The Hybrid-dimensional Darcy's Law: A Reinterpreted Discrete Fracture Model for Fracture and Barrier Networks on Non-conforming Meshes

TL;DR

This paper introduces a hybrid-dimensional Darcy's law model for simulating flow in fractured porous media with barriers, utilizing a Dirac-delta function approach on non-conforming meshes, and employs the LDG method for numerical solutions.

Contribution

It extends the reinterpreted discrete fracture model to include flow blocking barriers using a Dirac-delta based tensor approach on non-conforming meshes.

Findings

Accurately models flow with fractures and barriers on non-conforming meshes

Employs LDG method to handle pressure/flux discontinuities

Demonstrates effectiveness through numerical tests

Abstract

In this paper, we extend the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional Darcy's law into the hybrid-dimensional Darcy's law where fractures and barriers are represented as Dirac-delta functions contained in the permeability tensor and resistance tensor, respectively. As a natural extension of the reinterpreted discrete fracture model for highly conductive fractures, this model is able to account for the influence of both highly conductive fractures and blocking barriers accurately on non-conforming meshes. The local discontinuous Galerkin (LDG) method is employed to accommodate the form of the hybrid-dimensional Darcy's law and the nature of the pressure/flux discontinuity. The performance of the model is demonstrated by several numerical tests.