Flow in Porous Media with Fractures of Varying Aperture

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.

References in corpus (5)

• Benchmarks for single-phase flow in fractured porous media
• Verification benchmarks for single-phase flow in three-dimensional fractured porous media
• Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations
• A mathematical model for thermal single-phase flow and reactive transport in fractured porous media
• A Finite-Volume Moving-Mesh Method for Two-phase Flow in Fracturing Porous Media

Cited by in corpus (3)

• Asymptotic expansion for convection-dominated transport in a thin graph-like junction
• Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks
• Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture