Homogeneous models for porous catalysts and tubular reactors with heterogeneous reactions

Abstract

One-dimensional models for porous catalysts and laminar flow tubular reactors with first-order reactions at the walls are developed. The method which is used replaces the transport equations containing the local concentrations with equations, similar to those used in the dispersion theory, for the concentrations averaged over the cross section. The main assumption is the approximation of the coefficients in the dispersion equations by those valid for a pulse of concentration introduced at time zero at the mouth of the pore or at the inlet of the tube. The effectiveness factor depends not only on the Thiele modulus but also on the length-to-radius ratio of the catalyst pore. The one-dimensional model for the catalytic tubular reactor provides a good approximation to the area-mean concentration for β ( k sR / D) up to 1·0. The comparison is made with an exact orthogonal expansion solution developed also in the paper. For larger values of β, say β ≈ 100, the discrepancies between the exact solution and the one-dimensional model may be as high as 50 per cent. Therefore, a generalized dispersion solution is presented to obtain more accurate predictions for β > 1·0.