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Homework #6
ChE 361
Fall 2010
Consider a biochemical reactor where biomass and a desired product are produced by microbial
growth from a single, rate limiting substrate. Denote the biomass concentration as
X
, the sub
strate concentration as
S
, and the product concentration as
P
. The substrate is continuously
supplied to the bioreactor at volumetric ﬂow rate
F
and concentration
S
i
. A liquid stream is
continuously removed from the bioreactor at volumetric ﬂow rate
F
such that the liquid volume
V
remains constant. The speciﬁc growth rate has the form:
μ
(
S,P
) =
μ
m
‡
1

P
P
m
·
S
K
m
+
S
+
S
2
K
i
where the constants
K
i
and
P
m
reﬂect growth inhibition by high concentrations of substrate and
product, respectively. The bioreactor is described by the following mass balance equations:
dX
dt
=

DX
+
μ
(
S,P
)
X
=
f
1
(
X,S,P
)
dS
dt
=
D
(
S
f

S
)

1
Y
X/S
μ
(
S,P
)
X
=
f
2
(
X,S,P
)
dP
dt
=

DP
+ (
αμ
(
S,P
) +
β
)
X
=
f
3
(
X,S,P
)
where
D
=
F/V
. Consider the following parameter values:
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This document was uploaded on 02/06/2011.
 Spring '09

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