Higher-Order Compositional Modeling of Three-phase Flow in 3D Fractured Porous Media Using Cross-flow Equilibrium Approach

摘要

Numerical simulation of multiphase compositional flow in fractured porousmedia, when all the species can transfer between the phases, is a realchallenge. Despite the broad applications in hydrocarbon reservoir engineeringand hydrology, a compositional numerical simulator for three-phase flow infractured media has not appeared in the literature, to the best of ourknowledge. In this work, we present a three-phase fully compositional simulatorfor fractured media, based on higher-order finite element methods. To achievecomputational efficiency, we invoke the cross-flow equilibrium (CFE) conceptbetween discrete fractures and a small neighborhood in the matrix blocks. Weadopt the mixed hybrid finite element (MHFE) method to approximate convectiveDarcy fluxes and the pressure equation. This approach is the most naturalchoice for flow in fractured media. The mass balance equations are discretizedby the discontinuous Galerkin (DG) method, which is perhaps the most efficientapproach to capture physical discontinuities in phase properties at thematrix-fracture interfaces and at phase boundaries. In this work, we accountfor gravity and Fickian diffusion. The modeling of capillary effects isdiscussed in a separate paper. We present the mathematical framework, using theimplicit-pressure-explicit-composition (IMPEC) scheme, which facilitatesrigorous thermodynamic stability analyses and the computation of phase behavioreffects to account for transfer of species between the phases. A deceptivelysimple CFL condition is implemented to improve numerical stability andaccuracy. We provide six numerical examples at both small and larger scales andin two and three dimensions, to demonstrate powerful features of theformulation.