Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 185

TABLE 5.2 Reaction Space Time Requirement and Concentration Profile for Single Reactions in an
Isothermal Constant Density Plug Flow Reactor (PFR) with Simple Kinetic ModelsdCont'd

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

1
k f þ

k f C A 0 k b C B 0

s ¼

k b ln C B 0 Þ ; ð k f þ k b Þ C A k b ð C A 0 þ

k f C A 0 k b C B 0 exp k f þ k b s þ k b C A 0 þ C B 0
k f þ k b

C A ¼

C A
9. Catalytic first-order reversible: A

C B ¼ C A 0 þ C B 0

K C Þ
1 þ K A C A þ K B C B

k ð C A C B =

% B, r ¼

<
:

=
;

1 K B þ ln ð1 þ K C ÞC A 0 ðC A 0 þ C B 0 Þ

ð1 þ K C ÞC A ðC A 0 þ C B 0 Þ

K A

K C
kð1 þ K C Þ

K A K B
K C

s ¼

K B Þð C A 0 C A Þþ þð C A 0 þ C B 0 Þ

C B ¼ C A 0 þ C B 0 C A

10. Reversible decomposition: A % B þ C, r ¼ k f C A k b C B C C

q

½

2

4k b ð a ; b ¼ k f þ k b ð 2C A 0 þ C B 0 þ C C 0 Þ k f þ k b ð 2C A 0 þ C B 0 þ C C 0 Þ C A 0 þ C B 0 Þð C A 0 þ C C 0 Þ

Þ exp a

b

ð 2k b C A 0 ð 2k b C A 0 Þ

a b s b a

2

b ln ð

2k b C A 0 a Þð 2k b C A b Þ 1

2k b

2

Þ exp a

s ¼

Þ ; C A ¼ ð 2k b C A 0 Þð 2k b C A b

a b a

ð 2k b C A 0 b s ð 2k b C A 0 a Þ

2

C B ¼ C A 0 þ C B 0 C A ; C C ¼ C A 0 þ C C 0 C A

11. Reversible codimerization: A þ B % C, r ¼ k f C A C B k b C C

q

½k f ðC A 0 C B 0 Þk b

2

a ; b ¼ k f ðC A 0 C B 0 Þk b þ 4k f k b ðC A 0 þ C C 0 Þ

Þ exp

a b

a ð2k f C A 0 b b ð2k f C A 0 a Þ

s

2

a ln ð

2k f C A 0 a Þð 2k f C A b Þ 1

2k f

2

Þ exp

s ¼

Þ ;

C A ¼

b ð2k f C A 0 b Þð2k f C A a a b

ð 2k f C A 0 b ð 2k f C A 0 a Þ

s

2

C B ¼ C B 0 C A 0 þ C A ; C C ¼ C A 0 þ C C 0 C A

þ % þ

D, r

¼ k ( C A C B C C C D /K C )

12. Reversible bimolecular: A B C

p

a

a ¼ K C ð C A 0 C B 0 Þ 2C A 0 C C 0 C D 0 ; a ; b ¼ a

2

þ 4 ð K C 1 Þð C A 0 þ C C 0 Þð C A 0 þ C D 0 Þ

2K C

ln ½2ðK C 1ÞC A 0

a ½2ðK C 1ÞC A b

s ¼

; kð b a Þ ½2ðK C 1ÞC A 0 b ½2ðK C 1ÞC A a

exp

a b

2K C k

½ 2 ð K C 1 Þ C A 0 ½ 2 ð K C 1 Þ C A 0

a b s b a

1

exp

C A ¼

a b

2K C k

2 ð K C 1 Þ

½ 2 ð K C 1 Þ C A 0 b s ½ 2 ð K C 1 Þ C A 0 a

C B ¼ C B 0 C A 0 þ C A ; C C ¼ C A 0 þ C C 0 C A ; C D ¼ C A 0 þ C D 0 C A