A developed mathematical model for capturing carbon dioxide from gas streams by polymeric membranes in a concentrationdependent system

In addition to gas permeation simulation in polymeric membranes, many progresses have been attained on the theories whereby the mechanisms of transport are described. In this way, a numerous studies are assigned to achieve methods for determination of diffusion coefficient. Consequently, some correlated equations are obtained which consider diffusivity dependency on concentration, position or time, or any conjunction of them. Compared to the traditional time lag, a comprehensive approach developed by Frisch gives a general mathematical procedure for achieving the concentration dependent diffusion coefficient, disregarding the effect of membrane physical properties in the expression. In this study, a comprehensive algorithm is presented for direct determination of diffusion coefficient. It offers a predictive diffusivity (through the traditional time lag method) primarily, and then improves it to reach to a precise value (through the Frisch method). A comprehensive 2D mathematical model was developed and solved for CO2 gas permeation through the nonporous polymeric membranes. The results showed that considering the concentration dependency of diffusion coefficient via the Frisch method led to the small deviation of about 13 %, while the deviation of 360 % by the traditional time lag method was observed. Therefore, a reasonable conformity between the predicted values based on concentration dependant method and experimental available data for CO2 permeability is perceived.