Elastic Wave Propagation in Fractured Media Using the Discontinuous Galerkin Method

Abstract

Abstract

A realistic model of the subsurface in reservoir modeling should include fractures. We have developed a novel method to include discrete fractures into 2D or 3D elastic models in order to gain insight into the wave phenomena related to the presence of fractures.

In order to determine the presence of fractures in the subsurface one has to rely on seismic data. In particular, azimuthal velocity anisotropy has been observed in many regions and this has been attributed to aligned fractures. Other wave phenomena related to the presence of fractures are phase-shifting, frequency-filtering and scattering of the reflected, transmitted and converted waves. Furthermore, fracture interface waves have also been observed in practice.

There are two main approaches to incorporate the effects of fractures: Using equivalent medium theories or using a numerical scheme to simulate the fractures. There have been many theories proposed in the literature that predict the effective media parameters associated with a particular fracture distribution. All of these models make different assumptions about the fractures, in particular they usually assume small, circular, non-intersecting cracks. The advantage of the equivalent medium theories is that they provide analytic expressions for the media parameters as a function of the fracture parameters. On the other hand, they have limited applicability because of the large number of assumptions.

Regarding the numerical schemes to incorporate the fractures, there are many approaches that have been proposed in the literature. The main advantage of the numerical schemes is that they require few assumptions and therefore they have a broad applicability and are useful to validate the equivalent medium theories. In particular, the approaches based on the linear-slip model require the least number of assumptions.

We propose a new scheme that incorporates fractures using the linear-slip model into a discontinuous Galerkin method. This approach can be used to simulate a wide variety of wave phenomena related to fractures. We validate our method using a set of parallel fractures and compare the results with those obtained using an equivalent medium. We show results for a single elongated horizontal fracture and show numerical examples using 2D and 3D models with one fracture and two orthogonal fractures.

AAPG Datapages/Search and Discovery Article #90260 © 2016 AAPG/SEG International Conference & Exhibition, Cancun, Mexico, September 6-9, 2016