A Discontinuous Galerkin Method for Computing Time-of-Flight in Discrete-Fracture Models

Discrete fracture models, in which fractures are represented individually as
lower-dimensional objects, are beginning to appear in simulators for porous
media flow. Here we present a discontinuous Galerkin method for computing
time-of-flight in discrete-fracture models of fracture-fault systems.
Isocontours of time-of-flight are time-lines of porous-media flow and give
information about flow patterns, in particular for single-phase flow.

Recent numerical results show that the discontinuous Galerkin (dG) method is
efficient and accurate for solving the time-of-flight equation. In this paper,
we use two simplified grid models to examine various approaches for the dG
discretisation in fractured regions of the porous medium. Comparing the
numerical results of the dG approximation with those from a streamline
simulator, we demonstrate the importance of a sufficient grid resolution across
the fractures, even though the widths of the fractures are very small compared
to typical length scales of the unfractured parts of the reservoir.