Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 201

11. Second-order reversible: A % B þ C, r ¼ k f C A k b C B C C

q

½1 þ k f s þ k b s ðC B 0 þ C C 0 þ 2C A 0 Þ

2

1 þ k f s þ k b s ðC B 0 þ C C 0 þ 2C A 0 Þ 4k b s ½C A 0 þ k b s ðC B 0 þ C A 0 ÞðC C 0 þ C A 0 Þ

C A ¼

;

2k b s

C A 0 C A

s ¼

k f C A k b ð C A 0 þ C B 0 C A Þð C A 0 þ C C 0 C A Þ

12. Second-order reversible: A þ B % R, r ¼ k f C A C B k b C R

q

½

2

1 k f s ð C A 0 C B 0 Þþ k b s þ 4k f s ½ C A 0 þ k b s ð C A 0 þ C R 0 Þ 1 þ k f s ð C A 0 C B 0 Þ k b s

C A ¼

2k f s

C A 0 C A
k f C A ðC B 0 C A 0 þ C A Þk b ðC A 0 þ C R 0 C A Þ

s ¼

þ % þ

D, r

¼ k f C A C B k b C C C D

13. Second-order reversible: A B C

q

½

2

1 k f s ð C A 0 C B 0 Þþ k b s ð C C 0 þ C D 0 þ 2C A 0 Þ þ 4 ð k f k b Þ s ½ C A 0 þ k b s ð C A 0 þ C C 0 Þð C A 0 þ C D 0 Þ 1 þ k f s ð C A 0 C B 0 Þþ k b s ð C C 0 þ C D 0 þ 2C A 0 Þ

C A ¼

2ðk f k b Þ s

C A 0 þ k b s ðC A 0 þ C D 0 ÞðC A 0 þ C D 0 Þ

C A ¼ if k f ¼ b b

1 k f s ð C A 0 C B 0 Þþ k b s ð C C 0 þ C D 0 þ 2C A 0 Þ

C A 0 C A

s ¼

k f C A ð C B 0 C A 0 þ C A Þ k b ð C A 0 þ C C 0 C A Þð C A 0 þ C D 0 C A Þ