Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 200

TABLE 5.4 Steady-State Solutions of Reactions in a Constant Density CSTR with Simple Rate Law ExpressionsdCont'd

kC A
K A þ

7. Unimolecular catalytic: A / Products, r ¼

C A

q

ðK A C A 0 þ k s Þ

2

þ 4K A C A 0 K A þ C A 0 k s

C A 0 C A

kC A

C A ¼

; s ¼

ðK A þ C A Þ ;

2

kC 2 A
K A þ

8. Unimolecular: A / Products, r ¼

C A

q

K A þ 4ð1 þ k s ÞC A 0 K A

C A 0 C A

kC 2 A

C A ¼ ; s ¼ ð K A þ C A Þ

2ð1 þ k s Þ

9. First-order reversible: A % B, r ¼ k f C A k b C B

C A 0 þ k b s ð C A 0 þ C B 0 Þ
1 þðk f þ k b Þ s

C A 0 C A
k f C A k b ðC A 0 þ C B 0 C A Þ ;

C A ¼

; s ¼

kðC A C B =K C Þ
1 þ K A C A þ K B C B

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

q

½1 þ K B ð2C A 0 þ C B 0 Þþk s ð1 þ 1=K C ÞK A C A 0

2

4ðK A K B Þ½C A 0 þðC A 0 þ C B0 ÞðK B C A 0 þ k s =K C Þ 1 K B ð2C A 0 þ C B 0 Þk s ð1 þ 1=K C ÞþK A C A 0

C A ¼

;

2 ð K A K B Þ

C A 0 þð C A 0 þ C B 0 Þð K B C A 0 þ k s = K C Þ

C A ¼ if K A ¼ K B

1 þ K B ð 2C A 0 þ C B 0 Þþ k

s ð

1 þ 1 = K C Þ K A C A 0

C A 0 C A

s ¼

K C ½1 þ K A C A þ K B ðC A 0 þ C B 0 C A Þ k ½ C A ð C A 0 þ C B 0 C A Þ=