Modeling of Growth Kinetics
249
D
u
m ix
“ n
sf +KS
(
8
)
If we try to operate the stirred tank continuous reactor with
D >
Z)max the rate of removal of biomass will be
higher than the maximum specific rate of biomass production. No steady state will be possible except the
trivial
x
= 0 that is also a solution to Eq. (2).
Since from Table 7.1
Ks
is often in the ppm range the value of
s
in the reactor is usually orders of magnitude
lower than Sf except when
D
approaches
Dmax
and
s
sharply increases towards j r. Consequently
x
is
approximately equal to
j f until
D
approaches £>max that according to Eq. (8) with
K
, « sf is very close to
Mum
for most organisms fed with glucose.
In Fig. 7.5, experimental data are shown for growth of
Aerobacter aerogenes
in a chemostat with glycerol
as the limiting substrate. The biomass concentration is observed to be approximately constant for dilution
rates between 0.4 and 0.95 h'1. The glycerol concentration is very low for dilution rates below 0.95 hand
when the dilution rate approaches
=
1.0 h'1
the glycerol concentration increases rapidly to j -
sf -
10.0
gL'1
. The Monod model, i.e., Eqs. (6) and (7), with the following parameters listed:
M^-l.Oh1
IQ =
0.01 g glycerol L 1
Y„ =
0.55 g DW (g glycerol)'1
describes the glycerol concentration quite well in the whole dilution-rate range, and also the approximately
constant biomass concentration in the range 0.4-0.95 h'1. However, for low dilution rates the model predicts
too high biomass concentrations. This is explained by maintenance metabolism of the glycerol (see Section
5.2.1), which is not included in the Monod model. When substrates not used for maintenance processes are
limiting, e.g., the nitrogen source, the Monod model normally describes the biomass concentration in the
whole dilution range quite well (see Example 7.2).
Figure 7.5 Growth of
A. aerogenes
in a chemostat with glycerol as the limiting substrate. The lines are
model calculations using the Monod model. The data are taken from Herbert (1959).___________________
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