Mathematical modeling of temperature and pressure effects on permeability, diffusivity and solubility in polymeric and mixed matrix membranes

Abstract

Due to the temperature and pressure dependency of gas transport through polymeric and mixed matrix membranes, probing of their separation performance at different operational conditions seems crucial to determine an optimal operational condition. To minimize the number of costly and time consuming experiments, a modified form of van’t Hoff-Arrhenius model was developed to consider the simultaneous effects of temperature and pressure on the separation performance of polymeric and mixed matrix membranes. Moreover, the proposed model is capable to consider pressure dependency of energetic parameters of Arrhenius model including activation energies of permeability and diffusivity, heat of sorption and the corresponding pre-exponential factors. The validity of the proposed model was investigated by using permeation coefficients of CO2 and N2 in a binary mixture through 6FDA-DAM at different temperatures in the range of 35–55 °C and in the feed pressure range from 2 to 5 atm. Besides, from data taken from the literature, the proposed model was validated by the prediction of temperature and pressure dependency of transport properties of glassy and rubbery polymers as well as mixed matrix membranes (MMMs) for different gas molecules including He, H2, CO2, O2, N2, CH4 and C4H10. Predictions corresponding to 300 data points revealed that the maximum average absolute relative error was 5.1%.