Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 896

If the diffusion is not limiting, the effectiveness factor remains unchanged and thus the
increase in the overall net is clearer.
Therefore, if the effect of biocatalyst loading on the diffusivity is negligible, the overall
effect of higher biocatalyst loading is higher net reaction rate. However, there is a physical
limit on how much biocatalyst loading can be achieved. One can observe from Eqn (17.83)
that as long as the product of biocatalyst loading and effective diffusivity does not
decrease with increasing biocatalyst loading, increasing biocatalyst load is beneficial to
the reaction system. However, there is a cost associated with biocatalyst loading and
also the stability issue of biocatalyst at high loading, there is an optimum biocatalyst
loading.

17. 7. EXTERNAL AND INTERNAL SURFACE EFFE CTS

When the external surface area of the catalyst is significant as compared with the internal
surface area, one needs to consider the external surface area separately. The surface area of
porous particles can be expressed as

a c ¼ a e þ a i (17.84)

where a c is the total surface area (internal and external) per unit volume of the porous
particle, a i is the internal surface area per unit volume of the catalyst, and a e is the external
surface area per unit volume. For spherical particles,
a e ¼ 6 1 ε p
d p

(17.85)

where d p is the particle size and

ε p is the internal catalyst porosity. Let us define the ratio of
external to internal surface areas by

a e
a i

a r ¼ (17.86)

The rate of the reaction system is governed by

at surface þðr 0 AS Þa e

d C A
d x

k c aðC Ab C AS Þ¼aN A j To surface þðr 0 AS Þa e ¼D eA a

(17.87)

Based on our earlier definition for internal mass transfer effects:

at surface ¼ðr 0 AS Þa i h

d C A
d x

aN A j To surface ¼D eA a (17.88)

Let us now define an overall effectiveness factor for the total surface area, i.e.,

SN A j To surface þð r 0 AS Þ a e V
ðr 0 AS Þa c V

aN A j To surface þð r 0 AS Þ a e
ðr 0 AS Þa c

h s ¼ ¼ (17.89)