Propagation characteristics of dynamic wave in fluid-containing granular materials at unified high and low frequency

Abstract

Reservoir geologic fluid-bearing granular materials are characterized by multiscale nonuniformity and coupled multiphysical mechanisms, for which conventional poroelastic theory cannot accurately portray wave dispersion and attenuation characteristics. To design a suitable dielectric wave propagation model to characterize the dispersion and attenuation laws of dynamic waves in geologic reservoirs, first, the branching functions of frequency-dependent dynamic permeability and dynamic tortuosity are derived by considering the effects of the geometry and fractal structure of fluid-bearing granular materials on the high-frequency properties of permeability and tortuosity. Second, the stress‒strain relationship of the fluid-particle system is redrawn by the viscoelastic‒plastic constitutive relation, and the dynamic wave propagation model of fluid-containing granular materials at a unified frequency is constructed by an integrated dissipation mechanism including frictional dissipation, internal dissipation, and plastic energy dissipation-wave propagation model based on viscoelastic‒plastic constitutive relation and dynamic permeability (WVPDP model). Finally, the reliability of the WVPDP model is verified by carrying out wave velocity tests on saturated dolomite and sandstone, and the effects of different parameters on the wave velocity dispersion amplitude and attenuation peak are analysed. The results show that the WVPDP model can accurately characterize the dispersion and attenuation of dynamic waves in granular media under uniform high and low frequencies and can invoke different dissipation mechanisms at different excitation frequency intervals, which is shown by the fact that internal dissipation and the plastic mechanism play the main role in the low-frequency interval, and frictional dissipation gradually replaces internal dissipation and plastic dissipation to become the main dissipation mechanism with increasing excitation frequency. Parameters such as fluid viscosity, reference angular frequency and reference quality can have different effects on the dispersion amplitude and transition band range of the fast P-wave and S-wave, the two mechanical response mechanisms in the medium of fluid-containing granular materials.