354
Chapter 9
Introduction of dimensionless variables
S
and
X
S
5
SI
x= -
r~Sf
(9.25)
yields the following expressions for
D
and for the overall mass balance:
D _£aaxS_
.
x
=
i-S
(9.26)
S + a
where
a = Ks /sf
is a parameter quite similar to that defined in Eq. (9.9) for batch fermentation.
Now the natural scale factor is
sf
rather than v The largest possible value of
S
is 1, and
consequently, the largest possible dilution rate is
A™ =
7
^
(9.27)
1
+
a
and
washout
occurs when
D
exceeds
D ^ .
These basic features of steady-state operation of a continuous stinred tank reactor were already
introduced in Section 3.1 and discussed in Example 7.1. For any given function
= k A(p)fi (s),
the maximum dilution rate
can be found analogously to Eq. (9.27), which holds for
maintenance-free Monod kinetics only. Typically
is found for
S
= 1, but the maximum value
of
D
can also be found for an
S
value in the open interval ]0;1[. Thus for the substrate inhibition
kinetics given by Eq. (7.21),
s2/Ki + s + Ks
bS2
+S + a
(9.28)
where
K
s f
s f
K,
the function
p(S)
has an extremum:
u
_
Pjnax
_
___
Mnm.
__
^
_
V
extr~ 2 V 0 6 + l_ 2 V A / A +1
m ~\b
sf
(9.29)
Since E is an increasing function of
S
for 0 <
S <
SQtr, the maximum dilution rate is obtained from
one of the two expressions in Eq. (9.30):
previous page 377 Bioreaction Engineering Principles, Second Edition  read online next page 379 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off