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