Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 799

back in, they will remain out and no biomass would be produced. Steady state 2) is stable
can be explained based on Fig. E16-2.2 , or based on the fact that

d S ¼ X dSMR X

dMR X
d S

dMG X dSMG X

d S

d X
d S d S

þð SMR X SMG X Þ (E16-2.15)

At steady-state locations,

d S ¼ X dSMR X

dMR X
d S

dMG X dSMG X

d S

d S

(E16-2.16)

>

Therefore, if X 0, the above equation indicates that Eqn (16.12) is equivalent to

dSMR X
d S

dSMG X
d S

< (E16-2.17)

That is, the steady state is stable if the slope of the specific mass removal rate of biomass
(which is zero in Fig. E16-2.2 ) is smaller than the slope of the specific mass generation rate
of biomass [which is positive at the location represented by solution 2)]. Thus steady state
2) is stable. Steady state 3) does meet this condition ( E16-2.17 ).
Steady solution 2) is the desired operating point as the yield of biomass is the highest and
the substrate concentration is the lowest in the reactor effluent.

(c) You can start the reactor with a seed culture, first as a batch. Do not leave the culture to
grow for too long. However, make sure S

<

22.8 g/L before gradually start with very
small dilution rate, then gradually increase to D ¼ 0.04/h.

16.2. THERMAL STABILITY OF A CSTR

Based on the discussions in Section 16.1, MSS exist if the reaction rate could be lower at
high reactant concentrations (or at reactor inlet conditions). For an exothermic reaction oper-
ated under nonisothermal conditions, the reaction rate at the reactor inlet conditions can be
lower than that in the reactor. Therefore, stability issue as we discussed earlier could apply to
thermal stability in a CSTR for any exothermic reactions with any kinetics. For simplicity in
discussion, let us consider the steady-state operations of a CSTR in which a single reaction is
taking place:

Products
We do not eliminate the possibility of multiple reactants and/or multiple products. For
simplicity, we shall assume just one single reaction, although the analyses here are easily
to extend to multiple reactions.
Fig. 16.9 shows a schematic of jacketed CSTR where the heat generated in the reactor
is removed via a saturated liquid e vapor mixture. The simplification of using saturated
liquid e vapor mixture is that the temperature of the heat transfer fluid can be assumed
constant, and the heat transfer coefficient is usually high, ideal for industrial operations.
However, this setup can be varied, and our discussions will still be valid with modifications
in the heat-transfer term.

A /