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 {\displaystyle N_{W-P}={\dfrac {{\mathfrak {R}}R_{p}^{2}}{C_{s}D_{eff}}}\leq 3\beta }
Where R {\displaystyle {\mathfrak {R}}} is the reaction rate per volume of catalyst, R p {\displaystyle R_{p}} is the catalyst particle radius, C s {\displaystyle C_{s}} is the reactant concentration at the particle surface, and D e f f {\displaystyle D_{eff}} 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 {\displaystyle \eta } , and reaction order, n, the quantity β {\displaystyle \beta } is defined by the equation:
η = 3 R p 3 ∫ 0 R p [ 1 − β ( 1 − r / R p ) n ] r 2 d r {\displaystyle \eta ={\dfrac {3}{R_{p}^{3}}}\int _{0}^{R_{p}}[1-\beta (1-r/R_{p})^{n}]r^{2}\ dr}
for small values of beta this can be approximated using the binomial theorem:
η = 1 − n β 4 {\displaystyle \eta =1-{\dfrac {n\beta }{4}}}
Assuming η = 0.95 {\displaystyle \eta =0.95} with a reaction order n = 2 {\displaystyle n=2} gives value of β {\displaystyle \beta } equal to 0.1. Therefore, for many conditions, if N W − P ≤ 0.3 {\displaystyle N_{W-P}\leq 0.3} then pore diffusion limitations can be excluded.
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