Homogenization of a three-phase flow model in porous media

Abstract

We give homogenization results for an immiscible and incompressible three-phase flow model in a heterogeneous petroleum reservoir with periodic structure, including capillary effects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection–diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the flow. The determination of effective properties require the numerical resolution of local problems in a standard cell.

Keywords:

• Homogenization
• Two-scale convergence
• Three-phase flow
• Porous media
• AMS Subject Classifications: 35B27
• 74Q15
• 76M50
• 76S05

Acknowledgment

The work of the first author has been partially supported by grant from the CNRS ANDRA BRGM CEA EDF GdR 2439 whose support is gratefully acknowledged.