Analytical solution and new approximate model for a batch adsorber

A pore diffusion model for the operation of a batch adsorber with external film diffusion resistance and adsorption isotherm is formulated. The analyt ical solutions for three geometric adsorbents: a slab, a cylinder, and a sp here, with linear adsorption isotherm can be obtained but they converge too slowly to be of much use numerically when the partition ratio is large and /or the Blot number is large. A new two-stage model, which is a close appro ximation, can give good agreement with the analytical solution throughout t he time domain for wide range of partition ratio and Blot number. By compar ing with the analytical solution, it is proved that the new two-stage model is much better than the parabolic two-stage model and the parabolic profil e approximation. The influences of partition ratio and Blot number on the o peration of a batch adsorber are also studied.