Biomedical Engineering Reference
In-Depth Information
TABLE 16.1
Steady-state solutions of reactions in a CSTR with simple kinetic expressions.
s
D¼1.
(1)
Zero order: A
/
Products, r
¼
k
C
A
¼
max
½C
A0
k
s
; 0
;
r ¼ k
Products,
r ¼ kC
1=2
A
(2)
Half-order: A
/
p
k
2
k
2
p
k
2
2
2
þ2C
A0
k
þ4C
A0
k
2
s
s
s
C
A
¼
;
r ¼
2
þ4C
A0
k
s
s
2
(3)
First-order: A
/
Products, r
¼
kC
A
C
A0
1þk
kC
A0
1þ k
C
A
¼
r ¼
;
s
;
s
Products,
r ¼ kC
2
A
(4)
Second-order: A
/
p
1þ4k
p
1þ4k
C
A0
1
1þ2k
C
A0
C
A0
s
s
s
C
A
¼
;
r ¼
;
2
2k
s
2k
s
(5)
Second-order: A
þ
B
/
Products, r
¼
kC
A
C
B
q
½1 k
2
s
ðC
A0
C
B0
Þ
þ4k
s
C
A0
1þ k
s
ðC
A0
C
B0
Þ
C
A
¼
;
C
B
¼ C
B0
C
A0
þC
A
2k
s
q
½1k
2
1þ k
s
ðC
A0
þC
B0
Þ
s
ðC
A0
C
B0
Þ
þ4k
s
C
A0
r ¼
;
2k
2
s
(6)
Autocatalytic: A
þ
R
/
2R
þ
Products, r
¼
kC
A
C
R
q
½1þ k
2
1þk
s
ðC
A0
þC
R0
Þ
s
ðC
A0
þC
R0
Þ
4k
C
A0
s
C
A
¼
;
C
R
¼ C
R0
þC
A0
C
A
2k
s
q
½1þ k
2
r ¼
1þ k
s
ðC
A0
C
R0
Þþ
s
ðC
A0
þC
R0
Þ
4k
C
A0
s
;
2
2k
s
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