Environmental Engineering Reference
In-Depth Information
kinetics.
μ
can be large if either
V
is large or
F
is small. The maximum value of 1
/
θ
or
μ
is given by
μ
max
as in the Monod equation.
θ
+
k
decay
=
μ
max
[
S
]
∗
1
,
(6.243)
K
s
+[
S
]
∗
K
s
1
+
k
decay
θ
μ
max
θ −
1
+
k
decay
θ
.
[
S
]
∗
=
(6.244)
We next proceed to write an overall mass balance for the substrate, which gives
d
t
=
F(
[
S
]
in
−[
S
]
∗
)
−
V
μ[
X
]
,
V
d
[
S
]
(6.245)
y
x
where
y
X
is the yield factor as defined previously. At steady state, we have
[
X
]=
y
x
(
[
S
]
in
−[
S
]
∗
)
.
(6.246)
Substituting for [S]
∗
gives
.
+
k
decay
θ
μ
max
θ −
1
+
k
decay
θ
K
s
1
[
X
]=
y
x
[
S
]
in
−
(6.247)
Whenmicroorganismsaregrowninthereactor,andtheirdecayproceedssimultaneously
with constant
k
dec
, the observed yield factor
y
ob
X
has to be corrected to obtain the actual
y
X
thatshouldbeintroducedintotheaboveequation.Horan(1990)derivedthefollowing
equation for
y
X
:
12
10
[X]
8
6
4
2
[S]
*
0
0
0.2
0.4
0.6
0.8
Time/days
FIGURE 6.68
Microbial growth and substrate decomposition in a CSTR.
K
s
=
15 mg/L, [S]
in
=
25 d
−
1
.
15 mg/L,
Y
=
0.6,
μ
max
=
continued
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