344
Chapter 9
Example 9.1 Kinetic data from a batch experiment
We now consider a batch fermentation where the initial cell density
x0
is 10 mg L'1
,s0=
10 g L~l,
Ya =
0.2 g
g'1, andAT,= 10 mg L'1. Thus
10
0.2
104
0.005
0
)
a ~
(
2
)
10'J
+ X
(3)
With these typical parameter values, the last factor in Eq. (9.11) is equal to 1.002 for z = x /x 0 =10and
1.004
for
z
= 50. Consequently, during the time it takes for the biomass concentration to increase to 50
times its initial value (or 25% of the total increase of biomass concentration),
z
increases exponentially with
time and the time constant is equal to 1
!
Am»x • When both
a
and
Xo
are small, the value of
Ks
has virtually
no influence on the value of Am»*, which can be determined from a plot ofln(z) versus time.
Ks
can in principle be determined from the final part of the experiment, when
X * X 0
+1. Here one can
reasonably take
z
to be constant equal to 1 +
l/X„
and
a =K,!
s*i can be found from the slope of
Dimensionless time (©)
Figure 9.1. Profiles of dimensionless biomass and substrate concentration during a batch cultivation
following Monod kinetics.
(a
= 0.001 and 2^ = 0.005).
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