WeiszPrater

Weisz-Prater is a criterion used in chemical engineering to assess whether internal diffusion within a porous catalyst pellet limits the overall rate of a reaction. Also referred to as the Weisz-Prater number, it provides a dimensionless measure of the potential impact of intraparticle mass transport on observed kinetics. The concept helps engineers decide if a reaction rate is controlled by chemistry, diffusion inside the pellet, or a combination of both.

The standard form of the Weisz-Prater criterion is N_WP = (R_p^2 * (-r_A)) / (D_eff * C_A,s), where R_p is the pellet radius, D_eff is the effective diffusivity of the reactant A in the pellet, C_A,s is the concentration of A at the pellet surface, and -r_A is the apparent rate of consumption of A per unit pellet volume. The minus sign ensures a positive numerator for a consuming reactant. In this formulation, a value much less than 1 indicates diffusion inside the pellet is not limiting; a value around 1 or greater suggests significant internal diffusion resistance influencing the observed rate.

Usage and scope: The criterion is widely used to screen catalyst pellets, especially when they are large or highly active. It is often derived for spherical pellets, with variants for slabs or cylinders. It does not account for external mass transfer limitations, which are treated separately with film diffusion criteria. The Weisz-Prater test is a diagnostic tool to decide whether internal diffusion effects must be included in kinetic modeling.

History: The criterion was introduced by Josef Weisz and James T. Prater in the 1950s to provide a practical means of evaluating intraparticle diffusion in porous catalysts.