Page 167 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.2 Scale-up of Liquid-Phase Batch Reactor Data to the Design of a CSTR 139

If instead of two GSTRs in series we had n equal-sized CSTRs connected in
series (7, = z2 = = z, = z) operating at the sane temperature (k, == k, =
... zz k, = k), the concentration leaving the last reactor would be

(4-10)

The conversion for these n tank reactors in series would be
Conversion as a I
function of the (4-1 1)
number of
tanks in series

A plot of the conversion as a function of the number of reactors in series for a
first-order reaction is shown in Figure 4-4 for various values of the Damkohler

CSTRs in series

0 1 2 3 4 5 6 7 8 9 1 0 1 1 I 2 1 3
Number of tonks, n
Figure 4-4 Conversion as a function of the number of tanks in series for different
Damkohler numbers for a first-order reaction.

number zk. Observe from Figure 4-4 that when the product of the space time
and the specific reaction rate is relatively large, say, Da 2 1, approximately
90% conversion is achieved in two or three reactors; thus the cost of adding
subsequent reactors might not be justified. When the product zk is small,
Da - (3.1, the conyersion continues to increase significantly with each reactor
added.
The rate of disappearance of A in the nth reactor is

-rAn = kCAn = k -
c.40
(1 + zk)"