Design of fixed-bed catalytic reactors based on effective transport models

Abstract

A semi-analytical solution of the system of simultaneous second order partial differential equations appearing in the design of a chemical reactor with axial and radial profiles of temperature t( x, z) and conversion f ( x, z) is presented for the case that the rate equation may be approximated by the linear equation r A = P( z)[ A + Bf( x, z) + Ct( x, z)] The temperature and the conversion at any desired position ( x, z) are described in function of Dini series, the coefficients of which may be determined by integration of a system of first-order differential equations. This solution has been used for a rapid evaluation of the importance of the radial gradients and as a starting procedure for those cases where a singularity in the t-surface near the wall at the entrance excludes numerical integration in the first parts of the reactor. The method of numerical integration used to explore larger bed depths is due to Crank and Nicolson. It follows from this study that serious radial gradients may occur in fixed-bed catalytic reactors. In addition, it is shown that when steep gradients occur the bulk mean temperatures and conversions predicted by the simple model used until now in design calculations of this type differ considerably from those calculated by the more refined model used in this paper.