Environmental Engineering Reference
In-Depth Information
6.5.1.1
Batch Reactor
Thisisthesimplestmodeofanenzymereactororfermentor.Theequationrepresenting
the change in concentration of substrate with time is
d
]
d
t
=
[
S
V
max
[
S
]
−
,
(6.231)
K
m
+[
S
]
where Michaelis-Menten kinetics is assumed to hold. Rearranging and integrating,
we obtain
t
ln
[
[
1
t
.
1
S
]
0
V
max
K
m
−
S
]
0
−[
S
]
=
(6.232)
[
S
]
K
m
This is the integrated rate equation for an enzymatic reaction. For a batch reactor,
a plot of
(
1
/t)
ln ([S]
0
/[S]) versus ([S]
0
−
1
/K
m
as the slope
and
V
max
/K
m
as the intercept. From these the Michaelis-Menten parameters can be
evaluated. If we define the degree of conversion,
[S])/
t
should yield
−
χ
, such that
[
h
]=[
S
]
0
(
1
− χ
)
,we
can write
t
ln
1
V
max
K
m
[
1
t
.
]
0
χ
K
m
1
S
=
−
(6.233)
1
− χ
The above equation gives us the time required for a desired conversion in a batch
reactor.
E
XAMPLE
6.34 P
ESTICIDE
D
ISAPPEARANCE FROM
S
OIL IN A
B
ATCH
R
EACTOR
Meikleetal.(1973)performedanexperimentdesignedtoestimatethebiologicaldecom-
position of a pesticide (4-amino-3,5,6-trichloropicolinic acid or picloram) from a soil
matrix. The experiment was conducted in a batch reactor. The following results were
obtained after 423 days of treatment:
[
S
]
0
−[
S
]
1
t
ln
[S]
0
[S]
0
(ppmw)
[S] (ppmw)
(
t
=
423 days
)
[S]
3.2
1.56
0.003877
0.001698
3.2
1.76
0.003404
0.001413
1.6
0.51
0.002577
0.002703
1.6
0.69
0.002151
0.001988
0.8
0.24
0.001324
0.002846
0.8
0.21
0.001395
0.003162
0.4
0.12
0.000662
0.002846
continued
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