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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