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.
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