Slow compressional wave in porous media: Finite difference simulations on micro-scale

We perform wave propagation simulations in porous media on microscale in which a slow compressional wave can be observed. Since the theory of dynamic poroelasticity was developed by Biot (1956), the existence of the type II or Biot's slow compressional wave (SCW) remains the most controversial of its predictions. However, this prediction was confirmed experimentally in ultrasonic experiments. The purpose of this paper is to observe the SCW by applying a recently developed viscoelastic displacement-stress rotated staggered finite-difference (FD) grid technique to solve the elastodynamic wave equation. To our knowledge this is the first time that the slow compressional wave is simulated on first principles

Seismic Effects of Viscoelastic Pore Fill on Double-Porosity Rocks

© ASCE. We present a new model for elastic wave dispersion and attenuation in porous rocks saturated with viscous fluids and viscoelastic substances. The main idea is that the dispersion is mainly caused by frequency dependence of the normal and tangential stiffness of compliant pores that are hydraulically connected to stiff pores. First, we assume that the compliant pore (microcrack or grain-to-grain contact) is filled with an elastic solid. This allows us to obtain the stiffness of the compliant pore using a known solution of the elastic problem for a circular interlayer sandwiched between two parallel plates. The solution is then extended to viscoelastic pore fill using elastic/viscoelastic correspondence principle. The model predicts both, squirt-flow and viscous shear relaxation, and substantial increase in the rock rigidity with increasing frequency (or decreasing temperature) for rocks saturated with viscoelastic substances. The results are illustrated by an example of a typical rock saturated with water and with heavy oil

Seismic attenuation due to wave-induced fluid flow in a porous rock with spherical heterogeneities

Most natural porous rocks have heterogeneities at nearly all scales. Heterogeneities of mesoscopic scale that is, much larger than the pore size but much smaller than wavelength can cause significant attenuation and dispersion of elastic waves due to wave induced flow between more compliant and less compliant areas. Analysis of this phenomenon for a saturated porous medium with a small volume concentration of randomly distributed spherical inclusions is performed using Waterman-Truell multiple scattering theorem, which relates attenuation and dispersion to the amplitude of the wavefield scattered by a single inclusion. This scattering amplitude is computed using recently published asymptotic analytical expressions and numerical results for elastic wave scattering by a single mesoscopic poroelastic sphere in a porous medium.This analysis reveals that attenuation and dispersion exhibit a typical relaxation-type behavior with the maximum attenuation and dispersion corresponding to a frequency where fluid diffusion length (or Biot's slow wave length) is of the order of the inclusion diameter. In the limit of low volume concentration of inclusions the effective velocity is asymptotically consistent with the Gassmann theory in the low-frequency limit, and with the solution for an elastic medium with equivalent elastic inclusions (no-flow solution) in the low-frequency limit. Attenuation (expressed through inverse quality factor ) scales with frequency in the low frequency limit and with in the high frequency limit. These asymptotes are consistent with recent results on attenuation in a medium with a periodic distribution of poroelastic inclusions, and in continuous random porous media