Secondary Effectiveness Factors and Solubility Effects for Catalytic Reactions in Series

Thiele moduli and effectiveness factors are powerful ways to account for mass transfer limitations on reactions occurring within porous catalyst particles. Effectiveness factors have been developed for numerous rate laws, geometries, and nonisothermal situations, but not for reactions in series. This manuscript develops an effectiveness factor for the second step in the A → B → C reaction sequence with first-order kinetics and slab geometry. The expressions are more complicated than the familiar primary effectiveness factors because the intermediate B is being generated and consumed within the catalyst particle. We illustrate the application of the secondary effectiveness factor by modeling the conversion from A to B and C for plug flow through a porous ceramic monolith catalyst. Then we modeled A → B → C in a slurry of catalyst flakes within a well-stirred batch reactor, including equilibrium solvent-molecular sieve partition coefficients for the A and B species. When both Thiele moduli are small and the molecular sieve adsorbs A more strongly than B, the second reaction is suppressed. This situation can give essentially 100% yield of B, even when A and B have similar reactivities within the catalyst. Our results provide a framework for predicting the effects of interior mass transfer limitations and solvent-solid phase partitioning in heterogeneously catalyzed series reactions.