Weisz Prater Criterion

The Weisz-Prater Criterion is a method used to estimate the influence of pore diffusion on reaction rates in heterogeneous catalytic reactions. If the criterion is satisfied, pore diffusion limitations are negligible. The criterion is
N W − P = R R p 2 C s D e f f ≤ 3 β
Where R is the reaction rate per volume of catalyst, R p is the catalyst particle radius, C s is the reactant concentration at the particle surface, and D e f f is the effective diffusivity. Diffusion is usually in the Knudsen regime when average pore radius is less than 100 nm.
For a given effectiveness factor, η , and reaction order, n, the quantity β is defined by the equation:
η = 3 R p 3 ∫ 0 R p [ 1 − β ( 1 − r / R p ) n ] r 2   d r
for small values of beta this can be approximated using the binomial theorem:
η = 1 − n β 4
Assuming η = 0.95 with a reaction order n = 2 gives value of β equal to 0.1. Therefore for many conditions, if N W − P ≤ 0.3 then pore diffusion limitations can be excluded.