Macroscale continuum mechanics for multiphase porous-media flow including phases, interfaces, common lines and common points

• Published in: Advances in water resources Vol. 21; no. 4; pp. 261 - 281
• Main Authors: Gray, William G., Hassanizadeh, S.Majid
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 10.04.1998; Elsevier Science
• Subjects: averaging theory; Earth sciences; Earth, ocean, space; equations; Exact sciences and technology; groundwater flow; Hydrogeology; Hydrology. Hydrogeology; mathematical models; mathematics and statistics; multiphase flow; porous media; soil water movement; transport processes; averaging theory; multiphase flow; porous media; interfaces; entropy; mathematical models; thermodynamics; flow mechanism; transport; capillary pressure; energy
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/S0309-1708(96)00063-2

This paper provides the tools needed for analysis of multiphase flow in porous media. Contributions are in four areas. First, theorems are provided that allow global scale integral equations to be localized at the porous medium scale. This is a more general approach than the traditional averaging of microscale point equations. Second, conservation equations for mass, momentum, energy and entropy for phases, interfaces, common lines, and common points are obtained. The inclusion of common lines and common points completes the full description of multiphase flow in porous media. Third, the entropy inequality is developed for the full multiphase system. The interaction terms between phases, interfaces, common lines, and common points provide a clear direction as to whether the entropy equation for each of these components may be used in the development of a constitutive theory or if the constitutive theory will depend on a combined entropy inequality statement. Fourth, the simplification of the system of equations is presented for the case of massless interfaces and common lines where these constituents are still capable of sustaining stress and containing energy. These latter forms are particularly useful in consideration of capillary pressure terms when the mass of the interface may be considered negligible.