Chemical Reaction Engineering

Relevant Course: Nil

Relevant Department : Chemical Engineering 

Relevant Semester: 5th

Pre-requisite: Nil

Course Description & Outline :

   The information required for the design and operation of Chemical Reactors, which are the heart of any chemical process, will be presented. Background theory and applications will be discussed.

Schedule for Lecture Delivery

Session 1 : 3rd Aug 2015  (10-12 noon)

Session 2 : 4th Aug 2015  (10-12 noon)

Session 3 : 7th Aug 2015  (2-4 PM)

Teacher Forum

Introduction to Reactor Design

Introduction to Reactor Design

In reactor design we want to know what size and type of reactor and method of operation are best for a given job. Because this may require that the conditions in the reactor vary with position as well as time, this question can only be answered by a proper integration of the rate equation for the operation. This may pose difficulties because the temperature and composition of the reacting fluid may vary from point to point within the reactor, depending on the endothermic or exothermic character of the reaction, the rate of heat addition or removal from the system, and the flow pattern of fluid through the vessel. In effect, then, many factors must be accounted for in predicting the performance of a reactor. How best to treat these factors is the main problem of reactor design. Equipment in which homogeneous reactions are effected can be one of three general types; the batch, the steady-state flow, and the unsteady-state flow or semibatch reactor. The last classification includes all reactors that do not fall into the first two categories. These types are shown in Fig.1. 

Figure 1. Broad classification of reactor types. (a) The batch reactor. (b) The steady-state flow reactor. (c), (d), and (e) Various forms of the semibatch reactor.

Let us briefly indicate the particular features and the main areas of application of these reactor types. Naturally these remarks will be amplified further along in the text. The batch reactor is simple, needs little supporting equipment, and is therefore ideal for small-scale experimental studies on reaction kinetics. Industrially it is used when relatively small amounts of material are to be treated. The steady-state flow reactor is ideal for industrial purposes when large quantities of material are to be processed and when the rate of reaction is fairly high to extremely high. Supporting equipment needs are great; however, extremely good product quality control can be obtained. As may be expected, this is the reactor that is widely used in the oil industry. The semibatch reactor is a flexible system but is more difficult to analyze than the other reactor types. It offers good control of reaction speed because the reaction proceeds as reactants are added. Such reactors are used in a variety of applications from the calorimetric titrations in the laboratory to the large open hearth furnaces for steel production.

The starting point for all design is the material balance expressed for any reactant (or roduct). Thus, as illustrated in Fig. 2, we have

Figure 2 Material balance for an element of volume of the reactor

 Where the composition within the reactor is uniform (independent of position), the accounting may be made over the whole reactor. Where the composition is not uniform, it must be made over a differential element of volume and then integrated across the whole reactor for the appropriate flow and concentration conditions. For the various reactor types this equation simplifies one way or another, and the resultant expression when integrated gives the basic performance equation for that type of unit. Thus, in the batch reactor the first two terms are zero; in the steady-state flow reactor the fourth term disappears; for the semibatch reactor all four terms may have to be considered.

In nonisothermal operations energy balances must be used in conjunction with material balances.

Figure 3 Energy balance for an element of volume of the reactor

 Thus, as illustrated in Fig.3, we have

 

 Again, depending on circumstances, this accounting may be made either about a differential element of reactor or about the reactor as a whole. The material balance of Eq. 1 and the energy balance of Eq. 2 are tied together by their third terms because the heat effect is produced by the reaction itself. Since Eqs. 1 and 2 are the starting points for all design, we consider their integration for a variety of situations of increasing complexity in the chapters to follow.

When we can predict the response of the reacting system to changes in operating conditions (how rates and equilibrium conversion change with temperature and pressure), when we are able to compare yields for alternative designs (adiabatic versus isothermal operations, single versus multiple reactor units, flow versus batch system), and when we can estimate the economics of these various alternatives, then and only then will we feel sure that we can arrive at the design well fitted for the purpose at hand. Unfortunately, real situations are rarely simple.

Symbols and Relationship between CA and XA

Figure 4 Symbols used for batch reactors.

For the reaction with inerts iI, Figs.4 and 5 show the symbols commonly used to tell what is happening in the batch and flow reactors. These figures show that there are two related measures of the extent of reaction, the concentration CA and the conversion XA. However, the relationship between CA and XA is often not obvious but depends on a number of factors. This leads to three special cases, as follows.

Figure 5 Symbols used for flow reactors.

Special Case 1. Constant Density Batch and Flow Systems. This includes most liquid reactions and also those gas reactions run at constant temperature and density. Here CA and XA are related as follows:

To relate the changes in B and R to A we have

Special Case 2. Batch and Flow Systems of Gases of Changing Density but with T and π constant.

Here the density changes because of the change in number of moles during reaction. In addition, we require that the volume of a fluid element changes linearly with conversion, or

To follow changes in the other components we have

Special Case 3. Batch and Flow Systems for Gases in General (varying p, T, π) which react according to 

 Pick one reactant as the basis for determining the conversion. We call this the key reactant. Let A be the key. Then for ideal gas behavior,

 

Forum for Introduction to Reactor Design

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Ideal Reactors for a Single Reaction

Ideal Reactors for a Single Reaction

In this chapter we develop the performance equations for a single fluid reacting in the three ideal reactors shown in Fig.6. We call these homogeneous reactions. Applications and extensions of these equations to various isothermal and nonisothermal operations are considered in the following four chapters.

In the batch reactor, or BR, of Fig.6a the reactants are initially charged into a container, are well mixed, and are left to react for a certain period. The resultant mixture is then discharged. This is an unsteady-state operation where composition changes with time; however, at any instant the composition throughout the reactor is uniform. 

The first of the two ideal steady-state flow reactors is variously known as the plug flow, slug flow, piston flow, ideal tubular, and unmixed flow reactor, and it is shown in Fig.6b. We refer to it as the plugpow reactor, or PFR, and to this pattern of flow as plugpow. It is characterized by the fact that the flow of fluid through the reactor is orderly with no element of fluid overtaking or mixing with any other element ahead or behind. Actually, there may be lateral mixing of fluid in a plug flow reactor; however, there must be no mixing or diffusion along the flow path. The necessary and sufficient condition for plug flow is for the residence time in the reactor to be the same for all elements of fluid.

Figure 6 The three types of ideal reactors: (a) batch reactor, or BR; (b) plug flow reactor, or PFR; and (c) mixed flow reactor, or MFR.

The other ideal steady-state flow reactor is called the mixed reactor, the backmix reactor, the ideal stirred tank reactor, the C* (meaning C-star), CSTR, or the CFSTR (constant flow stirred tank reactor), and, as its names suggest, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. We refer to this type of flow as mixed pow, and the corresponding reactor the mixed flow reactor, or MFR. These three ideals are relatively easy to treat. In addition, one or other usually represents the best way of contacting the reactants-no matter what the operation. For these reasons, we often try to design real reactors so that their flows approach these ideals, and much of the development in this book centers about them

In the treatment to follow it should be understood that the term V, called the reactor volume, really refers to the volume of fluid in the reactor. When this differs from the internal volume of reactor, then V, designates the internal volume of reactor while V designates the volume of reacting fluid. For example, in solid catalyzed reactors with voidage  we have

1.  IDEAL BATCH REACTOR

Make a material balance for any component A. For such an accounting we usually select the limiting component. In a batch reactor, since the composition is uniform throughout at any instant of time, we may make the accounting about the whole reactor. Noting that no fluid enters or leaves the reaction mixture during reaction, Eq. 1, which was written for component A, becomes

Evaluating the terms of Eq. 7, we find

This is the general equation showing the time required to achieve a conversion XA for either isothermal or nonisothermal operation. The volume of reacting fluid and the reaction rate remain under the integral sign, for in general they both change as reaction proceeds. This equation may be simplified for a number of situations. If the density of the fluid remains constant, we obtain

For all reactions in which the volume of reacting mixture changes proportionately with conversion, such as in single gas-phase reactions with significant density changes, Eq. 9 becomes

Eqs. 8 to 11 are applicable to both isothermal and nonisothermal operations. For the latter the variation of rate with temperature, and the variation of temperature with conversion, must be known before solution is possible. Figure 7 is a graphical representation of two of these equations.

 Figure 7 Graphical representation of the performance equations for batch reactors, isothermal or nonisothermal

Space-Time and Space-Velocity

Just as the reaction time t is the natural performance measure for a batch reactor, so are the space-time and space-velocity the proper performance measures of flow reactors. These terms are defined as follows:

Space-time:

Space-velocity:

Thus, a space-velocity of 5 hr-l means that five reactor volumes of feed at specified conditions are being fed into the reactor per hour. A space-time of 2 min means that every 2 min one reactor volume of feed at specified conditions is being treated by the reactor.

Now we may arbitrarily select the temperature, pressure, and state (gas, liquid,or solid) at which we choose to measure the volume of material being fed to the reactor. Certainly, then, the value for space-velocity or space-time depends on the conditions selected. If they are of the stream entering the reactor, the relation between s and r and the other pertinent variables is

It may be more convenient to measure the volumetric feed rate at some standard state, especially when the reactor is to operate at a number of temperatures. If, for example, the material is gaseous when fed to the reactor at high temperature but is liquid at the standard state, care must be taken to specify precisely what state has been chosen. The relation between the space-velocity and space-time for actual feed conditions (unprimed symbols) and at

standard conditions (designated by primes) is given by In most of what follows, we deal with the space-velocity and space-time based on feed at actual entering conditions; however, the change to any other basis is easily made

2 STEADY-STATE MIXED FLOW REACTOR

The performance equation for the mixed flow reactor is obtained from Eq. 1, which 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. By selecting reactant A for consideration, Eq. 1 becomes

 input = output disappearance by reaction accumulation              (15)

As shown in Fig. 8, if the molar feed rate of component A to the reactor, then considering the reactor as a whole we have

input of A, moles/time = FA0(l – XA0) = FA0

output of A, moles/time = FA = FA0(l – XA)

disappearance of A moles A reacting volume of by reaction, = (-rA)V = 

Introducing these three terms into Eq. 15, we obtain

FA0XA = (-rA)V

which on rearrangement becomes

Figure 8 Notation for a mixed reactor

where XA and rA are measured at exit stream conditions, which are the same as the conditions within the reactor. More generally, if the feed on which conversion is based, subscript 0, enters the reactor partially converted, subscript i, and leaves at conditions given by subscript f, we have

 

For the special case of constant-density systems XA = 1 - CA/CA0in, which case the performance equation for mixed reactors can also be written in terms of concentrations or

These expressions relate in a simple way the four terms XA, -rA, V, FAO; thus, knowing any three allows the fourth to be found directly. In design, then, the size of reactor needed for a given duty or the extent of conversion in a reactor of given size is found directly. In kinetic studies each steady-state run gives, without integration, the reaction rate for the conditions within the reactor. The ease of interpretation of data from a mixed flow reactor makes its use very attractive in kinetic studies, in particular with messy reactions (e.g., multiple reactions and solid catalyzed reactions). Figure 9 is a graphical representation of these mixed flow performance equations. For any specific kinetic form the equations can be written out directly.

Figure 9 Graphical representation of the design equations for mixed flow reactor

As an example, for constant density systems CA/CA0, = 1 - XA  thus the performance expression for first-order reaction becomes

On the other hand, for linear expansion

thus for first-order reaction the performance expression of Eq. 16 becomes

For second-order reaction, A  ------>  products, -rA = k CA 2,   εA = 0, the performance equation of Eq. 16 becomes

Similar expressions can be written for any other form of rate equation. These expressions can be written either in terms of concentrations or conversions. Using conversions is simpler for systems of changing density, while either form can be used for systems of constant density.

3. STEADY-STATE PLUG FLOW REACTOR

In a plug flow reactor the composition of the fluid varies from point to point along a flow path; consequently, the material balance for a reaction component must be made for a differential element of volume dV. Thus for reactant A,  Eq. 1 becomes

input = output disappearance by reaction accumulation              (22)

Referring to Fig. 10, we see for volume dV that

input of A, moles/time = FA

output of A, moles/time = FA dFA

disappearance of A by

reaction, moles/time    = (-rA)dV

Figure 10 Notation for a plug flow reactor.

This, then, is the equation which accounts for A in the differential section of reactor of volume dV. For the reactor as a whole the expression must be integrated. Now FA0, the feed rate, is constant, but rA, is certainly dependent on the concentration or conversion of materials. Grouping the terms accordingly, we obtain

Equation 23 allows the determination of reactor size for a given feed rate and required conversion. Compare Eqs. 17 and 23. The difference is that in plug flow rA varies, whereas in mixed flow rA is constant. As a more general expression for plug flow reactors, if the feed on which conversion is based, subscript 0, enters the reactor partially converted, subscript i, and leaves at a conversion designated by subscript f, we have

 

in which case the performance equation can be expressed in terms of concentrations, or

Figure 11 Graphical representation of the performance equations for plug flow reactors.

 These performance equations, Eqs. 23 to 25, can be written either in terms of concentrations or conversions. For systems of changing density it is more convenient to use conversions; however, there is no particular preference for constant density systems. Whatever its form, the performance equations interrelate the rate of reaction, the extent of reaction, the reactor volume, and the feed rate, and if any one of these quantities is unknown it can be found from the other three. Figure 11 displays these performance equations and shows that the spacetime needed for any particular duty can always be found by numerical or graphical integration. However, for certain simple kinetic forms analytic integration is possible-and convenient. To do this, insert the kinetic expression for r, in Eq.23 and integrate. Some of the simpler integrated forms for plug flow are as follows: Zero-order homogeneous reaction, any constant εA

First-order irreversible reaction,, A   ------->  products, any constant εA,

 

Where the density is constant, put εA = 0 to obtain the simplified performance equation.

By comparing the batch expressions with these plug flow expressions we find:

(1)For systems of constant density (constant-volume batch and constant-density plug flow) the performance equations are identical, T for plug flow is equivalent to t for the batch reactor, and the equations can be used interchangeably.

(2) For systems of changing density there is no direct correspondence between the batch and the plug flow equations and the correct equation must be used for each particular situation. In this case the performance equations cannot be used interchangeably.

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Slides for Chemical Reactor Design

Slides for Chemical Reactor Design

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Videos For Chemical reaction Engineering Session - 1

Introduction 

Types Of Reactors

Design Of Chemical Reactor

Definition Of Homogeneous Rate 

Chemical Reaction Rate Expression

 

Interaction

Videos For Chemical Reaction Engineering Session - 2

Recap and Design of Chemical Reactors (contd.)

Continuous Reactors

Mixed Flow Reactor

Derivation of Batch Reactor Equations

 Interaction

Interaction (contd.)

Videos For Chemical Reaction Engineering Session - 3

Recap

Derivation 

Mixed Flow Reactor 

Comparison of Ideal Reactor

Examples 

Definition Of Space Time And Holding Time 

Chemical Reaction Engineering Interaction 

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Quiz

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Assignment

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Reference

Octave Levenspiel, Chemical Reaction Engineering, Third Edition,

John Wiley & Sons, 1999.

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Solutions

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Table of Contents