Kelvin-Voigt黏弹性介质井孔声场有限差分数值模拟与波形特征

doi:10.13278/j.cnki.jjuese.20210049

摘要/Abstract

摘要： 岩石介质具有黏滞性，黏弹性介质模型相对于弹性介质模型更为接近岩石介质的真实情况。根据Kelvin-Voigt黏弹性单元体模型本构关系，推导了柱坐标系下各向同性黏弹性介质时间域交错网格有限差分方程，进行了黏弹性介质井孔声场的数值模拟。模拟结果表明：品质因子和声源中心频率对黏弹性介质中的井内外声场均有影响：井外声场和井内声场的衰减均随品质因子的增大而减小，井外声波和井内反射波振幅随之增大；井外声场的衰减随声源中心频率的增大而减小，井外声波振幅随之增大，井内声场的衰减随声源中心频率的增大而增大，井内反射波振幅随之减小。

关键词: Kelvin-Voigt模型, 黏弹性介质, 交错网格有限差分, 井孔声场, 波形特征

Abstract: The rock medium has viscous properties, and the viscoelastic medium model is closer to the real situation of the rock medium than the elastic medium model. According to the constitutive relationship of the Kelvin-Voigt viscoelastic element model, the staggered grid finite difference equations of the viscoelastic isotropic medium in the cylindrical coordinate system are derived, and the numerical simulation of acoustic field of the wellbore in viscoelastic medium are completed. The simulation results show that the rock quality factor and the acoustic source center frequency have effects on the acoustic field inside and outside the well in the viscoelastic medium:The attenuation of the acoustic field outside and inside the well decreases with the increase of the quality factor, and the wave amplitude outside the well and the reflected wave amplitude increase accordingly; The attenuation of the acoustic field outside the well decreases with the increase of the source center frequency, and the wave amplitude outside the well increases accordingly; The attenuation of the acoustic field in the well increases with the increase of the source center frequency, and the wave amplitude in the well decreases accordingly.

Key words: Kelvin-Voigt model, viscoelastic medium, staggered grid finite difference, borehole acoustic field, waveform characteristics

中图分类号:

P631.8

岳崇旺, 王祝文. Kelvin-Voigt黏弹性介质井孔声场有限差分数值模拟与波形特征[J]. 吉林大学学报(地球科学版), 2021, 51(4): 1268-1275.

Yue Chongwang, Wang Zhuwen. Numerical Simulation and Waveform Characteristics of Borehole Acoustic Field in Kelvin-Voigt Viscoelastic Medium Well[J]. Journal of Jilin University(Earth Science Edition), 2021, 51(4): 1268-1275.

参考文献

[1] 孙成禹.地震波理论与方法[M]. 东营:中国石油大学出版社,2007. Sun Chengyu. Theory and Methods of Seismic Waves[M]. Dongying:China University of Petroleum Publishing House, 2007.
[2] Madja G, Chin R C Y, Followill F E. A Perturbation Theory for Love Waves in Anelastic Media[J]. Geophysical Journal of the Royal Astronomical Society, 1985, 80(1):1-34.
[3] 刘瑞珣,张秉良,张臣. 描述岩石黏弹性固体性质的开尔文模型[J]. 地学前缘,2008,15(3):221-225. Liu Ruixun, Zhang Bingliang, Zhang Chen. The Kelvin Model Describing Rock Materials with Behaviour of a Viscoelastic Solid[J]. Earth Science Frontiers, 2008, 15(3):221-225.
[4] Emmerich H, Korn M. Incorporation of Attenuation into Time-Domain Computations of Seismic Wave Fields[J]. Geophysics, 1987, 52(9):1252-1264.
[5] Robertsson J O A, Blanch J O, Symes W W. Viscoelastic Finite-Difference Modeling[J]. Geophysics, 1994, 59(9):1444-1456.
[6] Robertsson J O A. A Numerical Free-Surface Condition for Elastic/Viscoelastic Finite-Difference Modeling in the Presence of Topography[J]. Geophysics, 1996, 61(6):1921-1934.
[7] Saenger E H, Bohlen T. Finite-Difference Modeling of Viscoelastic and Anisotropic Wave Propagation Using the Rotated Staggered Grid[J]. Geophysics, 2004, 69(2):583-591.
[8] Bai Tong,Tsvankin I. Time-Domain Finite-Difference Modeling for Attenuative Anisotropic Media[J]. Geophysics, 2016, 81(2):c69-c77.
[9] 杜启振,杨慧珠. 线性黏弹性各向异性介质速度频散和衰减特征研究[J]. 物理学报,2002,51(9):2101-2108. Du Qizhen, Yang Huizhu. Velocity Dispersion and Attenuation in Anisotropic Linear Viscoelastic Media[J]. Acta Physica Sinica, 2002, 51(9):2101-2108.
[10] 杜启振. 各向异性黏弹性介质伪谱法波场模拟[J]. 物理学报,2004, 53(12):4428-4434. Du Qizhen. Wavefield Forward Modeling with the Pseudo-Spectral Method in Viscoelastic and Azimuthally Anisotropic Media[J]. Acta Physica Sinica, 2004, 53(12):4428-4434.
[11] 苑春方,彭苏萍,张中杰,等. Kelvin-Voigt均匀黏弹性介质中传播的地震波[J].中国科学:D辑:地球科学, 2005, 35(10):957-962. Yuan Chunfang, Peng Suping, Zhang Zhongjie, et al. Seismic Wave of Propagation in Homogeneous Kelvin-Voigt Viscoelastic Medium[J]. Science in China:Series D:Earth Sciences, 2005, 35(10):957-962.
[12] 孙成禹,印兴耀.三参数常Q黏弹性模型构造方法研究[J]. 地震学报,2007,29(4):348-357. Sun Chengyu, Yin Xingyao. Construction of Constant-Q Viscoelastic Model with Three Parameters[J]. Acta Seismologica Sinica, 2007, 29(4):348-357.
[13] 孙成禹,肖云飞,印兴耀,等. 黏弹介质波动方程有限差分解的稳定性研究[J].地震学报,2010,32(2):147-156. Sun Chengyu, Xiao Yunfei, Yin Xingyao, et al. Study on the Stability of Finite Difference Solution of Visco-Elastic Wave Equations[J].Acta Seismologica Sinica, 2010,32(2):147-156.
[14] 郭智奇. 黏弹各向异性介质波场模拟与储层信息研究[D]. 长春:吉林大学,2008. Guo Zhiqi. Wave Field Modeling in Viscoelastic Anisotropic Media and Reservoir Information Study[D]. Changchun:Jilin University, 2008.
[15] Guo Zhiqi, Liu Xiwu, Fu Wei, et al. Modeling and Anlysis of Azimuthal AVO Responses from a Viscoelastic Anisotropic Reflector[J]. Applied Geophysics, 2015, 12(3):441-452.
[16] 刘财,胡宁,郭志奇,等. 基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟[J].地球物理学报,2018,61(6):2446-2458. Liu Cai,Hu Ning, Guo Zhiqi, et al. Numerical Simulation of the Wavefield in a Viscous Fluid-Saturated Two-Phase VTI Medium Based on the Constant-Q Viscoelastic Constitutive Relation with a Fractional Temporal Derivative[J]. Chines Journal of Geophysics, 2018,61(6):2446-2458.
[17] 邵广周,赵凯鹏,吴华. 基于MPI的面波有限差分正演模拟[J].吉林大学学报(地球科学版),2020,50(1):294-303. Shao Guangzhou, Zhao Kaipeng, Wu Hua. Finite Difference Forward Modeling of Surface Waves Based on MPI[J]. Journal of Jilin University (Earth Science Edition), 2020, 50(1):294-303.
[18] 张壹,王赟,王祥春,等. 黏弹性介质地震波吸收衰减研究进展[J].石油物探,2021,60(2):238-250. Zhang Yi, Wang Yun, Wang Xiangchun, et al. Research Progress on the Absorption Attenuation of Seismic Waves in Viscoelastic Media[J]. Geophysical Prospecting for Petroleum, 2021, 60(2):238-250.
[19] Alford R M, Kelly K R, Boore D M. Accuracy of Finite-Difference Modeling of Acoustic Wave Equation[J]. Geophysics, 1974, 39(6):834-842.

相关文章 15

[1]	牟丹, 张丽春, 徐长玲. 3种经典机器学习算法在火山岩测井岩性识别中的对比[J]. 吉林大学学报(地球科学版), 2021, 51(3): 951-956.
[2]	邵才瑞, 原野, 张福明, 陈国兴, 曹先军. 随钻测录井地质导向二维分解实时绘图方法[J]. 吉林大学学报(地球科学版), 2021, 51(1): 256-265.
[3]	于洋, 王祝文, 宁琴琴, 徐方慧. 松辽盆地大庆长垣四方台组可地浸砂岩铀成矿测井评价[J]. 吉林大学学报(地球科学版), 2020, 50(3): 929-940.
[4]	秦敏, 申辉林, 丁磊, 刘欢, 黄信雄, 章利民. 基于微元动态物质平衡法模型确定水淹层混合液电阻率[J]. 吉林大学学报(地球科学版), 2020, 50(3): 919-928.
[5]	贾莹刚, 赵军, 蒋磊, 关力伟, 王小玄, 何亮. 伊犁地块北缘早古生代构造属性:来自温泉地区闪长岩的证据[J]. 吉林大学学报(地球科学版), 2019, 49(4): 1015-1038.
[6]	周翔. 松辽盆地北部营城组火山岩地球化学特征及地质意义[J]. 吉林大学学报(地球科学版), 2019, 49(4): 1001-1014.
[7]	叶涛, 韦阿娟, 黄志, 赵志平, 肖述光. 基于主成分分析法与Bayes判别法组合应用的火山岩岩性定量识别:以渤海海域中生界为例[J]. 吉林大学学报(地球科学版), 2019, 49(3): 872-879.
[8]	王祝文, 徐方慧, 刘菁华, 宁琴琴, 于洋. 辽河盆地东部凹陷含气孔、裂隙火成岩地层斯通利波响应特征[J]. 吉林大学学报(地球科学版), 2018, 48(6): 1876-1888.
[9]	廖东良, 曾义金. 利用测井资料建立地层剪破裂模型[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1268-1276.
[10]	张波, 曹洪恺, 孙建孟, 张鹏云, 闫伟超. 稠油热采地层阵列感应测井响应特性数值模拟[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1277-1286.
[11]	潘保芝, 刘文斌, 张丽华, 郭宇航, 阿茹罕. 一种提高储层裂缝识别准确度的方法[J]. 吉林大学学报(地球科学版), 2018, 48(1): 298-306.
[12]	肖凡, 陈建国. 基于RCGA的PPC模型在化探异常识别与提取中的应用[J]. 吉林大学学报(地球科学版), 2017, 47(4): 1319-1330.
[13]	李振苓, 沈金松, 李曦宁, 王磊, 淡伟宁, 郭森, 朱忠民, 于仁江. 用形态学滤波从电导率图像中提取缝洞孔隙度谱[J]. 吉林大学学报(地球科学版), 2017, 47(4): 1295-1307.
[14]	张恒荣, 何胜林, 吴进波, 吴一雄, 梁玉楠. 一种基于Kozeny-Carmen方程改进的渗透率预测新方法[J]. 吉林大学学报(地球科学版), 2017, 47(3): 899-906.
[15]	姜艳娇, 孙建孟, 高建申, 邵维志, 迟秀荣, 柴细元. 低孔渗储层井周油藏侵入模拟及阵列感应电阻率校正方法[J]. 吉林大学学报(地球科学版), 2017, 47(1): 265-278.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed