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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