3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers

Abstract

This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel L 2 -projection variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The L 2 -projection variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the method is further validated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the L 2 -projection method, is capable of modeling single-phase flow through realistic 3D fracture networks.

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

“…The study exposed the relative strengths and weaknesses between the participating methods, both in terms of accuracy and computational cost. After the publication of the results, these benchmark cases have been widely applied by the scientific community in testing numerical methods and new simulation tools ( Arrarás et al, 2019;Budisa and Hu, 2019;Köppel et al, 2019a;2019b;Odsaeter et al, 2019;Schädle et al, 2019 ).…”

Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

“…In this method, the discontinuities have higher permeability than the matrix and the pressure is assumed to be continuous across them. Schädle et al 22 . further extended the previous method in conjunction with a projection operator to simulate the single‐phase flow in a 3D space and applied it to different case studies, including highly complex fractured porous media.…”

“…Their three‐phase model included the porous solid, fracturing fluid and host fluid, and sensitivity analyses showed single‐phase models to significantly underestimate the leak‐off to the fracture network. Schädle et al 22 . highlighted that large‐scale problems can be challenging for XFEM‐based approaches, particularly in the case of 3D fracture networks due to the need for complex enrichment functions and integration procedures, and the large number of degrees of freedom to capture the discontinuities.…”

Frackit: a framework for stochastic fracture network generation and analysis

“…A number of mathematical models and numerical schemes, aiming at an accurate description of flow through fractured rock, have been presented recently (see e.g. R. Ahmed et al (2015); Raheel Ahmed et al (2017); Brenner et al (2018); Köppel et al (2019); Schädle et al (2019); Nordbotten et al (2019)). Many of these describe the fractures as lower-dimensional geometries, that is, as curves or planes embedded in two-or three-dimensional space, respectively.…”