Dispersion of flexural waves in a borehole with a tensile fracture in an anisotropic stress environment

Abstract

ABSTRACTThe effect of tensile fracture in a vertical borehole under anisotropic horizontal stress conditions is numerically investigated in terms of the dispersion of flexural wave generated in dipole sonic logging. Our three‐dimensional model comprises a borehole filled with water and a tensile fracture intersecting the borehole in the borehole axial direction. Two shear waves are excited individually to produce particle displacements polarized in two orthogonal radial directions using two dipole sources aligned in the two polarized directions. A vertical array of equispaced dipole sensors is placed at the centre of the borehole along the borehole axis. We assumed that the surrounding formation possesses transversally isotropic anisotropy with the isotropy plane parallel to the borehole axis due to horizontal stress anisotropy. We examined the dispersion of flexural waves travelling along a borehole in our numerical models that include either fast or slow formation with various depths of tensile fractures. Our numerical results show that the deeper the penetration depth of a tensile fracture, the higher the slowness of shear waves polarized perpendicular to the tensile fracture for both slow and fast formation models. Our results indicate that the flexural dispersion behaviour could be used to investigate the depth of penetration of a tensile fracture that can be produced by either drilling or hydraulic fracturing.