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. [Citation|last1=Weisz|first1=P. B.|last2=Prater|first2=C. D.|title=|journal=Advances in Catalysis|volume=6|date=1954|pages=143] If the criterion is satisfied, pore diffusion limitations are negligible. The criterion is

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 is defined by the equation:

for small values of beta this can be approximated using the binomial theorem:

Assuming $eta\; ge\; 0.95$ with a 1st or zero order reaction gives values of , 0.6 and 6 respectively. Therefore for many conditions, if $N\_\{W-P\}\; le\; 0.3$ then pore diffusion limitations can be excluded. [cite book|last=Vannice|first=M. Albert| title=Kinetics of Catalytic Reactions|publisher=Springer Science+Business Media|place=New York|year=2005|pages=63-65]

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