Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 861

where d p is the particle diameter, m f is the dynamic viscosity of the fluid (liquid or gas phase), r f
is the density of the fluid, and U is the superficial fluid flow velocity (i.e. computed as if solid
particles were absent in the bed: volumetric flow rate divided by cross-sectional area of flow).
Mass transfer coefficient is thus a function of temperature, pressure, flow rate, and particle size
( Tabl e 17. 2 ). The effect of transporting species only enters through the diffusivity D AB .

17.2. EXTERNAL MASS TRANSFER

When reaction is catalyzed by solid catalyst (or enzyme or cells), the reaction is not occur-
ring inside the bulk fluid phase. In this case, the reaction rate is only a function of the reactant
concentrations right on the surface of the catalyst. The average concentration in the bulk fluid
phase, C Ab for species A, and that on the catalyst surface, C AS for species A, are different in
general due to the consumption of reactants (or generation of products). Fig. 17.1 shows
a schematic of the reaction system. The solid catalyst is represented by a sphere with a radius
of d p /2, surface area of S and a volume of V . When pseudo-steady state is reached, the reac-
tion rate and the mass transfer rate between the bulk and the catalyst surface must be equal.
This is understood by a mass balance enclosing the catalyst (sphere) only:

d n A
d t

N A S 0 þ r AS V ¼ (17.5)

where n A is number of moles of species A inside the catalyst particles, and r AS istherateof
generation of A as evaluated by the concentrations on the surface of the catalyst (based on
the volume of the catalyst). Since species A is not able to penetrate the solid, it is not able to
accumulate inside the catalyst. Thus, the right-hand side is zero. Eqn (17.5) is thus reduced
to

k c aðC Ab C AS Þ¼r AS (17.6)

C A

2

C A | r = C Ab

S = d p

3

V = d p r = d p / 2

C A = C AS

r = 0

r

r = d p / 2

FIGURE 17.1 A schematic of a solid spherical particle and concentration of A in variation with the radial
direction of the sphere.