The 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.

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The characterization of fractures is essential to increase the production of hydrocarbon and geothermal resources. In this study, we investigate the effect of fluid flow in the longitudinal fracture along a borehole on the dispersion and attenuation behavior of Stoneley waves using numerical experiments. Generally, incorporating a fracture with the aperture of several tens to hundreds of micrometers into 3D seismic modeling is challenging with high calculational costs. We develop a novel numerical scheme that includes a 2D fluid flow simulation embedded into a 3D wave propagation modeling to address this problem. We devise an approach for capturing the effects of fluid flow in fractures of arbitrary aperture widths, which could be much thinner than the grid spacing of 3D wave propagation simulation. A comparison of the numerical results from our scheme with the analytical solution shows good agreement, supporting the method's validity. This developed scheme is applied to coupled simulation between Stoneley wave propagation along the borehole axis and induced fluid flow inside a longitudinal fracture with different fracture apertures, fluid viscosity, and dynamic hydraulic conductivity. The modified matrix pencil algorithm applied to the recorded waveforms estimates the dispersion and attenuation of Stoneley mode. The numerical results reveal the effect of the fracture aperture and fluid viscosity on the dispersion and attenuation behavior of the Stoneley waves. Based on the results, we propose our scheme as an innovative method for estimating the aperture of fracture and viscosity of the fluid by analyzing the dispersion and attenuation properties of the Stoneley waves.