An accurate analytical model and application method for squirt flow in anisotropic fractured rocks

The squirt flow in cracks or grain contacts at the pore scale is an important mechanism of seismic wave velocity dispersion and attenuation. We develop a simple and accurate analytical model for attenuation and dispersion caused by squirt flow between microcracks with different aspect ratios. The dual crack squirt flow model calculates compliance by considering the interconnectivity of two cracks with different aspect ratios. The crack diameter rather than radius was used as the characteristic length of the squirt flow, and the one-dimensional fluid pressure diffusion equation was used instead of the radial fluid pressure diffusion equation to describe the fluid squirt path. The analytical results of the dual crack model are in excellent agreement with the results obtained by numerical simulations. We use the dual crack model for inverse determination of multiple microcrack structures from pressure experimental data by applying the squirt flow model to each set of microcracks, and finally obtaining the attenuation and velocity dispersion in the rock. For the four examined rock samples, the predictions of the dual crack analytical model and the experimental measurements are in excellent agreement. The dual crack analytical model enables quantitative and qualitative analysis of seismic attenuation and velocity dispersion due to squirt flow between microcracks.