Flows of Two Slightly Miscible Fluids in Porous Media: Two-Scale Numerical Modeling

IF 2.7 3区工程技术 Q3 ENGINEERING, CHEMICAL

Transport in Porous Media Pub Date : 2024-04-11 DOI:10.1007/s11242-024-02080-1

Y. Amirat, V. Shelukhin, K. Trusov

引用次数: 0

Abstract

We address the two-scale homogenization of the Navier–Stokes and Cahn–Hilliard equations in the case of a weak miscibility of a two-component fluid. To this end a notion of the miscibility strength is formulated on the basis of a correlation between the upscaling parameter and the surface tension. As a result, a two-scale model is derived. Macro-equations turn out to be a generalization of the Darcy law enjoying cross-coupling permeability tensors. It implies that the Darcy velocity of each phase depends on pressure gradients of both phases. Micro-equations serve for determination both of the permeability tensors and the capillary pressure. An example is constructed by analytical tools to describe capillary displacement of oil by mixture of water with carbon dioxide in a system of hydrophobic parallel channels.

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两种轻度混溶流体在多孔介质中的流动：双尺度数值建模

我们探讨了双组分流体弱混溶性情况下纳维-斯托克斯方程和卡恩-希利亚德方程的双尺度均质化问题。为此，我们根据升尺度参数与表面张力之间的相关性，提出了混溶性强度的概念。因此，得出了一个双尺度模型。宏观方程是达西定律的一般化，享有交叉耦合渗透张量。这意味着每相的达西速度取决于两相的压力梯度。微方程可用于确定渗透率张量和毛细管压力。举例说明了在疏水平行通道系统中，水与二氧化碳混合物对油的毛细位移。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

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).