Comments on the DFM module for MRST
Introduction
This document contains various comments on the Discrete Fracture Matrix module, both in terms of
implementation details and guidelines for the discretization and simulation of fracture media. The
module is developed at the Department of Mathematics, University of Bergen mainly by Tor Harald
Sandve. Some utility files are provided by Uni Research. For a short overview of the module confer
the README file and examples in the DFM module.
Overview
The module provides control volume discretizations (two- and multi-point flux approximations) of
fractured media by representing fractures as lower-dimensional objects that still are represented as
cells in the computational grid. The discretization is described in (Karimi-Fard, et al., 2004; Sandve, et
al., 2012). The approach assumes that the fractures are represented as faces in the grid, thus the
module also provide some utility functions for triangulating fractured domains. Finally, the transport
solvers (both explicit and implicit) in the MRST core are modified to account for fracture transport.
MRST files that are modified have a suffix _DFM to distinguish them from the original files.
Known bugs / shortcomings
Discretizations and solvers are modified from core MRST functions to account for fracture
cells; look for files with suffix _DFM. The modifications are based on MRST version 2011a,
and are thus static with respect to modifications of the core functions.
A method for gridding general 3D fractures would have been nice. An import filter for TetGen
might be a way to go.
The MPFA flux calculation does not handle pyramids in 3D (more generally, each cell should
share exactly Nd faces with each of its vertexes). This puts some constraints on the gridding
tools in 3D.
The code has mostly been tested for horizontal problems, and seems to work well there.
When gravity is present, the TPFA routine seems to work there as well, whereas the MPFA
method for this problem is barely tested, and should be used with caution. In particular, the
elimination of small cells in fracture intersections is questionable.
Capillary pressure has not been tested.
The system for tags should be improved. See below.
Lessons learned in gridding of fractures
When discretizing a fractured media, ensuring the quality of the grid is highly important for the
overall simulation result. The grids for the DFM model should be conforming, meaning that the
fractures are represented as edges in the grid. This constrained gridding is non-trivial, see (Holm, et
al., 2006) for examples of typical challenges. Below we give a summary of lessons learned while
working with this, with the hope that it can be useful for others. Note that the observations should
be considered tricks / approximations that in many cases can be justified, but nevertheless should be
applied with caution:
