Design of Fermentation Processes
355
D
Aextr
y 'u , / ( i+ 1 + a)
for alb<
1
for alb>\
(9.30)
The value of
^ xlr
is independent of
sf ,
while for any given values of the kinetic parameters
K-,
and
Ks
it is seen that
Sextr
is inversely proportional to jy (whereas, of course,
is independent of
sf).
When
fj
is a monotonously increasing function of
S
, operation of the stirred tank reactor at a
D
value close to
Dmax
leads to very low productivity. The effluent substrate concentration is close to
sf
and, consequently, there is neither much biomass nor much product in the effluent stream. For
nonmonotonic kinetics such as Eq. (9.28), the highest specific growth rate and the highest
productivity may both be found at
D
values where
S
is appreciably smaller than 1; cf. the result in
Eq. (9.29) and the corresponding result for maximum productivity calculated in Example 9.13.
The
productivity
of a given species
i
in the stirred tank reactor is defined as
The highest productivity is in general
not
found where the specific growth rate is at its maximum
value. With simple Monod kinetics and sterile feed,
(9.31)
(9.32)
or
Px
S(\-S)
M ^ YsXSf
s + a
(9.33)
for which the maximum value is
The corresponding
D
value is
(9.35)
The results in Eqs. (9.33) - (9.35) can be expressed verbally as follows:
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