基于线性滑动模型的裂缝性地层声波测井响应数值模拟
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摘要
为了研究水平裂缝对声波波形的影响规律,把裂缝当作线性滑动界面,模拟在含有裂缝的地层中全波列声波测井响应。建立柱坐标系下穿过井孔的水平单条裂缝和多条裂缝计算模型,采用有限差分法模拟声波的传播,记录声波波形。通过分析不同源距、不同宽度裂缝和不同裂缝条数条件下透射波和反射波的波形变化,研究裂缝对纵波、横波和斯通利波波形的影响规律。结果表明:采用线性滑动模型描述的裂缝对纵波的影响很小,只有靠近裂缝的透射纵波幅度会发生改变;裂缝不仅引起横波很强的衰减和反射,而且使横波的相位发生了改变;接收器距离裂缝越远,横波的衰减越大;当裂缝延伸距离很短时,透射横波的幅度和相位随着裂缝延伸距离的改变会发生变化;裂缝也会引起斯通利波的衰减和反射,透射斯通利波对线性滑动裂缝的宽度变化不敏感,而对裂缝条数变化敏感。
To study the effects of horizontal fractures on acoustic logging waveforms, the full-wave acoustic logging responses in fractured formations are simulated based on a linear-slip model. Models of single and multiple fractures passing through borehole in a cylindrical coordinate system are computed. A finite-difference time domain method is used to simulate the propagation of acoustic logging waves.The waveform variations of transmitted and reflected waves with respect to source distance, aperture size,extended fracture distance and the number of fractures are analyzed. The effects of fractures described by the linear-slip model on the P-wave, S-wave and Stoneley wave waveforms are studied.The results show that the effects of linear-slip fractures on acoustic logging waveforms are as follows: the effect of fracturing on the P-wave is very small, and only the amplitude of transmitted P-wave near the fracture will change; fractures not only have strong attenuation and reflection effects on the S-waves, but also change the phase of shear waves;the greater the distance from fracture, the greater the attenuation of shear waves; when the extended distance of fracture is very small, the amplitude and phase of transmitted shear wave will depend on the variations in the extended distance; linear-slip fractures also have strong attenuation and reflection effects on the Stoneley waves, however, the transmitted Stoneley waves are not sensitive to the fracture aperture, but to the number of fractures.
To study the effects of horizontal fractures on acoustic logging waveforms, the full-wave acoustic logging responses in fractured formations are simulated based on a linear-slip model. Models of single and multiple fractures passing through borehole in a cylindrical coordinate system are computed. A finite-difference time domain method is used to simulate the propagation of acoustic logging waves.The waveform variations of transmitted and reflected waves with respect to source distance, aperture size,extended fracture distance and the number of fractures are analyzed. The effects of fractures described by the linear-slip model on the P-wave, S-wave and Stoneley wave waveforms are studied.The results show that the effects of linear-slip fractures on acoustic logging waveforms are as follows: the effect of fracturing on the P-wave is very small, and only the amplitude of transmitted P-wave near the fracture will change; fractures not only have strong attenuation and reflection effects on the S-waves, but also change the phase of shear waves;the greater the distance from fracture, the greater the attenuation of shear waves; when the extended distance of fracture is very small, the amplitude and phase of transmitted shear wave will depend on the variations in the extended distance; linear-slip fractures also have strong attenuation and reflection effects on the Stoneley waves, however, the transmitted Stoneley waves are not sensitive to the fracture aperture, but to the number of fractures.
引文
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[16] 吴国忱,秦海旭.裂缝介质旋转交错网格正演模拟[J].地震学报,2014,36(6):1075-1088.WU Guochen,QIN Haixu.Rotated staggering grid forward modeling in fractured medium[J].Acta Seismologica Sinica,2014,36(6):1075-1088.
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[19] 王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842-849.WANG Xiuming,ZHANG Hailan,WANG Dong.Modelling seismic wave propagation in heterogeneous poroelastic media using a high-order staggered finite-difference method[J].Chinese Journal of Geophysics,2003,46(6):842-849.
[20] 雍鹏,黄建平,李振春,等.优化的时空域等效交错网格有限差分正演模拟[J].中国石油大学学报(自然科学版),2017,41(6):71-79.YONG Peng,HUANG Jianping,LI Zhenchun,et al.Forward modeling by optimized equivalent staggered-grid finite-difference method for time-space domain[J].Journal of China University of Petroleum (Edition of Natural Science),2017,41(6):71-79.
[21] WANG T,TANG X.Finite-difference modeling of elastic wave propagation:a nonsplitting perfectly matched layer approach[J].Geophysics,2003,68(5):1749-1755.
[22] TANG X M,CHENG C H.A dynamic model for fluid flow in open borehole fractures[J].Journal of Geophysical Research:Solid Earth,1989,94(B6):7567-7576.
[23] 曲占庆,李小龙,李建雄,等.基于扩展有限元法的多径向井压裂裂缝形态[J].中国石油大学学报(自然科学版),2018,42(1):73-81.QU Zhanqing,LI Xiaolong,LI Jianxiong,et al.Crack morphology of multiple radial well fracturing based on extended finite element method[J].Journal of China University of Petroleum(Edition of Natural Science),2018,42(1):73-81.
[2] 金强,程付启,田飞.岩溶型碳酸盐岩储层中缝洞复合体及其油气地质意义[J].中国石油大学学报(自然科学版),2017,41(3):49-55.JIN Qiang,CHENG Fuqi,TIAN Fei.Identification of fracture-vug complex from karsted carbonates and its significance in petroleum geology[J].Journal of China University of Petroleum(Edition of Natural Science),2017,41(3):49-55.
[3] 赵建林,姚军,张磊,等.微裂缝对致密多孔介质中气体渗流的影响机制[J].中国石油大学学报(自然科学版),2018,42(1):90-98.ZHAO Jianlin,YAO Jun,ZHANG Lei,et al.Effects of micro-fractures on gas flow in tight porous media [J].Journal of China University of Petroleum(Edition of Natural Science),2018,42(1):90-98.
[4] MORRIS R L,GRINE D R,ARKFELD T E.Using compressional and shear acoustic amplitudes for the location of fractures[J].Journal of Petroleum Technology,1964,16(6):623-632.
[5] PAILLET F L.Acoustic propagation in the vicinity of fractures which intersect a fluid-filled borehole[C]//SPWLA 21st Annual Logging Symposium,Lafayette,Louisiana,July 8-11,1980:Society of Petrophysicists and Well-Log Analysts[2018-10-04].https://www.onepetro.org/conference-paper/SPWLA-1980-R.
[6] ZLATEV P,POETER E,HIGGINS J.Physical modeling of the full acoustic waveform in a fractured,fluid-filled borehole[J].Geophysics,1988,53(9):1219-1224.
[7] 魏周拓,陈雪莲,范宜仁,等.井旁裂缝的声场模拟及反射波提取方法[J].石油地球物理勘探,2010,45(5):748-756.WEI Zhoutuo,CHEN Xuelian,FAN Yiren,et al.Sonic field simulation for borehole-side fracture and reflection wave extraction method[J].Oil Geophysical Prospecting,2010,45(5):748-756.
[8] 龚丹,章成广.裂缝性致密砂岩储层声波测井数值模拟响应特性研究[J].石油天然气学报,2013,35(7):82-86.GONG Dan,ZHANG Chengguang.Research on numerical simulation response characteristics of acoustic logging for fractured tight sandstone reservoirs[J].Journal of Oil & Gas Technology,2013,35(7):82-86.
[9] MATUSZYK P J,TORRES-VERDíN C,PARDO D.Frequency-domain finite-element simulations of 2D sonic wireline borehole measurements acquired in fractured and thinly bedded formations[J].Geophysics,2013,78(4):D193-D207.
[10] 阎守国,谢馥励,龚丹,等.含有倾斜薄裂缝孔隙地层中的井孔声场[J].地球物理学报,2015,58(1):307-317.YAN Shouguo,XIE Fuli,GONG Dan,et al.Borehole acoustic fields in porous formation with tilted thin fracture[J].Chinese Journal of Geophysics,2015,58(1):307-317.
[11] 闫怡飞,赵云,宋胜利,等.基于反射声波测井有限元方法的井旁裂缝分布特征[J].中国石油大学学报(自然科学版),2018,42(3):57-63.YAN Yifei,ZHAO Yun,SONG Shengli,et al.Near wellbore fracture distribution characteristics based on acoustic reflection logging finite element method[J].Journal of China University of Petroleum(Edition of Natural Science),2018,42(3):57-63.
[12] SCHOENBERG M.Elastic wave behavior across linear slip interfaces[J].The Journal of the Acoustical Society of America,1980,68(5):1516-1521.
[13] PYRAK-NOLTE L J,COOK N G W.Elastic interface waves along a fracture[J].Geophysical Research Letters,1987,14(11):1107-1110.
[14] COATES R T,SCHOENBERG M.Finite-difference modeling of faults and fractures[J].Geophysics,1995,60(5):1514-1526.
[15] WU C,HARRIS J M,NIHEI K T,et al.Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture:comparison of thin-layer and linear-slip models[J].Geophysics,2005,70(4):T57-T62.
[16] 吴国忱,秦海旭.裂缝介质旋转交错网格正演模拟[J].地震学报,2014,36(6):1075-1088.WU Guochen,QIN Haixu.Rotated staggering grid forward modeling in fractured medium[J].Acta Seismologica Sinica,2014,36(6):1075-1088.
[17] VIRIEUX J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[18] 董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856-864.DONG Liangguo,MA Zaitian,CAO Jingzhong.Stability of the staggered-grid high-order difference method for first-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):856-864.
[19] 王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842-849.WANG Xiuming,ZHANG Hailan,WANG Dong.Modelling seismic wave propagation in heterogeneous poroelastic media using a high-order staggered finite-difference method[J].Chinese Journal of Geophysics,2003,46(6):842-849.
[20] 雍鹏,黄建平,李振春,等.优化的时空域等效交错网格有限差分正演模拟[J].中国石油大学学报(自然科学版),2017,41(6):71-79.YONG Peng,HUANG Jianping,LI Zhenchun,et al.Forward modeling by optimized equivalent staggered-grid finite-difference method for time-space domain[J].Journal of China University of Petroleum (Edition of Natural Science),2017,41(6):71-79.
[21] WANG T,TANG X.Finite-difference modeling of elastic wave propagation:a nonsplitting perfectly matched layer approach[J].Geophysics,2003,68(5):1749-1755.
[22] TANG X M,CHENG C H.A dynamic model for fluid flow in open borehole fractures[J].Journal of Geophysical Research:Solid Earth,1989,94(B6):7567-7576.
[23] 曲占庆,李小龙,李建雄,等.基于扩展有限元法的多径向井压裂裂缝形态[J].中国石油大学学报(自然科学版),2018,42(1):73-81.QU Zhanqing,LI Xiaolong,LI Jianxiong,et al.Crack morphology of multiple radial well fracturing based on extended finite element method[J].Journal of China University of Petroleum(Edition of Natural Science),2018,42(1):73-81.
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