Upscaled Model for Multicomponent Gas Transport in Porous Media Incorporating Slip Effect
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Upscaled Model for Multicomponent Gas Transport in Porous Media Incorporating Slip Effect C. Moyne1 · T. D. Le1 · G. Maranzana1 Received: 10 July 2020 / Accepted: 8 September 2020 © Springer Nature B.V. 2020
Abstract A two-scale model for multicomponent gas transport in porous media is developed. At the pore-scale, Stefan–Maxwell formulation is used to describe the multi-gas transport together with the mass and momentum conservation equations, whereas on the solid/fluid interface, a slip velocity according to the Kramers–Kistemaker condition is taken into account. The porescale equations are then upscaled using a formal homogenization procedure. The macroscopic model shows that the total average velocity is modified by a slip velocity which depends mostly on the diffusive flux of the light gas in the mixture. Application to hydrogen transport in electrochemical devices such as fuel cell, electrochemical hydrogen purifier/compressor, in which considerable contrast of molar mass between the gases occurs, is carried out. As a result, the gas slip effect can modify considerably the gas transport behavior within the porous medium of the devices. This is an important result because the gas transport mechanisms play a crucial role in their efficiency. Keywords Multicomponent gas transport · Slip effect · Homogenization method · Kramers–Kistemaker relation · Stefan–Maxwell formulation
1 Introduction Multicomponent gas transport in porous media has received considerable attention both from modeling and experimental points of view (Jackson 1977; Pisani 2008; Quintard et al. 2006; Fu et al. 2015). In the recent past decades, many applications based on hydrogen such as membrane fuel cells, electrolyzer, electrochemical hydrogen purifier/compressor, etc., have used porous materials (Gas Diffusion Layer, Porous Transport Layer) to diffuse gases (Brandon and Brett 2006). In this context, transport properties of hydrogen coexisting with
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T. D. Le [email protected] C. Moyne [email protected] G. Maranzana [email protected]
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CNRS, LEMTA, Université de Lorraine, 54000 Nancy, France
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other gases (oxygen, nitrogen, vapor water, methane, etc.) in porous media play a crucial role to characterize and to optimize these devices. However, modeling of multicomponent gas transport has often been restricted to macroscopic empirical models using classical Fickian and Darcy’s laws neglecting slippage flow effect. In the case of hydrogen with a very small molar mass compared to other gases, the slippage phenomenon becomes significant and needs to be taken into account (Young and Todd 2005). This paper aims at clarifying this issue. The simultaneous presence of several gases requires a Stefan–Maxwell-type formulation to describe the diffusive problem at the pore scale in the continuous regime when the Knudsen number is assumed to be small (Bird et al. 2002). The slip flow for one gas component has been examined in (Skjetne and Auriault 1999; Lasseux et al. 2014) When very differ
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