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

Abstract

Seismic wave propagation in porous rocks that are saturated with a liquid exhibits significant dispersion and attenuation due to fluid flow at the pore scale, so-called squirt flow. This phenomenon takes place in compliant flat pores such as microcracks and grain contacts that are connected to stiffer isometric pores. Accurate quantitative description is crucial for inverting rock and fluid properties from seismic attributes such as attenuation. Up to now, many analytical models for squirt flow were proposed based on simplified geometries of the pore space. These models were either not compared with a numerical solution or showed poor accuracy. We present a new analytical model for squirt flow which is validated against a three-dimensional numerical solution for a simple pore geometry that has been classically used to explain squirt flow; that is why we refer to it as classical geometry. The pore space is represented by a flat cylindrical (penny-shaped) pore whose curved edge is fully connected to a toroidal (stiff) pore. Compared with correct numerical solutions, our analytical model provides very accurate predictions for the attenuation and dispersion across the whole frequency range. This includes correct low- and high-frequency limits of the stiffness modulus, the characteristic frequency, and the shape of the dispersion and attenuation curves. In a companion paper (Part 2), we extend our analytical model to more complex pore geometries. We provide as supplementary material Matlab and symbolic Maple routines to reproduce our main results.