TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic qpansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations.

[1]  Homogénéisation d’équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux , 1989 .

[2]  Alain Bourgeat,et al.  Homogenized behavior of two-phase flows in naturally fractured reservoirs with uniform fractures distribution , 1984 .

[3]  G. Chavent,et al.  A new formulation of diphasic incompressible flows in porous media , 1976 .

[4]  Application des techniques d'homogénéisation aux écoulements diphasiques incompressibles en milieu poreux , 1988 .

[5]  Homogénéisation d'un modèle d'écoulements miscibles en milieu poreux , 1990 .

[6]  A. Bourgeat,et al.  Elements de comparaison entre la methode d'homogeneisation et la methode de prise de moyenne avec fermeture , 1988 .

[7]  Jérôme Jaffré,et al.  Discontinuous upwinding and mixed finite elements for two-phase flows in reservoir simulation , 1984 .

[8]  Jérôme Jaffré,et al.  Discontinuous and mixed finite elements for two-phase incompressible flow , 1987 .

[9]  G. Chavent.  Mathematical models and finite elements for reservoir simulation , 1986 .

[10]  Effective behavior of two-phase flow in heterogeneous reservoirs , 1987 .

[11]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[12]  S. Kružkov,et al.  BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF EQUATIONS OF TWO-PHASE POROUS FLOW TYPE; STATEMENT OF THE PROBLEMS, QUESTIONS OF SOLVABILITY, JUSTIFICATION OF APPROXIMATE METHODS , 1977 .

[13]  W. T. Cardwell,et al.  Average Permeabilities of Heterogeneous Oil Sands , 1945 .

[14]  Richard E. Ewing.  1. Problems Arising in the Modeling of Processes for Hydrocarbon Recovery , 1983 .

[15]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[16]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .