Effects of fractures on seismic waves in poroelastic formations
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Naturally fractured reservoirs have attracted an increased interest of exploration and production geophysics in recent years. In many instances, natural fractures control the permeability of the reservoir, and hence the ability to find and characterize fractured areas of the reservoir represents a major challenge for seismic investigations. In fractured and porous reservoirs the fluid affects elastic anisotropy of the rock and also causes significant frequency dependent attenuation and dispersion. In this study we develop a mathematical model for seismic wave attenuation and dispersion in a porous medium in a porous medium with aligned fractured, caused by wave induced fluid flow between pores and fractures. In this work fractures in the porous rock are modelled as very thin and highly porous layers in a porous background. Dry highly porous materials have low elastic moduli; thus dry skeleton of our system contains thin and soft layers, and is described by linear slip theory. The fluid saturated rock with high-porasity layers is described by equations of poroelasticity with periodically varying coefficients. These equations are analyzed using propagator matrix approach commonly used to study effective properties of layered system. This yields a dispersion equation for a periodically layered saturated porous medium taking into account fluid communication between pore spaces of the layers. Taking in this dispersion equation a limit of small thickness for high-porosity layers gives the velocity and attenuation as a function of frequency and fracture parameters. The results of this analysis show that porous saturated rock with aligned fractures exhibits significant attenuation and velocity dispersion due to wave induced fluid flow between pores and fractures.At low frequencies the material properties are equal to those obtained by anisotropic Gassmann theory applied to a porous material with linear-slip, interfaces. At high frequencies the results are equivalent to those for fractures with vanishingly small normal slip in a solid (non-porous) background. The characteristic frequency of the attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing. The wave induced fluid flow between pores and fractures considered in this work has exactly the same physical nature as so-called squirt flow, which is widely believed to by a major cause of seismic attenuation. Hence, the present model can be viewed as a new model of squirt-flow attenuation, consistent with Biot’s theory of poroelasticity. The theoretical results of this work are also limited by the assumption of periodic distribution of fractures. In reality fractures may be distributed in a random fashion. Sensitivity of our results to the violation of the periodicity assumption was examined numerically using reflectivity modelling for layered poroelastic media. Numerical experiments for a random distribution of fractures of the same thickness still show surprisingly good agreement with theoretical results obtained for periodic fractures. However this agreement may break down if fracture properties are allowed to vary from fracture to fracture. The results of this thesis show how to compute frequency dependences of attenuation and velocity caused by wave induced fluid flow between pores and fractures. These results can be used to obtain important parameters of fractured reservoirs, such as permeability and fracture weakness, from attenuation measurements. The major requirement for the success of such an approach is that measurements must be made in over a relatively broad frequency range.
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