Asymptotic Analysis of Intraparticle Diffusion in GAC Batch Reactors

Abstract

The homogeneous surface-diffusion model (HSDM) and the pore-surface-diffusion model (PSDM) for adsorption on granular activated carbon in a completely mixed batch reactor are examined in the near-equilibrium regime. In this asymptotic regime, linearized model equations yield analytic solutions for the measurable rate of adsorbate uptake involving effective diffusion coefficients. The theoretical asymptotic analysis is verified by numerical simulation of the complete equations. A basis is therefore provided for a method of determining diffusion coefficients from batch experiments that is simpler, more flexible, and more robust than those presently used. The present work also clarifies differences in the qualitative effects of pore and surface diffusion and suggests a preliminary graphical criterion for assessing directly from experimental data the possible importance of surface diffusion relative to other possible intraparticle transport mechanisms. A method for determining both poreand surface-diffusion coefficients when the pore-surface-diffusion model is appropriate and the appropriate data available are described. The proposed approach is illustrated by the analysis of two data sets available in the literature, and the resulting estimates are compared with those obtained by a more conventional method.