Biomedical Engineering Reference
In-Depth Information
(a)
(c)
10
2
XV/(YF
X/S
S
F
V
0
)
10
XV/(YF
X/S
S
F
V
0
)
, pseudo-steady state
1
10
1
XV/(YF
X/S
S
F
V
0
)
, pseudo-stead
y sta
te
SV/(S
F
V
0
)
0.1
SV/(S
F
V
0
)
, pseudo-steady state
XV/(YF
X/S
S
F
V
0
)
10
0
0
5
10
15
20
t
(b)
XV/(YF
X/S
S
F
V
0
)
, pseud
o-steady
state
10
1
SV/(S
F
V
0
)
10
-1
XV/(YF
X/S
S
F
V
0
)
10
0
SV/(S
F
V
0
)
, pseudo-ste
ady st
ate
10
-1
10
-2
10
-2
SV/(S
F
V
0
)
, pseudo-steady state
SV/(S
F
V
0
)
10
-3
0 2 4 6 8 0 2 4 6
0
5
10
15
20
t
t
(d)
(e)
10
1
10
1
XV/(YF
X/S
S
F
V
0
)
, pseudo-ste
ady sta
te
XV/(YF
X/S
S
F
V
0
)
XV/(YF
X/S
S
F
V
0
)
, pseudo-steady state
XV/(YF
X/S
S
F
V
0
)
10
0
10
0
SV/(S
F
V
0
)
10
-1
10
-1
SV/(S
F
V
0
)
, pseudo
-steady s
tate
10
-2
SV/(S
F
V
0
)
SV/(S
F
V
0
)
, pseudo-steady state
10
-2
0
2
4
6
8
10
0
2
4
6
8
10
12
14
16
t
t
FIGURE 13.10
Suitability of pseudo-steady state assumption for biomass production in the reactor at short
times with (a) a constant feed rate of
Q
¼ m
max
V
0
and initial conditions of
S
0
¼
S
F
and
X
0
¼
1.05 YF
X/S
S
F
; (b) an
exponential feed rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
) and initial conditions of
S
0
¼
S
F
and
X
0
¼
1.05 YF
X/S
S
F
;
(c) an exponential feed rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
) and initial conditions of
S
0
¼
S
F
and
X
0
¼
0.0105 YF
X/S
S
F
;
(d) an exponential feed rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
) and initial conditions of
S
0
¼
0.0125
S
F
and
X
I
¼
1.05 YF
X/
S
S
F
; (e) an exponential feed rate of
Q
¼
0.1
m
max
V
0
exp(0.2
m
max
t
) and initial conditions of
S
0
¼
S
F
and
X
0
¼
0.0105 YF
X/
S
S
F
. In the last case (e), there is a death rate of
k
d
¼
0.1
m
max
. In all cases, the Monod saturation constant
K
S
¼
0.05
S
F
.
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