Azimuth-, angle- and frequency-dependent seismic velocities of cracked rocks due to squirt flow

Abstract

Abstract. Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing noninvasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries, appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid–solid deformation at the pore scale based on coupled Lamé–Navier and Navier–Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. Furthermore, the overall anisotropy of a medium mainly increases due to squirt flow, but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface.

An accurate analytical model for squirt flow in anisotropic porous rocks — Part 1: Classical geometry

“…We recall a brief overview of the physics based on the previous analytical studies (Mavko and Jizba, 1991) with some additional information obtained from numerical simulations (Quintal et al, 2019;Alkhimenkov et al, 2020aAlkhimenkov et al, , 2020bLissa et al, 2020). In the physics of squirt flow, the cause of energy dissipation is fluid pressure diffusion at the pore scale.…”

“…This is called unrelaxed state. The slope of the high-frequency asymptote of the attenuation curve depends on the pore geometry (Alkhimenkov et al, 2020a(Alkhimenkov et al, , 2020b. If the pore space is represented by a penny-shaped crack connected to a toroidal pore, then 1∕Q at high frequencies is proportional to ≈ω −1∕2 .…”

“…If these three parameters are determined, the dispersion and attenuation curves can be plotted using, for example, a standard linear solid (SLS) rheology. The disadvantage of the SLS model is that the resulting 1∕Q is a symmetric curve if plotted in a bilogarithmic scale, which is usually not the case for attenuation caused by squirt flow (Alkhimenkov et al, 2020a(Alkhimenkov et al, , 2020bLissa et al, 2020).…”

“…For the validation, we consider several 3D models consisting of a pore space embedded in an elastic solid grain material. The numerical methodology is described in Appendix A and is introduced by Quintal et al (2016Quintal et al ( , 2019; the boundary conditions for the direct relaxation tests to compute all components of the stiffness matrix are described in Alkhimenkov et al (2020aAlkhimenkov et al ( , 2020b. The models considered are as follows:…”

“…Numerically, squirt flow can be modeled by solving a set of equations describing coupled fluid-solid deformation (Zhang et al, 2010;Zhang and Toksöz, 2012;Quintal et al, 2016Quintal et al, , 2019Das Manuscript received by the Editor 23 April 2021; revised manuscript received 11 November 2021; published ahead of production 26 December 2021; published online 16 February 202216 February . et al, 2019Alkhimenkov et al, 2020aAlkhimenkov et al, , 2020bLissa et al, 2020Lissa et al, , 2021. Quintal et al (2016Quintal et al ( , 2019 propose a simplified numerical solution based on the linearized quasistatic Navier-Stokes equation.…”