Squirt-flow in isotropic porous rocks with wedge-shaped cracks

Abstract Seismic wave propagation in fluid-saturated porous rocks exhibits significant dispersion and attenuation due to the pore-scale fluid flow, known as squirt flow. Squirt flow occurs at the microscopic scale and takes place in compliant pores (e.g., grain contacts or microcracks) connected to stiffer pores. Recently, an analytical model for squirt flow in wedge-shaped cracks connected to a stiff pore was developed to investigate wave dispersion and attenuation in isotropic porous rocks. To validate this model, we conducted three-dimensional (3D) numerical simulations of squirt flow using the finite element method (FEM). The numerical results revealed a significant discrepancy between the published analytical and the present numerical solutions. After modifying the published analytical model, the updated analytical solution showed a good agreement with the numerical solution. We also analyzed how wedge-shaped crack aperture and crack geometry affect the attenuation and dispersion responses. The results demonstrate that, using an equivalent crack aperture, the penny-shaped crack geometry serves as a physically consistent substitute for the wedge-shaped geometry. Furthermore, in numerical simulations of squirt flow, employing penny-shaped geometries presents great advantages compared to using wedge-shaped geometries due to the heavier discretization requirements of the latter.