A fully equivalent global pressure formulation for three-phases compressible flows

Abstract

We introduce a global pressure formulation for immiscible three-phase compressible flows in porous media, which is fully equivalent to the original equations, unlike the one introduced in Chavent and Jaffré, [Mathematicals Models and Finite Elements for Reservoir Simulation, Amsterdam, North-Holland, 1986. In this formulation, the total volumetric flow of the three fluids and the global pressure follow a classical Darcy law, which simplifies the resolution of the pressure equation. However, this global pressure formulation exists only for total differential (TD) three-phase data, which depend only on two functions of saturations and global pressure: the global capillary pressure and the global mobility. Hence we introduce class of interpolation which constructs such TD-three-phase data from any set of three two-phase data (for each pair of fluids) which satisfy a TD-compatibility condition.

Keywords:

• multiphase flow
• porous media
• compressible fluids
• global pressure

AMS Subject Classifications::

• 76S05
• 35L65
• 35M10
• 35A22