Page 165 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.2 Scale-Up of Liquid-Phase Batch Reactor Data to the Design of a CSTR 137

In10 -
k= ___ 2‘3 = 0.311 min-I (E4-1.8)
1% - t, 8.95 - I .55
the rate law becomes

(E% 1.9)

Thiis rate law can now be used in the design of an industrial CSTR.

4.2.2 Design of CSTRs

In Chapter 2 we derived the following design equation for a CSTR:

Mole balance (2- 13)

which gives the volume V necessary to achieve a conversion X. When the vol-
umetrrc flow rate does not change with reaction, (Le., u = u,) we can write

(4-6)

or in terms of the space time,

(4-7)

For a first-order irreversible reaction, the rate law is

Rate law -rA = kCA
We can combine the rate law and mole balance to give

Combine

Solving for the effluent concentration of A, CA, we obtain

(4-8)

For the case we are considering, there is no volume change during the
course of the reaction, so we can use Equation (3-29),

Relationship
between space time to Combine with Equation (4-8) to give
and conversion for a
first-order liquid- x= -
tk
phase reaction 1 +tk (4-9)