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# Prater Criterion

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 Title: Prater Criterion Author: World Heritage Encyclopedia Language: English Subject: Chemical reaction engineering Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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 \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.