A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface

A macroscopic description of a two-phase flow in a porous medium is given by writing, firstly, mass and momentum-balance equations and, secondly, phenomenological equations derived from the theory of irreversible thermodynamic processes. The main results are as follows: (i) the law of capillary pressure is extended to dynamic conditions, (ii) an extended formulation of Darcy's law is established for each fluid phase and also for fluid/fluid interface which is considered as a phase of the system, and (iii) a coupling may appear between fluid phases.

[1]  I. Fatt.  The Network Model of Porous Media , 1956 .

[2]  Stephen Whitaker,et al.  The transport equations for multi-phase systems , 1973 .

[3]  L. Schwartz.  Méthodes mathématiques pour les sciences physiques , 1961 .

[4]  Stephen Whitaker,et al.  Flow in porous media II: The governing equations for immiscible, two-phase flow , 1986 .

[5]  Irreversible Processes and Onsager Relations , 1985 .

[6]  Laurent Schwartz,et al.  Fonctions de Bessel : chapitre IX d'après le livre "Méthodes mathématiques pour les sciences physiques" , 1965 .

[7]  S. Whitaker.  Flow in porous media I: A theoretical derivation of Darcy's law , 1986 .

[8]  Philippe C. Baveye,et al.  The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers , 1984 .

[9]  William G. Gray,et al.  On the General Equations for Flow in Porous Media and Their Reduction to Darcy's Law , 1976 .

[10]  R. Lenormand,et al.  Application de la percolation à la physique des milieux poreux , 1984 .

[11]  R. D. Wyckoff,et al.  The Flow of Gas‐Liquid Mixtures Through Unconsolidated Sands , 1936 .

[12]  T. J. Lasseter,et al.  Two-phase flow in random network models of porous media , 1985 .

[13]  Stephen Whitaker,et al.  ADVANCES IN THEORY OF FLUID MOTION IN POROUS MEDIA , 1969 .

[14]  W. H. Somerton,et al.  Quantitative Modelling of Immiscible Displacement in Porous Media. a Network Approach , 1977 .

[15]  Charles-Michel Marle,et al.  On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media , 1982 .

[16]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 2. Motion of oil ganglia , 1986, Journal of Fluid Mechanics.

[17]  John H. Cushman,et al.  On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory , 1984 .

[18]  I. Prigogine,et al.  Tension superficielle et adsorption , 1951 .

[19]  Stephen Whitaker,et al.  Flow in porous media III: Deformable media , 1986 .

[20]  David Wilkinson,et al.  Invasion percolation: a new form of percolation theory , 1983 .

[21]  G. Matheron.  L'émergence de la loi de Darcy , 1984 .

[22]  Joel Koplik,et al.  Capillary displacement and percolation in porous media , 1982, Journal of Fluid Mechanics.

[23]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .