Pore and solid diffusion models for fixed‐bed adsorbers

TLDR

Fixed‑bed adsorber models typically use either homogeneous solid or pore diffusion, and for linear isotherms these two approaches can produce identical breakthrough curves. This study delineates the specific conditions under which the homogeneous and pore diffusion models are equivalent. The analysis shows that a bulk flow factor matters only at high adsorbate concentrations, the pore model’s porosity factor becomes critical as porosity decreases, and for comparable beds the homogeneous model predicts a delayed early‑time breakthrough relative to the pore model, with solutions for irreversible isotherms provided for both models.

Abstract

Abstract Most models for fixed bed adsorbers have used either the homogeneoussolid or pore diffusion model for the pellets. When the adsorption isotherm is linear, the two models can lead to identical breakthrough curves. The conditions for this equivalence are presented here. It is shown that one of the bulk flow factors that was included in the formulation of one pore diffusion model will be significant only for feedstreams containing a relatively high concentration of adsorbate. The prosity factor of the pore model is shown to be very important, especially as the porosity decreases. The importance of the two diffusional models with respect to the predicted breakthrough curves is demonstrated. For comparable beds, it is shown that the breakthrough curve based on the homogeneous model is delayed with respect to that based on the pore model at early times, regardless of the shape of the isotherm. Finally, the various possible solutions for an irreverisble isotherm are reviewed for each of the models, and a solution is presented for the general case of a pore model with an outside film resistance.