Frequency-dependent Seismic Anisotropy of Porous Rocks with Penny-shaped Cracks
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Porous reservoirs with aligned fractures exhibit frequency-dependent seismic anisotropy because of wave-induced fluid flow between pores and fractures. To relate the elastic properties of porous rocks with aligned fractures at low frequency, we use the linear slip model of fractures and anisotropic Gassmann fluid substitution. We combine this low-frequency anisotropic Gassmann model with a dispersion relationship, based on a penny-shaped crack model of fractures, to account for frequency-dependent anisotropy. The combined model is validated using experimental measurements of angle-dependent wave velocities of synthetic porous sandstone with aligned disc-shaped cracks. For the low-frequency anisotropic Gassmann model, the agreement between the measured and predicted velocities is reasonably good for both S-wave velocities, but P-wave anisotropy is overestimated by approximately 25%. This quantitative difference can be explained by fluid diffusion effects occurring at the relatively high frequencies used in the experiment (100 kHz), which are not accounted for by the low-frequency assumption of anisotropic Gassmann theory. The predictions of the combined frequency-dependent model, which considers this effect, give very good agreement with measured velocities.
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