Using a Partially-Linear Simplified Model for Gravitational Three Phase-Flow of Water, Oil and Supercritical C02 in Porous Media

Abstract

In this article we use a simplified model for vertical three-phase flow in porous media of immiscible fluids like water,
oil and supercritical-CO₂. The relative permeability functions of oil and CO₂ phases are assumed to be linear functions of the
respective saturations while the relative permeability of the water phase is a quadratic function of water saturation. For vertical
flow (gravity taken into account) and fluids having small density differences, the model intend to represent the case in which phases
supercritical-CO₂ and oil are inclined to miscibility when water phase is absent for certain temperature and pressure conditions,
while the flow gains some immiscibility properties as the water phase becomes present. This model leads to a 2x2 system of
conservation laws which loose strict hyperbolicity at three isolated coincidence points at the edges of the saturation triangle. We
use the wave curve method to solve a class of Riemann Problem.