搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

含少量气泡流体饱和孔隙介质中的弹性波

王婷 崔志文 刘金霞 王克协

引用本文:
Citation:

含少量气泡流体饱和孔隙介质中的弹性波

王婷, 崔志文, 刘金霞, 王克协

Propagation of elastic waves in saturated porous medium containing a small amount of bubbly fluid

Wang Ting, Cui Zhi-Wen, Liu Jin-Xia, Wang Ke-Xie
PDF
导出引用
  • 考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.
    It is very important to understand the acoustical properties of porous medium. To study the relationship between acoustical and other physical properties of porous medium will help us to use acoustical tools for determining the physical properties of porous medium. Many researchers have paid much attention to the properties of acoustic wave propagation in the gassy marine sediments based on the Biot model which is popularly used to predict the dispersion and attenuation of sound in saturated porous medium. The patchy model which contains gas inside the spherical water predicts that the existence of gas just has little effect on the propagation of acoustic wave in porous medium when the gas content is very small. However, the presence of a small number of bubbles in a fluid saturated sediment will lead to different acoustic responses. As is well known, the bubble vibration theory proposed by Keller and Miksis shows that a small number of bubbles existing in the liquid will have a great influence on sound velocity and attenuation. Therefore, in order to study the effect of a small amount of gas existing in fluid saturated porous medium on the property of acoustic wave propagation, we investigate a bubbly liquid saturated porous medium and consider the case of the bubbles vibrating linearly under the action of sound waves. First, we derive the continuity equation of the seepage according to the mass conservation of the pore fluid and the relationship between porosity differentiation and pore fluid pressure differentiation. Then, the bubble linear vibration theory given by Commander is used to deal with the time derivative of gas volume fraction in the continuity equation of the seepage, The bubble linear vibration theory gives the relationship between instantaneous bubble radius and background pressure of the medium. Through this relationship, we obtain the equation of time derivative of gas volume fraction and time derivative of pore fluid pressure. Then, we combine the obtained equation with the continuity equation of seepage, and obtain the modified continuity equation of seepage whose form is similar to that of Biot model. Finally, the modified Biot's equations for fluid saturated porous medium containing a small amount of bubbly fluid is obtained. As is well known, an effective density fluid model for acoustic propagation in sediments, derived from Biot theory, just can predict the acoustic properties of the fast compressional waves. However, the present model can predict the acoustic properties of fast, slow compressional waves and shear waves propagating in sediments. Through numerically calculating the dispersion, attenuation, amplitude ratios of pore fluid displacement to solid displacement for fast and slow compressional waves, it is found that the existence of a small number of bubbles has an influence on the acoustic properties of both the fast compressional waves and the slow compressional waves, especially the velocity of the fast compressional wave. In addition, the low-frequency speed approximation formula for the fast compressional wave is also presented. The approximate formula directly indicates the relationship between the velocity of fast compressional wave and the parameters of porous medium such as the gas volume fraction and the bubble radius. This study shows that the influence of a small number of bubbles in fluid saturated on acoustic wave propagation is noticeable. The modified Biot model presented in this paper provides one model to study the properties of acoustic waves in fluid saturated porous medium with a small number of bubbles.
      通信作者: 崔志文, cuizw@jlu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:41474098,11134011)、吉林省科技发展计划(批准号:20180101282JC)和声场声信息国家重点实验室开放基金资助的课题.
      Corresponding author: Cui Zhi-Wen, cuizw@jlu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41474098, 11134011), the Natural Science Foundation of Jilin Province of China (Grant No. 20180101282JC), and the State Key Laboratory of Acoustics, China.
    [1]

    Qiao W X, Wu W Q, Wang Y J 1996 Prog. Phys. 16 386(in Chinese) [乔文孝, 吴文虬, 王耀俊 1996 物理学进展 16 386]

    [2]

    Biot M A 1956 J. Acoust. Soc. Am. 28 168

    [3]

    Cui Z W, Wang K X, Cao Z L, Hu H S 2004 Acta Phys. Sin. 53 3083(in Chinese) [崔志文, 王克协, 曹正良, 胡恒山 2004 物理学报 53 3083]

    [4]

    Plona T J 1980 Appl. Phys. Lett. 36 259

    [5]

    Cui Z W, Wang K X 2003 Int. J. Eng. Sci. 41 2179

    [6]

    Pride S R, Berryman J G 2003 Phys. Rev. E 68 036604

    [7]

    Wang X M 2009 Appl. Acoust. 28 1(in Chinese) [王秀明 2009 应用声学 28 1]

    [8]

    Santos J E, Corber J M, Douglas J 1990 J. Acoust. Soc. Am. 87 1428

    [9]

    Cai Y Q, Li B Z, Xu C J 2006 Chin. J. Rock Mech. Eng. 25 2009(in Chinese) [蔡袁强, 李宝忠, 徐长节 2006 岩石力学与工程学报 25 2009]

    [10]

    Li W H 2002 Northwest. Seismological J. 24 303(in Chinese) [李伟华 2002 西北地震学报 24 303]

    [11]

    White J E, Mikhaylova N G, Lyakhovitskiy F M 1975 J. Acoust. Soc. Am. 57 S30

    [12]

    Johnson D L 2001 J. Acoust. Soc. Am. 110 682

    [13]

    Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628

    [14]

    Prosperetti A, Crum L A, Commander K W 1988 J. Acoust. Soc. Am. 83 502

    [15]

    Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732

    [16]

    Wang Y, Lin S Y, Zhang X L 2013 Acta Phys. Sin. 62 064304(in Chinese) [王勇, 林书玉, 张小丽 2013 物理学报 62 064304]

    [17]

    Wang Y, Lin S Y, Mo R Y, Zhang X L 2013 Acta Phys. Sin. 62 134304(in Chinese) [王勇, 林书玉, 莫润阳, 张小丽 2013 物理学报 62 134304]

    [18]

    Wang Y, Lin S Y, Zhang X L 2014 Acta Phys. Sin. 63 034301(in Chinese) [王勇, 林书玉, 张小丽 2014 物理学报 63 034301]

    [19]

    Zhu L G 2009 Ship Sci. Tech. 10 64(in Chinese) [祝令国 2009 舰船科学技术 31 64]

    [20]

    Wang H B, Wang Z Q, Zhang H Y, Zhang W P 2005 Shipbuild. China 46 44(in Chinese) [王虹斌, 王芝秋, 张洪雨, 张文平 2005 中国造船 46 44]

    [21]

    Anderson A L, Hampton L D 1980 J. Acoust. Soc. Am. 67 1890

    [22]

    Yang X M, Church C C 2005 J. Acoust. Soc. Am. 118 3595

    [23]

    Mantouka A, Dogan H, White P R, Leighton T G 2016 J. Acoust. Soc. Am. 140 274

    [24]

    Zheng G Y, Huang Y W 2016 Acta Phys. Sin. 65 234301(in Chinese) [郑广赢, 黄益旺 2016 物理学报 65 234301]

    [25]

    Dvorkin J, Nur A 1993 Geophysics 58 523

    [26]

    Biot M A 1941 J. Appl. Phys. 12 155

    [27]

    Hu H S 2003 Acta Phys. Sin. 52 1954(in Chinese) [胡恒山 2003 物理学报 52 1954]

  • [1]

    Qiao W X, Wu W Q, Wang Y J 1996 Prog. Phys. 16 386(in Chinese) [乔文孝, 吴文虬, 王耀俊 1996 物理学进展 16 386]

    [2]

    Biot M A 1956 J. Acoust. Soc. Am. 28 168

    [3]

    Cui Z W, Wang K X, Cao Z L, Hu H S 2004 Acta Phys. Sin. 53 3083(in Chinese) [崔志文, 王克协, 曹正良, 胡恒山 2004 物理学报 53 3083]

    [4]

    Plona T J 1980 Appl. Phys. Lett. 36 259

    [5]

    Cui Z W, Wang K X 2003 Int. J. Eng. Sci. 41 2179

    [6]

    Pride S R, Berryman J G 2003 Phys. Rev. E 68 036604

    [7]

    Wang X M 2009 Appl. Acoust. 28 1(in Chinese) [王秀明 2009 应用声学 28 1]

    [8]

    Santos J E, Corber J M, Douglas J 1990 J. Acoust. Soc. Am. 87 1428

    [9]

    Cai Y Q, Li B Z, Xu C J 2006 Chin. J. Rock Mech. Eng. 25 2009(in Chinese) [蔡袁强, 李宝忠, 徐长节 2006 岩石力学与工程学报 25 2009]

    [10]

    Li W H 2002 Northwest. Seismological J. 24 303(in Chinese) [李伟华 2002 西北地震学报 24 303]

    [11]

    White J E, Mikhaylova N G, Lyakhovitskiy F M 1975 J. Acoust. Soc. Am. 57 S30

    [12]

    Johnson D L 2001 J. Acoust. Soc. Am. 110 682

    [13]

    Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628

    [14]

    Prosperetti A, Crum L A, Commander K W 1988 J. Acoust. Soc. Am. 83 502

    [15]

    Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732

    [16]

    Wang Y, Lin S Y, Zhang X L 2013 Acta Phys. Sin. 62 064304(in Chinese) [王勇, 林书玉, 张小丽 2013 物理学报 62 064304]

    [17]

    Wang Y, Lin S Y, Mo R Y, Zhang X L 2013 Acta Phys. Sin. 62 134304(in Chinese) [王勇, 林书玉, 莫润阳, 张小丽 2013 物理学报 62 134304]

    [18]

    Wang Y, Lin S Y, Zhang X L 2014 Acta Phys. Sin. 63 034301(in Chinese) [王勇, 林书玉, 张小丽 2014 物理学报 63 034301]

    [19]

    Zhu L G 2009 Ship Sci. Tech. 10 64(in Chinese) [祝令国 2009 舰船科学技术 31 64]

    [20]

    Wang H B, Wang Z Q, Zhang H Y, Zhang W P 2005 Shipbuild. China 46 44(in Chinese) [王虹斌, 王芝秋, 张洪雨, 张文平 2005 中国造船 46 44]

    [21]

    Anderson A L, Hampton L D 1980 J. Acoust. Soc. Am. 67 1890

    [22]

    Yang X M, Church C C 2005 J. Acoust. Soc. Am. 118 3595

    [23]

    Mantouka A, Dogan H, White P R, Leighton T G 2016 J. Acoust. Soc. Am. 140 274

    [24]

    Zheng G Y, Huang Y W 2016 Acta Phys. Sin. 65 234301(in Chinese) [郑广赢, 黄益旺 2016 物理学报 65 234301]

    [25]

    Dvorkin J, Nur A 1993 Geophysics 58 523

    [26]

    Biot M A 1941 J. Appl. Phys. 12 155

    [27]

    Hu H S 2003 Acta Phys. Sin. 52 1954(in Chinese) [胡恒山 2003 物理学报 52 1954]

  • [1] 石志奇, 何晓, 刘琳, 陈德华. 基于有限差分的部分饱和双重孔隙介质弹性波模拟与分析. 物理学报, 2024, 73(10): 100201. doi: 10.7498/aps.73.20240227
    [2] 石志奇, 何晓, 刘琳, 陈德华, 王秀明. 毛细管压力作用下的非饱和双重孔隙介质中弹性波传播. 物理学报, 2023, 72(6): 069101. doi: 10.7498/aps.72.20222063
    [3] 李红星, 张嘉辉, 樊嘉伟, 陶春辉, 肖昆, 黄光南, 盛书中, 宫猛. 多尺度波致流非饱和孔隙介质波传播理论研究. 物理学报, 2022, 71(8): 089101. doi: 10.7498/aps.71.20211463
    [4] 李荫铭, 孔鹏, 毕仁贵, 何兆剑, 邓科. 双表面周期性弹性声子晶体板中的谷拓扑态. 物理学报, 2022, 71(24): 244302. doi: 10.7498/aps.71.20221292
    [5] 张先梅, 王成会, 郭建中, 莫润阳, 胡静, 陈时. 无界弹性介质球形液体空腔中的气泡的动力学. 物理学报, 2021, 70(21): 214305. doi: 10.7498/aps.70.20210869
    [6] 骆全斌, 黄学勤, 邓伟胤, 吴迎, 陆久阳, 刘正猷. 声子晶体板中的第二类狄拉克点和边缘传输. 物理学报, 2021, 70(18): 184302. doi: 10.7498/aps.70.20210712
    [7] 张陶然, 莫润阳, 胡静, 陈时, 王成会, 郭建中. 弹性介质包围的球形液体腔中气泡和粒子的相互作用. 物理学报, 2020, 69(23): 234301. doi: 10.7498/aps.69.20200764
    [8] 苏娜娜, 韩庆邦, 蒋謇. 无限流体中孔隙介质圆柱周向导波的传播特性. 物理学报, 2019, 68(8): 084301. doi: 10.7498/aps.68.20182300
    [9] 郑广赢, 黄益旺. 气泡线性振动对含气泡水饱和多孔介质声传播的影响. 物理学报, 2016, 65(23): 234301. doi: 10.7498/aps.65.234301
    [10] 王勇, 林书玉, 张小丽. 含气泡液体中的非线性声传播. 物理学报, 2014, 63(3): 034301. doi: 10.7498/aps.63.034301
    [11] 宋永佳, 胡恒山. 含定向非均匀体固体材料的横观各向同性有效弹性模量. 物理学报, 2014, 63(1): 016202. doi: 10.7498/aps.63.016202
    [12] 孔丽云, 王一博, 杨慧珠. 裂缝诱导TTI双孔隙介质波场传播特征. 物理学报, 2013, 62(13): 139101. doi: 10.7498/aps.62.139101
    [13] 王勇, 林书玉, 张小丽. 声波在含气泡液体中的线性传播. 物理学报, 2013, 62(6): 064304. doi: 10.7498/aps.62.064304
    [14] 王勇, 林书玉, 莫润阳, 张小丽. 含气泡液体中气泡振动的研究. 物理学报, 2013, 62(13): 134304. doi: 10.7498/aps.62.134304
    [15] 刘启能. 一维固-固结构圆柱声子晶体中弹性波的传输特性. 物理学报, 2011, 60(3): 034301. doi: 10.7498/aps.60.034301
    [16] 崔志文, 刘金霞, 王春霞, 王克协. 基于Biot-喷射流统一模型Maxwell流体饱和孔隙介质中的弹性波. 物理学报, 2010, 59(12): 8655-8661. doi: 10.7498/aps.59.8655
    [17] 张新明, 刘家琦, 刘克安. 一维双相介质孔隙率的小波多尺度反演. 物理学报, 2008, 57(2): 654-660. doi: 10.7498/aps.57.654
    [18] 杜启振, 刘莲莲, 孙晶波. 各向异性粘弹性孔隙介质地震波场伪谱法正演模拟. 物理学报, 2007, 56(10): 6143-6149. doi: 10.7498/aps.56.6143
    [19] 关 威, 胡恒山, 储昭坦. 声诱导电磁场的赫兹矢量表示与多极声电测井模拟. 物理学报, 2006, 55(1): 267-274. doi: 10.7498/aps.55.267
    [20] 胡恒山. 孔隙地层井壁上的声波首波及其诱导电磁场的原因. 物理学报, 2003, 52(8): 1954-1959. doi: 10.7498/aps.52.1954
计量
  • 文章访问数:  6312
  • PDF下载量:  197
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-01-28
  • 修回日期:  2018-03-08
  • 刊出日期:  2018-06-05

/

返回文章
返回