Fracture characterization from attenuation of Stoneley waves across a fracture

Fractures contribute significantly to the permeability of a for-mation. It is important to understand the fracture distribution and fluid transmissivity. Though traditional well logs can im-age fractures intersecting the borehole, they provide little in-formation on the lateral extent of the fractures, away from the borehole, or the fluid transmissivity. Experiments in the past demonstrated that fracture compliance can be a good proxy to fracture fluid conductivity. We describe a method to es-timate fracture compliance from the attenuation of Stoneley waves across a fracture. Solving the dispersion relation in the fracture, transmission coefficient of Stoneley waves across a fracture is studied over all frequency ranges. Based on the observations from the model, we propose that measuring the transmission coefficient near a transition frequency can help constrain fracture compliance and aperture. Comparing atten-uation across a finite fracture to that of an infinitely long frac-ture, we show that a bound on the lateral extent of the frac-ture can be obtained. Given the limitation on the bandwidth of acoustic logging data, we propose using the Stoneley waves generated during micro-seismic events for fracture characteri-zation