Stoneley Wave Propagation in a Fluid-filled Borehole with a Vertical Fracture

The propagation of Stoneley waves in a fluid-filled borehole with a vertical fracture is investigated both theoretically and experimentally. The borehole propagation excites fluid motion in the fracture and the resulting fluid flow at the fracture opening perturbs the fluid-solid interface boundary condition at the borehole wall. By developing a boundary condition perturbation technique for the borehole situation, we have studied the effect of this change in the boundary condition on the Stoneley propagation. Cases of both hard and soft formations have been investigated. It has been shown that the fracture has minimal effects on the Stoneley velocity except in the very low frequency range in which the Stoneley velocity drastically decreases with decreasing frequency. Significant Stoneley wave attenuation is produced because of the energy dissipation into the fracture. In general, the effects of the fracture are more important in the low frequency range than at higher frequencies. The quantitative behavior of these effects depends not only on fracture aperture and borehole radius, but also on the acoustic properties of the formation and fluid. Ultrasonic experiments have been performed to measure Stoneley propagation in laboratory fracture borehole models. Aluminum and lucite were used to simulate a hard and a soft formation, respectively. Array data for wave propagation were obtained and were processed using Prony's method to give velocity and attenuation of Stoneley waves as a function of frequency. In both hard and soft formation cases, the experimental results were found to agree well with the theoretical predictions. The important result of this study is that, we have found a quantitative relationship between the Stoneley propagation and the fracture character in conjunction with formation and fluid properties. This relationship can be used to provide a method for estimating the characteristics of a vertical fracture by means of Stoneley wave measurements.