Optimal Heat Exchanger Rating Models for Isothermal CSTR SO3 Hydration Using Vanadium

International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-2, Issue-5, May- 2016]
Infogain Publication (Infogainpublication.com) ISSN : 2454-1311
www.ijaems.com Page | 330
Optimal Heat Exchanger Rating Models for
Isothermal CSTR SO3 Hydration Using
Vanadium
Abowei M. F. N, Goodhead, T. O. , Wami, E. N
Department of Chemical/Petrochemical Engineering, Rivers State University of Science and Technology, Nkpolu, Rivers
State, Nigeria.
Abstract— This work deals with the development of
design models for heat exchanger rating in catalytic
sulphur trioxide hydration process at isothermal
condition exploiting the Abowei and Goodhead derived
continuous adsorption tower (CAST) heat generation per
unit volume equations at constant temperature. Shell and
Tube heat exchanger is invoked for this studies resulting
to novel design equations which were stochastically
examined and found to be capable of simulating the
rating performance dimensions as a function of kinetic
parameters. The rating performance models were further
generalized to inculcate fractional conversion
functionality. The novel design models were simulation to
evaluate the overall heat transfer coefficient, mass flow
rate of cooling fluid, tube side cross flow area and tube
side film coefficient using Matlab R2007B within the
operational limits of conversion degree at constant
temperature. The heat exchanger is used for the removal
of heat generated per reactor unit volume utilizing water
as cooling fluid, enters the shell side at 25o
C flowing
counter currently to the tube side at exit temperature of
85o
C in order to maintaining 97o
C isothermal condition.
The configuration of the exchanger is U–tube type and is
three (3) shell and six (6) tube passes. The results of the
rating dimensions showed a dependable relationship with
fractional conversion at constant temperature for various
reactor radius and number of tubes.
Keywords— CAST, heat exchanger Rating, isothermal,
hydration, sulphur trioxide.
I. INTRODUCTION
1.1 Stoichiometry
Catalytic hydration of sulphur trioxide using vanadium
catalyst results to production of sulphuric acid and it is
a n industrially very important chemical specie due to its
associated uses. Hence, the continuous search for the
development of suitable design model to optimize its
production capacity for reactor types is eminent [1]-[3].
Sulphuric acid otherwise called oil of vitrol and king of
chemicals is a diprotic acid with structural formula
presented in fig 1.
Fig.1: Sulphuric Acid Structural Profile
Sulphuric acid possesses high ionization and dissociation
capacities that influence its reactivity with other
chemicals resulting to useful finished industrial products
with high heat of reaction that needs to be controlled
using suitable heat exchanger. A heat exchanger or
interchanger is a device which makes possible the transfer
of heat from one fluid to another through a container wall
[4]-[6]. In a typical process industry application, a heat
exchanger may be a vessel in which an outgoing
processed hot liquid transfers some of its heat to an
incoming cold liquid about to be processed. The amount
of heat so transferred is not lost to the process but,
instead, is used again. Its equivalent heat need not be
supplied by new fuel but may be considered as cycled
heat [7]-[10]. Similarly, to maintain optimum condition
for a reaction to proceed at an appreciable rate, it is
imperative to control the temperature of the reaction with
the aid of heat exchangers.
Although the production of sulphuric acid is eminent and
known globally, related literatures have shown that
numerous treaties have been written and published on it
[11]. The purpose of this study is to continue
investigations into past works on the development of
performance models including associated heat exchangers
for reactor types for the production of sulphuric acid, and
to specifically identify and develop appropriate
performance models for the areas that are deficient in past
works. However, little or no known published work had
been recorded for the development of feasible heat
exchanger performance models for the production of the
acid using batch, continuous stirred adsorption tower, and

plug flow adsorption towers at isothermal and non-
isothermal conditions. Recently, works of Goodhead and
Abowei (2014) focused on development of design models
for H2SO4 production based on semi batch, isothermal
plug flow (IPF) non-isothermal plug flow (NIPF) and
non- isothermal continuous adsorption tower [12]
These works on the development of design models
covers heat generation per unit volume for all
adsorption tower types but advocated the necessity for
further studies on the development of suitable heat
exchanger units capable of maintaining desired
temperature to obtain products in adherence to plant
performance dimensions [14-[16].
Therefore, in this present paper we considered
development of heat exchanger performance rating
for continuous stirred tank reactor (CSTR) as a
function of kinetic parameters at isothermal condition
exploiting the heat generation per unit volume model of
Abowei And Goodhead (2014).
1.2 KINETIC EVALUATION
The stoichiometry in the manufacture of Sulphuric Acid
(H2SO4) is well cited in the works of Abowei and
Goodhead (2014) and summarized as follows;
Combustion
Chamber
(combustion of
sulfur)
-
Converter
(conversion of
sulfur dioxide)
->
Adsorption Tower
(sulfur trioxide
hydration process)
The Contact Process is a process involving the catalytic
oxidation of sulfur dioxide, SO2, to sulphur trioxide, SO3.
A vanadium catalyst (vanadium (V) oxide) is also used in
this reaction in order to speed up the rate of the reaction
[12]. The current work looked at the development of
performance evaluation models for vanadium catalyst
based isothermal continuous stirred adsorption tower
sulphur trioxide hydration process in the production of
sulphuric acid. The stoichiometric chemistry is given as,
S(s) + O2(g) → SO2(g)
SO2(g) + )(3)(22
1
gg SOO → (1)
SO3(g) + H2O(l) → H2SO4(l)
Substantial works had been done and documented on the
kinetics of sulphuric acid production [9]. Literatures have
shown that direct dissolution of sulphur trioxide in water
to produce the acid is not done due to very high heat of
reaction occasioned in the process. Instead sulphur
trioxide is absorbed in concentrated sulphuric acid to
form oleum, and subsequently diluted with water to form
sulphuric acid of 98%-100% concentration.
The reaction mechanism as presented in equation (3)
showed chain reaction characteristics reported on the
photo-catalysed oxidation of SO3
2-
by (dimethyl-
glyoximato) (SO3)2
3-
and its (Co(dimethyl-glyoximato)
(SO3)3
2 [1].
The work showed that the reaction
4223 SOHOHSO →+ (2)
is described as irreversible bimolecular chain reaction.
Further research into the works of Erikson, [1974]
established the reaction as second order reaction with rate
constant K2= 0.3 mole/sec. Blanding (1953) performed
abinitio calculation and determined the energetic barrier
and established conclusively that the irreversible
bimolecular nature of the reaction have ∆Hr = -
25kcal/mol at 25o
c.
Following the outcome of the work of Chenier (1987),
Charles (1997) as cited above, the rate expression for the
formation and production of sulphuric acid is summarized
as in equation 2.
-RA = K2 [ ] [ ]OHSO 23
(3)
Hence from equation 3 the amount of SO3 and H2O that
have reacted at any time t can be presented as;
[ ][ ]AABoAAAA XCCXCCKR 0002 −−=− (4)
Where
CAo = Initial concentration of SO3 (moles/Vol)
CBo = Initial concentration of H2O ( moles/Vol)
XA = Fractional conversion of SO3 (%)
-RA = Rate of disappearance of SO3 (mole/ Vol/t)
In this work, the rate expression (-RA) as in equation 4
will be used to develop the hypothetical continuous
stirred tank reactor tower design equations with
inculcation of the absorption coefficient factor as
recommended in the works of Van-Krevelen and
Hoftyger cited in Austein (1984) and Danner,(1983).
This is achieved by modifying equation 4 as illustrated
below. The hypothetical concentration profile of the
absorption of sulphur trioxide by steam (H2O) is
represented in fig.2 [1] and [17].
Fig.2: Absorption with chemical Reaction
Liquid film
Gas (SO3)
Liquid (steam)
Concentration CAi
Gas Film
ZL
CB
L
Interface
r
Distance normal to phase boundary
CBi

trioxide (A) is absorbed into the steam (B) by diffusion.
Therefore the effective rate of reaction by absorption is
defined by
( ) )( ALiALALiA
L
L
A CCrKCC
Z
rD
R −=−=− (5)
Invoking the works of Krevelen and Hoftyzer, the factor r
is related to CAi, DL and KL to the concentration of steam
B in the bulk liquid CBL and to the second order reaction
rate constant K2 for the absorption of SO3 in steam
solution. Thus
r = ( )
L
BLL K
CDK 2
1
2
(6)
Substituting equation 6 into 5 results in
- RA = (CA) 2
1
2
1
2
1
2 LBL DKC (7)
Previous reports shows the amount of SO3 (CA) and steam
(CBL) that have reacted in a bimolecular type reaction
with conversion XA is CAO XA [18] and [19].
Hence equation 7 can be rewritten as
- RA = ( ) ( )AAAAAOBOL XCCXCCDK 002
2
1
2
1
2
1
−−
= )1()( 2
1
2
3
2
1
2
1
02 AAAL XXmCDK −− (8)
Where
m =
0
0
A
B
C
C
m = The initial molar ratio of reactants
-RA = Rate of disappearance of SO3
K2 = Absorption reaction rate constant
DL = Liquid phase diffusivity of SO3.
KL = Overall liquid phase mass transfer coefficient
r = Ratio of effective film thickness for absorption
with chemical reaction
1.3 CSAT PERFOMANCE MODELS
Abowei and Goodhead (2014) developed CSAT
performance models as
Fig.3: Hypothetical model of a Jacketed CSAT
1. 3.1 Reactor Volume
The performance equation for isothermal mixed flow
reactor makes an accounting of a given component within
an element of volume of the system. But since the
composition is uniform throughout, the accounting may
be made about the reactor as a whole [20].
Thus,
Input = Output +disappearance by reaction +
accumulation (9)
Where,
Accumulation = O for steady state process.
If FAO = V0CA0 is the molar feed rate of SO3 to the
reactor, then considering the reactor as a whole we have
Input of SO3, moles/time = FA0 (1 – XA) = FA0
(10)
Output of SO3, moles/time = FA = FA0 (1 – XA)
(11)
Disappearance of SO3 by reaction, moles/time = (-RA) VR
(12)
Introducing the three terms in the material balance
equation (9) yields.
FA0 XA = (-RA)VR (13)
Which on re-arranging becomes
VR =
( )A
AAo
R
XF
−
(14)
But,
-RA= ( ) ( )AAAL
A
XXmCDK
dt
dC
−−= 12
1
2
3
2
1
2
1
02
Substitution in equation 14 results in
VR =
( ) ( )AAAOL
AAo
XXmCDK
XF
−− 12
1
2
3
2
1
2
1
2
(15)
FA0 = Molar feed rate of SO3, (mole/sec)
XA = Conversion degree
CA0 = Initial concentration of SO3, (mole/m3
)
K2 = Absorption reaction rate constant, (1/sec)
DL = Liquid phase diffusivity of SO3, (m2
/sec)
M = Initial molar ratio of reactants.
1. 3.2 Reactor Height
Considering a reactor with cylindrical shape we have
VR = πr2
h
h = 2
r
VR
π
(16)
=
( ) ( )AAAOL
AAO
XXmCDKr
XF
−− 12
1
2
3
2
1
2
1
2
2
π
(17)
For 0.1m < r < 1.0m

1.3.3 Heat Generation per Reactor Volume
Heat flow rate of CSAT is a function of heat of reaction
for S03 addition to water, molar feed rate and the
conversion degree. It is mathematically expressed as;
Q = (-∆HR) FA0 XA (19)
The heat generation per reactor volume is obtained by
dividing both sides of equation (22) by the reactor volume
and substituting equation (15) accordingly gives,
Rq= ( ) ( ) ( )AAALR
R
XXmCDKH
V
Q
−−∆−= 12
1
02
2
3
2
1
2
1
(20)
From the foregoing it is obvious that the CSAT heat
exchanger performance rating models are needed to
control the generated per unit volume of the adsorption
tower as reflected in equation (23)
There is utmost need to provide such unit for effective
operation of the plant to enhance productivity. Hence, this
study is focused appraise series of shell-and-tube heat
exchanger to solve the problem of heat effect involved in
SO3 hydration for the CSAT plant.
II. MATERIALS AND METHODS
2.1 Development of Models
In this heat exchanger the product (H2SO4) flows through
the tube side while the cooling fluid (water) passes
through the shell side counter currently. Shell-and-tube
heat exchangers are used commonly in industries and
aimed at maintaining constant temperature for the
production of sulphuric acid. Therefore highlighted herein
is development of heat exchange rating models in
evaluating overall heat transfer coefficient, heat transfer
surface (area), tube numbers per shell, mass flow rate of
cooling fluid, tube-side film coefficient, shell side film
coefficient using the models as developed from equations
(1) to (23) of this work. The diagram in fig. 1 shows the
configuration of the CSAT with the proposed shell-and-
tube heat exchanger for the study.
Fig.4: Hypothetical heat exchanger rating unit.
2.1.1 Overall Heat Transfer Coefficient (OHTC)
The design equation for OHTC is usually obtained from
the heat generation per unit volume of the reaction tower
as in equation (20) [21] and [22].
Thus,
= ∆ (21)
Equations (17), (20) and (21) could be compared resulting
in the design equation for the computation of OHTC as a
function of kinetic parameters;
= =
∆
! " # ! "
(22)
And equation (22) subsequently simplified to gives;
∆ = −∆% &'(
)(
#
(
*+
#
(
,-.
/
(
0 − 1-"
#
( 1 −
1-"
=
∆3 ! " # ! "
-∆45
2.1.2 Mass Flow rate of Cooling Fluid
In order to functionalized mass flow rate dependency on
total amount of heat generated per reaction tower volume,
and recalling that;
= = 6. ,8 ∆ (24)
Where G = Mass flow rate of cooling fluid
Cp = Heat capacity
∆T = Temperature
Mass flow could be computed by equating equations (24)
and (22) thus;
∆ = −∆% &'(
)(
#
(
*+
#
(
,-.
/
(
0 − 1-"
#
( 1 −
1-" 6 =
∆3 ! " # ! "
9 ∆45
Where ∆ is calculated from Logarithmic Mean
Temperature Difference (LMTD) as
LMTD = ( ) ( )
( )
( )22
11
2211
tT
tT
In
tTtT
−
−
−−− (26)
And further correlated;
∆Tm = (LMTD) * F (27)
Where F is a correction factor usually obtain from charts.
To read the charts values for P and R (temperature
coefficients) are calculated using the following
expressions.
P =
12
21
11
12
tt
TT
Rand
tT
tt
−
−
=
−
− (28)
2.1.3 Tube-Side models
(a) Tube Side Cross Flow Area
The tube side cross flow area is also correlated to reaction
tower height for effective control of heat throughput and
calculated from;
n
DiL
at
π
= (29)
H2O out let
H2O in let
SO3
H2O
(23)
(25)

Interestingly, kinetics parameters were invoked by
substituting equation (17) into (29) to giving;
:; = < = !
> ! " # ! "
(30)
Where at = tube side cross flow area
n = number of tube passes
L ⇒ H = Height of reactor tower
2.1.4 Tube side mass velocity model
The tube side mass velocity, Gt is given by
Gt =
ta
G (31)
Putting
? = &'(
)(
#
(
*+
#
(
,-.
/
(
(32)
Then, mass flow rate (G);
6 = − ∆% ? 0 − 1-"
#
( 1 − 1-"(33)
And
:; = < = !
> @ ! " # ! "
(34)
Substituting equations (33) and (34) into (31) results;
AB = C
∆DE F G HI"
J
K J HI"
LMN OIP HI
Q RS F G − HI"
J
K J −
HI"T (35)
Equation (35) further be summary to give;
AB =
∆DE FK U G HI" J HI"VKS
LMN OIP HI
(36)
III. PERFORMANCE RATING DESIGN
CALCULATION
Basic design calculation for the performance rating was
well evaluated using all the model equations in (13) to
(30). These design calculations are summarized as
A. Tube-Side Film Coefficient
The fundamental equation for turbulent heat transfer
inside tubes in given by perry and green (1997). [25]
Nu = 0.027 (Re)0.8
(Pr)0.33
(37)
Or
33.08.0
027.0 











=
W
WpW
W
ti
W
ii
K
CGD
K
Dh µ
µ
(38)
From equation 33, it was possible that,
hi = 0.027 33.08.0












w
ww
w
ti
i
w
K
CpGD
D
K µ
µ
(39)
Where hi is the tube side film coefficient
3.2 INTERNAL DIAMETER OF SHELL
The internal diameter of the shell can be calculated using
Reynold’s number (Re). when the Reynolds number is
less than 2100 we have a laminar flow but if the
Reynolds’s number is between 2100 and 10,000 then it is
in the transition regime. For turbulent flow of viscous
fluids the Reynold’s number is greater than 10,000. For a
baffled shell-and –tube exchanger, the turbulent regime is
preferred because it gives high heat transfer rates [21].
Taking Re = 10,100
Re = 100,10=
µ
DG (40)
D =
G
µRe
(41)
Where D – internal diameter of shell
Let as be the shell-side cross flow area, then
as
t
t
P
BCD **
= (42)
Where B - Baffle spacing = 1/5 (D)
For three shell passes, equation (37) is modified, Perry&
Green(1997) as
( )
t
t
s
P
BCD
a
**
3
1= (43)
3.3 SHELL-SIDE MASS VELOCITY
Let Gs be the shell side mass velocity, then
s
s
a
G
G 0
= (44)
The shell side equivalent diameter, De is given by
De =
( )
0
2
0
2
4/4
D
DP t
π
π−
(45)
3.4 SHELL-SIDE FILM COEFFICIENT
According to the Donohue equation, turbulent heat
transfer outside the tubes of a segmental baffled heat
exchanger is given by; [21]
( ) ( ) 33.06.00
re
s
PR
F
a
Nu = (46)
For tubes staggered in the tube bundles
6.133.00 == sFanda
Then equation (18) is written as
33.0
0
0
6.0
00
0
21.0 











=
K
CGD
K
Dh posee
µ
µ
(47)
3.5 FLUIDS PROPERTIES FOR SIMULATION
The heat exchanger model equations developed in section
2.0 contain unknown physical parameters such as the
density, viscosity, specific heat capacity, thermal
conductivity of the fluids. These physical parameters have
to be determined before equations (1) – (25) can be
evaluated. The operating conditions and physical
properties of the fluids specific for the heat exchanger are
presented in Table 1 and 2.
Table 1: Physical properties of Water
Physical Properties Values
Mass flow rate, Gw 1.334 Kg/Sec
Inlet temperature, T1 25o
C
Outlet temperature, T2 85o
C

Average temperature, Tav 55o
C
Specific heat capacity at 55o
C, CPw 4.2KJ/Kg K
Thermal Conductivity at 55o
C, Kw 0.6W/mK
Fouling Resistance at 55o
C, Fs 0.00005K.m2
/W
Viscosity at 55o
C, µw 5.0x10-4
Kg/ ms
Table 2: Physical properties of Sulphuric acid
Physical Properties Values
Mass flow rate, Gp 0.3858 Kg/Sec
Inlet temperature, t1 95o
C
Outlet temperature, t2 97o
C
Average temperature, tav 96o
C
Specific heat capacity at 96o
C, CPa 1.38KJ/Kg K
Thermal Conductivity at 96o
C, Ka 0.25W/mK
Fouling Resistance at 96o
C, Ft 0.003K.m2
/W
Viscosity at 96o
C, µa 5.0x10-3
Kg/ms
3.6 TUBE SPECIFICATION
The heat exchanger tube dimensions, tube clearance, and
tube pattern as obtained in Perry chemical engineer’s
handbook are presented in Table 3.The standard tube
dimension chosen is ¾” by 20ft.
Table 3: Tube Specification
Property Dimension
Outside diameter of tube, DO 19.05mm
Thickness of tube, XW 2.11mm
Internal diameter of tube, Di 14.83mm
Tube clearance, Ct 5.95mm
Tube pitch, Pt 25.0mm
Length of tube, L 6.10m (or 20ft)
Tube pattern Square
IV. COMPUTATIONAL FLOW CHART
The computation of the functional parameters of the heat
exchanger as shown in fig.1 is implemented in MATLAB,
and the computer flow chart describing the computation is
illustrated in fig 5.
Fig.5: Flow Chart Describing the computation of
functional parameters of Isothermal CSTR heat
exchanger Unit.
V. RESULTS AND DISCUSSION
Model equations as developed in equations (23) to (35)
were simulated using matlab 2014b for overall heat
transfer coefficient, mass flow rate of cooling fluid, tube
site flow area and tube side mass flow velocity exploiting
the kinetic parameters. The results obtained are presented
and discussed below.
5.1 OVERALL HEAT TRANSFER COEFFICIENT
Fig. 6 give results of overhead heat transfer coefficient as
a function of fractional conversion for various CSAT
radius.
START
INITIALIZE
XA = 0.95
READ
TLDDxKCpttF
KCTTFCpKGFH
iHHttt
WWpWSaaaaAR
∆
∆
,,,,,,,,,,,
,,Re,,,,,,,,,,
021
210
π
µµ
( )
mTUCLMTDFi
M
TCCLMTD
CLogCtTTTCtTtTCCU
S
F
t
FCCCChCKXC
hiCCCCh
W
K
WW
CpC
Ws
GDeC
De
W
KCDD
t
pDe
sa
W
GsGtPBtCDsaDB
W
G
W
D
CCChi
a
K
aa
CpC
a
GDiCDi
a
KC
t
a
a
G
t
G
nLDi
t
aT
pW
CQ
W
G
A
X
A
FHQ
14
;;
13
/
11
);
12
(
13
);
12
/()
21
(
12
);
12
()
21
(
11
;
10
/1
98710
;
0
/1
9
;
11
/
118
/1
7
;33.0
6
6.0
54
021.0
0
/
6
;/
5
/
4
;
0
/2
0
4/24
/;3/;2.0;/Re
33.0
3
8.0
21
27.0;/
3
/
42
;/
1
;/
/;/;
0
∆∗=∗=∆=
=−−=−−−==
++++===
=∧∗∧∗∗=
∗=∗=
=∗Π∧∗−∧∗=
=∗∗∗=∗=∗=
∧∗∧∗∗=∗=
∗===
∗∗=∆∗=∗∗∆−=





µµ
π
µ
µ
µ
π
PRINT
XA; Q ; U; A ; N
XA = XA + 0.01
XA > 0.99
STOP
No
Yes

Fig.6: overall heat transfer coefficient vs conversion
The results shows that overall heat transfer coefficient
decreases with increase in fractional conversion and the
plot demonstrated non-linearity with characteristics
slope(Su) defined as;
WX =
∆3
-∆45
(48)
Therefore, a novel model to predict overall heat transfer
coefficient can be summarized in equation (48), thus;
= WY 0 − 1-"
#
( 1 − 1-" (49)
5.2 MASS FLOW RATE OF COOLING FLUID
Result of mass flow rate of cooling fluid as a function of
conversion for various CSAT radius and heat exchanger
number of tubes are presented in fig. 7.
Fig.7: Mass Flow Rate of Cooling Fluid versus
Fractional conversion
The results as presented in fig.7 show that mass flow rate
of cooling fluid of the heat exchanger decrease with
fractional conversion for various CSAT radius. A slope
(Sm) describing the characteristic behavior of non-
linearity is given as;
W =
∆3
Z ∆45
(50)
Now, we substituted the slope as in equation (50) into
(25) gives a summarized mass flow rate of cooling fluid
predictive model as a function fractional conversion for a
typical isothermal CSAT heat exchanger unit; thus
6 = W 0 − 1-"
#
( 1 − 1-" (51)
5.3 TUBE SIDE CROSS FLOW AREA
Simulation was carried out to study the parametric
behavior of kinetics data particularly fractional
conversion dependency on tube side cross-flow area of
heat exchanger. The results obtain are well presented in
figure 8 for various CSAT radius and tube side numbers.
Fig.8: Tube side cross-flow area versus fractional
conversion
The results as reflected in fig. 8 show great dependency of
heat exchanger tube side cross-flow area as a function of
isothermal CSAT fractional conversion for various radius
and tube numbers. Increase in heat exchanger tube side
cross-flow area increases CSAT fractional conversion at
constant temperature. The slope (Sa), which demonstrate
non-linearity, describing his characteristic behavior is
given as;
W[ = < =
>
(52)
Therefore simplified model for the simulation of heat
exchanger tube side cross-flow area as a function of
CSAT fractional conversion at constant temperature was
obtain by substituting equation (51) into (30), giving;
:; =
] !
! " # ! "
(53)
5.4 TUBE SIDE MASS FLOW VELOCITY
Computation is made for heat exchanger mass flow rate
as a function of CAST fractional conversion for various
radius and tube side numbers, and results obtained are
presented in figure 9.

Fig.9: Tube Side Mass flow Velocity versus fractional
conversion
The results as reflected in fig. 9 demonstrated tube side
mass flow velocity dependency on CSAT fractional
conversion at constant temperature for various radius and
number of tubes. Increase in tube side mass flow velocity
of the heat exchanger decreases fractional conversion.
The behavior is more pronounced at 50% conversion
signifying optimal operational limit of the hydration
process of sulphur trioxide. The slope (Stv) of the graphs
was deduced resulting in;
W;^ =
∆3 @ >
< =
(54)
Equations (54) and (36) were compared in order to
provide a summarized predictive model of heat exchanger
tube side mass flow velocity as function of CSAT
fractional conversion at temperature, thus;
6; = W;^ U 0 − 1-" 1 − 1-"(V1-
#
(55)
Interestingly, the simulated results were captured to
reflect the realities of the CSAT heat exchanger unit at
isothermal condition and are summarized in table 4. The
as presented for the designed heat exchanger unit are
primarily to ensure removal of the heat of reaction in the
reactor at isothermal condition.
Table 4: Summary of the designed heat exchanger
S/N Parameter Shell-side Tube-side
1 Fluid Material Water Sulphuric acid
2 Flow rate (Kg/hr) 1.334 0.3858
3 Inlet temperature
(o
C)
25 95
4 Out let temperature
(o
C)
85 97
5 Fouling (K.m2
/W) 0.00005 0.003
6 Type U – tube
7 Service To maintain
isothermal
condition
8 Overall heat transfer coefficient
(W/m2
K)
62.714
9 Heat duty (KJ/sec) 342.9914
10 LMTD (o
C) 31.4
11 Surface Area (m2
) 170.66m2
12 Shell internal diameter (m) 3.79
13 Number of Shells 3.0
14 Type of Arrangement Series
15 Baffle type Segmental
16 Baffle spacing (mm) 200
17 Number of tubes per shell 175
18 Tube length (m) 6.1
19 Tube outside diameter (mm) 19.05
20 Tube pitch (mm) 25
21 Tube pattern Square
22 Material of construction Hastelloy
VI. CONCLUSION
Novel models were developed to design heat exchanger to
control the heat generated per unit volume in a continuous
stirred tank reactor at constant temperature for the
production of sulphuric acid. The heat exchanger rating
models were developed and generalized from theoretical
consideration and capable of predicting sulphuric plant
dimensions under isothermal condition.
The matlab based simulated results shows that overall
heat transfer coefficient mass flow rate of cooling fluid,
tube side mass flow velocity decreases with increase in
fractional conversion and the plots demonstrated non-
linearity. Similarly, Increase in heat exchanger tube side
cross-flow area increases fractional conversion at
constant temperature. The behavior is more pronounced at
50% conversion signifying optimal operational limit for
sulphur trioxide hydration process.
In addition, the analogy as presented above portrayed
compatibility of the results simulated for overall heat
transfer area, mass flow rate of cooling fluid, tube side
cross flow area and tube side mass flow velocity as
function of kinetic parameters at isothermal condition.
NOMENCLATURE
A, total heat transfer area
At, area of one tube
as, shell side cross flow area
at, tube side cross flow area
B, baffle spacing
CPa, specific heat capacity of sulphuric acid
CPw, specific heat capacity of water
Ct, tube clearance
D, internal diameter of shell
De, shell side equivalent diameter
Di, internal diameter of tube
Dm, mean diameter of tube
DO, outside diameter of tube
Ft, mean temperature difference correction factor

[21]R. Mukherjee, “Effective Design Shell-and-Tube
Heat Exchangers,” Chemical Engineering Progress,
Vol. 2, Feb, 1998. pp 25.
[22]Sinnott, R.K. Coulson, J.M. and J.F. Richardson,
“Chemical Engineering,” Vol.6, 2nd
ed, Oxford:
Butherworth- Heinemann, 1998. pp. 223-618.
[23]A. Isachenkoiv, “Heat Transfer,” Moscow: MIR
publisher, 1977. Pp 86-87.
[24]L.C. Thomas, “Chemical Engineering,” New Jersey:
Prentice Hall Inc., 1992. pp. 1–12.
[25]R.H. Perry and D.W. Green, “Perry’s Chemical
Engineers’ Handbook,” 7th
ed. New York: McGraw-
Hill, 1997. Pp 11–36.
[26]C.J. Geankoplis, “Transport processes and
separation process principles (includes unit
operations)” 4th
ed. Asoke K. Ghosh, Prentice-hall of
India Private Limited, M-97, 2003. Pp. 291-296.
[27]C.A. Melo and F. V. Sauvanaud, “Kinetic and
Decay Cracking Model for a Micordowner Unit
Applied Catalysis, General, 287 (1), 2005. pp 34-36.
[28]R. K. Sinnott, J. M. Coulson, and Richardson, J. F.
Chemical Engineering, Chemical Engineering
Design, Volume 6, Fourth Edition, Published by
Elsevier India, 1015 pages, 2005.

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