Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity-extended theory

摘要

The simplified macro-equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro-equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine-saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine-saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid-fluid combination behaviour properly.