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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