Design of Fermentation Processes
373
reactor in Section 9.1.1. Thus, for maintenance-free Monod kinetics, Eq. (9.10) is used to calculate
the effluent concentration from the plug flow reactor.
V_
v
1
+
a
In
X
a
1
+ X
0
ln
(1
+ A
0
-
X
)
(9.69)
V
is the total reactor volume and v the volumetric flow rate. The ratio
Vi
v is termed the residence
time (T in chemical engineering literature).
As explained in connection with Eq. (9.10), the scaling factor used in
a
and
X0
is the substrate
concentration
s0
at the start of the batch. Here
s0
is the inlet substrate concentration to the plug flow
reactor. When, as often happens in practice, the plug flow reactor is installed downstream from a
stirred tank reactor, it is more practical to use the inlet substrate concentration
sf
of the sterile feed
to the stirred tank as scaling factor. Thus, for maintenance-free kinetics
^ = “
- = — -1
(9.70)
^ 0
*0
and
a
Sq
1 +
X q
Sy
(9.71)
Furthermore,
l + X
X
=
Sf
+
^Sx^s° ~ s^ = Sf
Sf
+5°
s
-
i
Sn
^
(9.72)
Consequently, Eq. (9.69) can be written in the more convenient form
AmMr = (l + a f)ln |
y
\~af
lnl j -
(9.73)
for the case of an unbroken chain of reactors. If side streams are admitted, the simplifications of Eq.
(9.73) cannot be applied, but Eq. (9.69) still holds.
Example 9.9.
A chemostat followed by a plug flow reactor
It is desired to reduce the concentration of substrate in a sterile stream with
S/—
60 to 3 g m’\ This is to be
done in a combination of two reactors, a chemostat followed by a plug flow reactor. The kinetics is
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