Page 315 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WITHOUT CONVECTION 295

Analysis

a) The use of Eq. (B) in Table 8.10 with CA~ = CA,, CA~ = CA,, R1 = R and
Rz = 00 gives the molar rate of tmnsfer of species A to the fluid as

-
R
b) The concentration distribution is obtained jbm Eq. (0) of Table 8.10 in the
form
CA -CA, R
=-
CAW - CA, r
c) The molar transfer rate can also be calculated from Eq. (3.3-7) as

‘??,A = 4TR2(kc>(CA,,, - CAm)

Equating Eqs. (1) and (3) leads to

Therefore, the Sherwood number is

8.4.4 Diffusion and Reaction in a Catalyst Pore

At first, it may seem strange to a student to have an example on a reaction in
a catalyst pore in a chapter which deals with ‘‘steady-state microscopic balances
without generation.” In general, reactions can be classified as heterogeneous
and homogeneous reactions. A heterogeneow reaction occurs on the surface and is
usually a catalytic reaction. A homogeneous reaction, on the other hand, occurs
throughout a given phase. In Chapter 5, the rate of generation of species i per
unit volume as a result of a chemical reaction, Ri, was given by Eq. (5.3-26) in the
form
%i=air (8.4-41)
in which the term r represents a homogeneous reaction rate. Therefore, a ho-
mogeneous reaction rate appears in the inventory of chemical species, whereas a
heterogeneous reaction rate appears in the boundary conditions.
Consider an idealized single cylindrical pore of radius R and length L in a
catalyst particle as shown in Figure 8.31. The bulk gas stream has a species A
concentration of CA~. Species A diffuses through the gas film and its concentration