Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 893

The rate of reaction can be expressed as

r max C A
K m þ C A

r A ¼ (E17-4.3)

when the reaction rate and concentration of A are evaluated based on the gel volume. The
kinetic parameters are given by r max ¼ 2 g/m 3 -gel. To compute

the effectiveness factor, we need both K b and f . From the saturation constant,

0.4 g/(s/m 3 -gel) and K m ¼

K m
C AS

K b ¼ (E17-4.4)

and the Thiele modulus can be computed by Eqn (17.31) or

r

r max
2D eA C AS

Þ 1=2 ½1 K b lnð1 þ K 1

d p
6

b

f ¼ (E17-4.5)

1 þ K b

Both K b and f require C AS , which is an unknown that needs to be determined from Eqn
(E17-4.2) . Therefore, iterative scheme is needed to solve the problem.
Since C AS <

1 g/m 3 , we know from Eqn (E17-4.4) that K b >

C Ab ¼ 2. We can start the iter-

ative solution by assuming K b / N . Eqn (E17-4.5) leads to

r

r max
D eA K m

d p
6

f j K b / N ¼ (E17-4.6)

f

K b / N¼

11.18. From Eqn (17.52) ,

f cothð3 f Þ1=3

h

1 ¼

(E17-4.7)

f 2

h ¼ 0.08678. With a value of h , we can solve for concentration of nitrate on the gel surface

through Eqn (E17-4.2) ,or

h r max C AS

K m þ C AS V gel ¼ k c a c VðC Ab C AS Þ

(E17-4.8)

r max V gel
k c a c V ¼

0:4 0:2
10 5 6ð1 0:2Þ
1:5 10 3

m 3 m 3 . Eqn (E17-4.8) is reduced to Let K r ¼ g = ¼ 2:5 g =

K r C AS
K m þ C AS ¼ðC Ab C AS Þ

h (E17-4.8)

which can be solved to give (only the root that is physical is retained):

q

ðC Ab K m hK r Þ 2 þ 4K m C Ab C Ab K m hK r þ

C AS ¼ (E17-4.9)

2

0.93108 g/m 3 . That is, C AS ¼