Modeling of Growth Kinetics
255
e>
Figure 7.6 Growth o f
A. cterogenes
in a chem ostat w ith glycerol as the lim iting substrate. The lines are
model calculations using the M onod m odel including m aintenance. The data are taken from H erbert (1959).
With Eq. (2), the steady-state concentration o f the lim iting substrate is still given by Eq. (5) in Exam ple 7.1,
since in both cases d =
D
at steady state. H ow ever, the steady-state biom ass concentration is different from
that found w hen the sim ple M onod m odel is used. C om bination o f the tw o balances yield
D
Y T D + m.
i s/ ~ s)
(3)
By com parison with Eq. (7.26), it is observed that Eq. (3) is an analogue o f Eq. (6) in Exam ple 7.1. A t low
dilution rates the term ms is significant and the biom ass concentration becom es sm aller than if m aintenance
is neglected. This is illustrated in Fig. 7.6, w here it is observed that the m odel correctly describes the
biomass concentration in the w hole dilution-rate range. T he m odel param eters in the revised m odel are:
d
= 1 O h“1
“ max
1
tKJ
11
K, =
0.01 g glycerol L '1
ffl, = 0.08 g glycerol (g D W h )'1
C
“ = 1.82 g glycerol (g DW )-1
With these values the yield coefficient IT* is calculated to 0.53 and 0.56 at dilution rates o f 0.4 h ! and 0.8 h'
respectively. This is close to the constant value o f the yield coefficient for the sim ple M onod m odel used
in Exam ple 7.1._____________________________________________________________________________________________
Including maintenance is in principle the same as considering two reactions in the model: a reaction
where substrate is converted to biomass and a reaction where substrate is used for cellular
maintenance. Extending the number of reactions, but still describing the biomass with a single
variable, may allow modeling of more complex phenomena as illustrated in Examples 7.3 and 7.4.
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