Biomedical Engineering Reference
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and
k
1
e
k
2
t
k
2
e
k
1
t
k
1
k
2
C
C
¼ C
A
0
C
A
C
B
¼ C
A
0
C
A
0
(E5-8.7)
This maximum concentration of B (or the production rate of B) can be obtained by setting
s
m
¼ r
B
¼ k
1
C
A
0
e
k
1
s
m
d
C
B
d
k
1
k
2
k
1
e
k
1
s
m
e
k
2
s
m
0 ¼
k
2
C
A
0
ð
Þ
(E5-8.8)
s
which gives the contact time required for maximum production of B
ln
ð
k
2
=
k
1
Þ
k
2
k
1
s
m
¼
(E5-8.9)
and the corresponding concentration of B is given by
(E5-8.10)
k
2
k
1
k
2
k
2
k
1
C
B
max
¼ C
A
0
2. CSTR. We next examine the productivity from a CSTR.
Figure E5-8.2
shows a schematic diagram of the constant density CSTR.
C
A0
Q
A B C
C
A
C
B
C
C
Q
C
A
C
C
C
B
FIGURE E5-8.2
A schematic diagram of a constant density CSTR.
Mole balance for species A and B in the CSTR volume at steady state leads to
ðQC
A
Þ
0
QC
A
þ r
A
V ¼ 0
(E5-8.11)
0 ðQC
B
Þþr
B
V ¼ 0
(E5-8.12)
Noting also
s
¼
V
/
Q
, we arrive from
Eqns (E5-8.11) and (E5-8.12)
C
A
0
1 þ k
1
s
C
A
¼
(E5-8.13)
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