On the theory of Biot-patchy-squirt mechanism for wave propagation in partially saturated double-porosity medium

Reservoir rocks are usually composed of a coherent heterogeneous porous matrix saturated by multiple fluids. At long wavelength limit, the composite material of solid skeleton is usually regarded as homogeneous media. However, at grain scale or high loading rate, non-uniform fluid flow at internal interface of heterogeneity plays essential role in wave dispersion and attenuation. Formulating wave propagation in partially saturated and fractured rocks is challenging and of great interests in geoscience. Here we raise a Biot-patchy-squirt (BIPS) model to characterize wave dispersion/attenuation in fractured poroelastic media saturated by two immiscible fluids. BIPS model incorporates the mechanism of local fluid-interface flow (LFIF) and squirt flow into global fluid flow simultaneously. Theoretical analysis show that wave attenuations caused by viscous dissipation, squirt flow and patchy interface vibration are distinct from each other. BIPS is intrinsically consistent with Biot theory, squirt and LFIF model and reduces to such mechanism in limiting conditions. More interestingly, numerical results show that coupling between LFIF and squirt flow is of evident importance to P-wave dispersion and attenuation. Comparisons with experimental data indicate that BIPS model is computationally reliable and in reasonably good agreement with experimental data. This study advance our understanding of the fundamental physics of wave propagation in natural reservoir rocks and push forward the potential applications of the triple dispersion/attenuation mechanism to wave velocity estimation in deep earth.