Effects of Multiscale Fluid Flows on Wave Propagation in Partially Saturated Porous Rock
摘要
This work investigates the effect of multi-scale fluid-flow mechanisms on wave propagation in partially saturated porous rock. By integrating the mesoscopic Rayleigh model of bubble oscillations and the microscopic squirt-flow model into Santos’ poroelasticity theory, a unified model is developed, incorporating loss mechanisms at all the microscopic, mesoscopic, and macroscopic scales, as well as the influence of capillary forces. The plane-wave analysis reveals the velocity dispersion and attenuation of four wave modes, namely, the fast P1 wave, the fast SV wave, and two slow waves, all of which are strongly influenced by multi-scale fluid flows. Specifically, the mesoscopic, macroscopic and microscopic fluid flows sequentially induce three distinct P1-wave attenuation peaks, consequently resulting in a three-stage, step-like phase velocity dispersion. Two sets of experimental data show reasonable agreement with the plane-wave predictions, thereby confirming the validity of the proposed theory. The model is then used to investigate wave propagation at the surface of porous media, including reflection and surface waves, to quantitatively explore the influences of multi-scale fluid flows. Analytical expressions for solving reflection coefficients and surface-wave velocities are derived for both open and sealed boundary conditions (BCs). Numerical results reveal an observable three-stage reflection dispersion pattern and also three distinct surface-wave attenuation peaks, sequentially induced by the mesoscopic, macroscopic, and microscopic fluid-flow mechanisms. The BCs mainly influence high-frequency surface-wave propagation, due to the propagation of two slow wave modes. The sealing BCs predict two additional slow surface-wave modes, which closely resemble the two slow compressional waves. This study provides valuable insights for a better understanding of wave propagation in partially saturated porous solids.