374
Chapter 9
4
s
-3,-i
qx = - -
-----x gm h
3 4 + 5
0
)
i.e., the Monod constant is 4 g m
~3
while
= 4/3 h'1. Furthermore,
<?s = -
10
(g g "
)-qx
(2)
and
v = 2.5 m
3
h
(3)
With two bioreactors in series, it is possible to minimize the total reactor volume necessary to reduce
5
from
60 to 3 g m"\ The chemostat should be run at an S' value for which
qx
is maximum, i.e.,
S —
—ay
+
+
a.j- —
------- h ,|| — |
h
---- —
0.2
± J ± ) +±
60
VUoj
60
(4)
or
and
Sfj
-0.2•60 = 12 g m
-3
;
x
0
=0.1 -(60-12)-4.8 gm
’3
(5)
4
4 + 12
=
1
h
1
(
6
)
i.e.,
Vs =
2.5 m3. With this degree of preconversion, the plug flow reactor takes over at the point where
qx
starts to decrease with decreasing
s
i.e. at the minimum on the curves in figure 9.3. It is known from any
textbook on reaction engineering that a plug flow reactor is the best reaction vessel whenever the rate of
conversion is a monotonically increasing function of the reactant concentration.
From Eq. (9.73),
In
0.1 (60-3)
4.8
= 0.2068 h
(7)
i.e.,
= 0.206
‘ 2.5 = 0.517 m3.
No other chemostat-plus-plug flow reactor combination could give a smaller total reactor volume than
V,
+V2-
3.017 m
3
if the substrate content of a feed stream 2.5 m
3
h
'1
is to be reduced from 60 to 3 g m
3
We shall now assume that another stream v, = 0.5 m
3
h l of
s =
30 g m
3
and
x
= 0 is introduced after the
chemostat. The combined streams are to be treated in the plug flow reactor to give an effluent of
s =
3 g
m \
The chemostat is still operated so that the effluent is
(jc,
s )
=
(4.8, 12) g m3, i.e., at its maximum production
rate. Conditions at the inlet to the plug flow reactor are
previous page 397 Bioreaction Engineering Principles, Second Edition  read online next page 399 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off