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

TL;DR

This paper introduces a novel fully compositional three-phase flow simulator for fractured porous media, utilizing advanced finite element methods and the cross-flow equilibrium concept to improve accuracy and efficiency in complex multiphase flow modeling.

Contribution

The work presents the first three-phase compositional simulator for fractured media using higher-order finite element methods combined with the cross-flow equilibrium approach.

Findings

Effective modeling of three-phase flow in fractured media.

Demonstrated accuracy and stability through numerical examples.

Enhanced computational efficiency with the CFE concept.

Abstract

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.