The hybrid dimensional representation of permeability tensor: a reinterpretation of the discrete fracture model and its extension on nonconforming meshes

TL;DR

This paper reinterprets the discrete fracture model (DFM) using a hybrid-dimensional permeability tensor approach, extending its applicability to non-conforming meshes and curved fractures with variable thickness, enhancing simulation flexibility.

Contribution

It introduces a new perspective on DFM based on permeability tensor representation, enabling non-conforming mesh implementation without fundamental changes.

Findings

DFM can be extended to non-conforming meshes with the new approach.

The proposed model degenerates to classical DFM on conforming meshes.

Numerical tests confirm accuracy and efficiency on benchmark problems.

Abstract

The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g. line entries in 2D media and face entries in 3D media) on the interfaces of matrix cells and then couple the matrix and fracture flow systems together based on the principle of superposition with the fracture thickness used as the dimensional homogeneity factor. Because of this methodology, DFM is considered to be limited on conforming meshes and thus may raise difficulties in generating high quality unstructured meshes due to the complexity of fracture's geometrical morphology. In this paper, we clarify that the DFM actually can be extended to non-conforming meshes without any essential changes. To show it clearly, we provide another perspective for DFM based on hybrid-dimensional representation of permeability tensor to describe fractures as one-dimensional line Dirac delta functions contained in permeability tensor. A finite element DFM scheme for single-phase flow on non-conforming meshes is then derived by applying Galerkin finite element method to it. Analytical analysis and numerical experiments show that our DFM automatically degenerates to the classical finite element DFM when the mesh is conforming with fractures. Moreover, the accuracy and efficiency of the model on non-conforming meshes are demonstrated by testing several benchmark problems. This model is also applicable to curved fracture with variable thickness.