Biomedical Engineering Reference
In-Depth Information
(a)
(b)
10
1
1
X/(YF
X/S
S
0
)
XV/(YF
X/S
S
F
V
0
)
10
0
0.1
10
-1
0.01
10
-2
S/S
0
SV/(S
F
V
0
)
10
-3
0.001
0
2
4
6
8
10
0
2
4
6
8
10
FIGURE 13.7
Biomass production and substrate accumulation in the reactor at short times for exponential feed
rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
). The initial conditions are
S
0
¼
0.0125
S
F
and
X
0
¼
1.05 YF
X
/
S
S
F
. The Monod
saturation constant
K
S
¼
0.05
S
F
.
(a)
(b)
10
1
1
XV/(YF
X/S
S
F
V
0
)
X / (YF
X/S
S
0
)
10
0
0.1
10
-1
SV/(S
F
V
0
)
S / S
0
10
-2
0.01
0
2
4
6
8
10
12
14
16
1
10
100
1000
FIGURE 13.8
Biomass production and substrate accumulation in the reactor at short times for exponential feed
rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
) and
k
d
¼
0.1
m
max
. The initial conditions are
S
0
¼
S
F
and
X
0
¼
0.0105 YF
X/S
S
F
. The
Monod saturation constant
K
S
¼
0.05
S
F
.
Fig. 13.7
shows the variations of the reactor contents as functions of time for the same feed
and growth conditions as shown in
Fig. 13.5
. However, the initial substrate concentration is
lowered from
S
0
¼
0.0125
S
F
. This is particularly an interesting case since one of
applications of fed-batch reactor is to produce high biomass concentration for cells that do
not grow in concentrated media. In this case, the biomass concentration decreases very
slowly from 1.05 YF
X/S
S
F
to the steady value of ~YF
X/S
S
F
. The substrate concentration
decreases rapidly to below 0.006
S
F
before recovering slowly.
Fig. 13.8
shows the variations of the reactor contents as functions of time for the same feed
and initial conditions as shown in
Fig. 13.6
. However, the specific death rate of the cells is of
a finite value, at
k
d
¼
S
F
to
S
0
¼
0.0125
S
F
. One can observe that the trends of this case are
nearly identical to those with negligible cell death rate. However, the concentration of
0.1
m
max
to
S
0
¼
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