Revisedre+reactors+and+fundamentals+of

PHARMACEUTICAL ENGINEERING

Reactors and Fundamentals of Reactors Design for Chemical Reaction

Dr. Sanju Nanda
M.Pharm, Ph.D. (IIT Delhi)
Dept. of Pharmaceutical Sciences
M.D. University
Rohtak – 124001
Haryana

(24-01-2008)

CONTENTS
Introduction
Batch Process
Continuous Process
Semi Batch Process
Catalytic Processes
Homogeneous Reactions
Heterogeneous Reactions
Reactor Geometry
Fundamentals of Reactor Design
Design Procedure and Reactor Designing
Reactor Designing- Mathematical Models
Basic Elements of Reactor Designing
Type of Reactor Models

Keywords
Chemical Reactions, Chemical Reactors, Batch, CSTR, Plug Flow, Reactor Designing.

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Introduction
A Chemical reaction is a process that results in the conversion of chemical substances. The
substance or substances initially involved in a chemical reaction are called reactants. These
reactants are characterized by a chemical change and they yield one or more products. These
products are generally different from the original reactants. Chemical reactions may be of
different nature depending on the type of reactants, type of product desired, conditions and
time of the reaction, for example, synthesis, decomposition, displacement, percipitation,
isomerization, acid-base, redox or organic reactions. These reactions are being given in
Table 1, stating their area of utility, advantages, limitations and examples.

Table 1 : Types Of Chemical Reactions

Type of Reaction Area of Utility Advantages Limitations Examples
Combinatio To synthesize new Two or more Some N2 + 3H2
n compounds reactants make on undesirable 2NH3
industrially useful byproducts may Nitrogen Hydrogen
compound be produced Ammonia
Decompositi Breakdown of More number of High energy Fractional distillation
on larger, unuseful useful products involved of petroleum and
compounds/ generated coke
A. complexes into
Inor smaller useful
gani compounds
c Substitution Salt formation Obtaining Sometimes lead 2KI + Pb
New compounds compounds of choice to (No3)2
formation which are otherwise unwanted/undesi Pot. Iodide Lead
available with red substitution Nitrate
difficulty 2KNO3 + PbI
Pot. Nitrate Lead
Iodide
Isomerizatio A chemical Physico-chemical Sometimes give Thalidomide
n compound properties may be undesirable
undergoes a modified. compounds
structural New compounds may
rearrangement be obtained
without any change
in the atomic
composition
Esterificatio A reaction between Important Limited to CH3CH2OH +
n an organic acid and pharmaceutical reaction between CH3COOH
an alcohol forming compounds including an organic acid Methanol
an ester and water. prodrugs can be or acid chloride Acetic Acid
B. prepared CH3CH2OOCH3 +
Orga H2O
nic Methyl Acetate
Hydrolysis A large molecule is New compounds may Just having water CH3COOCCH2CH3 +
split into two be formed present as the H2O
smaller molecules solvent does not Methyl propionate
in the presence of make a reaction CH3OH +
water a hydrolysis CH3CH2COOH
reaction Methanol Propionic
acid
Hydrogenati Hydrogen is added New saturated Needs the CH2=CH2+H2
on across a double compounds may be presence of a CH3CH3
bond or a triple synthesized catalyst Ethene
bond Ethane

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Substitution One small group in New compounds may Being an organic CH3CH2OH+HCl C
a molecule is be synthesized compound, H3CH2Cl+
replaced by another substitution Ethyl alcohol
small group reactions are not Ethyl chloride
so easy H2O

Chemical reactors are vessels designed to contain chemical reactions2. It is the site of
conversion of raw materials into products and is also called the heart of a chemical process.
The design of a chemical reactor where bulk drugs would be synthesized on a commercial
scale would depend on multiple aspects of chemical engineering. Since it is a very vital step
in the overall design of a process, designers ensure that the reaction proceeds with the highest
efficiency towards the desired output, producing the highest yield of product in the most cost
effective way.

Reactors are designed based on features like mode of operation or types of phases present or
the geometry of reactors. They are thus called:
• Batch or Continuous depending on the mode of operation.
• Homogeneous or Heterogeneous depending upon the phases present.

They may also be classified as :
• Stirred Tank Reactor, or
• Tubular Reactor, or
• Packed Bed Reactor, or
• Fluidized Bed Reactor,

depending upon the flow pattern and manner in which the phases make contact with each
other. A detailed comparison of various chemical reactors is tabulated in Table-2.

Table 2 : Comparison Of Chemical Reactors

S. Type of Principle of Advantages Limitations Area of
No. Reactor Working Application
1. Batch Reactor All reactants are • Suitable for small • Not Batch processes
added at the scale production suitable for are used in
commencement and • Suitable for large batch chemical (inks,
the product processes where a sizes dyes, polymers)
withdrawn at the range of different • It is a and food
completion of the products or grades closed industry
reaction. They are is to be produced system in
conducted in tanks in the same which once
attached with equipment the
impellers, gas • Suitable for reactants
bubbles or pumps. reactions are added
requiring long in the
reaction times reactor,
• Suitable for they will
reactions with come out as
superior products
selectivity only after
the
completion
of the
reaction
2. Continuous One or more fluid • Highly flexible • More Chemical

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Stirred Tank reagents are device complex industry
Reactor introduced into a • By products may and especially
(CSTR) tank reactor be removed in expensive involving
equipped with an between the than liquid/gas
impeller while the reaction tubular reactions
reactor effluent is • It is economically units
recovered. A stepped beneficial to • All
up concentration operate several calculations
gradient exists CSTRs in series or performed
in parallel. with
• Reaction can be CSTRs
carried out in assume
horizontal as well perfect
as vertical mixing
reactors • At steady
state, the
flow rate in
must equal
the flow
rate out,
otherwise
the tank
will
overflow or
go empty
3 Plug Flow One or more fluid • Higher efficiency • Not The tubular
Reactor (PFR) reagents are pumped than a CSTR of economical reactor is
through a pipe or the same volume for small specially suited
tube. These are • PFRs may have batches to cases needing
characterized by several pipes or considerable
continuous gradients tubes in parallel heat transfer,
of concentration in • Both horizontal where high
the direction of flow and vertical pressures and
operations are very high or
common very low
• They can be temperatures
jacketed occur
• Reagents may be
introduced at
locations even
other then inlet

Batch Process
A process in which all the reactants are added together at the beginning of the process and
products removed at the termination of the reaction is called a batch process. In this process,
all the reagents are added at the commencement and no addition or withdrawal is made while
the reaction is progressing (Fig. 1). Batch processes are suitable for small production and for
processes where a range of different products or grades is to be produced in the same
equipment for example, pigments, dye stuff and polymers.

Figure 1: Batch Process Figure 2: Continuous Process

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Continuous Process
A process in which the reactants are fed to the reactor and the products or byproducts are
withdrawn in between while the reaction is still progressing (Fig. 2). For example, Haber
Process for the manufacture of Ammonia. Continuous production will normally give lower
production costs as compared to batch production, but it faces the limitation of lacking the
flexibility of batch production. Continuous reactors are usually preferred for large scale
production.

Semi Batch Process
Process that do not fit in the definition of batch or a semibatch reactor is operated with both
continuous and batch inputs and outputs and are often referred to as semi continuous or semi-
batch. In such semi-batch reactors, some of the reactants may be added or some of the
products withdrawn as the reaction proceeds. A semi-continuous process can also be one
which is interrupted periodically for some specific purpose, for example, for the regeneration
of catalyst, or for removal of gas for example, a fermentor is loaded with a batch, which
constantly produces carbon dioxide, which has to be removed continuously. Another example
is chlorination of a liquid.

Catalytic Processes
Most of the chemical reactions either proceed in the presence of catalysts or increases their
yield in the presence of catalysts. A catalyst is a substance that, without itself undergoing any
permanent chemical change, increases the rate of a reaction. The rate of a catalytic reaction is
proportional to the amount of catalyst the contact with a fluid phase reagents. This is
proportional to the exposed area, efficiency of diffusion of reagents in and products out, type
of mixing (turbulent, etc). The assumption of perfect mixing cannot be assumed. A catalytic
reaction pathway is often multistep with intermediates that are chemically bound to the
catalyst. Since the chemical binding is also a chemical reaction, it may affect the reaction
kinetics. The behaviour of the catalyst is also a consideration. Particularly in high
temperature petrochemical processes, catalysts are deactivated by sintering, coking and
similar processes.

Homogeneous Reactions
Homogeneous reactions are those in which the reactants, products and any catalyst used form
one continuous phase; for example, gaseous or liquid. Homogeneous gas phase reactors will
always be operated continuously. Tubular (Pipe line) reactors are normally used for
homogeneous gas phase reactions; for example, in the thermal cracking of petroleum, crude
oil fractions to ethylene, and the thermal decomposition of dichloroethane to vinyl chloride.
Homogeneous liquid phase reactors may be batch or continuous. Batch reactions of single or
miscible liquids are almost invariably done in stirred or pump around tanks. The agitation is
needed to mix multiple feeds at the start and to enhance heat exchange with cooling or
heating media during the process.

Heterogeneous Reactions
In a heterogeneous reaction two or more phases exist and the overriding problems in the
reactor design is to promote mass transfer between the phases.
The possible combination of phases are :
1) Liquid-Liquid :- Liquid reactions of industrial importance are fairly numerous. For
example, reactions such as the nitration of toluene or benzene with mixed acids,
emulsion polymerizations, saponification, etc. Such reactions can be carried out in
any kind of equipment that is suitable for physical extraction, including mixer-settlers

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and towers of various kinds, for example empty or packed, still or agitated, etc.
Mechanically agitated tanks are favoured because the interfacial area can be made
large as much as 100 times that of spray towers. When agitation is sufficient to
produce a homogeneous dispersion and the rate varies with further increase of
agitation, mass-transfer rates are likely to be significant.

2) Liquid-Solid :- The solid may be a reactant or catalyst. For example, platinum acts as
a catalyst in the hydrogenation of oils. In the design of reactors for liquids in the
presence of granular catalysts, account must be taken of heat transfer, pressure drop
and contacting of the phases and sometimes provision for periodic or continuous
regeneration of deteriorated catalyst. Several different kinds of vessel configurations
for continuous processing are in commercial use. Most solid catalytic processes
employ fixed beds. Although fluidized beds have the merit of nearly uniform
temperature and can be designed for continuous regeneration, they cost more and
more, difficult to operate, require extensive provisions for dust recovery, and suffer
from back mixing.

3) Liquid-Solid Gas :- In reactions involving gas, liquid and solid phases, the solid
phase is generally a porous catalyst. For example, gasoline cracking using zeolite
catalysts. It may be in a fixed bed or it may be suspended in fluid mixture. In general,
the reaction occurs either in the liquid phase or at the liquid / solid interface. In trickle
bed reactors both phases usually flow down, the liquid as a film over the packing. In
flooded reactors, the gas and liquid flow upward through a fixed bed, the slurry
reactors keep the solids in suspension mechanically; the overflow may be a clear
liquid or a slurry, and the gas disengages from the vessel. In fluidized bed reactors a
stable bed of solids is maintained in the vessel and only the fluid phases flow through,
except for entrained very fine particles.

4) Solid-Solid :-Many reactions of solids are industrially feasible only at elevated
temperatures which are often obtained by contact with combustion gases, particularly
when the reaction is done on a large scale. For example, decomposition of azides,
diazo compounds and nitramines. A product of reaction also is often a gas that must
diffuse away from a remaining solid, sometimes through a solid product. Thus
thermal and mass-transfer resistances are major factors in the performance of solid
reactions.

5) Gas-Solid :- In some reactions, the solid either takes part in the reaction or act as a
catalyst. For example, finely divided nickel is used in the preparation of nickel
carbonyl (b.p. 420C). Other examples of solid /gas reactions include combustion of
solid fuels, atmospheric corrosion, manufacture of hydrogen by action of steam on
iron, chlorination of ores of uranium, titanium, zirconium and aluminum, conversion
of ferrous oxide to magnetic ferric oxide in contact with reducing atmosphere of CO
in combustion gases.

6) Gas-Liquid :- In certain processes, liquid may either take part in the reaction or act as
catalyst. Gas/liquid reaction processes are generally employed by the industry either
for the purpose of gas purification or the removal of relatively small amounts of
impurities such as CO2, CO, SO2, H2S, NO and others from air, natural gas, hydrogen
for ammonia, synthesis, etc. This type of reaction is also utilized in the manufacture
of pure products such as sulphuric acid, nitric acid, nitrates, phosphates, adipic acid,

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etc. or processes like hydrogenation, halogenation oxidation, nitration, alkylation, etc.
Bio-chemical processes such as fermentation oxidation of studies sludges, production
of proteins etc. are also examples of gas/liquid reactions. There could be at least three
ways in which the reaction between a gas and a liquid may be made to react, that is,
the gas may be either dispersed as bubbles in the liquid (Fig. 3), the liquid may be
dispersed as droplets in the gas (Fig. 4) or the liquid and gas are brought together as
their films over a packing or wall (Fig. 5). The choice between these models is critical
and is dependent on factors. Such as magnitude and distribution of the residence times
of the phases, the power requirements, the scale of the operation, etc.

Figure 3: Bubble Tower Figure 4: Spray Tower

Figure 5: Falling Liquid Film Figure 6: CSTR Jacketed

Figure 7: CSTR with Internal coils Figure 8: CSTR with Internal Tubes

Reactor Geometry
The reactors used for established processes are usually complex designs which have been
developed and evolved over a period of years to suit the requirements of the process, and are

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unique designs. However, it is convenient to classify reactor designs into the following broad
categories.
A. Stirred Tank Reactors :- Stirred tank agitated reactors consist of a tank fitted with a
mechanical agitator and a cooling jacket or coils (Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig.
10). They are operated as batch reactors or continuous reactors. Several reactors may
be used in series.

Figure 9: CSTR with External Heat Exchanger Figure 10: CSTR with Air Heater

The stirred tank reactor can be considered the basic chemical reactor; modeling on a large
scale the conventional laboratory flask. Tank sizes range from a few litres to several thousand
litres. They are used for homogeneous and heterogeneous liquid-liquid and liquid-gas
reactions and for reactions that involve freely suspended solids, which are held in suspension
by the agitation. As the degree of agitation is under the designers control, stirred tank reactors
are particularly suitable for reactions where good mass transfer or heat transfer is required.

When operated as a continuous process the composition in the reactor is constant and the
same as the product stream and except for very rapid reactions, this will limit the conversion
that can be obtained in one stage.

The power requirements for agitation will depend on the degree of agitation required and will
range from about 0.2kW/m3 for moderate mixing to 2kW/m3 for intense mixing.

B. Tubular Reactors : Tubular reactors are generally used for gaseous reactions, but are
also suitable for some liquid phase reactions. If high heat transfer rates are required
small diameter tubes are used to increase the surface area to volume ratio. Several
tubes may be arranged in parallel, connected to a manifold or fitted into a tube sheet
in a similar arrangement to a shell and tube heat exchangers. For high temperature
reactions the tubes may be arranged in a furnace.

C. Packed Bed Reactors :- There are two basic types of packed bed reactor; those in
which the solid is a reactant and those in which the solid is a catalyst (Fig.11 and Fig.
12).

In chemical process industries, the emphasize is mainly on the designing of catalytic
reactors. Industrial packed bed catalytic reactors range in size from small tubes, a few
centimeters diameter to large diameter packed beds. Packed-bed reactors are used for
gas and gas-liquid reactions. Heat-transfer rates in large diameter packed beds are

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poor therefore, where high heat-transfer rates are required, fluidised beds should be
considered.

Fig: 11: Packed Bed Reactor Fig. 12: Multibed Reactors with Interstage Heaters

D. Fluidised Bed Reactors :- A fluidized-bed reactor (Fig. 13) is a combination of the
two most common, packed-bed and stirred tank, continuous flow reactors. It is very
important to chemical engineering because of its excellent heat and mass transfer
characteristics. The essential features of a fluidised bed reactor is that the solids are
held in suspension by the upward flow of the reacting fluid. This promotes high mass
and heat transfer rates and good mixing. Heat-transfer coefficients in the order of 200
W/m2 0C to jackets and internal coils are typically obtained. The solids may be a
catalyst, a reactant in fluidized combustion processes or an inert powder, added to
promote heat transfer.Though the principal advantage of a fluidised bed over a fixed
bed is the higher heat transfer rate, fluidised beds are also useful where it is necessary
to transport large quantities of solids as part of the reaction processes, such as where
catalysts are transferred to another vessel for regeneration.Fluidisation can only be
used with relatively small sized particles, that is less than 300µm. This is the
limitation of the process.

Figure 13: Flow Distribution in a Fluidized bed Figure 14: Aerosol Nanoparticle Reactor

Fundamentals of Reactor Design
The design of a chemical reactor deals with multiple aspects of chemical engineering.
Chemical reactions, chemical energetics and equations/laws of thermodynamics play an
important role in the selection and design of chemical reactors.

Chemical Reactions: Brief representation of the chemical change in terms of symbols and
formulae of the reactants and products is called a chemical equation. For example, when zinc
reacts with hydrochloric acid, zinc chloride and hydrogen are produced.

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Zinc + Hydrochloric acid Zinc chloride + Hydrogen

If symbols and formulae of various reactants and products are used, the above reaction may
be represented as :

Zn + HCl ZnCl2 + H2 ……….…(1)

As per Dalton’s atomic theory that atoms are neither created nor destroyed during chemical
changes, therefore the number of atoms of various elements should be equal on the reactant
side as well as on the product side. Equations such as above, in which no attempt has been
made to equalize the number of atoms of various elements on both the sides are called
Skeleton equations. Therefore, in order to equitize the number of atoms of various elements,
various species are multiplied with appropriate numbers. This process is called balancing of
a chemical equation. The above equation (1) can be balanced by multiplying HCl with 2

Zn + 2 HCl ZnCl2 + H2 …………….(2)

A chemical equation in which the number of atoms to each element is equal on the reactant
side and product side is called a balanced equation.

A chemical equation, therefore must fulfill the following conditions:
a) It should represent, a true chemical change, and if a reaction is not possible between
certain substances, it cannot be represented by a chemical equation.
b) It should be balanced
c) It should be molecular, i.e. all the species should be represented in their molecular
form. For example, elementary gases like hydrogen, oxygen, etc., should be
represented as H2 and O2.

A chemical equation has both qualitative as well as quantitative significance. Qualitatively, a
chemical equation tells us the names of the various reactants and products. Quantitatively, it
expresses
a) The relative number of molecules of the reactants and products taking part in the
reaction.
b) The relative number of moles of reactants and products.
c) The relative volumes of gaseous reactants and products.

For example :

2H2 + O2 2H2O ………………..(3)

Qualitatively, it tells us that hydrogen and oxygen reacts to form water. Quantitatively, it
conveys the following information.
a) Two molecules of hydrogen react with one molecule of oxygen to form two
molecules of water.
b) Two moles of hydrogen react with one mole of oxygen to form two moles of water.
c) 4 g of hydrogen react with 32 g of oxygen to form 36 g of water.

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d) Two volumes of hydrogen react with one volume of oxygen to form two volumes of
water vapour.

The chemical equation can be made more informative by incorporating the following
changes:
a) The physical states of reactants and products can be indicated by using the
abbreviations, for example, (s) for solids, (l) for liquid, (g) for gas and (aq) for
aqueous solution. For example,

Zn(s) + 2HCl(aq) ZnCl2(aq) + H2(g) ……………..(4)

b) In order to indicate the strength of acid or base, dil for dilute or conc for concentration
is written before the formula of acid or base.

Zn(s) + 2 dil HCl(aq) ZnCl2(aq) + H2(g) …………….(5)

c) The reaction conditions such as presence of catalyst, temperature, pressure, etc., may be
written above the arrow between the reactants and products.
V2O5, 7750K
2SO2 (g) + O2(g) 2SO3(g) …………..(6)

d) Heat change taking place during the reaction may be expressed in any one of the
following two ways.

N2(g) + 3H2(g) 2NH3(g) + 93.6 KJ…………………….(7)
Or N2(g) + 3H2(g) 2NH3(g);
∆ H* = -9.36KJ

*∆H = change in enthalpy, that is heat evolved or absorbed in a reaction at constant
temperature and pressure. Enthalpy is the total energy associated with any system
which includes its internal energy and also energy due to environmental factors such
as pressure-volume conditions. It is denoted by H.

Chemical equations give the quantitative relationship between the reactants and the products.
This quantitative information can be utilized to carry out variety of calculations which are
required many a times, to assess the economic viability of the chemical process.

Calculations based on the quantitative relationship between the reactants and the products are
also referred to as Stoichiometry. The word stoichiometry is derived from the Greek words
Stoicheron meaning element and metron meaning measure. Stoichiometry is therefore, that
area of chemistry and chemical technology on which determination of quantities of reactants
and products of chemical reaction is based.

Chemical Energetics: Chemical reactions are always associated with energy changes. Quite
often, the energy change accompanying a chemical reaction is more significant than the
reaction itself. The branch of science which deals with the energy changes associated with
chemical reactions is called chemical energetics. The energy changes occurring during the
chemical reactions may not always appear as heat energy, but also as electrical energy, work
energy and radiant energy as well. Thus, it is evident that chemical reactions are

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accompanied by energy changes appearing in different forms. These energy changes take
place because during chemical reactions certain bonds are cleaved and certain new bonds are
formed. Energy is consumed during cleavage of bonds while energy is released during the
formation of bonds.

Thermodynamics: Since the bond energy varies from one bond to another, the chemical
reactions are always accompanied by absorption or release of energy. Most of the time the
energy is in the form of heat. Therefore, it becomes imperative that some concepts of
thermodynamics may be understood. Thermodynamcis literally means conversion of heat into
work and vice-versa because therm refers to heat and dynamics refers to movement.
Thermodynamics may, therefore, be defined as the branch of science which deals with the
quantitative relationship between heat and other forms of energies. When thermodynamics of
chemical processes is studied, it is often referred to as chemical thermodynamics.

Thermodynamics is primarily based upon three fundamental generalisations, popular as
Laws of Thermodynamics. They are :
1) First Law of Thermodynamics, which deals with the equivalence of different forms
of energies.
2) Second Law of thermodynamics, which deals with the direction of chemical change.
3) Third Law of thermodynamics, which helps to evaluate the thermodynamic parameter
like entropy.

Therefore, the design of an industrial chemical reactor must satisfy the following
requirements:
1. The chemical factors : The kinetics of the reaction. The design must provide
sufficient residence time for the desired reaction to proceed to the required degree of
conversion.
2. The mass transfer factors : With hetereogeneous reactions, the reaction rate may be
controlled by the rates of diffusion of the reacting species, rather than the chemical
kinetics.
3. The heat transfer factors : The removal or addition of the heat of reaction.
4. The safety factors :- The confinement of hazardous reactants and products and the
control of the reaction and the process conditions.
5. Economic factors : Minimum amount of money should be required to purchase and
operate. Normal operating expenses include energy input, energy removal, raw
material costs, labour, etc. Energy changes can come in the form of heating or
cooling, pumping, agitation, etc. The need to satisfy these are interrelated and often
contradictory factors makes reactor design a complex and difficult task. However, in
many instances one of the factors will predominate and will determine the choice of
reactor type and the design method.

Design Procedure and Reactor Designing
An industrial chemical reactor is a complex device in which heat transfer, mass transfer,
diffusion and friction must be considered and it must be safe and controllable. In large
vessels, problem of mixing of reactants, flow distribution, residence time distribution and

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efficient utilization of the surface of porous catalysts also arise. A successful commercial unit
is an economic balance of all these factors.

A general procedure for reactor design is outlined below:
1. The kinetic and thermodynamic data on the desired reaction is initially collected.
Values will be needed for the rate of reaction over a range of operating conditions, for
example, pressure, temperature, flow rate and catalyst concentration. This data may
be normally obtained from either laboratory or pilot plant studies.
2. Data on physical properties is required for the design of the reactor. This may be
either estimated, or collected from the literature or obtained by taking laboratory
measurements.
3. The rate controlling mechanism which has a predominant role is then identified, for
example, kinetic, mass or heat transfer.
4. A suitable reactor type is then chosen, based on experience with similar studies or
from the laboratory and pilot plant work.
5. Selection of optimal reaction conditions is initially made in order to obtain the desired
yield
6. The size of the reactor is decided and its performance estimated. Since exact
analytical solutions of the design relationship are rarely possible, semiemperical
methods based on the analysis of idealized reactors are used.
7. Materials for the construction of the reactor is/are selected.
8. A preliminary mechanical design for the reactor including the vessel design, heat
transfer surfaces etc., is made.
9. The design is optimized and validated
10. An approximate cost of the proposed and validated design is then calculated.

In choosing the reactor conditions, and optimizing the design, the interaction of the reactor
design with the other process operations must not be overlooked. The degree of conversion
of raw materials in the reactor will determine the size and the cost of any equipment needed
to separate and recycle unreacted materials. In these circumstances the reactor and associated
equipment must be optimized as a unit.

Reactor Designing – Mathematical Models
Chemical reactors are vessels designed to contain chemical reactions. The design of a
chemical reactor deals with multiple aspects of chemical engineering including mathematical
modeling. A model of a reaction process is a set of data and equation that is believed to
represent the performance of a specific vessel configuration (mixed, plug flow, laminar,
dispersed, etc.). Chemical engineers, design reactors to maximize net present value for the
given reaction. Designers ensure that the reaction proceeds with the highest efficiency
towards the desired output product, producing the highest yield of product. The equations
used in mathematical modeling include the stoichiometric relations, rate equations, heat and
material balances and auxiliary relations such as those of mass transfer, pressure variation,
residence time distribution, etc.

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The data not only describe physical and thermodynamic properties but also the economic
factors. Correlations of heat and mass – transfer rates are fairly well developed and can be
incorporated in models of a reaction process, but the chemical rate data must be determined
individually. Since equipments are now widely available to obtain such data, hence an initial
exploratory work can be carried out.

Once fundamental data is obtained, the goal is to develop a mathematical model of the
process, which may be further utilized to explore possibilities such as product selectivity,
start-up and shut down behaviour, vessel configuration, temperature, pressure and
conversion profiles, etc.

Any mathematical model has two components, the symbols in which it is expressed and their
relationship to the quantities in the real world and the equations that link the symbols and
through which the values of certain variables are computed. These two elements normally co-
evolve, but they are often separated for the sake of presentation into the parameter and
variable definitions and their equations.

Principle: First a mechanism is assumed and then a model is designed accordingly, for
example, whether the reaction is steady or unsteady, completely mixed, or plug flow or
laminar or with dispersion or with bypass or recycle or dead space, etc.

Then, for a differential element of space and/or time, the elements of conservation are
formulated and put together.

Inputs + Sources = Outputs + Sinks + Accumulations
Any transport properties are introduced through known correlations together with the
parameters of specified rate equations. The model can be used to find the performance under
various conditions, or its parameters can be evaluated from experimental data.

Basic Elements of Reactor Designing
Reactions are carried out as batches or with continuous streams through a vessel. There are
two main basic vessel types, viz.;
• Tank Reactor – a tank
• Tubular Reactor – a pipe or tube
Most commonly, reactors are run at a steady-state, but can also be operated in a transient
state. Transient state is a state in which the key process variables like residence time, volume,
temperature, pressure or concentration of chemical species, etc., change with time. Such a
situation generally arises when either the reactor is purchased new or is brought back in
operation after maintenance or inoperation. Chemical reactors may be designed keeping in
view the various process variables. Key process variables include:
• Residence Time Distribution (τ)
• Volume (v)
• Temperature (T)
• Pressure (P)
• Concentrations of chemical species (C1, C2, C3------C4)
• Heat transfer coefficients (h, U)

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Residence Time Distribution (RTD) (τ): The residence time distribution (RTD) of a
chemical reactor or vessel is a description of the time that different fluid elements spend
inside the reactor. The concept was first proposed by MacMullin and Weber in 1935, but was
not used extensively until P.V. Danckwerts analyzed a number of important RTDs in 19533.

RTD will vary from one reactor type to another. For example, an ideal plug flow reactor has a
fixed residence time. Any fluid that enters the reactor at time ‘t’ will exit the reactor at time t
+ τ, where τ is the residence time of the reactor.

Flow reactors are distinguished by the degree of mixing of successive inputs. The ideal
situations are
1) Complete mixing :- For example Continuous Stirred Tank Reactor (CSTR) (Fig. 6),
and
2) No axial mixing – For example, Plug Flow Reactor (PFR)

Real reactors deviate more or less from these ideal behaviours. Deviations may be detected
with RTDs obtained with the aid of tracer tests. The commonest models are combinations of
CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely
mixed in the vicinity of the impeller or a plug flow near outlet.

Heat Transfer
Temperature affects rates of reaction, degradation of catalysts and equilibrium conversion.
Many reactors with fixed beds of catalysts pellets have divided beds, with heat transfer
between the individual sections. Such units can take advantage of initial high rates at high
temperatures and higher equilibrium conversions at lower temperatures.

Since reactors come in a variety of configurations with a variety of operating modes and may
handle mixed phases, the design of provisions for temperature control draws on a large body
of heat transfer theory and data.

Mass Balance
A mass balance (also called a material balance) is an accounting of material entering and
leaving a system7. Fundamental to the balance is the conservation of mass principle, i.e., that
matter can not disappear or be created. Mass balances are used, for example, to design
chemical reactors, analyse alternative processes to produce chemicals, in pollution dispersion
models, etc. In environmental monitoring the term budget calculations is used to describe
mass balance equations where they are used to evaluate the monitoring data (comparing input
and output, etc.). The dynamic energy budget theory for metabolic organisation makes
explicit use of time, mass, and energy balances.

The mass that enters a system must (conservation of mass principle) either leave the system
or accumulate within the system, i.e.

IN = OUT + ACC ……………………………..(8)

where IN denotes what enters the system, OUT denotes what leaves the system and ACC
denotes accumulation within the system (which may be negative or positive). Mass balances
are often developed for total mass crossing the boundaries of a system, but they can also
focus on one element (e.g. carbon) or chemical compound (e.g. water). When mass balances

16

are written for specific compounds, number of individuals in a population, etc. rather than for
the total mass of the system, a production term (PROD) is introduced such that

IN + PROD = OUT + ACC ……………………………(9)

The PROD describes the chemical reaction rates, the difference between births and deaths,
etc. PROD might be positive or negative, just as for ACC.

Mass balances are either Integral Mass Balances or Differential Mass Balances. An integral
mass balance is a black box approach and focus on the overall behaviour of a system whereas
a differential mass balances focuses on mechanisms within the system (which in turn affect
the overall behavior).

Integral Mass Balance is made by initially identifying the system boundaries, that is, how the
system is connected to the rest of the world and how the rest of the world influences the
system. For example, for a tank reactor the walls of the tank are the system boundaries and
the outer world influences the system through the inlet and outleet. Differential mass balance
is described by assuming the interior of the systems, for example, a perfectly mixed
(homogeneous) system. Based on these basic descriptions of the system and its boundaries,
reactor models are described. They are either
1. Ideal (continuously stirred) Batch reactor
2. Ideal tank reactor, also named Continuously Stirred Tank Reactor (CSTR)
3. Ideal Plug Flow Reactor (PFR)

Ideal Batch Reactor: It is a closed system. The mass balance for a substance ‘A’ becomes

IN + PROD = OUT + ACC

……………………………………(10)

where rA denote the rate at which substance A is produced, V is the volume (which may be
constant or not), nA the number of moles (n) of substance A.

In a fed-batch reactor some reactants/ingredients are added continuously or in pulses.

Ideal tank reactor/Continuously Stirred Tank Reactor: It is an open system. A lake can
be regarded as a tank reactor and lakes with long turnover times (e.g. with a low flux to
volume ratio) can for many purposes be regarded as continuously stirred (e.g. homogeneous
in all respects). The mass balance becomes

IN + PROD = OUT + ACC

………………………………….(11)

where Q0 and Q denote the volumetric flow in and out of the system respectively and CA,O
and CA the concentration of A in the inflow and outflow respective.

17

Ideal Plug Flow Reactor (PFR): It is an open system with no mixing along the reactor
but perfect mixing across the reactor. It is often used for systems like water pipes, if the flow
is turbulent. When a mass balance is made for a tube, an infinitesimal part of the tube is first
considered and a mass balance is made using the ideal tank reactor model. That mass balance
is then integrated over the entire reactor volume to obtain:

…………………………………….(12)

More complex problems: In reality, reactors are often non-ideal, in which combinations of
the reactor models above are used to describe the system. Not only chemical reaction rates,
but also mass transfer rates may be important in the mathematical description of a system,
especially in heterogeneous systems. As the chemical reaction rate depends on temperature it
is often necessary to make both an energy balance (often a heat balance rather than a full
fledged energy balance) as well as mass balances to fully describe the system. A different
reactor models might be needed for the energy balance: A system that is closed with respect
to mass might be open with respect to energy because since heat may enter the system
through conduction.

Types of Reactor Models
There are three main basic models used to estimate the most important process variables of
different chemical reactors.
• Batch Reactor Model (Batch)
• Continuous Stirred-Tank Reactor Model (CSTR) and
• Plug Flow Reactor Model (PFR)
These basic models may be modified as per requirement of a chemical process.

Batch Reactor Models: Batch reactors are used in batch processes. Batch processes are
suited to small production rates, to long reaction times, or to reactions, where they may have
superior selectivity, as in some polymerizations.

They are conducted in tanks with stirring of the contents by internal impellers, gas bubbles
or pump around. Control of temperature is done with the help of jackets, reflux condensers or
pump around through an exchanger.

Batch processes are currently used in the chemical and food process industries. Their
automation and optimization pose difficult issues mainly because it is necessary to operate
concurrently with countinous (algebric or differential equations) and discrete (state machines)
models. Andreu et al14, have tried to analyse how techniques developed in the field of
discrete manufacturing systems (DMS) can be extended to batch systems.

A semi-batch reactor is operated with both continuous and batch inputs and outputs. A
fermentor, for example, is loaded with a batch which constantly produces carbon dioxide,
which has to be removed continuously. Similarly, in a reaction like chlorination, where one
of the reactant is gas (chlorine), if it is introduced continuously, most of it bubbles off,
therefore a continuous feed of gas is injected into the batch of a liquid.

Large daily production rates are mostly conducted in continuous equipment, either in a series
of stirred tanks or in units in which some degree of plug flow is attained.

18

Continuous Stirred Tank Reactor (CSTR) Model : In a CSTR, one or more fluid reagents
are introduced into a tank reactor equipped with an impeller while the reactor effluent is
recovered. The impeller stirs the reagents to ensure proper mixing. Therefore, it can be seen
that in these reactors, reactants are continuously fed to the first vessel, they overflow through
the others in succession, while being thoroughly mixed in each vessel. Though the
composition is uniform in individual vessels, but a stepped concentration gradient exists in
the system as a whole.

The average amount of time spent by a discrete quantity of reagent inside the tank or the
residence time can be obtained by simply dividing the volume of the tank by the average
volumetric flow rate through the tank. The expected completion rate of the reaction, in
percent can be calculated using chemical kinetics.
Some important aspects of the CSTR are :
• All calculations performed with CSTRs assume perfect mixing.
• The reaction proceeds at the reaction rate associated with the final (output)
concentration.
• At steady state, the flow rate in must equal the mass flow rate out, otherwise the tank will
overflow or go empty (transient state).
• It is often economically beneficial to operate several CSTRs in series or in parallel. A
series of five or six vessels may behave like a plug flow reactor. This allows the first
CSTR to operate at a higher reagent concentration and therefore a higher reaction rate. It
is also possible that instead of being in distinct vessels, the several stages of a CSTR
battery can be put in a single shell.
• If horizontal, the multistage reactor is compartmented by vertical wires of different
heights, over which the reacting mixture cascades.
• When the reactants are of limited miscibilities and have a sufficient density difference,
the vertical staged reactor lends itself to counter current operation. This can be
advantageous for reversible reactions.
• A small fluidized bed is essentially completely mixed. A large commercial fluidized bed
reactor is a nearly uniform temperature, but the flow patterns consist of mixed and plug
flow and in-between zones.

The CSTR model is used to estimate the key unit operation variables when using a continuous
agitated tank reactor to reach a specified output. The mathematical model works for all fluids
: liquids, gases and slurries.

Perfect Mixing: This is a fair assumption due to the fact that it merely requires the region of
variable composition at the inlet area is very small when compared to the entire reactor
contents and the time required to mix tank contents is very small when compared to the
residence time of the reactor. This is required due to the strong dependence of the reaction
rate on the concentration of the reagent species.

[accumulation] = [in] – [out] + [generation] …………………………(13)

d Ni = Fio – Fi + Vvir - - - - - - - (i) …………………………(14)
dt

19

Where Fio is the molar flow rat of species ‘i’
Ni no. of species ‘i’
vi is the stoichiometric coefficient
r is the reaction rate

As the temperature increases, the rate of reaction also changes.
Plug Flow Reactor (PFR) Model: In a PFR, one or more fluid reagents are pumped
through a pipe or tube. It is also referred to as Tubular Flow Reactors (TFRs).
• PTRs may have several pipes or tubes in parallel,. The reactants are charged
continuously at one end and products are removed at the other end.
• The chemical reaction proceeds as the reagents travel through the PFR.
• In this type of reactor, the reaction rate is gradient, that is, at the inlet to the PFR the rate
is very high, but as the concentrations of the reagents decrease and the concentration of
the product(s) increases the reaction rate slows. Normally a steady state is attained.
• Both horizontal and vertical operations are common.
• When heat transfer is needed, individual tubes are jacketed or shell and tube construction
is used. In the latter case, the reactants may be on either the shell or the tube side.
• The reactant side may be filled with solid particles, either catalytic (if required) or inert,
to improve interphase contact in heterogeneous reactions.
• Large diameter vessels with packing or trays may approach plug flow behaviour and are
widely employed.
• Some of the configurations in use are axial flow, radial flow, multiple shell with built in
heat exchangers, horizontal, vertical and so on.

Some important aspects of the PFR are :

• All calculations performed with PFRs assume no upstream or downstream mixing, as
implied by the term “plug flow”.
• Reagents may be introduced into the PFR at locations in the reactor other than the inlet.
In this way a higher efficiency may be obtained, or the size and cost of the PFR may be
reduced.
• A PFR typically has a higher efficiency than a CSTR of the same volume. That is, given
the same space-time, a reaction will proceed to a higher percentage completion in a PFR
than in a CSTR.

For most chemical reactions, it is impossible for the reaction to proceed to 100% completion.
The rate of reaction decreases as the percent completion increases until the point where the
system reaches dynamic equilibrium (no net reaction, or change in chemical species occur).
The equilibrium point for most systems is less than 100% complete. For this reason a
separation process such as distillation often follows a chemical reactor in order to separate
any remaining reagents or by products from the desired product. These reagents may
sometimes be reused at the beginning of the process, such as in the Haber process.

The PFR model is used to estimate the key unit operation variables when using a continuous
tubular reactor to reach a specified output. The mathematical model works for all fluids :

20

liquids, gases and slurries. In a PFR the fluid passes through a coherent manner, so that the
residence time ‘τ’, is the same for all fluid elements. The coherent fluid passing through the
ideal reactor is known as a plug. As a plug flows through a PFR, the fluid is perfectly mixed
in the radial direction but not in the axial direction (forwards or backwards). Each plug of
differential volume is considered as a separate entity (practically a batch reactor) As it flows
down the tubular PFR.

Application of PFRs (Also see Table 2): PFRs are used to model the chemical
transformation of compounds as they are transported in systems resembling pipes. Plug flow
reactors are used for some of the following applications:
• Large scale reactions
• Fast reactions
• Homogeneous or Heterogeneous Reaction
• Continuous Production
• High Temperature Reactions

An ideal pug flow reactor has a fixed residence time, that is, any fluid (plug) that enters the
reactor at time ‘t’ will exist the reactor at time ‘t+τ’, where ‘τ’ is the residence time of the
reactor. A real plug flow reactor has a residence time distribution that is a narrow pulse
around the mean residence time distribution.

Plug flow reactors have a high volumetric unit conversion run for long periods of time
without labour, and have excellent heat transfer. The limitations encountered with plug flow
reactors are that temperatures are difficult to control and can result in undesirable temperature
gradients. It is more expensive.

Catalytic Reactors
Although catalytic reactors are often implemented as plug flow reactors, their analysis
requires more complicated treatment. The rate of a catalytic reaction is proportional to the
amount of catalyst the reagents contact. In case of solid phase catalyst and fluid phase
reagents, the rate of reaction is proportional to the exposed area, efficiency of diffusion of
reagents in and products out, and turbulent mixing or lack thereof.

A catalytic reaction pathway, in fact, is often multi step reaction because not only the initial
reactants will bound to the catalyst but even some intermediates may bind to the catalyst and
pose as a chemical reaction.

The behaviour of the catalyst is also important in the kinetics of this reaction particularly in
high temperature petrochemical processes, catalysts are deactivated by sintering, coking and
similar processes.

Application of plug flow reactors in allied fields based on new technologies:
• Plug- flow reactors for biomass conversion: The experiments are conducted in a
continuous high pressure plant made from stainless steel. The pressure can be set to a
maximum of 35 MPa. There are several reactor sizes available so that residence times
from 0.5 to 600 seconds can be covered. In order to reach temperatures above 300 °C
two electrically heated reactors can be used. They cover residence times up to 250 resp.
180 seconds. The feed solutions are delievered via HPLC-pumps.

21

• Aerosol nanoparticle plug flow reactors (APFR): There is considerable interest in the
synthesis and use of nanosized particles for a variety of applications including
superalloys and thick film conductors for the electronics industry. Furthermore, other
areas of interest include measurements of magnetic susceptibility, far-infrared
transmission and nuclear magnetic resonance. For these systems, it is necessary to
produce fine particles of controlled size. Particle sizes can typically be in the range from
10 to 500 nm.

Owing to their size, shape, and high specific surface area, these particles can also be used in
pigments in cosmetics, membranes, photo catalytic reactors, catalysts and ceramic and
catalytic reactors. Examples of uses of nanoparticles include SnO2 for carbon monoxide gas
sensors, TiO2 for fiber optics, SiO2 for fumed silica and optical fibers, carbon for carbon
black fillers in tyres, iron for recording materials, nickel for batteries and to a lesser extent
palladium, magnesium, bismuth and others; all these materials have been synthesized in
aerosol reactors. In the bioarea, nanoparticles are used to prevent and treat wound infections
in artificial bone implants, and for use in imaging the brain.

Example of APFR : production of aluminum particles (Fig. 14). A stream of argon gas
saturated with aluminum vapor is cooled in a APFR, with a diameter of 18 mm and a length
of 0.5 m, from 1600°C at a rate of 1000°C/sec. As the gas stream flows through the reactor,
the nucleation and growth of aluminum particles take place. Flow rate of the carrier gas is 2
dm3/min and the pressure inside the PFR is 1 atm (1.013 Pa). Moving with the gas velocity U,
the cooling rate inside the reactor is 1000 K/s and hence the temperature profile down the
reactor is given by:

…………………..(15)

As it moves down the reactor the gas gets cooled and becomes supersaturated. Thus super
saturation leads to the nucleation of particles. This nucleation is a result of molecules
colliding, escaping (evaporating) and agglomerating until a critical nucleus size is reached
and a particle is formed. As these particles move down the supersaturated gas molecules
condense on the particles causing them to grow in size.

Conclusion
Pharmaceutical substances are basically chemicals showing therapeutic effects. After their
safety, efficacy and bioavailability is established, these substances are given the status of
drugs by the drug regulatory bodies and allowed to be produced on industrial scale for
commercial purposes. These drugs which are required to be synthesized in bulk are produced
in special vessels called reactors. An industrial chemical reactor is a complex device in which
heat transfer, mass transfer, diffusion and friction may occur along with chemical reaction
and it must be safe and controllable. The design of these chemical reactors require a good
understanding of multiple aspects of pharmaceutical engineering because in large vessels,
question of mixing of reactants, flow distribution, residence time distribution and efficient
utilization of the surface of porous catalysts also arise. The selection of the type of reactor
will be dictated by the type of reaction type, type of reactants, time of reaction and conditions
of reaction. A knowledge of various aspects of pharmaceutical (chemical) engineering would
help the engineers to design, and select such reactors in which the resources are optimally
utilized and the reaction proceeds with highest efficiency giving the best possible yields.

22

References
1. Verma, N.K., Khanna, S.K. and Kapila, B, ‘Comprehensive Chemistry,’ Laxmi Publications (P) Ltd.,
New Delhi, 2003-04.
2. Coulson, J.M., Richardson, J.P. Sinnott, R.K., ‘Chemical Engineering : An introduction to Chemical
Engineering Design, Vol 6, Pergamon Press, London, 3rd Ed., 2000.
3. Chemical Reactors, Section 23, Walas, Stanely M. In Perrys Chemical Engineering Handbook, Seventh
Edition, Editors, Green D.W. and Maloney, James, O, The McGraws Hill Companies Inc, 1999.
4. ‘Fluidized Bed Reactor’, www.rpi.edu/Dept/Chem-eng/Biotech-Environ/IMMOB/Fluidized/bed.htm
accessed in may 2007.
5. ‘Semibatch Reactors’ www.engin.umich.edu/~CRE/asyLEARN/bits/semibatch/index.htm accessed in
May 2007
6. Tyner D, Soroush, M, Grady MC, Richards, J and Congalidis, J.P., ‘Mathematical Modelling and
Optimization of a Semibatch Polymerization Reactor’, www.physics.udel.edu/~richards/ADCHEM_
2000 Paper.pdf, accessed in May 2007.
7. ‘Mass Balance’ en.wikipedia.org/wiki/Mass-balance, accessed in May 2007.
8. ‘Stirred Chemical Laboratory, Pilot – Plant Reactors’, CSTRs, Autoclaves and fixed bed reactors’,
www.pdc machines.com/Benefit_SR.htm, accessed in May 2007.
9. ‘Chemical Reactors’ en.wikipedia.org/wiki/chemical-reactors, accessed in May 2007.
10. ‘Types of Continuous Stirred Tank Reactor’, coweb.cc.gatech.edu/process.accessed in May 2007.
11. ‘Continuous stirred-tank reactor model’; http://en.wikipedia.org/wiki/continuous_stirred_tank_reactor,
accessed in May 2007.
12. ‘Plug-flow reactors for biomass conversion’, www.ct.chemie.tudarmstadt.de/ak_vogel/lott/lott_
analge_en.html, accessed in May 2007.
13. ‘Plug flow reactor model’, http://en.wikipedia.org/wiki/plug-flow-reactor-model, accessed in May
2007.
14. Andreu, D, Pascal, JC Pingaud, H and Valette, R, ‘Batch Process modeling using Petrinets’,
www./aas.fr/~robert/hybrid.d/ieeesmc94-b.html, accessed in May 2007.
15. ‘Plug Flow Reactor Example’, www.owl.net.rice.edu/~ceng4003/hysys/pfex.htm, accessed in May
2007.
16. ‘Aerosol nanoparticle Plug Flow Reactors’, www.eengine.umich.edu/~CER/web_mod/aerosol/
frame01_introd/introduction.html, accessed in May 2007
17. ‘Residence Time Destribution’, Wikipedia the free encyclopedia, http:/lenwikipedia.orgwiki/
residence_time_distribution, accessed in May 2007

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