Equivalent viscoelastic solids for heterogeneous fluid-saturated porous rocks

Abstract

Different theoretical and laboratory studies on the propagation of elastic waves in real rocks have shown that the presence of heterogeneities larger than the pore size but smaller than the predominant wavelengths ͑mesoscopic-scale heterogeneities͒ may produce significant attenuation and velocity dispersion effects on seismic waves. Such phenomena are known as "mesoscopic effects" and are caused by equilibration of wave-induced fluid pressure gradients. We propose a numerical upscaling procedure to obtain equivalent viscoelastic solids for heterogeneous fluidsaturated rocks. It consists in simulating oscillatory compressibility and shear tests in the space-frequency domain, which enable us to obtain the equivalent complex undrained plane wave and shear moduli of the rock sample. We assume that the behavior of the porous media obeys Biot's equations and use a finiteelement procedure to approximate the solutions of the associated boundary value problems. Also, because at mesoscopic scales rock parameter distributions are generally uncertain and of stochastic nature, we propose applying the compressibility and shear tests in a Monte Carlo fashion. This facilitates the definition of average equivalent viscoelastic media by computing the moments of the equivalent phase velocities and inverse quality factors over a set of realizations of stochastic rock parameters described by a given spectral density distribution. We analyzed the sensitivity of the mesoscopic effects to different kinds of heterogeneities in the rock and fluid properties using numerical examples. Also, the application of the Monte Carlo procedure allowed us to determine the statistical properties of phase velocities and inverse quality factors for the particular case of quasi-fractal heterogeneities.

Seismoacoustic signatures of fracture connectivity

“…This is compounded by the necessity to employ small enough grid spacings to properly discretize the fractures, which is an issue both in the low-and high-frequency ranges. To overcome these problems, we employ a numerical upscaling procedure similar to that presented by Rubino et al [2009]. We do, however, impose strain boundary conditions instead of stress boundary conditions, as relaxation experiments turned out to be more suitable for analyzing the P wave seismic response of rock samples containing very strong compressibility contrasts (M. Milani, personal communication, 2014).…”

Seismoelectric effects due to mesoscopic heterogeneities

“…The fluid is not allowed to flow into or out of the sample. To obtain the response of the sample, we numerically solve the equations of quasi-static poroelasticity under corresponding boundary conditions [Rubino et al, 2009]. This methodology allows for computing the relative fluid velocity field P w which is then employed to calculate the corresponding seismoelectric signal.…”

Seismic Reflectivity in Carbon Dioxide Accumulations: A Review

“…There are many studies about numerical modeling of these effects, e.g. [25], [26], [27], showing that they are strongly dependent on the shapes and characteristic lengths of the patches. Given that these parameters are rarely known, to avoid dealing with this uncertainty, in our analysis we assume elastic layers where no attenuation-dispersion phenomena, associated with the patchy fluid distribution take place.…”