Design of Fermentation Processes
353
Figure 9.2. Structured model for lactic acid fermentation in a batch reactor. For two different values of
a
(Eq 9.17 a) the growth of biomass
x/x0
and of the active compartment
XA
are shown as functions of
time. A :
a~3,
B :
a =
10. c,(£q 9.16)= 1.
With Monod kinetics and sterile, product-free feed, the steady-state balances already introduced in
Chapter 3 are:
qx = y x = v mix^
— x = Dx
(9.21)
s + K,
qs
=
= -D(sf
- 5)
(9.22)
qP
= yxp^ = DP
(9.23)
D =
x = Ysx{sf -s)\
p = Ysp{sf -s)
(9.24)
For a given value of
D,
the concentrations of substrate, biomass, and metabolic product are
calculated from Eq. (9.24). Obviously, any one of the concentrations could also be used as the key
variable from which values of the remaining variables could be calculated.
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