The influence of particle shape on the dynamics of fixed beds

Abstract

Transient mass transfer in a fixed-bed is studied mathematically. A previous analytical solution for beds of spherical particles is generalized to include ”infinite” slabs and cylinders. Processes that are accounted for are advection and longitudinal dispersion in the interparticle void space, fluid-to-particle diffusion, intraparticle diffusion, and reversible first-order adsorption for a first-order reaction on the interior particle surface. The same generalization of a solution is also obtained for the conversion in continuous-slurry and batch reactors. Calculations show that if the area-to-volume ratio of the slabs, cylinders and spheres is the same, identical breakthrough curves are produced for short and long contact times. In the intermediate range the first breakthrough times are in the order of spheres < cylinders < slabs. In the case of a chemical reaction the steady-state concentrations are in the order of slabs < cylinders < spheres. However, the differences are, in most situations, not very large. In many cases they should be of relatively minor importance. In systems with no chemical reaction, using a shape factor, based on the matching of second central moments, gives better agreement for intermediate bed lengths and longer times. At early times a poor agreement is obtained.