Estimation of mixed-gas selectivity of membranes using the linear friction-based model

The development of analytical models for predicting the transport properties of membranes in the separation of multicomponent mixtures is highly relevant because (1) measurements of permeability and sorption of gas mixtures in membrane materials are laborious and time-consuming, and (2) estimation of transport properties based on pure gas measurements is desirable, however, rather unreliable and can lead to serious errors. In this paper, within the framework of the well-known frictional-coefficient formalism, we present nonlinear equations for the fluxes of gas mixture components through the membrane, which take into account the diffusional coupling of the fluxes compared to independent gas transport. As a result, an analytical equation for the mixed-gas selectivity was obtained. This equation has an implicit form, which is not quite convenient for practical application, since it has to be solved numerically. A simple explicit expression for mixed gas selectivity was derived using the so-called linear transport model, which is a linearized version of the original nonlinear flux equations. It is important to emphasize that a comparison of the linear model with the formally more rigorous nonlinear model showed only minor quantitative differences. The input parameters for the model are the single gas transport parameters. Testing the linear model using experimental data for the separation of hydrocarbons (n-butane/methane, n-butane/i-butane, propylene/propane) revealed an acceptable fit. A comparison of the model with recent experimental data on the separation of CO2-containing mixtures using microporous polymers is also presented. It is found that the calculated CO2/N2 mixed gas selectivity is in good agreement with the experimental data, while only a semi-quantitative agreement is observed for the CO2/CH4 separation. Besides, it is shown that the model developed for binary gas separation can be extended to ternary gas mixtures.