Design of Fermentation Processes
395
Figure 9.11. Phase diagram showing
X
= x/(sy F„) vs.
S
=
s/sf
for the substrate inhibited kinetics of
Figure 9.9. The straight line shows the progress of a batch reaction started with an infinitely small
inoculum. On the line are marked the two steady state solutions to the mass balances for
D
= 0.3185 h'1
and the trivial steady state solution at
S ~
l.The curves are trajectories followed after a switch to
continuous cultivation at a given set of initial values for
S
and
X.
The trajectories always bend away from
the saddle-point at the unstable steady state at
S =
0.42162.
Starting the batch with larger inoculum
(X0
finite) moves the straight line to the right, and the
asymptotically stable steady state is also reached when the batch is stopped at a larger value of
S.
A
sufficiently large pulse
AS
(> 1) will also destabilize the asymptotically stable steady state.
In (8), (9) the initial
S
for the chemostat operation is equal to the desired steady-state value, and
X
is 0.05
higher than the corresponding steady-state value. The extra biomass is washed out and the steady state is
reached with no difficulties.
WhenX0 = 0.05 and
S(tb) =
0.5325 [or
X(tb)
= 0.5175], batch operation has stopped at
tb =
9 h.
Figure 9.11 shows that the transient starting at this initial point ends at
S
= 1,
X=
0._____________________
The stability of a steady state continuous reactor, and in general the dynamics of the stirred tank
reactor, can be studied numerically for any type of growth kinetics. In this way real problems can
be investigated. In Section 9.3 we have chosen to highlight the fundamental aspects of reactor
dynamics, and in the final section 9.3.3 the simultaneous presence of several competing (or
mutually supporting) microbial species in the culture will introduce new facets of the subject
without complicating the issue by using a “real” kinetic expression. Obviously the previous
discussion is severely hampered by the knowledge of real kinetics that has become available in
recent years. But some progress can still be made without introducing excessive complications.
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