On the formulation of linear driving force approximations for adsorption and desorption of multicomponent gaseous mixtures in sorbent particles

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A generalized linear driving force (LDF) approximation for multicomponent adsorption-based separations is formulated in this study. It is based on the three-parameter dusty-gas model and accounts for bulk diffusion, Knudsen diffusion, Knudsen flow and viscous flow in the sorbent particle. No restrictions are imposed on the type of adsorption isotherm. The generalized LDF approximation equations are derived using global or piecewise continuous polynomial approximations for the intraparticle partial pressure profiles and applying the subdomain method of weighted residuals to the mass balance equations. Similar expressions are derived using the Fickian diffusion model and the Fickian diffusion/convection model. The validity of the various approximations is examined by comparing their predictions to the exact solution of the corresponding intraparticle models. Since the generalized LDF approximation permits the inclusion of convective coupling among the various species, it can satisfactorily predict the overshoot in the uptake of the less adsorbable/faster moving species in a multicomponent mixture. This phenomenon cannot be described by existing LDF approximations, since their derivation is based on transport and adsorption models that do not account for the coupling of the fluxes of the components of the multicomponent mixture. For short cycle times, the accuracy of the approximation increases with the degree of the polynomial. However, a generalized LDF approach, based on a fourth degree global polynomial approximation, may suffice in most applications.