Mixed-Hybrid and Vertex-Discontinuous-Galerkin Finite Element Modeling of Multiphase Compositional Flow on 3D Unstructured Grids

TL;DR

This paper introduces a novel finite element modeling approach for simulating complex three-phase multiphase flow in 3D unstructured grids, improving accuracy and handling heterogeneity in reservoir simulations.

Contribution

It presents the first application of fully compositional 3D multiphase flow modeling on unstructured grids using mixed hybrid finite elements and vertex-discontinuous Galerkin methods.

Findings

Outperforms face-based DG implementations in accuracy.

Provides globally continuous pressure and flux fields.

Demonstrates robustness in heterogeneous and fractured reservoirs.

Abstract

Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element methods accurately describe flow on unstructured meshes with complex geometries, and their flexible formulation allows implementation on different grid types. In this work, we consider for the first time the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by any combination of tetrahedra, prisms, and hexahedra. We employ a mass conserving mixed hybrid finite element (MHFE) method to solve for the pressure and flux fields. The transport equations are approximated with a higher-order vertex-based discontinuous Galerkin (DG) discretization. We show that this approach outperforms a face-based implementation of the same polynomial order. These methods are well suited for heterogeneous and fractured reservoirs, because they provide globally continuous pressure and flux fields, while allowing for sharp discontinuities in compositions and saturations. The higher-order accuracy improves the modeling of strongly non-linear flow, such as gravitational and viscous fingering. We review the literature on unstructured reservoir simulation models, and present many examples that consider gravity depletion, water flooding, and gas injection in oil saturated reservoirs. We study convergence rates, mesh sensitivity, and demonstrate the wide applicability of our chosen finite element methods for challenging multiphase flow problems in geometrically complex subsurface media.