Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

TL;DR

This paper presents a novel non-conforming discretization approach combining EDFM and EFEM for simulating coupled multiphase flow and geomechanics in fractured porous media, improving accuracy and meshing simplicity.

Contribution

It introduces an embedded discretization framework that effectively models complex fracture networks with reduced meshing challenges and compares enrichments including linear, constant, and XFEM.

Findings

The method achieves good convergence and accuracy in synthetic tests.

EFEM reduces geometric complexity and improves system properties.

Application to realistic scenarios demonstrates practical relevance.

Abstract

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the Embedded Discrete Fracture Model (EDFM) and the Embedded Finite Element Method (EFEM) for the flow and the mechanics, respectively. This non-conforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finiten volumes which exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an Extended Finite Element (XFEM) approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.