A study of effectiveness factors for reaction mixtures and pellets with non-uniform diffusivities

This work investigates the influence of internal diffusional and external mass transfer resistances on the effectiveness of porous catalyst pellets when many reactions proceed in parallel. The usual approach to this problem stems from the consideration of certain mean properties such as, the overall reaction rate and the mean effective diffusivity of the reacting species but completely neglects the effect of their distribution. In the present study, the effect of distribution of rate constants and diffusivities of various reacting species is considered and the result clearly demonstrates that the usual approach often misleads to higher effectiveness factor values. The asymptotic simplification of the effectiveness factor and the magnitude of the resulting errors is also discussed. In most works on the calculation of effectiveness factor for a single reaction, the effective diffusivity within a catalyst is assumed to be constant. However, the assumption is not valid when the catalyst exhibits a wide pore size distribution. Hence, a model that accounts for the variation of diffusivity with pore size is proposed to calculate the effective diffusivity of the reacting species. It correlates better with the values of diffusivities as back calculated from the reaction rates. Finally, the applicability of Petersen's criterion to neglect diffusional resistance in a catalyst is examined. It is shown that for certain kinetic expressions, the asymptotic solution of the effectiveness factor may deviate tremendously from its exact form.