各向异性渗流条件下弹性波的传播特征

王丁; 张美根

doi:10.7498/aps.63.069101

摘要

研究了弹性波在非均匀裂纹孔隙介质中的传播特性，建立了各向异性喷射流模型. 当弹性波通过裂纹孔隙介质时，由于波的扰动及裂纹和孔隙几何结构的不一致，导致在裂纹内部及裂纹与周边孔隙之间同时存在着流体压力梯度. 此时的弹性波波动响应中包含着裂纹内连通性特征和背景孔隙渗透率信息. 流体的动态流动过程使得介质的等效弹性参数为复数（非完全弹性），并且具有频率依赖性. 当弹性波为低频和高频极限时，介质为完全弹性；当处于中间频段时，波有衰减和频率依赖. 裂纹孔隙介质的各向异性连通性（渗透率）对应着各向异性特征频率（当渗流长度等于非均匀尺度时的弹性波频率），波的传播受到裂纹内连通性的影响. 在一定频段内，随着裂纹厚度的增加，将出现第二峰值，峰值大小同时受到裂纹厚度和半径的影响.

关键词:

Abstract

A theoretical model of elastic wave propagation in a cracked porous medium is developed in this paper. When elastic wave propagates through the cracked porous medium, the different physical properties and geometries in different pores structures lead to the fluid pressure gradient in cracks and between cracks and pores. The squirt-flow will take place in two mutually-perpendicular directions, thus, it has anisotropic characteristic. The wave respond contains the crack and background medium permeability information simultaneously. Owing to the fluid dynamic flow process, the effective elastic modulus is complex and frequency-dependent. When the wave frequencies are in high and low limit, the porous medium is elastic. The wave attenuation is obvious and the attenuation is frequency-dependent in the middle frequency region. The anisotropic permeability corresponding to anisotropic characteristic times in the cracked porous medium causes the wave propagation to be affected by the crack connectivity. There appears a second attenuation peak for larger thickness value of crack, meanwhile, and the peak of attenuation is influenced by the thickness value and radius of crack.

Keywords:

作者及机构信息

王丁^{1 2},
张美根¹

1.
中国科学院地质与地球物理研究所, 油气资源研究重点实验室, 北京 100029;

2.
中国科学院大学, 北京 100049

基金项目: 国家科技重大专项（批准号：2011ZX05035-002-003HZ）和国家重大仪器设备开发专项（批准号：ZDYZ2012-1-06）资助的课题.

Authors and contacts

Wang Ding^{1 2},
Zhang Mei-Gen¹

1.
Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, the Chinese Academy of Sciences, Beijing 100029, China;

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

Funds: Project supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX05035-002-003HZ) and the National Special Fund for the Development of Major Research Equipment and Instruments of the National Natural Science Fundation of China (Grant No. ZDYZ2012-1-06).

参考文献

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[2]	Gurevich B, Osypov K, Ciz R, Makarynska D 2008 Geophysics 73 E115
[3]	Biot M 1956 J. Acoust. Soc. Am. 28 168
[4]	Biot M 1956 J. Acoust. Soc. Am. 28 179
[5]	Biot M 1962 J. Appl. Phys. 33 1482
[6]	Zhao H B, Wang X M, Chen H 2006 Chin. Phys. 15 2819
[7]	Mller T M, Gurevich B, Lebedev M 2010 Geophysics 75 A147
[8]	Picotti S, Carcione J M, Rubino J M, Santos J E 2007 Geophysics 72 N11
[9]	Gurevich B 2002 Geophysics 67 264
[10]	White J E 1975 Geophysics 40 224
[11]	Crampin S 1984 Geophys. J. Roy. Astr. Soc. 76 135
[12]	Dvorkin J, Nur A 1993 Geophysics 58 524
[13]	Gassmann F 1951 Viertel. Naturforsch. Ges. Zrich. 96 1
[14]	Chapman M 2001 Ph. D. Dissertation (Edinburgh: University of Edinburgh)
[15]	Song Y J, Hu H S 2013 Acta Mech. Sin. 45 395 (in Chinese) [宋永佳, 胡恒山 2013 力学学报 45 395]
[16]	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]
[17]	Tang X M 2011 Sci. China D: Earth Sci. 41 784 (in Chinese) [唐晓明 2011 中国科学D辑: 地球科学 41 784]
[18]	Chapman M 2003 Geophys. Prospect. 51 369
[19]	Hudson J A, Liu E R, Crampin S 1996 Geophys. J. Internat. 124 105
[20]	Pride S R, Berryman J G 2003 Phys. Rev. E 68 036603
[21]	Pride S R, Berryman J G 2003 Phys. Rev. E 68 036604
[22]	Gurevich B, Brajanovski M, MllerT M, Galvin R J, Stewart T J 2009 Geophys. Prospect. 57 225
[23]	Lambert G, Gurevich B, Brajanovski M 2006 Geophysics 71 N41
[24]	Norris A N 1993 J. Acoust. Soc. Am. 94 359
[25]	Johnson D L, Koplik J, Dashen R 1987 J. Fluid. Mech. 176 379
[26]	Snow D T 1969 Water. Resour. Res. 5 1273
[27]	MllerT M, Rothert E 2006 Geophys. Res. Lett. 33 L16305

施引文献

[1]	Quintal B 2012 J. Appl. Geophys. 82 119
[2]	Gurevich B, Osypov K, Ciz R, Makarynska D 2008 Geophysics 73 E115
[3]	Biot M 1956 J. Acoust. Soc. Am. 28 168
[4]	Biot M 1956 J. Acoust. Soc. Am. 28 179
[5]	Biot M 1962 J. Appl. Phys. 33 1482
[6]	Zhao H B, Wang X M, Chen H 2006 Chin. Phys. 15 2819
[7]	Mller T M, Gurevich B, Lebedev M 2010 Geophysics 75 A147
[8]	Picotti S, Carcione J M, Rubino J M, Santos J E 2007 Geophysics 72 N11
[9]	Gurevich B 2002 Geophysics 67 264
[10]	White J E 1975 Geophysics 40 224
[11]	Crampin S 1984 Geophys. J. Roy. Astr. Soc. 76 135
[12]	Dvorkin J, Nur A 1993 Geophysics 58 524
[13]	Gassmann F 1951 Viertel. Naturforsch. Ges. Zrich. 96 1
[14]	Chapman M 2001 Ph. D. Dissertation (Edinburgh: University of Edinburgh)
[15]	Song Y J, Hu H S 2013 Acta Mech. Sin. 45 395 (in Chinese) [宋永佳, 胡恒山 2013 力学学报 45 395]
[16]	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]
[17]	Tang X M 2011 Sci. China D: Earth Sci. 41 784 (in Chinese) [唐晓明 2011 中国科学D辑: 地球科学 41 784]
[18]	Chapman M 2003 Geophys. Prospect. 51 369
[19]	Hudson J A, Liu E R, Crampin S 1996 Geophys. J. Internat. 124 105
[20]	Pride S R, Berryman J G 2003 Phys. Rev. E 68 036603
[21]	Pride S R, Berryman J G 2003 Phys. Rev. E 68 036604
[22]	Gurevich B, Brajanovski M, MllerT M, Galvin R J, Stewart T J 2009 Geophys. Prospect. 57 225
[23]	Lambert G, Gurevich B, Brajanovski M 2006 Geophysics 71 N41
[24]	Norris A N 1993 J. Acoust. Soc. Am. 94 359
[25]	Johnson D L, Koplik J, Dashen R 1987 J. Fluid. Mech. 176 379
[26]	Snow D T 1969 Water. Resour. Res. 5 1273
[27]	MllerT M, Rothert E 2006 Geophys. Res. Lett. 33 L16305

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