PHYSICAL REVIEW E 89, 023301 (2014) Wave propagation in disordered fractured porous media Hossein Hamzehpour, 1 , * Fatemeh Haghsheno Kasani, 1 Muhammad Sahimi, 2 and Reza Sepehrinia 3 1 Department of Physics, K. N. Toosi University of Technology, Tehran 15875-4416, Iran 2 Mork Family Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA 3 Department of Physics, University of Tehran, Tehran 14395-547, Iran (Received 3 August 2013; published 10 February 2014) 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. DOI: 10.1103/PhysRevE.89.023301 PACS number(s): 62.65.+k, 91.55.Jk, 91.30.Ab, 47.56.+r I. INTRODUCTION Large-scale porous media, such as oil, gas, and geothermal reservoirs, as well as groundwater aquifers are often fractured [1,2], with the fractures distributed spatially over several distinct length scales. One of the most important problems, among the many issues that must be addressed by those who study such porous media, is their characterization. For example, despite years of study, the problem of accurate identification of fractures’ spatial distribution remains an active area of research [1,2]. Although the permeability of fractures is much larger than that of the porous matrix in which they are embedded and thus permeability data measured at various depths may provide insight into the spatial distribution of fractures, there is usually an insufficient volume of such data for any fractured porous medium. Borehole-wall imaging is a very reliable method of mapping the fractures and faults. However, such imaging techniques are expensive and are not always included in a logging run. In addition, such images are not available for, for example, many of the older oil reservoirs. Characterization of any type of porous media belongs to a wider class of problems that have been studied for decades in which one seeks a link between the static and dynamical properties of heterogeneous media. In a disordered solid material, one is interested [3,4] in the relation between the morphology—the shape, size, and the spatial distribution of the microscopic elements—and the dynamics of any process that takes place in the material at the macroscale, such as transport of electrical current or stress. Such relations are important in view of the fact that it is usually much easier to measure the macroscopic properties of disordered materials * Corresponding author: hamzehpour@kntu.ac.ir than characterizing with precision the spatial distribution of the microscopic heterogeneity. An important tool for obtaining information on the mor- phology and contents of inhomogeneous media has been the study of how waves, both acoustic and elastic, propagate in them. For example, seismic wave propagation and reflection are utilized [5] to estimate not only the hydrocarbon content of a potential oil field, but also the spatial distribution of its porosity, fractures, and faults. In addition, understanding wave propagation in heterogeneous media is fundamental to such important problems as detecting earthquake precursors, underground nuclear explosions, and what happens on the seafloor. The same basic techniques are also used in such diverse fields as materials science and medicine [5] for imaging, characterizing materials, and human organs. In this paper we study propagation of acoustic waves in a fractured porous medium. Our interest is in obtaining a deeper understanding of the effect of the fractures’ geometry and connectivity on wave propagation. In a fractured porous medium, the P and S waves strongly interact and mix and thus one must in principle solve the full elastic wave equation in order to study wave propagation in such a medium. However, simulation of the elastic wave equation is highly complex and intensive. Thus, as a prelude to a study of propagation of elastic waves in fractured porous media, which is of tremendous importance to a wide variety of problems that were already mentioned, we first study in this paper propagation of acoustic waves in order to identify the most important factors that affect wave propagation. We will then study their influence on elastic wave propagation. In particular, we study the relation between several characteristics of the waves and the morphology of the inhomogeneous fractured porous medium in which they propagate. The rate of decay of the amplitude of a wave that undergoes multiple scattering strongly influences how far the wave propagates in the medium. The amplitude decay is by 1539-3755/2014/89(2)/023301(10) 023301-1 ©2014 American Physical Society