Environmental Engineering Reference
In-Depth Information
where
F
in
is the influent feed rate and
V
is the volume of the reactor. Thus,
]
K
m
+[
S
]
=−
F
in
V
max
[
S
d [S]
d
V
.
(6.235)
Rearranging and integrating, we obtain
V
max
]
ln
(
[S]
/
[S]
0
)
=
[S]
0
−[
S
τ
ln
(
[S]
/
[S]
0
)
−
K
m
,
(6.236)
τ =
where
V/F
in
is the residence time for the substrate in the reactor. A plot of
(
[S]
0
−[
]
τ
/
ln
(
[S]
/
[S]
0
)
can be used to arrive at
V
max
and
K
m
from the slope and intercept, respectively. The total volume of the reactor required
for a given removal is
S
/
ln
(
[S]
/
[S]
0
))
versus
F
in
V
max
K
m
ln
[
.
]
0
[
S
]
S
V
=
+[
S
]
0
−[
S
]
(6.237)
6.5.1.3
Continuous Stirred Tank Enzyme Reactor
If the influent and effluent rates are matched, then from Section 6.1.1.2, the following
general equation should represent the behavior of a CSTR:
[
]
d
t
=
V
d
S
F
in
(
[
S
]
in
−[
S
]
)
−
Vr
S
,
(6.238)
where
r
S
=
V
max
[
S
]
/K
m
+[
S
]
. At steady state d[S]/d
t
is zero, and hence we have
V
max
τ[
S
]
[
S
]−
K
m
+
]
in
)
,
(6.239)
(
[
S
]−[
S
where
V/F
in
. From the above equation, one can also obtain the size (volume) of
a reactor required for a specific enzymatic degradation of the substrate.
τ =
F
in
V
max
1
(K
m
+[
−
[
S
]
in
V
=
S
]
)
.
(6.240)
[
S
]
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