The problem for reaction and diffusion in a catalyst pellet is
Weisz and Hicks [1962] showed how to transform this problem into one which can be solved using initial value methods. The problem can be written as
by using r = b z and d = b f. For any d we choose an arbitrary c(0) = c0 and integrate until the concentration reaches 1.0. Suppose that occurs at z = z1. Then we let
and we have the solution for the problem without iteration. We do not know in advance what f we have solved the problem for, so this techique is especially useful when we wish to solve the problem for a range of f. To employ this method requires a code that will stop when the dependent variable (here c) equals some value, rather than one which stops when the independent variable (here z) equals some value.
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