Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 788

DC A0

I

Slope = - D

II

III

0

C

0 C A0 C

*

C A0,1

*

Ae

A0,2

C A

FIGURE 16.4 Steady-state solutions change with feed concentration C A0 .

DC A0

Slope = -D 2

I

II

Slope = - D*

1

III

0

C Ae

0 C A0

C A

FIGURE 16.5 Steady-state solution variation with dilution rate.

both Eqns (16.8) and (16.9) hold are also called bifurcation points. On one side of the bifur-
cation point (for example C A0 < C A0 ), there exists only one single steady state. On the other

side of this bifurcation point, there exist MSS.
Since

dMS A
d C A ¼D

< 0 (16.10)

For all CSTR operations, one simpleway of checkingwhetherMSS is possible is to determine if

dMC A
d C A ¼

d ð r A Þ
d C A < 0

(16.10)