A Fully Equivalent Global Pressure Formulation for Three-Phase Compressible Flow
This work addresses a theoretical gap in reservoir simulation by providing an exact global pressure formulation for three-phase flow, though its practical impact is limited by the TD data requirement.
The authors propose a new global pressure formulation for three-phase compressible flow in porous media that is fully equivalent to the original equations, unlike prior work. The formulation simplifies pressure equation resolution but requires Total Differential (TD) data, for which they introduce an interpolation method from compatible two-phase data.
We introduce a new 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 \cite{CJ86}. 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 a 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.