A semi-empirical approach for predicting the performance of mixed matrix membranes containing selective flakes

A successful model for mixed matrix membrane performance must address the complex geometry of the problem and accurately treat the diffusion behavior of the host-guest systems being considered. Detailed calculations based on the Maxwell-Stefan equations provide a widely accepted means of treating the diffusion of gases within zeolites. However, a full numerical solution of these equations for a complex mixed matrix membrane geometry does not offer the convenience and transparency that comes with an analytical treatment. At the same time, existing analytical equations which were formulated specifically to address mixed matrix geometry do so under the assumption of very simplistic models for diffusion. Here, an approach is presented for predicting the permeability and selectivity of mixed matrix membranes containing zeolite flakes that combines well-known analytical expressions for mixed matrix membrane performance with Maxwell-Stefan modeling for zeolite diffusion. The constant permeabilities required by the analytical models are calculated by the Maxwell-Stefan equations as a function of operating conditions, and these calculated effective permeabilities are used to predict mixed matrix membrane performance at corresponding operating conditions. The method is illustrated through two case studies: normal- and iso-butane separation by a membrane containing silicalite-1 flakes and carbon dioxide/methane separation by membranes containing CHA-type zeolites. Predictions are compared to experimental results found in the literature for both cases. Also, the applicability of the Maxwell and Cussler analytical models for mixed matrix membrane performance is explored as a function of flake loading and aspect ratio.