Biomedical Engineering Reference
In-Depth Information
(a)
(b)
XV/(YF
X/S
V
0
S
F
)
, pseud
osteady state
10
1
XV/(YF
X/S
V
0
S
F
)
,
pseudostea
dy state
10
2
XV/(YF
X/S
V
0
S
F
)
XV/(YF
X/S
V
0
S
F
)
10
1
10
0
SV/(V
0
S
F
)
10
0
SV
/(V
0
S
F
)
, pseudo-stea
dy state
10
-1
SV/(V
0
S
F
)
, peudosteady state
SV/(V
0
S
F
)
10
-1
0
2
4
6
8
10
0 200 400 600 800 1000
t
t
FIGURE 13.11
Suitability of pseudo-steady state assumption for biomass production in the reactor at short
times for constant feed rate of
Q
¼ m
max
V
0
. The initial conditions are
S
0
¼
S
F
and
X
0
¼
1.05 YF
X/S
S
F
. The growth
constants are
K
S
¼
0.05
S
F
and
k
d
¼
0.01
m
max
.
from which the cell biomass accumulation can be obtained
YF
X
=
S
¼
ðS
F
SÞ
XV
Q ¼
ðS
F
SÞ
k
d
Q
(13.38)
m
G
Substituting
Eqn (13.36)
into
Eqn (13.37)
, we obtain
Q
k
d
XV
YF
X
=
S
¼
K
S
k
d
m
max
k
d
S
F
(13.39)
For the case shown in
Fig. 13.11
,
Eqns (13.39) and (13.36)
gave
XV
S
F
V
0
1
0:05 0:01
1 0:01
0:01
¼
98:95
1
YF
X
=
S
¼
0:99
z
99:95
S
F
¼
0:05 0:01
S
¼
0:05
99
z
5:0505 10
4
1 0:01
Example 13-1. Penicillin is produced by
Penicillium chrysogenum
in a fed-batch culture with
the intermittent addition of glucose solution to the culture medium. The initial culture
volume is
V
0
¼
200 L, and glucose-containing nutrient solution is added with a flow rate
of
Q
30 L/h. Glucose concentration in the feed solution and the initial concentrations in
the reactor are
S
F
¼
¼
300 g/L,
S
0
¼
1 g/L, and
X
0
¼
20 g/L. The kinetic and yield factors of
m
max
¼
0.2/h,
K
S
¼
0.5 g/L, and YF
X/S
¼
the organism are
0.3 g-dw/g-glucose. Using the
pseudo-steady state approximation, we determine
(a) the culture volume at
t
24 h;
(b) the concentration of glucose at
t
¼
24 h;
(c) the concentration and total amount of cells when
t
¼
24 h;
(d) the product (penicillin) concentration in the vessel at 24 h, if
¼
m
P
¼
0.05 g-product/(g-cells h)
and
P
0
¼
0.1 g/L.
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