The Attenuation and Dispersion Analyses in Porous and Fractured Medium with Arbitrary Fracture Fill Liyun Kong1, Boris Gurevich2, Tobias M. Müller3, Yibo Wang4,*, Huizhu Yang1 1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China 2 Department of Exploration Geophysics, Curtin University of Technology, Western Australia 6845, Australia 3 CSIRO Petroleum Resources, ARRC, Western Australia 6151, Australia 4 Institute of Geology and Geophysics, Chinese Academy of Science, Beijing 100029, China * Corresponding author: wangyibo@mail.igcas.ac.cn Abstract To study the effect of fractu,re fill on the elastic anisotropy of the rock and frequency-dependent attenuation and dispersion in fractured reservoirs, a model for porous and fractured medium is developed. In this model, the fractured medium is considered as a periodic system of alternating layers of two types: thick porous layers representing the background, and very thin and highly compliant porous layers representing fractures. By taking the simultaneous limits of zero thickness and zero normal stiffness of the thin layers, we obtain expressions for dispersion and attenuation of the P-waves. The results show that in the low-frequency limit the elastic properties of such a medium can be described by Gassmann equation with a composite fluid, while the P-wave speed is relatively high at high frequencies for two layers can be treated as ‘hydraulically isolated’. However, there appears to be a critical case where no dispersion is observed, which is caused by the balance of fractures compliance and fluid compressibility filling in them. Keywords porous media, fracture , attenuation, dispersion 1 Introduction Flow of the pore fluid by the passing wave is widely believed to be the main cause of attenuation and dispersion of elastic waves in porous rocks. In particular, flow that occurs due to spatial variations of rock or fluid properties on mesoscopic scale (larger than the pore size but smallerthan the wavelength) is considered to be significant at seismic frequencies [1-4]. The magnitude of attenuation and dispersion caused by mesoscopic wave-induced flow is proportional to the squared contrast (variance) of spatial variations of rock or fluid properties. Thus attenuation and dispersion are only significant if the contrast of spatial variations is large. In recent years, two situations with large contrast in rock/fluid properties have been identified: partial saturation and fractured rock. Partial saturation refers to the situation where a rock is saturated with a mixture of two immiscible fluids with large difference between their properties (say, liquid and gas). When an elastic wave propagates through such a rock, the patches of rock saturated with gas and liquid will deform differently, resulting in pressure gradients and fluid flow [5-8]. Fractured rock refers to a situation where a porous rock is permeated by open fractures. When a wave propagates through such a rock, fractures will deform to a greater extent than the porous background, resulting in fluid flow between pores and fractures [9-13]. These situations (partial saturation and fractures) are usually treated separately: analysis of wave propagation in a partially saturated rock usually ignores variations in elastic properties of the solid frame, while the porous rock permeated by fractures is usually assumed to be saturated with a uniform fluid. However, in some situations, particularly when a fluid such as water or carbon dioxide is injected into a tight hydrocarbon reservoir, fractures may be filled with a different fluid (with capillary forces
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