Weisz-Prater Criterion
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The Weisz-Prater Criterion is a method used to estimate the influence of pore diffusion on reaction rates in heterogeneous catalytic reactions.[1] 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 \(\eta \ge 0.95\) with a 1st or zero order reaction gives values of \(\beta\), 0.6 and 6 respectively. Therefore for many conditions, if \(N_{W-P} \le 0.3\) then pore diffusion limitations can be excluded.[2]
References
de:Weisz-Prater-Kriterium
