Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 889

The effectiveness factor is defined by Eqn (17.27) ,or

¼ r A ; obs
r AS

h (E17-3.2)

Assuming that the Thiele modulus for Run 1 is f 1 , from Eqn (E17-3.1) the Thiele modulus for
Run 2 is given by

d p 2
d p 1

f

2 ¼

f

1 ¼ 0:1

f (E17-3.3)

1

since only particle size has changed. From Eqns (E17-3.2) and (17.52) , we have

f f 1 r A ; obs 1

r A ; obs 2 ¼

h f

1 cothð3

f

1 Þ1=3 h

¼

2 Þ1=3

(E17-3.4)

f

2 cothð3

f

2

which leads to

2:00
10:5 ¼

f

1 cothð3

f

1 Þ1=3

1 Þ1=3 0:01

0:1 f

1 cothð0:3

f

or

0:0525 ¼ 0:1

f

1 cothð0:3

f

1 Þ1=3

(E17-3.5)

f

1 cothð

f

1 Þ1=3

This equation can be solved to give f 1 ¼ 5.9103. Therefore, we can compute

h 1 ¼ 0.15965 by using Eqn (17.52) ;

f 2 ¼ 0.59103 by using Eqn (E17-3.3) ;

h 2 ¼ 0.83188 by using Eqn (17.52) .

For negligible intraparticle diffusion effects, we set h 3 > 0.95. From Eqn (17.52) , we obtain

f 3 < 0.299529.

From Eqn (E17-3.1) , f

d p 3
d p 1

f

d p 1 < 0:299529
5:9103

f 3

¼ .Thus, d p 3 ¼ 2:54 mm ¼ 0.1287 mm.

f

1 1

Therefore, when the pellet size is smaller than 0.1287 mm, the internal diffusion effects are
virtually eliminated.
Example 17-4. Isothermal internal effectiveness factor for different kinetics. We have dis-
cussed the internal kinetics using a particular example, Eqn (17.8) , which is an irreversible
rate equation. What happens if different kinetics is observed? The least we can be sure is
that the procedure we have learned can be applied to any kinetics. In some cases, the results
can even be directly used. Here is an example: reaction

A B (E17-4.1)

%

occurs on a single site solid catalyst. LHHW kinetics is given by

k 0 ðC A C B =K C Þ
1 þ K 0 A C A þ K 0 B C B

r A ¼ (E17-4.2)