Elastic wave attenuation and dispersion induced by mesoscopic flow in double-porosity rocks

The double-porosity, dual-permeability theory is employed to predict the wave attenuation and phase velocity dispersion induced by wave-induced mesocopic fluid flow. Instead of using an up-scaled, single-porosity approximation scheme proposed by previous researchers, we develop an analytical method to exactly solve the wave equations for double-porosity materials. We first propose a new form of wave equations formulated in terms of displacements. This new form of wave equations enables us to decouple the field equations into two second-order symmetric dynamic systems, namely, the P-system for compressional waves and the S-system for shear wave. We then implement Newton iteration for solving the cubic dispersion equation for compressional waves. Finally, to understand the loss mechanism caused by mesoscopic flow, we compare the attenuation curves of the first (P1-wave), the second (P2-wave), and the third compressional waves (P3-wave), as well as the shear wave (S-wave), with the mesoscopic flow present to those with the mesoscopic flow absent. Furthermore, the effects of matrix porosity, pore-fluid viscosity, and values of fluid transport coefficient on wave attenuation are also investigated in numerical examples.