Upscaling and Effective Behavior for Two-Phase Porous-Medium Flow Using a Diffuse Interface Model

IF 2.7 3区 工程技术 Q3 ENGINEERING, CHEMICAL
Mathis Kelm, Carina Bringedal, Bernd Flemisch
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Abstract

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations.

Abstract Image

使用扩散界面模型的两相多孔介质流的放大和有效行为
我们研究了多孔介质中的两相流动,并推导出一个双尺度模型,该模型将孔隙尺度的相分布和表面张力纳入较大达西尺度的有效行为中。孔隙尺度的自由边界问题采用扩散界面方法建模,其形式为耦合的 Allen-Cahn Navier-Stokes 系统,由于表面张力的作用,该系统具有额外的动量通量。利用周期均质化和形式渐近展开,得出了一个具有相变和速度贡献单元问题的双尺度模型。我们研究了计算出的有效参数及其与不同流体分布的饱和度之间的关系,并与常用的相对渗透饱和度曲线进行了比较。双尺度模型得出了相对渗透率和饱和度的非单调关系。单元问题所捕捉到的局部流体分布和效应的强烈依赖性凸显了将孔隙尺度信息纳入宏观尺度方程的重要性。
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来源期刊
Transport in Porous Media
Transport in Porous Media 工程技术-工程:化工
CiteScore
5.30
自引率
7.40%
发文量
155
审稿时长
4.2 months
期刊介绍: -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).
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