An accurate analytical model for squirt flow in anisotropic porous rocks — Part 2: Complex geometry

Abstract

Seismic waves exhibit strong attenuation and velocity dispersion when they propagate in porous rocks saturated with a fluid. The main cause of such energy dissipation is fluid flow in the pore space, so called squirt flow. Squirt flow takes place between interconnected pores and cracks or grain-to-grain contacts. The corresponding theory can be used to characterize porous rocks in the subsurface with noninvasive seismic methods. We extend the analytical model for a classical pore geometry presented in part 1 of our paper to more complex geometries of the pore space, where the crack edge is partially connected to multiple pores. This pore geometry is much more closely representative of rocks than the classical geometry where the crack edge is fully connected to a toroidal pore. We develop an approach to calculate the model compliance taking into account the interconnectivity of the crack and pores. We redefine a squirt flow length parameter which takes into account the geometrical configuration of the multiple connections between a crack and the surrounding pores. This configuration will control the geometrical flow pattern and thus the diffusion length scale or, in other words, the characteristic frequency. We validate our analytical model against inherently accurate 3D numerical solutions. The analytical and numerical results are in excellent agreement for a range of different pore geometries. Published analytical solutions expect the user to know the dry stiffness (e.g., from laboratory measurements), but in our work, we also provide a way to calculate analytically the dry stiffness for the precise geometry that we consider. The new analytical model redefines the quantitative and qualitative description of seismic attenuation and velocity dispersion due to squirt flow. We provide the MATLAB and symbolic Maple routines to reproduce our main results.