The Effects of the Viscous Flow of a Gas and the Porous Structure of a Support on the Permeability of a Composite Membra
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Effects of the Viscous Flow of a Gas and the Porous Structure of a Support on the Permeability of a Composite Membrane V. V. Ugrozova, b, * and A. V. Volkova aTopchiev
Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, 119991 Russia
bDepartment of Data Analysis, Decision Making Theory, and Financial Technology, Financial University under the Government
of the Russian Federation, Moscow, 123995 Russia *e-mail: [email protected] Received January 15, 2020; revised March 10, 2020; accepted March 12, 2020
Abstract—The resistance model has been employed to derive an expression for the permeability of a composite membrane taking into account the viscous flow of a gas and the porous structure of a membrane support. Mathematical simulation has been used to show that, when the material of a selective layer does not penetrate into the pores of the skin layer of the support, the viscous flow of a gas in the support may noticeably affect the permeability and selectivity of the composite membrane, and the effect is enhanced with a decrease in the effective porosity and an increase in the permeability of the selective layer. It has been found that the influence of the porous structure of the support on the permeability of the composite membrane diminishes with a rise in the effective porosity of the support skin layer and the average pore size. The case in which selective layer material fills the pores of the support to the entire depth of the skin layer has been analyzed in detail. It has been shown that, in this case, the effect of the support on the membrane permeability is governed only by the porosity of the skin layer and the ratio between the thicknesses of the support skin layer and the selective layer. DOI: 10.1134/S1061933X20040158
1. INTRODUCTION At present, new efficient gas-separating composite membranes are being intensely developed and experimentally studied [1–10]. They are two- and multilayer membranes, in which a nonporous selective polymer layer (denoted by symbol “s” below) responsible for the gas separation is applied onto a porous support. The support of a composite membrane (CM) has an asymmetric structure and consists of a porous layer, which, according to [11], will below be referred to as a skin layer (symbol “sk”), and a macroporous layer (symbol “p”), which reinforces the membrane and exhibits no marked resistance to the gas transfer (Fig. 1a). The gas transfer in CMs is traditionally described using a resistance model (RM) [12, 13], in which, a gas flow through an RM is considered as a current running through series-connected constant resistors that simulate the selective layer and the support of the CM (Fig. 1b). The development of new CMs, in which the permeability of the selective layer is comparable with that of the support, entails the need in the simulation of gas transfer through such membranes with account of the effect of the porous structure of the support on their permeability [14]. Previously, this effect was ignored in the RM. This effect may be essential when the
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