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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