Universality of Riemann solutions in porous media

Abstract

Universality, a desirable feature in any system. For decades, elusive measurements of three-phase flows have yielded countless permeability models that describe them. However, the equations governing the solution of water and gas co-injection has a robust structure. This universal structure stands for Riemann problems in green oil reservoirs. In the past we established a large class of three phase flow models including convex Corey permeability, Stone I and Brooks–Corey models. These models share the property that characteristic speeds become equal at a state somewhere in the interior of the saturation triangle. Here we construct a three-phase flow model with unequal characteristic speeds in the interior of the saturation triangle, equality occurring only at a point of the boundary of the saturation triangle. Yet the solution for this model still displays the same universal structure, which favors the two possible embedded two-phase flows of water-oil or gas-oil. We focus on showing this structure under the minimum conditions that a permeability model must meet. This finding is a guide to seeking a purely three-phase flow solution maximizing oil recovery.