. 41. W.B. Gosney, Principles of Refrigeration, Cambridge University Press, Cambridge, 1982. 42. E.E. Ludwig, Applied Process Design for Chemical and Petroleum Plants, Gulf, Houston, 1983, Vol. 1, pp. 201-250. 43. Y.R. Mehra, Refrigerating properties of ethylene, ethane, propylene and propane, Chem. Eng., 97 (18 Dec. 1978); 131 (15 Jan. 1979); 95 (12 Feb. 1979); 165 (26 Mar. 1979).
- 250. 9 DRYERS AND COOLING TOWERS T he processes of the drying of solids and the evaporative cooling of process water with air have a common foundation in that both deal with interaction of water and air and involve simultaneous heat and mass transfer. Water cooling is accomplished primarily in packed towers and also in spray ponds or in vacuum spray chambers, the latter for exceptionally low temperatures. Although such equipment is comparatively simple in concept it is usually large and expensive, so that efficiencies and other aspects are considered proprietary by the small number of manufacturers in this field. In contrast, a great variety of equipment is used for the drying of so/ids. Thomas Register lists about 35 pages of U.S. manufacturers of drying equipment, classified with respect to type or the nature of the material being dried. In a major respect, dryers are so/ids handling and transporting equipment, notable examples being perforated belt conveyors and pneumatic conveyors through which hot air is blown. Solids being dried cover a range of sizes from micron-sized particles to large slabs and may have varied and distinctive drying behaviors. As in some other long-established industries, drying practices of necessity have outpaced drying theory. In the present state of the art, it is not possible to design a dryer by theory without experience, but a reasonably satisfactory design is possible from experience plus a little theory. Performances of dryers with simple flow patterns can be described with the aid of laboratory drying rate data. In other cases, theoretical principles and correlations of rate data are of value largely for appraisal of the effects of changes in some operating conditions when a basic operation is known. The essential required information is the residence time in the particular kind of dryer under consideration. Along with application of possible available rules for vessel proportions and internals to assure adequate contacting of solids and air, heat and material balances then complete a process design of a dryer. In order to aid in the design of dryers by analogy, examples of dimensions and performances of the most common types of dryers are cited in this chapter. Theory and correlation of heat and mass transfer are treated in detail elsewhere in this book, but their use in the description of drying behavior will be indicated here. 9.1. INTERACTION OF AIR AND WATER Besides the obvious processes of humidification and dehumidifica- tion of air for control of environment, interaction of air and water is a major aspect of the drying of wet solids and the cooling of water for process needs. Heat and mass transfer then occur simul- taneously. For equilibrium under adiabatic conditions, the energy balance is k&h -PI = W - Lh (9.1) where p, is the vapor pressure at the wet bulb temperature T,. The moisture ratio, H lb water/lb dry air, is related to the partial pressure of the water in the air by H,!! p -18p ~- 29P-p 29P’ the approximation being valid for relatively small partial pressures. Accordingly, the equation of the adiabatic saturation line may be written H, -H = (h/lk)(T - T,) (9.3) = (C/1)(2- - T,). (9.4) For water, numerically C = h/k, so that the wet bulb and adiabatic saturation temperatures are identical. For other vapors this conclusion is not correct. For practical purposes, the properties of humid air are recorded on psychrometric (or humidity) charts such as those of Figures 9.1 and 9.2, but tabulated data and equations also are available for greater accuracy. A computer version is available (Wiley Professional Software, Wiley, New York). The terminal properties of a particular adiabatic humification of air are located on the same saturation line, one of those sloping upwards to the left on the charts. For example, all of these points are on the same saturation line: (T, H) = (250,0.008), (170, 0.026) and (100,0.043); the saturation enthalpy is 72Btu/lb dry, but the individual enthalpies are less by the amounts 2.5, 1.2, and 0, respectively. Properties such as moisture content, specific volume, and enthalpy are referred to unit mass of dry air. The units employed on Figure 9.1 are lb, tuft, “F, and Btu; those on Figure 9.2 are SI. The data are for standard atmospheric pressure. How to correct them for minor deviations from standard pressure is explained for example in Chemical Engineers’ Handbook (McGraw-Hill, New York, 1984, 12.10). An example of reading the charts is with the legend of Figure 9.1. Definitions of common humidity terms and their units are given following. 1. Humidity is the ratio of mass of water to the mass of dry air, H = WJW,. (9.5) 2. Relative humidity or relative saturation is the ratio of the prevailing humidity to the saturation humidity at the same temperature, or the ratio of the partial pressure to the vapor pressure expressed as a percentage, %RH = lOOH/H, = lOOp/p,. 3. The relative absolute humidity is (9.6) 4. Vapor pressure of water is given as a function of temperature by ps = exp(11.9176 - 7173.9/(T + 389.5)), atm, “F. (9.8) 231
- 251. 232 DRYERS AND COOLING TOWERS temperorurc c Figure 9.1. Psychrometric chart in English units (Currier Corp. Syracuse, NY). Example: For air at 200°F with H = 0.03 lb/lb: T, = 106.5”F, V, = 17.4 tuft/lb dry, lOOH/H, = 5.9%, h = h, + D = 84 - 1.7 = 82.3 Btuhb dry.
- 253. 234 D R Y E R S A N D C O O L I N G T O W E R S EXAMPLE 9.1 Conditions in an Adiabatic Dryer The air to a dryer has a temperature of 250°F and a wet bulb temperature of 101.5”F and leaves the process at 110°F. Water is T, Tti H “h =250 F ,= 101.5 F = 0.010 lb/lb dry = 18.2 tuft/lb dry Water 1500 Ib/hr 100 F 0.043 7 3 % 15.3 cuftllb dry evaporated off the surface of the solid at the rate of lSOOlb/hr. Linear velocity of the gas is limited to a maximum of 15 ft/sec. The diameter of the vessel will be found. Terminal conditions of the air are read off the adiabatic saturation line and appear on the sketch: Dry air = 1500 = 0.043 - 0.010 45,455 lb/hr ~ 45*455uw = 229.8 & 3600 D = d229.8/15(~/4) = 4.4 ft. 5 . 6. The humid volume is the volume of 1 lb of dry air plus the volume of its associated water vapor, V,, = 0.73(1/29 + h/18)(T + 459.6)/P, cuft/(lb dry air). Humid specific heat is (9.9) C,, = C, + C,H = 0.24 + 0.45H, Btu/(F)(lbdryair). (9.10) The wet bulb temperature T, is attained by measurement under standardized conditions. For water, Yf,, is numerically nearly the same as the adiabatic saturation temperature T,. The adiabatic saturation temperature T, is the temperature attained if the gas were saturated by an adiabatic process. With heat capacity given by item 6, the enthalpy of humid air is h = 0.24T + (0.45T + 11OO)H. (9.11) On the psychrometric chart of Figure 9.1, values of the saturation enthalpy h, and a correction factor D are plotted. In these terms the enthalpy is h=h,+D. (9.12) In Figure 9.2, the enthalpy may be found by interpolation between the lines for saturated and dry air. In some periods of drying certain kinds of solids, water is brought to the surface quickly so that the drying process is essentially evaporation of water from the free surface. In the absence of intentional heat exchange with the surrounding or substantial heat losses, the condition of the air will vary along the adiabatic saturation line. Such a process is analyzed in Example 9.1. For economic reasons, equilibrium conditions cannot be approached closely. In a cooling tower, for instance, the effluent air is not quite saturated, and the water temperature is not quite at the wet bulb temperature. Percent saturation in the vicinity of 90% often is feasible. Approach is the difference between the temperatures of the water and the wet bulb. It is a significant determinant of cooling tower size as these selected data indicate: Approach (“F) 5 1 0 15 20 25 Relative tower volume 2.4 1.6 1.0 0.7 0.55 Other criteria for dryers and cooling towers will be cited later. 9.2. RATE OF DRYING In a typical drying experiment, the moisture content and possibly the temperature of the material are measured as functions of the time. The inlet and outlet rates and compositions of the gas also are noted. From such data, the variation of the rate of drying with either the moisture content or the time is obtained by mathematical differentiation. Figure 9.3(d) is an example. The advantage of expressing drying data in the form of rates is that their dependence on thermal and mass transfer driving forces is more simply correlated. Thus, the general drying equation may be written - f $;= h(T, - T) = k,(P - Pg) = k,(H - H,), (9.13) where subscript g refers to the gas phase and H is the moisture content, (kg/kg dry material), corresponding to a partial or vapor pressure P. Since many correlations of heat and mass transfer coefficients are known, the effects of many changes in operating conditions on drying rates may be ascertainable. Figures 9.3(g) and (h) are experimental evidence of the effect of humidity of the air and (i) of the effect of air velocity on drying rates. Other factors, however, often complicate drying behavior. Although in some ranges of moisture contents the drying process may be simply evaporation off a surface, the surface may not dry uniformly and consequently the effective amount of surface may change as time goes on. Also, resistance to diffusion and capillary flow of moisture may develop for which phenomena no adequate correlations are known. Furthermore, shrinkage may occur on drying, particularly near the surface, which hinders further movement of moisture outwards. In other instances, agglomerates of particles may disintegrate on partial drying. Some examples of drying data appear in Figure 9.3. Commonly recognized zones of drying behavior are represented in Figure 9.3(a). Equilibrium moisture contents assumed by various materials in contact with air of particular humidities is represented by (b). The shapes of drying rate curves vary widely with operating conditions and the physical state of the solid; (b) and others are some examples. No correlations have been developed or appear possible whereby such data can be predicted. In higher ranges of moisture content of some materials, the process of drying is essentially evaporation of moisture off the surface, and its rate remains constant until the surface moisture is depleted as long as the condition of the air remains the same. During this period, the rate is independent of the nature of the solid. The temperature of
- 254. 9.2. RATE OF DRYING 235 mture content (tMC) Ttme (a) Final moisture cOntent IFMC) 0 4 60 P' % S A T U R A T I O N (cl 5 - leather, sole, oak tann 1.16 Relatwe, humidity f?& (b) 0 .02 .04 .06 .06 .10 .I2 .I. .I6 .I6 .ZP UOlSTURE CDNTENT.LES./LB.OF DRY SAND (4 Figure 9.3. (a) Classic drying curve of moisture content against time; a heat-up period in which no drying occurs also is usually present (Proctor and Schwartz, Inc.; Schweitzer, p. 4.144). (b) Equilibrium moisture content as a function of relative humidity; many other data are tabulated in Chemical Engineers Handbook (McGraw-Hill, New York, 1984, 20.12). (These data are from National Academy of Science, copyright 1926.) (c) Rate of drying as a function of % saturation at low (subscript 1) and high (subscript 2) drying rates: (A) glass spheres, 60 pm, bed 51 mm deep; (B) silica flour, 23.5 pm, 51 mm deep; (C) silica flour, 7.5 pm, 51 mm bed; (D) silica flour, 2.5 p, 65 mm deep (data of Newitt et al., Trans. Inst. Chem. Eng. 27, 1 (1949). (d) Moisture content, time and drying rates in the drying of a tray of sand with superheated steam; surface 2.35 sqft, weight 27.125 lb. The scatter in the rate data is due to the rough numerical differentiation (Wenzel, Ph.D. thesis, University of Michigan, 1949). (e) Temperature and drying rate in the drying of sand in a tray by blowing air across it. Dry bulb 76.1”C, wet bulb 36.o”C (Ceaglske and Hougen, Trans. AIChE 33, 283 (1937). (f) Drying rates of slabs of paper pulp of several thicknesses [after McCready and McCabe, Trans. AIChE 29, 131 (1933)]. (g) Drying of asbestos pulp with air of various humidities [McCready and McCabe, Trans. AIChE 29, 131 (1933)]. (h) Effect of temperature difference on the coefficient K of the falling rate equation -dW/dO = KW [Sherwood and Comings, Trans. AIChE 27, 118 (1932)]. (i) Effect of air velocity on drying of clay slabs. The data are represented by R = ~.OU’.‘~(H,,, - H). The dashed line is for evaporation in a wetted wall tower (Walker, Lewis, McAdams, and Gilliland, Principles of Chemical Engineering, McGraw-Hill, New York, 1937).
- 255. 236 D R Y E R S A N D C O O L I N G T O W E R S 0 r .z 0 0.4 0.3 0.2 4 0.1 '; 40 z 0 30 0 5 IO I5 20 25 30 3 5 FREE MOISTURE CONTENT, GM.H,O PER GM.ORY SAND (e) 0.4 T, “C t A 0 x 0 65 80 7055 X, FREE MOISTURE, LB/LB DRY SOLID (f) TWB. ‘C I 0.3 Y= 2 0‘ ; 0.2 6 L F F n 0.1 0 0 0.05 0.10 0.15 0.20 Average free moisture content, lb/lb (9) 0.40 (L 5 0.30 N t 5 _lozo P 2 0 z & 010 n cc- 0 0 0.5 1.0 23.7 m m 1.5 2 0 Time i n Minutes = 60 6 (h) 2 1%) 00 E > 60 5.0 4.0 30 040.506 IO 70 30 40 5.DbO 100 Atr klo&y. Meters per Second (4 Figure 9.3-4cont~nued)
- 256. 9.3. CLASSIFICATION AND GENERAL CHARACTERISTICS OF DRYERS 237 EXAMPLE 9.2 Drying Tie over Constant and FaUiig Rate Periods with Constant Gas Conditions The data of Figure 9.3(d) were obtained on a sample that contained 27.125 lb dry sand and had an exposed drying surface of 2.35 sqft. Take the case of a sample that initially contained 0.168 lb moisture/lb dry material and is to be dried to W = 0.005 lb/lb. In these units, the constant rate shown on the graph is transformed to 1 dW 0.38 ---=- 2.35 de 21.125 (lb/lb)/(hr)(sqft), which applies down to the critical moisture content WC = 0.04 lb/lb. The rate behavior over the whole moisture range is dW 0.03292, 0.04 < W < 0.168, --= de 0.823W, W < 0.04. Accordingly, the drying time is = 6.42 hr. This checks the reading off the plot of the original data on Figure 9.3(d). the evaporate assumes the wet bulb temperature of the air. Constant rate zones are shown in (d) and (e), and (e) reports that temperatures are truly constant in such a zone. The moisture content at which the drying rate begins to decline is called critical. Some of the variables on which the transition point depends are indicated in Figures 9.3(c) and (g). The shape of the falling rate curve sometimes may be approximated by a straight line, with equation - $p k(W - We), where W, is the equilibrium moisture content. When W, is zero as it often is of nonporous granular materials, the straight line goes through the origin. (d) and (h) illustrate this kind of behavior. The drying time is found by integration of the rate plots or equations. The process is illustrated in Example 9.2 for straight line behavior. Other cases require numerical integration. Each of the examples of Figure 9.3 corresponds to a particular substantially constant gas condition. This is true of shallow bed drying without recirculation of humid gas, but in other kinds of drying equipment the variation of the rate with time and position in the equipment, as well as with the moisture content, must be taken into account. An approximation that may be justifiable is that the critical moisture content is roughly independent of the drying conditions and that the falling rate curve is linear. Then the rate equations may be written -a$;= Ws - Hg)> w,<w<w,, k(H, - H,)(W- W,) we < w < WC. (9.15) w,- w, ’ Examples 9.3 and 9.4 apply these relations to a countercurrent dryer in which the humidity driving force and the equilibrium moisture content vary throughout the equipment. LABORATORY AND PILOT PLANT TESTING The techniques of measuring drying of stationary products, as on trays, are relatively straightforward. Details may be found in the references made with the data of Figure 9.3. Mass transfer resistances were eliminated by Wenzel through use of superheated steam as the drying medium. In some practical kinds of dryers, the flow patterns of gas and solid are so complex that the kind of rate equation discussed in this section cannot be applied readily. The sizing of such equipment is essentially a scale-up of pilot plant tests in similar equipment. Some manufacturers make such test equipment available. The tests may establish the residence time and the terminal conditions of the gas and solid. Dusting behavior and possible need for recycling of gas or of dried material are among the other factors that may be noted. Such pilot plant data are cited for the rotary dryer of Example 9.6. For the pneumatic conveying dryer of Example 9.8, the tests establish heat and mass transfer coefficients which can be used to calculate residence time under full scale operation. Scale-up factors as small as 2 may be required in critical cases, but factors of 5 or more often are practicable, particularly when the tests are analyzed by experienced persons. The minimum dimensions of a test rotary dryer are 1 ft dia by 6 ft long. A common criterion is that the product of diameter and rpm be in the range 25-35. A laboratory pneumatic conveying dryer is described by Nonhebel and Moss (1971). The veseel is 8 cm dia by about 1.5 m long. Feed rate suggested is lOOg/min and the air velocity about 1 m/set. They suggest that 6-12 passes of the solid through this equipment may be needed to obtain the requisite dryness because of limitations in its length. The smallest pilot spray dryer supplied by Bowen Engineering Co. is 30 in. dia by 2.5-6.0 ft high. Atomization is with 15 SCFM of air at 1OOpsig. Air rate is 250 actual cfm at 150-1000°F. Evaporation rates of 15-801b/hr are attained, and particles of product range from 5 to 40 pm. A pilot continuous multitray dryer is available from the Wyssmont Co. It is 4 ft dia by 5 ft high with 9 trays and can handle 25-200 lb/hr of feed. Batch fluidized bed dryers are made in quite small sizes, of the order of 100 Ib/hr of feed as the data of Table 9.14(a) show, and are suitable for pilot plant work. ;;y3.RfSSIFICATION AND GENERAL CHARACTERlSTlCS OF Removal of water from solids is most often accomplished by contacting them with air of low humidity and elevated temperature. Less common, although locally important, drying processes apply heat radiatively or dielectrically; in these operations as in freeze drying, the role of any gas supply is that of entrainer of the humidity. The nature, size, and shape of the solids, the scale of the operation, the method of transporting the stock and contacting it with gas, the heating mode, etc. are some of the many factors that
- 257. 238 D R Y E R S A N D C O O L I N G T O W E R S Drying with Changing Humidity of Air in a Tunnel Dryer A granular material deposited on trays or a belt is moved through a tunnel dryer countercurrently to air that is maintained at 170°F with steam-heated tubes. The stock enters at 14OOlbdty/hr with W = 1.16 lb/lb and leaves with 0.1 lb/lb. The air enters at 5% relative humidity (H, = 0.0125 lb/lb) and leaves at 60% relative humidity at 170°F (Hg = 0.203 lb/lb). The air rate found by moisture balance is 7790 lb dry/hr: EXAMPLE 9.3 1 7 0 F,H,=0.203 4 1400 Ib/hr We1.16 7790 Ib/hr 170F,Hp= 2 STM r 0.0125 4 w W=O.lO Drying tests reported by Walker, Lewis, McAdams, and Gilliland, Principles of Chemical Engineering, McGraw-Hill, New York, (1937, p. 671) may be represented by the rate equation -1oo dJ’= 0.28 (lb/lb)/hr, d0 I 0.58<W<1.16, 0.28(W - W,)/(O.58 - W,), W, < W ~0.58. (1) The air was at 95°F and 7% relative humidity, corresponding to a humidity driving force of H, - H, = 0.0082. Equilibrium moisture content as a function of the fraction relative humidity (RH), and assumed independent of temperature, is represented by W, = 0.0036 + O.l539(RH) - O.O97(RH)*. (2) The critical moisture content is assumed indpendent of the drying rate. Accordingly, under the proposed operating conditions, the rate of drying will be ( 0.28(H, - H,) 0.58<W<1.16, dW 0.0082 ’ -l@%= 0.28(H, - H,)(W - W,) W, < W < 0.58. (3) 0.0082(0.58 - 0.014) ’ With moisture content of the stock as a parameter, the humidity of the air is calculated by moisture balance from H, = 0.0125 + (1400/779O)(W - 0.1). (4) The corresponding relative humidities and wet bulb temperatures and corresponding humidities H, are read off a psychrometric chart. The equilibrium moisture is found from the relative humidity by Eq. (2). The various corrections to the rate are applied in Eq. (3). The results are tabulated, and the time is found by integration of the rate data over the range 0.1 < W < 1.16. w Y 1.16 0.203 1.00 0.174 0.9 0.156 0.8 0.138 0.7 0.120 0.58 0.099 0.50 0.094 0.4 0.066 0.3 0.049 0.2 0.030 0.1 0.0125 The drying time is 4 0.210 0.182 0.165 0.148 0.130 0.110 0.096 0.080 0.061 0.045 0.0315 R H w, 0.335 0.044 0.29 0.040 0.24 0.035 0.18 0.028 0.119 0.021 0.050 0.011 Rate 1 /Rate 0.239 4.184 0.273 3.663 0.303 3.257 0.341 2.933 0.341 2.933 0.356 2.809 0.333 3.003 0.308 3.247 0.213 4.695 0.162 6.173 0.102 9.804 I 0.10 O= * = 4.21 hr, 1.16 rate by trapezoidal rule. The length of tunnel needed depends on the space needed to ensure proper circulation of air through the granular bed. If the bed moves through the dryer at 10 ft/hr, the length of the dryer must be at least 42 ft. have led to the development of a considerable variety of equipment. The most elaborate classification of dryers is that of Kr611 (1978) which assigns one of 10 letters for the kind of solid and one of seven numbers for the kind of operation. As modified by Keey (1972), it comprises 39 main classes and a total of 70 with subclasses. Less comprehensive but perhaps more practical classifications are shown in Table 9.1. They take into account the method of operation, the physical form of the stock, special features, scale of production, and drying time. In a later section, the characteristics and performances of the most widely used equipment will be described in some detail. Many types are shown in Figure 9.4. Here some comparisons are made. Evaporation rates and thermal efficiencies are compared in Table 9.2, while similar and other data appear in Table 9.3. The wide spreads of these numbers reflect the diversity of individual designs of the same general kind of equipment, differences in moisture contents, and differences in drying properties of various materials. Fluidized bed dryers, for example, are operated as batch or continuous, for pharmaceuticals or asphalt, at rates of hundreds or many thousands of pounds per hour. An important characteristic of a dryer is the residence time distribution of solids in it. Dryers in which the particles do not move relatively to each other provide uniform time distribution. In spray, pneumatic conveying, fluidized bed, and other equipment in which the particles tumble about, a substantial variation in residence time develops. Accordingly, some particles may overdry and some remain wet. Figure 9.5 shows some data. Spray and pneumatic conveyors have wide time distributions; rotary and lluidized bed units have narrower but far from uniform ones. Differences in particle size also lead to nonuniform drying. In pneumatic con- veying dryers particularly, it is common practice to recycle a portion of the product continuously to ensure adequate overall drying. In other cases recycling may be performed to improve the handling characteristics when the feed material is very wet.
- 258. 9.3. CLASSIFICATION AND GENERAL CHARACTERISTICS OF DRYERS 2% EXAMPLE 9.4 Effects of Moist Air Recycle and Increase of Fresh Air Rate in Belt Conveyor Drying The conditions of Example 9.3 are taken except that recycle of moist air is employed and the equilibrium moisture content is assumed constant at We = 0.014. The material balance in terms of the recycle ratio R appears on the sketch: A = 7790 R W=1501.4R c!&d=FE A = air, W = water, S = dry solid Humidity of the air at any point is obtained from the water balance H = 1581.4R + 97.4 + 14OO(W - 0.1) t? 7790(R + 1) (1) The vapor pressure is ps = exp[11.9176 - 7173.9/(T, + 389.5)] atm. The saturation humidity is H, = (18/29)p,/(l -p,). The heat capacity is (2) (3) C = 0.24 + 0.45H,. (4) With constant air temperature of 170”F, the equation of the adiabatic saturation line is 170 - r, = ; (H, - H,) = F (H, - H.J. (5) The drying rate equations above and below the critical moisture content of 0.58 are R=O -lo!!!! d0 134.15(R + l)Os(H, - H,), 0.58<W<1.16, ( 6 ) = 60.33(R+ l)‘.s(H,- H,)(W-0.014), W <0.58. (7) When fresh air supply is simply increased by a factor R + 1 and no recycle is employed, Eq. (1) is replaced by H = 97.4(R + 1) + 1400( W - 0.1) * 7790(R + 1) The solution procedure is: 1. Specify the recycle ratio R (Ibs recycle/lb fresh air, dry air basis). 2. Take a number of discrete values of W between 1.16 and 0.1. For each of these fmd the saturation temperature T, and the drying rates by the following steps. 3. Assume a value of T,. 4. Find H,, P,, H,, and C from Eqs. (l)-(4). 5. Find the value of T, from Eq. (5) and compare with the assumed value. Apply the Newton-Raphson method with numerical derivatives to ultimately find the correct value of T, and the corresponding value of H,. 6. Find the rate of drying from Eqs. (6), (7). 7. Find the drying time by integration of the reciprocal rate as in Example 9.3, with the trapezoidal rule. The printout shows saturation temperatures and reciprocal rates for R = 0, 1, and 5 with recycle; and for R = 1 with only the fresh air rate increased, using Eq. (8). The residence times for the four cases are R = 0, moist air, 8 = 3.667 hrs = 1, moist air, = 2.841 = 5, moist air, = 1.442 = 1, fresh air, = 1.699. Although recycling of moist air does reduce the drying time because of the increased linear velocity, an equivalent amount of fresh air is much more effective because of its lower humidity. The points in favor of moist air recycle, however, are saving in fuel when the fresh air is much colder than 170°F and possible avoidance of case hardening or other undesirable phenomena resulting from contact with very dry air. R = 1, fresh air Tlz 1 I Rate
- 259. 240 DRYERS AND COOLING TOWERS EXAMPLE B.G(continued) R = 1, moist air 53 1 I Rate 1561 21 145.15 146.77 1 4 5 . 3 3 143.:21 142.21 1 4 1 .a:3 148.52 138.7;2 136. :32 1 3 4 . 7 9 132.62 10 ! ExamPle 9 . 4 . B e l t Conyej/nr d r :r‘ i n 4 2 0 R=l ! chansc f o r o t h e r cases 3 0 INPUT W 40 Hl=C1551.4*~R+1~+97.4+1400~~ W-.ljj~7790/CR+l) 4 5 ! H1=~97.4*~R+lj+1400tO >p’7790/CR+lj ! RQPI~CQ l i n e 4 0 rdith t h i s when n o recrclc i s u s e d . 50 C=.24+.45XHl 6 0 T=120 ! T r i a l s a t tcmp 7 0 GDSUB 200 3 0 Yl=Y 9 0 T=l.0001XT 100 GDSUB 200 110 Y2=Y 120 K=.0001tTSYl~~Y2-Y1> 1 3 0 T=T/1.0001-K ! Newton-Raphso n 140 150 160 170 175 150 2 0 0 2 1 0 220 H=.621*F/(l-Fj ! sat humidit R = 5, moist air 1 / Rate I F ABSCK/Tj<=.00001 T H E N 1 6 0 GDTD 7 0 P R I N T U S I N G 1 7 0 ; W>T, l.‘Rl ! Subst R 2 f o r Rl when W<.58 IMAGE D.DD>2X>DDD.DD,2X>D.DD i&l 3 0 END ! SR for sat temp F=EXF~11.917~-7173.9/iT+389. 5)) 2 3 0 ;=170-T-900SIH-HlL’C 2 4 0 R1=34.15*~R+1~*.8*~H-H1) 2 5 0 R2=60.33SCR+l>*.8t<H-Hl)tCW- 014) 2 6 0 RE T U R N 2 7 0 END PRODUCTS C O S T S More than one kind of dryer may be applicable to a particular product, or the shape and size may be altered to facilitate handling in a preferred kind of machine. Thus, application of through- circulation drying on tray or belt conveyors may require prior extrusion, pelleting, or briquetting. Equipment manufacturers know the capabilities of their equipment, but they are not always reliable guides to comparison with competitive kinds since they tend to favor what they know best. Industry practices occasionally change over a period of time. For example, at one time rotary kilns were used to dry and prepare fertilizer granules of a desired size range by accretion from concentrated solutions onto the mass of drying particles. Now this operation is performed almost exclusively in fluidized bed units because of economy and controlability of dust problems. Differences in thermal economies are stated in the comparisons of Table 9.2 and other tables. Some equipment cost data are in Chapter 20. When the capacity is large enough, continuous dryers are less expensive than batch units. Those operating at atmospheric pressure cost about l/3 as much as those at vacuum. Once-through air dryers are one-half as expensive as recirculating gas equipment. Dielectric and freeze driers are the most expensive and are justifiable only for sensitive and specialty products. In the range of l-50 Mtons/yr, rotary, fluidized bed and pneumatic conveying dryers cost about the same, although there are few instances where they are equally applicable. SPECIFICATION FORMS Typical examples of products that have been handled A listing of key information relating to dryer selection and design is successfully in particular kinds of dryers are listed in Table 9.4. The in Table 9.5. Questionnaires of manufacturers of several kinds of performance data of later tables list other examples. dryers are in Appendix C.
- 260. 9.4. BATCH DRYERS 241 evaporation increases roughly with the 0.8 power of the linear velocity, high velocities are desirable and are usually achieved by internal recirculation with fans. In order to maintain humidity at operable levels, venting and fresh air makeup are provided at rates of 5-50% of the internal circulation rate. Rates of evaporation of 0.05-0.4 lb/(hr)(sqft tray area) and steam requirements of 1.5-2.3 Ibs/lb evaporation are realized. Drying under vacuum is commonly practiced for sensitive materials. Figure 9.6 shows cross and through circulation tray 9.4. BATCH DRYERS Materials that require more than a few minutes drying time or are in small quantity are treated on a batch basis. If it is granular, the material is loaded on trays to a depth of l-2in. with spaces of approximately 3 in. between them. Perforated metal bottoms allow drying from both sides with improved heat transfer. Hot air is blown across or through the trays. Cross velocities of lOOOft/min are feasible if dusting is not a problem. Since the rate of TABLE 9.1. Classification of Dryers by Several Criteriaa (al Classification of dryers based on method of operation Dr et I I B&h ContiAuous Conduction Convection Conduction I I I I ’ Vacuum Atmos. I I I ‘neumati8 Fluid I I bed Paste Prclorm Granular Fibrous Paste Preform Preform Granular Hard Fibrous Granular L Fibrous 1 Sheet 1 1 Sheet j 1 Sheet 1 lb) Classification of dryers based on physical form of feed wet feed I Evaporate Evaporate P1CS.S Grind Grind or back-mix or preform Liquid Pumpable slurry Soft oaste Hard paste Free-tlowina Fibrous Sheet Vacuum band I Prelormed - paste I I Pa& Vacuum tray Agitated batch Convection tray FluId bed Vacuum band DIUlll Spray Pneumatic Convection band I Reform Vacuum tray Convection tray Batch through- circulation Fluid bed Pneumatic Convection band Cont. tray Cont. lhrough- circulation c Convection tray Vacuum tray Agitated batch Convection tray Batch through- circulation Fluid bed Vacuum tray Convection tray Batch through- circulation Fluid bed Indirect rotary lndwect rotary Pneumatic Direct rotary cont. tray Cont. through- circulation Convection band Cont. tray *See Figure 9.4 for sketches of dryer types. [Items (a)-(d) by Nonhebel and Moss, 1971, pp. 45,48-501.
- 261. 242 DRYERS AND COOLING TOWERS TABLE 9.1-(continued) (cl Classification of dryers by scale of production Pr0WS.S Smali scale Medium scale to 20/50 kg/h I 50 to loo0 kg/h I I Large scale tonnes/h I Through-circulation I I I Hazards I Classification of dryers by suitability for special features PKXCSS I I Dust I I Toxic I I I Flame I I Sensitive product I I Oxidation I I Temperature Mechanical I I Vacuum tray Vacuum band Spray Special form of product Low capital cost per unit arrangements. The typical operating data of Table 9.6 cover a wide range of drying times, from a fraction of an hour to many hours. Charging, unloading, and cleaning are labor-intensive and time-consuming, as much as S-6 hr for a 200-tray dryer, with trays about 5 sqft and l-l.5 in. deep, a size that is readily handled manually. They are used primarily for small productions of valuable and thermally sensitive materials. Performance data are in Tables 9.6(b) and (c). Through circulation dryers employ perforated or open screen bottom tray construction and have baffles that force the air through the bed. Superficial velocities of 150 ft/min are usual, with pressure drops of 1 in. or so of water. If it is not naturally granular, the material may be preformed by extrusion, pelleting, or briquetting so that it can be dried in this way. Drying rates are greater than in cross flow. Rates of 0.2-2lb/(hr)(sqft tray area) and thermal efficiencies of 50% are realized. Table 9.7(d) has performance data. Several types of devices that are used primarily for mixing of granular materials have been adapted to batch drying. Examples appear in Figure 9.8. They are suited to materials that do not stick to the walls and do not agglomerate during drying. They may be jacketed or provided with heating surfaces in the form of tubes or platecoils, and are readily arranged for operation under vacuum when handling sensitive materials. The double-cone tumbler has been long established. Some operating data are shown in Table 9.7. It and V-shaped dryers have a gentle action that is kind to fragile materials, and are discharged more easily than stationary cylinders or agitated pans. The fill proportion is 50-70%. When heated with 2 atm steam and operating at 10 Torr or so, the evaporation rate is 0.8-l.Olb/(hr)(sqft of heating surface). Fixed cylinders with rotating ribbons or paddles for agitation and pans with vertical agitators are used to a limited extent in batch operation. Pans are used primarily for materials that become sticky during drying. Table 9.7 and Figure 9.7 are concerned with this kind of equipment. A detailed example of capital and operating costs of a jacketed vacuum dryer for a paste on which they have laboratory drying data is worked out by Nonhebel and Moss (1971, p. 110). Fluidized bed dryers are used in the batch mode on a small scale. Table 9.14(a) has some such performance data. 9.5. CONTINUOUS TRAY AND CONVEYOR BELT DRYERS Trays of wet material loaded on trucks may be moved slowly through a drying tunnel: When a truck is dry, it is removed at one end of the tunnel, and a fresh one is introduced at the other end. Figure 9.8(c) represents such equipment. Fresh air inlets and humid
- 262. 9.5. CONTINUOUS TRAY AND CONVEYOR BELT DRYERS TABLE 9.2. Evaporation Rates and Thermal Efficiencies of Dryers E q u i p m e n t Figure 9.4 WhrVwft fIb/hr)/cuft Efficiency” (%) Belt conveyor e 46-58 Shelf Flow through a 0.02-2.5 18-41 Flow past a 0.02-3.1 18-41 R o t a r y Roto-louvre 7.2-15.4 23-66 Parallel current direct fired 6.1-16.4 6 5 Parallel current warm a i r f 6.1-16.4 5 0 Countercurrent direct fired 6.1-16.4 6 0 Countercurrent warm air f 6.1-16.4 4 5 Steam tube h 6.1-16.4 8 5 Indirect fired 9 6.1-16.4 2 5 T u n n e l 36-42 Pneumatic 0.5 mm dia granules 0 6.2 26-63 l.Omm 1.2 26-63 5mm 0 . 2 5 26-63 Spray m 0.1-3 21-50 Fluidized bed n 50-l 60 20-55 D r u m I 1.4-5.1 36-73 Spiral agitated High moisture I 1-3.1 36-63 Low moisture I 0.1-0.5 36-63 Splash paddle k 5 . 6 65-70 Scraped multitray d 0.8-l .6 “Efficiency is the ratio of the heat of evaporation to the heat input to the dryer. TABLE 9.3. Comparative Performances of Basic Dryer Types Basic Drver Tvoe Tray Conveyor Rotary Bprav Flash Fluid Bed Product filter cake Drying time (min) 1320 Inlet gas temperature (“F) 300 Initial moisture (% dry basis) 233 Final moisture 1% dry basis) 1 Product loading (lb dry/$) 3 . 2 5 Gas velocity (ft/min) 500 Product dispersion in gas slab Characteristic product shape thin slab Capacity [lb evap./(h)(dryer area)) 0 . 3 4 Energy consumed (Btu/lb evap.) 3000 Fan [hb/(lb evap./h)) 0 . 0 4 2 9.; 420 2 5 5 . 3 16.60 295 packed bed 2 0 . 6 3 1.35e 1700 2500 0.0049 0.0071 s a n d 12 1650 6 0 . 0 4 5 N.A. 700 gravity flow granules TiO 4 490 100 0 N.A. 5 0 wrav spherical drops 0.27’ 1300 0 . 0 1 9 spent grain <I.0 1200 150 1 4 N.A. 2000 dispersed grains loa 1900 0 . 0 1 7 2 . 0 1000 1 6 7 . 5 21 in. deep 1000 fluid bed $-in. particles 285 2000 0.105 a lb evap./(h)(dryer, volume). (Wentz and Thygeson, 1979: tray column from Perry, Chemical Engineers’ Handbook, 4th ed., p. 20-7; conveyor and spray columns from Proctor and Schwartz, Division of SCM; rotary, flash, and fluid bed columns from Williams-Gardner, 1971, pp. 75, 149, 168, 193). air outlets are spaced along the length of the tunnel to suit the rate of evaporation over the drying curve. This mode of operation is suited particularly to long drying times, from 20 to 96 hr for the materials of Table 9.6(e). In the rotating tray assembly of Figure 9.8(a), material enters at the top and is scraped onto successive lower trays after complete revolutions. A leveler on each tray, shown in Figure 9.8(b), ensures uniform drying. Although the air flow is largely across the surface of the bed, the turnover of the material as it progresses downward makes the operation more nearly through-circulation. A cooling zone is readily incorporated in the equipment. The contacting process is complex enough that laboratory tray drying tests are of little value. A pilot plant size unit is cited in Section 9.2. Some industrial data on rotary tray drying are in Table 9.9, and some other substances that have been handled successfully in this equipment are listed in Table 9.4. An alternate design has fixed jacketed trays for indirect heating. Scrapers attached to the central shaft drop the material from tray to tray. Like the rotating tray equipment, this equipment is limited to free flowing materials, but has the advantage of being essentially dust free. Equipment developed essentially for movement of granular solids has been adapted to drying. Screw conveyors, for instance, have been used but are rarely competitive with belt conveyors,
- 263. Feed (al Vacuum- chamber (c) SUPPlY ndensote Product removal kd (9) Ond Condensate (h) rodtally (Id Generally Knife steam heated & . . . (I) (4 (i) (e) (i) (0) Figure 9.4. Types of dryers cited in Tables 9.1 and 9.2. (a) Tray or compartment. (b) Vacuum tray. (c) Vertical agitated batch vacuum drier. (d) Continuous agitated tray vertical turbo. (e) Continuous through circulation. (f) Direct rotary. (g) Indirect rotary. (h) Agitated batch rotary (atmos or vacuum). (i) Horizontal agitated batch vacuum drier. (j) Tumble batch dryer. (k) Splash dryer. (I) Single drum. (m) Spray. (n) Fluidized bed dryer. (0) Pneumatic conveying (mostly after Nonhebel and Moss, 1971). 2 4 4
- 264. Pneumatic conveying dryer ” Ttme r (a) 0 8 1 6 24 32 40 46 56 6 4 T i m e , s - (b) Y t I I 0 1 2 3 4 (cl Figure 9.5. Residence time distribution in particle dryers. (a) Four types of dryers (McCormick, 1979). (b) Residence time distribution of air in a detergent spray tower; example shows that 27% (difference between the ordinates) has a residence time between 24 and 32sec [Place et al., Trans. Inst. Chem. Eng. 37,268 (1959)]. (c) Fluidized bed drying of two materials (Vanacek et al., Fluidized Bed Drying, 1966). particularly for materials that tend to degrade when they are moved. From the point of view of drying, belt conveyors are of two types: with solid belts and air flow across the top of the bed, called convection drying, or with perforated belts and through circulation of the air. The screw conveyor of Figure 9.8(f) has indirect heating. Solid belts are used for pastes and fine powders. Through 9.5. CONTINUOUS TRAY AND CONVEYOR BELT DRYERS 245 TABLE 9.4. Examples of Products Dried in Specific Kinds of Equipment 1. Spray dryers: rubber chemicals, sulfonates, inorganic phosphates, ceramics, kaolin, coffee, detergents, pharmaceuticals, pigments, inks, lignosulfonate wood waste, melamine and urea formaldehyde resins, polyvinyl chloride, microspheres, skim milk, eggs, starch, yeast, silica gel, urea, salts 2. Drum dryers: potatoes, cereals, buttermilk, skim milk, dextrins, yeasts, instant oat meal, polyacylemides, sodium benzoate, propionates, acetates, phosphates, chelates, aluminum oxide, m-disulfuric acid, barium sulfate, calcium acetate-arsenate- carbonate-hydrate-phosphate, caustic, ferrous sulfate, glue, lead arsenate, sodium benzene sulfonate, and sodium chloride 3. Vacuum drum dryers: syrups, malted milk, skim milk, coffee, malt extract, end glue 4. Vacuum rotary dryers: plastics, organic polymers, nylon chips, chemicals of all kinds, plastic fillers, plasticizers, organic thickeners, cellulose acetate, starch, and sulfur flakes 4. Belt conveyor dryers: yeast, charcoal briquettes, synthetic rubber, catalysts, soap, glue, silica gel, titanium dioxide, urea formaldehyde, clays, white lead, chrome yellow, and metallic stearates 6. Pneumatic conveyor dryers: yeast filter cake, starch, whey, sewage sludge, gypsum, fruit pulp, copper sulfate, clay, chrome green, synthetic casein, and potassium sulfate 7. Rotary multitray dryer: pulverized coal, pectin, penicillin, zinc sulfide, waste slude, pyrophoric zinc powder, zinc oxide pellets, calcium carbonate, boric acid, fragile cereal products, calcium chloride flakes, caffein, inorganic fluorides, crystals melting near lOO”F, prilled pitch, electronic grade phosphors, and solvent-wet organic solids 8. Fluidized bed dryer: lactose base granules, pharmaceutical crystals, weed killer, coal, sand, limestone, iron ore, polyvinyl chloride, asphalt, clay granules, granular desiccant, abrasive grit, and salt 9. Freeze dryers: meat, seafood, vegetables, fruits, coffee, concentrated beverages, pharmaceuticals, veterinary medicines, and blood plasma 10. Dielectric drying: baked goods, breakfast cereals, furniture timber blanks, veneers, plyboard, plasterboard, water-based foam plastic slabs, and some textile products 11. infrared drying: sheets of textiles, paper and films, surface finishes of paints and enamels, and surface drying of bulky nonporous articles. circulation belts are applied to granules more than about 3 mm in narrowest dimension. When the feed is not in suitable granular form, it is converted in a preformer to a size range usually of 3-15 mm. Belts are made of chain mail mesh or metal with 2 mm perforations or slots of this width. Several arrangements of belt dryers are shown in Figures 9.8(c)-(e). In the wet zone, air flow usually is upward, whereas in the drier and cooling zones it is downward in order to minimize dusting. The depth of material on the belt is l-8in. Superficial air velocities of 5 ft/sec usually are allowable. The multizone arrangement of Figure 9.8(e) takes advantage of the fact that the material becomes lighter and stronger and hence can be loaded more deeply as it dries. Each zone also can be controlled separately for air flow and temperature. The performance data of Table 9.9 cover a range of drying times from 11 to 2OOmin, and thermal efficiencies are about 50%. Laboratory drying rate data of materials on trays are best obtained with constant air conditions. Along a belt conveyor or in a tray-truck tunnel, the moisture contents of air and stock change with position. Example 9.3 shows how constant condition drying tests can be adapted to belt conveyor operation. The effects of recycling moist air and of increasing the air velocity beyond that studied in the laboratory tests are studied in Example 9.4. Recycling does reduce drying time because of the increased air velocity, but it
- 265. 246 D R Y E R S A N D C O O L I N G T O W E R S TABLE 9.5. Specification Form for a Dryer” 3. Product 5. Utilities 1. Operation 2. Feed m o d e operating cycle (a) material to be dried (b) feed rate (c) nature of feed (d) physical properties of solids: initial moisture content hygroscopic-moisture content heat capacity bulk density, wet particle size (e) moisture to be removed: chemical composition boiling point at 1 bar heat of vaporization heat capacity (f) feed material is (g) source of feed (a) final moisture content (b) equilibrium-moisture content at 60% r.h. (c) bulky density (d) physical characteristics 4. Design restraints (a) maximum temperature when wet when dry (b) manner of degradation (c) material-handling problems, when wet when dry (d) will flue-gases contaminate product? (e) space limitations (a) steam available at maximum quantity costing (b) other fuel at with heating value costing (c) electric power frequency p h a s e s costing 6. Present method of drying 7. Rate-of-drying data under constant external conditions: ordata from existing plant 8. Recommended materials of construction (a) parts in contact with wet material (b) parts in contact with vapors ‘Questionnaires of several manufacturers are in Appendix C. (Keey, 1972, p. 325). batch/continuous - h - kg/h solution/slurry/sludge/granular/ fibrous/sheet/bulky - kg/kg - kg/kg - kJ/kg”C - kg/m3 - m m - “C - MJ/kg - kJ/kg”C scaling/corrosive/toxic/abrasive/ explosive - kg/kg - kg/kg - kg/m3 granular/flaky/fibrous/powdery/ sheet/bulky - “C - “C - - bar pressure t106N/mZ) - kg/h - Wkg - - kg/h - MJ/kg - $/kg - V - h z - $/kWh - - is not as effective in this regard as the same increase in the amount becomes of fresh air. Recycling is practiced, however, to reduce heat consumption when the fresh air is cold and to minimize possible undesirable effects from over-rapid drying with low humidity air. H = 97.4(R + 1) + 1400(1.16 - W) 8 7790(R + 1) Parallel current operation also avoids overrapid drying near the end. For parallel flow, the moisture balance of Example 9.4 and replaces line 30 of the computer program. (9.16)
- 266. 9.6. ROTARY CYLINDRICAL DRYERS 247 Air exhaust Heat sour4 1 I Fan Dlying‘chamber sack (a) ‘END ENTRANCE SIDE EXIT FOR/ -. .- FOR WET TRUCKS DRY TRUCKS tlDN)IREdT HEATING SYSTEM (c) Figure 9.6. Tray dryer arrangements, batch and continuous. Performance data are in Table 9.5. (a) Air flow across the surfaces of the trays. (b) Air circulation forced through the beds on the trays (Proctor and Schwartz Inc.). (c) Continuous drying of trays mounted on trucks that move through the tunnel; air Row may be in parallel or countercurrent (P.W. Kilpatrick, E. Lowe, and W.B. Van Arsdel, Advances in Food Research, Academic, New York, 1955, Vol. VI, p. 342). When heating by direct contact with hot gases is not feasible because of contamination or excessive dusting, dryers with jacketed shells or other kinds of heat transfer surfaces are employed. Only enough air to entrain away the moisture is employed. The temperature of the solid approaches the boiling temperature of the water in the constant rate period. Figure 9.10 shows designs in which the heating tubes are fixed in space or are attached to the rotating shell. Table 9.10 gives some performance data. The kind of data desirable in the design of through-circulation Combined indirect and indirect dryers pass the hot gases first drying are presented for a particular case by Nonhebel and Moss through a jacket or tubes, and then wholly or in part through the (1971, p. 147). They report on effects of extrusion diameters of the open dryer. Efficiencies of such units are higher than of direct units, original paste, the bed depth, air linear velocity, and air inlet being in the range 60-80%. Table 9.10(d) shows performance data. humidity, and apply these data to a design problem. Since the surfaces are hot, this equipment is not suitable for 9.6. ROTARY CYLINDRICAL DRYERS Rotating cylindrical dryers are suited for free-flowing granular materials that require drying times of the order of 1 hr or less. Materials that tend to agglomerate because of wetness may be preconditioned by mixing with recycled dry product. Such equipment consists of a cylindrical shell into which the wet material is charged at one end and dry material leaves at the other end. Figure 9.9 shows some examples. Drying is accomplished by contact with hot gases in parallel or countercurrent flow or with heat transfer through heated tubes or double shells. Designs are available in which the tubes rotate with the shell or are fixed in space. Diameters typically are 4-10 ft and lengths are 4-15 diameters. The product of ‘pm and diameter is typically between 25 and 35. Superficial gas velocities are 5-lOft/sec; but lower values may be needed for fine products, and rates up to 35 ft/sec may be allowable for coarse materials. To promote longitudinal travel of the solid, the shell is mounted on a slope of 1 in 40 or 20. In a countercurrent dryer the exit temperature of the solid approaches that of the inlet gas. In a parallel current dryer, the exit gas is lo-20°C above that of the solid. For design purposes the temperature of the exit solid in parallel flow may be taken as 100°C. Flights attached to the shell lift up the material and shower it as a curtain through which the gas flows. Cross sections of some dryers are shown in Figure 9.10. The shape of flights is a compromise between effectiveness and ease of cleaning. The number is between 2 and 4 times the diameter of the shell in feet, and their depth is between & and Q of the diameter. Holdup in the dryer depends on details of design and operation, but 7-8% is a usual figure. Cross-sectional holdup is larger at the wet end than at the dry end. An 85% free cross section commonly is adopted for design purposes; the rest is taken up by flights and settled and cascading solids. Residence time depends on the nature of the material and mechanical features of the dryer. The performance data of Table 9.10 show a range of 7-9Omin. A formula cited by Williams- Gardner (1971, p. 133) for the geometrical residence time is 0 = kL/nDS, (9.17) where L is the length, D is the diameter, II is rpm, and S is the slope (in./ft). The coefficient k varies from 3 to 12 for various countercurrent single shell dryers. The formula may be of some value in predicting roughly the effects of changes in the quantities included in it. The only safe way of designing a rotary dryer is based on pilot plant tests or by comparison with known performance of similar operations. Example 9.5 utilizes pilot plant data for upscaling a dryer. The design of Example 9.6 also is based on residence time and terminal conditions of solid and air established in a pilot plant.
- 267. TABLE 9.6. Performance Data of Batch Tray and Tray-Truck Dryers (a) Cross-Flow Operation C o a t e d Tablets Capacity, wet charge (lb) 120 8 0 5 6 2 0 , 0 0 0 1800 3000 2800 4300 Number of trays 4 0 2 0 2 0 320 7 2 8 0 8 0 8 0 Tray area (ft’) 140 7 0 7 0 4800 1130 280 280 280 Depth of loading (in.) 0 . 5 1.0 0 . 5 2.0 2 . 0 1.0 1.0 1.5 Initial moisture (% w/w basis) 2 5 25-30 15 71 4 6 7 0 7 0 8 0 Final moisture (% w/w basis) nil 0 . 4 0 . 5 0 . 5 2 . 0 1.0 1.0 0 . 2 5 Maximum air temperature (“F) 113 284 122 200 180 300 200 200 Loading (lb/f?) 0 . 9 1.2 0 . 4 0 . 9 0.91 3 . 2 5 3 . 0 4 11.7 Drying time (hr) 12 5 . 5 1 4 2 4 4 . 5 2 2 4 5 12 Overall drying rate (Ib/hr) 2 . 6 5.3 0 . 8 4 6 2 . 5 185 9 6 . 6 4 3 . 2 so Evaporative rate (lb/hr/ft’) 0 . 0 1 8 6 0 . 0 5 0 . 0 0 8 0 . 0 1 3 0 . 3 2 7 0.341 0 . 1 8 4 0 . 3 1 7 Total installed HP 1 1 1 4 5 6 4 2 2 P T F E C h a l k Filter Cake (Williams-Gardner, 1971, p. 75, Table 12: first three columns courtesy Calmic Engineering Co.; last five columns courtesy A.P.V.-Mitchell (Dryers) Ltd.) (b) Vacuum Dryers with Steam Heated Shelves Soluble Paint Ferrous Ferrous Lithium T u n g s t e n Stabilized Aspirin P i g m e n t Glutinate Succinate H y d r o x i d e Alloy D i a z a m i n Capacity, wet product (lb/h) 4 4 Tray area (ft*) 108 Depth of loading (in.) Initial moisture (% w/w basis) Final moisture (% w/w basis) Max temp f”F) Loading [lb charge (wet) ft*] Drying time (hr) Overall drying rate (lb moisture evaporated/ft*/hr) Total installed HP 7 2 . 4 1.25 104 6.1 15 0 . 2 9 3 6 3 0 . 5 4 1 . 6 5 2 . 5 3 6 . 8 12.8 4 . 6 108 108 108 5 4 215 172 2 0 . 5 1 1 0 . 5 0 . 7 5 4 9 . 3 2 5 3 7 . 4 5 9 1.6 22.2 0 . 7 5 0 . 5 18.8 0 . 9 nil 0 . 5 158 203 203 122 239 9 5 102 2 . 3 1.94 3 . 0 8 7 . 1 6 1.22 3 6 6 4 4 . 5 12 4 . 8 0 . 1 4 0.11 0.11 0.034 0 . 0 1 3 0 . 0 0 5 8 6 6 6 3 2 5 Vacuum (in. Hg) 2 9 . 5 2 8 2 7 2 7 2 7 2 9 22-23 (Williams-Gardner, 1971, p. 88, Table 15: courtesy C a l m i c Engineering Co.) (c) Vacuum Dryers with Steam-Heated Shelves Material Sulfur Black C a l c i u m C a l c i u m C a r b o n a t e Phosphate Loading (kg dry material/m’) 2 5 17 3 3 Steam (kPa gauge) pressure 410 410 205 Vacuum (mm Hg) 685-710 685-710 685-7 10 Initial moisture content f%, wet basis) 5 0 5 0 . 3 3 0 . 6 Final moisture content f%, wet basis) 1 1.15 4 . 3 Drying time (hr) 8 7 6 Evaooration rates fka/sec m*) 8.9 x 1O-4 7.9 x 1om4 6.6 x 1o-4 (Chemical Engineers’ Handbook, McGraw-Hill, New York, 1984, p. 20.23, Table 20.8). (d) Through Circulation Dryers Kind of Material Vegetable Capacity (kg product/hr) 122 Number of trays 1 6 Tray spacing (cm) 4 3 Tray size (cm) 91.4x 104 Depth of loading (cm) 7 . 0 Physical form of product c r u m b s Initial moisture content (%, dry basis) 11.1 Final moisture content (%, dry basis) 0.1 Air temperature f”C) 8 8 Air velocity, superficial (m/set) 1.0 Tray loading (kg product/m2) 16.1 Drying time (hr) 2 . 0 Overall drying rate (kg water evaporated/hr m*) 0 . 8 9 Steam consumption (kg/kg water evaporated) 4 . 0 Installed (kW) p o w e r 7 . 5 4 2 . 5 2 7 . 7 2 4 2 4 4 3 4 3 91.4x 104 85 x 98 6 4 0.6~cm diced w a s h e d cubes s e e d s 6 6 9 . 0 1 0 0 . 0 5 . 0 9 . 9 77 dry-bulb 3 6 0.6-l .O 1.0 5 . 2 6 . 7 8 . 5 5 . 5 1 1 . 8 6 1.14 2 . 4 2 6 . 8 19 19 (Proctor and Schwartz Co.).
- 268. TABLE 9.9-(continued) (e) Tray and Tray-Truck Dryers Material Color Chrome Yellow Toluidine Red Color Type of dryer Z-truck 16-tray dryer 16-tray 3-truck Capacity (kg product/hr) 11.2 16.1 1.9 56.7 Number of trays 8 0 16 1 6 180 Tray spacing (cm) 1 0 10 10 7 . 5 Tray size (cm) 60~75x4 6 5 x 100 x 2.2 65x100~2 60x70x3.8 Depth of loading (cm) 2.5-5 3 3 . 5 3 Initial moisture (%, bone-dry basis) 207 4 6 220 223 Final moisture (%, bone-dry basis) 4 . 5 0 . 2 5 0.1 2 5 Air temperature (“C) 85-74 100 5 0 9 5 Loading (kg product/m’) 10.0 3 3 . 7 7 . 8 14.9 Drying time (hr) 3 3 21 41 2 0 Air velocity (m/set) 1.0 2 . 3 2 . 3 3 . 0 Drying (kg water evaporated/hr m2) 0 . 5 9 6 5 0.41 1.17 Steam consumption (kg/kg water evaporated) 2 . 5 3 . 0 - 2 . 7 5 Total installed power (kW) 1.5 0 . 7 5 0 . 7 5 2 . 2 5 Z-truck 4 . 8 120 9 6 0 x 70 x 2.5 116 0 . 5 9 9 9 . 2 8 9 6 2 . 5 0.11 1.5 (Proctor and Schwartz Co.). TABLE 9.7. Performance of Agitated Batch Dryers (See Fig. 9.7) (a) Double-Cone Tumbler Tun sten ‘b Car ide Penicillin Hydroquinone Prussian Blue Pigment Volatile ingredient Physical nature of charge Dryer dia fft) Dryer capacity (f?) Method of heating Heating medium temperature (“F) Vacuum (mm Hg abs) Initial volatile content (% w/w basis) Final volatile content 1% w/w basis) Weight of charge (lb) Bulk density of charge (lb/f?) Dtvina time tmin) naphtha heavy slurry 2 2 . 5 hot water 180 40-84 18.0 nil 640 256 155 water pellets 2 2 . 5 240 12-18 0 . 3 4 0.01 130 5 1 . 5 215 acetone p o w d e r 2 2 . 5 hot water 140 4 0 2 7 . 9 nil 5 5 2 1 . 5 9 0 water 2 2 . 5 hot water 150 50-100 5.0 0 . 2 5 61 2 6 . 5 5 0 filtercake 2 2 . 5 steam 225 40-110 8 3 4 . 8 1 4 2 . 5 5 8 . 5 480 fCourtesy Patterson Division, Banner Industries Inc.; Williams-Gardner, 1971). (b) Paddle, Ribbon, and Pan” Material Mean Sire(;fm;ryer Initial Absolute D;G;rg Wet Moisture Pressure Jacket Z-S!!’ Type of Content (%, Wet Basis) in Dryer Temp DWWeg Dryer Length Dia (HP1 hb) (“Cl (hr) CW,% “c) Organic paste Different fine aromatic organic compound crystals Anthracene (water and pyridine) Dyestuff paste Different organic pastes 1 Different dyestuff oastes HCRP 5500 1200 HCRP 3800 1350 HCRP 3800 1350 HCRP 5500 1200 1 5 1 5 4000 0 . 3 6 3 0 2260 0.2 6 8 4660 0 . 4 7 5 2100 0.2 6 265 265 200 8 0 1 5 3 5 125 6 4 5 125 8 6 0 125 4 2 5 HCRP 8900 1800 3 5 37000 0.72 7 6 665-1000 170 16 7 5 HCSB 2750 1200 1 0 2000 0 . 3 7 0 265 105 1 4 3 0 PVP 1800 1 5 1080 0 . 4 41 1000 125 3 2 3 5 PVP 2450 2 5 800 0 . 4 3 5 665 125 7; 2 5 PVP 1800 1 5 1035 0 . 4 61 1000 125 11 135 PVP 2450 20-30 2400 0 . 7 6 4 470 125 12 115 ’ HCRP = paddle agitator; HCSP = ribbon agitator; PVP = pan with vertical paddles. (Nonhebel and Moss, 1971). 249
- 269. 250 DRYERS AND COOLING TOWERS TABLE 9.7-(continued) (c) Pan Dryer S o d i u m Potassium Thiosulphate Zeolite Arsenic Pentoxide Dryer diameter Dryer depth Capacity (lb product) Initial moisture (% w/w basis) Final moisture (% w/w basis) Method of heating Atmospheric (a) or vacuum (b) Drying temperature: material (“F) Drying temperature: shelf (“F) Bulk density product (lb/f-t31 Drying time (hr/batch) Material of construction 6ftOin. 2ftOin. 12cwt 3 7 0 steam bl 26 Hg 5 ss 2ft3in. 1 ROin. 14 lb 4 0 1 steam (a) 60 Ib/in.*/gauge 153c 8ftOin. 2ftOin. 2: ton/day 3 5 2-3 steam lb) 3 8 MS ss [Courtesy A.P.V.-Mitchell (Dryers) Ltd., Williams-Gardner, 19711. Chain casing Steam or hot water inlet Condensate or hot water return Variable speed and brake motor optional ---+oncrete or kkkchorg opening L--J I-.,, r..r,,....“- (a) b) Figure 9.7. Tumbling and agitated heated dryers for atmospheric and vacuum batch operation. (a) Double cone tumbler; performance data in Table 9.6(a) (P ennsalt Chem. Co.). (b) V-shaped tumbler. (c) Ribbon agitated cylinder; performance data in Table 9.6(b). (A) jacketed shell; (B) heads; (C) charging connections; (D) discharge doors; (E) agitator shaft; (F) stuffing box; (G) shaft bearings; (H) agitator blades; (J) vapor outlets; (K) steam inlets; (L) condensate outlets; (M) discharge siphon for shaft condensate (Buflovak Equip. Div., Blaw Knox Co.) (d) Paddle agitated cylinder. Performance data in Table 9.6(b). (e) H orizontal pan with agitator blades. Data are Table 9.6(b).
- 270. Figure 9.7-(continued) (d J-j’ ,,Turbinas ( f a n s ) - - - ,- I ’ ,’ 1Heating elements f 1’ ‘i-’ 1 t II A 1 / -: II ‘Z0 8 II (a) bl 9.6. ROTARY CYLINDRICAL DRYERS 251 ., ., MATERIAL FALLING TO TRAY BELOW PILE OF MATERIAL FROM TRAY ABOVE Sealing partition Transfer section (cl (d) Figure 9.8. Rotary tray, through-circulation belt conveyor, and heated screw conveyor dryers. (a) Rotary tray dryer (Wyssmont Co.!. (b) Action of a rotating tray and wiper assembly (Wyssmont Co.). (c) A single conveyor belt with air upflow in wet zone and downflow in dry (Proctor and Schwartz Inc.). (d) A two-stage straight-through belt conveyor dryer. (e) A three-belt conveyor dryer; as the material becomes dryer, the loading becomes deeper and the belt longer (Proctor and Schwartz Inc.). (f) Screw conveyor dryer with heated hollow screw (Bepex Corp.).
- 271. (e) Figure 9.~(conrinued) TABLE 9.8. Performance of Rotary Tray and Pan Dryers (a) Multitray Dryers at Atmospheric Pressure Dryer height Dryer diameter Tray area (ft’) China C l a y - - 7000 Bread Cu-Ni Crumbs Concentrate ci%~t C a l c i u m Vitamin Kaolin Chloride Urea P o w d e r - - 23ft 23R 47ft 47ft 12ft - - 19ft 19ft 31 ft 15ft 9ft 2000 2900 - - - - - (drying) 1000 Capacity fIb/product/hr) Initial moisture (% w/w basis) (cooling) 3 1 , 0 0 0 1680 1 9 , 0 0 0 4200 1 0 , 0 0 0 2 4 , 0 0 0 5000 200 3 0 3 6 2 2 4 5 3 5 2 5 2 0 2 0 Final moisture (% w/w basis) 10 5 5 1 8 5 1 0 . 2 5 Product temperature (“F) 160 100 200 - - - - - Residence time (min) 40 4 0 2 5 - - - - - (drying) 2 0 Evaporation rate (lb/ft*/hr) (cooling) 9 . 1 0 0 804 4060 2050 4600 Method of heating external steam external external external oil oil gas oil Heat consumption (Btu/lb moisture evaporated) 1750 - 2200 1750 1850 Installed HP 80 2 5 6 0 2 3 4 7 Williams-Gardner, 1971). (First three columns courtesy Buell Ltd.; last five columns courtesy The Wyssmont Co., Inc.). 1 1 , 0 0 0 100 3 7 internal external external gas steam steam 1800 3500 2700 6 5 7 5 2; (b) Multiple Vacuum Pan Dryer S o d i u m Hydrosulphite Maneb Melamine AgaivvI:VbBgttd Dryer diameter (pans) (m) N u m b e r o f p a n s Area fapprox)(m*) Dry product (Ib/hr) Initial moisture (% w/w) Final moisture (% w/w) Heating Pan temperature (“C) Evaporation rate (Ib/f?/hr) Drying time (min) (Data of Krauss-Maffei-Imperial GmbH). 2 5 12.4 1100 4 0.1 hot water 9 8 0 . 3 2 5 15 2 2 2 17 1 1 17 4 2 . 8 2 7 . 6 4 2 . 8 660 1870 440 2 3 1 1 6 2 0 . 5 0 . 0 3 3 steam steam steam 1.3 atm 2.5 atm 2.5 atm 105 125 125 0 . 3 2 5 0 . 7 9 0 . 7 8 170 12 3 0 252
- 272. 9.6 ROTARY CYLINDRICAL DRYERS 253 TABLE 9.9. Petformance of Through-Circulation Belt Conveyor Dryers [See Figs. 9.8(c)-(e)] (a) Data of A.P.V.-Mitchell (Dryers) Ltd. Fertilizers Bentonite Pigment Nickel Metallic Hydroxide Stearate Effective dn/er length Effective band width Capacity (lb productlhr) Method of feeding Feedstock preforming > Initial moisture (% w/w basis) Final moisture (% w/w basis) Drying time (min) Drying rate (lb evaporated/f?/hrJ Air temperature range 1°F) Superficial air velocity (ft/min) Heat consumption (Btu/lb evaporated) Method of heating Fan installed HP 42ft6in. 60ftOin. 24ftOin. 8ft6in. 8ft6in. 4ftOin. 2290 8512 100 oscillator 30 10.0 14 6.5 - 200 - direct oil 50 45.0 2.0 ’ 16 7.0 - 200 - direct oil 35 58.9 0.2 60 2.0 - 180 - steam 14 24ftOin. 4ftOin. 125 extruder 75 0.5 70 7.5 180 - steam 14 41 ft 3 in. 6ftOin. 125 extruder 75 0.2 60 1.5 - 125 - steam 28 (Williams-Gardner, 1971). (b) Data of Krauss-Maffei-Imperial GmbH Aluminium Polyecrylic Hydrate Nitrile Sulfur Calcium Titanium Carbonate Dioxide Effective dryer length Effective band width Capacity (lb product/hr) Method of feeding Feedstock preforming > Initial moisture (% w/w basis) Final moisture I% w/w basis) Drying time (min) Drying rate (lb evaporated/hr/$ Air temperature range (“F) Superficial air velocity Ift/min) Heat consumption (lb steam/lb evaporated) Method of heating Fan installed hp (approx.) 32ft9in. 6h6in. 615 grooved drum 38.0 0.2 26 2.88 233 140 43ftOin. 28ftOin. 50ftOin. 108ftOin. 6ft6in. 6ft6in. 6ft3in. 9ft6in. 2070 660 1800 6000 extruder extruder extruder extruder 55.0 45.0 60.0 50.0 1.0 1.0 0.5 0.5 52 110 40 45 3.37 3.57 5.73 6.0 186/130 194/230 320 3141392 100/216 140 160 150 1.7-1.8 1.8-1.9 1.8-1.9 50 lb/in.’ 25 lb/in.* 90 lb/in.’ steam steam steam 25 65 20 1.7-1.8 160 lb/in steam 35 2 1.8-1.9 260 lb/in.’ steam 80 (Williams-Gardner, 1971) (c) Data of Proctor and Schwartz Inc. Kind of Material Inorganic Pigment Cornstarch Fiber Staple Charcoal Briquettes Gelatin Inorganic Chemical Capacity (kg dry product/hr) 712 Approximate dryer area (m’) 22.11 Depth of loading (cm) 3 Air temperature (‘X1 120 Loading (kg product/m? 18.8 Type of conveyor (mm) 1.59 by 6.35 slots Preforming method or feed Type and size of preformed particle (mm) Initial moisture content (% bone-dry basis) Final moisture content (% bone- dry basis) Drying time (min) Drying rate [kg water evaporated/(hr m’)] Air velocity (superficial)(m/sec) Heat source per kg water evaporated [steam kg/kg gas h3/kgll Installed power (kW) 29.8 119.3 194.0 82.06 179.0 41.03 rolling filtered and extruder scored 6.35-diameter scored filter extrusions cake 120 85.2 0.5 35 38.39 1.27 gas 0.11 4536 66.42 4 115-140 27.3 1.19 by 4.76 slots 1724 Stage A Stage 6 57.04 35.12 - - 130-100 100 3.5 3.3 2.57.diameter holes, perforated plate fiber feed cut fiber 110 13.6 9 24 11 42.97 17.09 1.12 0.66 steam steam 2.0 1.73 5443 295 52.02 16 135-120 182.0 8.5 x 8.5 mesh screen pressed 104.05 5 32-52 9.1 4.23 x 4.23 mesh screen extrusion 64 x 51 x 25 2-diameter extrusions 37.3 300 5.3 105 22.95 1.12 waste heat 11.1 192 9.91 1.27 steam 2.83 30.19 4 121-82 33 1.59 x 6.35 slot rolling extruder 6.35.diameter extrusions 111.2 1.0 70 31.25 1.27 9s 0.13 (Perrys Chemical Engineers Handbook, McGraw-Hill, New York, 1984).
- 273. 254 DRYERS AND COOLING TOWERS /Feed chute Fr~ctlon seat assembly Drive - (a) Cyclone type collectors Air lock Air heater Entering’ air z b) Product discLarge Trundn ,,;I ossembly Breechng seals Figure 9.9. Rotary dryer assemblies. (a) Parts of the shell of a direct fired rotary dryer (C.E. Raymond Bartlett Snow Co.). (b) Assembly of a rotary dryer with pneumatic recycle of fines (Standard Steel Corp.). (c) Steam tube dryer with mechanical conveyor for partial recycle of product for conditioning of the feed. thermally sensitive materials and, of course, may generate dust if the gas rate through the open dryer is high. In the Roto-Louvre design of Figure 9.10(b) the gas enters at the wall, flows first through the bed of particles and subsequently through the shower of particles. Performance data are in Tables 9.10(b) and (c). A formula for the power required to rotate the shell is given by Wentz and Thygeson (1979): P = 0.45W,v, + O.l2BDNf, (9.18) where P is in watts, W, is the weight (kg) of the rotating parts, v, is the peripheral speed of the carrying rollers (m/set), B is the holdup of solids (kg), D is diameter of the shell (m), N is rpm, and f is the number of flights along the periphery of the shell. Information about weights may be obtained from manufacturers catalogs or may be estimated by the usual methods for sizing vessels. Fan and driver horsepower are stated for the examples of Tables 9.10(a)-(c). The data of Table 9.10(a) are represented roughly by P=5+O.llDL, (9.19) where P is in HP and the diameter D and length L are in feet. 9.7. DRUM DRYERS FOR SOLUTIONS AND SLURRIES Solutions, slurries and pastes may be spread as thin films and dried on steam heated rotating drums. Some of the usual arrangements are shown on Figure 9.11. Twin drums commonly rotate in opposite directions inward to nip the feed, but when lumps are present that could damage the drums, rotations are in the same direction. Top feed with an axial travelling distributor is most common. Dip feed is shown in Figure 9.11(d) where an agitator also is provided to keep solids in suspension. When undesirable boiling of the slurry in the
- 274. 9 . 8 . P N E U M A T I C C O N V E Y I N G D R Y E R S 255 b) (cl (4 Figure 9.10. Cross sections of rotary dryers. (a) Action of the flights in cascading the drying material. The knockers are for dislodging material that tends to cling to the walls. (b) Cross section of chamber of rotolouvre dryer showing product depths and air flows at feed and discharge ends. The air enters at the wall and flows through the bed as well as through the cloud of showered particles (Link-Belt Co.). (c) Showering action in a dryer with fixed steam tubes and rotating shell. (d) Section and steam manifold at the end of a dryer in which the steam tubes rotate with the dryer. pan could occur, splash feed as in Figure 9.11(c) is employed. Example 9.7 describes some aspects of an actual installation. For mechanical reasons the largest drum made is 5 ft dia by 12 ft with 188 sqft of curved surface. A 2 x 2 ft drum also is listed in manufacturers’ catalogs. Performance data are in Tables 9.11 and 9.12. The material comes off as flakes l-3 mm or less thick. They are broken up to standard size of about a in. square. That process makes fines that are recycled to the dryer feed. Drying times fall in the range of 3-12sec. Many laboratory investigations have been made of drying rates and heat transfer coefficients, but it appears that the only satisfactory basis for sizing plant equipment is pilot plant data obtained with a drum of a foot or more in diameter. Usually plant performance is superior to that of pilot plant units because of steadier long time operation. Rotation speeds of the examples in Table 9.12 show a range of l-24rpm. Thin liquids allow a high speed, thick pastes a low one. In Table 9.13(c) the evaporation rates group in the range 15-30 kg/m2 hr, but a few of the data are far out of this range. The few data in Table 9.13(a) show that efficiencies are comparatively high, 1.3 lb steam/lb water evaporated. A safe estimate of power requirement for double drum dryers is approx 0.67 HP/(rpm)(lOO sqft of surface). Maintenance can be as high as lO%/yr of the installed cost. Knives last from 1 to 6 months depending on abrasiveness of the slurry. Competitors for drum dryers are solid belt conveyors that can can handle greater thicknesses of pasty materials, and primarily spray dryers that have largely taken over the field. 9.8. PNEUMATIC CONVEYING DRYERS Free-flowing powders and granules may be dried while being conveyed in a high velocity air stream. The necessary equipment is variously called pneumatic conveying dryer, pneumatic dryer, air lift dryer, or flash dryer. The basic system consists of an air heater, solids feeding device, vertical or inclined drying leg, cyclone or other collector and an exhaust fan. Figure 9.12 shows some of the many commercial equipment. Provision for recycling some of the product generally is included. Some of the materials being handled successfully in pneumatic dryers are listed in Table 9.5. Readily handled particles are in the size range l-3 mm. When the moisture is mostly on the surface, particles up to 10mm have been processed. Large particles are brought down to size in dispersion devices such as knife, hammer or roller mills. Typical performance data are summarized in Table 9.13. In practice air velocities are lo-30 m/set. The minimum upward velocity should be 2.5-3 m/set greater than the free fall velocity of the largest particles. Particles in the range of l-2 mm correspond to an air velocity of 25 m/set. Since agglomerates may exist under drying conditions, the safest design is that based on pilot plant tests or prior experience.
- 275. 256 D R Y E R S A N D C O O L I N G T O W E R S EXAMPLE 9.5 Scale-Up of a Rotary Dryer Tests on a laboratory unit come up with the stated conditions for drying a pelleted material at the rate of 1000 lb dry/hr: The residence time is 20min. The speed is 3-4rpm. On the average, 7.5% of the cross section is occupied by solid. Because of dusting problems, the linear velocity of the air is limited to 12 ft/sec. The diameter and length will be found. Since the inlet and outlet conditions are specified and the moisture transfer is known, the heat balance can be made. The heat capacity of the solid is 0.24: moisture evap = 1000(0.6-0.05) = 550 lb/hr air rate = 550/(0.0428 - 0.013) = 18,456 lb/hr Off a psychrometric chart, the sp vol of the air is 15.9 cuft/(lb dry). The diameter is 18,456(15.9) > 112 D = 3600(12)(1-0.075)x/4 = 3.06 ft, say 3.0 ft. The length is L= 30(20/w 0.075nD2/4 = 18.9 ft. EXAMPLE 9.6 Design Details of a Countercurrent Rotary Dryer Pilot plants indicate that a residence time of 3 hr is needed to accomplish a drying with the conditions indicated on the sketch. For reasons of entrainment, the air rate is limited to 750 lbs dry/(hr)(sqft cross section). Properties of the solid are 501b/ tuft and 0.22Btu/(lb)(“F). Symbols on the sketch are A = dry air, S = dry solid, W = water: 136F 150 psig steam A Ib/hr 60 F Air 4 H = 0.008 In terms of the dry air rate, A lb/hr, the average moist heat capacity is In the dryer, the enthalpy change of the moist air equals the sum of the enthalpy changes of the moisture and of the solid. Add 7% for heat losses. With steam table data, (0.2436 + 74.93/A)A(290 - 136) = 1.07[333(1120.3) + l(228) + 1000(0.22)(260 - 60) - 334(28)] = 1.07(407,936) = 43,649], :. A = 11,633 lb/hr. The exit humidity is H = 0.008 + 333/11,633 = 0.0366 lb/lb, which corresponds to an exit dewpoint of 96”F, an acceptable value. With the allowable air rate of 750 lb/hr sqft, the diameter of the dryer is D = dl1,633/750n/4 =4.44ft, say 4.5 ft. Say the solid occupies 8% of the cross section. With a solids density of 50 lb/tuft, the dryer volume, v = 3(1000/50)/0.08 = 750 tuft, and the length is L =750/(4.5)=x/4=47.2 ft. The standard number of flights is 2-4 times the diameter, or number = (2-4)4.5 = 9-18, say 12. The product of rpm and diameter is 25-35 :. rpm = (25-35)/4.5 = 5.5-7.8, say 6.7. The stm heater duty is Q, = 11,633(0.2436)(290 - 60) = 651,733 Btu/hr, 150 psig stm, stm = 651,733/857 = 760.5 lb/hr. Evaporation efficiency is 7 = 333/760.5 = 0.438 lb water/lb stm. The efficiency of the dryer itself is qd = 407,936/651,733 = 0.626 Btu/Btu.
- 276. TABLE 9.10. Performance Data of Rotary Dryers (a) Direct Heated Dryers Sugar ceet C a l c i u m Blast Lead Pulp C a r b o n a t e ” Furnace Slaga Concentrateb Sandb Zinc Ammonium Concentrateb Sulphate” Fine Salt” Crystalsd Chemicalsd Air flow parallel parallel parallel parallel parallel parallel counter Dryer length 9ft2in. 6ft3in. 7 ft 2 in. 4ft6in. 4ft6in. 7ft6in. 9hOin. Dryer length 46ftOin. 34ftOin. 40ftOin. 35ftOin. 32R6in. 60ftOin. 40ftOin. Method of heating oil oil oil oil gas oil gas Method of feed Initial moisture (% w/w) Final moisture (% w/w) Evaporation (Ib/hr) Capacity (lb evaporated/f? dryer volume) Efficiency (Btu supplied/water evaporated) Inlet air temperature (“F) Outlet air temperature (“F) Residence time (av. min) Fan HP Motive HP Fan capacity (std. air ft3/min) screw belt belt screw chute screw a 2 1 3 . 5 3 3 1 4 5 . 6 5 ia 10 0 . 5 nil a 0 . 0 4 3 a 3 4 , 0 0 0 6000 1 1 , 6 0 0 1393 701 8060 1 1 6 7 2 . 5 1 . 3 5 2.3 2.5 0.2 1120 0 . 5 1420 1940 1710 2100 1850 1920 2100 1650 - 1560 1560 1560 1300 1650 1500 400 230 220 248 200 222 200 180 2 0 2 5 3 0 2 0 12 2 0 15 7 0 4 0 5 0 2 0 5 7 5 2 5 15 2 0 2 5 1 0 1 0 5 5 6 0 45000 a500 I a.000 2750 2100 12,000 la.500 5 ft 0 in. 40ftOin. steam f e e d e r screw 5.0 7 . 0 0.1 a . 9 9 400 1150 0 . 5 2 0 . 2 4 5 280 170 4 0 a 15 counter 1OftOin. 60ftOin. steam 302 144 7 0 - 6 0 - indirect counter 4ft6in. 27 ft 0 in. Louisville steam tube screw 1 . 5 0.1 6 3 - - 1Courtesy Buell Ltd. Courtesy Head Wrightson (Stockton) Ltd. ‘Courtesy Edgar Allen Aerex Ltd. dCourtesy Constantin Engineers Ltd.-Louisville Dryers; Williams-Gardner, 1971. (b) Roto-Louvre Dryers Bone Meal Sugar’ Sulfate of Bread Ammonia” C r u m b s Bentonite Dryer diameter Dryer length Initial moisture (% w/w basis) Final moisture (% w/w basis) Method of feed Evaporation rate (Ib/hr) Efficiency (Btu supplied/lb evaporation) Method of heating Inlet air temperature PF) Outlet air temperature PF) Residence time, min Fan HP (absorbed) Motive HP (absorbed) Fan capacity (f?/min) Inlet 7ft6in. 7ft6in. 12hOin. 25ftOin. 17.0 1 . 5 7 . 0 0 . 0 3 screw screw 1660 500 7 4 . 3 4 0 steam steam 203 194 122 104 9 . 3 1 2 . 5 4 9 . 3 5 2 . 2 a 12.5 1 8 , 0 0 0 16,000 5380 2 0 , 0 0 0 7ft6in. 25 ft 0 in. 1.0 0 . 2 chute 400 - steam 246 149 9 . 0 5 5 1 5 4ft6in. 6ftlOin. 20ftOin. 30ftOin. 3 7 4 5 2 . 5 1 1 chute chute 920 7100 5 5 6 2 . 5 gas oil 572 642 158 176 25.7 3 7 . 3 13.7 5 4 . 3 2.3 2 0 . 0 Outlet 14,000 2 2 , 3 0 0 2 1 , 0 0 0 5100 2 5 , 0 0 0 “Combined two-stage dryer-cooler. (Courtesy Dunford and Elliott Process Engineering Ltd.; Williams-Gardner, 1971). (continued)
- 277. TABLE 9.1~(continued) (c) Roto-Louvre Dryers Material Dried Ammonium Sulfate Foundry Sand Mett;k;gical D r y e r d i a m e t e r Dryer length Moisture in feed (% wet basis) Moisture in product (% wet basis) Production rate (Ib/hr) Evaporation rate (Ib/hr) Type of fuel Fuel consumption Calorific value of fuel Efficiency (Btu supplied per lb evaporation) Total power reauired (HP) 2ft7in. 6ft4in. lOft3in. loft 24ft 3oft 2.0 6 . 0 18.0 0.1 0 . 5 0 . 5 2500 3 2 , 0 0 0 3 8 , 0 0 0 50 2130 8110 steam gas oil 255 Ib/hr 4630 f?/hr 115 gal/hr 837 Btu/lb 1000 Btu/ft3 150,000 Btu/gal 4370 2170 2135 4 41 7 8 (FMC Corp.; Chemical Engineers’ Handbook, 1984, p. 20.20). (d) Indirect-Direct Double Shell Dryers D r y e r d i a m e t e r Dryer length Initial moisture content (% w/w basis) Final moisture (% w/w basis) Evaporation rate (Ib/hr) Evaporation-volume ratio (lb/f?/hr) Heat source Efficiency (Btu supplied/lb water evaporated) Inlet air temperature (“F) Outlet air temperature (“F) (Courtesy Edgar Allen Aerex Ltd.; Williams-Gardner, 1871). Indirect-Direct Double Shell Coal Anhydrite C o k e 7ft6in. 5ft10in. 5ftlOin. 46ftOin. 35 ft 0 in. 35ftOin. 2 2 6 . 0 15 6 1 . 0 1.0 5800 2300 1600 3 . 5 3 . 1 5 2.2 coal oil oil 1250 1250 1340 1200 1350 1350 160 160 200
- 278. (e) Steam Tube Dryers Class 1 Class 2 Class 3 Class of materials Description of class Normal moisture content of wet feed (% dry basis) Normal moisture content of product (% dry basis) Normal temperature of wet feed (K) Normal temperature of product (K) Evaporation per product (kg) Heat load per lb product (kJ) Steam pressure normally used (kPa gauge) Heating surface required per kg product (m*) Steam consumption per kg product kg) high moisture organic, distillers’ grains, brewers’ grains, citrus pulp wet feed is granular and damp but not sticky or muddy and dries to granular meal 2 3 3 pigment filter cakes, blanc fixe. barium carbonate, precipitated chalk wet feed is pasty, muddy, or sloppy, product is mostly hard pellets 100 finely divided inorganic solids, water- ground mica, water-ground silica, flo- tation concentrates wet feed is crumbly and friable, product is powder with very few lumps 5 4 1 1 0 . 1 5 0 . 5 3 1 O - 3 2 0 280-290 2 8 0 - 2 9 0 3 5 0 - 3 5 5 380-410 3 6 5 - 3 7 5 2 1 0 . 5 3 2 2 5 0 1190 6 2 5 8 6 0 8 6 0 8 6 0 0.34 3 . 3 3 0.4 1 . 7 2 0.072 0 . 8 5 (Chemical Engineers’ Handbook, 1984).
- 279. 260 DRYERS AND COOLING TOWERS (a) .YOR VAPOR OUTLET U In RUM y DRUM Figure 9.11. Drum dryers for solutions and thin slurries (Bu~7ouak Equip. Div., Blaw Knox Co.). (a) Single drum dryer with dip feed and spreader. (b) Double drum dryer with splash feed. (c) Double drum dryer with top feed, vapor hood, knives and conveyor. (d) Double drum dryer with pendulum feed, enclosed for vacuum operation. Single pass residence times are OS-3 set, but most commercial operations employ some recycling of the product so that average residence times are brought up to 60sec. Recycling also serves to condition the feed if it is very wet. The spread of residence times in pneumatic dryers, as indicated by Figure 9.5(a), is broad, so feed that has a particularly wide size distribution may not dry uniformly. Recycling, however, assists uniformity, or several dryers in series or preclassification of particle sizes may be employed. Since the contact time is short, heat-sensitive materials with good drying characteristics are particularly suited to this kind of dryer, but sticky materials obviously are not. Moreover, since attrition may be severe, fragile granules cannot be handled safely. Other kinds of dryers should be considered for materials that have substantial falling rate drying periods. Pilot plant work is essential as a basis for full scale design. It may be directed to finding suitable velocities, temperatures and drying times, or it may employ more basic approaches. The data provided for Example 9.8, for instance, are of particle size distribution, partial pressure of water in the solution, and heat and mass transfer coefficients. These data are sufficient for the EXAMPLE~.~ Description of a Drum Drying System A detergent drying plant handles 86,722 lb/day of a slurry containing 52% solids and makes 45,923 lb/day of product containing 2% water. The dryers are two sets of steam-heated double drums, each 3.5 ft dia by loft, with a total surface of 44Osqft. Each drum is driven with a 10HP motor with a variable speed transmission. Each trolley top spreader has a 0.5 HP motor. Each side conveyor has a 1 HP motor and discharges to a common belt conveyor that in turn discharges to a bucket elevator that feeds a flaker where the product is reduced to flakes less than 0.25 in. square. Fines are removed in an air grader and recycled to the dryer feed tank.
- 280. 9.8. PNEUMATIC CONVEYING DRYERS 261 TABLE 9.11. Performance Data of Drum Dryers (a] Drum Dryers Yeast S t o n e Starch Zirconium Brewers Cream Slop Solutions G l a z e Silicate Yeast tlY; Feed solids (% by weight) Product moisture (% w/w basis) Capacity (lb prod./hr) Dryer type (a) single, (b) twin, (c) double D r u m d i a m e t e r length Type of feed method Steam pressure (lb/in* gauge) Atmospheric or vacuum Steam consumption (lb/lb evaporated) Average effective area (%) Evaporation/ft*/hr 16 5.7 168 (a) 40 36 5 300-400 (a) 6 4 7 0 2 5 7 5 0 . 2 5 9 1120 146 4000 (a) (a) (a) 48 in. 120 in. side 4 0 atmos. 1.35 6 5 8 . 4 0 . 2 420 (a) 0.2 225 (a) 4ftOin. 10ftOin. top roller 8 0 atmos. - 2ft6in. 5ftOin. dip 6 0 atmos. - - 4 48 in. 18 in. 120 in. 36 in. top roller side 8 0 - atmos. atmos. 1.3 1.3 8 6 - 5 9 36in. 72 in. dip 8 0 a t m o s . - 28 in. 60 in. center nip 4 0 - - - 6 6 . 5 8 . 4 (Courtesy A.P.V. Mitchell Dryers, Ltd.; Williams-Gardner, 1971). (b) Drum Dryers in the Size Range 0.4 x 0.4-0.8 x 2.25 ma Type of Dryer and Feed Size by Letter, A, B, or C D r u m Steam Speed Press (rev/min) (bar. a) TYpe of Physical Form Material of Feed Solids in Feed (%I WS’ output Evaporation in of Dried Rate of Product Product Water w (g/see m2) Wsec m2) Single (dip) 4 . 4 3.5b Single (splash) 1 3 . 0 Twin (splash) A 3 3 . 0 Double 3-8 5.0 Double and twin 7-9 2-3 Double and twin 5-9 4-6 inorganic salts alk. carbs Mg(OW, WOW, Na Acetate Na,S04 Na,HP04 - 5 0 8-12 thick slurry 3 5 0 . 5 thin slurry 2 2 3 . 0 solution 2 0 0.4-10 solution 2 4 0.15-5.5 solution 44 0.8-0.9 Twin (dip) A 5 5.5 organic salts solution 2 7 2 . 8 Twin A 3 5 . 5 organic salts solution 3 3 13.0 Twin B 2 ” 3 . 5 organic salts solution 2 0 1.0 T w i n C 5 5 . 5 organic salts solution 3 9 0 . 4 T w i n C 5; 5 . 5 organic salts solution 4 2 1.0 T w i n C 6 5 . 5 organic salts solution 3 5 5.0 Twin (splash) A 3-5 5 . 0 organic salts thin slurry 2 0 1.7-3.1 Double A 5; 6 . 0 organic salts solution 1 1 - Double B 6; 5-6 organic salts solution 4 0 3 Twin (dip) A Twin A Double Double organic c o m p o u n d s thin slurry 3 0 viscous soln. 2 8 viscous soln. - thin slurry 2 5 Twin (dip) Twin T w i n 5 5 2 4; 5 10 10 5 . 5 5 . 0 3 . 0 3 . 5 5 . 0 5 . 5 5 . 5 la) solution 2 5 (b) thick slurry 3 0 (c) thick slurry 3 5 1.2 10.5 6 . 0 1.0 0 . 5 2 . 5 - Double 11 5 . 5 organic compounds of low surface tension similar letters f o r s a m e c o m p o u n d (b) thin paste 4 6 Double 1 2 5 . 5 Double 11 5 . 5 (c) thick paste 5 8 (a) solution 2 0 - - 0 . 5 5 . 5 4 . 9 1.9 1.5 4 . 3 1.3 2.0-7.0 8-24 4.7-6.1 11-12 8.2-l 1.1 9-14 1.9 5.2 1.4 2 . 6 1.0 3 . 8 3 . 9 6.1 2.1 4 . 6 4.1 7 . 2 1.0-I .9 3.7-7.3 1.1 9 3 . 4 4 . 9 2 . 4 5 . 5 1.9 4 . 2 0.7 - 0.4-l .9 3.5-5.0 0 . 3 0 . 8 2 . 0 4 . 6 3.1 - 6 . 4 7 . 3 6 . 0 4 . 3 0 . 2 4 1.0 ‘Dryer dia and width (ml: (A) b Plus external hot air flow. 0.457 x 0.457; (B) 0.71 x 1.52; (C) 0.91 x 2.54. ‘Stainless steel drum. (Nonhebel and Moss, 1971).
- 281. 262 D,RYEt?S AND COOLING TOWERS TABLE 9.12. Performance of Drum Dryers (a) Single, Double drum and Vacuum Drums Material Method of Feed Moisture Content, (% Wet Basis) Feed Product Steam Pressure, (Ib/sq in.) D r u m C a p a c i t y [lb product/ (hrllsq WI Vacuum (in. Hg) Double-drum dryer Sodium sulfonate Sodium sulfate Sodium phosphate Sodium acetate Sodium acetate Sodium acetate Single-drum dryer Chromium sulfate Chromium sulfate Chromium sulfate Chromium sulfate Chromium sulfate Chromium sulfate Vegetable glue Calcium arsenate Calcium carbonate Twin-drum dryer Sodium sulfate Sodium sulfate Sodium sulfate Sodium sulfate Sodium sulfate Sodium sulfate Sodium phosphate Sodium phosphate Sodium sulfonate Vacuum single-drum dryer Extract Extract Extract Extract Extract Skim milk Malted milk Coffee Malt extract Tanning extract Vegetable glue trough 5 3 . 6 6 . 4 6 3 8; 164 7 . 7 5 trough 7 6 . 0 0 . 0 6 5 6 7 150 3 . 0 8 trough 5 7 . 0 0 . 9 9 0 9 180 8 . 2 3 trough 3 9 . 5 0 . 4 4 7 0 3 205 1.51 trough 4 0 . 5 10.03 6 7 8 200 5 . 1 6 trough 6 3 . 5 9 . 5 3 6 7 8 170 3 . 2 6 spray film 4 8 . 5 5.47 5 0 5 - 3 . 6 9 dip 4 8 . 0 8 . 0 6 5 0 4 - 1.30 pan 5 9 . 5 5 . 2 6 2 4 23 158 1.53 splash 5 9 . 5 4 . 9 3 5 5 1: 150 2.31 splash 5 9 . 5 5 . 3 5 5 3 42 154 3 . 7 6 dip 5 9 . 5 4 . 5 7 5 3 5: 153 3 . 3 6 pan 60-70 10-12 20-30 6-7 - l - l . 6 slurry 75-77 0.5-l .o 45-50 3-4 - 2-3 slurry 7 0 0 . 5 4 5 2-3 - 1.5-3 dip top top splash splash splash dip top pan pan pan pan pan pan pan pan spray film pan pan 7 6 0 . 8 5 5 5 7 110 3 . 5 4 6 9 0 . 1 4 6 0 9; 162 4 . 2 7 6 9 5.47 3 2 9; 116 3 . 5 6 71 0 . 1 0 6 0 6 130 4 . 3 0 7 1 . 5 0 . 1 7 6 0 12 140 5 . 3 5 7 1 . 5 0 . 0 9 6 0 10 145 5 . 3 3 5 2 . 5 0 . 5 9 5 8 5; 208 8 . 6 9 5 5 0 . 7 7 6 0 5; 200 6 . 0 5 5 3 . 5 E-10 6 3 8; 172 10.43 5 9 5 9 5 9 5 6 . 5 5 6 . 5 6 5 6 0 6 5 6 5 50-55 7 . 7 5 3 5 8 - 4.76 2 . 7 6 3 5 6 - 1.92 2 . 0 9 3 6 4 - 1.01 1.95 3 5 7; - 3 . 1 9 1.16 5 0 2f - 0 . 7 5 2-3 10-12 4-5 - 2.5-3.2 2 30-35 4-5 - 2 . 6 2-3 5-10 1-1; - 1.6-2.1 3-4 3-5 0.5-1.0 - 1.3-l .6 E-10 30-35 E-10 - 5.3-6.4 10-12 15-30 5-7 - 2-4 60-70 2 7 . 9 2 7 . 9 atmos. 2 2 . 7 atmos. (ferns Chemical Engineers Handbook, McGraw-Hill, 1950 edition) calculation of residence time when assumptions are made about terminal temperatures. 9.9. FLUIDIZED BED DRYERS Free flowing granular materials that require relatively short drying times are particularly suited to fluidized bed drying. When longer drying times are necessary, multistaging, recirculation or batch operation of fluidized beds still may have advantages over other modes. A fluidized bed is made up of a mass of particles buoyed up out of permanent contact with each other by a Rowing fluid. Turbulent activity in such a bed promotes high rates of heat and mass transfer and uniformity of temperature and composition throughout. The basic system includes a solids feeding device, the fluidizing chamber with a perforated distributing plate for the gas, an overflow duct for removal of the dry product, a cyclone and other equipment for collecting fines, and a heater and blower for the gaseous drying medium. Much ingenuity has been applied to the design of fluidized bed drying. Many different arrangements of equipment are illustrated and described in the comprehensive book of Kriill (1978) for instance. Figure 9.13(a) depicts the basic kind of unit and the other items are a few of the many variants. Tables 9.14 and 9.15 are selected performance data. Shallow beds are easier to maintain in stable fluidization and of course exert a smaller load on the air blower. Pressure drop in the air distributor is approximately 1 psi and that through the bed equals the weight of the bed per unit cross section. Some pressure drop data are shown in Table 9.14. The cross section is determined by the gas velocity needed for fluidization as will be described. It is usual to allow 3-6 ft of clear height between the top of the bed and the air exhaust duct. Fines that are entrained are collected in a cyclone and blended with the main stream since they are very dry
- 282. TABLE 9.12-(continued) 9.9. FLUIDIZED BED DRYERS 263 (b) Single and Double Drum with Various Feed Arrangements Kind of Dr er, Kind of Htack Moisture Content V a p o r Pressure Rotation ,k, out Absolute csf%i, Unit Prqduct D;wkg I%) (bar) (gfYfl%Yr) kg/m2 hr) Single drum, dip feed Alkali carbonate Double drum, dip feed Organic salt solution Organic compound, dilute slurry Organic compound, solution Single drum with spreading rolls Skim milk concentrate Whey concentrate Cuprous oxide Single drum, splash feed Magnesium hydroxide, dense slurry Double drum, splash feed Iron hydroxide, dilute slurry Organic salt, dilute slurry Sodium acetate Sodium sulfate Double drum, top feed Beer yeast Skim milk, fresh Organic salt solution Organic salt solution Organic compound, dilute slurry Double drum with spreading rolls Potato pulp 7 6 . 2 11.4 8 5 2 2 . 5 61.1 50 8 bis 12 3 . 5 . 7 3 2 . 8 5.5 7 0 1.2 5.5 7 5 0 . 5 5.0 5 0 4 3 . 8 4 5 4 . 3 5 . 0 5 8 0 . 5 5 . 2 6 5 0 . 5 3 . 0 7 8 3 . 0 3 . 0 3 15.4 4 . 7 8 0 1.7 bis 3.1 5.0 3 bis 5 3 . 6 bis 6 . 8 13.3 bis 2 6 . 2 5 0 4 . 0 6 . 0 5 10.0 9 . 3 7 0 2.3 7 . 8 5 18.0 4 0 . 4 8 0 8 . 0 6 . 0 5 10.0 3 8 . 2 9 1 . 2 4 . 0 6 . 4 12 6 . 2 6 1 . 5 8 9 - 6 . 0 5 . 5 4 3 2 . 3 6 0 3 5 bis 6 6 . 5 12.2 17.7 7 5 1 3 . 5 4 . 5 1.4 bis 6 . 8 12.6 bis 1 8 4 . 4 5 5 5 24 16 10 1 2 0 1 7 . 8 8 . 8 18.8 8 . 6 19.6 1.1 1.9 15.8 14.2 10 bis 11.8 7.4 bis 8.8 11.0 14.3 6 . 8 5 . 4 (Kroll, 1978, p. 348). due to their small size. Normally entrainment is 510% but can be higher if the size distribution is very wide. It is not regarded as feasible to permit high entrainment and recycle back to the drying chamber, although this is common practice in the operation of catalytic cracking equipment. Mixing in shallow beds is essentially complete; Figure 9.5(c) shows some test data in confirmation. The corresponding wide distribution of residence times can result in nonuniform drying, an effect that is accentuated by the presence of a wide distribution of particle sizes. Multiple beds in series assure more nearly constant residence time for all particles and consequently more nearly uniform drying. The data of Table 9.14(b) are for multiple zone dryers. Figures 9.13(c) and (d) have additional zones for cooling the product before it leaves the equipment. Another way of assuring TABLE 9.13. Performance Data of Pneumatic Conveying Dryers (Sketches in Fig. 9.12) (a) Raymond Flash Dryer Fine Mineral Organic C h e m i c a l Chicken Droppings Fine Coal Filter Cake Method of feed Material size, mesh Product rate (Ib/hr) Initial moisture content (% w/w basis) Final moisture content (% w/w basis) Air inlet temperature (“F) Air outlet temperature (“F) Method of heating Heat consumption (&u/lb water evaporated) Air recirculation Material recirculation Material of construction Fan capacity (std. fts/min) Installed fan HP Product exit temperature (“F) pump -100 2 7 , 0 0 0 2 5 nil 1200 200/300 direct oil 1.6 x lo3 n o yes MS 1 8 , 0 0 0 110 - 9000 6 0 12 1200 200/300 direct oil 1.9 x 10s n o yes MS/SS 2 2 , 0 0 0 180 - screw pump -30 - 900 2300 3 7 7 0 3 12 450 1300 200/300 200/300 direct direct oil oil 3.1 x lo3 1.9 x lo3 n o n o n o yes MS MS 4300 8500 3 0 5 0 - screw -30 2000 3 0 8 . 5 1200 200/300 direct oil 1.4x 10s n o G 1500 10 135 (Courtesy International Combustion Products Ltd.; Williams-Gardner, 1971)
- 283. 264 DRYERS AND COOLING TOWERS TABLE 9.134continued) (b) Buttner-Rosin Pneumatic Dryer Metallic Stearate Starch Ai3z Fiber coyiter Method of feed sling sling screw distributor distributor Material size fine fine -30 mesh -a in. -30 mesh Product rate (Ib/hr) 280 1 3 , 2 3 6 1 0 , 0 0 0 2610 67,200 Initial moisture (% w/w basis) 4 0 3 4 1 0 6 2 . 4 3 2 Final moisture (% w/w basis) 0 . 5 13 0 . 2 10 6 Air inlet temperature (“F) 284 302 320 752 1292 Air outlet temperature (“F) 130 122 149 230 212 Method of heating steam steam steam oil P F Heat consumption (Btu/lb/water evaporated) 2170 1825 2400 1720 1590 Air recirculation n o n o n o n o yes Material recirculation ves n o ves ves ves Fan capacity (std. f?/min) 1440 2 6 , 5 0 0 9500 1 2 , 5 0 0 2 7 , 0 0 0 Installed fan HP 1 5 220 6 5 6 0 250 Product exit temperature (“F) 104 9 5 120 140 158 (Courtesy Rosin Engineering Ltd.; Williams-Gardner, 1971). (c) Pennsalt-Berks Ring Dryer Metala S p e n t ” Stearates Grains Sewage’ Sludge S t a r c h e s Method of Feed belt f e e d e r r o t a r y valve b a c k m i x e r r o t a r y valve vibratory feeder r o t a r y valve cascading r o t a r y valve screen vibratory f e e d e r r o t a r y valve Product rate (Ib/hr) 240 Initial moisture (% w/w basis) 5 5 Final moisture (% w/w basis) 1 Air inlet temperature (“F) 250 Air outlet temperature t”F) 150 Method of heating steam Heat consumption (Btu/lb water evaporated) 2900 Air recirculation n o Material recirculation ves Material of construction ss Fan capacity (std fts/min) 3750 Installed fan HP 2 0 a Ring dryer application. (Courtesy Pennsalt Ltd.; Williams-Gardner, 1971). (d) Various Pneumatic Dryers 1120 4300 8 0 4 5 5 12 500 600 170 170 gas oil 1800 1750 n o n o yes yes MSG MS 1 6 , 5 0 0 8250 7 5 6 0 3 5 10 300 130 steam 2000 n o hi:G 1 5 , 0 0 0 6 0 5000 n o z 900 7 . 5 Air/Solid Material Location G a s Ratio Tube Tube R a t e Gas Temp (“C) pali) Solid Temp PC) Moisture (%I Water D i a Hfigy W{$) (cm) m In Out (kg/hr) In Out In out (NTl$n3’fi&kg) Evaporated (kdhr) Ammonium sulphate Japan 1 8 Sewage sludge filter cake U.S.A. - C o a l 6 m m U.S.A. H e x a m e t h y l e n e tetramine Germany 3 0 “23 m vertical, 15 m horizontal. (Nonhebel and Moss, 1971). 1 1100 215 7 6 950 3 8 . 5 6 3 2 . 7 5 0 . 2 8 1.2 1.5 2 3 . 5 - 1200 700 121 2270 15 71 8 0 10 5 . 3 7 . 2 1590 5 0 , 0 0 0 371 8 0 5 1 , 0 0 0 15 5 7 9 3 1.0 1.3 4350 38* 3600 9 3 5 0 2500 - 4 8 6-10 0.08-0.15 1.4 1.9 18.1
- 284. 9 . 9 . FLUIDIZED B E D D R Y E R S 265 ‘Outlet Igases (a) I. Fan 2. Rmg duct 3. Manifold 4. Injector 5. Air outlet 6. Feeder 7. Filter 8. Heoter 9. Cyclone IO. Dwntegrotor II. Bog filter 12. Discharge Expansion- bellows Change over flap , I D fan Recirculated materlol Y Dkble paddle mixer _-.- Combustion chamber lb) Figure 9.12. Examples of pneumatic conveying dryers; corresponding performance data are in Table 9.13. (a) Raymond flash dryer, with a hammer mill for disintegrating the feed and with partial recycle of product (Raymond Division, Combustion Engineering). (b) Buttner-Rosin pneumatic dryer with separate recycle and disintegration of large particles (Rosin Engineering Ltd.). (c) Berks ring dryer; the material circulates through the ring-shaped path, product is withdrawn through the cyclone and bag filter (Penndt Chemical Co.). complete drying is a recirculation scheme like that of Figure 9.13(e). In batch operation the time can be made as long as necessary. Stable fluidization requires a distribution of particle sizes, preferably in the range of a few hundred microns. Normally a size of 4mm or so is considered an upper limit, but the coal dryers of Tables 9.15(a) and (b) accommodate sizes up to 0.5in. Large and uniformly sized particles, such as grains, are dried successfully in spouted beds [Fig. 9.13(f)]: H ere a high velocity gas stream entrains the solid upward at the axis and releases it at the top for flow back through the annulus. Some operations do without the mechanical draft tube shown but employ a naturally formed central channel. One way of drying solutions or pastes under fluidizing conditions is that of Figure 9.13(g). Here the tluidized mass is of auxiliary spheres, commonly of plastic such as polypropylene, into which the solution is sprayed. The feed material deposits uniformly on the spheres, dries there, and then is knocked off automatically as it leaves the drier and leaves the auxiliary spheres behind. When a mass of dry particles can be provided to start a fluidized bed drying process, solutions or pastes can be dried after deposition on the seed material as on the auxiliary spheres. Such a process is employed, for instance, for growing fertilizer granules of desired larger sizes, and has largely replaced rotary dryers for this purpose. A few performance data of batch fluid dryers are in Table
- 285. 266 D R Y E R S A N D C O O L I N G T O W E R S EXAMPLE 9.8 Sizing a Pneumatic Conveying Dryer A granular solid has a moisture content of 0.035 kg/kg dry material which is to be reduced to 0.001 kg/kg. The charge is at the rate of 9.72 kg/set, is at 60°C and may not be heated above 90°C. Inlet air is at 450°C and has a moisture content of 0.013 kg/kg dry air. T;,g,-I----I-T,sw, Specific gravity of the solid is 1.77 and its heat capacity is 0.39 Cal/g “C. The settling velocity of the largest particle present, 2.5 mmdia, is lOm/sec. Heat capacity of the air is taken as 0.25 Cal/g “C and the latent heat at 60°C as 563 Cal/g. Experimental data for this system are reported by Nonhebel and Moss (1971, pp. 240ff) and are represented by the expressions: Heat transfer coefficient: hn = 0.47 cal/(kg solid)(C) Vapor pressure: P = exp(13.7419 - 5237.0/T), atm, K Mass transfer coefficient: &a = exp(-3.1811- 1.7388 In w - 0.2553(ln w)*, where w is the moisture content of the solid (kg/kg) in the units kg water/(kg solid)(atm)(sec). In view of the strong dependence of the mass transfer coefficient on moisture content and the 35-fold range of that property, the required residence time and other conditions will be found by analyzing the performance over small decrements of the moisture content. An air rate is selected on the assumption that the exit of the solid is at 85°C and that of the air is 120°C. These temperatures need not be realized exactly, as long as the moisture content of the exit air is below saturation and corresponds to a partial pressure less than the vapor pressure of the liquid on the solid. The amount of heat transferred equals the sum of the sensible heat of the wet solid and the latent heat of the lost moisture. The enthalpy balance is based on water evaporating at 60°C: iirJ(O.39 + 0.001)(85 - 60) + (0.035 - 0.001)(85 - 60 + 563)] = fiJ(O.25 + 0.480(0.001))(450 - 120) + 0.48(0.034)(120 - 60)], fi _ 29.77~~ _ 29.77(9.72) 3.46 kg/set, 0 83.64 83.64 7.08 m3/sec at 450°C 3.85 m3/sec at 120°C. At a tower diameter of 0.6 m, “=A= 0.36~14 1 25.0 m/set at 45O”C, 13.6m/sec at 120°C. These velocities are great enough to carry the largest particles with settling velocity of 10 m/set. Equations are developed over intervals in which WI+ W,, T,+ Tz, and T;+ T;. The procedure will be: 1. Start with known WI, T,, and T{. 2. Specify a moisture content W,. 3. Assume a value T, of the solid temperature. 4. Calculate T; from the heat balance. 5. Check the correctness of T2 by noting if the times for heat and mass transfers in the interval are equal. Q Q -= eh = ha(AT),, 0.47(AT),, Heat balance: fis[0.391(T,- Tl) + (W, - W&T,- Tl +563)] = &{[0.25 + 0.48(0.001](T; - T;) + 0.48(W, - W,)(T; - 60)). Substitute fiJfiI, = 9.7213.46 = 2.81 and solve for T& T;= -0.25048T; + 28.8(W, - W,) + 2.81 x [0.39(T, - Tl) + (WI - W,)(T, - Tl + 563)] 0.48( WI - W,) - 0.25048 (1) g, = 0.013 +;;(W, - 0.013) = 0.013 + 2.81(W, - 0.013). (2) pl= g, 18/29 + g, = o,62t$ + g, (partial pressure in air). (3) g, = 0.013 + 2.81(W, - 0.013). (4) (5) Pa, = exp[13.7419 - 5237.9/(T, + 273.2)], vapor pressure. (6) Pa, = exp[13.7419 - 5237.9/(T, + 273.2)]. (7) (Pa1 - PII - (Pa, - P*) (“)im =ln[(Pa, - P,)/(Pa, - PJ] T;-T,-(T;-T,) (AT)im=ln[(T; - T,)/(T;- TJ] (8) (9) AQ =0.391(&- TJ + (WI - W,)(T,- Tl +563), per kg of solid. (10) iir = 0.5(W, + W,). (11) k,a = exp[-3.1811- 1.7388 In W - 0.2553(ln %‘)*I. (12) oh = AQ/ha(AT),, = AQ/O.43(AT),,, heating time. (13) em = (WI - W,)/k,a(AP),,, mass transfer time. (14) 2 = Oh - 8, + 0 when the correct value of T2 has been selected. (15) After the correct value of Tz has been found for a particular interval, m a k e W,+ WI, T2+Tl, and T;+ T;. Specify a
- 286. EXAMPLE 9.8-(continued) decremented value of W,, assume a value of TZ, and proceed. The solution is tabulated. w T T ’ elsd 0.035 60 450 0 0.0325 73.04 378.2 0.0402 0.03 75.66 352.2 0.0581 0.025 77.41 315.3 0.0872 0.02 77.23 286.7 0.1133 0.015 76.28 261.3 0.1396 0.01 75.15 236.4 0.1687 0.005 74.67 208.4 0.2067 0.003 75.55 192.4 0.2317 0.001 79.00 165.0 0.2841 When going directly from 0.035 to 0.001, Tz = 80.28, T; = 144.04, 0=0.3279sec. The calculation could be repeated with a smaller air rate in order to reduce its exit temperature to nearer 12O”C, thus improving thermal efficiency. In the vessel with diameter = 0.6 m, the air velocities are 1 25.0 m/set at 450°C inlet ” = 5.15 m/set at 165°C outlet 2 0 . 1 m/set average. The vessel height that will provide the needed residence time is H = ii,0 = ZO.l(O.2841) = 5.70 m. Very fine particles with zero slip velocity will have the same holdup time as the air. The coarsest with settling velocity of 10 m/set will have a net forward velocity of ti, = 20.1 - 10 = 10.1 m/set, which corresponds to a holdup time of 0 = 5.7/10.1= 0.56 set, which is desirable since they dry more slowly. After the assumption of Tz, other quantities are evaluated in the order shown in this program. 1 0 ! E x a m p l e 9 . 3 . Pneuma t ic cm verins d r y e r 2 0 ! Findinq the e x i t s o l i d s t e rnp T2 br t r i a l , t h e n a l l dep s n d e n t q u a n t i t i e s 3 0 :: 6 0 7 0 ;i 100 110 120 130 140 150 160 170 180 190 2 0 0 2 1 0 2 2 0 230 9 . 9 . FLUIDIZED B E D D R Y E R S 2 6 7 I N P U T Wl,W2,Tl,Al ! HI i s t h e i n l e t a i r temp T l ’ I N P U T T2 ! T r i a l v a l u e A2=~2.8lS~.391%<T2-Tl~+~Wl-W 2>S{T2-T1+563))-.25048*f11+28 8Y~Wl-W2~~~~.48t~Wl-W2~-.25 848) G1=.013+2.8ltCWl-.013) Pl=Gl/C.6207+Gl) G2=.013+2.81%CW2-.013> P2=G2/(.6207+G2) Ql=EXPC13.7419-5237.9/(T1+27 3.2)) ! v a p o r p r e s s u r e @2=EXPCl3.7419-5237.9,(TZ+Z7 3.2)) P3=<Ql-Pl-Q2+P2~~LOG<~Ql-P1~ /(@2-P2>> ! ChP>lm T3=CAl-Tl-H2+T2>,LOGO /CAZ-T2)> ! ChTjlm Q=.39l*~T2-Tlj+~Wl-W2>~~T2-T 1+563> Hl=U~.47/T3 ! heatin t i m e W=.5*cwl+W2> K=EXPC-3.1811-1.738#*LOGCW>- .2533SLOGCW)“2) HZ=CWl-W2j/K/P3 ! vaporizati o n t i m e Z=Hl-H2 ! t i m e d i f f e r e n c e s h o u l d b e zero D I S P z DISP A2,Hl GOTO 40 ! if Z is not near e noush t o zcroj o t h e r w i s e t h e c o r r e c t v a l u e o f T 2 h a s bee n f o u n d END D a t a f o r t h e f i r s t i n t e r v a l Ml= ,035 w2= .0325 T2= 7 3 . 0 4 T3 ’ = 3 7 8 . 1 6 9 6 9 1 1 1 Time= 4.02283660795E-2 9.14(a). This process is faster and much less labor-intensive than tray drying and has largely replaced tray drying in the pharma- ceutical industry which deals with small production rates. Drying rates of 2-lOlb/(hr)(cuft) are reported in this table, with drying times of a fraction of an hour to several hours. In the continuous operations of Table 9.15, the residence times are at most a few minutes. Thermal efficiency of fluidized bed dryers is superior to that of many other types, generally less than twice the latent heat of the water evaporated being required as heat input. Power requirements are a major cost factor. The easily dried materials of Table 9.15(a) show evaporation rates of 58-1031b/(hr)(HP installed) but the more difficult materials of Table 9.15(d) show only 5-18 Ib/(hr) (HP installed). The relatively large power requirements of fluidized bed dryers are counterbalanced by their greater mechanical simplicity and lower floor space requirements. Air rates in Table 9.15 range from 13 to 793 SCFM/sqft, which is hardly a guide to the selection of an air rate for a particular case. A gas velocity twice the minimum fluidization velocity may be taken as a safe prescription. None of the published correlations of minimum fluidizing velocity is of high accuracy. The equation of Leva (Fluidization, McGraw-Hill, New York, 1959) appears to be as good as any of the later ones. It is G,f = 688D;83[p,(ps - ps)]o.94/po.88,
- 287. 268 DRYERS AND COOLING TOWERS where G,,,f is in lb/(hr)(sqft), pg and ps are densities of the gas and solid (lb/tuft), D, is the particle diameter (in.), and p is the gas viscosity (cP). In view of the wide scatter of the data on which this correlation is based, shown on Figure 6.14(f), it appears advisable to find the fluidization velocity experimentally for the case in hand. Although it is embarrassing again to admit the fact, unfortunately all aspects of fluidized bed drying must be established with pilot plant tests. The wide ranges of performance parameters in Tables 9.14 and 9.15 certainly emphasize this conclusion. A limited exploration of air rates and equipment size can be made on the basis of a drying rate equation and fluidization correlations from the literature. This is done in Example 9.9. A rough approximation of a drying rate equation can be based on through circulation drying of the granular material on a tray, with gas flow downward. t Clean gas discharge Heat source -4s . . inlet -F/ud’zing b l o w e r 9.10. SPRAY DRYERS Suitable feeds to a spray dryer are solutions or pumpable pastes and slurries. Such a material is atomized in a nozzle or spray wheel, contacted with heated air or flue gas and conveyed out of the equipment with a pneumatic or mechanical type of conveyor. Collection of fines with a cyclone separator or filter is a major aspect of spray dryer operation. Typical equipment arrangements and flow patterns are shown in Figure 9.14. The action of a high speed spray wheel is represented by Figure 9.14(e); the throw is lateral so that a large diameter vessel is required with this form of atomization, as shown in Figure 9.14(a). The flow from nozzles is largely downward so that the dryer is slimmer and taller. Parallel flow of air and spray downward is the most common collector 1 Wet material I Dry material cyclone (a) b) Figure 9.13. Fluidized bed dryers. (a) Basic equipment arrangement (McCabe and Smith, Unit Operations in Chemical Engineering, McGraw-Hill, New York, 1984). (b) Multiple bed dryer with dualflow distributors; performance data are in Table 9.14(b) (Romankov, in Davidson and Harrison, Fluidisation, Academic, New York, 1971). (c) A two-bed dryer with the lower one used as cooler: (a, b, c) rotary valves; (d) drying bed; (e) cooling bed; (f, g) air distributors; (h, i) air blowers; (k) air filter; (1) air heater; (m) overflow pipe; (n) product collector (KroN, 1978). (d) Horizontal multizone dryer: (a) feeder; (b) air distributor; (c) fluidized bed; (d) partitions; (e) dust guard; (f) solids exit; (g) drying zone; (h) cooling zone; (i, k) blowers; (1, m) air plenums; (n) air duct; (0) dust collector; (p) exhaust fan (Kroll, 1978). (e) Circulating fluidized bed used for removal of combined water from aluminum hydroxide: (a) feed; (b) fluidized bed; (c) solids exit; (d) fuel oil inlet; (e) primary air inlet; (f) secondary air inlet; (g) gas exit (Kroll, 1978). (f) Spouted bed with draft tube for drying coarse, uniform-sized granular materials such as grains [Yang and Keairns, AIChE Symp. Ser. 176, 218 (1978), Fig. 11. (g) Fluidized bed dryer for sludges and pastes. The fluidized solids are fine spheres of materials such as polypropylene. The wet material is sprayed in, deposits on the spheres and dries there. At the outlet the spheres strike a plate where the dried material is knocked off and leaves the dryer as flakes. The auxiliary spheres remain in the equipment: (a) feed; (b) distributor; (c) spheres loaded with wet material; (d) returning spheres; (e) striking plate; (f) hot air inlet; (g) air and solids exit (Kroll, 1978).
- 288. 9.10. SPRAY DRYERS 269 a I e (el Figure 9.1~(continued) I ’ Y’ Draf’ lube -- Downcomer 3241 Car Distributor Plate Allernative Solids Feed - I Gas and Solids Feed if) -Solid Flow --- Gas Flow (d arrangement, but the left-hand figure of Figure 9.14(d) is in particles, but may be harmful to thermally sensitive products counterflow. Figure 9.14(c) has tangential input of cooling air. In because they are exposed to high air temperatures as they leave the some operations, the heated air is introduced tangentially; then the dryer. The flat bottomed dryer of Figure 9.14(c) contacts the exiting process is called mixed flow. Most of the entries in Table 9.16(a) are solids with cooling air and is thus adapted to thermally sensitive parallel flow; but the heavy duty detergent is in counterflow, and materials. titanium dioxide is either parallel or mixed flow. Counterflow is Two main characteristics of spray drying are the short drying thermally more efficient, results in less expansion of the product time and the porosity and small, rounded particles of product. Short
- 289. 270 DRYERS AND COOLING TOWERS TABLE 9.14. Performance Data of Fluidized Bed Dryers: Batch and Multistage Equipment (a) Batch Dryers Ammonium B r o m i d e Lactose Base Granules Pharmaceutical Liver Weed Crystals Residue Killer Holding capacity (lb wet product) Bulk density, dry (lb/f?) Initial moisture (% w/w basis) Final moisture 1% w/w basis) Final drying temperature 1°F) Drying time (min) Fan capacity (fts/min at 11 in. w.g.) Fan HP Evaporation rate (lb H,O/hr) 100 104 160 280 250 7 5 3 0 2 0 3 0 3 5 6 10 6 5 5 0 20-25 1 2 0 . 4 5 . 0 1.0 212 158 248 140 140 2 0 9 0 120 7 5 210 750 1500 3000 4000 3000 5 10 2 0 2 5 2 0 1 5 5 . 7 5 2 100 17 (Courtesy Calmic Engineering Co. Ltd.; Williams-Gardner, 1971). (b) Multistage Dryers with Dual-flow Distributors [Equipment Sketch in Fig. 9.13(b)] Function Heater Cooler D r i e r Cooler Material Wheat Grains Slag Particle size (diameter)(mm) Material feed rate (metric tons/hr) Column diameter (m) Perforated trays (shelves): Hole diameter (mm) Proportion of active section Number of trays Distance between trays (mm) Total pressure drop on fluidized bed (kgf/m*) Hydraulic resistance of material on one tray (kgf/m’) Inlet gas temperature (“C) Gas inlet velocity (m/set) Material inlet temperature (“C) Material discharge temperature (“C) Initial humidity (% on wet material) Final humidity (% on wet material) Blower conditions Pressure (kgf/m*) Throughput (ms/min) 5 x 3 5 x 3 0 . 9 5 1.5 1.5 7 . 0 0 . 9 0 0 . 8 3 1.60 2 0 0 . 4 1 0 2 0 113 7 . 8 265 8 . 0 2 6 8 175 2 5 2 . 8 2 0 0 . 4 6 2 0 6 4 9 . 2 3 8 3 . 2 2 175 5 4 20; 10 0.4; 0.4 1; 2 25; 40 708 20; 10 300 4 . 6 0 2 0 170 8 0 . 5 450 250 420 250 180 130 360 100 (80°C) (50°C) (70°C) (35°C) 1 . 4 4 . 0 1.70 2 0 0 . 4 2 0 15 4 0 1.8 2 0 0 . 7 4 350 2 2 - - Power consumption (HP) 5 0 2 0 7 5 7 . 5 a With grids and two distributor plates. (Romankov, in Davidson and Harrison, Fluidisation, Academic, New York, 1971). drying time is a particular advantage with heat sensitive materials. Porosity and small size are desirable when the material sub- sequently is to be dissolved (as foods or detergents) or dispersed (as pigments, inks, etc.). Table 9.17 has some data on size distributions, bulk density, and power requirements of the several types of atomizers. The mean residence time of the gas in a spray dryer is the ratio of vessel volume to the volumetric flow rate. These statements are made in the literature regarding residence times for spray drying: /feat Exchanger Design Handbook (1983) McCormick (1979) Masters (1976) Nonhebel and Moss (1971) Peck (1983) Wentz and Thygeson (1979) Williams-Gardner (1971) Time (set) 5-60 2 0 20-40 (parallel flow) ~60 5-30 ~60 4-10 (<15ftdia) lo-20(>15ftdia) Residence times of air and particles are far from uniform; Figure 9.5(a) and (b) is a sample of such data. Because of slip and turbulence, the average residence times of particles are substantially greater than the mean time of the air, definitely so in the case of countercurrent or mixed flow. Surface moisture is removed rapidly, in less than 5 set as a rule, but falling rate drying takes much longer. Nevertheless, the usual drying operation is completed in 5-30 sec. The residence time distribution of particles is dependent on the mixing behavior and on the size distribution. The coarsest particles fall most rapidly and take longest for complete drying. If the material is heat-sensitive, very tall towers in parallel flow must be employed; otherwise, countercurrent or mixed flows with high air temperatures may suffice. In some cases it may be feasible to follow up incomplete spray drying with a pneumatic dryer. Drying must be essentially completed in the straight sided zones of Figures 9.14(a) and (b). The conical section is for gather- ing and efficient discharge of the dried product. The lateral throw of spray wheels requires a vessel of large diameter to avoid
- 290. 9.10. SPRAY DRYERS 271 TABLE 9.15. Performance Data of Continuous Fluidized Bed Dryers (a) Data of Fluosatatic Ltd. Coal S a n d Silica Sand L i m e s t o n e Iron Ore Material size, mesh Method of feed Product rate (lb product/hr) Initial moisture (% w/w basis) Final moisture f% w/w basis) Residence time (min) Dryer diameter (ft) Fluid bed height fin.) Air inlet temperature (“F) Air outlet temperature (“F) Air quantity (fts/min std.) Material exit temperature (“F) Evaporation (Ib/hr) Method of heating Heat consumption (Btu/lb water Fan installed HP $0 -25-o twin bucket screw elev. 448,000 2 2 , 4 0 0 11 6 5 . 5 0.1 1 1.25 10 3 . 0 18 12 1000 1200 170 212 4 0 , 0 0 0 2000 140 220 2 4 , 6 4 0 1430 coal gas 1830 1620 240 2 0 -18-O S-0 +J conv. CO”“. conv. 1 1 2 , 0 0 0 6 7 , 0 0 0 6 15 0.1 0.1 1.5 1.25 7.25 5 . 5 12 12 1200 1200 212 212 9000 1 3 , 0 0 0 220 220 6 7 2 0 1 1 , 8 8 0 oil oil 1730 1220 8 0 115 8 9 6 , 0 0 0 3 0.75 0 . 5 8 . 5 18 1200 212 45,000 220 2 0 , 4 0 0 oil 2300 (Williams-Gardner, 1971). (b) Data of Head Wrightston Stockton Ltd. Coal Silicicr % Y S a n d Asphalt Method of feed Material size Product rate (lb product/hr) Initial moisture I% w/w basis) Final moisture (% w/w basis) Residence time (min) Dryer diameter Fluid bed height (in.) Air inlet temperature (“F) Air outlet temperature (“F) Air quantity (f?/min std) Material exit temp f”F) Evaporated rate (Ib/hr) Method of heating Heat consumption (Btu/lb water evaporated) Fan installed HP screw f e e d e r -; in. 1 9 0 , 0 0 0 14 7 2 7ft3in. 21 1000 135 2 0 , 0 0 0 140 1 1 , 2 0 0 coke- oven gas 2000 210 chute chute c h u t e -&in. 1 7 , 9 2 0 5 0 1; 3ftOin. 12 1400 230 2000 230 896 gas oil -36 mesh 1 5 , 6 8 0 7 0 3 4ft6in. 12 1400 230 2000 230 1 0 9 7 t o w n gas -&in. -&in. 33,600 2 2 , 4 0 0 5 5 0 0 . 5 3 1 0 6ft6in. 8ftOin. 12 2 4 1400 470 230 220 3500 7000 230 220 1680 1120 gas oil gas oil 2250 2000 2200 1800 32; 18 3 0 9 0 (Williams-Gardner, 1971). (c) Data of Pennsalt Ltd. C l a y Granules S a n d Granular Desiccant Product rate (Ib/hr) Initial moisture (% w/w basis) Final moisture (% w/w basis) Air inlet temperature (“F) Air outlet temperature (“F) Method of heating Heat consumption fBtu/lb water Bulk density (lb/@) Average drying time (min) Fan capacity (ft3/min std.) Installed fan HP 2200 9 dry evaporated) 580 210 gas 2700 120 2 . 5 2 . 5 10 1000 1 4 , 0 0 0 150 1 3 , 5 0 0 2 2 6 2 5 4 3 dry 7 0 . 0 3 160 325 300 390 120 140 205 230 steam gas gas steam 3800 2700 3600 5100 6 0 9 0 3 0 6 0 3 0 3 2 4 4 1.35 1.05 0 . 8 4 1.05 4 5 2 5 5 5 0 (Williams-Gardner, 1971).
- 291. 2 7 2 DRYERS AND COOLING TOWERS TABLE 9.1~(continued) (d) Data of Rosin Engineering Ltd. S o d i u m Weed Perborate Killer P V C Coal S a n d Method of feed screw vibrator screw vibrator vibrator Material size 30-200 5-l mm 60-l 20 3 mesh- 30-120 mesh flake mesh zero mesh Product rate (lb product/hr) 1 1 , 4 0 0 5100 1 0 , 0 7 5 440,000 1 1 2 , 0 0 0 Initial moisture (% w/w basis) 3 . 5 1 4 2 . 0 8 8 Final moisture (% w/w basis) 0 . 0 0 . 2 0 . 2 1 0 . 2 Residence time (min) 1.5 1 1 3 0 0 . 3 0 . 4 5 Drier bed size (ft x ft) 22.5 x 5.5 18 x 4.5 23 x 6 16 x 6.6 12.5 x 3.2 Fluid bed height (in.) 4 3 1 8 5 6 Air inlet temperature (“F) 176 212 167 932 1202 Air outlet temperature (“F) 104 150 122 180 221 Air quantity (fta/min std) 6600 1 4 , 2 0 0 5400 6 7 , 3 3 0 8000 Material exit temperature (“F) 104 205 122 180 212 Evaporation (Ib/hr) 400 720 183 3 3 , 4 4 0 9750 Method of heating steam steam steam coke-oven oil gas Heat consumption (Btu/lb water evaporated) 2100 3060 4640 1970 2200 Fan installed HP 3 3 40 34 600 70 (Williams-Gardner, 1971). EXAMPLE 9.9 Sizing a Fluidiied Bed Dryer A wet solid at 100°F contains W = 0.3 lb water/lb dry and is to be dried to W = 0.01. Its feed rate is 100 lb/hr dry. The air is at 350°F and has H,,= 0.015 lb water/lb dry. The rate of drying is represented by the equation - $y= 6O(H, - H,), (Ib/lb)/min. The solid has a heat capacity 0.35 Btu/(lb)(“F), density 150 Ib/cuft, and average particle size 0.2pm (0.00787in.). The air has a viscosity of 0.023 CP and a density of 0.048 Ib/cuft. The fluidized bed may be taken as a uniform mixture. A suitable air rate and dimensions of the bed will be found: I Tg (51. ;Wa, Hg 5’ _--___--------__ S = 100 Ib/hr w, = 0 . 3 - - - - - - - - T,, = 100 F (T,) A 1 * Hp,, = 0.015 (H,) w = 0 . 0 1 Tsc = 350 F (T,) Ts (T,) Symbols used in the computer program are in parentheses. Minimum fluidizing rate by Leva’s formula: G mf = 688D~s3[0.048(150 - 0.048)]“-94 PS8 = 688(0.C0787)‘s3[0.048(150 - 0.048)]“.94 (0.023)oss = 17.17 lb/(hr)(sqft). Let G, = 2G,/ = 34.34 lb/(hr)(sqft). Expanded bed ratio (L/Z,,) = (G, /G,,,,)“.22 = 2°.22 = 1.16. Take voidage at minimum fluidization as Em, = 0.40, :. Ef = 0.464. Drying time: w,-w 0.3 - 0.01 I3 = 6o(H, - H,) = 6o(H, - Hg) (2) Since complete mixing is assumed, H, and H, are exit conditions of the fluidized bed. Humidity balance: i(H, - Hgo) = s(W, - W), H, = 0.015 + 0.29s/A. Average heat capacity: Cg = $(C,, + C,) = 0.24 + 0.45[(0.015 + H,)/2] = 0.2434 + 0.225H,. Heat balance: (3) AC.&, - T,) = S[(C, + W)(T, - T,,) + nmo - WI, (&s&(350 - Tg) = 0.36(T, - 100) + 900(0.29). (4)
- 292. EXAMPLE 9.9-(continued) Adiabatic saturation line: T,-T,=$(H,-H,)=F(H,-II,). g L? Vapor pressure: P, = exp[11.9176 - 7173.9/(T, + 389.5)]. (6) Saturation humidity: H-18 P, ' 291-e' (7) Eliminate T3 between Eqs. (4) and (5): T +,-0.36(& -la)+261 s RCtz =T +9WfG-W 4 c&T , [T3= Tg, T4- T,]. (8) Procedure: For a specified value of R = A/S, solve Eqs. (6), (7), and (8) simultaneously. R T. 7-a Y 4 8 (min) 5 145.14 119.84 0.0730 0.0803 0.862 6 178.11 119.74 0.0633 0.0800 0.289 8 220.09 119.60 0.0513 0.0797 0.170 10 245.72 119.52 0.0440 0.0795 0.136 12 262.98 119.47 0.0392 0.0794 0.120 Take R = 10 lb air/lb solid, A = lO(100) = 1000 lb/hr, 0 = 0.136 min. Cross section: A/G, = 1000/34.34 = 29.12 sqft, 6.09 ft dia. Avg density: $(1/20.96 + l/19.03) = 0.0501 lb/tuft. Linear velocity: u=-!?L= 34.34 p&(60) 0.0501(0.464)(60) = 24.62 fpm. Bed depth: L = u8 = 24.62(0.136) = 3.35 ft. Note: In a completely mixed fluidized bed, the drying time is determined by the final moisture contents of the air and solid. 9.10. S P R A Y D R Y E R S 273 When drying is entirely in the falling rate period with rate equation dW WWfJW wsw --= d0 WC ’ =’ the drying time will be w, ’ = k(H, - Hg)W where H,, H,, and W are final conditions. When the final W is small, 0.01 in the present numerical example, the single stage drying time will be prohibitive. In such cases, multistaging, batch drying, or some other kind of drying equipment must be resorted to. 1e ! Example 9.9. Fluidized bed 38 48 50 68 7 8 88 99 168 110 128 130 140 150 160 170 180 290 210 22B 230 2 4 9 258 268 278 R I N P U T I? ! =HsSj ratio of r.a? e5 of flow of air and solid H3= ,:1=: 015+.29/f? ! =Hq 2434+.225*H3 INPUT T4 ! Trial value o f Ts GDSUE( 2 0 9 5’1=y T4=1.0001tT4 GDSUB 288 ‘1’2Zjj K=, 0001*Yl/CY2-Yl> T4=T4/1 008 1 -K DISP T 4 IF FiE?SCK.~T42 i=. 00001 T H E N 16 :DTD 69 DISP U S I N G 17r3 i R,T3,T4>H3, H4.TS i‘rhtc DD>X,DDD.D,X,DDD.D>X~. D D D D ,X, .DDDD>X> . D D D END ! SR for T4 P=EXP{11.9176-7173.9.(T4+3S9 5 j j H4=18fP./Z9/Cl-P> ! = Hs TS=T4+9001iHJ-H3)/Cl ! = T9 Y=-T3+358-i.36*<T4-1@0>+261~ /R/C 1 T5=.29x’CH4-H3)JG@ ! = time RETURN END T -2L s I1s Time Hg------- 5 145’.1 119.84 07.X@ @8Q3 ,662 .- t* 1 7 8 . 1 119.74 .@E;33 .@a#@ ,289 8 2 2 8 . 1 119.61 .0513 .0797 1 i 111 la 2 4 5 . 7 119.53 .0440 ,079s :136 263.8 119.47 .0392 .8794 ,128 2 8 8 . 4 1 1 9 . 4 2 .8343 .a792 .10S
- 293. 274 DRYERS AND COOLING TOWERS I Feed liquor lrom Pump FEED + A I R 120 t A I R 2 3 0 - FEED 9 350 AIR 60 30 181 F E E D 210 - 2 3 0 A I R Tonptnhol Cool-Ob LnW$ 6 0 60 100 90 9 0 9 0 110 1 1 0 105 ~ i 100 100 1 0 0 100 AIR LO 2LI 270 XI 301 330 350 AIR v PRODUCT I Molor/drtven olrswttptr jets err onlo nor floor + PRODUCT PRODUCT (d) (e) Figure 9.14. Spray dryer arrangements and behavior. (a) Spray dryer equipped with spray wheel; straight section L/D = 0.5-1.0 (Proctor and Mnvartz Inc.). (b) Spray dryer equipped with spray nozzle; straight section L/D = 4-5 (Nonhebel and Moss, 1971). (c) Spray dryer for very heat sensitive products; flat bottom, side air ports and air sweeper to cool leaving particles. (d) Distribution of air temperatures in parallel and countercurrent flows (Mu.sters, 1976, p. 18, Fig. 1.5). (e) Droplet-forming action of a spray wheel (Stork-Bowen Engineering CO.).
- 294. TABLE 9.16. Performance Data of Spray Dryers (a) Data of Kriill(l978) 9.10. S P R A Y D R Y E R S 275 Kind of Stock Moisture C o n t e n t In (%I out (%) Spray F l o w Device Pattern Air Temperature In WI out (“c) Skim milk, d = 60 @rn Whole milk 50-60 2 . 5 Eggs, whole Eggs, yolks Eggs, whites Coffee, instant, 300 pm Tea, instant Tomatoes Food yeast Tannin PVC emulsion, 90% > 80 pm <60pm Melamine-urethane-formaldehyde resins Heavy duty detergents Kaolin 48-55 4 50-60 4 74-76 2-4 50-55 2-4 87-90 7-9 75-85 3-3.5 6 0 2 65-75 3-3.5 76-78 8 50-55 4 40-70 0.01-0.1 30-50 35-50 35-40 0 8-13 1 wheel or nozzle 170-200 bar wheel or nozzle loo-140 b a r wheel or nozzle wheel or nozzle wheel or nozzle nozzle nozzle, 27 bar w h e e l w h e e l w h e e l wheel or nozzle or pneumatic w h e e l 140-160 m/set nozzle, 30-60 bar w h e e l parallel 250 95-100 95-100 parallel 170-200 parallel 140-200 50-80 parallel 140-200 50-80 parallel 140-200 50-80 parallel 270 110 parallel 1 SO-250 parallel 140-150 parallel 300-350 parallel 250 100 so parallel parallel counter 350-400 90-110 parallel 600 120 165-300 200-275 65-75 (b) Performance of a Dryer 18ft Dia by 18ft High with a Spray Wheel and a Fan Capacity of 11,000 cfm at the Outlet” Material Air Temp (“F) % Water Evaporation In out in Feed Rate (Ib/hr) Blood, animal Yeast Zinc sulfate Lignin Aluminum hydroxide Silica gel Magnesium carbonate Tanning extract Coffee extract A Coffee extract 8 Magnesium chloride 330 440 620 400 600 600 600 330 300 500 810 160 6 5 140 8 6 230 5 5 195 6 3 130 9 3 170 9 5 120 9 2 150 4 6 180 7 0 240 47 305 5 3 Detergent A 450 250 5 0 Detergent B 460 240 6 3 D e t e r g e n t C 450 250 4 0 Manganese sulfate 600 290 5 0 Aluminum sulfate 290 170 7 0 Urea resin A 500 180 6 0 Urea resin B 450 190 7 0 Sodium sulfide 440 150 5 0 P i g m e n t 470 140 7 3 780 1080 1320 910 2560 2225 2400 680 500 735 1140 (to dihydrate) 660 820 340 720 230 505 250 270 1750 eThe fan on this dryer handles about 11,000cuft/min at outlet conditions. The outlet-air temperature includes cold air in-leakage, and the true temperature drop caused by evaporation must therefore be estimated from a heat balance. (Bowen Engineering Inc.).
- 295. 276 DRYERS AND COOLING TOWERS TABLE 9.17. Particle Diameters, Densities, and Energy Requirements (a) Atomizer Performance Type Size Range (pm) Power input (kWh/lOOO L) Single fluid nozzle Pneumatic nozzle Spray wheel Rotatina CUD 8-800 0.3-0.5 3-250 2-550 0.8-l .O 25-950 (b) Dry Product Size Range Product w Skim milk 2 0 - 2 5 0 Coffee 5 0 - 6 0 0 Egga 5 - 5 0 0 Egg white l - 4 0 Color pigments l-50 Detergents 2 0 - 2 0 0 0 Ceramics 15-500 (c) Bulk Density of Sprayed Product as Affected by Air Inlet Temperature and Solids Content of Feed” W t 5; s o l i d s i n f e e d 0 . 8 0 d-m 100 200 300 400 500 600 A i r i n l e t , ‘C ‘The full lines are against temperature, the dashed ones against concentration: (a) sodium silicate; (b) coffee extract, 22%; (c) water dispersible dye, 19.5%; (d) gelatin. [Data of Duffie and Marshall, Chem. Eng. Prog. 49, 417 480 (1953)]. accumulation of wet material on the walls; length to diameter ratios of 0.5-1.0 are used in such cases. The downward throw of nozzles permits small diameters but greater depths for a given residence time; L/D ratios of 4-5 or more are used. ATOMIZATION DESIGN Proper atomization of feed is the key to successful spray drying. The three devices of commercial value are pressure nozzles, pneumatic nozzles, and rotating wheels of various designs. Usual pressures employed in nozzles range from 300 to 4OOOpsi, and The design of spray dryers is based on experience and pilot plant determinations of residence time, air conditions, and air flow rate. Example 9.10 utilizes such data for the sizing of a commercial scale spray dryer. orifice diameters are 0.012-0.15 in. An acceptably narrow range of droplet sizes can be made for a feed of particular physical properties by adjustment of pressure and diameter. Multiple nozzles are used for atomization in large diameter towers. Because of the expense of motive air or steam, pneumatic nozzles are used mostly in small installations such as pilot plants, but they are most suitable for dispersion of stringy materials such as polymers and fibers. The droplet size increases as the motive pressure is lessened, the range of 60-100 psi being usual. The action of a rotating wheel is indicated in Figure 9.14(e). Many different shapes of orifices and vanes are used for feeds of various viscosities, erosiveness, and clogging tendencies. Operating conditions are up to 60,000 lb/hr per atomizer, speeds up to 20,OOOrpm, and peripheral speeds of 250400 ft/sec. The main variables in the operation of atomizers are feed pressure, orifice diameter, flow rate and motive pressure for nozzles and geometry and rotation speed of wheels. Enough is known about these factors to enable prediction of size distribution and throw of droplets in specific equipment. Effects of some atomizer characteristics and other operating variables on spray dryer performance are summarized in Table 9.18. A detailed survey of theory, design and performance of atomizers is made by Masters (1976), but the conclusion is that experience and pilot plant work still are essential guides to selection of atomizers. A clear choice between nozzles and spray wheels is rarely possible and may be arbitrary. Milk dryers in the United States, for example, are equipped with nozzles, but those in Europe usually with spray wheels. Pneumatic nozzles may be favored for polymeric solutions, although data for PVC emulsions in Table 9.16(a) show that spray wheels and pressure nozzles also are used. Both pressure nozzles and spray wheels are shown to be in use for several of the applications of Table 9.16(a). APPLICATIONS For direct drying of liquids, slurries, and pastes, drum dryers are the only competition for spray dryers, although fluidized bed dryers sometimes can be adapted to the purpose. Spray dryers are capable of large evaporation rates, 12,000-15,OOOlb/hr or so, whereas a 300sqft drum dryer for instance may have a capacity of only 3000 lb/hr. The spherelike sprayed particles often are preferable to drum dryer flakes. Dust control is intrinsic to spray dryer construction but will be an extra for drum dryers. The completely enclosed operation of spray dryers also is an advantage when toxic or noxious materials are handled. THERMAL EFFICIENCY Exit air usually is maintained far from saturated with moisture and at a high temperature in order to prevent recondensation of moisture in parallel current operation, with a consequent lowering of thermal efficiency. With steam heating of air the overall efficiency is about 40%. Direct fired dryers may have efficiencies of 80-85% with inlet temperatures of 500-550°C and outlet of 65-70°C. Steam consumption of spray dryers may be 1.2-1.8 lb steam/lb evapor- ated, but the small unit of Table 9.19(b) is naturally less efficient. A 10% heat loss through the walls of the dryer often is taken for design purposes. Pressure drop in a dryer is 15-50in. of water, depending on duct sizes and the kind of separation equipment used.
- 296. 9.1 I. THEORY OF AIR-WATER INTERACTION IN PACKED TOWERS 277 TABLE 9.18. Effects of Variables on Operation of Spray Dryers Variable Increased Factors Increased Factors Decreased Chamber inlet temperature Chamber outlet temperature Gas volume rate Feed concentration Atomizer speed Atomizer disc diameter For stable lattices For unstable lattices Atomizer vane depth Atomizer vane number Atomizer vane radial length Feed surface tension Chamber inlet gas humidity Feed rate and thus: product rate, particle size (b), product moisture content, chamber wall build-up (a) product thermal degradation (a) feed rate and thus: product rate, particle size (b), product moisture content, chamber wall build-up (a) product rate, bulk density (b), particle size (b) bulk density coagulation (a) and thus: particle size, product moisture content, chamber wall build-up bulk density (b) bulk density (b) product moisture content, chamber wall build-up (a) bulk density (b) feed rate and thus: product rate particle size (b) product moisture content chamber wall build-up residence time particle size and thus: product moisture content chamber wall build-up particle size (b) and thus: product moisture content, chamber wall build-up For unstable lattices particle size chamber wall build-up particle size (b) eThis factor will only occur if a critical value of the variable is exceeded. b Not for suspensio&. (Nonhebel and Moss, 1971). The smallest pilot unit supplied by Bowen Engineering has a diameter of 30 in. and straight side of 29 in., employs parallel flow, up to 25ACFM, 150-1000”F, particle sizes 30-40pm average, either pneumatic nozzle or spray wheel. The performance of this unit is given in Table 9.19. The magnitude of the “product number” is arrived at by pilot plant work and experience; it increases with increased difficulty of drying or thermal sensitivity or both. Although much useful information can be obtained on this small scale, Williams-Gardner (1971) states that data on at least a 7 ft dia dryer be obtained for final design of large capacity units. 9.11. THEORY OF AIR-WATER INTERACTION IN PACKED TOWERS The key properties of mixtures of air and water vapor are described in Section 9.1. Here the interactions of air and water in packed towers under steady flow conditions will be analyzed. The primary objectives of such operations may be to humidify or dehumidify the air as needed for particular drying processes or other processes, or to cool process water used for heat transfer elsewhere in the plant. Humidification-dehumidification usually is accomplished in spray towers, whereas cooling towers almost invariably are filled with some type of packing of open structure to improve contacting but with minimum pressure drop of air. Analysis of the interaction of air and water involves the making of material and enthalpy balances. These are made over a differential section of the tower shown on Figure 9.15(a) and are subsequently integrated to establish the size of equipment for a given performance. In terms of empirical heat, kh, and mass, k,,,, transfer coefficients, these balances are Gdh=LC,dT=LdT (9.21) = k,(h, -h) dz (9.22) = k,(T - T,) dz. (9.23) In Eq. (9.21) the heat capacity of water has been taken as unity. The approximations that are involved in making an enthalpy difference a driving force are discussed for example by Foust et al. (1980). Rearrangement and integration leads to the results (9.24) =- I=* dT T, 4-h G =- L I h2 dh h, h,’ (9.25) (9.26)
- 297. Product number 278 DRYERS AND COOLING TOWERS TABLE 9.19. Product Numbers and Performance of a 39 x 29 in. Pilot Plant Spray Dryer Both forms of the integral are employed in the literature to define the number of transfer units. The relation between them is (a) Product Numbers of Selected Materials Morerial k,Z/G = (L/G)(NTU). The height of a transfer unit is (9.27) 1. COLOURS Reactive dyes P i g m e n t s Dispersed dyes 2. FOODSTUFFS Carbohydrates M i l k Proteins 3. PHARMACEUTICALS Blood insoluble/soluble Hydroxide gels Riboflavin Tannin 4. RESINS Acrylics Formaldehyde resin Polystyrene 5. CERAMICS Alumina Ceramic colours (Bowen Engineering Inc.). 5m 6 5-11 16-26 14-20 17 16-28 II--22 6-10 15 16-20 IO--II 18-28 12-15 Il.-l5 10 HTU = Z/(NTU) = L/k, = (L/G)(G/k,). (9.28) The quantity G/k, sometimes is called the height of a transfer unit expressed in terms of enthalpy driving force, as in Figure 9.16, for example: G/k, = (G/L)(HTU). (9.29) Integration of Eq. (9.21) provides the enthalpy balance around one end of the tower, L(T - TJ + G(h -h,). (9.30) Combining Eqs. (9.22) and (9.23) relates the saturation enthalpy and temperature, h, = h + (k,/k,)(T - T,). (9.31) In Figure 9.15(c), Eq. (9.31) is represented by the line sloping upwards to the left. The few data that apparently exist suggest that the coefficient ratio is a comparatively large number. In the absence of information to the contrary, the ratio commonly is taken infinite, which leads to the conclusion that the liquid film resistance is negligible and that the interface is at the bulk temperature of the water. For a given value of T, therefore, the value of h, in Eq. (9.25) is found from the equilibrium relation (h,, T,) of water and the corresponding value of h from the balance Eq. (9.30). When the coefficient ratio is finite, a more involved approach is needed to find the integrand which will be described. The equilibrium relation between T, and h, is represented on the psychrometric charts Figures 9.1 and 9.2, but an analytical representation also is convenient. From Section 9.1, /b)b);tr$rmance of the Pilot Unit as a Function of Product PROOUCTNUMBER(ORYINGEFFECTIVENESS) ‘Example: For a material with product number = 10 and air inlet temperature of 500°F. the evaporation rate is 53Ib/hr, input Btu/lb evaporated = 1930, and the air outlet temperature is 180°F. (Bowen Engineering). h, = 0.24T, + (18/29)(0.45T, + llOO)[p,/(l -p,)], (9.32) where the vapor pressure is represented by pS = exp[11.9176 - 7173.9/(T, + 389.5)]. (9.33) Over the limited ranges of temperature that normally prevail in cooling towers a quadratic fit to the data, h,=a+bT,+cT; may be adequate. Then an analytical integration becomes possible for the case of infinite k,/k,. This is done by Foust et al. (1980) for example. The Cooling Tower Institute (1967) standardized their work in terms of a Chebyshev numerical integration of Eq. (9.25). In this method, integrands are evaluated at four temperatures in the interval, namely, T2 + O.l(T, - T,), corresponding integrand Z1, q + 0.4( T2 - q), corresponding integrand Z2, Tl - 0.4(T, - T,), corresponding integrand Z3, (9.34) T, - 0. l( Tz - T,), corresponding integrand 4. Then the integral is ~ = 0.25(T, - Tl)(Il + I2 + Z3 + ZJ. (9.35)
- 298. 9.11. THEORY OF AIR-WATER INTERACTION IN PACKED TOWERS 279 EXAMPLE 9.10 Siziig a Spray Dryer on the Basis of Pilot Plant Data Feed to a spray dryer contains 20% solids and is to be dried to 5% moisture at the rate of 5OOlb/hr of product. Pilot plant data show that a residence time of 6sec is needed with inlet air of 230”F, H = 0.008 lb/lb, and exit at 100°F. Ambient air is at 70°F and is heated with steam. Enthalpy loss to the surroundings is 10% of the heat load on the steam heater. The vessel is to have a 60” cone. Air rate and vessel dimensions will be found. Enthalpy, humidity, and temperatures of the air are read off the psychrometric chart and recorded on the sketch. W 475 pph Water 1900 pph ;’ Air 100 F Enthalpy loss of air is 0.1(69.8 - 28.0) = 4.2 Btu/lb. Exit enthalpy of air is h = 69.8 - 4.2 = 65.6. At 100°F and this enthalpy, other properties are read off the psychrometric chart as H = 0.0375 lb/lb, V= 14.9 tuft/lb. Air rate is DW 475 pph - Water 23 pph Total 500 pph A = 1900-25 0.0375 - 0.008 = 63,559 lb/hr With a residence time of 6 set, the dryer volume is V, = 287(6) = 1721.4 tuft. Make the straight side four times the diameter and the cone 60”: 0.866aD3 1721.4 = 40(~-&/4) + 12 = 3.3683D3, :_ D = 8.0 ft. When k,/k, --* m, evaluation of the integrands is straightforward. When the coefficient ratio is finite and known, this procedure may be followed: 1. For each of the four values of T, find h from Eq. (9.30). 2. Eliminate h, between Eqs. (9.31) and (9.32) with the result h + @,lk,)(~ - T,) = 0.24T, + (18/29)(0.451; + llOO)[p,/(l -p,)]. (9.36) Substitution of Eq. (9.33) into (9.36) will result in an equation that has T, as the only unknown. This is solved for with the Newton-Raphson method. Substitution of this value of T, back into Eq. (9.31) will evaluate h Txe integrand l/(h, -h) now may be evaluated at each temperature and the integration performed with Eq. (9.35). Example 9.11 employs this method for finding the number of transfer units as a function of liquid to gas ratio, both with finite and infinite values of k,/k,. The computer programs for the solution of this example are short but highly desirable. Graphical methods have been widely used and are described for example by Foust et al. (1980). TOWER HEIGHT The information that is ultimately needed about a cooling tower design is the height of packing for a prescribed performance. This equals the product of the number of transfer units by the height of each one, 2 = (NTU)(HTU). (9.37) Some HTU data for cooling tower packing have been published, for example, those summarized on Figure 9.16. Other data appear in the additional literature cited for this chapter. Several kinds of tower fill made of redwood slats are illustrated in Figure 9.17. The numbers N of such decks corresponding to particular NTLJs and (L/G)s are given by the equation N=[(NW -0.071(L~IG)~ a Values of a and b are given for each type of fill with Figure 9.17. These data are stated to be for 120°F inlet water. Although the authors state that corrections should be estimated for other temperatures, they do not indicate how this is to be done. For example, with deck type C, NTU =2 and L/G = 1.2: N = (2 - 0.07)(l.2)“.~/0.092 = 23.4 decks, or a total of 31.2 ft since the deck spacing is 16 in. The data of Figure 9.16 are used in Example 9.11.
- 299. 280 DRYERS AND COOLING TOWERS L T, G, h, L. T, G , h, (a) c- i I T, Ts T, T. (b) (cl Figure 9.15. Relations in a packed continuous flow air-water contactor. (a) Sketch of the tower with differential zone over which the enthalpy and material balances are made. (b) Showing equilibrium and operating lines from which the integrand l/(/r, - h) can be found as a function of liquid temperature T. (c) Showing interfacial conditions as determined by the coefficient ratio k,/k,; when this value is large, interfacial and saturation temperatures are identical. G/L I” Figure 9.16. Data of heights of transfer units of packings characterized by the specific surface ud (sqft/cuft). The ordinate is G/k, = Z/l &r/(/t, - h), which is related to the form of NTU used in this chapter by HTU = Z/NTU = Z &, = L/k, = (G/k,)(L/G). s The equation of the London line is equivalent to HTU = 5.51(L/G)0.59. (Sherwood et al., 1975). 9.12. COOLING TOWERS Cooling of water in process plants is accomplished most eco- nomically on a large scale by contacting it with air in packed towers. For reasons of economy, the tower fill is of a highly open structure. Efficient ring and structured packings of the sort used for distillation and other mass transfer processes are too expensive and exert too high a power load on the fans. Standard cooling tower practice allows a maximum of 2in. of water pressure drop of the air. Water loadings range 500-2000 lb/(hr)(sqft) or l-4 gpm/sqft. Gas loadings range 1300-MOOlb/(hr)(sqft) or between 300 and 4OOft/min. The liquid to gas ratio L/G normally is in the range 0.75-1.50 and the number of transfer units or the tower characteristic, HTU = k,Z/L, vary from 0.5 to 2.50. The most common fill is of wooden slats of rectangular or triangular cross section arranged as in Figure 9.17. Corrugated sheets of asbestos-concrete have some application and also PVC construction unless the temperatures are above 160°F. Fan power consumption is the major operating cost and can be counterbalanced in part by greater investment in natural draft construction. In the majority of process applications, fan-operated towers are preferred. Very large installations such as those in power plants employ chimney assisted natural draft installations. A limited use of atmospheric towers is made in areas where power costs are especially high. The main types of cooling towers are represented on Figure 9.18. Their chief characteristics and some pros and cons will be discussed in order.
- 300. 9.12. COOLING TOWERS 281 EXAMPLE 9.11 Sizing of a Cooling Tower: Number of Transfer Units and Height of Packing Water is to be cooled from 110 to 75°F by contact with air that enters countercurrently at 90°F with a dewpoint of 60°F. The data of London et al. (1940) of Figure 9.16 for height of transfer unit are applicable. Calculations will be made for two values of the coefficient ratio k,/k,, namely, 25 and m Btu/(“F) (lb dry air), of Eq. (9.31). The effect of the ratio of liquid to gas rates, L/G, will be explored. 6 L T,=llOF Air Water x- L To2. = 90 T,=75 H = 0.011 h =27 The maximum allowable L/G corresponds to equilibrium between exit air and entering water at 110. The saturation enthaipy at 110°F is 92, so that Eq. (9.30) becomes L 0 z max =92= 1.857, 110 - 75 The several trials will be made at L/G = (0.6, 1.0, 1.4, 1.7). The applicable equations with numerical substitutions are listed here and incorporated in the computer program for solution of this problem [Eqs. (9.30)-(9.33)]: h = 27 + (L/G)(T - 75), h, = h + 25( T - 75), h, = 0.24T + (18/29)(0.45T + llOO)P,/(l - P,), P, = exp[11.9176 - 7173.9/(T, + 389.5)]. When k,,Jk,,+m, T, in Eq. (9.33) is replaced by T. The four temperatures at which the integrands are evaluated for the Chebyshev integration are found with Eq. (9.34) and tabulated in the calculation summary following. Equations (9.30) and (9.31) are solved simultaneously for h and h, with the aid of the Newton-Raphson method as used in the computer program; the integrands are evaluated and the integration are completed with Eq. (9.35). The number of transfer units is sensitive to the value of L/G, but the effect of km/k, is more modest, at least over the high range used; data for this ratio do not appear to be prominently recorded. Figure 9.16 shows a wide range of heights of transfer units for the different kinds of packings, here characterized by the surface ad (sqft/cuft) and substantial variation with L/G. The last line of the calculation summary shows variation of the tower height with L/G. Data of London et al. (1940) of Figure 9.16: (G/L)(HTU) = 5.51(G/L)0.41 or HTU = 5.51(L/G)0.59. Tower height: Z = (HTU)(NTU). For several values of L/G: LIG 0.6 1 1.4 1.7 HTU (ft) 4.08 5.51 6.72 7.54 Evaluation of interfacial temp and the NTU for L/G = 1 with k,/k, = 25: T h r, l/(h, -h) 78.5 30.5 78.099 0.0864 89 41 88.517 0.0709 96 48 95.400 0.0575 106.5 58.5 105.581 0.0385 0.2533 :. NTU = (110 - 75(0.2533)/4 = 2.217. For other values of L/G: l/t&-h) T h L/G=O.6 1 1.4 1.7 78.5 30.5 0.0751 0.0864 0.0943 0.1043 89 41 0.0518 0.0709 0.1167 0.2200 96 48 0.0398 0.0575 0.1089 0.3120 106.5 58.5 0.0265 0.0385 0.0724 0.1987 - - - - 0.1933 0.2533 0.3923 0.8350 NTU --f 1.691 2.217 3.433 7.306 With k,,,/k,, + 03: l/U&-h) T h L/G=0.6 1 1.4 1.7 78.5 30.5 0.0725 0.0807 0.90 0.1006 89 41 0.0494 0.0683 0.1107 0.2070 96 48 0.0376 0.0549 0.1020 0.2854 106.5 106.5 0.0248 0.0361 0.0663 0.1778 - - - - 0.1844 0.2400 0.3700 0.7708 NTU + 1.613 2.100 3.238 8.745 Z-, 6.58 11.57 21.76 50.86
- 301. 1 1.4 i t h i. t-4 i i t-1 i t p DECKS A B B VERTICAL SPACING A.S”, 8: 12” D E C K E VERTICAL SPACING 24” DECK G d/B”r I -?/a” VERTICAL SPACING 24” DECK I l/2 “X I ” w l-l/e” VERTICAL SPACING 24” DECKS C 8 D VERTICAL SPACING C:l6”. D ~24” D E C K F VERTICAL SPACING 24” D E C K H 7/8”x ?/8* * 2-l/4” VERTICAL SPACING 24” D E C K J VERTICAL SPACING 24” Factors in Eq. 9.38 for the Number of Decks Deck Type a b A 0.060 0.62 B 0.070 0.62 C 0.092 0.60 D 0 . 1 1 9 0.58 E 0 . 1 1 0 0.46 F 0 . 1 0 0 0.51 G 0.104 0.57 H 0.127 0.47 I 0.135 0.57 J 0.103 0.54 Figure 9.17. Kinds of fill made of redwood slats for cooling towers, and factors for determining the required number of decks with inlet water at 120°F (Cheremisinofl and CheremkinofJ 1981). a. Atmospheric towers are effective when prevailing wind velocities are 5 miles/hr or more. For access to the wind they are narrow but long, lengths of 2000 ft having been constructed. Water drift losses are relatively large. The savings because of elimination of tall chimney or fan power is counterbalanced by increased size because of less efficient cross flow and variations in wind velocity. b. Chimney assisted natural draft towers also eliminate fans. Most of the structure is the chimney, the fill occupying only lo-12% of the tower height at the bottom. The temperature and humidity of the air increase as the air flows upward so that its buoyancy increases and results in rapid movement through the chimney. Smaller units are made as circular cylinders since these can be built rapidly. The hyperboloidal shape has greater strength for a given wall thickness. In towers as large as 25Oft dia and 450ft high, wall thicknesses of 5-8in. of rein- forced concrete are adequate. The enlarged cross section at the top converts some kinetic energy into pressure energy which assists in dispelling the exit humid air into the atmosphere. The ratio of base diameter to height is 0.75-0.85, the ratio of throat and base diameters is 0.55-0.65, and the ratio of vertical depth of air opening to base diameter is 0.1-0.12. Air velocity through the tower is 3-6ft/sec, water flow rates range from 600 to 1800 lb/(hr)(sqft). Two towers each 375 ft high are able to service a 500 MW power plant. Natural draft towers are uneconomical below heights of 70 ft. The upper limit is imposed principally by environmental visual considerations; towers 500 ft high are in existence. A cost comparison is made with item d. c. Hyperbolic fan assisted towers can have as much as three times the capacity of the same size natural draft towers. The fans provide greater control than the natural draft systems; for example, they may be turned on only at peak loads. Rules of thumb cited by Cheremisinoff and Cheremisinoff (1981) for relative sizing is that fan assisted hyperbolic towers may have diameters 2/3 and heights l/2 those of purely natural draft designs. d. Countercurrent-induced draft construction is the most widely used type in process industries. Mechanical draft is capable of a greater degree of control than natural draft and such towers are able in some cases to cool the water within 2°F of the wet bulb temperature of the air. The elevated fan location introduces some structural and noise problems. The flow of air is quite uniform across the cross section and its discharge is positive and at high velocity so that there is little backflow of humid air into the tower. A cost comparison (dated 1978) with hyperbolic towers is made by Singham (1983, Sec. 3.12.4.1). The case is for a water rate of 6.1 m3/sec, cooling range of 8.5”C, approach of lO”C, and wet bulb of 17°C. The cost of the natural draft tower
- 302. 9.12. COOLING TOWERS 283 AIR OUTLET +-I--+ - A i r - (a) b) (4 lMOTOR -DRIVEN f HOT-WATER FANS INLET (cl Figure 9.18. Main types of cooling towers. (a) Atmospheric, dependent on wind velocity. (b) Hyperbolic stack natural draft. (c) Hyperbolic assisted with forced draft fans. (d) Counterflow-induced draft. (e) Crossflow-induced draft. (f) Forced draft. (g) Induced draft with surface precooler for very hot water; also called wet/dry tower. [(b)-(e) fr o m Cheremisinoff and Cheremisinoff, 1981).
- 303. 284 DRYERS AND COOLING TOWERS 6 0 ?ET -B”: 75 00 AIR TEMPERATURE (OF) 7 5 7 5 6 0 6 0 6 5 6 5 7 0 7 0 7 5 7 5 8 0 8 0 AIR WET -BULB TEMPERATURE (*F) AIR WET -BULB TEMPERATURE (*F) - 9 5 ! ! ! I I I k 110% WATER FLOW 6 0 6 5 7 0 7 5 8 0 AIR WET-BULB TEMPERATURE (@F 1 Figure 9.19. Typical cooling tower performance curves (Cherembinof and Cheremisinof, 1981). TABLE 9.20. Selected Data Required with Bids of Cooling Towers A. Cooling Tower 1. Number of cells 2. Cell dimensions, ft. in. 3. Tower length, ft, in. 4. Tower width, ft. in. 5. Tower height, ft, in. 6. Casing, material and dimensions 7. Structure, material and dimensions 8. Fill decks, material and dimensions 9. Partitions and baffles, materials and dimensions 10. Drift eliminators, material and dimensions 11. Fan stacks, material and dimensions 12. Fan deck, material and dimensions 13. Louvers, material and dimensions 14. Board feet of fill 15. Board feet total tower 16. Height of fan stacks, fi, in. 17. Post extension below curb, ft. in. 18. Total shipping weight, lb 19. Total operating weight, lb B. Fans 1. Number of units 2. Type and manufacturer 3. Diameter, ft, in. 4. Number of blades per fan 5. Blade material 6. Hub material 7. rpm 8. Tip speed, fpm 9. Mechanical efficiency, % 10. Static efficiency, % 11. Weight, lb C. Motors 1. Number of units 2. Size, HP 3. Type and manufacturer 4. Full load speed, rpm 5. Frame size 6. Full load current, amps 7. Locked rotor current amps 8. Weight, lb H. Distribution System 1. Number and size of inlet flanges 2. Height of water inlet above curb, ft. in. 3. Header material 4. Lateral material 5. Nozzle, or downspout material J. Design Performance 1. Pumping head from top of basin curb, R 2. Spray loss, max % 3. Evaporation loss, max % 4. Fill wetted surface, ft* 5. Total wetted surface, ft* 6. Effective splash surface, ft’ 7. Effective cooling volume, fts (from elimi- nators to water level) 8. Air volume per fan, cfm 9. Static pressure, inches of water 10. Output horsepower/motor/(turbine) 11. Tower loading, gpm/ft* K. Drawings and Performance Curves 1. Tower outline elevation 2. Foundation outline 3. Fill rack details 4. Drift eliminator details 5. Tower sheeting arrangement 6. A series of guaranteed performance curves within limits of CTI Test Procedure ATP-105, latest revision (Excerpted from Cheremisinoff and Cheremisinoff, 1981).
- 304. REFERENCES 285 was 1.2 M pounds and that of the mechanical draft was 0.75 M pounds, but the fan power was 775 kW. The opinion was expressed that mechanical draft towers are more economical at water rates below 1.25 m3/sec (19,800gpm). packed section where it is cooled further by direct contact with air. Separate dampers for air to the dry and wet sections can throw greater load on the wet section in summer months. e. Crossflow induced draft offer less resistance to air flow and can operate at higher velocities, which means that less power and smaller cell sizes are needed than for counterflows. The shorter WATER FACTORS travel path of the air makes them less efficient thermally. The cross flow towers are made wider and less high, consequently with some saving in water pumping cost. f. Forced draft towers locate the fans near ground level which requires simpler support structures and possibly lower noise levels. A large space must be provided at the bottom as air inlet. Air distribution is uoor because it must make a 90” turn. The humid air is discharged at low velocity from the top of the tower and tends to return to the tower, but at the same time the drift loss of water is less. The pressure drop is on the discharge side of the fan which is less power-demanding than that on the intake side of induced draft towers. Evaporation losses are about 1% of the circulation for every 10°F of cooling range. Windage or drift losses are 0.3-1.0% for natural draft towers and O.l-0.3% for mechanical draft. Usually the salt content of the circulating water is limited to 3-7 times that of the makeup. Blowdown of 2.5-3% of the circulation accordingly is needed to maintain the limiting salt concentration. TESTING AND ACCEPTANCE At the time of completion of an installation, the water and air conditions and the loads may not be exactly the same as those of the design specification. Acceptance tests performed then must be analyzed to determine if the performance is equivalent to that under the design specifications. Such tests usually are performed in accordance with recommendations of the Cooling Tower Institute. g. Wet-dry towers employ heat transfer surface as well as direct contact between water and air. Air coolers by themselves are used widely for removal of sensible heat from cooling water on a comparatively small scale when cooling tower capacity is limited. Since dry towers cost about twice as much as wet ones, combinations of wet and dry sometimes are applied, particularly when the water temperatures are high, of the order of 160”F, so that evaporation losses are prohibitive and the plumes are environmentally undesirable. The warm water flows first through tubes across which air is passed and then enters a conventional The supplier generally provides a set of performance curves covering a modest range of variation from the design condition, of which Figure 9.19 is a sample. Some of the data commonly required with bids of cooling tower equipment are listed in Table 9.20, which is excerpted from a lo-page example of a cooling tower requisition by Cheremisinoff and Cheremisinoff (1981). REFERENCES 14. A. Williams-Gardner, Industrial Drying, Leonard Hill, Glasgow, 1971. Drying Cooling Towers 1. W.L. Badger and J.T. Banchero, Introduction to Chemical Engineering, McGraw-Hill, New York, 1955. 2. C.W. Hall, Dictionary of Drying, Dekker, New York, 1979. 3. R.B. Keey, Drying Principles and Practice, Pergamon, New York, 1972. 4. R.B. Keey, Introduction to Industrial Drying Operations, Pergamon, New York, 1978. 5. K. KrBll, Trockner und Trocknungsverfahren, Springer-Verlag, Berlin, 1978. 6. P.Y. McCormick, Drying, in Encyclopedia of Chemical Technology, Wiley, New York, 1979, Vol. 8, pp. 75-113. 7. K. Masters, Spray Drying, George Godwin, London, 1976. 8. A.S. Mujumdar (Ed.), Advances in Drying, Hemisphere, New York, 1980-1984, 3 ~01s. 9. G. Nonhebel and A.A.H. Moss, Drying of Solids in the Chemical Industry, Butterworths, London, 1971. 10. R.E. Peck, Drying solids, in Encyclopedia of Chemical Processing and Design, Dekker, New York, 1983, Vol. 17, pp. 1-29. 11. E.U. Schliinder, Dryers, in Heat Exchanger Design Handbook, Hemisphere, New York, 1983, Sec. 3.13. 12. G.A. Schurr, Solids drying, in Chemical Engineers Handbook, McGraw-Hill, New York, 1984, pp. 20.4-20.8. W. T.H. Wentz and J.R. Thygeson, Drying of wet solids, in Handbook of Separation Techniques for Chemical Engineers, (Schweitzer, Ed.), McGraw-Hill, New York, 1979. 1. N.P. Cheremisinoff and P.N. Cheremisinoff, Cooling Towers: Selection, Design and Practice, Ann Arbor Science, Ann Arbor, MI, 1981. 2. Cooling Tower Institute, Performance Curves, CTI, Spring, TX, 1967. 3. A.S. Faust et al., Principles of Unit Operatiorw, Wiley, New York, 1980. 4. D.Q. Kern, Process Heat Transfer, McGraw-Hill, New York, 1950. 5. T.K. Sherwood, R.L. Pigford, and CR. Wilke, Mass Transfer, McGraw-Hill, New York, 1975. 6. J.R. Singham, Cooling towers, in Heat Exchanger Design Handbook, Hemisphere, New York, 1983, Sec. 3.12. Data on Performance of Cooling Tower Packing 1. Hayashi, Hirai, and Okubo, Heat Transfer Jpn. Res. 2(2) l-6 (1973). 2. Kelly and Swenson, Chem. Eng. Prog. 52, 263 (1956), cited in Figure 9.16. 3. Lichtenstein, Trans. ASME 66, 779 (1943), cited in Figure 9.16. 4. London, Mason, and Boelter, Trans. ASME 62, 41 (1940). cited in Figure 9.16. 5. Lowe and Christie, Proceedings, International Heat Trartsfer Conference, Boulder, CO, 1961, Part V, pp. 933-950. 6. Simpson and Sherwood, Refiig. Eng. 52, 535 (1946), cited in Figure 9.16. 7. Tezuka, Heat Transfer Jpn. Res. 2(3), 40-52 (1973).
- 305. 10 MIXING AND AGITATION A gitation is a means whereby mixing of phases can be accomplished and by which mass and heat transfer can be enhanced between phases or with external surfaces. In its most general sense, the process of mixing is concerned with a// combinations of phases of which the most frequent/y occurring ones are 1. gases with gases. 2. gases into liquids: dispersion. 3. gases with granular solids: fluidization, pneumatic conveying, dving. 4. liquids into gases: spraying and atomization. 5. liquids with liquids: dissolution, emulsification, dispersion. 6. liquids with granular solids: suspension. 7. pastes with each other and with solids. 8. solids with solids: mixing of powders. Interaction of gases, liquids, and solids a/so may take place, as in hydrogenation of liquids in the presence of a slurried solid catalyst where the gas must be dispersed as bubbles and the solid particles must be kept in suspension. Three of the processes involving liquids, numbers 2, 5, and 6, employ the same kind of equipment; namely, tanks in which the liquid is circulated and subjected to a certain amount of shear. This kind of equipment has been studied most extensive/y. Although some unusual cases of liquid mixing may require pilot p/ant testing, genera/ rules have been developed with which mixing equipment can be designed somewhat satisfactorily. This topic will be emphasized in this chapter. The other mixing operations of the list require individual kinds of equipment whose design in some cases is less quantified and is based largely on experience and pilot plant work. Typical equipment for such purposes will be illusrrated later in this chapter. Phase mixing equipment which accomplishes primarily mass transfer between phases, such as distillation and extraction towers, a/so are covered elsewhere. Stirred reactors are discussed in Chapter 77. Circulation and shear of the liquid in a vessel can be accomplished with external pumps and appropriate locarion of suction and discharge nozzles, but a satisfactory combination of vertical and lateral flows is obtained more economically by internal impellers, baffles, and draft tubes. Some genera/ statements about dimensions, proportions, and internals of a liquid mixing vessel can be made. 10.1. A BASIC STIRRED TANK DESIGN The dimensions of the liquid content of a vessel and the dimensions and arrangement of impellers, baffles and other internals are factors that influence the amount of energy required for achieving a needed amount of agitation or quality of mixing. The internal arrangements depend on the objectives of the operation: whether it is to maintain homogeneity of a reacting mixture or to keep a solid suspended or a gas dispersed or to enhance heat or mass transfer. A basic range of design factors, however, can be defined to cover the majority of cases, for example as in Figure 10.1. THE VESSEL A dished bottom requires less power than a flat one. When a single impeller is to be used, a liquid level equal to the diameter is optimum, with the impeller located at the center for an all-liquid system. Economic and manufacturing considerations, however, often dictate higher ratios of depth to diameter. BAFFLES Except at very high Reynolds numbers, baffles are needed to prevent vortexing and rotation of the liquid mass as a whole. A baffle width one-twelfth the tank diameter, w = D,/12; a length extending from one half the impeller diameter, d/2, from the tangent line at the bottom to the liquid level, but sometimes terminated just above the level of the eye of the uppermost impeller. When solids are present or when a heat transfer jacket is used, the baffles are offset from the wall a distance equal to one- sixth the baffle width. Four radial baffles at equal spacing are standard; six are only slightly more effective, and three appreciably less so. When the mixer shaft is located off center (one-fourth to one-half the tank radius), the resulting flow pattern has less swirl, and baffles may not be needed, particularly at low viscosities. DRAFT TUBES A draft tube is a cylindrical housing around and slightly larger in diameter than the impeller. Its height may be little more than the diameter of the impeller or it may extend the full depth of the liquid, depending on the flow pattern that is required. Usually draft tubes are used with axial impellers to direct suction and discharge streams. An impeller-draft tube system behaves as an axial flow pump of somewhat low efficiency. Its top to bottom circulation behavior is of particular value in deep tanks for suspension of solids and for dispersion of gases. About a dozen applications are illustrated by Sterbacek and Tausk (1965, pp. 283ff) and a chapter is devoted to their use by Oldshue (1983,469ff). IMPELLER TYPES A basic classification is into those that circulate the liquid axially and those that achieve primarily radial circulation. Some of the many shapes that are being used will be described shortly. IMPELLER SIZE This depends on the kind of impeller and operating conditions described by the Reynolds, Froude, and Power numbers as well as individual characteristics whose effects have been correlated. For the popular turbine impeller, the ratio of diameters of impeller and vessel falls in the range, d/D, = 0.3-0.6, the lower values at high rpm, in gas dispersion, for example. t 287
- 306. 288 MIXING AND AGITATION Offset =d/2 Baffle width, < w-D,/12 Offset = w I6 0) E m ” t H/3 H/2 Draft tube :dlB Figure 10.1. A basic stirred tank design, not to scale, showing a lower radial impeller and an upper axial impeller housed in a draft tube. Four equally spaced baffles are standard. H = height of liquid level, 0, = tank diameter, d = impeller diameter. For radial impellers, 0.3 5 d/D, 5 0.6. IMPELLER SPEED With commercially available motors and speed reducers, standard speeds are 37, 45, 56, 68, 84, 100, 125, 155, 190, and 320rpm. Power requirements usually are not great enough to justify the use of continously adjustable steam turbine drives. Two-speed drives may be required when starting torques are high, as with a settled slurry. I M P E L L E R L O C A T I O N Expert opinions differ somewhat on this factor. As a first approximation, the impeller can be placed at l/6 the liquid level off the bottom. In some cases there is provision for changing the position of the impeller on the shaft. For off-bottom suspension of solids, an impeller location of l/3 the impeller diameter off the bottom may be satisfactory. Criteria developed by Dickey (1984) are based on the viscosity of the liquid and the ratio of the liquid depth to the tank diameter, h/D,. Whether one or two impellers are needed and their distances above the bottom of the tank are identified in this table: Viscosity [cP (Pa set)] Maximum level N u m b e r o f Impeller Clearance h/4 Impellers L o w e r Upper <25,000 (~25) 1 . 4 1 h/3 - <25,000 (~25) 2.1 2 Q/3 W3M >25,000 (>25) 0 . 8 1 h/3 - >25,000 (>25) 1.6 2 Q/3 (2/3)h Another rule is that a second impeller is needed when the liquid must travel more than 4 ft before deflection. Side entering propellors are placed 18-24 in. above a flat tank floor with the shaft horizontal and at a 10” horizontal angle with the centerline of the tank; such mixers are used only for viscosities below 500 CP or so. In dispersing gases, the gas should be fed directly below the impeller or at the periphery of the impeller. Such arrangements also are desirable for mixing liquids. 10.2. KINDS OF IMPELLERS A rotating impeller in a fluid imparts flow and shear to it, the shear resulting from the flow of one portion of the fluid past another. Limiting cases of flow are in the axial or radial directions so that impellers are classified conveniently according to which of these flows is dominant. By reason of reflections from vessel surfaces and obstruction by baffles and other internals, however, flow patterns in most cases are mixed. When a close approach to axial flow is particularly desirable, as for suspension of the solids of a slurry, the impeller may be housed in a draft tube; and when radial flow is needed, a shrouded turbine consisting of a rotor and a stator may be employed. Because the performance of a particular shape of impeller usually cannot be predicted quantitatively, impeller design is largely an exercise of judgment so a considerable variety has been put forth by various manufacturers. A few common types are illustrated on Figure 10.2 and are described as follows: a. The three-bladed mixing propeller is modelled on the marine propeller but has a pitch selected for maximum turbulence. They are used at relatively high speeds (up to 18OOrpm) with low viscosity fluids, up to about 4OOOcP. Many versions are avail- able: with cutout or perforated blades for shredding and breaking up lumps, with sawtooth edges as on Figure 10.2(g) for cutting and tearing action, and with other than three blades. The stabilizing ring shown in the illustration sometimes is included to minimize shaft flutter and vibration particularly at low liquid levels. b. The turbine with flat vertical blades extending to the shaft is suited to the vast majority of mixing duties up to 100,000 CP or so at high pumping capacity. The simple geometry of this design and of the turbines of Figures 10.2(c) and (d) has inspired extensive testing so that prediction of their performance is on a more rational basis than that of any other kind of impeller. c. The horizontal plate to which the impeller blades of this turbine are attached has a stabilizing effect. Backward curved blades may be used for the same reason as for type e. d. Turbine with blades are inclined 45” (usually). Constructions with two to eight blades are used, six being most common. Combined axial and radial flow are achieved. Especially effective for heat exchange with vessel walls or internal coils. e. Curved blade turbines effectively disperse fibrous materials without fouling. The swept back blades have a lower starting torque than straight ones, which is important when starting up settled slurries. f. Shrouded turbines consisting of a rotor and a stator ensure a high degree of radial flow and shearing action, and are well adapted to emulsification and dispersion. g. Flat plate impellers with sawtooth edges are suited to emul- sification and dispersion. Since the shearing action is localized, baffles are not required. Propellers and turbines also are sometimes provided with sawtooth edges to improve shear. II. Cage beaters impart a cutting and beating action. Usually they are mounted on the same shaft with a standard propeller. More violent action may be obtained with spined blades.
- 307. (a) (d) (j) (Id Figure 10.2. Representative kinds of impellers (descriptions in the text). 289 (i)
- 308. 290 M I X I N G A N D A G I T A T I O N i. J* k . I. Anchor paddles fit the contour of the container, prevent sticking of pasty materials, and promote good heat transfer with the wall. Gatepaddlesareusedinwide,shallowtanksandformaterialsofhigh viscosity when low shear is adequate. Shaft speeds are low. Some designs include hinged scrapers to clean the sides and bottom of the tank. Hollow shaft and hollow impeller assemblies are operated at high tip speeds for recirculating gases. The gas enters the shaft above the liquid level and is expelled centrifugally at the impeller. Circulation rates are relatively low, but satisfactory for some hydrogenations for instance. This arrangement of a shrouded screw impeller and heat exchange coil for viscous liquids is perhaps representative of the many designs that serve special applications in chemical processing. 10.3. CHARACTERIZATION OF MIXING QUALITY Agitation and mixing may be performed with several objectives: 1. Blending of miscible liquids. 2. Dispersion of immiscible liquids. 3. Dispersion of gases in liquids. 4. Suspension of solid particles in a slurry. 5. Enhancement of heat exchange between the fluid and the boundary of a container. 6. Enhancement of mass transfer between dispersed phases. When the ultimate objective of these operations is the carrying out of a chemical reaction, the achieved specific rate is a suitable measure of the quality of the mixing. Similarly the achieved heat transfer or mass transfer coefficients are measures of their respective operations. These aspects of the subject are covered in other appropriate sections of this book. Here other criteria will be considered. The uniformity of a multiphase mixture can be measured by sampling of several regions in the agitated mixture. The time to bring composition or some property within a specified range (say within 95 or 99% of uniformity) or spread in values-which is the blend time-may be taken as a measure of mixing performance. Various kinds of tracer techniques may be employed, for example: 1. A dye is introduced and the time for attainment of uniform color is noted. 2. A concentrated salt solution is added as tracer and the measured electrical conductivity tells when the composition is uniform. 3. The color change of an indicator when neutralization is complete when injection of an acid or base tracer is employed. 4. The residence time distribution is measured by monitoring the outlet concentration of an inert tracer that can be analyzed for accuracy. The shape of response curve is compared with that of a thoroughly (ideally) mixed tank. The last of these methods has been applied particularly to chemical reaction vessels. It is covered in detail in Chapter 17. In most cases, however, the RTDs have not been correlated with impeller characteristics or other mixing parameters. Largely this also is true of most mixing investigations, but Figure 10.3 is an uncommon example of correlation of blend time in terms of Reynolds number for the popular pitched blade turbine impeller. As expected, the blend time levels off beyond a certain mixing intensity, in this case beyond Reynolds numbers of 30,000 or so. The acid-base indicator technique was used. Other details of the test work and the scatter of the data are not revealed in the published information. Another practical solution of the problem is typified by Table 10.1 which relates blend time to power input to 10’ l(r 10’ 10” Reynolds number. D*Nplp Figure 10.3. Dimensionless blend time as a function of Reynolds number for pitched turbine impellers with six blades whose W/D = l/5.66 [Dickey and Fenic, Chem. Eng. 145, (5Jan. 1976)]. vessels of different sizes and liquids of various viscosities. A review of the literature on blend times with turbine impellers has been made by Brennan and Lehrer [Trans. Inst. Chem. Eng. 54, 139-152 (1975)], who also did some work in the range lo4 < NRe < lo5 but did not achieve a particularly useable correlation. An impeller in a tank functions as a pump that delivers a certain volumetric rate at each rotational speed and corresponding power input. The power input is influenced also by the geometry of the equipment and the properties of the fluid. The flow pattern and the degree of turbulence are key aspects of the quality of mixing. Basic impeller actions are either axial or radial, but, as Figure 10.4 shows, radial action results in some axial movement by reason of deflection from the vessel walls and baffles. Baffles contribute to turbulence by preventing swirl of the contents as a whole and elimination of vortexes; offset location of the impeller has similar effects but on a reduced scale. Power input and other factors are interrelated in terms of certain dimensionless groups. The most pertinent ones are, in common units: NRe = 10.75Nd2S/p, Reynolds number, (10.1) Np = 1.523(1013)P/N3d5S, Power number, (10.2) Np = l.037(10s)Q/Nd3, Flow number, (10.3) bN, Dimensionless blend time, (10.4) “Motor horsepowers for various batch volumes, viscosities in cP, blend times in minutes. l Denotes single four-bladed, 45” axial-flow impeller (unshaded selections). t Denotes portable geardrive mixer with single 1.5-pitch propeller (“shaded” selections). (Oldshue, 1983, p. 91).
- 309. 10.3. CHARACTERIZATION OF MIXING QUALITY 291 a b d Figure 10.4. Agitator flow patterns. (a) Axial or radial impellers without baffles produce vortexes. (b) Offcenter location reduces the vortex. (c) Axial impeller with baffles. (d) Radial impeller with baffles. NFr = 7.454(10p4)N2d, Froude number, d = impeller diameter (in.), D = vessel diameter (in.), N = rpm of impeller shaft, P = horsepower input, Q = volumetric pumping rate (cuft/sec), S = specific gravity, tb = blend time (min) , p = viscosity (cP). (10.5) The Froude number is pertinent when gravitational effects are significant, as in vortex formation; in baffled tanks its influence is hardly detectable. The power, flow, and blend time numbers change with Reynolds numbers in the low range, but tend to level off above Nne= 10,ooO or so at values characteristic of the kind of impeller. Sometimes impellers are characterized by their limiting Np, as an Np = 1.37 of a turbine, for instance. The dependencies on Reynolds number are shown on Figures 10.5 and 10.6 for power, in Figure 10.3 for flow and in Figure 10.7 for blend time. Rough rules for mixing quality can be based on correlations of power input and pumping rate when the agitation system is otherwise properly designed with a suitable impeller (predominantly either axial or radial depending on the process) in a correct location, with appropriate baffling and the correct shape of vessel. The power input per unit volume or the superficial linear velocity can be used as measures of mixing intensity. For continuous flow reactors, for instance, a rule of thumb is that the contents of the vessel should be turned over in 5-10% of the residence time. Specifications of superficial linear velocities for different kinds of operations are stated later in this chapter. For baffled turbine agitation of reactors, power inputs and impeller tip speeds such as 0.10 0.01 1 10 100 1000 1 0 0 0 0 100000 1000000 REYNOLDS NUMBER (a) Figure 10.5. Power number, N, = PgJN’D’p, against Reynolds number, NRe = ND*p/y, for several kinds of impellers: (a) helical shape (OUrhue, 1983); (b) anchor shape (Old&e, 1983); (c) several shapes: (1) propeller, pitch equalling diameter, without baffles; (2) propeller, s = d, four baffles; (3) propeller, s = 2d, without baffles; (4) propeller, s = 2d, four baffles; (5) turbine impeller, six straight blades, without baffles; (6) turbine impeller, six blades, four baffles; (7) turbine impeller, six curved blades, four baffles; (8) arrowhead turbine, four baffles; (9) turbine impeller, inclined curved blades, four baffles; (10) two-blade paddle, four baffles; (11) turbine impeller, six blades, four baffles; (12) turbine impeller with stator ring; (13) paddle without baffles (data of Miller and Mann); (14) paddle without baffles (data of White and Summerford). All baffles are of width O.lD [after Rushton, Costich, and Everett, Chem. Eng. Prog. 46(9), 467 (1950)].
- 310. 292 MIXING AND AGITATION 100 80-m 40 20 8.29 6 : s 2 8 O.B& $ ,“I; 0 . 1 0.01 - .-_ 1 1 0 100 1000 1 0 0 0 0 1 0 0 0 0 0 1000000 REYNOLDS NUMBER Figure 10.S(continued) M the following may serve as rough guides: Operation HP/1000 gal Tip Speed (ft/.sec) Blending 0.2-0.5 Homogeneous reaction 0.5-l .5 7.5-10 Reaction with heat transfer 1.5-5.0 10-15 Liquid-liquid mixtures 5 15-20 Liquid-gas mixtures 5 - 1 0 15-20 Slurries 10 The low figure shown for blending is for operations such as 011 I I I I I I f0 t0O’ IO” to‘ IO5 to6 Re (c) incorporation of TEL into gasoline where several hours may be allowed for the operation. Example 10.1 deals with the design and performance of an agitation system to which the power input is specified. Some degree of consistency is found between the several rules that have been cited. 10.4. POWER CONSUMPTION AND PUMPING RATE These basic characteristics of agitation systems are of paramount importance and have been investigated extensively. The literature is I VERTICAL I D I S K t BLADE BLADE NRe = “D’p/p VERTICAL CURVED BLADE BLADE CURVE 4 CURVE 5 Figure 10.6. Power number against Reynolds number of some turbine impellers [Bates, Fondy, and Corpstein, Ind. Eng. Chem. Process. Des. Dev. 2(4) 311 (1963)].
- 311. Reynolds number. NR, = D2Np/,,, Figure 10.7. Flow number as a function of impeller Reynolds number for a pitched blade turbine with N, = 1.37. D/T is the ratio of impeller and tank diameters. [Dickey, 1984, 12, 7; Chem. Eng., 102-110 (26Apr. 1976)]. reviewed, for example, by Oldshue (1983, pp. 155-191), Uhl and Gray (1966, Vol. l), and Nagata (1975). Among the effects studied are those of type and dimensions and locations of impellers, numbers and sizes of baffles, and dimensions of the vessel. A few of the data are summarized on Figures 10.5-10.7. Often it is convenient to characterize impeller performance by single numbers; suitable ones are the limiting values of the power and flow numbers at high Reynolds numbers, above lO,OOO-30,000 or so, for example: 10.4. POWER CONSUMPTION AND PUMPING RATE 2% Type No. baffles % 42 Propeller 0 0 . 3 Propeller 3-8 0.33-0.37 0.40-0.55 Turbine, vertical blade 0 0.93-l .08 0.33-0.34 Turbine, vertical blade 4 3-5 0.70-0.85 Pitched turbine, 45” 0 0 . 7 0 . 3 Pitched turbine, 45” 4 1.30-1.40 0.60-0.87 Anchor 0 0 . 2 8 A correlation of pumping rate of pitched turbines is shown as Figure 10.7. Power input per unit volume as a measure of mixing intensity or quality was cited in Section 10.3 and in Chapter 17. From the correlations cited in this section, it is clear that power input and Reynolds number together determine also the pumping rate of a given design of impeller. This fact has been made the basis of a method of agitator system design by the staff of Chemineer. The superficial linear velocity-the volumetric pumping rate per pnit cross section of the tank-is adopted as a measure of quality of mixing. Table 10.2 relates the velocity to performance of three main categories of mixing: mixing of liquids, suspension of solids in slurries, and dispersion of gases. A specification of a superficial velocity will enable selection of appropriate impeller size, rotation speed, and power input with the aid of charts such as Figures 10.6 and 10.7. Examples 10.1 and 10.2 are along these lines. The combination of HP and rpm that corresponds to a particular superficial velocity depends on the size of the tank, the size of the impeller, and certain characteristics of the system. Tables 10.3, 10.4, and 10.5 are abbreviated combinations of horsepower and rpm that are suitable at particular pumping rates for the three main categories of mixing. More complete data may be found in the literature cited with the tables. 1. For mixing of liquids, data are shown for a viscocity of 5OOOcP, but data also have been developed for 25,000 cP, which allow for EXAMPLE 10.1 Impeller Size and Speed at a Specified Power Input For a vessel containing 5000 gal of liquid with specific gravity = 0.9 and viscosity of lOOcP, find size and speed of a pitched turbine impeller to deliver 2 HP/1000 gal. Check also the superficial linear velocity and the blend time. The dimensions of the liquid content are 9.5ft high by 9.5 ft dia. Take d = 0.40 = 0.4(9.5)(12) = 45.6 in., say 46 in., impeller, P=2V=2(5)=10HP, N Re = 10.75SNd2= 10.75(0.9)(46)‘N = 20,47N P 1000 N P = 1.523(1013)P= 1523(1013)(10) 821,600 N3D5S 0.9(46)5N3 = 7 Solve for N by tria: with the aid of curve 6 of Figure 10.6. T r i a l N 4. I$ N(Eq. (211 5 6 1146 1.3 8 5 . 8 a 4 1720 1.3 8 5 . 8 Take N = 84 rpm. According to Figure 10.7 at d/D = 0.4, N, = 0.61, Q = NQNd3 = 0.61(84/60)(46/12)3 = 48.1 cfs, y = 48.1/[(~/4)(9.5)~] = 0.68 fps. This value corresponds to moderate to high mixing intensity according to Table 10.2. From Figure 10.3, at NRe = 1720, blend time is given by tbN(d/D)Z.3 = 17.0 or 17 r, = ~ - 1.67 min. 84(0.4)2.3 - According to Table 10.1, the blend time is less than 6min, which agrees qualitatively.
- 312. 294 MIXING AND AGITATION TABLE 10.2. Agitation Results Corresponding to Specific Superficial Velocities ft/!WC Description ftfsec Description Liquid Systems 0.1-0.2 low degree of agitation; a velocity of 0.2 ft/sec will a. blend miscible liquids to uniformity when specific gravity differences are less than 0.1 b. blend miscible liquids to uniformity if the ratio of viscosities is less than 100 c. establish liquid movement throughout the vessel d. produce a flat but moving surface 0.3-0.6 characteristic of most agitation used in chemical processing; a velocity of 0.6ft/sec will e. blend miscible liquids to uniformity if the specific gravity differences are less than 0.6 f. blend miscible liquids to uniformity if the ratio of viscosities is less than 10,000 g. suspend trace solids (less than 2%) with settling rates of 2-4 ft/min h. produce surface rippling at low viscosities 0.7-l .o high degree of agitation; a velocity of 1.0 ft/sec will i. blend miscible liquids to uniformity if the specific gravity differences are less than 1.0 j. blend miscible liquids to uniformity if the ratio of viscosities is less than 100,000 k. suspend trace solids (less than 2%) with settling rates of 4-6 ft/min I. produce surging surface at low viscosities Solids Suspension 0.1-0.2 minimal solids suspension; a velocity of 0.1 ft/sec will a. produce motion of all solids with the design settling velocity b. move fillets of solids on the tank bottom and suspend them intermittently 0.3-0.5 characteristic of most applications of solids suspension and dissolution; a velocity of 0.3 ft/sec will 0.6-0.8 0.9-l .o c. suspend all solids with the design settling velocity completely off the bottom of the vessel d. provide slurry uniformity to at least one-third of the liquid level e. be suitable for slurry drawoff at low exit nozzle locations when uniform solids distribution must be approached; a velocity of 0.6 ft/sec will f. provide uniform distribution to within 95% of liquid level g. be suitable for slurry drawoff up to 80% of liquid level when the maximum feasible uniformity is needed. A velocity of 0.9 ft/sec will h. provide slurry uniformity to 98% of the liquid level i. be suitable for slurry drawoff by means of overflow Gas Dispersion 0.1-0.2 0.3-0.5 0.6-1.0 used when degree of dispersion is not critical to the process; a velocity of 0.2 ft/sec will a. provide nonflooded impeller conditions for coarse dispersion b. be typical of situations that are not mass transfer limited used where moderate degree of dispersion is needed; a velocity of 0.5 ft/sec will c. drive fine bubbles completely to the wall of the vessel d. provide recirculation of dispersed bubbles back into the impeller used where rapid mass transfer is needed; a velocity of 1 .O ft/sec will e. maximize interfacial area and recirculation of dispersed bubbles through the impeller [Chemineer, Co. Staff, Chem. Eng., 102-110 (26 April 1976); 144-150 (24 May 19%); 141-148 (19 July lg76)]. Effects of the Ratios of Impeller and Tank Diameters Power and rpm requirements will be investigated and compared with the data of Table 10.3. The superficial velocity is 0.6ft/sec, V = 5000 gals, Sp Gr = 1.0. Viscosities of 100 CP and 5000 CP will be considered. With h/D = 1, D = h = 9.47 ft, pumping rate Q = 0.6(n/4)(9.47)’ = 42.23 cfs, N, = l.037(105)Q/Nd3 = 4.3793/Nd3 NRC = 10.7NdzS/p = 0.00214Nd2, /A = 5000, P = N,N3d5S/1.523(10’3), (1) (2) (3) N, from Figure 10.6. For several choices of d/D, solve Eqs. (1) and (2) simultaneously with Figure 10.7. With p = 5000 cP; d/D d [E$$] (Fig20.7) % P(HP) 0 . 2 5 2 8 . 4 300 0 . 6 3 7 518 0 . 6 4 1.4 4 5 . 9 0 . 3 3 3 7 . 5 145 0 . 5 7 3 436 0 . 5 7 1 . 4 5 2 1 . 5 0 . 5 0 5 6 . 8 5 2 0 . 4 6 0 359 0 . 4 5 1.5 8.2 With p = 100 cP, turbulence is fully developed. d/D d N nb 4. (Fig%l.7) NP P 0 . 2 5 2 8 . 4 228 0.839 1 8 , 9 9 0 0 . 8 4 1.3 18.7 0 . 3 3 3 7 . 5 112 0.742 1 6 , 8 5 0 0 . 7 4 1.3 8 . 9 0 . 5 0 5 6 . 8 40 0.597 1 3 , 8 0 0 0 . 6 0 1.3 3 . 2 Table 10.3 gives these combinations of HP/rpm as suitable: 25/125, 20/1OO, 10/56, 7.5/37. The combination lo/56 checks roughly the last entry at 5OOOcP. Table 10.3 also has data for viscosities of 25,OOOcP, thus allowing for interpolation and possibly extra- polation.
- 313. 10.5. SUSPENSION OF SOLIDS 2% TABLE 10.3. Mixing of Liquids; Power and Im eller Speed (hp/rpm) for Two Viscosities, as a Function oPthe Liquid Superficial Velocity; Pitched Blade Turbine Impeller ftfsec 1 0 0 0 5OoocP 2000 Volume (gal) 5000 1 0 0 0 25,000 CP 2000 5000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2/280 2/190 l/l90 l/100 21190 l/100 21125 m4 1.5184 21125 3/84 1.5184 I.5156 m4 1.5156 51125 3184 51125 3168 3/56 2/45 7.51125 5184 5/100 3168 3156 2/45 7.5/125 5/w 151155 lO/lOO 7.5184 3137 lo/84 7.5168 5145 lo/125 10168 7.5/100 7.5156 151155 15184 lo/loo lo/56 7.5184 7.5145 10164 7.5168 30/155 50/100 251125 40184 20/m 30/68 15168 25156 2/100 51125 3184 3168 2145 7.51125 5/100 5184 3156 lo/84 7.5168 5/45 3137 15/100 10/68 7.5145 251125 20/100 lo/56 7.5/37 15168 15156 10145 10137 30/100 25184 20168 15145 601155 40/100 2/125 -a34 1.5184 1.5156 3/84 2184 1.5156 51125 5184 3166 2145 7.5184 5156 5/125 3184 3168 2145 151155 7.5168 5145 3137 lo/84 7.5145 151155 lO/lOO lo/84 7.5/68 201155 151125 25/155 15164 30/155 251125 20/100 251125 20/100 15184 IO/56 251100 15168 15156 10/45 401155 30/100 25184 20168 50/155 401125 401155 30/125 25/100 401125 30/100 751190 60/155 40/100 30/68 60/125 50/100 50/84 40184 7.51125 5/100 5/84 3156 lo/84 7.5168 5145 3137 20/100 15168 10145 7.5137 30/100 25184 20/68 1OJ37 751190 601155 40/100 15/45 40184 30168 25156 20137 751125 50184 30145 751100 60/64 50168 40/56 75184 60/68 50156 1251125 100/100 75/68 60/56 [Hicks, Morton, and Fenic, Chem. Eng., 102-110 (26 April 1976)]. interpolation and possibly extrapolation. The impeller is a pitched-blade turbine. 2. For suspension of solids, the tables pertain to particles with settling velocities of lOft/min, but data are available for 25 ft/min. The impeller is a pitched-blade turbine. 3. For gas dispersion the performance depends on the gas rate. Data are shown for a superficial inlet gas rate of 0.07 ft/sec, but data are available up to 0.2 ft/sec. Four baffles are specified and the impeller is a vertical blade turbine. Example 10.2 compares data of Table 10.4 with calculations based on Figures 10.6 and 10.7 for all-liquid mixing. Power and rpm requirements at a given superficial liquid velocity are seen to be very sensitive to impeller diameter. When alternate combinations of HP/rpm are shown in the table for a particular performance, the design of the agitator shaft may be a discriminant between them. The shaft must allow for the torque and bending moment caused by the hydraulic forces acting on the impeller and shaft. Also, the impeller and shaft must not rotate near their resonant frequency. Such mechanical details are analyzed by Ramsey and Zoller [Chem. Eng., 101-108 (30 Aug. 1976)]. 10.5. SUSPENSION OF SOLIDS Besides the dimensions of the vessel, the impeller, and baffles, certain physical data are needed for complete description of a slurry mixing problem, primarily: 1. Specific gravities of the solid and liquid. 2. Solids content of the slurry (wt %). 3. Settling velocity of the particles (ft/min). The last of these may be obtained from correlations when the mesh size or particle size distribution is known, or preferably experimentally. Taking into account these factors in their effect on suspension quality is at present a highly empirical process. Tables
- 314. 296 MIXING AND AGITATION TABLE 10.4. Suspension of Solids; Power and Impeller Speed (hp/r m) for Two Settling Velocities, as a Function of the Supe rfr- clal Velocity of the Liquid; Pitched Blade Turbine Impeller Volume (gal) lOR/min 25ft/min ft/sac 1000 2000 5ooo 1000 2000 5000 0.1 l/190 0.2 l/100 0.3 21190 0.4 2/155 1.5/100 0.5 1.5184 21125 0.6 2/100 1.5168 0.7 w4 1.5156 0.8 3184 0.9 1.0 7.5/155 51125 5/100 3168 7.51125 5/84 2/190 l/100 21125 1.5184 m4 1.5156 51155 3184 51125 3168 3156 2145 7.51155 7.51125 5184 7.5184 5156 15/155 lo/loo 7.5168 20/100 15184 lo/84 51125 3184 3166 2145 7.51125 51100 5184 3156 3137 21190 l/190 l/100 21125 1.5184 7.5184 m4 5156 1.5156 15/155 lO/lOO 7.5168 5145 10184 2/m 2156 3184 5156 15184 lo/56 7.5145 7.5137 251125 20/100 15168 10145 401155 30/100 25184 20168 50/100 40184 30168 7.51155 51125 51100 3/68 7.51125 5/84 lo/125 7.5/100 151155 lO/lOO 21125 m4 1.5184 1.5/56 3184 51125 3166 2145 7.51155 51100 3156 7.51125 5184 151155 lO/lOO 7.5184 7.5168 1o/84 15/84 301155 251125 20/100 51125 3184 3168 2145 151155 lO/lOO 7.5168 5145 lo/84 7.5145 15184 lo/56 7.5137 251125 20/100 15168 10145 30/100 25184 20168 15156 60/155 40/100 30168 25156 751190 60/125 50/100 40184 751125 751100 60184 50184 [Gates, Morton,and Fondy, Chem. Eng., 144-150(24 May 1976)1. 10.2-10.5 are one such process; the one developed by Oldshue (1983) will be examined shortly. Suspension of solids is maintained by upward movement of the liquid. In principle, use of a draft tube and an axial flow impeller will accomplish this flow pattern most readily. It turns out, however, that such arrangements are suitable only for low solids contents and moderate power levels. In order to be effective, the cross section of the draft tube must be appreciably smaller than that of the vessel, so that the solids concentration in the draft tube may become impractically high. The usually practical arrangement for solids suspension employs a pitched blade turbine which gives both axial and radial flow. For a given tank size, the ultimate design objective is the relation between power input and impeller size at a specified uniformity. The factors governing such information are the slurry volume, the slurry level, and the required uniformity. The method of Oldshue has corrections for these factors, as F,, F,, and F’. When multiplied together, they make up the factor F4 which is the ordinate of Figure 10.8(d) and which determines what combinations of horsepower and ratio of impeller and vessel diameters will do the required task. Example 10.3 employs this method, and makes a comparison with the Chemineer method of Tables 10.2 and 10.3. 10.6. GAS DISPERSION Gases are dispersed in liquids usually to facilitate mass transfer between the phases or mass transfer to be followed by chemical reaction. In some situations gases are dispersed adequately with spargers or porous distributors, but the main concern here is with the more intense effects achievable with impeller driven agitators. SPARGERS Mixing of liquids and suspension of solids may be accomplished by bubbling with an inert gas introduced uniformly at the bottom of the tank. For mild agitation a superficial gas velocity of 1 ft/min is used, and for severe, one of about 4 ft/min.
- 315. TABLE 10.5. Dispersion of Gases; Power and Impeller Speed (hr/r m) for Two Gas Inlet Superficial Velocities, as a Punction of the Liquid Superficial Velocity; Vertical Blade Turbine Impeller Volume (gal) 0.07ftJsec 0.20 */set R/set 1500 3000 5000 1500 3000 5000 0.1 2156 5/m 0.2 2145 7.51125 0.3 3184 3168 3J56 0.4 0.5 0.6 51125 5184 5JlOO 5J45 7.51125 7.51155 7.5/68 7.5184 lOJ84 10/100 7.5168 5145 7.5/84 5156 lo/84 1 O/l 00 1o/45 lo/56 15/l 55 15J68 15184 15145 20/l 00 20;45 0.7 lo/56 0.8 15/l 55 15184 25/l 25 25/84 25/l 00 25156 30/l 55 3OJlOO 301125 0.9 1.0 15168 3OJ68 401155 40184 7.5168 151155 IO/84 7.5145 1o/45 1O/56 15168 20/l 00 15184 20168 25/l 25 25184 25JlOO 25156 30/l 55 3OJlOO 30/l 25 30168 40/l 55 40184 40/l 00 40156 50/l 00 w@J 50184 50145 60/l 25 60/l 55 60184 60156 751190 75/100 751125 3156 3145 5/100 5184 7.51155 5156 7.51125 7.5168 7.5/84 1 O/84 10/100 lo/56 151155 f5/84 15168 7.5168 lO/lOO 151155 1O/84 7.5145 1o/45 1 O/56 15168 15184 15145 15156 20/l 00 20168 251125 25184 25/100 25156 3OJl55 30/100 30/l 25 25/l 25 40/l 55 25184 40184 1o/45 SYSTEM DESIGN 15168 20/100 251125 The impeller commonly used for gas dispersion is a radial turbine with six vertical blades. For a liquid height to diameter ratio hfD 11, a single impeller is adequate; in the range 1 rh/Ds1.8 two are needed, and more than two are rarely used. The lower and upper impellers are located at distances of l/6and 2/3 of the liquid level above the bottom. Baffling is essential, commonly with four baffles of width l/l2 that of the tank diameter, offset from the wall at l/6 the width of the baffle and extending from the tangent line of the wall to the liquid level. The best position for inlet of the gas is below and at the center of the lower impeller; an open pipe is commonly used, but a sparger often helps. Since ungassed power is significantly larger than gassed, a two-speed motor is desirable to prevent overloading, the lower speed to cut in automatically when the gas supply is interrupted and rotation still is needed. 30/l 55 20168 15145 15156 25184 25/100 25/56 30/100 30/125 30168 30145 40/l55 40184 4OJlOO 40156 5OJlOO 50168 50184 50/56 60/125 60/155 60184 60/56 751190 75JlOO 75/l 25 [Hicks and Gates, Chem. Eng., 141-148 (13 July 1976)]. MASS TRANSFER The starting point of agitator design is properly a mass transfer coefficient known empirically or from some correlation in terms of parameters such as impeller size and rotation, power input, and gas flow rate. Few such correlations are in the open literature, but some have come from two of the industries that employ aerated stirred tanks on a large scale, namely liquid waste treating and fermentation processes. A favored method of studying the absorption of oxygen is to measure the rate of oxidation of aqueous sodium sulfite solutions. Figure 10.9 summarizes one such investigation of the effects of power input and gas rate on the mass transfer coefficients. A correlation for fermentation air is given by Dickey (1984, 12-17): k,a = rate/(concentration driving force) = O.O64(P /V)“.7ut2, i? l/set, (10.6) with P,/V in HP/1000 gal and superficial gas velocity ur in ft/sec. A general correlation of mass transfer coefficient that does not have 10.6. GAS DISPERSION 297 power input as a factor is given by Treybal (Ma.ss Transfer Operations, McGraw-Hill, New York, 1980, 156); presumably this is applicable only below the minimum power input here represented by Figure 10.11. When mass transfer coefficients are not determinable, agitator design may be based on superficial liquid velocities with the criteria of Table 10.2. MINIMUM POWER Below a critical power input the gas bubbles are not affected laterally but move upward with their natural buoyancy. This condition is called gas flooding of the impeller. At higher power inputs the gas is dispersed radially, bubbles impinge on the walls and are broken up, consequently with improvement of mass transfer. A correlation of the critical power input is shown as Figure 10.10. POWER CONSUMPTION OF GASSED LIQUIDS At least partly because of its lower density and viscosity, the power to drive a mixture of gas and liquid is less than that to drive a liquid. Figure 10.11(a) is a correlation of this effect, and other data at low values of the flow number Q/Nd3 are on Figure 10.11(b). The latter data for Newtonian fluids are correlated by the equation P,lP = 0.497(Q/Nd3)-0.38(N2d3p,/u)-o.18, (10.7) where the last group of terms is the Weber number, pL is the density of the liquid, and u is its surface tension. SUPERFICIAL LIQUID VELOCITY When mass transfer data are not known or are not strictly pertinent, a quality of mixing may be selected by an exercise of judgment in terms of the superficial liquid velocity on the basis of the rules of Table 10.2. For gas dispersion, this quantity is related to the power input, HP/1000 gal, the superficial gas velocity and the ratio d/D in Figure 10.12. DESIGN PROCEDURES On the basis of the information gathered here, three methods are possible for the design of agitated gas dispersion. In all cases the size of the tank, the ratio of impeller and tank diameters and the gas feed rate are specified. The data are for radial turbine impellers with six vertical blades.
- 316. 298 MIXING AND AGITATION SLURRY VOL. - m3 I;~ 7 ; 1; 172; 3p40TOqO 1; 1000 2000 4000 6000 10000 20000 30000 SLURRY VOL. - GRLLONS (a) S E T T L ING VELOCITY (m04IN.l I I I I I 1.0 2.0 3.0 4.06.0 8.0 10.0 2t D SETTLING VELOCITY (FT./MIN.l (c) 1.0 - 0.9 - 0.8 - 0.7 - 0.6 - 0.5 0.51 I IIII I I IIII I I I I 0.3 0.3 0.4 0.4 0.50.60.7 0.50.60.7 0.8 0.8 1.0 1.0 1.5 1.5 2.0 2.0 Z/T Z/T b) I- 100 HP 300 200 6 0 4 0 100 8 0 2 5 6 0 4 0 3 0 2 0 10.0 8.0 k8” 0..6 0.4 0.3 0.2 -._ 0.10.2 0.30.4 0.6 D/T id) ??igure 10.8. Suspension of solids. Power and ratio of diameters of impeller and tank, with four-bladed 45” impeller, width/diameter = 0.2. [method of Oldrhue (1983)]. (a) The factor on power consumption for slurry volume, Ft. (b) The factor on power requirement for single and dual impellers at various h/D ratios, Fa. (c) The effect of settling velocity on power consumption, Fs. (d) Suspension factor for various horsepowers: F4 = F,F,F,.
- 317. 1 0 . 6 . G A S D I S P E R S I O N 2% Design of the Agitation System for Maintenance of a Slurry These conditions are taken: V = 5000 gal, h/D = 1, settling velocity = 10 ft/min, solids content = 10 wt % Reading from Figure 10.8, F, = 4, &=l.l, off bottom, uniform. The relation between the ratio of impeller and vessel diameters, d/D and HP is read off Figure 10.8(d). H P d/D Off btm Uniform 0.2 20 65 0.4 7.5 25 0.6 4 12 Comparing with readings from Tables 10.2 and 10.3, Superficial liq. velocity HP/rpm 0.3 (off btm) 1 O/45,1O/56 0.6 (uniform) 30/155,30/125,30/100,30/68 These results correspond roughly to those of the Oldshue method at d/D = 0.4. The impeller sizes can be determined with Figures 10.6 and 10.7. Start with a known required mass transfer coefficient. From a correlation such as Figure 10.9 or Eq. (10.6) the gassed power per unit volume will become known, and the total gassed power to the tank will be Pg. The ratio of gassed power to ungassed power is represented by Figure 10.11(a) and the equations given there; at this stage the rotation speed N is not yet known. This value is found by trial by simultaneous solution with Figure 10.6 which relates the Reynolds and power numbers; the power here is the ungassed power. The value of N that results in the precalculated Pg will be the correct one. Curve 2 of Figure 10.6 is the one applicable to gas dispersion with the data of this section. Start with a choice of superficial liquid velocity uL made in accordance with the criteria of Table 10.2. With the aid of the known gas velocity U, and d/D, find P,/V from Figure 10.12. Then proceed to find N by trial with Figures 10.11(a) and 10.6 as in method 1. 0 . 1 I 1 I D/T = .25-.40 LB MOLES FT3/HR/ATM .02 0 . 3 0 . 6 1 . 0 2 . 0 4 . 0 8 . 0 1 0 HP / 1000 GAL. GASSED FIgare 10.9. Typical data of mass transfer coefficients at various power levels and superficial gas rates for oxidation of sodium sulfite in aqueous solution. d/D = 0.25-0.40 (O&hue, 1983). 3. As soon as a superficial liquid velocity has been selected, a suitable combination of HP/rpm can be taken from Table 10.5. These procedures are applied in Example 10.4. As general rules, levels of 5-12HP/lOOOgal are typical of aerobic fermentation vessels. and 1-3 HP/1000 gal of aerobic waste treatment; concentrations and oxygen requirements of the microorganisms are different in the two kinds of processes. Superficial gas relocity. 1 t/s Figure 10.10. Minimum power requirement to overcome flooding as a function of superficial gas velocity and ratio of impeller and tank diameters, d/D. [Hicks and Gates, Chem. Eng., 141-148 (19 July 1976)].
- 318. 300 MIXING AND AGITATION ( ) % T , 0 . 0 0.1 0.S 0 . 5 +- 0 0:02 0.64 O.&S 0.6s (i-y (t-4 Figure 10.11. Power consumption. (a) Ratio of power consumptions of aerated and unaerated liquids. Q is the volumetric rate of the gas: (0) glycol; ( x ) ethanol; (v) water. [After Calderbank, Trans. Inst. Chem. Eng. 36, 443 (1958)]. (b) Ratio of power consumptions of aerated and unaerated liquids at low values of Q/Nd3. Six-bladed disk turbine: (Cl) water; (0) methanol (10%); (A) ethylene glycol (8%); (A) glycerol (40%); P’ = gassed power input; P = ungassed power input; Q = gas flow rate; N = agitator speed; d = agitator- impeller diameter. [Luong and Volesky, AIChE J. 25, 893 (1979)]. 10.7. IN-LINE BLENDERS AND MIXERS When long residence time is not needed for chemical reaction or other purposes, small highly powered tank mixers may be suitable, with energy inputs measured in HP/gal rather than HP/lOOOgal. They bring together several streams continuously for a short contact time (at most a second or two) and may be used whenever the effluent remains naturally blended for a sufficiently long time, that is, when a true solution is formed or a stable emulsion-like mixture. When it is essential that the mixing be immediate each stream will 1 & 0.8 5 0.6 ‘; 2 0.4 >II 0 . 2 0.1 4 . 6 80.1 2 4 6 8 1 2 X = (P/V)(d/D)‘= Figure 10.12. Relation between power input, P/VHP/lOOOgal, superficial liquid velocity u,ft/sec, ratio of impeller and tank diameters, d/D, and superficial gas velocity u, ft/sec. [Hicks and Gates, Chem. Eng., 141-148 (19JuZy 1976)]. have its own feed nozzle, as in Figure 10.13(b), but usually the streams may be combined externally near the blender and then given the works, as in Figure 10.13(a). One manufacturer gives these power ratings: Tanksize (gal) 1 5 10 30 M o t o r H P 0.5 1 2 3 Another ties in the line and motor sizes: Line size, (in.) l - 4 6-8 10-12 M o t o r H P 0.5 1 2 But above viscosities of 1OcP a body one size larger than the line size is recommended. Other devices utilize the energy of the flowing fluid to do the mixing. They are inserts to the pipeline that force continual changes of direction and mixing. Loading a section of piping with tower packing is an example but special assemblies of greater convenience have been developed, some of which are shown in Figure 10.14. In each case manufacturer’s literature recommends the sizes and pressure drops needed for particular services. The Kenics mixer, Figure 10.14(a), for example, consists of a succession of helical elements twisted alternately in opposite directions. In laminar flow for instance, the flow is split in two at each element so that after n elements the number of striations becomes 2”. The effect of this geometrical progression is illustrated in Figure 10.14(b) and points out how effective the mixing becomes after only a few elements. The Reynolds number in a corresponding empty pipe is the major discriminant for the size of mixer, one manufacturer’s recommendations being 4, Number of Elements Less than 10 2 4 10-2000 12-18 More than 2000 6 Besides liquid blending applications, static mixers have been used for mixing gases, pH control, dispersion of gases into liquids, and dispersion of dyes and solids in viscous liquids. They have the advantages of small size, ease of operation, and relatively low cost. The strong mixing effect enhances the rate of heat transfer from viscous streams. Complete heat exchangers are built with such
- 319. 1 0 . 8 . M I X I N G O F P O W D E R S A N D P A S T E S 301 EXAMPLE 10.4 HP and ‘pm Requirements of an Aerated Agitated Tank A tank contains 5OOOgal of liquid with sp gr = 1.0 and viscosity 1OOcP that is aerated and agitated. The ratio of impeller to tank diameters is d/D = 0.4. Two sets of conditions are to be examined. a. The air rate is 972SCFM or 872ACFM at an average submergence of 4 ft. The corresponding superficial gas velocity is 0.206ft/sec or 0.063 m/set. A mass transfer coefficient k,a = 0.2/set is required; Dickey’s equation (10.6) applies. Find the power and rpm needed. b. The air rate is 296ACFM, 0.07 ft/sec, 0.0213 m/set. The required intensity of mixing corresponds to a liquid superficial velocity of 0.5 ft/sec. Find the power, rotation speed, and mass transfer coefficients for sulfite oxidation and for fermentation. a . d=0.4(9.47)=3.79ft,45.46in., k,a = 0.064(P,/V)“~7u~2 = 0.2, P,/V = [0.2/0.064(0.206)“~2]“o~7 = 8.00 HP, Pg = 5(8.0) = 40.0 HP/5000 gal, Q/Nd3 = 872/(379)3N = 16.02/N, NRe = 10.75Nd2S/p = 10.75(45.46)2N/100 = 222N. Equation (10.2), N, = 1.523(10’3)P/N3dSS = 78,442P/N3. Curve 2 of Figure (10.6) applies. P,/P from Figure 10.10(a). Solve by trial. N Cl/Nd” p,/P NRs N,, P 4 100 0.160 0.324 22,200 4 51 16.5 150 0.107 0.422 33,300 4 172 72.6 127 0.1261 0.3866 28,194 4 104.5 40.4-40.0 The last entry of Pp checks the required value 40.0. Find the corresponding superficial liquid velocity with Figure 10.12: X = (P/V)(d/D)‘.” = 8.04(0.4)‘-85 = 1.48, at uG = 0.206 ft/sec, Y = 2.0, :. uL = 2/10(0.4)‘-* = 0.60 ftlsec. From Table 10.2, a liquid velocity of 0.6-0.7 ft/sec will give moderate to high dispersion. Table 10.5 gives possible HP/rpm combination of 30/125, somewhat less than the value found here. b. With liquid circulation velocity specified, uL = 0.5 ftlsec. Use Figure 10.12: Y = iou,(d/D)‘.2 = 10(0.5)(0.4)‘.’ = 1.67, X= 0.8, P,IV = 0.8/(0.4)‘-85 = 4.36 HP/1000 gal (this does exceed the minimum of 1.6 from Figure lO.ll), P, = 5(4.36) = 21.8, $ = 296/(3.79)3N = 5.437/N, NRe = 222N (part a), N=y (part a). Solve by trial, using Figure 10.10(a) and curve 2 of Figure 10.6. N O/N2 p,/P 47. q7 p 5 100 0.0544 0.5194 22,200 4 51 26.5 94 0.0576 0.5130 4 42.35 21.7-2.8 The closest reading from Table 10.5 is HP/rpm = 25/100 which is a good check. For sulfite oxidation, at ug = 0.07 ft/sec, P,/V = 4.36 HP/1000 gal, from Figure 10.9, k,a = 0.07 lb mol/(cuft)/(hr)(atm). For fermentation, Eq. 10.6 gives k,a = 0.064(4.36)“.7(0. 07)“.2 = o, 1o5 lb mol/(cuft)(sec) lb mol/cuft mixing inserts in the tubes and are then claimed to have 3-5 times normal capability in some cases. 10.8. MIXING OF POWDERS AND PASTES Industries such as foods, cosmetics, pharmaceuticals, plastics, rubbers, and also some others have to do with mixing of high viscosity liquids or pastes, of powders together and of powders with pastes. Much of this kind of work is in batch mode. The processes are so diverse and the criteria for uniformity of the final product are so imprecise that the nonspecialist can do little in the way of equipment design, or in checking on the recommendations of equipment manufacturers. Direct experience is the main guide to selection of the best kind of equipment, predicting how well and quickly it will perform, and what power consumption will be. For projects somewhat out of direct experience and where design by analogy may not suffice, testing in pilot plant equipment is a service provided by many equipment suppliers. A few examples of mixers and blenders for powders and pastes are illustrated in Figure 10.15. For descriptions of available equipment-their construction, capacity, performance, power consumption, etc.--the primary sources are catalogs of manufac- turers and contact with their offices. Classified lists of manu- facturers, and some of their catalog information, appear in the Chemical Engineering Catalog (Reinhold, New York, annually) and in the Chemical Engineering Equipment Buyers Guide (McGraw-Hill, New York, annually). Brief descriptions of some types of equipment are in Perry’s Chemical Engineers Handbook (McGraw-Hill, New York, 1984 and earlier editions). Well-classified descriptions, with figures, of paste mixers are in Ullmann (1972,
- 320. 302 MIXING AND AGITATION t (a) M Figure 10.13. Motor-driven in-line blenders: three-inlet model made by Cleveland Mixer Co. (a) Double impeller made by Nettco Corp.; (b) (a) bl (d) Element Number ixidiD6 2 4 6 16 3 2 Number of Striations (e) (4 Figure 10.14. Some kinds of in-line mixers and blenders. (a) Mixing and blending with a recirculating pump. (b) Injector mixer with a helical baffle. (c) Several perforated plates (orifices) supported on a rod. (d) Several perforated plates flanged in. (e) Hellical mixing elements with alternating directions (Kenics Corp.). (f) Showing progressive striations of the flow channels with Kenics mixing elements.
- 321. 1 0 . 8 . M I X I N G O F P O W D E R S A N D P A S T E S 303 (a) (cl (dl Muller wheels Dfwen shaft b-1 -.. __ t L -.._ a h) Figure 10.15. Some mixers and blenders for powders and pastes. (a) Ribbon blender for powders. (b) Flow pattern in a double cone blender rotating on a horizontal axis. (c) Twin shell (Vee-type); agglomerate breaking and liquid injection are shown on the broken line. (d) Twin rotor; available with jacket and hollow screws for heat transfer. (e) Batch muller. (f) Twin mullers operated continuously. (g) Double-arm mixer and kneader (Baker-Perkins Inc.). (h) Some types of blades for the double-arm kneader (Baker-Perkins Inc.).
- 322. 304 MIXING AND AGITATION Vol. 2, pp. 282-300) and a similar one for powder mixers (lot. cit., pp. 301-311). Since this equipment industry has been quite stable, older books are still useful, notably those of Riegel (1953), Mead (1964), and particularly Kieser (1934-1939). REFERENCES 1. R.S. Brodkey (Ed.), Turbulence in Miring Operations, Academic, New York, 1975. 2. Chemineer Co. Staff, Liquid Agifation, Reprint of 12 articles from Chemical Engineering, 8 Dec. 1975-6 Dec. 1976. 3. D.S. Dickey, In Handbook of Chemical Engineering Calculations, (N.P. Chopey and T.G. Hicks Eds.), McGraw-Hill, New York, 1984. 4. S. Harnby, M.F. Edwards, and A.W. Nienow, Mixing in the Process Industries, Butterworths, Stoneham, MA, 1985. 5. A.J. Kieser, Handbuch der chemisch-technixhen Apparate, Springer- Verlag, Berlin, 1934-1939. 6. W.J. Mead, Encyclopedia of Chemical Process Equipment, Reinhold, New York, 1964. I. S. Nagata, Mixing Principles and Applications, Wiley, New York, 1975. 8. J.Y. Oldshue, Fluid Mixing Technology, McGraw-Hill, New York, 1983. 9. E.R. Riegel, Chemical Process Machinery, Reinhold, New York, 1953. 10. Z. Sterbacek and P. Tausk, Miring in the Chemical Industry, Pergamon, New York, 1965. 11. J.J. Ulbrecht and G.K. Patterson, Mixing of Liquids by Mechanical Agitation, Gordon & Breach, New York, 1985. IZ. V. Uhl and J.B. Gray (Eds.), Mixing Theory and Practice, Academic, New York, 1966, 1967, 2 ~01s. W. lJlbnnnn’s Encyclopedia of Chemical Technology, Verlag Chemie, Weinheim, Germany, 1972, Vol. 2, pp. 249-311.
- 324. SOLID-LIQUID SEPARATION S o/id-liquid separation is concerned with mechanical processes for the separation of liquids and finely divided insoluble solids. 11.1. PROCESSES AND EQUIPMENT Much equipment for the separation of liquids and finely divided solids was invented independently in a number of industries and is of diverse character. These developments have occurred without benefit of any but the most general theoretical considerations. Even at present, the selection of equipment for specific solid-liquid separation applications is largely a process of scale-up based on direct experimentation with the process material. The nature and sizing of equipment depends on the economic values and proportions of the phases as well as certain physical properties that influence relative movements of liquids and particles. Pressure often is the main operating variable so its effect on physical properties should be known. Table 11.1 is a broad classification of mechanical processes of solid-liquid separation. Clarification is the removal of small contents of worthless solids from a valuable liquid. Filtration is applied to the recovery of valuable solids from slurries. Expression is the removal of relatively small contents of liquids from compressible sludges by mechanical means. Whenever feasible, solids are settled out by gravity or with the aid of centrifugation. In dense media separation, an essentially homogeneous liquid phase is made by mixing in finely divided solids (less than lOOmesh) of high density; specific gravity of 2.5 can be attained with magnetite and 3.3 with ferrosilicon. Valuable ores and coal are floated away from gangue by such means. In flotation, surface active agents induce valuable solids to adhere to gas bubbles which are skimmed off. Magnetic separation also is practiced when feasible. Thickeners are vessels that provide sufficient residence time for settling to take place. Classifiers incorporate a mild raking action to prevent the entrapment of fine particles by the coarser ones that are to be settled out. Classification also is accomplished in hydrocyclones with moderate centrifugal action. TABLE 11 .I. Chief Mechanical Means of Solid-Liquid Separation 1. Settling a. by gravit i. in thic eners 1 ii. in classifiers b. by centrifugal force c. by air flotation d. by dense media flotation e. by magnetic properties 2. Filtration a. on screens, by gravity b. on filters i. by vacuum ii. by pressure iii. by centrifugation 3. Expression a. wjth batch presses b. ytth continuous presses . screw presses ii. rolls iii. discs Freely draining solids may be filtered by gravity with horizontal screens, but often filtration requires a substantial pressure difference across a filtering surface. An indication of the kind of equipment that may be suitable can be obtained by observations of sedimentation behavior or of rates of filtration in laboratory vacuum equipment. Figure 11.1 illustrates typical progress of sedimentation. Such tests are particularly used to evaluate possible flocculating processes or agents. Table 11.2 is a classification of equipment based on laboratory tests; test rates of cake formation range from several cm/set to fractions of a cm/hr. Characteristics of the performance of the main types of commercial SLS equipment are summarized in Table 11.3. The completeness of the removal of liquid from the solid and of solid from the liquid may be important factors. In some kinds of equipment residual liquid can be removed by blowing air or other gas through the cake. When the liquid contains dissolved substances that are undesirable in the filter cake, the slurry may be followed by (A) (B) CC) (D) (E) I Ttme Figure 11.1. Sedimentation behavior of a slurry, showing loose and compacted zones (Osborne, 1981). 305
- 325. 306 SOLID-LIQUID SEPARATION TABLE 11.2. Equipment Selection on the Basis of Rate of Cake Buildup Process Type Rapid filtering Rate of Cake Buildup 0.1-10 cm/set Medium filtering S l o w filtering O.l-lOcm/min 0.1-10 cm/hr Clarification negligible cake Suitable Equipment gravity pans; horizontal belt or top feed drum; continuous pusher type centrifuge vacuum drum or disk or pan or belt; peeler type centrifuge pressure filters; disc and tubular centrifuges; sedimenting centrifuges cartridges; precoat drums; filter aid systems; sand deep bed filters (Tiller and Crump, 1977; Flood, Parker, and Rennie, 1966). pure water to displace the residual filtrate. Qualitative cost comparisons also are shown in this table. Similar comparisons of filtering and sedimentation types of centrifuges are in Table 11.19. Final selection of filtering equipment is inadvisable without some testing in the laboratory and pilot plant. A few details of such work are mentioned later in this chapter. Figure 11.2 is an outline of a procedure for the selection of filter types on the basis of appropnate test work. Vendors need a certain amount of in- formation before they can specify and price equipment; typical inquiry forms are in Appendix C. Briefly, the desirable information includes the following. 1. 2. Flowsketch of the process of which the filtration is a part, with the expected qualities and quantities of the filtrate and cake. Properties of the feed: amounts, size distribution, densities and chemical analyses. 3. Laboratory observations of sedimentation and leaf filtering rates. 4. Pretreatment options that may be used. 5. Washing and blowing requirements. 6. Materials of construction. A major aspect of an SLS process may be conditioning of the slurry to improve its filterability. Table 11.4 summarizes common pretreatment techniques, and Table 11.5 lists a number of flocculants and their applications. Some discussion of pretreatment is in Section 11.3. 11.2. THEORY OF FILTRATION Filterability of slurries depends so markedly on small and unidentified differences in conditions of formation and aging that no correlations of this behavior have been made. In fact, the situation is so discouraging that some practitioners have dismissed existing filtration theory as virtually worthless for representing filtration behavior. Qualitatively, however, simple filtration theory is directionally valid for modest scale-up and it may provide a structure on which more complete theory and data can be assembled in the future. As filtration proceeds, a porous cake of solid particles is built up on a porous medium, usually a supported cloth. Because of the fineness of the pores the flow of liquid is laminar so it is represented by the equation The resistance R is made up of those of the filter cloth Rf and that of the cake R, which may be assumed proportional to the weight of the cake. Accordingly, dV AAP AAP Q = dt = p(~,+ R,) = p(Rf + c~cVI-4) ’ (Y = specific resistance of the cake (m/kg), c = wt of solids/volume of liquid (kg/m3), p = viscosity (N set/m’) P = pressure difference (N/m’) A = filtering surface (m’) V = volume of filtrate (m3) Q = rate of filtrate accumulation (m3/sec). Rf and (Y are constants of the equipment and slurry and must be evaluated from experimental data. The simplest data to analyze are those obtained from constant pressure or constant rate tests for which the equations will be developed. At constant pressure Eq. (11.2) is integrated as AAP Tt=RfV+$‘2 and is recast into linear form as (11.4) The constants Rf and (Y are derivable from the intercept and slope of the plot of t/V against V. Example 11.1 does this. If the constant pressure period sets in when I = to and V = V,, Eq. (11.4) becomes t--o _ v-v,-&~RF+&Q’+KJ. A plot of the left hand side against V + V, should be linear. At constant rate of filtration, Eq. (11.2) can be written QL AAP t p(Rf + WV/A) and rearranged into the linear form !?=!!!=!!R +!%V, Q V/t A F A2 (11.6) (11.7) The constants again are found from the intercept and slope of the linear plot of AP/Q against V. After the constants have been determined, Eq. (11.7) can be employed to predict filtration performance under a variety of constant rate conditions. For instance, the slurry may be charged with a centrifugal pump with a known characteristic curve of output pressure against flow rate. Such curves often may be represented by parabolic relations, as in Example 11.2, where the data are fitted by an equation of the form P=a-Q(b+cQ). (11.8) The time required for a specified amount of filtrate is found by integration of I v t= dVlQ. (11.9) 0
- 326. TABLE 11.3. Comparative Performance of SLS Equipment’ Feed Conditions Product Parameters Favoring Use Equipment Characteristics Direct Costs Solids Liquid in Liquid in Solid Wash* Solids Solids Particle Product Product Possibilities Concentration D e n s i t y S i z e P o w e r S p a c e Holdup Initial Operating Maintenance Filtration V a c u u m d r u m filter Disc filters Horizontal filter Precoat filter Leaf (Kelly) filter Sedimentation T h i c k e n e r Clarifier Classifier Centrifugation D i s c Solid bowl gasket Liquid cyclones L a r g e Small multiple S c r e e n s Ultrafiltration F F F E G to Ed G to E G P F to G P P to F P Pto F P E G G G P** F Pto F P P to F P to F Ed P to F G to Ed P to F** F to G P v e r y P P to F P Pto F Ed P v e r y P P P high to m e d . m e d i u m high to m e d . very low l o w m e d i u m l o w m e d i u m low to med. med. to high med. to high low to med. l o w med. to high l o w - - - - - d e n s e m e d . d e n s e d e n s e m e d i u m m e d i u m - high med. to high - - m e d i u m fine c o a r s e s l i m y fine, s l i m y m e d i u m fine c o a r s e fine med. to fine c o a r s e m e d i u m fine coarse to m e d . very fine high high high high to m e d . med. to low low very l o w low high high high med. to l o w med. to l o w l o w med. to high m e d i u m m e d i u m m e d i u m m e d i u m m e d i u m very high v-v high high l o w l o w l o w l o w l o w very l o w high m e d i u m m e d i u m m e d i u m m e d i u m m e d i u m “en/ high very high high l o w l o w l o w l o w l o w very l o w high high med. to high m e d i u m high m e d i u m med. to l o w med. to l o w med. to l o w high med. to high m e d i u m very low l o w very l o w high high high high very high very high l o w l o w l o w high high high medium m e d i u m m e d i u m high m e d i u m m e d i u m m e d i u m m e d i u m m e d i u m very low very low l o w high high high high m e d i u m med. to high vet-y high a P = Poor. F = Fair. G = Good. E = Excellent. l Decantation wash always possible. d Displacement wash feasible. **Solids product contaminated by precoat material. (Purchas, 1981).
- 327. 308 SOLID-LIQUID SEPARATION Laboratory routine Fmol test work Final sizmg and process costing I I lube centrifuge test I Sedmvzntotion I test - Hydrocyclonc test I I I Select ttlter mcdtum from those t wth sultablc chcmlcal rcwstancc Buchncr test Select another medwn Try grade either side of chosen medium and chooSe lostcst pcrmlsslbtc grade t Is form rate a ‘/IS rich in 3min Perforated basket centrifuge test Vacuum leaf test I Pr*ssure leaf test I Magnetic separator Scdmentotlon c e n t r i f u g e s - - Co”tl”uous nozzle Botch tubular bowl Botch dec bowl Botch disc bowl, self -Opening Continuous rotary prccoat filter Botch ccntritugol filters - Continuous rotary vacuum filter Centrifugal filters Con1 inuous pusher Cont 1nu0us w0rm dischorgc Continuous oscillating screen ncl~col conveyor dccontcr - centrifuge Continuous toblc t iltcr - Various pressure filters - Continuous drum Batch leaf Batch ptatc Botch tubular ctcmcnt Botch cartridge Batch plotr and fromc Figure 11.2. Experimental routine for aiding the selection of solid-liquid separation equipment (Davies, 1965).
- 328. TABLE 11.4. Action and Effects of Slurry Pretreatments Action On Technique ElSCtS 2. Solid particles 3. Concentration of solids 4. Solid/liquid interaction 1. Liquid 1. heating 2. dilution with solvent I 3. degassing and stripping 1. coagulation by chemical additives 2. flocculation by natural or forced convection 3. aging 1. increase by appropriate first-stage device such as settling tank, cyclone flotation cell or filter/thickener 2. classify to eliminate fines, using sedimentation or cyclone 3. add filter powder (e.g., diatomite) or other solids to act as ‘body aid’ 1. heat treatment, e,g,, Porteus process involving pressure cooking 2. freeze/thaw 3. ultrasonics 4. ionized radiation I 5. addition of wetting agents reduction of viscosity, thereby speeding filtration and settling rates and reducing cake moisture content prevents gas bubbles forming within the medium or cake and impeding filtration destabilizes colloidal suspensions, allow- ing particles to agglomerate into microflocs microflocs are brought into contact with each other to permit further agglomera- tion into large floes size of individual particles increases, e.g., by crystal growth rate of filtration increased, especially if initial concentration 12% rate of filtration increased and cake moisture content reduced rate of filtration increased by more porous cake and possibly by high total solid concentration physical methods which condition sludge and induce coagulation and/or flocculation reduces the interfacial surface tension, improves the draining characteristics of the cake, and decreases the residual moisture content (Purchas, 1981). TABLE 11.5. Natures and Applications of Typical Flocculants Normal Normal Ty eor 1 Typical Range of pH Effective Apy,“,” Trade Name Composition Met anism Apphcation Effectiveness Concentration per Ibe Manufacturer Alum AI,(SO,),.XH,O electrolytic and water treatment 5-10 15wm a inorganic chemical coagulation manufacturers Ferric Fe,(SO,)XH,O electrolytic water treatment any 5-100 ppm 3 inorganic chemical sulfate coagulation and chemical manufacturers processing Sodium sodium carboxy- coagulation and mineral 3-9 0.03-0.5 lb/ton 50e Hercules, DuPont C M C methylcellulose bridging processing Kelgin W algins coagulation and water treatment 4-11 up to 5 ppm $ 1 . 5 0 Kelco Co. bridging Separan a c r y l a m i d e bridging chemical 2-10 0.2-10 ppm $l.OO-$2.00 Dow Chemical Co. p o l y m e r processing Fibrefloc animal glue electrolytic waste treatment l - 9 5-30 ppm 18e Armour and Co. Corn corn starch bridging mineral 2-10 10 lb/ton 7e - starch processing Polynox polyethylene bridging chemical 2-10 l-50 ppm $2.00 Union Carbide oxide processing Silica sol activated electrolytic waste treatment 4-6 l-20 ppm 1.5$ as inorganic chemical silica sol coagulation s o d i u m manufacturers silicate Sodium s o d i u m coagulation water treatment 3-12 2-10 ppm 1oe National Aluminate aluminate aluminate Guar gum g u a r g u m bridging mineral 2-12 0.02-0.3 lb/ton 356 General Mills processing Sulfuric H,SO, electrolytic waste treatment 1-5 highly variable 1) inorganic chemical acid manufacturers a 1966 prices, for comparison only. (Purchas, 1981). 309
- 329. 310 SOLID-LIQUID SEPARATION EXAMPLE 11.1 Constants of the Filtration Equation from Test Data Filtration tests were performed on a CaCO, slurry with these properties: C = 135 kg solid/m3 liquid, y = 0.001 N set/m’. The area of the filter leaf was 500cm2. Data were taken of the volume of the filtrate (L) against time (set) at pressures of 0.5 and 0.8 bar. The results will be analyzed for the filtration parameters: 0 . 5 bar 0 . 8 bar u V/A t t/(VlA) t t/(V/Al 0.5 0.01 6.8 680 4.8 480 1 0.02 19.0 950 12.6 630 1.5 0.03 36.4 1213 22.8 760 2 0.04 53.4 1335 35.6 890 2.5 0.05 76.0 1520 50.5 1010 3 0.06 102.0 1700 69.0 1150 3.5 0.07 131.2 1874 88.2 1260 4 0.08 163.0 2038 112.0 1400 4.5 0.09 - - 5 0.10 165.0 1650 The units of V/A are m3/m2. Equation (11.2) is d(VIA) A P -zz dt ,u(Rr + c&V/A) ’ whose integral may be written R, LYC v t ~- AP/p + 2(AP/p) A = m Intercepts and slopes are read off the linear plots. At 0.5 bar, AP/p = 0.5(105)/0.001 = OS(lO’), Rf = 6OOAP/P = 3.0(10”) m-i, (Y = [18,000(2)/C]AP/~ = 36,ooO(0.5)(10*)/135 = 1.333(10i”) m/kg. At 0.8 bar, AP/p = 0.8(108), Rf = 375(0.8)(10’) = 3(10i”) m-‘, (Y= 12,750(2)(0.8)(10s)/135 = 1.511(10’“) m/kg. Fit the data with Almy-Lewis equation, Eq. (11.24), (Y = kp”, ln(cr,/cu,) n=ln(P,lP,)= ln(1.511/1.333) = o,2664 ln(0.8/0.5) k = 1.511(10’“)/0.80-~661 = 1.‘604(10’“), :. (Y= 1.604(10’“)Po~2664, m/kg, P in bar. 2000 1500 t 3 1000 2 . 500 0 r I- l- / / 0 I I I I I 0.02 0.04 0.06 0.08 0.10 V / A - Basic filtration Eq. (11.2) is solved for the amount of filtrate, (11.10) Equations (11.8) and (11.10) are solved simultaneously for AP and Q at specified values of V and the results tabulated so: V AP Q l/Q t 0 - - - 0 - - - - - V‘i”., - - - t‘,“a, Integration is accomplished numerically with the Simpson or trapezoidal rules. This method is applied in Example 11.2. When the filtrate contains dissolved substances that should not remain in the filter cake, the occluded filtrate is blown out; then the cake is washed by pumping water through it. Theoretically, an amount of wash equal to the volume of the pores should be sufficient, even without blowing with air. In practice, however, only 30-85% of the retained filtrate has been found removed by one-displacement wash. Figure 11.3(b) is the result of one such test. A detailed review of the washing problem has been made by Wakeman (1981, pp. 408-451). The equations of this section are applied in Example 11.3 to the sizing of a continuous rotary vacuum filter that employs a washing operation. COMPRESSIBLE CAKES Resistivity of filter cakes depends on the conditions of formation of which the pressure is the major one that has been investigated at length. The background of this tcpic is discussed in Section 11.3, but here the pressure dependence will be incorporated in the filtration equations. Either of two forms of pressure usually is taken, Lr = cu,P” (11.11) or (Y = a,(1 + kP)“. (11.12)
- 330. 11.2. THEORY OF FILTRATION 311 EXAMPLE 11.2 Filtration Process with a Centrifuyl Charge Pump A filter press with a surface of 50m handles a slurry with these properties: p = 0.001 N set/m’, C = 10 kg/m3, a= l.l(lO’i) m/kg, Rf= 6.5(10’“) m-i. The feed pump is a centrifugal with a characteristic curve represented by the equation trapezoidal rule: V AP 0 t (hd 0 0.1576 43.64 0 10 0.6208 39.27 0.24 20 0.9896 35.29 0.51 30 1.2771 31.71 0.81 40 1.4975 28.53 1.14 60, 5; 1.6648 , 25.72 1.; , AP = 2 - Q(O.OO163Q - 0.02889), bar (1) with Q in m3 hr. Find (a) the time required to obtain 50m3 of filtrate; (b) the volume, flow rate, and pressure profiles. Equation (11.2) of the text solved for V becomes V=$c *$-pRf i > - 6.5(107)] > (2) Equations (1) and (2) are solved simultaneously to obtain the tabulated data. The time is found by integration with the The first of these does not extrapolate properly to resistivity at low pressures, but often it is as adequate as the more complex one over practical ranges of pressure. Since the drag pressure acting on the particles of the cake varies from zero at the face to the full hydraulic pressure at the filter cloth, the resistivity as a function of pressure likewise varies along the cake. A mean value is defined by (11.13) where AP, is the pressure drop through the cake alone. In view of the roughness of the usual correlations, it is adequate to use the overall pressure drop as the upper limit instead of the drop through the cake alone. With Eq. (11.12) the mean value becomes c~,k(l - n)AP ’ = (1 + kAP)‘-“- 1’ The constants (Ye, k, and n are determined most simply in compression-permeability cells as explained in Section 11.4, but those found from filtration data may be more appropriate because the mode of formation of a cake also affects its resistivity. Equations (11.14) and (11.2) together become cu,ck(l- n)AP V -* Rf+(l+kAp)“-‘-l~ 1 ’ (11.15) which integrates at constant pressure into (11.16) The four unknown parameters are cro, k, n, and Rr. The left-hand side should vary linearly with V/A. Data obtained with at least three different pressures are needed for evaluation of the parameters, but the solution is not direct because the first three parameters are involved nonlinearly in the coefficient of V/A. The analysis of constant rate data likewise is not simple. The mean resistivity at a particular pressure difference can be evaluated from a constant pressure run. From three such runs-AP,, AP,, and AP3-three values of the mean resistivity- &i, Su,, and %,-can be determined with Eq. (11.2) and used to find the three constants of the expression for an overall mean value, E = rro(l + kAP)“, (11.17) which is not the same as Eq. (11.12) but often is as satisfactory a representation of resistivity under practical filtration conditions. Substituting Eq. (11.17) into Eq. (11.2), the result is WI*) A P -= dt p[Rf + cu,c(l + kAP)“(VIA)] Integration at constant pressure gives the result (11.18) (11.19)
- 331. 312 SOLID-LIQUID SEPARATION I I IO 0.1 0.2 0.4 0.6 I 2 4 Time. minutes (a) -. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.0 L 2 DRY TIME - MIN. B (c) EFFICIENCY ! 0-i I 1 I f 0.5 1.0 1.5 2.0 2.5 WASH RATIO b) (4 Figure 11.3. Laboratory test data with a vacuum leaf filter. (a) Rates of formation of dry cake and filtrate. (b) Washing efficiency. (c) Air flow rate vs. drying time. (d) Correlation of moisture content with the air rate, pressure difference AP, cake amount W lb/sqft, drying time 0, min and viscosity of liquid (Dahlrtrom and Silverblatt, 1977). EXAMPLE 11.3 Rotary Vacuum Filter Operation A TiO, slurry has the properties c = 200 kg solid/m’ liquid, p, = 4270 kg/m3, p = 0.001/3600 N hr/m’, (Y= 1.6(E12) m/kg (item 4 of Fig. 11.2), .s=O.6. Cloth resistance is I$ = l(E10) m-l. Normal peripheral speed is about 1 m/min. Filtering surface is l/3 of the drum surface and washing surface is l/6 of the drum surface. The amount of wash equals the pore space of the cake. The cake thickness is to be limited to 1 cm. At suitable operating pressures, find the drum speed in rph and the drum diameter: c cake thickness = 0.01 m = ~5 P# - ~1 A 200 v, =___- 4270(0.4) A ’ If= 0.01(4270)(0.4) = o 0854 m3,m2 A 200 . wash liquid = pore volume = O.Ol(O.6) = 0.006 m2 m2. With the pressure difference in bar, W/A) lOsAP, dt - (0.001/3600)[10’” + 160(10’“)V/A] 36AP, =1+16OV/A’ (2)
- 332. EXAMPLE 11.3-(continued) The integral at constant pressure is 80(Vf/A)’ + Vf/A = 36AP& With Vf/A = 0.0854, (3) AP& = 0.01858, 4 = O.O1858/AP, = l/35 (4) tif = 17.94AP,, (5) where irf is the rph speed needed to make the 1 cm thick cake. From Eq. (2) the washing rate is 36AP, ‘w = 1 + 160(o.0854) = 2.455Af’tc Washing time: 0.006 0.00244 1 t c-----z-~- w 2.455AP, AP, ii,’ (7) 11.3. RESISTANCE TO FILTRATION 313 rii, 5 68.3AP, (8) Comparing (5) and (8), it appears that an rph to meet the filtering requirements is 68.3/17.94 = 3.8 times that for washing and is the controlling speed. With a peripheral speed of 60 m/hr 60 = IrDn, D = 60/m = 19.1/L The parameters at several pressures are (9) AP, (bar) 0.2 0.4 0.6 0.8 i,(rph) 3.59 7.18 10.76 14.35 D(m) 5.3 2.66 1.78 1.33 If the peripheral speed were made 1.22m/min, a drum 1.0 m dia would meet the requirements with AP = 0.8 bar. Another controllable feature is the extent of immersion which can be made greater or less than l/3. Sketches of a rotary vacuum filter are in Figure 11.12. Eq. (11.19) could be written in terms of & from Eq. (11.17) and would then have the same form as Eq. (11.2), but with only R, as a parameter to be found from a single run at constant pressure. In Example 11.1, the mean resistivity is found from the simpler equation & = cu,(AP)“. (11.20) Analysis of the filtration of a compressible material is treated in Example 11.4. 11.3. RESISTANCE TO FILTRATION The filtration equation Q- Ap 2 - p(Rf + acVIA) (11.2) considers the overall resistance to flow of filtrate to be made up of contributions from the filter medium Rf, and from the cake with specific resistance (Y. FILTER MEDIUM In practice, a measured Rf includes the effects of all factors that are independent of the amount of the cake; in a plate-and-frame press, for instance, piping and entrance and exit losses will be included, although most of the resistance usually is due to the medium itself. Aging and the resulting increase in resistance is a recognized behavior, particularly of media made of fibers. Particles are gradually occluded in the media so thoroughly that periodic cleaning cannot restore the original condition. The degree of penetration of the medium depends on the porosity, the pore sizes, particles sizes, and velocity. Normally R, is found to depend on the operating pressure; on plots like those of Example 11.1, the two intercepts may correspond to different values of Z$ at the two pressures. Data for some filter media are shown in Table 11.6. Although these porosities and permeabihties are of unused materials, the relative values may be useful for comparing behaviors under filtration conditions. Permeability Kp normally is the property reported rather than the resistivity that has been discussed here. It is defined by the equation Q/A = K,APIPL (11.21) where L is the thickness. The relation to the resistivity is R, = L/K,. (11.22) Thus the filtration resistivity of the medium includes its thickness. Typical measured values of Rf are of the order of lOlo m-‘; for comparison, the fine filter sheet of Table 1.6, assuming it to be 1 mm thick, has L/K, = 0.001/0.15(10-‘*) = 0.7(10r”) m-r. CAKE RESISTIVITY A fundamental relation for the flow resistance of a bed of particles is due to Kozeny (Ber. Wien. Akad. 1351, 1927, 271-278): (Y = K&l - &)/&3, K = approximately 5 at low porosities, se = specific surface of the particles, ps = density of the particles, (11.23) E = porosity, volume voids/volume of cake. Because the structure of a cake is highly dependent on operating conditions and its history, the Kozeny equation is only of qualitative value to filtration theory by giving directional effects. At increasing pressures, the particles or aggregates may be distorted and brought closer together. The rate of flow also may affect the structure of a cake: at low rates a loose structure is formed, at higher ones fine particles are dragged into the previously formed bed. The drag pressure at a point in a cake is the difference between the pressure at the filter medium and the pressure loss due to friction up to that point. As the drag pressure at a distance from the filter cloth increases, even at constant filtering pressure, the porosity and resistance adjust themselves continuously. Figure 11.4(a) shows such effects of slurry concentration and filtering rates
- 333. 314 SOLID-LIQUID SEPARATION EXAMPLE 11.4 Filtering period is Filtration and Washing of a Compressible Material A kaolin slurry has the properties c = 200 kg solid/m3 filtrate, tf =0.25+ 0.0035(Vf -0.0423)+ 7O.O(V;-0.0018). Daily production rate, P = 0.001 N set/m*, 2.78(E - 7) N hr/m*, ps = 200 kg/m3, (Y = 87(ElO)(l+ P/3.45)o.7 m/kg with P in bar, E = 1 - 0.460(1 + P/3.45)0.‘*. R, = (no of batches/day)(filtrate/batch) _ 245 _ wf td + + - 1 + rr I m3/b2)(W The equations for & and E are taken from Table 11.8. Filtration will proceed at a constant rate for 15 mitt, the pressure will rise to 8 bar and filtration will continue at this pressure until the end of the operation. Filter cloth resistance is R, = l(lOt”) m-l. The down time per batch is 1 hr. a. Find the maximum daily production of filtrate. b. The filtrate will be blown and then washed with a volume of water equal to the pore space of the cake. Find the maximum daily production of filtrate under these conditions. = 1.25 + O.o035(vf - 0.0423) + 7O(V; - 0.0018) The tabulation shows that R, is a max when Vf = 0.127. v, t % 0.12 1.3507 0.126 1.3526 0.127 1.2533 1.3527 (max) 0.128 1.3526 0.129 1.3525 0.130 1.3522 Part (a) Basis 1 m* of filtering surface. At P = 8 bar, or 8(105) Pa Part(b) cr = 87(101’)(1 + g/3.45)‘.‘= 2.015(10’*) m/kg, E = 1 - 0.46(1 + 8/3.45)‘.‘* = 0.47, PC& = (0.001/3600)(200)(2.015)(10’*) = 1.12(108) N hr/m4. Amount of wash liquid = fi= ~~($4571) = O.O709vf, s The filtration equation (11.2) is wash rate = filtering rate at the conclusion of the filtration dV A A P A P dt = ,u(R~ + &V/A) = (0.001/3600)[1010 + 2.015(10’*)(200)V] A P =2780 + 1.12(108)V’ The rate when t = 0.25/r and AP = 8(105) Pa, 8( 105) 8( 105) ’ = 2780 + 1.12(108)Qt =2780 + 0.28(108)Q = 0.1691 m3/m2 hr. The amount of filtrate at this time is V. = Qt = 0.1691(0.25) = 0.0423 m3. The integral of the rate equation at constant P is 278O(vf - 0.0423) + 0.56(108)(V; - (0.00423)*] = S(lO”)(t, - 0.25). 24V, AP 8(105) =p(Rf + acv,)=2780+ 1.12(108)vf’ m3/hr, t w = wash time = 0.709Vf[2780 + 1.12(108)Vf] 8( 105) = Vf(0.000246+ 9.926Vf), R,= 245 1 + tr + t, 24Vf = [l + O.O035(V - 0.0423) + 7OlO(Vf - 0.0018) + vf(O.000246 + 9.926vf)]. The optimum operation is found by trial: Vf = 0.105, tf = 1.0805, t, = 0.1095, R, = 1.1507 (max), daily production rate. on the parameters of the correlating equation COMPRESSIBILITY-PERMEABILITY (CP) CELL MEASUREMENTS cr = ab(AP)“. (11.24) The measurements were obtained with a small filter press. Clearly, the resistivity measured at a particular rate is hardly applicable to predicting performance at another rate or at constant pressure. The probable success of correlation of cake resistivity in terms of all the factors that have been mentioned has not been great enough to have induced any serious attempts of this nature, but the effect of pressure has been explored. Although the (Y’S can be deduced from
- 334. TABLE 11.6. Porosities and Permeabilities of Some Filter Media Porosity (96) Wedge wire screen Perforated sheet Wire mesh: Twill weave S q u a r e Porous plastics, metals, ceramics Crude kieselguhr Porous ceramic, special Membranes, plastic foam Asbestos/cellulose sheets Refined filter aids (diatomaceous earth ex- p a n d e d perlite) P a p e r Scott plastic foam Permeability, lO’*K,, (m*) (compare Eq. (11.22)) Filter aids Fine Medium C o a r s e Cellulose fibre pulp Cellulose fibre + 5% asbestos Filter sheets Polishing Fine Clarifying Sintered metal 3 pm pore size 8 pm pore size 28 pm pore size 75 pm pore size 5-10 2 0 15-25 30-35 30-50 50-60 7 0 8 0 8 0 80-90 60-95 9 7 0.05-0.5 l - 2 4-5 1.86 0 . 3 4 0 . 0 1 7 0 . 1 5 1.13 0 . 2 0 1.0 7 . 5 7 0 (Purchas, 1981). filtration experiments, as done in Example 11.1, a simpler method is to measure them in a CP cell as described briefly later in this chapter. Equation (11.24) for the effect of pressure was proposed by Ahny and Lewis (1912). For the materials of Figure 1.2(b), for instance, it seems to be applicable over at least moderate stretches of pressure. Incidentally, these resistances are not represented well by the Kozeny porosity function (1 - .s)/c3; for substance 6, the ratio of resistivities at 100 and 1 psia is 22 and the ratip of the porosity functions is 2.6. The data of Table 11.7 also show a substantial effect of pressure on resistivity. Since the drag pressure varies along the cake as a result of friction, porosity and resistivity also will vary with position. Figure 11.5 shows such data at three different overall pressures. The axial profile of the normalized pressure, Ploca,/Pfacer appears to be a unique function of fractional distance along the cake, independent of the filtering pressure. The resistivity will vary along the cake just as the porosity does. As the cake builds up, moreover, the drag pressure, porosity, and resistivity at a particular distance from the filter medium also will vary. Consequently, since the resistivity does not necessarily change linearly with position, any mean value also is likely to vary as the cake builds up. Thus, in the filtration equation even a mean value of (Y has to be expressed as a function of P and V. The proper mathematical representation of a filtration process is by means of an integro-differential equation with a moving boundary (the face of the cake). Such an analysis was made by Wakeman (1978) and a similar one by Tiller, Crump, and Ville (1979). At present, unfortunately, such a mathematical approach to filtration problems is more of academic than practical value. One of the factors that is not taken into account is the effect of flow rate on 11.4. THICKENING AND CLARIFYING 315 the formation and stability of loose cake structures; such behavior normally is not reproducible. ANOTHER FORM OF PRESSURE DEPENDENCE Equation (11.24) cannot be entirely valid because it predicts zero resistivity at zero pressure, whereas cakes do have structures and significant resistivities even at minimal operating pressures. Modified Eq. (11.12) is extrapolatable, and is rewritten here as (Y = cra(1+ kP) (11.25) with a similar one for porosity & = 1 - (1 - &a)(1 + kP)“. (11.26) Some data fitted to these equations by Tiller et al. (1979) are in Table 11.8; here the constant k is the same for both LY and E, although this is not necessarily generally the case. Unfortunately, these data show that the parameters are not independent of the pressure range. Apparently the correlation problem has not been solved. Perhaps it can be concluded that insofar as the existing tiltration theory is applicable to real filtering behavior, the approximation of Almy and Lewis may be adequate over the moderate ranges or pressures that are used commonly, somewhere between 0.5 and 5 atm. PRETREATMENT OF SLURRIES Since the sizes of particles and agglomerates of the slurry are a main determinant of a rate of filtration, any methods of influencing these sizes are of great practical value. For example, Figures 1.2(b) and (c) show CaCO, and TiO, each to be precipitated at two different values of pH with resultant great differences in resistivity and porosity. At lOpsia, for instance, the resistivities of the two CaCO,‘s are in the ratio of 5, with corresponding differences in rate of filtration. Pretreatment of a slurry to enhance coagulation and particle growth is an important aspect of filter process design. Another method of long standing for improving filtration behavior is the formation of an open cake structure by addition of relatively large and rigid particles of a filter aid. The common methods of pretreatment are listed in Table 11.4, and some chemical flocculants that are of practical value are described in Table 11.5. These effects cannot be predicted safely and must be measured. 11.4. THICKENING AND CLARIFYING When dilute slurries are encountered on a large scale, it is more economical to concentrate them before filtering. This is accomplished by sedimentation or thickening in tanks for an appropriate period. Typical designs of thickeners are sketched in Figure 11.6. The slurry is introduced at the top center, clear liquid overflows the top edge, whereas the solids settle out and are worked gradually towards the center with slowly rotating rakes towards the discharge port at the bottom center. The concentrated slurry then is suitable for tiltration or other further processing. Clarifiers are similar devices, primarily for recovering clear liquids from dilute suspensions. Some characteristics of sedimentation equipment are given in Table 11.3 and typical applications are listed in Table 11.9 and 14.7. Sedimentation rates often are assisted by addition of flocculating agents, some of which are listed in Table 11.5. Specifically, pilot plant testing is advisable when 1. The expecting filtering area is expected to be substantial, measured in tens of m*. 2. Cake washing is critical.
- 335. 316 SOLID-LIQUID SEPARATION 3 3. 1 1.5 2 2.5 (a) 0.9 0.8 0,7 T Or6 0.5 0,4 0‘3 5 Cornpresswe pressure (P, I, psia I-Superlite C&O, (flocculated), pH = 9.8 4-~-110 grade TIO*, PH = 3.5 2-Superlite C&O,, pH = 10.3 5-Znr. Type B, PH = 9.1 3-A-1 10 grade TiO, Iflocculated), pti = 7.8 &ZnS, Type A, PH = 9.1 (b) Compressive pressure ! P, l. Psla (4 Figure 11.4. Data of compressibilities and porosities of filter cakes. (a) Parameters of the correlation (Y = cu,(AP)” for resistivity of CaSiOa filter cakes at two rates and two concentrations (Rushron and Kufsoulus, 1984). (b) Resistivity as a function of pressure measured m a compressibility-permeability (CP) cell [Grace, Chem. Eng. Prog. 49, 303, 367, 427 (1953)]. (c) P orosity as a function of pressure for the same six materials (Grace, Zoc. cit.).
- 336. 11.5. LABORATORY TESTING AND SCALE-UP 317 3. Cake drying is critical. 4. Cake removal may be a problem. 5. Precoating may be needed. 11.5. LABORATORY TESTING AND SCALE-UP Laboratory filtration investigations are of three main kinds: 1. observation of sedimentation rates; 2. with small vacuum or pressure leaf filters; 3. with pilot plant equipment of the types expected to be suitable for the plant. Sedimentation tests are of value particularly for rapid evaluation of the effects of aging, flocculants, vibration, and any other variables that conceivably could affect a rate of filtration. The results may suggest what kinds of equipment to exclude from further con- sideration and what kind is likely to be worth investigating. For instance, if sedimentation is very rapid, vertical leaves are excluded, and top feed drums or horizontal belts are indicated; or it may be indicated that the slurry should be preconcentrated in a thickener before going to filtration. If the settling is very slow, the use of filter aids may be required, etc. Figure 11.1 illustrates typical sedimentation behavior. Figure 11.2 summarizes an experimental routine. Vacuum and pressure laboratory filtration assemblies are shown in Figure 11.7. Mild agitation with air sometimes may be preferable to the mechanical stirrer shown, but it is important that any agglomerates of particles be kept merely in suspension and not broken up. The test record sheet of Figure 11.8 shows the kind of data that normally are of interest. Besides measurements of filtrate and cake amounts as functions of time and pressure, it is desirable TABLE 11.7. “,z&fic Resistances of Some Filter Material Filtration Pressure psi Rg&tst;sx m/kg ’ High grade kieselguhr Ordinary kieselguhr Carboraffin charcoal Calcium carbonate (precipitated) Ferric oxide (pigment) Mica clay Colloidal clay Magnesium hydroxide (gelatinous) Aluminium hydroxide (gelatinous) Ferric hydroxide (gelatinous) Thixotropic mud Theoretical figures for rigid spheres: d= IOum d=lym d = 0.1 pm - 2 5 100 1.4 1 0 2 5 100 2 5 100 2 5 100 2 5 100 2 5 100 2 5 100 2 5 100 8 0 1.64 x 10s 1.15x IO” 1.31 x 10” 3.14 x 1o’O 5 . 8 4 x 10” 2.21 x 10” 2 . 6 8 x 10” 8 . 0 4 x 10” 1 4 . 1 2 x 10” 4.81 x 10” 8 . 6 3 x 10” 5 . 1 0 x lo= 6 . 4 7 x 1O’s 3 . 2 4 x 10” 6 . 9 7 x lo’* 2 . 1 6 x IO- 4 . 0 2 x IO- 1 . 4 7 x lo- 4.51 x lo= 6 . 7 7 x lo- 6.37 x 1 OS 6.37 x 10” 6.37 x 1 O’s to test washing rates and efficiencies and rates of moisture removal with air blowing. Typical data of these kinds are shown in Figure 11.3. Detailed laboratory procedures are explained by Bosley (1977) and Dahlstrom and Silverblatt (1977). Test and scale-up procedures for all kinds of SLS equipment are treated in the book edited by Purchas (1977). Before any SLS equipment of substantial size is finally selected, it is essential to use the results of pilot plant tests for guidance. Although many vendors are in a position to do such work, pilot equipment should be used at the plant site where the slurry is made. Because slurries often are unstable, tests on shipments of slurry to the vendors pilot plant may give misleading results. It may be possible to condition a test slurry to have a maximum possible resistivity, but a plant design based on such data will have an unknown safety factor and may prove uneconomical. COMPRESSION-PERMEABILITY CELL Such equipment consists of a hollow cylinder fitted with a permeable bottom and a permeable piston under controlled pressure. Slurry is charged to the slurry, cake is formed with gentle suction, and the piston is lowered to the cake level. The rate of flow of filtrate at low head through the compressed cake is measured at a series of pressures on the piston. From the results the resistivity of the cake becomes known as a function of pressure. The data of Figures 11.4(b) and (c) were obtained this way; those of Figure 11.4(a) by filtration tests. There is much evidence, however, that the resistivity behavior of a cake under filtration conditions may be different from that measured in a CP cell. The literature is reviewed by Wakeman (1978). CP cell data are easily obtained and may be of value in a qualitative sense as an indication of the sensitivity of resistivity to pressure, but apparently are not of acceptable engineering accuracy for the design of filtration equipment. The deduction of resistivities from filtration tests is illustrated in Example 11.1. THE SCFT CONCEPT No serious attempt has yet been made to standardize filtration tests and to categorize filtration behavior in generally accepted terms. A possibly useful measure of filterability, however, has been proposed by Purchas (1977; 1981). The time in minutes required to form a cake 1 cm thick when the cell is operated with a differential of 500 Torr (0.67 bar) is called the Standard Cake Formation Time (SCFT), tp The pressure of 5OOTorr is selected because it is obtained easily with common laboratory equipment. The procedure suggested is to make a series of tests at several cake thicknesses and to obtain the SCFT by interpolation, rather than to interrupt a single test to make observations of cake thickness. A direct relation exists, of course, between the SCFI and resistivity o; some examples are Material a (m/kg) SCFT tF (min) Filter aid 1.64(E9) 0 . 2 6 CaCO, 2.21 (El 1) 3 4 . 6 Colloidal clay 5.10(E12) 798 Full scale filtration equipment requirements can be estimated quickly in terms of rp For instance, when the resistance of the filter medium is neglected, the constant pressure Eq. (11.3) may be written as (11.27) (Carman, 1938). where L is the thickness of the cake in meters. Upon rationing in
- 337. 318 SOLID-LIQUID SEPARATION O i j- j- 01 02 03 OL 05 06 07 06 09 10 X/L-----, (a) x x x Y x x x x . . -I85 x/L---+ b) I I I I 1 I I I I I 0 01 02 03 OL 05 06 07 08 09 1C Figure 11.5. Axial distribution of pressure and porosity of an ignition-plug clay measured in a CP cell. (a) Normalized pressure distribution as a function of normalized distance [(- - -) experimental filtration data; theoretical curves: (x) AP = 98 kN m-‘; (0) AP = 294 kN m-‘; (A) AP = 883 kN m-*1. (b) Porosity distributions at three pressures. The curves are by Wakeman (1978). the SCFI data for 0.01 m, &g = (loozy, F (11.28) with AP in bar. From this relation the filtering time can be found at a specified pressure and cake thickness and when t, is known. SCALE-UP Sizing of full scale equipment on the basis of small scale tests requires a consideration of possible ranges of at least the following variables: 1. filterability as measured by cake and medium resistivity; 2. feed rate and concentration; 3. operating conditions, particularly pressure and high initial rates; 4. behavior of the filter cloth with time. Safety factors for scale up from laboratory leaf tests are difficult to generalize. On the basis of pilot plant work, adjustments of ll-21% are made to plate-and-frame filter areas or rates, and 14-20% to continuous rotary filters, according to Table 1.4. The performance of solid-liquid separation equipment is difficult to predict by the engineer without some specific experience in this area. Unfortunately, it must be again recommended that the advice of experienced vendors should be sought, as well as that of expert consultants. 11.6. ILLUSTRATIONS OF EQUIPMENT Equipment for solid-liquid separation is available commercially from many sources. About 150 names and addresses of suppliers in the United States and abroad are listed by Purchas (1981). Classifications of vendors with respect to the kind of equipment are given, for instance, in Chemical Engineering Catalog (Reinhold, New York, annual) and in Chemical Engineering Equipment Buyers Guide (McGraw-Hill, New York, annual). The variety of solid-liquid separation equipment is so great that only a brief selection can be presented here. The most extensive modern picture gallery is in the book of Purchas (1981). The older encyclopedia of Kieser (Spamer-Springer, Berlin, 1937, Vol. 2) has 250 illustrations in 130 pages of descriptions; the pictures do not appear to have aged particularly. Illustrations in manufacturers catalogs are definitive and often reveal the functioning as well as aspect of the equipment. The selected figures of this chapter are primarily line drawings that best reveal the functioning modes of the equipment. Figure 11.9 shows two models of sand filters whose purpose is to remove small contents of solids from large quantities of liquids. The solids deposit both on the surface of the bed and throughout the bed. They are removed intermittently by shutting off the main
- 338. 11.6. ILLUSTRATIONS OF EQUIPMENT TABLE 11.8. Parameters of Equations for Resistivity a and Porosity E of Some Filter Cakes Material CaCO, (ref. 7) CaCO, (ref. 8) Darco-B (ref. 8) Kaolin-AI,SO, (ref. 8) Solka-Floe (ref. 8) Talc-C (ref. 8) TiO, (ref. 8) Tungsten (ref. 8) Hong Kong pink kaolin (ref. 9) Pressure range, P.. =o. kPa kPa m kg-’ x 106’ n (1-GJ B” 3-480 1 11 0.15 0.209 0.06 7-550 7 5.1 0.2 0.225 0.06 550-7000 790 8.1 0.9 0.263 0.22 7-275 1.7 1.1 0.4 0.129 0.08 275-7000 520 4.7 1.8 0.180 0.18 7-415 7 43 0.3 0.417 0.04 415-7000 345 87 0.7 0.460 0.12 7-275 2.75 0.00058 1.0 0.132 0.16 275-7000 260 0.13 2.0 0.237 0.26 7-1400 5.5 4.7 0.55 0.155 0.16 1400-7000 1400 35 1.8 0.339 0.25 7-7000 7 18 0.35 0.214 0.1 7-480 7 0.39 0.15 0.182 0.05 480-7000 520 0.38 0.9 0.207 0.22 1-15 1 42 0.35 0.275 0.09 15-1000 12 70 0.55 0.335 0.1 Gairome clay (ref. IO) 4-1000 3.4 370 0.55 0.309 0.09 (Tiller et al, 1979) flow and backwashing with liquid. The concentrated sludge then must be disposed of in some way. Beds of charcoal are employed similarly for clarification of some organic liquids; they combine adsorption and mechanical separation. Clarification of a large variety of liquids is accomplished with cartridge filters which come in a large variety of designs. Usually the cartridges are small, but liquid rates in excess of 5OOOgpm have been designed for. The filtering surface may be a fine metal screen or an assembly of closely spaced disks whose edge face functions as the filtering surface, or woven or matted fibers. The operation is intermittent, with either flushing back of the accumulated solids or replacement of the filtering elements in the body of the cartridge, or in some instances the solids are scraped off the filtering surface with a built-in mechanism and then flushed out in concentrated form. The variety of cartridge filters are described in detail in books by Warring (1981) Purchas (1981) and Cheremisinoff and Azbel (1983). Table 11.10 is a selected list of some of their applications and the minimum sizes of particles that are removed. Figure 11.6 is of two types of sedimentation equipment, and Figure 12.2(e) of another. They are used for clarifying a valuable liquid or for preparing a concentrated slurry for subsequent filtration. They depend on gravitational sedimentation. Removal is assisted by rake action, or by the conical sides of the vessel of Figure 11.6(b). Figure 11.10 is of the main kinds of filters that can be operated at superatmospheric pressures which may be necessary with otherwise slow filtering slurries. Commercial sizes are listed in Table 11.11. They all operate on intermittent cycles of cake formation, washing, dewatering with air blowing and cake removal. The plate-and-frame design of Figure 11.10(a) is the most widely recognized type. In it, cake removal is effected after separating the plates. The horizontal plate design of Figure 11.10(b) is popular in smaller sizes under, 2ft dia or so; the plates are lifted out of the casing for cake removal. The other units all have fixed spacings between the leaves. From them the cakes may be blown back with air or flushed back or scraped off manually. The Vallez unit of Figure 11.10(f) ordinarily does not require the case to be opened for cleaning. Figure 11.11 is of continuous horizontal filtering equipment that operate primarily with vacuum, although they could be housed in pressure-tight casings for operation at superatmospheric pressure or with volatile liquids. Both the belt and the rotary units are well suited to rapidly settling and free draining slurries. In comparison with rotary drum vacuum filters, the horizontal equipment of Figure 11.11(c) has the merit of more readily accessible piping, a real advantage from a servicing point of view. Figure 11.12 represents the main kinds of rotary drum filters. Commercial sizes are listed in Table 11.14. The flowsketch of Figure 11.12(a) identifies the main auxiliaries required for this kind of filtration process. Feed to the drum may be dip-type as in Figure 11.12(b), but top feed designs also are widely used. The unit with internal filtering surface of Figure 11.12(c) is suited particularly to rapidly settling solids and has been adapted to pressure operation. Cake removal usually is with a scraper into a screw or belt conveyor, but Figure 11.12(d) depicts the use of a drum with a filtering belt that is subject to a continual cleaning process. Some filters have a multi parallel string discharge assembly whose path follows that of the belt shown. The double drum filter of Figure 11.12(e) has obvious merit particularly when top feeding is desirable but it is not used widely nowadays. Disk filters of the type of Figure 11.12(f) are the most widely used rotary type when washing of the cake is not necessary. Figure 11.13 is of a variety of devices that utilize centrifugal force to aid in the separation of solid and liquid mixtures. Figure
- 339. 320 SOLID-LIQUID SEPARATION (a) -+ Thick sludge discharge W Flocculant ccntro! valve Cer iUf :cntrol % Baffled !eed -,- I sander I,1’.ti:‘.‘n’. / “-a-Clarified ggater :ro!le: Figure 11.6. Thickeners for preconcentration of feed to filters or for disposal of solid wastes [see also the rake classifier of Fig. 12.2(e)]. (a) A thickener for concentrating slurries on a large scale. The rakes rotate slowly and move settled solids towards the discharge port at the center. Performance data are in Table 11.11 (Brown, Unit Operations, Wiley, New York, 1950). (b) Deep cone thickener developed for the National Coal Board (UK). In a unit about 10 ft dia the impellers rotate at about 2 ‘pm and a flow rate of 70m3/sec with a solids content of 6 wt %, concentrates to 25-35 wt % (Strarousky, 1981). 11.13(a) performs cake removal at reduced rotating speed, whereas the design of Figure 11.13(d) accomplishes this operation without slowing down. The clarifying centrifuge of Figure 11.13(e) is employed for small contents of solids and is cleaned after shutdown. The units of Figures 11.13(b) and (c) operate continuously, the former with discharge of cake by a continuous helical screw, the latter by a reciprocating pusher mechanism that operates at 30-70 strokes/mio and is thus substantially continuous. Hydrocyclooes generate their own, mild centrifugal forces. Since the acceleration drops off rapidly with diameter, hydrocy- TABLE 11 .S. Performances of Sedimentation Equipment (a) Thickenersa 96 solids Unit area, sq. ft. /ton. Feed U n d e r f l o w day Alumina, Bayer process: Red-mud primary settlers R e d - m u d w a s h e r s Red-mud final thickener Trihydrate seed thickener Cement, West process Cement kiln dust Coral Cyanide slimes Lime mud: Acetylene generator Lime-soda process Paper industry Magnesium hydroxide from brine Metallurgical (flotation or gravity concentration): Copper concentrates Copper tailings Lead concentrates Zinc concentrates Nickel: Leached residue Sulfide concentrate Potash slimes Uranium: Acid leached ore Alkaline leached ore Uranium precipitate 3-4 lo-25 20-30 6-8 15-20 10-15 6-8 20-35 10-15 2-8 30-50 12-30 16-20 60-70 15-25 9-10 45-55 3-18 12-18 45-55 15-25 16-33 40-55 5-13 12-15 30-40 15-33 9-11 35-45 15-25 8-10 32-45 14-18 8-10 25-50 60-100 14-50 40-75 2-20 10-30 45-65 4-10 20-25 60-80 7-18 10-20 50-60 3-7 2 0 6 0 8 3-5 6 5 2 5 l - 5 6-25 40-l 25 1 O-30 25-65 2-10 2 0 6 0 1 0 l-7 10-25 50-125 (b) Clarifiers Overflow rate, Application gal./min., sq. ft. Detentio: time, Primary sewage treatment (settleable-solids removal) 0 . 4 2 Secondary sewage treatment (final clarifiers-activated sludge and trickling filters) 0.55-0.7 1.5-2 Water clarification (following 30- min. flocculation) 0.4-0.55 3 Lime and lime-soda softening (high rate-upflow units) 1.5 2 Industrial wastes Must be tested for each application “See also Table 14.7. (Perry’s Chemical Engineers Handbook, McGraw-Hill, New York, 1963, pp. 19.49,19.52). clones are made only a few inches in diameter. For larger capacities, many units are used in parallel. The flow pattern is shown schematically in Figure 11.13(f). The shapes suited to different applications are indicated in Figure 11.13(g). 10 Figure 11.13(h), the centrifugal action in a hydrocyclooe is assisted by a high speed impeller. This assistance, for example, allows handling of 6% paper pulp slurries in comparison with only 1% in unassisted units. Hydrocyclones are perhaps used much more widely for dust separation than for slurries. 11.7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT Data of commercially available sizes of filtration equipment, their typical applications, and specific performances are available only to a limited extent in the general literature, but more completely in
- 340. Depth Sulllclenl TO Hold Slurry vol. for one Test t MeA Shim filter Clamp- By-Parr Valve for Vacuum Regulation (a) ( Jacket - ““‘%- t- Therm - To Gas Mew + Filtrate WI Figure 11.7. Two types of laboratory filter arrangements. (a) Vacuum test filter arrangement; standard sizes are 0.1, 0.05, or 0.025 sqft (Dahlsfrom and Siluerblatt, 1977). (b) Laboratory pressure filter with a vertical filtering surface and a mechanical agitator; mild air agitation may be preferred (Bosley, 1977). manufacturers’ literature. Representative data are collected in this section and summarized in tabular form. One of the reasons why more performance data have not been published is the difficulty of describing each system concisely in adequate detail. Nevertheless, the limited listings here should afford some perspective of the nature and magnitude of some actual and possibly potential applications. Performance often is improved by appropriate pretreatment of the slurry with flocculants or other means. An operating practice that is finding increasing acceptance is the delaying of cake deposition by some mechanical means such as scraping, brushing, severe agitation, or vibration. In these ways most of the filtrate is 11 7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT 321 expelled before the bulk of the cake is deposited. Moreover, when the cake is finally deposited from a thickened slurry, it does so with an open structure that allows rapid filtration. A similar factor is operative in belt or top feed drum filters in which the coarse particles drop out first and thus form the desirable open structure. A review of such methods of enhancement of filtration rates is by Svarovsky (1981). The relative suitability of the common kinds of solid-liquid separation equipment is summarized in Table 11.3. Filtration is the most frequently used operation, but sedimentation as a method of pretreatment and centrifugation for difficulty filterable materials has many applications. Table 11.15 gives more detail about the kinds of filters appropriate to particular services. Representative commercial sizes of some types of pressure filters for operation in batch modes are reported in Table 11.11. Some of these data are quite old, and not all of the equipment is currently popular; thus manufacturers should be consulted for the latest information. Commercially available size ranges of continuous belt, rotary drum, rotary disk, and horizontal rotary filters are listed in Table 11.12. For the most part these devices operate with vacua of 500 Torr or less. Sedimentation equipment is employed on a large scale for mineral and ore processing. These and other applications are listed in Table 11.9(a). The clarification operations of Table 11.9(b) are of water cleaning and sewage treatment. The sludges that are formed often are concentrated further by filtration. Such applications are listed in Table 11.16 along with other common applications of plate-and-frame filter presses. Sludge filter cakes are compressible and have high resistivity so that the elevated pressures at which presses can be operated are necessary for them. Among the kinds of data given here are modes of conditioning the slurries, slurry concentrations, cake characteristics, and cycle times. Clarification of a great variety of industrial liquids is accomplished on smaller scales than in tank clarifiers by application of cartridge filters; some of these applications are listed in Table 11.10. Cycle times, air rates, and minimum cake thicknesses in operation of rotary drum filters are stated in Table 11.13. A few special applications of horizontal belt filters are given in Table 11.14, but in recent times this kind of equipment is taking over many of the traditional functions of rotary drum filters. Belt filters are favored particularly for freely filtering slurries with wide range of particle sizes. The applications listed in Table 11.17 and 11.18 are a few of those of rotary drum, rotary disk, and tipping or tilting pan filters. The last type employs a number of vacuum pans on a rotating circular track; after the cake is formed, the pans are blown back with air and then tipped to discharge the cake. The data of these tables include particle size range, moisture content of the cake, filtering rate, solids handling rate, vacuum pump load and degree of vacuum. Clearly a wide range of some of these variables occurs in practice. Characteristics of centrifugal filters and sedimentation centri- fuges are in Table 11.19. The filtering types are made to handle from less than 5 tons/hr to more than 100 tons/hr of solids, with g-levels ranging from 30 to 3000. For sedimentation types, the g-levels listed range up to 18,000, but high values can be used only with small diameter equipment because of metal strength limitations. Capacity of sedimentation types is measured in terms of liquid rates, the maximum listed here being lOO,OOOL/hr. An outstanding feature of centrifugal separators is the small sizes of particles that can be handled satisfactorily; the values in the table cover the range l-4OOpm. Short retention time is a feature of centrifuge operation that may be of interest when unstable materials need to be processed.
- 341. 322 S O L I D - L I Q U I D S E P A R A T I O N FlLlRAllON LEAF TEST DATA SHEET - VACUUM AND PRESSURE C mP-l Mot’1 0, Rcccw.d: Dote 1.~1 No. Address Solids: % Dote 1.st.d Analysis b Liquid: 5 Location Filter Type - Leaf Size F1.2 An.ly.is Used Shim: No Y.r Pmccmt Forming Liquid Temp. “F/T Figure 11.8. A filtration leaf test data sheet (Dahlstrom and Siluerblatt, 1977). I I NLEl Backwash ,SuppJy Ime, discharge C o n c r e t e - n Backwash feed Valve .’ OUTLET Figure 11.9. Deep bed sand filters for removal of small contents of solids from large quantities of liquids. Accumulations from the top and within the bed are removed by intermittent backwashing. Charcoal may be used instead of sand for clarifying organic liquids. (a) Gravity operation. (b) Pressure operation.
- 342. 11.7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT 323 TABLE 11.10. Application of Cartridge Filters in Industry and TABLE 11 .ll. Sizes of Commercial Discontinuous Pressure Typical Particle Size Ranges Removed Filters Industry and Liquid Typical Filtration Rsnge (aLrn2pr;rE$te Area and Cake Capacity for Various Sizes of Plate and Chcnrical Industry Alum Brine Ethyl Alcohol Ferric Chlorkic Herbicidcs/Pcsticides Hydrochloric Acid Mineral Oil Nitric Acid Phosphoric Acid Sodium Hydrosidc Sodium Hypochloritc Sodium Sulfate Sulfuric Acid Synthetic Oils Pctrolcum Industry Atmospheric Reduced Crude Completion Fluids DEA Dcasphaltcd Oil Decant Oil Diesel Fuel Gas Oil Gasoline Hydrocarbon Wax lsobutane M E A Naphtha Produced Water for lnjcction Residual Oil Seawater Steam Injection Vacuum Gas Oil Ail lndustrics Adhcsivcs Boiler I:ccd Water Caustic Soda (‘hillcr Water City Warcr Clay Slip (ceramic and china) C o a l - B a s e d Synfucl Condensate Coolant Water Cooling Tower Water Deionized Water Ethylcnc Glycol Floor Polish Clyccrinc I n k s Liquid Dctcrgcnt Machine Oil Pcllctizcr Water Phcnolic Resin Binder Photographic Chemicals Pump Seal W31cr Quench Water R e s i n s Scrubber Water Was Wcllwatcr 60 mesh-60 Mm 100-400 mesh S-10 rrm 30-250 mesh 100-700 mesh lOOmeshtoS-IOrm 400 mesh 40 mesh to S-10 pm 100 mesh to S-10 em l-3 lo 5-10&m l-3 to S-IO firn 5-10 pm 250 mesh to l-3 rm 25-30 pm 25-75 pm 200 mesh to l-3 rm 250 mesh to 5- 10 rm 200 mesh 60 mesh 100 mesh 25-75 urn l-3 rm 25-30 urn 250 mesh 200 mesh to 5-10 pm 25-30 pm l-3 to IS-20 pm 25-50 urn S-IO pm 5-10crm 25-75 urn 30-150 mesh 5-10 pm 250 mesh 200 mesh 500 mesh to l-3 pm 20-700 mesh 60 mesh 200 mesh to 5-10 pm 500 mesh 150-250 mesh loo-250 mesh 100 mesh to 1-3 pm 250 mesh 5-10 pm 40-150 mesh 40 mesh I50 mesh 250 mesh 60 mesh 25-30 rm 200 mesh IO 5-10 grn 250 mesh 30-150 mesh 40- 100 Illcsll 20-200 lllCSll 60 mesh IO l-3 /.tm Size of filter plate (mm) Effective Filtration )rea per Chamber (m 1 Cast Iron W o o d Cake-Holding Capacity per Chamber per 25 mm of Chamber Thickness I Cast Iron W o o d 250 0 . 0 9 6 0.054 360 0 . 2 0 . 1 2 3 470 0 . 3 5 0.21 630 0 . 6 6 0 . 4 5 600 1.1 0 . 7 6 5 1000 1 . 7 4 1.2 1200 2 . 5 1.76 1450 3 . 7 2 . 4 6 2: 4 . 4 6 . 3 13.7 2 1 . 6 2 3 1 . 4 46.24 0 . 6 1.43 2 . 5 5.4 -. 9 . 3 14.6 2 1 . 3 6 3 0 . 2 (b) Sizes of Kelly Filters (in.) 30X49 40X108 48X120 80X108 N u m b e r of frames 6 8 10 12 Spacing between frames (in.) 5: 25;: 4 Filter area (sqft) 450 65;: (c) Standard Sweetland Filter 1 10 20; 9 5 8 4; 550 2 1 6 36; 1 6 9 46 2 3 2150 ; t: ;: 3041 :: 252 185 123 92 7300 9350 10 31 109 5 4 2 7 523 262 16500 12 3 7 145 7 2 3 6 1004 502 29600 (d) Vallez Filter (Largest Size Only, 2Oft Long, 7 ft high, 7 ft wide)d Spacin o f 7 No. of Leaves In.1 Leaves O.DjofjLeaf i Filteeiee Cake(E$y;acity 3 1232 6 5 4 3”: 5”; 924 7 2 : F3 :; 734 646 7992 (e) Characteristics of Typical Vertical-Tank Pressure Leaf Filters’ Tank D i a m Filter Area bqftl :: 2 7 io” 12 125 320 370 440 510 2 Leaves Leaf “ly”;nrJ I . ::i 1.7 2.2 7 . 2 i:: 8 . 0 3 0 . 0 3 5 . 0 2 8 . 0 3 2 . 0 Tank Volume (gal) ii 3 8 12 132 128 132 435 500 435 500 Approx. Approx. Overall Shipping H;aht “;a”’ 5 . 5 625 6 . 0 650 5 . 5 650 6 . 0 675 6 . 5 1125 7 . 0 1200 6 . 5 1180 7 . 0 1275 6 . 8 2900 2; 3050 3125 9 . 3 3325 ‘F. H. Schule, Ltd. b Diameter of leaf 1 in. less. ‘Filled with water. dThere are smaller sizes with leaves the outside diameters of which are 444, 36, 30, and 22 in.; for the 30 in. leaves, four lengths of shell are available. eT. Shriver & Co.. Inc. (Courtesy of Ronningen-Petter Division, Dover Corporation, Portage, Ml; Cheremisinoff and Azbel, 1983).
- 343. 324 SOLID-LIQUID SEPARATION Cloth 7Plate - Frame Solid5 conect I” frames ,Flxed h e a d Mwable had (Frame (a) FlItrate outlets (cl Figure 11.10. Pressure filters for primarily discontinuous operation. (a) Classic plate-and-frame filter press and details; the plates are separated for manual removal of the cake (T. Shriuer Co.). (b) Horizontal plate filter; for cleaning, the head is removed and the plates are lifted out of the vessel (Sparkler Mfg. Co.). (c) Pressure leaf filter; the leaf assembly is removed from the shell and the cake is scraped off without separating the leaves (Ametek Irrc.). (d) The Kelly filter has longitudinal leaves mounted on a carriage; for cleaning, the assembly is slid out of the shell (Oliver United Filters). (e) The Sweetland filter has circular leaves and a split casing; the lower half of the casing is dropped to allow access for removal of the cake (Oliver United Filters). (f) The Vallez filter has circular leaves rotating at about 1 rpm to promote cake uniformity when the solids have a wide size range; removal of blown-back or washed back cake is accomplished with a built-in screw conveyor without requiring the shell to be opened (Gosh-Birmingham Co.).
- 344. ,sproyp/~s inspection door, Discharge doa-- ilnletconnections ',j Figure ll.lO.-(continued) (f) (a) arge Grooves ‘Cl;th’ printing Upper ply Filtrate evacuation hole Cloth reinforcement R u b b e r .Screw drive-gear for fi/ter ? : - Cahe , ' 7~_-A__. / Perforated meiolclotb-support' “Cloths in place (c) Figure 11.11. Continuous horizontal vacuum filters especially suited to free settling and draining solids. (a) Principle of the conveyor belt filter; units may operate up to 0.5 m/set with a cycle time up to 10 min and produce cake thicknesses up to 15 cm. (b) Showing the construction of a grooved rubber belt support for the filter cloth of the belt filter (Purchas, 1981). (c) Rotating horizontal vacuum filter; the unit has readily accessible piping and is amenable to thorough washing of free draining solids (Dorr-Oliver Inc.). 325
- 345. 326 SOLID-LIQUID SEPARATION tr connechon Conh7uous rotary filter Moisture IfOp ril I a Vacuum receivers (a) Cake saturated f with wash kquor Cake saturated& with filtrate Cake saturated with wash I (Discharge, lb) (cl Figure 11.12. Continuous rotary drum filters. (a) Flowsketch of continuous vacuum filtration with a rotary drum filter. The solids are taken away with a screw or belt conveyor (McCabe and Smith, Unit Operations of Chemical Engineering, McGraw-Hill, New York, 19.56). (b) Cross section of a dip-type rotary drum filter showing the sequence of cake formation, washing, dewatering and cake removal; units also are made with top feed (Oliver United Filters). (c) Cross section of a rotary drum filter with internal filtering surface, suited particularly to free settling slurries (Oliver United Filters). (d) Rotary filter with a filtering belt that is discharged and cleaned away from the drum; in the similarly functioning string discharge filters, the filtering cloth remains on the drum but the string assembly follows the path shown here for the belt. (e) Double drum filter, particularly suited to rapidly settling slurries, and may be adapted to cake washing which is not shown in this unit (System Gerlach, Nordhausen, E. Germany). (f) Vacuum disk filter , the main kind in use when cake washing is not required (Dorr-Oliver Inc.).
- 346. 11.7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT 327 Water sprays for (e) T Drying area Liquid in pan Filtrate Scraper and blow back for solids discharge TABLE 11.12. Sizes of Commercial Continuous Vacuum Filters (a) Horizontal Belt Filters’ Series Ft* Range No. Vat. Pans 2600 1 o-45 1 4600 45-200 1 6900 150-700 1 9600 130-500 2 1 3 , 6 0 0 600-1200 2 (Eimco). (b) Rotary Drum, Disk, and Horizontal Filters Rotary Drum Component Filtersb Filter Surface Area Isqft) Drum’ DK Length (ft) 4 6 6 Ill 12 14 16 16 20 22 24 6 76 113 151 189 226 8 200 250 300 350 400 10 310 372 434 496 558 620 1 2 456 532 608 684 760 836 912 Disk Component Filtersd Disk diam (ft)” 6 7 6 9 1 0 11 Number of disks Min. 2 3 4 5 6 7 Max. 8 9 10 11 12 13 Filtering area per disk (sqfi) 4 7 6 7 9 0 117 147 180 Horizontal Filters Dia (ft)’ 6 6 10 13 15 16 17 16 19 20 22 24 Area fsqft) N o m 28 50 7 8 133 177 201 227 254 283 314 380 452 Eff 25 45 6 5 120 165 191 217 244 273 304 372 444 ‘Filtrate IO-1600 Ib/fhrHsqft). bAdaptable to knife, wire, string, belt, or roll discharge. CAll-plastic construction filters also available in 3 and 4 ft drum dia, providing filter areas of 9 to 100 sqft. dAll disks are composed of 10 sectors. Disk spacing is 16 in. eThe American filter, a similar disk filter, also available in 4f-t diameter, with 20 sqft disk. ‘Also available in 3, 4, and 11.5 ft diameter. (Dorr-Oliver Inc.). Figure 11.~(continued)
- 347. drawaff Removable valve pfate discharge (a) Feed mlel a + - -Sol/ds ccke . FEED k/SOLID DISCHARGE EFFLUENT (b) Basket Screen Reciprocating piston rod HANISM 1 DISCHARGE COVERS AIR SPACE LIGHT LlaJlD SOLIDS HEA”7 LIOUID ROTATlNG BOWL I ---BRAKE (e) Figure 11.13. Filtering centrifuges. (a) Top suspended batch centrifugal filter; the cake is scraped off the screen intermittently at lowered rotation speeds of 50 rpm or so, cake thicknesses of 2-6 in., cycle time per load 2-3 min (McCabe and Smith, Unit Operations of Chemical Engineering, McGraw-Hill, New York, 1956). (b) A solid bowl centrifugal filter with continuous helical screw discharge of the cake (Bird Machine Co.). (c) Pusher type of centrifuge in which the cake is discharged with a reciprocating pusher mechanism that operates while the machine is at full speed (Baker-Perkins Co.). (d) Horizontal centrifugal with automatic controls for shutting off the feed, washing the cake and scraping it off, all without slowing down the rotation (Baker-Perkin Co.). (e) Supercentrifuge for removing small contents of solids from liquids; dimensions 3-6in. by 5 ft, speed 1OOOrps, acceleration 5O,OOOg, 50-5OOgal/hr, cleaned after shutdown. (f) Pattern of flow in a hydrocyclone. (g) The shape of hydrocyclone adapted to the kind of service. (h) Centrifugal action of a cyclone assisted by a high speed impeller (Voight Gmbh). 328
- 348. 11.7. APPLICATIONS AND PERFORMANCE OF EQUIPMENT 329 Classifying Thickening IfI (cl) (h) Figure ll.l3-(continued) TABLE 11.13. Typical Applications of Industrial Filters CENTR I FUGAL Material Characteristics Equipment Type’ Filtrate Rate kg/(m’)(hr) A B C D E Vacuum Pressure (Torr) (atm) Flotation concentrates Sedimentation concentrates Crystals and granules Beverages, juices Pigments Limestone, oxide minerals Cane sugar mud Mineral oils Liquid fuels Varnishes, lacquers Fats, oils, waxes Sewage sludge Pulp and paper C e m e n t minerals, 10.3 m > 0.3 mm 0.05-0.3 mm worthless solids, use filter aids smeary, sticky, 0.06 mm fine, high density fibrous, viscous high viscosity, l-20% bleaching clays low viscosity, bleaching clays cloudy, viscous, solid adsorbents worthless solids, Fro-70°C colloidal, slimy fibrous, free filtering fine limestone, shale, clay, etc 300-1000 6000-42.000 600-2000 150-5000 120-300 b a t c h m o d e 200-1000 b a t c h m o d e 100-1000 800-2500 15-18 500-800 15-150 150-500 300-1000 - - - x - x - x x - - x x - - - - - - x - x - x x x x - x - - - x x x - x - x - x - - - - x x x - - - - x - - x - - - - - - - - x x x - - - - - - - - - - - - - 450-600 - 50- 150 - 100-300 - - 2.5-3.5 500-680 - 450-600 - - 2.5-4 - 2.5-4 - - - - - 550-600 150-500 450-630 4 <4 1 - - - - OUT B Equipment type: (A) filter press; (B) leaf pressure filters, such as Kelly, Sweetland, etc.; (C) continuous vacuum filter; (D) batch rotary filter; (E) continuous rotary filter.
- 349. 330 SOLID-LIQUID SEPARATION TABLE 11.14. Design and Operating Factors for Continuous Vacuum Filters (a) Typical Factors for Cycle Design Filter type Submergence. Effective Apparent Maximum Total underb Active Vat o r Preeeure % of Cycle Max’ Max ford f o r D e w a t e r i n g W a s h i n g O n l y “O?EE Discharge D r u m Standard scraper Roll discharge Belt Coil or string Precoat Horizontal belt Horizontal table as req’d as req’d Tilting pan as req’d as req’d Disc 3 5 2 8 3 5 3 0 3 5 3 0 3 5 3 0 3 5 3 0 35, 55, 85 35, 55, 85 as req’d as req’d 8 0 8 0 7 5 7 5 9 3 as req’d 8 0 7 5 7 5 2 9 50-60 2 0 2 9 50-60 2 0 2 9 45-50 2 5 2 9 45-50 2 5 3 0 10 5 as req’d as reqd 0 as req’d as req’d as req’d 2 0 as req’d 2 5 45-50 2 5 ‘Total available for effective subm., cake washing, drying, etc. ‘Value for bottom feed filters assume no trunnion stuffing boxes, except for precoat. Consult manufacturers for availability of higher submergences. ‘Maximum washing on a drum filter starts at horizontal centerline on rising side and extends to 15 past top dead center. dDewatering means drainage of liquor from cake formed during submergence. (b) Typical Air Flow Rates (c) Minimum Cake Thickness for Effective Discharge Type of Filter Air Flow at 5 0 0 T o r r V a c u u m [m’/(h)(m2M R o t a r y d r u m 50-80 Precoat drum 100-150 N u t s c h e 30-60 Horizontal belt or pan 100-150 Filter Type D r u m Belt Roll discharge Std scrapter Coil String discharge Precoat Horizontal belt Horizontal table Tilting pan Disc Minimum Design Thickness (in.) l/8-3/1 6 3-5 l/32 1 714 6 l/8-3/16 3-5 t/4 6 O-118 max O-3 max l/8-3/16 3-5 314 2 0 314-l 20-25 3/E- l/2 10-13 [(a, b) Purchas, 1981; (c) Purchas, 19771. TABLE 11.15. Typical Performance Data for Horizontal Belt Filters Application Filter area, m2 Slurry feed W a s h r a t i o Solubles Final cake characteristics m o i s t u r e % solids (wt/wt based recovery PB t/hr on dry solids) 96 % Dewatering metallic concentrates Brine precipitate sludge Calcine leach Uranium leach Pulp Cyanide leach aold DUlD 8 4 0 - 2 0 - - 7 2 5 1 2 - 1 8 so 5 0 6 0 4 5 10 7 8 1 99.7 1 4 120 5 0 l - 2 300 0 . 4 9 9 . 3 1 8 120 5 0 10-11 8 0 0 . 6 9 9 . 6 2 0 (Delfilt Ltd.; Purchas, 1981).
- 350. TABLE 11.16. Examples of Filter Press Performance for Dewatering of Wastes in Municipal, Potable Water and Industrial Effluents Type of Material Nature and kvel of conditioning Filtration Solids CA@ cw cycle time feed wtmt tlsidcnar Remarks uld wtlwt (%I (mm) /%I Fine waste slurry Frothed tailings Primary sewage sludge Digested sewage sludge Heat treated sludge Mixed sewage sludge including surplus activated Paper Mill Humus sludge Up to 3% aluminium chlorohydrata (Al203 basic) or 30% lime with 30% copperas or 3-8% F ECI 3 l%ACH Paper Mill pool effluent sludge 10% lime, 10% copperas of 1% FECI J Pickling end plating sludge Up to 10% lime if required Potable water traetment sludge In some instances no conditioning is raquirad 0.2-l 1% polyelectrolyte (Fre- quently it is possible to decant large quantities of clarified water after conditioning end before filtration). Brine sludge Hydroxide sludge Lead hydroxide sludge Polvelectrolvtes 0.05-0.3 lb/ton 0.5-2 Pol~electrolytes 0.05-0.3 lb/ton l - 2 . 5 5-25% lime with 5-l 5% copperas. 5-25% 3-7 lime and 36% ferric chloride 1.5-2 or l-2% ACH(A1203) 2 - 3 1 mgll polyelectrolyte or 10% lime 15-35 75-82 25-40 15-35 73-80 25-40 4 - 7 40-55 25-32 3 - 6 35-50 25-32 l - 2 12-15 50-70 32 3 - 6 UP to 4 30-45 32 2 - 4 up to 4 3 0 4 0 25 8 0.5-l .5 3 0 4 5 25 1 - 3 l - l . 5 40-55 25 1.5-3 3 - 8 1.5-3 1.5-3 0.5 2 - 3 30-45 0.5-3 25-35 25-32 19-25 10-25 60-70 20-25 0.5-l .5 35-45 25-32 45 80 32 More than 80% below 2408s mesh Proportion of surplus activ. sludge is 40% by weight (Edwards and Jones Ltd.).
- 351. TABLE 11.17. Operating Data of Some Vacuum Filter Applications Application Type of vacuum filter frequency usedb Solids conlenf of feed, WI/W So&is handling rate. kg dry solids h-l mm2 filter surface’ Mobure Air ow conrenl of m’ h-l I rn- Vacuum. cake, W/W filter surfaced mmHg ChemiMLc Alumina hydrate Top feed drum 40 450-750 15 9 0 125 Barium nitrate T o p feed d r u m 8 0 1250 5 450 250 Barium sulphate D r u m 40 50 3 0 18 Bicarbonate of soda D r u m 5 0 1750 I2 540 z Calcium carbonate D r u m 5 0 125 2 2 3 6 Sal Calcium carbonate (precipitated) D r u m 3 0 I50 40 3 6 550 Calcium sulphate Tipping pan 35 6ao 3 0 9 0 450 Caustic lime mud D r u m 3 0 750 5 0 108 375 Sodium hypochlorite Belt discharge drum 12 I50 3 0 5 4 500 Titanium dioxide D r u m 3 0 125 4 0 3 6 500 Zinc stearate D r u m 5 25 6 5 5 4 500 Minerals Frothed coal (coarse) Top feed drum 3 0 750 18 7 2 300 Frothed coal (fine) Drum or disc 35 2 2 2 5 4 375 Frothed coal tailings D r u m 4 0 3 0 3 6 550 Copper concentrates D r u m 5 0 300 IO 3 6 525 Lead concentrates D r u m 7 0 loo0 12 5 4 550 Zinc concentrates D r u m 7 0 750 10 3 6 500 Flue dust (blast furnace) ,Drum 4 0 150 2 0 iii 500 Fluorspar D r u m 5 0 loo0 12 375 Notes: ’ The information given should only be used as a general guide, for slight differences in the nature. size range and concentration of solids, and in the nature and temperature of liquor in which they are suspended, can significantly affect the performance of any filter. b It should not be assumed that the type of filter stated is the only suitable unit for each application. Other types may be suitable, and the ultimate selection will normally be a compromise based on consideration of many factors regarding the process and the design features of the filter. ’ The handling rate (in kg h-’ mm2) generally refers to dry solids except where specifically referred to as filtrate. ’ The air volumes stated are measured at (he operating vacuum (i.e. they refer to attenuated air). (Osborne, 1981).
- 352. TABLE 11.18. Typical Performance Data of Rotary Vacuum Filters Material Dlrc fllter Flotation coal Copper concentrates Magnetic concentrates Coal refuse Magnesium hydroxide Approximate particle size 33-43%-200 mesh SO%-200 mesh 80-95%-325 mesh 35-50%250 mesh 15 microns av. size Vacuum Pump (9) Feed solids Filtration rate (9) cont. WI % W(m*) W m3/(m2)(min) mm Hg 2 2 - 2 6 300-600 1.5 5 0 0 60-70 250-450 0.5 55-65 1ooo-2ooo 2.5-3 0 i&50 35-40 log-125 0.6 500 lo-15 40-6fI 0.6 5 0 0 Drum flttar (1) Sugar cane mud CaCOs mud recausticising (2) Corn starch Sewage sludge Primary Primary digested (3) Leached uranium ore Kraft pulp (4) Kaolin clay Belt drum filter (5) Sugar cane mud Sewage sludge Primary Primary digested Corn gluten Corn starch (3) Gold cyanide leached off (3) Spent vegetable carbon Dextrose processing Steel mill dust (3) Sodium hypochlorite Top feed drum Iron ore concentrates (6) Sodium Chloride Bone char (6) Ammonium sulphate Limed for flocculation 7-18 by vol. 25-75 0.2 500 - 35-40 !=m-600 1.8-2 25X380 15-18 microns, av. size 3242 llg-150 0.9-l 560 Flocculated Flocculated 5&60%-200 mesh Flocculated Lcng fibre 9a75%-2 micron 5-8 5zl 1 5 - 3 0 1 O-20 15rJ-220 05 E- 500 5 0 9 5 0 0 l-11 22&3Otl Barometric leg 2 5 - 3 5 3tX75 05 Seperan flocculated 7-18 by vol. 9(1-250 0.2 0.5 0.5 500 Flocculated 5-8 30-50 Flocculaled 4-7 1535 Self flocculating la-20 oz/u.S. gal 15-30 15-l 8 microns, av. size 32-42 1ErI-250 06 0.9-l 2: SW 500 65%-200 mesh SE%-325 mesh 5tI-60 100-l 30 gm/litres 300-6w 3rI-50 500 x0 20-40%-2 microns Fine 4o50 12 17Moo 150 0.5 1.5 0.6-l .2 0.9 500 5 0 0 2-4%200 mesh 8 mesh top size 5-l 0%-l 00 mesh 1%-70 mesh 5-15%-35 mesh 3 5 63C10-7300 2 5 - 3 5 1000-l 500 a20 1200-1700 35-409/o by vol. 1000-l 700 15 3 0 4 0 45-60 150 150 9 0 75 Tlltlng pan filter (7) Gypsum from digested 4&50 micron av. 3-o 600-900 1.2-1.5 500 phosphate rock (8) Leached cobalt residue -200 mesh 4550 2 5 0 3 3 6 0 (8) Alumina-silica gel catalyst - 12 2 7 0 0.9 500 (7) Pentaerythritol - 3cUo 75100 3.6 500 Notes: (1) Filtrate very dirty-must be recirculated back to clarifier-cake washed. (2) String discharge filter. (3) Cake washed. (4) Roller discharge drum filter. (5) Filtrate very clean+toes directly to evaporation-cake washed. (6) lop feed filter drier. (7) Two or three stages of counter-current washing. ee stages of counter-current washing. (8) Three stages of counter-current washing. fes of counter-current washing. (9) Based on total filter area. total filter area. (Data of Envirotech Corp.). TABLE 11.19. Data of Centrifugal Filters and Sedimentation Centrifuges (Purchas, 1977) (a) Operating Ranges of Main Types of Centrifugal Filters Type of Centrifuge Minimum Solid Minimum Automatically Automatically Concentration Filtrability Maximum Discharged at Discharged at g-Factor in Feed 1% by Possibility y$!.!!$~ Coefficient Retention Continuous Full Speed Reduced Speed Range (F,I Volume &.I of Washing Size, mm (k)(m/sec) l i m e (Sac) Oscillating x Tumbler X Worm Screen X Pusher x Peeler X Pendulum (Hultsch and Wilkesmann; Purchas, 1977). X X 30-120 50-300 500-3000 300-2000 300-l 600 200-1200 333 40 40 20 30 5 5 n o 0.3 5 x 1o-4 6 n o 0.2 2 x 1o-4 6 poor 0.06 1 x 10-5 15 g o o d 0.08 5 x 1o-5 60 very good 0.01 2 x lo-’ as wanted very g o o d 0.005 1 x lo-’ as wanted (continued)
- 353. 334 SOLID-LIQUID SEPARATION TABLE ll.lg-(continued) (b) Criteria for Selection of Sedimentation Centrifuges Parameter Tubular Bowl Skimmer Pipe Disc Scroll Solids concentration. vol./vol. Particle size range processable for density difference under 1 g/cc and liquor viscosity 1 cP Settling time of 1 litre under 1 g Settling time of 50 cc at 2000 g Approximation maximum throughput for largest machine Approximate nominal throughput for largest machine Nature of bottle spun solids Batch or continuous Floe applicable g levels used Maximum sigma value x 107cm2 <l% $50 pm Few hours to infinity ;hrtodays 5-15 min l-5 min 5000 litre/hr 15,000 litre/hr 1250 litre/hr 12,000 litre/hr Can be any consistency Batch Possibly but not usual Up to 18,000. 80,000 Laboratory model 5 up to about 40% lOpm-6mm Must be fluid to paw Semi Yes Up to 1600 4 up to about 20% l-400 urn several hours 5-10 min 100,000 litre/hr 40,000 litre/hr Must not be too cohesive Semi or continuous N o 4500-l 2,000 10 any as long as it remains pumpable 5 wm-6 mm i-1 hr l-5 min 70,000 litre/hr 30,000 litre/hr Preferably compact and cohesive Continuous Yes 500-4000 1 4 (F.A. Records). REFERENCES 1. C. Almy and W.K. Lewis, Factors determining the capacity of a filter press, Ind. Eng. Chew. 4, 528 (1912). 2. N.P. Cheremisinoff and D. Azbel, Liquid Fihlion, Ann Arbor Science, Ann Arbor, MI, 1981. 3. R. Bosley, Pressure vessel filters, in Purchas, Ref. 14, 1977, pp. 367-401. 4. D.A. Dahlstrom and C.E. Silverblatt, Continuous filters, in Purchas, Ref. 14, 1977, pp. 445-492. 5. E. Davies, Filtration equipment for solid-liquid separation, Trans. In.sf. Chem. Eng. 43(S), 256-259 (1965). 6. J.E. Flood, H.E. Parker, and F.W. Rennie, Solid-liquid separation, C/rem. Eng. 163-181 (30 June 1966). 7. M.P. Freeman and J.A. Fitzpatrick (Eds.), Theory, practice and process principles for physical separations, Proceedings of the Engineering Foundation Conference, Pacific Grove California, Oct.-Nov. 1977, Engineering Foundation or AIChE, 1981. 8. C. Gelman, H. Green, and T.H. Meltzer, Microporous membrane filtration, in Azbel and Cheremisinoff, Ref. 3, 1981, pp. 343-376. 9. C. Gelman and R.E. Williams, Ultrafiltration, in Cheremisinoff and Azbel, Ref. 3, 1981, pp. 323-342. 10. J. Gregory (Ed.), Solid-Liquid Separation, Ellis Horwood, Chichester, England, 1984. 11. K.J. Ives, Deep bed filtration, in Svarovsky, Ref. 17, 1981, pp. 284- 301. 12. D.G. Osborne, Gravity thickening, in Svarovsky, Ref. 17, 1981, pp. 120-161. W. D.G. Osborne, Vacuum filtration, in Svarovsky, Ref. 17, 1981, pp. 321-357. 14. D.B. Purchas, (Ed.), Solid-Liquid Separation Equipment Scale-Up, Uplands Press, London, 1977. 15. D.B. Purchas, Solid-Liquid Separation Technology, Uplands Press, London, 1981. 16. A. Rushton and C. Katsoulas, Practical and theoretical aspects of constant pressure and constant rate filtration, in Gregory, Ref. 10, 1984, pp. 261-272. 17. L. Svarovsky (Ed.), Solid-Liquid Separation, Butterworths, London, 1981. 18. F.M. Tiller (Ed.), Theory and Practice of Solid-Liquid Separation, University of Houston, Houston, 1978. 19. F.M. Tiller and J.R. Crump, Solid-liquid separation: an overview, Chem. Eng. Prog., 73(10), 65-75 (1977). 20. F.M. Tiller, J.R. Grump, and C. Ville, Filtration theory in its historical perspective; a revised approach with surprises, Second World Filtration Congress, The Filtration Society, London, 1979. 21. R.J. Wakeman, A numerical integration of the differential equations describing the formation of and flow in compressible filter cakes. Tranr. ht. Chem. Eng. 56, 258-265 (1978). 22. R.J. Wakeman, Filter cake washing, in Svarovsky, Ref. 17, 1981, pp. 408-451. 23. R.H. Warring, Filters and Filtration Handbook, Gulf, Houston, 1981. 24. Solids Separation Processes, International Symposium, Dublin, April 1980, EFCE Publication Series No. 9, Institution of Chemical Engineers, Symposium Series No. 59, Rugby, England, 1980.
- 354. 12 DISINTEGRATION, AGGLOMERATION, AND SIZE SEPARATION OF PARTICULATE SOLIDS F rom the standpoint of chemical processing, size reduction of so/ids is most often performed to make them more reactive chemically or to permit recovery of valuable constituents. Common examples of comminution are of ores for separation of valuable minerals from gangue, of limestone and shale for the manufacture of cement, of coal for combustion and hydrogenation to liquid fuels, of cane and beets for recovery of sugar, of grains for recovery of oils and flour, of wood for the manufacture of paper, of some flora for recovery of naturaal drugs, and so on. Since the process of disintegration ordinarily is not high/y selective with respect to size, the product usually requires separation into size ranges that are most suitable to their subsequent processing. Very small sizes are necessary for some applications, but in other cases intermediate sizes are preferred. Thus the byproduct fines from the crushing of coal are briquetted with pitch binder into 3-44in. cubes when there is a demand for coal in lump form. Agglomeration in general is practiced when larger sizes are required for ease of handling, or to reduce dust nuisances, or to densify the product for convenient storage or shipping, or to prepare products in final form as tablets, granules, or prills. Comminution and size separation are characterized by the variety of equipment devised for them. Examples of the main types can be described here with a few case studies. For real, it is essential to consult manufacturers’ catalogs for details of construction, sizes, capacities, space, and power requirements. They are properly the textbooks for these operations, since there are few generalizations in this area for prediction of characteristics of equipment. A list of about 90 U.S. and Canadian manufacturers of size separation equipment is given in the Encyclopedia of Chemical Technology 121, 137 (7983)], together with identification of nine equipment types. The Chemical Engineering Equipment Buyers Guide (McGraw-Hi//, New York) and Chemical Engineering Catalog (F’enton/Reinho/d, New York) a/so provide listings of manufacturers according to kind of equipment. 12.1. SCREENING Separation of mixtures of particulate solids according to size may be accomplished with a series of screens with openings of standard sizes. Table 12.1 compares several such sets of standards. Sizes smaller than the 38pm in these tables are determined by elutriation, microscopic examination, pressure drop measurements, and other indirect means. The distribution of sizes of a given mixture often is of importance. Some ways of recording such data are illustrated in Figure 16.4 and discussed in Section 16.2. The distribution of sizes of a product varies with the kind of disintegration equipment. Typical distribution curves in normalized form are presented in Figure 12.1, where the size is given as a percentage of the maximum size normally made in that equipment. The more concave the curves, the greater the proportion of fine material. According to these correlations, for example, the percentages of material greater than 50% of the maximum size are 50% from rolls, 15% from tumbling mills, and only 5% from closed circuit conical ball mills. Generalization of these curves may have led to some loss of accuracy since the RRS plots of the data shown in Figure 12.1(c) deviate much more than normally from linearity. In order to handle large lumps, separators are made of sturdy parallel bars called grizzlies. Punched plates are used for intermediate sizes and woven screens for the smallest sizes. Screening is best performed dry, unless the feed is the product of wet grinding or is overly dusty and an equipment cover is not feasible. Wetting sometimes is used to prevent particles from sticking together. Types of screens and other classifiers to cover a range of sizes are shown in Figure 12.2. Usually some kind of movement of the stock or equipment is employed to facilitate the separations. REVOLVING SCREENS OR TROMMELS One type is shown in Figure 12.2(a). They are perforated cylinders rotating at 15-20rpm, below the critical velocity. The different- sized perforations may be in series as shown or they may be on concentric surfaces. They are suitable for wet or dry separation in the range of 60-10 mm. Vertically mounted centrifugal screens run at 60-80 rpm and are suitable for the range of 12-0.4 mm. Examples of performance are: (1) a screen 3 ft dia by 8 ft long with 5-mesh screen at 2 rpm and an inclination of 2” has a capacity of 600 cuft/hr of sand; (2) a screen 9 ft dia by 8 ft long at 10 rpm and an inclination of 7” can handle 4000 cuft/hr of coke. Flat screel~~ are vibrated or shaken to force circulation of the bed of particles and to prevent binding of the openings by oversize particles. Usually several sizes are arranged vertically as in Figures 12.2(b) and (c), but sometimes they are placed in line as in the cylindrical screen of Figure 12.2(a). Inclined screens vibrate at 64lO-7000 strokes/min. They are applicable down to 38pm or so, but even down to 200 mesh at greatly reduced capacity. Horizontal screens have a vibration component in the horizintal direction to convey the material along; they operate in the range of 300-3000 strokes/min. Shaking or reciprocating screens are inclined slightly. Speeds are in the range of 30-1000 strokes/min; the lower speeds are used for coal and nonmetallic minerals down to 12mm, and higher speeds may size down to 0.25 mm. The bouncing rubber balls of Figure 12.2(c) prevent permanent blinding of the perforations. Rotary sifters are of either gyratory or reciprocating types. They operate at 500-600rpm and are used for sizes of 12mm- 50 pm, but have low capacity for fine sizes. CAPACITY OF SCREENS For coarse screening, the required area per unit of hourly rate may be taken off Figure 12.3. More elaborate calculation procedures that take into account smaller sizes and design features of the equipment appear in the following references: Mathews, Chem. Eng. 76 (10 July 1972) and presented in Chemical 335
- 355. 336 DISINTEGRATION, AGGLOMERATION, AND SIZE SEPARATION OF PARTICULATE SOLIDS TABLE 12.1. Comparison Table of United States, Tyler, Canadian, British, French, and German Standard Sieve Series . TahndAd I 12smm loamm ‘SE 7s mm 3 ii3 zi souun 46 mm 37.6 mm - 31.5 mm 26.6 mm 26.0 mm E ii2 . 4 5 mrm 170 76 rm 2 0 0 arm 2 3 0 s3m 2 7 0 46 rm 325 3 8 &lm 400 - -,I TVLER (2) CANADIAN (3) MBBh Drigaatioa StBdBrd AlbrMu I 125 mm I I 108 mm i.24’ 100 mm E E 3 ” 63 mm - I 63 mm % 50 mm 9 45 mm 37.6 Lnm - - %! 2i.z 1H’ 1.05” 2610 mm 1.06” ,883” ----l 22.4 mm ‘“1 ” .742a 19.0 mm 9 )4I .624” 16.0 mm %” .525* 13.2 mm .S30” I 12.6 mm .441” 11.2 mal E E 3%” 3 617 mm ‘W .265’ 6.3 mm %” .- 3% I 5.6 mm N o . t 4.75 Mm 4 4.00 rim 5 6 3.35 mm 6 87 2.60 mm 2.36 mm 9 I 2.00 mm 10 --I 1.70 mm 1 2 .- 1.40 ulm 7 1: 12 14 14 doa I 1.18 mm 1.00 mm 850 l&m - 2 4 I 710 pm 600~ so0 @Ia 425 m :68 2 0 4 2 I 335 pm -I iii! 48 212 250300 mmapm 80 I 1mW / E 160 I 15o@n I 125 rm 106 rm 1 170 90 rm 7 5 rm 2 5 0 63 rm 270 - 53jAm 2 5 3”: 40 4 6 60 % 8 0 100 120 140 170 GERMAN (6) OPl. BRITISH (4) Nomid Nominal Aporturo h4d1 No No. 26.0 mm 20.0 mm 18.0 mm 16.0 mm 12.6 mm 10.0 mm 8.0 mm 6.3 mm 38 5.0 mm 3 7 4.0 mm 3 6 3.16 mm 3 5 2.5 mm 2 2.0 mm 1.6 mm 3 2 1.25 mm 31 1.0 mm 30 I fJoom 29 / 630~ 2 8 5OOrm 2 7 4@Jw 2 6 316 ban 26 mrm 2 4 2@3rm 2 3 1mrm 2 2 1=P= 5.ooo 4.000 3 . 1 5 0 2.600 2.000 1.600 1.250 1.000 -3m- .630 .soo 3.35 mm 5 2.60 mm I 6 2.40 mm 7 2.00 mm 1.68 mm 10s 1.40 mm 12 1.20 mm 14 1.00 mm 16 8Wrm 10 710 #la 2 2 6Wrm bWrm :i 420 rm --is- 356 j&In 4 4 3oorm 6 2 25OWJ so 210 j4m 7 2 lMb- a5 150 @m - m - - 125 pm 120 lobUll 150 mrm 170 75 b-l 2 0 0 63 rm 2 4 0 63 rm 300 45 rm 3 5 0 200 I 230 2 7 0 3 2 5 400 .400 .31b -.250 .200 .160 .125 .lOO -xm-- .063 .060 .040 I * These sieves correspond to those recommended by IS0 (International Standards Organization) as an International Standard and this designation should be used when reporting sieve analysis intended for international publication. (1) U.S.A. Sieve Series-ASTM Specification E-l I-70 (2) Tyler Standard Screen Scale Sieve Series. (3) Canadian Standard Sieve Series 8-GP-ld. (4) British Standards Institution, London BS-410-62. (5) French Standard Specifications, AFNOR X-l l-501. (6) German Standard Specification DlN 4188.
- 356. 12.2. CLASSIFICATION WITH STREAMS OF AIR OR WATER 337 Primary gyrator, straight-element breaking headandconcaves Standard cone crusher Hammer mill, no cage - Rolls, open-circuit, free-crushing Y YO t.0 % of limiting aperture (a) Trunnionoverflow cylindrical ball mill, closed I Grate ball mill, closed circuit circuit ‘“2 % of limiting aperture (b) 3 -0 v”- f 80. z” 70. 5 60. i% . c$? 5o 8 40. 3 i 30. 3 20. 15. 1 ,I”! 5 IO 2 0 0 b0 Id0 % of limiting aperture (c) Figure 12.1. Normalized cumulative size distribution curves of comminuted products. (a) From various kinds of crushing equipment. (b) From rod and ball mills. (c) RRS plots of two curves (Z’aggart, 1951). Engineers’ Handbook, McGraw-Hill, New York, 1984, p. 21.17. Kelly and Spottiswood, Introduction to Mineral Processing, 1982, p. 193. V.K. Karra, Development of a model for predicting the screening performance of a vibrating screen, CIM Bull. 72, 167-171 (Apr. 1979). The last of these procedures is in the form of equations suitable for use on a computer. 12.2. CLASSIFICATION WITH STREAMS OF AIR OR WATER Entrainment of particles with streams of air or water is particularly suitable for removal of small particles from mixtures. Complete distribution curves can be development by employing several stages operating at suitable conditions in series. AIR CLASSIFIERS Although screens of 150 mesh and finer are made, they are fragile and slow, so that it is often preferable to employ air elutriation to
- 357. FEED w (a) (d) 0-4 ’ Rakes Overflow (e) Figure 12.2. Equipment for classifying particulate solids by size from more than 0.5 in. to less than 1.50 mesh. (a) Rotating cylinder (trammel) for sizing particles greater than 0.5 in., 2-10 rpm, 10-20” inclination. (b) Heavy duty vibrating screen, 1200-1800 vib/min (Tyler-Niagara, Combustion Engineering Inc.). (c) Three-product reciprocating flat screen, 500400 rpm, with bouncing rubber balls to unbind the openings, dry products to 100 mesh (Rotex Inc.). (d) Air classifier for products less than 150 mesh. Feed enters at A, falls on the rotating plate B, fines are picked up by air suction fans C, transferred to zone D where they separate out and fall to the discharge, and air recirculates back to fans C (Sturtevant Mill Co.). (e) Dorr drag rake wet classifier. (f) Hydrocyclone. 338
- 358. 1 2 . 3 . S I Z E R E D U C T I O N 3% equation for the cut point is ,&+ O v e r f l o w ,-Vortex tinder Feed entrance valve dlschorge (f) Figure l2.2-(continued) remove fine particles. The equipment of Figure 12.2(d) employs a rotating plate that throws the particles into the air space from which the finer particles are removed and subsequently recovered. WET CLASSIFIERS These are used to make two product size ranges, oversize and undersize, with some overlap. The break commonly is between 28 and 200 mesh. A considerable variety of equipment of this nature is available, and some 15 kinds are described by Kelly and Spot- tiswood (1982, pp. 200-201). Two of the most important kinds, the drag rake classifier and the hydrocyclone, will be described here. The classifier of Figure 12.2(e) employs two set of rakes that alternately raise, lower, and move the settled solids up the incline to the discharge. Movement of the rakes is sufficient to keep the finer particles in suspension and discharge them at the lower end. More construction detail of the Dorr classifier may be found in older books, for example, the 1950 edition of the Chemical Engineers Handbook (McGraw-Hill, New York). The stroke rate may be 9/min when making separation at 200 mesh and up to 32/min for 28 mesh rapid settling sands. Widths range from 1 to 2Oft, lengths to 4Oft, capacity of 5-850 tons slurry/hr, loads from 0.5 to 150HP. The solids content of the feed is not critical, and that of the overflow may be 2-20% or more. Hydrocyclones, also called hydroclones, employ self-generated mild centrifugal forces to separate the particles into groups of predominantly small and predominantly large ones. Because of bypassing, the split of sizes is not sharp. The characteristic diameter of the product is taken as d,,, the diameter than which 50 wt % of the material is greater or less. The key elements of a hydrocyclone are identified on Figure 12.2(f). A typical commercial unit made by Krebs Engineers has an inlet area about 7% of the cross-sectional area between the