[1] Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of wave-induced pore fluid flow. Various theoretical models quantify dispersion and attenuation of normal incident compressional waves in finely layered porous media. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave-induced fluid flow effects in media with a more complex distribution of medium heterogeneities. By using finite element simulations of poroelastic relaxation, the total frequency-dependent complex stiffness tensor can be computed for a porous medium with arbitrary internal heterogeneity. From the stiffness tensor, velocity dispersion and frequency-dependent attenuation are derived for compressional and shear waves as a function of the angle of incidence. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion. In the case of the ellipsoidal inclusion, compressional and shear wave modes show significant attenuation, and the characteristic frequency dependence of the effect is governed by the spatiotemporal scale of the pore fluid pressure relaxation. In our anisotropic examples, the angle dependence of the attenuation is stronger than that of the velocity dispersion. It becomes clear that the spatial attenuation patterns show specific characteristics of waveinduced fluid flow, implying that anisotropic attenuation measurements may contribute to the inversion of fluid transport properties in heterogeneous porous media.Citation: Wenzlau, F., J. B. Altmann, and T. M. Müller (2010), Anisotropic dispersion and attenuation due to wave-induced fluid flow: Quasi-static finite element modeling in poroelastic solids,
Numerical modeling of seismic waves in heterogeneous, porous reservoir rocks is an important tool for interpreting seismic surveys in reservoir engineering. Various theoretical studies derive effective elastic moduli and seismic attributes from complex rock properties, involving patchy saturation and fractured media. To confirm and further develop rockphysics theories for reservoir rocks, accurate numerical modeling tools are required. Our 2D velocity-stress, finite-difference scheme simulates waves within poroelastic media as described by Biot's theory. The scheme is second order in time, contains high-order spatial derivative operators, and is parallelized using the domain-decomposition technique. A series of numerical experiments that are compared to exact analytical solutions allow us to assess the stability conditions and dispersion relations of the explicit poroelastic finite-difference method. The focus of the experiments is to model waveinduced flow accurately in the vicinity of mesoscopic heterogeneities such as cracks and gas inclusions in partially saturated rocks. For that purpose, a suitable numerical setup is applied to extract seismic attenuation and dispersion from quasi-static experiments. Our results confirm that finite-difference modeling is a valuable tool to simulate wave propagation in heterogeneous poroelastic media, provided the temporal and spatial scales of the propagating waves and of the induced fluid-diffusion processes are resolved properly.
[1] Reservoir rocks saturated with two immiscible fluids may exhibit considerable wave attenuation and dispersion due to wave-induced fluid flow. Attenuation-and velocitysaturation relations of P-waves are developed for partially saturated porous media in which the fluid patches form random fractals on the mesoscopic scale. Depending on the fractal dimension of the pore fluid distribution the velocitysaturation relation can vary between the exact GassmannWood and Gassmann-Hill bounds. The results indicate that the fractal dimension is an additional measure that should be accounted for to consistently model effective acoustic properties of partially saturated rocks. Citation: Müller, T. M., J. Toms-Stewart, and F. Wenzlau (2008), Velocity-saturation relation for partially saturated rocks with fractal pore fluid distribution, Geophys. Res. Lett., 35, L09306,
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