Acoustic Wave Propagation In A Fluid-Filled Borehole With A Horizontal Fracture

The propagation of guided waves in a fluid-filled borehole with an open horizontal fracture is investigated both theoretically and experimentally. The fracture is modeled as a fluid layer that separates the domain of propagation into two regions. For the solution of the problem, we use a hybrid method to generate wave modes in the two regions. The modes are then summed to match the boundary conditions at the fracture surfaces. A singularity problem arises in matching the surface conditions and is regularized using a physical model based on the conservation of mass. Using the theory developed in this study, we study the transmission and reflection characteristics of borehole guided waves (Le., Stoneley and pseudo-Rayleigh waves) due to the fracture. At low frequencies, the effects of a fracture on the Stoneley wave are dominated by the fluid flow into the fracture. As frequency increases, mode conversion at the fracture becomes significant. Above the cut-off frequency of the pseudo-Rayleigh wave, part of the incident Stoneley wave is converted to pseudo-Rayleigh waves, which is demonstrated by synthetic microseismograms. The pseudo-Rayleigh wave is substantially affected by the fracture. Because this wave requires the formation shear strength to sustain its propagation, even a thin fracture with zero shear strength can significantly attenuate the wave amplitude and produce strong reflection. This effect is more pronounced towards the cut-off frequencies than away from the frequencies. Consequently, the lack of pseudo-Rayleigh energy across a fracture may be used as a sensitive indicator in fracture detection and characterization. Ultrasonic experiments have been performed to measure the transmission of guided waves across laboratory borehole fracture models. For the Stoneley waves, we performed the experiment below the cut-off frequency of the pseudo-Rayleigh wave and the experimental results are in good agreement with the theory. For the pseudo-Rayleigh wave, we performed the experiment in a higher frequency range. The experiment has verified the substantial effects of a fracture on this wave mode. The weak early arrivals of the transmitted waves have also been observed for thin as well as thick fractures. This confirms the theoretical prediction that the transmission of the pseudo-Rayleigh wave is the smallest towards the cut-off frequencies. The measured transmission coefficients agree with theoretical results. In summary, we have presented an analysis on the guided wave propagation across a borehole horizontal fracture. The wave characteristics in the vicinity of a fracture as described in this study may be used to provide useful information for the detection and characterization of borehole fractures using acoustic logging techniques.United States. Dept. of Energy (Grant DE-FG02-86ER13636)Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu