Chapter 3 ideal reactors for single reactions

Ideal Reactors for a Single ReactionIn nonisothermal operations energy balances must be used in conjunction with material balances.. Ideal Reactors for a Single ReactionIn this chapter w

Chemical Reaction Engineering

(Homogeneous Reactions in Ideal Reactors)

Mai Thanh Phong, Ph.D.

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

FACULTY OF CHEMICAL ENGINEERING

Chapter 3 Ideal Reactors for a Single Reaction

1 Material and energy balances

The starting point for all design is the material balance expressed for any

reactant (or product)

Thus, as illustrated in Fig 3.1, we have

Figure 3.1 Material

balance for an element

of volume of the reactor

Chapter 3 Ideal Reactors for a Single Reaction

In nonisothermal operations energy balances must be used in conjunction with

material balances

Thus, as illustrated in Fig 3.2, we have

Figure 3.2 Energy balance for

an element of volume

of the reactor

Chapter 3 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 3.3 We call these homogeneous

reactions

Figure 3.3 The three types of ideal reactors: (a) batch reactor, or BR; (b) plug

flow reactor, or PFR; and (c) continuously stirred tank reactor, or CSTR.

Chapter 3 Ideal Reactors for a Single Reaction

2 Batch reactor (BR)

Make a material balance for any component A Noting that no fluid enters or

leaves the reaction mixture during reaction, the material balance written for

component A is

or

(3.1)

Chapter 3 Ideal Reactors for a Single Reaction

By replacing these two terms in Eq 3.1, we obtain

(3.3) Rearranging and integrating then gives

If the density of the fluid remains constant, we obtain

n

Chapter 3 Ideal Reactors for a Single Reaction

For all reactions in which the volume of reacting mixture changes

proportionately with conversion, Eq 3.4 becomes

3 Continuously stirred tank reactor (CSTR)

Figure 3.4 Notation for a CSTR

r Af = r A

Chapter 3 Ideal Reactors for a Single Reaction

By selecting reactant A for consideration, material balance for a CSTR can be written as follows

As shown in Fig 3.4, if F A0 = v 0 C A0 is the molar feed rate of component A to

the reactor, then considering the reactor as a whole we have

(3.7)

Introducing these three terms into Eq 3.7, we obtain

(3.8)

Chapter 3 Ideal Reactors for a Single Reaction

which on rearrangement becomes

(3.9)

Chapter 3 Ideal Reactors for a Single Reaction

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

(3.10)

For the case of constant-density systems X A = 1 – CA/CA0:

(3.11)

Chapter 3 Ideal Reactors for a Single Reaction

Figure 3.5 is a graphical representation of these mixed flow performance

equations

Chapter 3 Ideal Reactors for a Single Reaction

4 Plug flow tubular reactor (PFTR)

At the steady-state, the material balance for reactant A becomes

Figure 3.6 Notation for a plug

flow tubular reactor

(3.12)

Chapter 3 Ideal Reactors for a Single Reaction

Referring to Fig 3.6, we see for volume dV that

Introducing these three terms into Eq 3.12, we obtain

Noting that

Chapter 3 Ideal Reactors for a Single Reaction

For the reactor as a whole the expression must be integrated Grouping the terms accordingly, we obtain

Thus

(3.14)

For a more general expression, we have

(3.15)

Chapter 3 Ideal Reactors for a Single Reaction

For the special case of constant-density systems

We have

(3.16)

Chapter 3 Ideal Reactors for a Single Reaction

Figure 3.7 Graphical representation of the performance equations for plug flow

tubular reactors

Fig 3.7 displays these performance equations and shows that the space-time

needed for any particular duty can always be found by numerical or graphical

3.14

3.16