Flow in Porous Media with Fractures of Varying Aperture

TL;DR

This paper introduces a new mixed-dimensional model for single-phase flow in fractured porous media with varying aperture, accounting for asymmetric and curvilinear fractures, and validates it through numerical experiments.

Contribution

The paper develops a generalized mixed-dimensional model that incorporates asymmetric and spatially varying fracture apertures, extending previous models.

Findings

Model accurately describes flow in complex fracture geometries

Discontinuous Galerkin discretization is effective for the model

Numerical experiments validate the model's applicability

Abstract

We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n\ge 2$. In particular, we suggest a generalization of the model in [22] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.