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Chapter 9
The two most obvious feed policies are
Choose
v(t)
so that
s =
s„
throughout the fermentation.
Choose v(f) so that
qx
= <
7
° throughout the fermentation.
The two policies correspond to fermentation at constant specific growth rate and at constant
volumetric rate of biomass production, respectively. Both policies have obvious practical
applications. When
s
is kept at a level below that at which part of the added substrate is converted
to undesired products, a large amount of biomass (together with an associated protein which may
be the real product) is produced at a reasonably high rate and a high final biomass concentration can
be obtained. Neither the continuous stirred tank reactor (one is afraid that the subtle qualities of the
yeast that gives the optimal leavening properties of the product will be lost in a long fermentation
run) nor the batch reactor (diversion of glucose to ethanol, which inhibits the growth and represents
a considerable loss of substrate) are suitable for baker's yeast production, but fed-batch operation is
universally applied. The constant volumetric rate policy is important if removal of the heat of
reaction is a problem or if the capability to supply another substrate, e.g., oxygen is exceeded when
Calculation of v(f) corresponding to constant
s= sn
(which means that
^
is constant and equal to
^,)
is quite simple. From Eq. (9.52), and with
xf - 0:
=>
xV= x0V0cxp
O V )
(9.54)
at
while the substrate balance taken from (9.53) reads:
= - r ^ x + ^ l s r -s)
(9.55)
or
v(t)= I ^ x V ^ I ^ - x 0V0
exp(/V)
(9.56)
s f
So
Sf
s o
V(t)
is found by integration of (9.56) from
t
= 0, and x(t) by inserting
V(t)
in (9.54).
~ -1 - hx
0
+
bx0
exp(/V)
(9.57)
* fi
where
b = Yxt!(sf - s 0),
and