基于黏弹性介质波动理论的页岩超声波数值模拟
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摘要
利用超声波透射法来研究页岩的超声波响应特征,是页岩气开发过程中利用测井资料解决地质和工程问题的基础,而目前对于以页岩地层声波测井为目的的声学响应研究成果则鲜有报道且相关研究将页岩当作弹性介质来处理,未考虑页岩的黏弹性特征。为此,基于黏弹性介质波动理论,结合超声波透射实验背景,构建初始条件、振源条件、边界条件和稳定性条件,采用交错网格有限差分法模拟不同层理角度页岩的超声波透射实验。研究结果表明:①数值模拟计算和物理实验所得到的页岩声波特性变化趋势相互吻合;②基于理想和真实岩心的数值模拟计算和物理实验所得到的页岩衰减系数随测试频率、层理角度变化的规律均一致;③在层理尺度和密度恒定的条件下,随着层理角度的增大,波速呈幂函数递减,衰减系数呈线性增加。结论认为:①基于黏弹性介质声波波动理论,结合高阶交错网格差分技术建立的模拟页岩超声波透射实验的数值计算方法计算科学合理,具有较强的适应性;②利用该数值模拟方法可以从微观角度分析页岩层理特征对超声波传播特性的影响规律;③新方法拓展了层理性页岩地层声学研究的思路、避免了人为误差、节约了实验成本,具有重要理论价值和实际意义。
Using the ultrasonic transmission method to study the ultrasonic response characteristics of shale is the basis for the use of logging data to solve geological and engineering problems in shale gas development. However, among few literatures about such related research by present, shale has been only regarded as an elastic medium with its viscoelastic characteristics being unfortunately ignored. In view of this, based on the theory of viscoelastic medium waves, combined with the ultrasonic penetration experiments, we simulated an initial and vibration sources environment as well as boundary and stability conditions. On this basis, we made the ultrasonic transmission experiments of shale with different bedding angles by the staggered grid finite difference method. The following findings were obtained.(1) The waveform trend obtained by numerical simulation is coincided with the physical experiment result.(2) The rules of shale attenuation coefficients varied along with the test frequencies and the bedding angles obtained by numerical simulation calculation and physical experiment based on ideal and real cores agree well with each other.(3) Under a certain constant bedding size and density, the wave velocity declined in power function and the attenuation coefficient increases linearly. In conclusion, this numerical computation method proposed in this paper is scientific and reasonable and is of strong adaptability and can not only be used to analyze the influence of shale bedding characteristics on ultrasonic propagation characteristics from a microscopic point of view, but avoid human errors and save the experimental cost, therefore it is of important theoretical and practical significance.
Using the ultrasonic transmission method to study the ultrasonic response characteristics of shale is the basis for the use of logging data to solve geological and engineering problems in shale gas development. However, among few literatures about such related research by present, shale has been only regarded as an elastic medium with its viscoelastic characteristics being unfortunately ignored. In view of this, based on the theory of viscoelastic medium waves, combined with the ultrasonic penetration experiments, we simulated an initial and vibration sources environment as well as boundary and stability conditions. On this basis, we made the ultrasonic transmission experiments of shale with different bedding angles by the staggered grid finite difference method. The following findings were obtained.(1) The waveform trend obtained by numerical simulation is coincided with the physical experiment result.(2) The rules of shale attenuation coefficients varied along with the test frequencies and the bedding angles obtained by numerical simulation calculation and physical experiment based on ideal and real cores agree well with each other.(3) Under a certain constant bedding size and density, the wave velocity declined in power function and the attenuation coefficient increases linearly. In conclusion, this numerical computation method proposed in this paper is scientific and reasonable and is of strong adaptability and can not only be used to analyze the influence of shale bedding characteristics on ultrasonic propagation characteristics from a microscopic point of view, but avoid human errors and save the experimental cost, therefore it is of important theoretical and practical significance.
引文
[1]Josh M,Esteban L,Delle Piane C,Sarout J,Dewhurst DN&Clennell MB.Laboratory characterisation of shale properties[J].Journal of Petroleum Science and Engineering,2012,88/89(2):107-124.
[2]Kuila U,Dewhurst DN,Siggins AF&Raven MD.Stress anisotropy and velocity anisotropy in low porosity shale[J].Tectonophysics,2011,503(1):34-44.
[3]Spaid J,Dahl J,Carrilero SG,Carpenter G,Shearer E&Buller D.A completion staging case study in the Barnett Shale using advanced LWD quadrapole sonic and borehole imaging[J].Journal of Natural Gas Science and Engineering,2016,33(4):1190-1200.
[4]Le Gonidec Y,Schubnel A,Wassermann J,Gibert D,Nussbaum C,Kergosien B,et al.Field-scale acoustic investigation of a damaged anisotropic shale during a gallery excavation[J].International Journal of Rock Mechanics and Mining Sciences,2012,51(1):136-148.
[5]尹丛彬.页岩压裂裂缝渗透率的测试与分析[J].天然气工业,2018,38(3):60-68.Yin Congbin.Test and analysis on the permeability of fractured fractures in shale reservoirs[J].Natural Gas Industry,2018,38(3):60-68.
[6]潘仁芳,李笑天,金吉能,朱正平,孟江辉.渝东南盆缘转换带常压页岩气储层非均质性特征及主控因素[J].天然气工业,2018,38(12):26-36.Pan Renfang,Li Xiaotian,Jin Jineng,Zhu Zhengping&Meng Jianghui.Heterogeneity characteristics and controlling factors of normal-pressure shale gas reservoirs in the basin-margin transition zone of SE Chongqing[J].Natural Gas Industry,2018,38(12):26-36.
[7]乔辉,贾爱林,贾成业,位云生,袁贺.长宁地区优质页岩储层非均质性及主控因素[J].西南石油大学学报(自然科学版),2018,40(3):23-33.Qiao Hui,Jia Ailin,Jia Chengye,Wei Yunsheng&Yuan He.Factors controlling heterogeneity in the high-quality shale reservoirs of the Changning region[J].Journal of Southwest Petroleum University(Science&Technology Edition),2018,40(3):23-33.
[8]Jones LEA&Wang HF.Ultrasonic velocities in Cretaceous shales from the Williston Basin[J].Geophysics,1981,46(3):288-297.
[9]Sondergeld CH&Rai CS.Elastic anisotropy of shales[J].The Leading Edge,2011,30(3):324-331.
[10]Horne S,Walsh J&Miller D.Elastic anisotropy in the Haynesville Shale from dipole sonic data[J].First Break,2012,30(2):37-41.
[11]Domnesteanu P,McCann C&Sothcott J.Velocity anisotropy and attenuation of shale in under-and overpressured conditions[J].Geophysical Prospecting,2002,50(5):487-503.
[12]Szewczyk D,Bauer A&Holt RM.Stress-dependent elastic properties of shales--laboratory experiments at seismic and ultrasonic frequencies[J].Geophysical Journal International,2018,212(1):189-210.
[13]邓继新,史謌,刘瑞珣,俞军.泥岩、页岩声速各向异性及其影响因素分析[J].地球物理学报,2004,47(5):862-868.Deng Jixin,Shi Ge,Liu Ruixun&Yu Jun.Analysis of the velocity anisotropy and its affection factors in shale and mudstone[J].Chinese Journal of Geophysics,2004,47(5):862-868.
[14]王倩,王鹏,项德贵,冯宇思.页岩力学参数各向异性研究[J].天然气工业,2012,32(12):62-65.Wang Qian,Wang Peng,Xiang Degui&Feng Yusi.Anisotropic property of mechanical parameters of shales[J].Natural Gas Industry,2012,32(12):62-65.
[15]陈乔,刘向君,刘洪,王森,王莉莎,范晓文,等.层理性页岩地层超声波透射实验[J].天然气工业,2013,33(8):140-144.Chen Qiao,Liu Xiangjun,Liu Hong,Wang Sen,Wang Lisha,Fan Xiaowen,et al.An experimental study of ultrasonic penetration through bedding shale reservoirs[J].Natural Gas Industry,2013,33(8):140-144.
[16]熊健,梁利喜,刘向君,冉伟,吴涛.川南地区龙马溪组页岩岩石声波透射实验研究[J].地下空间与工程学报,2014,10(5):1071-1077.Xiong Jian,Liang Lixi,Liu Xiangjun,Ran Wei&Wu Tao.Experimental study on acoustic penetration through the Longmaxi Formation shale rock in south region of Sichuan Basin[J].Chinese Journal of Underground Space and Engineering,2014,10(5):1071-1077.
[17]Saenger EH&Shapiro SA.Effective velocities in fractured media:A numerical study using the rotated staggered finite-difference grid[J].Geophysical Prospecting,2002,50(2):183-194.
[18]Saenger EH,Ciz R,Krüger OS,Schmalholz SM,Gurevich B&Shapiro SA.Finite-difference modeling of wave propagation on microscale:A snapshot of the work in progress[J].Geophysics,2007,72(5):293-300.
[19]Zhu YP,Liu ER,Martinez A,Payne MA&Harris CE.Understanding geophysical responses of shale-gas plays[J].The Leading Edge,2011,30(3):332-338.
[20]Baechle G,Colpaert A,Eberli GP&Weger RJ.Modeling sonic velocity in carbonates using thin section[J].AAPG,2008,1012-1018.
[21]Weger RJ,Eberli GP,Baechle GT,Massaferro JL&Sun YF.Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[J].AAPG Bulletin,2009,93(10):1297-1317.
[22]EL Husseiny AH,Vega S,Al Mesaabi S,Ali MY,Weger RJ&Eberli GP.Correlation of outcrop,seismic,core plugs and thin sections in Cretaceous carbonate rocks from Wasia Group in the U.A.E[C]//Abu Dhabi International Petroleum Exhibition and Conference,1-4 November 2010,Abu Dhabi,UAE.
[23]Xu SY&Payne MA.Modeling elastic properties in carbonate rocks[J].The Leading Edge,2009,28(1):66-74.
[24]Tseng PY,Chang YF,Chang CH&Shih RC.Traveltimes and conversion-point positions for P-SV converted wave propagation in a transversely isotropic medium:Numerical calculations and physical model studies[J].Exploration Geophysics,2018,49(1):30-41.
[25]Yao Y,Sa LM&Wang SX.Research on the seismic wave field of karst cavern reservoirs near deep carbonate weathered crusts[J].Applied Geophysics,2005,2(2):94-102.
[26]王立华,魏建新,狄帮让.溶洞物理模型地震响应及其属性分析[J].石油地球物理勘探,2008,43(3):291-296.Wang Lihua,Wei Jianxin&Di Bangrang.Seismic response of karst cave physical model and analysis of its attributes[J].Oil Geophysical Prospecting,2008,43(3):291-296.
[27]王森,刘向君,陈乔,梁利喜,周龙涛.碳酸盐岩储层孔隙度超声波评价数值模拟[J].地球物理学进展,2015,30(1):267-273.Wang Sen,Liu Xiangjun,Chen Qiao,Liang Lixi&Zhou Longtao.Carbonate reservoir porosity ultrasonic evaluation by numerical simulation[J].Progress in Geophysics,2015,30(1):267-273.
[28]陈乔,刘向君,梁利喜,王森,杨超.裂缝模型声波衰减系数的数值模拟[J].地球物理学报,2012,55(6):2044-2052.Chen Qiao,Liu Xiangjun,Liang Lixi,Wang Sen&Yang Chao.Numerical simulation of the fractured model acoustic attenuation coefficient[J].Chinese Journal of Geophysics,2012,55(6):2044-2052.
[29]严红勇,刘洋.Kelvin-Voigt黏弹性介质地震波场数值模拟与衰减特征[J].物探与化探,2012,36(5):806-812.Yan Hongyong&Liu Yang.Numerical modeling and attenuation characteristics of seismic wavefield in Kelvin-Voigt viscoelastic media[J].Geophysical and Geochemical Exploration,2012,36(5):806-812.
[30]董良国,马在田,曹景忠,王华忠,耿建华,雷兵,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(6):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,Wang Huazhong,Geng Jianhua,Lei Bing,et al.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):411-419.
[31]Cerjan C,Kosloff D,Kosloff R&Reshef M.A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[32]范翔宇,段美恒,张千贵,赵鹏斐,贾光圣.页岩层理与含水率对声波传播影响的实验研究[J].西南石油大学学报(自然科学版),2017,39(2):53-61.Fan Xiangyu,Duan Meiheng,Zhang Qiangui,Zhao Pengfei&Jia Guangsheng.An experimental study on the effects of shale stratification and hydration on the transmission of acoustic waves[J].Journal of Southwest Petroleum University(Science and Technology Edition),2017,39(2):53-61.
[2]Kuila U,Dewhurst DN,Siggins AF&Raven MD.Stress anisotropy and velocity anisotropy in low porosity shale[J].Tectonophysics,2011,503(1):34-44.
[3]Spaid J,Dahl J,Carrilero SG,Carpenter G,Shearer E&Buller D.A completion staging case study in the Barnett Shale using advanced LWD quadrapole sonic and borehole imaging[J].Journal of Natural Gas Science and Engineering,2016,33(4):1190-1200.
[4]Le Gonidec Y,Schubnel A,Wassermann J,Gibert D,Nussbaum C,Kergosien B,et al.Field-scale acoustic investigation of a damaged anisotropic shale during a gallery excavation[J].International Journal of Rock Mechanics and Mining Sciences,2012,51(1):136-148.
[5]尹丛彬.页岩压裂裂缝渗透率的测试与分析[J].天然气工业,2018,38(3):60-68.Yin Congbin.Test and analysis on the permeability of fractured fractures in shale reservoirs[J].Natural Gas Industry,2018,38(3):60-68.
[6]潘仁芳,李笑天,金吉能,朱正平,孟江辉.渝东南盆缘转换带常压页岩气储层非均质性特征及主控因素[J].天然气工业,2018,38(12):26-36.Pan Renfang,Li Xiaotian,Jin Jineng,Zhu Zhengping&Meng Jianghui.Heterogeneity characteristics and controlling factors of normal-pressure shale gas reservoirs in the basin-margin transition zone of SE Chongqing[J].Natural Gas Industry,2018,38(12):26-36.
[7]乔辉,贾爱林,贾成业,位云生,袁贺.长宁地区优质页岩储层非均质性及主控因素[J].西南石油大学学报(自然科学版),2018,40(3):23-33.Qiao Hui,Jia Ailin,Jia Chengye,Wei Yunsheng&Yuan He.Factors controlling heterogeneity in the high-quality shale reservoirs of the Changning region[J].Journal of Southwest Petroleum University(Science&Technology Edition),2018,40(3):23-33.
[8]Jones LEA&Wang HF.Ultrasonic velocities in Cretaceous shales from the Williston Basin[J].Geophysics,1981,46(3):288-297.
[9]Sondergeld CH&Rai CS.Elastic anisotropy of shales[J].The Leading Edge,2011,30(3):324-331.
[10]Horne S,Walsh J&Miller D.Elastic anisotropy in the Haynesville Shale from dipole sonic data[J].First Break,2012,30(2):37-41.
[11]Domnesteanu P,McCann C&Sothcott J.Velocity anisotropy and attenuation of shale in under-and overpressured conditions[J].Geophysical Prospecting,2002,50(5):487-503.
[12]Szewczyk D,Bauer A&Holt RM.Stress-dependent elastic properties of shales--laboratory experiments at seismic and ultrasonic frequencies[J].Geophysical Journal International,2018,212(1):189-210.
[13]邓继新,史謌,刘瑞珣,俞军.泥岩、页岩声速各向异性及其影响因素分析[J].地球物理学报,2004,47(5):862-868.Deng Jixin,Shi Ge,Liu Ruixun&Yu Jun.Analysis of the velocity anisotropy and its affection factors in shale and mudstone[J].Chinese Journal of Geophysics,2004,47(5):862-868.
[14]王倩,王鹏,项德贵,冯宇思.页岩力学参数各向异性研究[J].天然气工业,2012,32(12):62-65.Wang Qian,Wang Peng,Xiang Degui&Feng Yusi.Anisotropic property of mechanical parameters of shales[J].Natural Gas Industry,2012,32(12):62-65.
[15]陈乔,刘向君,刘洪,王森,王莉莎,范晓文,等.层理性页岩地层超声波透射实验[J].天然气工业,2013,33(8):140-144.Chen Qiao,Liu Xiangjun,Liu Hong,Wang Sen,Wang Lisha,Fan Xiaowen,et al.An experimental study of ultrasonic penetration through bedding shale reservoirs[J].Natural Gas Industry,2013,33(8):140-144.
[16]熊健,梁利喜,刘向君,冉伟,吴涛.川南地区龙马溪组页岩岩石声波透射实验研究[J].地下空间与工程学报,2014,10(5):1071-1077.Xiong Jian,Liang Lixi,Liu Xiangjun,Ran Wei&Wu Tao.Experimental study on acoustic penetration through the Longmaxi Formation shale rock in south region of Sichuan Basin[J].Chinese Journal of Underground Space and Engineering,2014,10(5):1071-1077.
[17]Saenger EH&Shapiro SA.Effective velocities in fractured media:A numerical study using the rotated staggered finite-difference grid[J].Geophysical Prospecting,2002,50(2):183-194.
[18]Saenger EH,Ciz R,Krüger OS,Schmalholz SM,Gurevich B&Shapiro SA.Finite-difference modeling of wave propagation on microscale:A snapshot of the work in progress[J].Geophysics,2007,72(5):293-300.
[19]Zhu YP,Liu ER,Martinez A,Payne MA&Harris CE.Understanding geophysical responses of shale-gas plays[J].The Leading Edge,2011,30(3):332-338.
[20]Baechle G,Colpaert A,Eberli GP&Weger RJ.Modeling sonic velocity in carbonates using thin section[J].AAPG,2008,1012-1018.
[21]Weger RJ,Eberli GP,Baechle GT,Massaferro JL&Sun YF.Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[J].AAPG Bulletin,2009,93(10):1297-1317.
[22]EL Husseiny AH,Vega S,Al Mesaabi S,Ali MY,Weger RJ&Eberli GP.Correlation of outcrop,seismic,core plugs and thin sections in Cretaceous carbonate rocks from Wasia Group in the U.A.E[C]//Abu Dhabi International Petroleum Exhibition and Conference,1-4 November 2010,Abu Dhabi,UAE.
[23]Xu SY&Payne MA.Modeling elastic properties in carbonate rocks[J].The Leading Edge,2009,28(1):66-74.
[24]Tseng PY,Chang YF,Chang CH&Shih RC.Traveltimes and conversion-point positions for P-SV converted wave propagation in a transversely isotropic medium:Numerical calculations and physical model studies[J].Exploration Geophysics,2018,49(1):30-41.
[25]Yao Y,Sa LM&Wang SX.Research on the seismic wave field of karst cavern reservoirs near deep carbonate weathered crusts[J].Applied Geophysics,2005,2(2):94-102.
[26]王立华,魏建新,狄帮让.溶洞物理模型地震响应及其属性分析[J].石油地球物理勘探,2008,43(3):291-296.Wang Lihua,Wei Jianxin&Di Bangrang.Seismic response of karst cave physical model and analysis of its attributes[J].Oil Geophysical Prospecting,2008,43(3):291-296.
[27]王森,刘向君,陈乔,梁利喜,周龙涛.碳酸盐岩储层孔隙度超声波评价数值模拟[J].地球物理学进展,2015,30(1):267-273.Wang Sen,Liu Xiangjun,Chen Qiao,Liang Lixi&Zhou Longtao.Carbonate reservoir porosity ultrasonic evaluation by numerical simulation[J].Progress in Geophysics,2015,30(1):267-273.
[28]陈乔,刘向君,梁利喜,王森,杨超.裂缝模型声波衰减系数的数值模拟[J].地球物理学报,2012,55(6):2044-2052.Chen Qiao,Liu Xiangjun,Liang Lixi,Wang Sen&Yang Chao.Numerical simulation of the fractured model acoustic attenuation coefficient[J].Chinese Journal of Geophysics,2012,55(6):2044-2052.
[29]严红勇,刘洋.Kelvin-Voigt黏弹性介质地震波场数值模拟与衰减特征[J].物探与化探,2012,36(5):806-812.Yan Hongyong&Liu Yang.Numerical modeling and attenuation characteristics of seismic wavefield in Kelvin-Voigt viscoelastic media[J].Geophysical and Geochemical Exploration,2012,36(5):806-812.
[30]董良国,马在田,曹景忠,王华忠,耿建华,雷兵,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(6):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,Wang Huazhong,Geng Jianhua,Lei Bing,et al.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):411-419.
[31]Cerjan C,Kosloff D,Kosloff R&Reshef M.A nonreflecting boundary condition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[32]范翔宇,段美恒,张千贵,赵鹏斐,贾光圣.页岩层理与含水率对声波传播影响的实验研究[J].西南石油大学学报(自然科学版),2017,39(2):53-61.Fan Xiangyu,Duan Meiheng,Zhang Qiangui,Zhao Pengfei&Jia Guangsheng.An experimental study on the effects of shale stratification and hydration on the transmission of acoustic waves[J].Journal of Southwest Petroleum University(Science and Technology Edition),2017,39(2):53-61.