Effectiveness factors for continuous mixtures

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Abstract
Catalyst effectiveness factors provide a quantitative estimate of diffusion resistance for chemical reactions in porous particles. The objective of this research is to develop an approach to calculate liquid‐phase, porous‐particle effectiveness factors, which are based on spherical reactant molecules and cylindrical pores that both have size distributions. Reactants larger than a given pore are excluded from the pore. A first‐order reaction occurs when reactant molecules diffuse into pores that hinder their movement due to steric interactions with the pore wall. The reactant size distribution is described by rectangular or gamma distributions, and the pore‐size distribution is modeled by continuous rectangular or discrete fractal distributions. Effectiveness factors are defined and evaluated for (a) one‐size reactants in one‐size pores, (b) all reactants in one‐size pores, (c) one‐size reactants in all pores, and (d) all reactants in all pores. Most of the discussion deals with equal‐length pores, but the effect of a distribution of pore lengths is also considered.