250
Chapter 7
It is not to be expected that the empirical Monod model can be used to fit all kinds of fermentation
data. Many authors have tried to improve on the Monod model, and some of these embellished
models are listed in Table 7.2. Except for the Moser model, all the models contain two adjustable
parameters. The logistic law equation contains a constant
K*
that must obviously depend on the
substrate feed concentration. It cannot either be true that M
is independent of the substrate level in
the reactor. The Contois model includes inhibition of the specific growth rate by the biomass. For
very high biomass concentration the biotic phase may take up a substantial part of the total reactor
volume, and the uptake of substrates could presumably be hampered just by the presence of the
biomass. It is, however, difficult to imagine how cells by their mere presence should inhibit their
own growth, and probably the ability of the Contois kinetics to fit experimental data is explained by
some unaccounted-for effect of substrates or of the metabolic products, which may be toxic. One
may have endless discussions concerning the pros and cons of empirical rate expressions such as
the Monod model or its relatives in Table 7.1. They may serve a useful purpose as data fitters and
as control models in industrial fermentations, but their value for research purposes is very limited
since they reveal next to nothing about the possible mechanisms behind the observed phenomena.
All the unstructured models presented above assume that there is only one limiting substrate, but
often more than one substrate concentration influences the specific growth rate. In these situations
complex interactions can occur, which are difficult to model with unstructured models unless many
adjustable parameters are admitted. Tsao and Hansen (1975) proposed a general, multiparameter,
unstructured model for growth on multiple substrates
P
=
i+ I -
n
+ K *4 ) J S j + K s
(7.17)
Table 7.2 Compilation of different unstructured, kinetic models.
Name
Kinetic exnression
Teissier
Moser
K ,
Contois
M ~ Mm- s + Ksx
Blackman
yU™ —
;
S<2K1
M = \
2KS
U™*
;
s > i k s
Logistic law
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