Design of Fermentation Processes
393
0.8
0.6
X
0.4
S
0.2
0.0
0
2
4
6
8
10
12
14
16
T im e {h)
Figure 9.10 Perturbation of the steady state (
S0
,X
0) - (0.26, 0.62876) with a substrate pulse
AS
=0.24.
Monod kinetics with maintenance (
b
= 0.1).
a = K/sf
= 0.2.
Example 9.13
Startup of a chemostat ■
When the steady state is unstable for some
S
values in ]0, 1[ the startup of a chemostat from a batch may
require some thought. At the end of the batch fermentation, the substrate and biomass concentrations may
be far from their steady-state values, and although the desired steady state may be stable, it is not certain
that it will be reached after the switchover to continuous operation of the bioreactor.
Consider the substrate inhibition kinetics of Eq. (9.28) with the same values of the kinetic parameters
/Uma_x =
0.5 h"1,
a
= 1/16,
b -
1 as have been used before (Fig. 9.9). It is desired to operate the steady-state chemostat
at the
S - sis/
value for which maximum cell productivity is obtained:
=pi= px
or
Px
S(l-S)
(
1
)
bS2 +S + a
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