Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 866

which is clearly mass transfer limiting. Eqn (17.17c) leads to

1
1 þ

1
1 þ 937:05 ¼ 1:066 10 3

h e ¼

f e ¼

The effective reaction rate is

h e ðr Ab Þ¼1:066 10 3 12:414 0:24 m 3 -beads

r A ; obs ¼ mol-O

2 =

0:24 þ 0:24

¼ 6:617 10 3 mol-O m 3 -beads

2 =

2. U ¼ 1m/s,Re ¼ d p Ur L / m ¼ 0.001 1 1000/0.001 ¼ 1000

10 9 )

ε ¼ 1 0.4 ¼ 0.6, Sc ¼ m /( r L D AB ) ¼ 0.001/(1000 2.3 ¼ 434.78.

Eqn (17.3) leads to

Sh ¼ 0:4548 Sc 1=3 Re 0:5931
ε

k c d p
D AB

¼ (E17-1.2)

Thus,

k c ¼ 0:4548 Sc 1=3 Re 0:5931
ε d p

D AB

¼ 2:3 10 9 0:4548 434:78 1=3 1000 0:5931
0:6 0:001

m 2 = s

¼ 7:945 10 4 m 2 =

s

From Eqn (17.13)

r max
ðk c aÞðK m þ C Ab Þ ¼

12:414
7:945 10 6 ð6=0:001Þð0:24 þ 0:24Þ ¼ 5:425

f e ¼

Applying Eqn (17.14) , we obtain

(

9
=

s

1
4

2

h e ¼ f e

1 þ f e K A

C Ab

K A
C Ab

K A
C Ab

1 þ 1 f e ð1 þ

f e Þ þ

2 ;

( )

r

1
4 ½1 5:425 ð1 þ 5:425Þ1 2 þ 1

1
5:425

1 þ 5:425
2

¼ ð1 þ 1Þ

¼ 0:16748
The effective reaction rate is

h e ðr Ab Þ¼0:16748 10 3 12:414 0:24

m 3 -beads

r A ; obs ¼

mol-O 2 =

0:24 þ 0:24

m 3 -beads ¼ 1:0396 mol-O 2 =