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

100%

Yan B. , Ou W. , Huang X. , da Silva N. V.

Acta Geophysica

2020

tom Vol. 68, no. 6

1715--1726

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 fnite-diference method. As the fracture aperture is very small, it needs to be represented in a very fne gird when carrying out fnite-diference simulation. Therefore, the variable-grids fnite-diference 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 fnite-diference by benchmarking against that obtained with the real-axis integrating method. We investigated the efects of several important parameters including fracture aperture, distance from receiver to fracture, borehole radius and extended distance utilizing that benchmarked variable-grid fnite diference code. We determined a good linear relationship between the attenuation coefcient of shear wave amplitude and the fracture aperture. Then, the efects of distance from receiver to fracture, the borehole radius and the extended distance of fracture on shear wave attenuation are also studied. The attenuation coefcient 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 efect characteristics are conducive to the use of shear wave to evaluate fractures.

Numerical simulation of borehole Stoneley wave refection by a fracture based on variable grid spacing method

88%

Ou W. , Wang Z. , Ning Q. , Xu F. , Yu Y.

Acta Geophysica

2019

tom Vol. 67, no. 4

1119--1129

In this paper, the finite difference method is used to model the Stoneley wave refection by a horizontal fracture in a borehole. The fracture shape is described by some finite difference grids. Therefore, the fracture aperture can be varied in the radial direction, thus extending previous researches on the assumption that the fracture aperture is constant throughout the fracture. Finite difference grids can also be used to describe a fracture which extends a finite distance in the radial direction. In addition, the finite difference algorithm can deal with the problem of inhomogeneous formation. Therefore, it allows the variation of formation elasticity in the model. Fine grids are needed to describe the small fracture aperture, and variable grid spacing is employed by finite difference method to improve computational efficiency. The Stoneley wave propagation is simulated by the variable grid spacing finite difference method in several models with variable fracture aperture, finite extension fracture and models with heterogeneous formation. The variable grid spacing finite difference method is validated through a comparison with real axis integration method and the analytical method. We get some conclusions by simulating and investigating effects of the variation of fracture aperture, the fracture of finite extension and inhomogeneity of formation on the Stoneley wave refection. Although the fracture aperture changes along the fracture extension direction, the refection coefficient of Stoneley wave is mainly controlled by the fracture aperture near the borehole. The Stoneley wave in the fracture is reflected back into the borehole, by the tip of finite extension fracture, which results in some notches in the refection coefficient curve. If the Stoneley wave propagates from the formation with small elastic modulus to the formation with large elastic modulus, the refection coefficient of Stoneley wave will be larger than that of homogeneous model with small elastic modulus. And if Stoneley wave propagates from the formation with large elastic modulus to the formation with small elastic modulus, the refection coefficient of Stoneley wave will be smaller that of homogeneous model with large elastic modulus. These results provide some basis for the use of Stoneley wave to detect the fracture properties in formation.