Design of Fermentation Processes
349
maintenance has little influence when the specific growth rate is high since the ratio between
m,
and
is the relevant parameter in the dimensionless substrate balance in Eq. (4) of Example 9.2.
Consequently, it is in the continuous stirred tank reactor or in the fed batch reactor rather than in the
batch reactor that one should be worried about maintenance losses (that is, if biomass and not the
metabolite is the desired product).
Example 9.2 Effect of maintenance on distribution of substrate between biomass and product
Assume that
= Ama* throughout the fermentation. Whether this approximation is reasonable or not
depends on the value of
a ~ X s/sQ.
If a is less than 0.01, virtually all biomass is formed with a constant
specific growth rate. With the typical values for kinetic parameters and operating conditions used in
Example 9.1, the maximum possible increase of biomass concentration is
= 2 g L . When 98% of the
available
substrate
has
been
consumed,
S
is
still
20
times
as
large
as
a
(s = 200mgL~‘ andAT^ =10m gL_l), and the approximation
M
= /jrmax
is reasonable. Whether
is
constant or starts to decrease for smaller values of
s
has no visible influence on the total biomass yield,
which can at most increase by a further 2%-and probably considerably less, since much of the remaining
substrate goes to maintenance.
With substitution of
for
Ysx
in the definition of the dimensionless variables given by Eq. (9.9) we have:
(
1
)
for which the solution is
X = X 0
exp(Ö) =
X 0
exp(/w O
S = l- 2 f o(l + è)[exp(0)-lj
(4)
(3)
where
(5)
Similarly, for a metabolic product,
(6)
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