Maxwell–Stefan modeling of slowing-down effects in mixed gas permeation across porous membranes

Abstract

Micro and meso-porous materials such as zeolites, Metal-organic Frameworks (MOFs), Covalent-organic Frameworks (COFs), Zeolitic Imidazolate Frameworks (ZIFs), Vycor glass, MCM-41 and SBA-15 are used in membrane separation in a wide variety of applications such as CO₂ capture. For process development and design purposes the Maxwell–Stefan (M–S) equations are widely used for modeling mixed gas permeation. In the M–S formulation we have basically two types of diffusivities: (a) D_i, that characterize species i–wall interactions in the broadest sense and (b) exchange coefficients D_ij that reflect how the facility for transport of species i correlates with that of species j. Such correlations have the effect of slowing-down the more mobile partner species in the mixtures. In many cases the D_i corresponds to the value of the pure component i; consequently these can be estimated from unary permeation data. The D_ij, on the other hand are not directly accessible from experimental data. The major objective of this communication is to stress the importance of proper estimation of the exchange coefficients D_ij. To achieve this objective and to illustrate the variety of issues involved, we consider permeation of CO₂/H₂, CO₂/N₂, CO₂/CH₄ and CH₄/H₂ mixtures across membranes with crystalline layers of four different materials: MFI (intersecting channels of 5.5 Å size), BTP-COF (one-dimensional hexagonal-shaped channels of 34 Å), LTA-Si zeolite (11.2 Å cages separated by 4.11 Å × 4.47 Å sized windows) and MgMOF-74 (1D hexagonal-shaped channels of 10.4 Å size). The required data on pure component adsorption isotherms are obtained from Configurational-bias Monte Carlo (CBMC) simulations. The M–S diffusivities are determined from Molecular Dynamics (MD) simulations. Our studies show that the permeation selectivities are crucially dependent on the proper modeling of the correlation effects. Increased upstream feed pressures lead to significant enhancement in permeation selectivities; this enhancement is directly traceable to the increase of the correlation effects with increased loadings. Use of some commonly used approaches, suggested in the published literature, lead to severe underestimation of permeation selectivities.