Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 790

3) CSTR operating at III
When the system is experienced with a fluctuation from feed, the CSTR could be upset in
two ways. If the feed fluctuation caused the concentration in the reactor to shift left (i.e. lower)
and then the fluctuation stopped, the mass consumption rate of A is increased slightly while
the mass supply rate of A is increased more: MC A <

MS A . The net effect is an increase in the
availability of A in the reactor and thus the reactor-operating conditions shift gradually back to
point III. If the feed fluctuation caused the concentration in the reactor to shift right (i.e. higher)
and then the fluctuation stopped, the mass consumption rate of A is decreased slightly while
the mass supply rate of A is decreased more: MC A >

MS A . The net effect is a decrease in the
availability of A in the reactor and thus the reactor-operating conditions shift gradually
back to point III. Therefore, CSTR operated at point III has the ability to dampen the feed fluc-
tuation caused steady-state shift. This is a stable steady state. This is a stable steady state that is
not desirable in most industrial operations as the conversion is very low.
From Fig. 16.3 , we observe that

I > I II < II III > III

dMC A
d C A

dMS A
d C A

dMC A
d C A

dMS A
d C A

dMC A
d C A

dMS A
d C A

; ;

Thus, the stable steady states satisfy Eqn (16.8) and

dMC A dMS A

d C A

d C A >

(16.10)

Inequality (16.10) indicates that the slope of the mass consumption rate curve is greater that
the slope of mass supply rate line. Inequality (16.10) is referred to as the slope condition for
CSTR feed stability.
If the working concentration we have chosen is not a reactant, rather a product is chosen,
then the stability condition is changed to

MG j ¼ MR j (16.11)

and

dMG j
d C A >

dMR j
d C A

(16.12)

where MG j is the molar generation rate of (product) species j and MR j is the molar removal
rate of (product) species j.

16.1.3. Effect of Feed Parameters on MSS

Let us now continue on the discussion in Section 16.11. MSS exist if the rate low gives
lower reaction rates at very high-feed reactant concentrations (than that at lower reactant
concentrations). Feed conditions also affect whether MSS exits or not. In this section, we shall
focus on the effect of feed conditions on the steady-state operations.
From Figs. 16.4 and 16.5 , one can observe that there are two bifurcation points. When the
feed parameter (C A0 or D) is set between the two bifurcation points, there are three solutions
possible; otherwise there is only one steady-state solution. To illustrate clearly,

this