Page 337 - Modelling in Transport Phenomena A Conceptual Approach

8.5. MASS TRANSPORT WITH CONVECTION 317

Note that although XA, is a known quantity, the mole fraction of species A in
the gas phase at the catalytic surface, XA~, is unknown and must be determined
from the boundary condition. For heterogeneous reactions, the rate of reaction is
empirically specified as
at Z = 6 NA, = kSCA = kSCXA (8.556)

is
where IC" is the surface reaction rate constant. Therefore, XA~ expressed from
Eq. (8.556) as
(8 5-57)

Substitution of Eq. (8.5-57) into Eq. (8.555) results in

(8.558)

which is a transcendental equation in NA,. It is interesting to investigate two
limiting cases of Eq. (8.5-58).

Case (i) IC" is large

Since In( 1 - x) N - x for small values of x, then
h[1-0.5(N~,/Ck')] 11 -0.5(N~,/Ck~) (8.559)

so that Eq. (8.5-58) reduces to

2 CDAB
A2
NAz = - 1 (8.560)
6
(m) - 0.5~~~)
In
(1
in which A represents the ratio of the rate of heterogeneous reaction to the rate of
diffusion and it is given by
(8.561)

Case (ii) ks = 03
This condition implies instantaneous reaction and Eq. (8.558) takes the form
NA. = - 1 )
2cDABln(
6 1 - 0.5 XA, (8.5-62)
When k" = 00, once species A reaches the catalytic surface, it is immediately
converted to species B so that XA~ = 0. Note that Eq. (8.562) can also be obtained
from Eq. (8.5-55) by letting XA~ = 0.