Wave propagation in disordered fractured porous media

Abstract

Extensive computer simulations have been carried out to study propagation of acoustic waves in a two-dimensional disordered fractured porous medium, as a prelude to studying elastic wave propagation in such media. The fracture network is represented by randomly distributed channels of finite width and length, the contrast in the properties of the porous matrix and the fractures is taken into account, and the propagation of the waves is studied over broad ranges of the fracture number density ρ and width b. The most significant result of the study is that, at short distances from the wave source, the waves' amplitude, as well as their energy, decays exponentially with the distance from the source, which is similar to the classical problem of electron localization in disordered solids, whereas the amplitude decays as a stretched exponential function of the distance x that corresponds to sublocalization, exp(-x(α)) with α < 1. Moreover, the exponent α depends on both ρ and b. This is analogous to electron localization in percolation systems at the percolation threshold. Similar results are obtained for the decay of the waves' amplitude with the porosity of the fracture network. Moreover, the amplitude decays faster with distance from the source x in a fractured porous medium than in one without fractures. The mean speed of wave propagation decreases linearly with the fractures' number density.

Transport and Localization of Elastic Waves in Two‐Dimensional Fractured Media: Consequences on Scattering Attenuation

“…In some DFN models, fractures were idealized as open cracks (Kelner et al, 1999;Murai, 2007), which may, however, not realistically represent actual subsurface conditions since fracture walls are usually in contact under subsurface compressive state (Cook, 1992). Alternatively, a fracture may be conceptualized either as a layer of a finite thickness (more applicable for infilled/cemented fractures) (Hamzehpour et al, 2014(Hamzehpour et al, , 2016 or as a non-welded interface of a vanishing thickness (more applicable for non-infilled fractures) (Coates & Schoenberg, 1995;Vlastos et al, 2003Vlastos et al, , 2007. By using such DFN representations, complex interactions between fractures and waves may be captured.…”

“…By using such DFN representations, complex interactions between fractures and waves may be captured. However, previous research only studied the wave behavior in highly simplified fracture systems either with a constant length distribution (Hamzehpour et al, 2014(Hamzehpour et al, , 2016 or a parallel directional configuration (Vlastos et al, 2003;Yousef & Angus, 2016). The effects of the geometric distribution and mechanical properties (e.g., length, density, stiffness, etc.)…”

A Numerical Study of Elastic Wave Arrival Behavior in a Naturally Fractured Rock Based on a Combined Displacement Discontinuity-Discrete Fracture Network Model

“…It will be difficult to define the conventional wave front according to the wave phase since the receivers only record statistical wave signals with different oscillation patterns from the incident waves (Mandelis 2000;Hamzehpour et al 2014). Instead of using the wave phase, the wave amplitude of a point can be alternatively used to represent wave energies passing the point (Aki and Richards 2002;Hamzehpour et al 2014Hamzehpour et al , 2016. In this regard, we use the wave amplitude to determine the leading front of wave energies to describe the arrival behavior of waves at receivers, which is defined as the front of first-arrival wave (FFAW).…”

“…If waves encounter a finite-sized fracture, wave scattering and diffraction may occur at fracture tips (Liu and Zhang 2001 ; Rodriguez-Castellanos et al 2006 ; Zhu et al 2020 ; Lei and Sornette 2021a , 2021b ). Many previous studies further explored the wave behavior in simplified fracture networks either with a constant length distribution (Kelner et al 1999a ; Deng et al 2012 ; Hamzehpour et al 2014 , 2016 ; Khoshhali and Hamzehpour 2015 ; Chai et al 2016 ) or a parallel/orthogonal directional configuration (Kelner et al 1999b ; Vlastos et al 2003 ; Huang et al 2014 ; Chen et al 2015 ; Shao and Pyrak-Nolte 2016 ; Yousef and Angus 2016 ).…”

Two-Phase Flow Effects on Seismic Wave Anelasticity in Anisotropic Poroelastic Media

“…The authors consider the existence of connected pores that may or may not percolate, obtain the macroscopic coefficients and apply the results to a synthetic porous medium. Hamzehpour et al [24] study acoustic waves in two-dimensional fractured porous media using finite differences to discretize the differential equations. This analysis concludes that, near the source, waves amplitude decay exponentially.…”