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
$N_{W-P}={\dfrac {{\mathfrak {R}}R_{p}^{2}}{C_{s}D_{eff}}}\leq 3\beta$
Where ${\mathfrak {R}}$ 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 $D_{eff}$ 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,$\eta$, and reaction order, n, the quantity $\beta$ is defined by the equation:
$\eta ={\dfrac {3}{R_{p}^{3}}}\int _{0}^{R_{p}}[1-\beta (1-r/R_{p})^{n}]r^{2}\ dr$
for small values of beta this can be approximated using the binomial theorem:
$\eta =1-{\dfrac {n\beta }{4}}$
Assuming $\eta =0.95$ with a reaction order $n=2$ gives value of $\beta$ equal to 0.1. Therefore, for many conditions, if $N_{W-P}\leq 0.3$ then pore diffusion limitations can be excluded.