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

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) Ði, that characterize species i–wall interactions in the broadest sense and (b) exchange coefficients Ðij 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 Ði corresponds to the value of the pure component i; consequently these can be estimated from unary permeation data. The Ðij, 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 Ðij. 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.