Borehole acoustic fields in porous formation with tilted thin fracture
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摘要: 应用三维交错网格应力-速度有限差分方法,数值模拟了含有倾斜裂缝孔隙介质地层中点声源所激发的井孔声场问题.为满足薄裂缝计算需求,开发了不均匀网格有限差分算法,提高了计算精度及计算速度.利用将孔隙介质方程参数取为流体极限的办法来处理裂缝中的流体,实现了流体-孔隙介质界面处的差分方程统一,使界面处的计算更加灵活方便.在验证了方法正确性的基础上,分别考察了单裂缝宽度、裂缝带宽度、裂缝倾斜角度以及孔隙介质渗透率等参数的变化对井轴上阵列波形的影响并进行了分析.结果表明,声波经过裂缝时可能产生反射横波及斯通利波,后者随裂缝宽度的减小而减小,而前者随裂缝宽度的改变,变化不大,在裂缝很小(20 μm)时依然存在;裂缝带的宽度、密度越大,反射斯通利波越强;当裂缝(裂缝带)倾斜时,反射横波消失,但反射斯通利波受裂缝倾斜角度的影响较小;渗透率的改变对斯通利波的衰减影响较为明显.Abstract: As the improvement of global oil and gas exploration, the fractural reservoir becomes one of the most important objects. The fractures complicatedly influence the array waveforms of logging because of the diversity distribution of fracture zone, which causes the recognition and evaluation become one of the most difficult problems in acoustic logging. In this paper, we research the acoustic field of the borehole surrounded by a porous formation with tilt fractures by numerical simulation, and also investigate the characteristics of borehole fields in the formations with different fracture parameters.#br#We numerically simulate the acoustic fields excited by a point source in the borehole surrounded by a porous formation with tilt fractures using the 3-D staggered grid stress-velocity finite difference method. We design a non-uniform grid finite difference method in order to satisfy the computation of thin fractures, the precision and speed of calculation are improved significantly. We process the fluid inside fractures through setting the parameters of constitutive functions as fluid limitation, which uniforms the difference equations on the fluid-porous media boundary and makes the computation more flexible. We investigate and compare many parameters influencing on the array waveforms, such as fracture width, fracture zone width, tilt angle and permeability.#br#By the computations and analysis of borehole acoustic fields in different conditions, we can get conclusions as follows: 1. The fractures barely influence body waves because the fracture width is much less than the acoustic wavelength, but the reflected shear wave and reflected Stoneley wave still could exist when Stoneley wave goes through the fracture. 2. When the fractures are horizontal, only reflected Stoneley wave can be observed if the source is low frequency (2.5 kHz), while the reflected shear wave and reflected Stoneley wave both exist if the source is high frequency (5 kHz and above). The amplitude of reflected Stoneley wave decreases when the width of fracture reduces, though the amplitude of reflected shear wave is unchanged. The reflected shear wave still exists when the fracture width reduces to 20 m. 3. The density and width of fracture zone significantly influence the amplitude of reflected waves. When the density is small, the reflected waves are weak due to the low density causes the small fractures' interaction; as the density increasing, the reflected waves get stronger. 4. When the fracture cross the borehole and tilt, the reflected shear wave disappears, however the reflected Stoneley wave still exists, this is good for testing tilt fractures. 5. The attenuation of Stoneley waves increases along with the permeability increases. This causes the amplitude of inflected Stoneley waves on the fracture boundary decreases, so the reflected Stoneley wave could not be observed when the fractures are long away from source.#br#In this paper, 3-D non-uniform grid finite difference method is used to numerically simulate the acoustic field of the borehole surrounded by a porous formation with fracture and fracture zone. The conclusions are obtained by calculation and analysis as follows: The inflected Stoneley wave on the fracture causes the existence of reflected shear wave and reflected Stoneley wave. The reflected Stoneley wave's amplitude decreases with the decrease of the fracture width, however, the reflected shear wave is not sensitive to the fracture width changing, this is good for detecting the existence of a single thin horizontal fracture. The reflected Stoneley wave's amplitude increases along with the fracture zone density and width increasing; when the fracture (fracture zone) tilt, the reflected shear wave disappears, but the reflected Stoneley wave is not sensitive to the change of fracture angle, this is good for detecting the existence of the tilted fracture zone.
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Key words:
- Finite-difference /
- Nonuniform grid /
- Tilted fracture /
- Borehole acoustic fields
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