The generalized adsorption models are developed to simulate the unsteady state mass transfer behavior in a packed column. Based on the nature of adsorbent particles, the adsorption models may be classified into two categories: (1) the surface adsorption model, (2) the pore diffusion model. In the first model, it is assumed that the internal diffusion is negligible, and the adsorption rate is determined by external diffusion and surface adsorption. In the second model, the effect of internal diffusion is considered as significant as that of external diffusion. For both models, the effect of axial dispersion in fluid phase is emphasized. A total of four different kinds of adsorption models are solved analytically-two in each category.

In the modelling of adsorption process with axial dispersion (dispersion model), the boundary conditions provided in published literatures are inadequate to describe the real situations. In this study, a novel and rigorous approach using the mass conservation law is employed to set up the proper boundary conditions. Two different sets of boundary conditions are used for the dispersion model; one set is specified by the continuity equation of adsorbate at the inlet of the column (at z=0) , and the other set is characterized by the total material balance of adsorbate over the entire column. The analytic solutions are presented as dimensionless effluent concentration (C_A/C_Ao) versus effluent volume or elapsed time in terms of the variations of system parameters. These results provide quantitative information for the design and scale-up of packed bed operations. Moreover, the proposed adsorption models are verified experimentally with the system of hemoglobin-albumin-CM sepharose-DEAE sepharose. The theoretical predictions of concentration variations are shown to be a good representation of experimental data.