Biomedical Engineering Reference
In-Depth Information
TABLE 5.4
Steady-State Solutions of Reactions in a Constant Density CSTR with Simple Rate Law Expressions
1. Zero order: A
/
Products,
r
¼
k
C
A0
,
C
A0
,
C
B0
,
C
B0
,
C
C0
,
C
C0
,
C
D
0
,
C
D0
,
C
R0
C
R0
C
A
0
C
A
k
Q
Q
C
A
¼ max½
C
A
0
k
s
;
0
; s
¼
kC
1/2
2. Half-order: A
/
Products,
r
¼
p
k
2
k
2
2
2
þ 2C
A
0
k
s
þ 4C
A
0
C
A
0
C
A
kC
1=2
A
s
s
C
A
¼
; s
¼
2
3. First-order: A
/
Products,
r
¼
kC
A
A, B, C, D, R
A, B, C, D, R
C
A
0
C
A
0
C
A
kC
A
C
A
¼
s
; s
¼
;
1
þ
k
Q
Q
V
V
τ
=
τ
=
Q
Q
kC
2
4. Second-order: A
/
Products,
r
¼
C
A
,
C
A
,
C
B
,
C
B
,
C
C
,
C
C
,
C
D
,
C
D
,
C
R
C
R
p
1
þ
4k
s
C
A
0
1
C
A
0
C
A
kC
2
A
C
A
¼
; s
¼
;
2k
s
5. Second-order: A
þ
B
/
Products,
r
¼
kC
A
C
B
q
½1 k
s
ðC
A
0
C
B
0
Þ
2
þ 4k
s
C
A
0
1 þ k
s
ðC
A
0
C
B
0
Þ
C
A
¼
C
B
¼
C
B
0
C
A
0
þ
C
A
;
2k
s
C
A
0
C
A
s
¼
C
A
Þ
;
kC
A
ð
C
B
0
C
A
0
þ
þ
/
þ
Products,
r
¼
kC
A
C
R
6. Autocatalytic: A
R
2R
q
½
2
1
þ
k
s
ð
C
A
0
þ
C
R
0
Þ
1
þ
k
s
ð
C
A
0
þ
C
R
0
Þ
4k
C
A
0
s
C
A
¼
C
R
¼
C
R
0
þ
C
A
0
C
A
;
2k
s
C
A
0
C
A
s
¼
C
A
Þ
;
kC
A
ð
C
A
0
þ
C
R
0
(
Continued
)
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