Elastodynamic equations and wave propagation for multiscale wave-induced fluid flow in partially saturated media from energy conservation

The elastodynamic equations in multiphase porous media are fundamental to understanding acoustic wave propagation in subsurface environments. This paper presents a formulation of the dynamic equations of motion for partially saturated porous media derived directly from the principle of energy conservation. The model incorporates three distinct scales of wave-induced fluid flow-macroscopic, mesoscopic, and squirt flow-through explicit kinetic, potential, and dissipation energy density functions. Based on the derived equations, the paper analyzes the dispersion and attenuation characteristics of wave propagation under multiscale effects and examine the influence of key parameters. Numerical results reveal that mesoscopic flow introduces an additional dispersion band and attenuation peak for the P1 wave in the low-frequency range (seismic band), while squirt flow produces similar effects at high frequencies (ultrasonic band). The S1 wave exhibits a dispersion transition and attenuation peak only due to squirt flow at high frequencies. The slow waves (P2 and P3) show minimal attenuation at high frequencies and remain largely unaffected by squirt flow. The model predictions are validated against experimental data from partially saturated Berea sandstone, demonstrating good quantitative agreement. This energy-conservation-based framework provides a unified, physically grounded approach for modeling multiscale wave-induced fluid flow in partially saturated porous media.