Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 803

kC A
K A þC A

(7) Unimolecular catalytic: A / Products, r ¼

q

ðK A C A0 þk

q

ðK A C A0 þk

2 2

s Þ

þ4K A C A0 K A þC A0 k K A þC A0 þ k

s s Þ

þ4K A C A0

s

C A ¼ ; r ¼ ;

2 2 s

kC 2 A
K A þC A

(8) Unimolecular: A / Products, r ¼

q

K A þ4ð1þk

q

K A þ4C A0 ð1þ k

s ÞC A0

K A K A þ2C A0 ð1þk

s Þ s Þ

C A ¼ ; r ¼

2ð1þk s Þ 2ð1þ k s Þ s

(9) First-order reversible: A % P , r ¼ k f C A k b C P

k f C A0 k b C P 0
1þðk f þk b Þ s

C A0 þ k b s ð C A0 þ C P 0 Þ
1þðk f þk b Þ s

C A ¼ ; r ¼ ;

K C Þ
1þK A C A þK B C B

kðC A C B =

(10) First-order reversible catalytic: A % B , r ¼

q

½1þK B ð2C A0 þC B0 Þþk

2

s ð1þ1=

K C ÞK A C A0 4ðK A K B Þ½C A0 þðC A0 þC B0 ÞðK B C A0 þk

s =

K C Þ 1K B ð2C A0 þC B0 Þk

s ð1þ1=

K C ÞþK A C A0

C A ¼ ;

2ðK A K B Þ

C A0 þðC A0 þC B0 ÞðK B C A0 þk

s =

K C Þ

C A ¼ if K A ¼ K B

1þK B ð2C A0 þC B0 Þþk s ð1þ1= K C ÞK A C A0

(11) Second-order reversible: A % BþC , r ¼ k f C A k b C B C C

1 þ k f s þ k b s ð C B0 þ C C0 þ 2C A0 Þ

q

2

½1þ k f s þk b s ðC B0 þC C0 þ2C A0 Þ 4k b s ½C A0 þk b s ðC B0 þC A0 ÞðC C0 þC A0 Þ

C A ¼

;

2k b s

(Continued)