Page 251 - Introduction to chemical reaction engineering and kinetics

9.1 Gas-Solid (Reactant) Systems 233

We can eliminate Y, from this equation in favor of fn, from a relation based on the
shrinking volume of a sphere:

(9.1-27)

to obtain

1 [
1 - 3(1 - Q’s + 2(1 - fn) + +& 1 - (1 - Q’s

(9.1-28)

If we denote the time required for complete conversion of the particle (fn = 1) by tl,
then, from equation 9.1-28,

(9.1-29)

t, is a kinetics parameter, characteristic of the reaction, embodying the three parameters
characteristic of the individual rate processes, kAg, D,, and kkc, and particle size, R.

Equations 9.1-28 and -29 both give rise to special cases in which either one term (i.e.,
one rate process) dominates or two terms dominate. For example, if D, is small com-
pared with either kAg or kAs, this means that ash-layer diffusion is the rate-determining
or controlling step. The value of t or ti is then determined entirely by the second term
in each equation. Furthermore, since each term in each equation refers only to one rate
process, we may write, for the overall case, the additive relation:

t = t(film-mass-transfer control) + t(ash-layer-diffusion control) (9.1-30)
1
+ t(surface-reaction-rate control)

and similarly for tl .

For the situation in Example 9-1, derive the result for t(fE) for reaction-rate control,’ that
is, for the surface reaction as the rate-determining step (rds), and confirm that it is the

‘As noted by Froment and Bischoff (1990, p. 209), the case of surface-reaction-rate control is not consistent
with the existence of a sharp core boundary in the SCM, since this case implies that diffusional transport could
be slow with respect to the reaction rate.