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

Abstract

Reservoir rocks have 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 plays an essential role in wave dispersion and attenuation. Formulating wave propagation in partially saturated and fractured rocks is challenging and is of great interest in geoscience. Recent studies have shown that the mechanisms of wave attenuation caused by viscous dissipation, patchy-saturation, and squirt flow are different. However, the relationship among these mechanisms and the combined effect on wave attenuation are not clear. Here, a Biot-patchy-squirt (BIPS) model is proposed to characterize wave dispersion/attenuation in fractured poroelastic media saturated by immiscible fluids. BIPS model incorporates local fluid-interface flow (LFIF) and squirt flow into global fluid flow simultaneously. Theoretical analysis shows that BIPS is consistent with the Biot theory, squirt flow, and LFIF models, and is reduced to these models under extreme conditions. More interestingly, numerical simulations reveal that the existence of squirt flow partially counterbalances the dissipative effect of LFIF at the patch interface. The attenuation-frequency relationship observed in experiments capturing evidence of squirt flow and patchy-saturation interface flow is reproduced by using the BIPS model. The results show that BIPS model is computationally reliable and is in reasonably good agreement with laboratory data. The findings advance understanding of the physics of wave propagation in natural reservoir rocks and push forward the potential applications of the triple dispersion/attenuation mechanism to wave velocity prediction.