非均匀饱含黏性流体孔隙介质中声波传播及井孔声场分析

彭凡; 张秀梅; 刘琳; 王秀明

doi:10.7498/aps.72.20221858

摘要

声波在饱含流体孔隙介质中的传播特性与流体的黏滞性及孔隙介质的非均匀性密切相关. 本文在Biot理论基础上, 考虑了孔隙流体的剪切应力及孔隙结构的非均匀性, 采用含黏性流体孔隙介质中的波动理论, 研究了孔隙介质中四种体波的频散和衰减特性, 分析了慢横波对快纵波转换散射的影响, 进一步推导了孔隙地层井孔中的模式波及其声场的解析解, 研究了非均匀孔隙介质中井孔模式波和波列的特征. 研究结果表明, 含黏性流体孔隙介质中存在慢横波, 慢横波的频散很强, 其传播特征受到介质孔隙度、渗透率及孔隙流体黏度的影响. 在非均匀孔隙介质中, 与慢横波相关的剪切应力平衡过程不仅导致快纵波的频散和衰减, 还会影响井孔伪瑞利波及斯通利波的传播特征. 本文的工作完善了孔隙介质中声波传播的物理机制, 为孔隙地层井孔声波的解释与应用提供了理论指导.

关键词:

Abstract

Sound field in fluid-saturated porous medium is closely related to the viscosity of fluid and the heterogeneity of porous medium. In order to improve the physical mechanism of wave propagation in porous medium and expand its application in borehole acoustic field, the shear stress of porous fluid and the heterogeneity of pore structure are considered. The wave theory in porous medium containing viscous fluid is deduced based on the Biot theory. The influence of porous medium parameters on slow shear wave is analyzed, and the dispersion and attenuation of elastic wave caused by shear stress balance in porous fluid under the influence of inhomogeneous pore structure are studied. The analytical solution of borehole acoustic field in porous medium containing viscous fluid is further derived. The phase velocity and attenuation of borehole mode waves in heterogeneous porous medium, and the waveform of borehole full wave are calculated. The influence of pore fluid viscosity on borehole full wave is analyzed. The results show that there are slow shear waves in the porous medium containing viscous fluid. The slow shear wave is characterized by low velocity and large attenuation. In heterogeneous porous medium, the balance process of shear stress related to slow shear wave not only leads to the dispersion and attenuation of fast P-wave, but also affects the propagation characteristics of borehole pseudo Rayleigh wave and Stoneley wave. In addition, the pore fluid viscosity has a great influence on the borehole Stoneley wave. The present work improves the physical mechanism of acoustic wave propagation in porous medium and provides theoretical guidance for the explanation and application of borehole acoustic waves in porous formations.

Keywords:

作者及机构信息

1.
中国科学院声学研究所, 声场声信息国家重点实验室, 北京　100190

2.
中国科学院大学, 北京　100049

3.
中国科学院声学研究所, 北京市海洋深部钻探研究中心, 北京　100190

通信作者: 张秀梅, zhangxiumei@mail.ioa.ac.cn

基金项目: 国家自然科学基金 (批准号: 11974018, 11734017)和中国科学院战略性先导科技专项 (批准号: XDA14020303)资助的课题.

Authors and contacts

1.
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

2.
University of Chinese Academy of Sciences, Beijing 100049, China

3.
Beijing Engineering Research Center of Sea Deep Drilling and Exploration, Beijing 100190, China

Corresponding author: Zhang Xiu-Mei, zhangxiumei@mail.ioa.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974018, 11734017) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA14020303).

文章全文

参考文献

[1]	李红星, 张嘉辉, 樊嘉伟, 陶春辉, 肖昆, 黄光南, 盛书中, 宫猛 2022 物理学报 71 089101 Google Scholar Li H X, Zhang J H, Fan J W, Tao C H, Xiao K, Huang G N, Sheng S Z, Gong M 2022 Acta Phys. Sin. 71 089101 Google Scholar
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[3]	Benoit G, Heinkélé C, Gourdon E 2013 J. Acoust. Soc. Am. 134 4782 Google Scholar
[4]	Biot M A 1956 J. Acoust. Soc. Am. 28 168 Google Scholar
[5]	Biot M A 1956 J. Acoust. Soc. Am. 28 179 Google Scholar
[6]	Biot M A 1962 J. Appl. Phys. 33 1482 Google Scholar
[7]	Rosenbaum J H 1974 Geophysics 39 14 Google Scholar
[8]	Li K S, Gao J, Ju X D, Sun H F 2018 J. Geophys. Eng. 15 2266 Google Scholar
[9]	杨博, 章成广, 蔡明, 甘泉, 蔡德洋, 朱雷 2019 地球物理学进展 34 1127 Google Scholar Yang B, Zhang C G, Cai M, Gan Q, Cai D Y, Zhu L 2019 Progress in Geophysics 34 1127 Google Scholar
[10]	Qi Q M, Fu L Y, Deng J X, Cao J X 2021 Geophysics 86 1 Google Scholar
[11]	Winkler K W 1985 J. Geophys. Res. Solid Earth 90 6793 Google Scholar
[12]	Gist G A 1991 J. Acoust. Soc. Am. 90 2370 Google Scholar
[13]	邓继新, 史謌, 俞军 2003 北京大学学报(自然科学版) 39 835 Google Scholar Deng J X, Shi X, Yu J 2003 Acta Scientiarum Naturalium Universitatis Pekinensis 39 835 Google Scholar
[14]	Feng J X, Teng Q Z, He X H, Qing L B, Li Y 2018 Comput. Mater. Sci. 144 181 Google Scholar
[15]	陈培元, 杨辉廷, 贾兆扬 2018 中国海上油气 30 31 Google Scholar Chen P Y, Yang H T, Jia Z Y 2018 Chin. Offshore Oil Gas 30 31 Google Scholar
[16]	Liu Q R, Katsube N 1990 J. Acoust. Soc. Am. 88 1045 Google Scholar
[17]	魏修成, 卢明辉, 巴晶, 杨慧珠 2008 地球物理学报 51 213 Google Scholar Wei X C, Lu M H, Ba J, Yang H Z 2008 Chin. J. Geophys. 51 213 Google Scholar
[18]	Gao W 2016 SEG Technical Program Expanded Abstracts 2016 Dallas, Texas, October 16-21, 2016 pp3871–3875
[19]	Sahay P N 2008 Geophysics 73 N19 Google Scholar
[20]	Ciz R, Gurevich B, Markov M 2006 Geophys. J. Int. 165 957 Google Scholar
[21]	Müller T M, Gurevich B 2005 J. Acoust. Soc. Am. 117 2732 Google Scholar
[22]	Mavko G, Nur A 1975 J. Geophys. Res. 80 1444 Google Scholar
[23]	Dvorkin J, Nur A 1993 Geophysics 58 524 Google Scholar
[24]	崔志文, 刘金霞, 王春霞, 王克协 2010 物理学报 59 8655 Google Scholar Cui Z W, Liu J X, Wang C X, Wang K X 2010 Acta Phys. Sin. 59 8655 Google Scholar
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[28]	Müller T M, Sahay P N 2011 J. Acoust. Soc. Am. 129 2785 Google Scholar
[29]	Müller T M, Sahay P N 2011 Phys. Rev. E 84 026329
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[31]	卢明辉, 巴晶, 杨慧珠 2009 工程力学 26 36 Lu M H, Ba J, Yang H Z 2009 Eng. Mech. 26 36
[32]	Zhang X M, Müller T M 2019 Geophysics 84 WA1 Google Scholar
[33]	Bourbie T, Coussy O, Zinszner B, Junger M C 1992 J. Acoust. Soc. Am. 91 3080 Google Scholar
[34]	Müller T M, Sahay P N 2011 Appl. Phys. Lett. 98 168 Google Scholar
[35]	崔志文, 刘金霞, 王克协 2005 吉林大学学报(理学版) 43 803 Cui Z W, Liu J X, Wang K X 2005 J. Jilin Univ. (Sci. Ed.) 43 803
[36]	Markova I, Ronquillo J G, Markov M, Gurevich B 2014 Geophys. J. Int. 196 1082 Google Scholar

施引文献

图 1 四种体波的相速度与衰减　(a) 快纵波; (b) 快横波; (c) 慢纵波; (d) 慢横波

Fig. 1. Phase velocity and attenuation of four kinds of body waves: (a) Fast P-wave; (b) fast S-wave; (c) slow P-wave; (d) slow S-wave.

下载: 全尺寸图片幻灯片

图 2 慢横波的相速度与衰减随孔隙介质参数的变化　 (a) 孔隙度; (b) 渗透率; (c) 流体黏度

Fig. 2. Variation of phase velocity and attenuation of slow shear wave with porous media parameters: (a) Porosity; (b) permeability; (c) fluid viscosity.

下载: 全尺寸图片幻灯片

图 3 均匀及不同非均匀孔隙介质中快纵波的相速度与衰减

Fig. 3. The phase velocity and attenuation of fast P wave in homogeneous porous medium and different inhomogeneous porous media

下载: 全尺寸图片幻灯片

图 4 k(ω)的归一化幅值与相位

Fig. 4. Normalized amplitude and phase of $ k(\omega ) $.

下载: 全尺寸图片幻灯片

图 5 非均匀孔隙介质地层井孔模型

Fig. 5. Borehole model of heterogeneous porous media formation.

下载: 全尺寸图片幻灯片

图 6 模式波的相速度与衰减　(a) 斯通利波; (b) 一阶伪瑞利波; (c) 二阶伪瑞利波

Fig. 6. Phase velocity and attenuation of mode waves: (a) Stoneley wave; (b) the first order pseudo Rayleigh wave; (c) the second order pseudo Rayleigh wave.

下载: 全尺寸图片幻灯片

图 7 全波波形　(a) 源距为4 m时的单道波形; (b) 8道阵列全波波形

Fig. 7. Full wave waveform: (a) Single channel waveform at source distance of 4 m; (b) 8-channel array full wave waveform.

下载: 全尺寸图片幻灯片

图 8 低频斯通利波测井(a)及常规单极子测井(b)的全波波形

Fig. 8. Full wave waveform of low-frequency Stoneley wave logging (a) and conventional monopole logging (b).

下载: 全尺寸图片幻灯片

图 9 斯通利波的相速度与衰减随孔隙流体黏度的变化

Fig. 9. Phase velocity and attenuation of Stoneley wave changing with pore fluid viscosity.

下载: 全尺寸图片幻灯片

表 1 孔隙介质参数

Table 1. Parameters of porous media.

参数	${\rho _{\rm{s}}}$/(kg·m^–3)	${\rho _{\rm{f}}}$/(kg·m^–3)	$ {k_0} $/D	$ \eta $/%	${\mu _{\rm{f}}}$/(Pa·s)	$ {S^\infty } $	${K_{\rm{f}}}$/GPa	$ {K_0} $/GPa	${K_{\rm{s}}}$/GPa	$ {\mu _0} $/GPa	${\mu _{\rm{s}}}$/GPa
值	2650	1000	1	20	10^–3	3	2.25	14.39	35.7	14	44

下载: 导出CSV

表 2 水在不同温度下的黏度

Table 2. Viscosity of water at different temperatures.

温度/℃	20	50	150
黏度/(10^–3 Pa·s)	1.00	0.55	0.21

下载: 导出CSV

[1]	李红星, 张嘉辉, 樊嘉伟, 陶春辉, 肖昆, 黄光南, 盛书中, 宫猛 2022 物理学报 71 089101 Google Scholar Li H X, Zhang J H, Fan J W, Tao C H, Xiao K, Huang G N, Sheng S Z, Gong M 2022 Acta Phys. Sin. 71 089101 Google Scholar
[2]	乔厚, 何锃, 张恒堃, 彭伟才, 江雯 2019 物理学报 68 128101 Google Scholar Qiao H, He Y, Zhang H K, Peng W C, Jiang W 2019 Acta Phys. Sin. 68 128101 Google Scholar
[3]	Benoit G, Heinkélé C, Gourdon E 2013 J. Acoust. Soc. Am. 134 4782 Google Scholar
[4]	Biot M A 1956 J. Acoust. Soc. Am. 28 168 Google Scholar
[5]	Biot M A 1956 J. Acoust. Soc. Am. 28 179 Google Scholar
[6]	Biot M A 1962 J. Appl. Phys. 33 1482 Google Scholar
[7]	Rosenbaum J H 1974 Geophysics 39 14 Google Scholar
[8]	Li K S, Gao J, Ju X D, Sun H F 2018 J. Geophys. Eng. 15 2266 Google Scholar
[9]	杨博, 章成广, 蔡明, 甘泉, 蔡德洋, 朱雷 2019 地球物理学进展 34 1127 Google Scholar Yang B, Zhang C G, Cai M, Gan Q, Cai D Y, Zhu L 2019 Progress in Geophysics 34 1127 Google Scholar
[10]	Qi Q M, Fu L Y, Deng J X, Cao J X 2021 Geophysics 86 1 Google Scholar
[11]	Winkler K W 1985 J. Geophys. Res. Solid Earth 90 6793 Google Scholar
[12]	Gist G A 1991 J. Acoust. Soc. Am. 90 2370 Google Scholar
[13]	邓继新, 史謌, 俞军 2003 北京大学学报(自然科学版) 39 835 Google Scholar Deng J X, Shi X, Yu J 2003 Acta Scientiarum Naturalium Universitatis Pekinensis 39 835 Google Scholar
[14]	Feng J X, Teng Q Z, He X H, Qing L B, Li Y 2018 Comput. Mater. Sci. 144 181 Google Scholar
[15]	陈培元, 杨辉廷, 贾兆扬 2018 中国海上油气 30 31 Google Scholar Chen P Y, Yang H T, Jia Z Y 2018 Chin. Offshore Oil Gas 30 31 Google Scholar
[16]	Liu Q R, Katsube N 1990 J. Acoust. Soc. Am. 88 1045 Google Scholar
[17]	魏修成, 卢明辉, 巴晶, 杨慧珠 2008 地球物理学报 51 213 Google Scholar Wei X C, Lu M H, Ba J, Yang H Z 2008 Chin. J. Geophys. 51 213 Google Scholar
[18]	Gao W 2016 SEG Technical Program Expanded Abstracts 2016 Dallas, Texas, October 16-21, 2016 pp3871–3875
[19]	Sahay P N 2008 Geophysics 73 N19 Google Scholar
[20]	Ciz R, Gurevich B, Markov M 2006 Geophys. J. Int. 165 957 Google Scholar
[21]	Müller T M, Gurevich B 2005 J. Acoust. Soc. Am. 117 2732 Google Scholar
[22]	Mavko G, Nur A 1975 J. Geophys. Res. 80 1444 Google Scholar
[23]	Dvorkin J, Nur A 1993 Geophysics 58 524 Google Scholar
[24]	崔志文, 刘金霞, 王春霞, 王克协 2010 物理学报 59 8655 Google Scholar Cui Z W, Liu J X, Wang C X, Wang K X 2010 Acta Phys. Sin. 59 8655 Google Scholar
[25]	Berryman J G, Wang H F 2000 Int. J. Rock Mech. Min. Sci. 37 63 Google Scholar
[26]	赵延林, 曹平, 唐劲舟, 马文豪, 李树清, 王卫军 2017 中南大学学报(自然科学版) 48 168 Google Scholar Zhao Y L, Cao P, Tang J Z, Ma W H, Li S Q, Wang W J 2017 J. Cent. South Univ. (Sci. Technol.) 48 168 Google Scholar
[27]	邵婕, 唐杰, 孙成禹 2016 地球物理学进展 31 334 Google Scholar Shao J, Tang J, Sun C Y 2016 Progr. Geophys. 31 334 Google Scholar
[28]	Müller T M, Sahay P N 2011 J. Acoust. Soc. Am. 129 2785 Google Scholar
[29]	Müller T M, Sahay P N 2011 Phys. Rev. E 84 026329
[30]	胡恒山, 王克协 2001 地球物理学报 44 135 Google Scholar Hu H S, Wang K X 2001 Chin. J. Geophys. 44 135 Google Scholar
[31]	卢明辉, 巴晶, 杨慧珠 2009 工程力学 26 36 Lu M H, Ba J, Yang H Z 2009 Eng. Mech. 26 36
[32]	Zhang X M, Müller T M 2019 Geophysics 84 WA1 Google Scholar
[33]	Bourbie T, Coussy O, Zinszner B, Junger M C 1992 J. Acoust. Soc. Am. 91 3080 Google Scholar
[34]	Müller T M, Sahay P N 2011 Appl. Phys. Lett. 98 168 Google Scholar
[35]	崔志文, 刘金霞, 王克协 2005 吉林大学学报(理学版) 43 803 Cui Z W, Liu J X, Wang K X 2005 J. Jilin Univ. (Sci. Ed.) 43 803
[36]	Markova I, Ronquillo J G, Markov M, Gurevich B 2014 Geophys. J. Int. 196 1082 Google Scholar

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