Modelling in mixed matrix membranes for gas separation

Various gas permeation models including Maxwell model, Bruggeman model, Lewis-Nielson model and Pal model were compared via a modelling approach with the relative permeance of CO2 against published experimental data on silica filled polysulfone/polyimide (PSF/PI) mixed matrix membranes (MMMs). However, none of the tested models were able to predict the data with good accurately. A closer look at the cross-sectional image by scanning electron microscopy (SEM) indicated that the fillers were actually prolate ellipsoids dispersed within the matrix. Maxwell-Wagner-Sillar model was then employed to investigate the prolate effect and it was observed that the optimization curves of maximum packing (φm) and shape factor (n) showed least deviations. The percentage average absolute relative error (AARE %) value for fitted shape factor (nf) was found to be in the range of 1.12–2.17 at 2–10 bar pressure which showed its robustness. A further evaluation from SEM image showed that the shape factor along z-direction (nz) displayed a minimum deviation of 17.52 % for prolates at 0.102 ± 0.01. By using nz as upper limit and estimated shape factor ne through generalization, the error was reduced to 6.01 %. The AAR % deviation was found in the order of nf <ne < nz,which indicated the importance of shape factor parameter for estimating true CO2 permeance.