Effect of local fluid flow on the propagation of elastic waves in a transversely isotropic double-porosity medium

Abstract

This study considers the propagation of elastic waves in a fluid-saturated double-porosity solid. Constitutive relations are derived for the double porosity medium having the transverse isotropy with vertical axis of symmetry. The equations of motion are solved for the propagation of harmonic waves. Then, the amount of wave-induced fluid flow at any point is expressed in terms of normal strain components in the composite medium. For propagation in a plane, the equations of motion decouple into two independent systems. One of these represents the particle motion normal to the plane and identifies the SH-type motion for solid particles. The other system represents the in-plane motion of particles and governs the propagation of four coupled waves. Among these four waves, three are quasi-longitudinal (qP1, qP2, qP3) waves and one is a quasi-transverse (qSV) wave. A numerical example is solved to calculate the velocity and attenuation anisotropy of the five waves. Effect of local fluid flow is observed on the wave velocities as well as the polarization of the constituent particles in double porosity medium. Effects of wave-frequency, propagation direction, pore-fluid viscosity, permeability and radius of spherical inclusions are analysed on the velocities and attenuation.