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

$$N_{W-P} = \dfrac{\mathfrak{R} R^2_p}{C_s D_{eff}} \le 3\beta$$

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:

$$\eta = \dfrac{3}{R^3_p} \int_{0}^{R_p} [1-\beta (1-r/R_p)^n] r^2\ dr$$

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 $$N_{W-P} \le 0.3$$ then pore diffusion limitations can be excluded.