Effects of ellipsoidal heterogeneities on wave propagation in partially saturated double-porosity rocks

Abstract

Reservoir rocks are heterogeneous porous media saturated with multiphase fluids, in which strong wave dissipation and velocity dispersion are closely associated with fabric heterogeneities and patchy saturation at different scales. The irregular solid inclusions and fluid patches are ubiquitous in nature, whereas the impact of geometry on wave dissipation is still not well-understood. We have investigated the dependence of wave attenuation and velocity on patch geometry. The governing equations for wave propagation in a porous medium, containing fluid/solid heterogeneities of ellipsoidal triple-layer patches, are derived from the Lagrange equations on the basis of the potential and kinetic energies. Harmonic functions describe the wave-induced local fluid flow of an ellipsoidal patch. The effects of the aspect ratio on wave velocity are illustrated with numerical examples and comparisons with laboratory measurements. The results indicate that the P-wave velocity dispersion and attenuation depend on the aspect ratio of the ellipsoidal heterogeneities, especially in the intermediate frequency range. In the case of Fort Union sandstone, the P-wave velocity increases toward an upper bound as the aspect ratio decreases. The example of a North Sea sandstone clearly indicates that introducing ellipsoidal heterogeneities gives a better description of laboratory data than that based on spherical patches. The unexpected high-velocity values previously reported and ascribed to sample heterogeneities are explained by varying the aspect ratio of the inclusions (or patches).

An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

“…The dual-porosity model was proposed by Pride and Berryman [3,4] and extended to Biot-Rayleigh theory by Ba et al [5] by combining the conventional dual-porosity model and the bubble oscillation equation [6] to describe the seismic wave attenuation and dispersion characteristics. Additionally, several models have been developed by analyzing different inclusions or patches under the framework of the Biot-Rayleigh theory [7][8][9][10][11].…”

Characterization of a Volcanic Gas Reservoir Using Seismic Dispersion and Fluid Mobility Attributes

“…With the progress in rock physical methods, velocity dispersion and attenuation associated with wave-induced fluids flow in a porous medium with complex microstructures were investigated [6][7][8][9][10][11][12][13]. Chapman et al [14] found that the reflection coefficient for hydrocarbon reservoirs represents strong frequency-dependence and thus suggested characterizing reservoirs using seismic dispersion anomaly.…”

Seismic wave attenuation and dispersion induced by fluid flow within various cracks and a small amount of bubbly fluid

“…The double-porosity model is proposed by Pride andBerryman [2003a, 2003b] and extended to many special situations [Ba et al, 2011[Ba et al, , 2017Sun et al, 2018;Zhao et al, 2018;Zhang et al, 2019]. The patchy-saturated model is first proposed by White [1975] and developed by Odé [1979a, 1979b] and Vogelaar et al [2007].…”