A simple hydromechanical approach for simulating squirt-type flow

Abstract

The deformations caused by an acoustic wavefield in subsurface rock can induce fluid flow within hydraulically interconnected mesoscopic fractures, from one fracture into the other. The viscous friction associated with this squirt-type fluid flow parallel to the fracture walls results in energy dissipation and velocity dispersion. We have developed a quasi-static hydromechanical approach that is suitable for simulating squirt-type flow in the mesoscopic scale range and microscopic squirt flow. Our approach couples Navier-Stokes equation with Hooke’s law to describe the laminar flow of a viscous compressible fluid in conduits embedded in an elastic solid background. Results from the proposed method were compared with those obtained with Biot’s equations for a model containing interconnected mesoscopic fractures embedded in a background of very low porosity and permeability. Despite significant differences in the flow and dissipation spatial patterns, we have observed an essentially perfect agreement of the attenuation and modulus dispersion characteristics predicted by the two approaches. The difference in the flow and dissipation spatial patterns are associated with the “upscaling” inherent to Biot’s equations and, correspondingly, with differing boundary conditions at the fracture walls. Our results demonstrate that the proposed hydromechanical approach can provide additional insights on the physics of squirt-type flow in the mesoscopic and microscopic scale ranges.