Biomedical Engineering Reference
In-Depth Information
(a)
(b)
10
90
X/(YF
X/S
S
F
)
10
80
1
10
70
10
60
XV/(YF
X/S
S
F
V
0
)
0.1
10
50
10
40
S/S
F
10
30
SV/(S
F
V
0
)
0.01
10
20
10
10
10
-1
0.001
0 200 400 600 800 1000
0
200
400
600
800
1000
max
t
max
t
(c)
(d)
10
1
XV/(YF
X/S
S
F
V
0
)
1
X/(YF
X/S
S
0
)
10
0
0.1
10
-1
0.01
SV/(S
F
V
0
)
10
-2
S/S
0
10
-3
0.001
0
2
4
6
8
10
12
14
16
0
2
4
6
8
10
12
14
16
max
t
max
t
FIGURE 13.5
Biomass production and substrate accumulation in the reactor for an exponential feed rate of
Q
¼
m
max
V
0
exp(0.2
m
max
t
). The initial conditions are
S
0
¼
S
F
and
X
0
¼
1.05 YF
X/S
S
F
. The Monod saturation
0.1
constant
K
S
¼
0.05
S
F
.
and substrate are
S
0
¼
1.05 YF
X/S
S
F
, respectively. The biomass yield factor is YF
X/
S
, and the death rate is negligible,
k
d
¼
S
F
and
X
0
¼
0. While the biomass accumulation increases monot-
onously with time, the increase is more rapid initially, as one can observe from
Fig. 13.4
a. The
substrate accumulation in the reactor, on the other hand, decreases sharply at the beginning
and the amount of substrate in the reactor remains nearly constant after a short period of
time.
Fig. 13.4
c shows the variations of biomass production and substrate accumulation in
the reactor at short times. One can clearly observe these trends.
Fig. 13.4
b shows the variations of biomass concentration and substrate concentration in
the reactor with time. One can observe that biomass concentration decreases rapidly at the
beginning from the initial
X
0
¼
YF
X/S
S
F
and remains at this
maximum conversion at long times. Nearly all the substrate added to the reactor is converted
to biomass. The concentration of the substrate in the reactor kept decreasing.
Fig. 13.4
d shows
more clearly the changes at short times.
Fig. 13.5
shows the variations of the reactor contents as functions of time for the same
initial and growth conditions as those shown in
Fig. 13.4
. However, the feed rate is exponen-
tial at
Q
1.05 YF
X/S
S
F
to nearly
X
¼
¼
0.1
m
max
V
0
exp(0.2
m
max
t
). This feeding rate is less than that the maximum growth
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