A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media

TL;DR

This paper introduces a simple, flexible embedded finite element method for coupled flow and transport in fractured porous media, emphasizing local velocity conservation and compatibility with existing EFEM frameworks.

Contribution

It develops a locally conservative velocity model and couples it with a finite volume transport method within the EFEM framework, simplifying simulation of fractured media.

Findings

The method achieves promising results on synthetic and realistic problems.

It maintains flexibility in fracture geometry and meshing.

The approach is straightforward to implement and integrate.

Abstract

Accurate simulation of fluid flow and transport in fractured porous media is a key challenge in subsurface reservoir engineering. Due to the high ratio between its length and width, fractures can be modeled as lower dimensional interfaces embedded in the porous rock. We apply a recently developed embedded finite element method (EFEM) for the Darcy problem. This method allows for general fracture geometry, and the fractures may cut the finite element mesh arbitrarily. We present here a velocity model for EFEM and couple the Darcy problem to a transport problem for a passive solute. The main novelties of this work is a locally conservative velocity approximation derived from the EFEM solution, and the development of a lowest order upwind finite volume method for the transport problem. This numerical model is compatible with EFEM in the sense that the same computational mesh may be applied, so that we retain the same flexibility with respect to fracture geometry and meshing. Hence, our coupled solution strategy represents a simple approach in terms of formulation, implementation and meshing. We demonstrate our model by some numerical examples on both synthetic and realistic problems, including a benchmark study for single-phase flow. Despite the simplicity of the method, the results are promising.