Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 229

k 1 s C A 0
ð1 þ k 1 s Þð1 þ k 2 s Þ

C B ¼ (E5-8.14)

This maximum concentration of B (or the production rate of B) can be obtained by setting

s m ¼ ð 1 þ k 1 s m Þð 1 þ k 2 s m Þ s m ½ k 1 ð 1 þ k 2 s m Þþ k 1 ð 1 þ k 2 s m Þ

d C B
d

0 ¼ k 1 C A 0 (E5-8.15)

2 2

s

ð1 þ k 1 s m Þ ð1 þ k 2 s m Þ

which gives the contact time required for maximum production of B in a CSTR

1
k 2 k 1

s m ¼

p (E5-8.16)

and the corresponding concentration of B is given by

(E5-8.17)

s ! 2

k 2
k 1

C B max ¼ C A 0 1 þ

Figure E5-8.3 shows the ratio of the maximum concentration B in a PFR, Eqn (E5-8.10) to that
in a CSTR, Eqn (E5-8.17) , as a function of the kinetic rate constant k 2 / k 1 . One can observe that the
productivity to B is higher in a PFR than in a CSTR, as the ratio is always greater than unity.
Therefore, the optimum reactor type is PFR, with a contact time given by Eqn (E5-8.9) if the
desired product is the intermediate product B.
Example 5-8 shows that PFR is better suited for intermediate product production. This can be
easily interpreted from the concentration distributions. In a CSTR, the reactant concentration is

1.5

1.4

1.3

1.2

1.1

1.0

10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4

k/k

2 1

FIGURE E5-8.3 The ratio of the maximum intermediate product B in a PFR to that in a CSTR as a function of the
kinetic rate constant ratio.