Page 426 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.5 Bioreactors 397
Ks ccCs CS I
rg = Pmax - (7-103)
+

In many systems the product inhibits the rate of growth. A classic exam-
ple of ithis inhibition is in wine-making, where the fermentation of glucose to
produce ethanol is inhibited by the product ethanol. There are a number of dif-
ferent equations to account for inhibition; one such rate law takes the forni

(7-1104)

where
z;J

Product inhibition k obs = [ 1-2 (7 - 1.05)

with

CT, = product concentration at which all metabolism ceases, g/dm3
n = empirical constant
For the glucose-to-ethanol fermentation, typical inhibition parameters are

nZ0.5 and C; = 93gldm3
In addition to the Monod equation, two other equations are also commclnly
used to describe the cell growth rate; they are the Tessier equation,
[ 31
rg = pmax 1 -exp - - Cc (7-106)

and the Moser equation,

Pmax Cc
rg = (7-1107)
(1 + kCS-*)

where X and k are empirical constants determined by a best fit of the data.
The Moser and Tessier growth laws are often used because they have
been found to better fit experimental data at the beginning or end of fermenta-
tion. Other growth equations can be found in Dean.I8
Thie cell death rate is given by

where CY, is the concentration of a substance toxic to the cell. The specific
death rate constants kd and k, refer to the natural death and death due to a toxic

l8& R. C. Dean, Growth, Function, and Regdation in Bacterial Cells, Oxford Univer-
sity Press, Lcimhm44.
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