Numerical simulation of shear wave attenuation in borehole inserted by a horizontal fracture

The amplitude of shear waves is attenuated when passing through horizontal fractures crossing a borehole. In this study, we investigate the amplitude attenuation of shear waves throughout simulation of full-wave acoustic logging with the finite-difference method. As the fracture aperture is very small, it needs to be represented in a very fine gird when carrying out finite-difference simulation. Therefore, the variable-grids finite-difference method is adopted to avoid over-sampling in the non-fracture regions, yielding substantial savings in computational cost. We demonstrate the accuracy of waveform modeling with the variable-grid finite-difference by benchmarking against that obtained with the real-axis integrating method. We investigated the effects of several important parameters including fracture aperture, distance from receiver to fracture, borehole radius and extended distance utilizing that benchmarked variable-grid finite difference code. We determined a good linear relationship between the attenuation coefficient of shear wave amplitude and the fracture aperture. Then, the effects of distance from receiver to fracture, the borehole radius and the extended distance of fracture on shear wave attenuation are also studied. The attenuation coefficient of shear wave becomes smaller with the increasing borehole radius. While, it increases as the distance from receiver to fracture and the extended distance of fracture increase. These effect characteristics are conducive to the use of shear wave to evaluate fractures.