Modeling the Effect of Multiscale Heterogeneities on Wave Attenuation and Velocity Dispersion

Wave attenuation and velocity dispersion are of great significance to fluid evaluation in fluid-saturated rocks. Inspired by the double-porosity and cracked porous elastic wave theory, we develop a multiscale heterogeneities elastic wave theory to better describe the attenuation characteristics caused by wave-induced fluid flow at various scales in saturated rocks. First, we introduce penny-shaped and narrow-shaped coupled cracks into double-porosity model. The potential energy function is given by the stress–strain relationship. The kinetic energy function and dissipation function are derived based on the generalized Biot’s theory. Next, we derive the multiscale wave equations through the Lagrange equation and obtain three compressional waves and one shear wave. According to the novel wave equations, we work out the phase velocity and inverse quality factor in double-porosity and cracked media based on plane-wave analysis. The numerical simulation results show that there are four attenuation peaks in the whole frequency band, corresponding to mesoscopic fluid flow, and two kinds of squirt flow and Biot flow, respectively. Then, we investigate the effect of poroelastic parameters on wave propagation. It is found that porosity, inclusion size, crack aspect ratio, and other parameters significantly affect the dispersion and attenuation. Finally, we compare experimental data and theoretical prediction. Moreover, the new elastic wave theory can degenerate into classical Biot’s theory, double-porosity theory, and pore-crack theory under certain conditions, which demonstrates the consistency of this method. The proposed theory can better predict and simulate the wave propagation by incorporating the effects of microscopic, mesoscopic, and macroscopic heterogeneities.