A multiscale model for carbon adsorption of BTX compounds: Comparison of volume averaging theory and experimental measurements

In this work, the method of volume averaging is applied for the mathematical modeling of transport and adsorption of benzene, toluene, and xylene in a packed bed of activated particles. One benefit of this approach is that it allows one to directly incorporate measured microscale information into macroscale models for predicting the effective transport and adsorption process. This work is novel in that it combines two levels of upscaling and a nonlinear adsorption process. The first level of upscaling develops an effective model for the mass transport and reaction in an activated carbon particle; within the particle, only diffusion and reaction are considered because of the very small pore sizes. The second level of upscaling develops the effective model for a collection of carbon particles forming the porous medium contained in a fixed-bed reactor; here, convection, diffusion, and dispersion are considered. The resulting model resembles a classical mobile-immobile representation of the transport and adsorption process. As part of the upscaling process, we develop the homogenized transport equations and their associated effective parameters using two different averaging volume support scales (i.e., at two disparate length scales). The effective parameters are all diffusion or dispersion tensors. These include (1) the effective diffusion tensor defining diffusion in the homogenized carbon particle, (2) the effective diffusion tensor for the immobile phase in the two-region representation of the medium, and (3) the effective hydrodynamic dispersion tensor (which included diffusion and dispersion) for the mobile region of the porous catalyst bed. Each of these effective parameters are determined by numerically solving closure problems over an idealized spatially periodic model of a porous medium. One novel feature of these particular closure problems is that they describe nonlinear adsorption at the microscale, which is a problem that is not currently represented in the literature. Once derived, the two-scale, two-equation mobile-immobile model was applied to predict experimentally-measured concentration breakthrough curves from packed bed columns with activated carbon from coconut shell as the adsorbent to the removal of petrochemical contaminants (BTX) by adsorption. There were no adjustable parameters in this modeling effort; the only modeling choice was whether the mass transfer coefficient should be computed from the correlations of Wakao and Funazkri (1978) for BTX components. The equations from closure problems and Darcy's scale of transport of this work were discretized using the finite volumes method and the solutions are found numerically through of a computational code and some packages from the free software OpenFOAM (R), version 2.2.x. This work has been selected by the Editors as a Featured Cover Article for this issue. (C) 2018 Elsevier Ltd. All rights reserved.