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 ( φ_m) and shape factor (n) showed least deviations. The percentage average absolute relative error (AARE %) value for fitted shape factor (n_f) 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 (n_z) displayed a minimum deviation of 17.52 % for prolates at 0.102 ± 0.01. By using n_z as upper limit and estimated shape factor n_e through generalization, the error was reduced to 6.01 %. The AAR % deviation was found in the order of n_f <n_e < n_z,which indicated the importance of shape factor parameter for estimating true CO₂ permeance. [ABSTRACT FROM AUTHOR]