Abstract
This study considers the propagation of harmonic plane waves in a double-porosity dual-permeability solid saturated with single viscous fluid. Christoffel system is obtained to explain the existence of three longitudinal waves and a transverse wave in the medium considered. Each wave is identified with a complex velocity, which is resolved for inhomogeneous propagation to calculate the phase velocity and attenuation of the wave. Pore-fluid pressures are expressed in terms of velocities of solid particles corresponding to the propagation of three longitudinal waves. Then, transfer rate of pore-fluid between two porosities induced by each longitudinal wave is calculated as a function of its complex velocity. Numerical example is solved to study the dispersion in phase velocity and attenuation for each of the four waves. Effects of pore-fluid viscosity, wave-inhomogeneity and composition of double porosity on inhomogeneous propagation are analysed graphically. Transfer rate of pore-fluid, induced by each of the three longitudinal waves, is calculated as a periodic waveform. Variations in the fluid-flow profile are exhibited for different values of pore-fluid viscosity, skeleton permeability, wave-frequency and wave-inhomogeneity.
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