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.