Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 869

D AB ¼ 4:5 10 4

m
rD AB ¼

n

Sc ¼

3:47 10 4 ¼ 1:297

From Eqn (17.3) , we obtain

D AB
d p

D AB

ε d p 0:4548Sc 1=3 Re 0:5931

k c ¼ Sh ¼

3:47 10 4
0:35 3:663 10 3 0:4548 1:297 1=3 81:4 0:5931 m

¼ =

s

s
The specific surface area from Eqn (E17-2.4) ,

¼ 1:824 m =

a c ¼ 2 d c þ 4 h c
d c h c

ð1 ε Þ¼ 2 2:54 þ 4 5:08
2:54 5:08

mm 1 ¼ 1:280 10 3 m 1 ð1 0:35Þ

From Eqn (E17-2.8) ,

U L

1:824 1:280 10 3
10

k c a c

f Ae ¼ 1 exp ¼ 1 exp 0:0508

¼ 1 7:06 10 6 z 1
That is, near complete conversion.

17.3. REACTIONS IN ISOTHERMAL POROUS CATAL YSTS

When active reaction sites are also available inside porous particles in addition to the external
(outer) surface, one needs to account for the reaction occurring inside the particles. In solid
catalysis, catalyst is supported by a solid matrix and the active sites are distributed on the
surfaces inside the pores of the catalyst. In reactions catalyzed by biocatalysts, one commonly
constrains biocatalyst in capsules (spherical particles), growing biocatalysts into a “thin” film,
or by attaching on surfaces (slabs). In these cases, the catalytic reaction is not just occurring on
the external surfaces but inside the “porous solid particles” as well. Especially in the case of
encapsulation, the reaction is negligible on the external surface of the particle itself. Reaction
and diffusion occur in the same time inside the particles. Therefore, internal (intraparticle)
diffusion and reaction can be dominant in most heterogeneous reaction systems.
Fig. 17.4 shows two commonly encountered geometries of catalysts. The concentration of
reactant A is highest in the bulk fluid phase. Mass transfer takes species from the bulk fluid
phase to the solid (catalyst) external surface. Reactant A diffuses into the porous catalyst and
reacted away. When it reaches the farthest side of catalyst, the concentration of A is the
lowest, and no mass flow passing the farthest side.
Fig. 17.5 shows a schematic of a porous catalyst layer, which is a simplification and gener-
alization from Fig. 17.4 a and b. Other than the side marked as “outer surface” at x

¼ d p , all the
surfaces are either impermeable (solid wall) or symmetrical conditions (i.e. zero normal