Simulating squirt flow in realistic rock models using graphical processing units (GPUs)

Abstract

SUMMARY Understanding the underlying mechanisms of seismic attenuation and moduli dispersion in fluid-saturated cracked porous rocks is of great importance for the development of non-invasive methods to characterize the subsurface. Wave-induced fluid flow at the pore scale, so-called squirt flow, is responsible for seismic attenuation and moduli dispersion at sonic and ultra-sonic frequencies and may be relevant at seismic frequencies. The squirt flow associated attenuation is usually quantified using analytical models. However, numerical experiments suggest that the squirt flow related dissipation is sensitive to fine details of the pore geometry, which can only be modelled numerically. Most of the existing numerical studies explore this phenomenon using simplified models, and there is a lack of numerical studies that model the physics in realistic pore geometries with sufficient numerical resolution. As a result, the impact of wave-induced fluid flow on the effective static and time-dependent mechanical characteristics in realistic settings is still poorly understood. I address these issues by developing a numerical method to model the effective mechanical properties of a hydromechanically coupled system at the pore scale suitable for graphical processing units. A numerical evaluation of attenuation and modulus dispersion due to squirt flow in models based on 3-D microtomography images of cracked Carrara marble is presented. It is shown that the local hydraulic conductivity can be quantitatively estimated from the numerically evaluated effective properties. The accuracy of the numerical results is carefully analysed. This study improves the understanding of the underlying mechanisms of attenuation and moduli dispersion in fluid-saturated cracked rocks. The new method can be applied to model squirt flow for entire laboratory samples in the centimetre scale which was not possible a decade ago.