Three-Phase Compositional Modeling with Capillarity in Heterogeneous and Fractured Media

Abstract Capillary pressure can have a significant effect on multiphase flow in heterogeneous and fractured media, even when there is species transfer between the phases. Modeling the combined non-linearities from phase behavior and capillarity in the multiphase flow equations for heterogeneous and fractured media may be one of the most complicated problems in reservoir simulation. In this work, we present an efficient numerical scheme that uses higher-order methods for the first time to model capillarity in fully compositional three-phase flow. We introduce a simple local computation of the capillarity pressure gradients in the fractional flow formulation in terms of the total flux. Complications arising from gravity and capillarity are resolved in the upwinding with respect to phase fluxes. Our choice of the Mixed Hybrid Finite Element Method for the pressure and flux fields is an accurate and natural approach to compute the capillary pressure gradients and fluxes at the interface between regions of different permeabilities. We present various examples on both core- and large-scales to demonstrate powerful features of our capillary pressure modeling and the upwinding with gravity and capillary pressure. The examples include layered and fractured domains.