双相组分孔隙介质波场数值模拟
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摘要
孔隙介质理论的研究以往常用试验分析方法,详细介绍了双相组分孔隙介质理论。基于宏观上等效的一系列体积分数加权平均组分分量方程,得到双相组分孔隙介质整体弹性矩阵与所有组分弹性矩阵之间的体积分数及耦合系数加权关系,得出各弹性参数的表达式。结合弹性波动力学中的Cauchy、Navier和本构三个方程,得到弹性波在等效后的组分孔隙介质中传播满足的波动方程。应用交错网格有限差分法求解该波动方程。采用不同孔隙度双相组分孔隙介质模型波场数值模拟,精确得到了混合波场。总结了双相组分型弹性孔隙流体介质中地震波传播的特点和规律。
The primary methods for studying porous media are experimental measurements and data analysis.Based on a series of components equation,the volume fraction and coupling coefficient between the elastic matrix of bi-phase medium and the elastic matrix of components are got,and then the elastic parameters expression is got.Combining the Navier,Cauchy and constitutive equation,the wave equation of porous medium is got.This wave equation with a one-order staggered-grid finite difference scheme is solved.The wave filed of porous medium with different porosity and summarizes seismic wave propagation characteristics of biphasic porous medium also are numerical modeled.
The primary methods for studying porous media are experimental measurements and data analysis.Based on a series of components equation,the volume fraction and coupling coefficient between the elastic matrix of bi-phase medium and the elastic matrix of components are got,and then the elastic parameters expression is got.Combining the Navier,Cauchy and constitutive equation,the wave equation of porous medium is got.This wave equation with a one-order staggered-grid finite difference scheme is solved.The wave filed of porous medium with different porosity and summarizes seismic wave propagation characteristics of biphasic porous medium also are numerical modeled.
引文
1 Biot M A.Theory of propagation of elastic waves in a fluid-saturatedporous solid.1.Low-frequency range.J Acoust Soc Am,1956;28:168—178
2 Biot M A.Theory of propagation of elastic waves in a fluid-saturatedporous solid.1.higher-frequency range J Acoust Soc Am,1956;28:179—191
3 Biot M A.Mechanics deformation and acoustic propagation in porousmedia.J Appl Phys,1962;33:1482—1498
4 Biot M A.Generalized theory of acoustic propagation in porous dissi-pative media.J Acoust Soc Am,1962;34:1254—1264
5 Gassmann F.Uber die elastizitat poroser medien:verteljahrsschrift dernaturforschenden gesellschaft in zurich,1951;96:1—21
6 Gassmann F.Elastic waves through a packing of spheres.Geophysics,1951;16(4):673—685
7 Brown R J S,Korringa J.On the dependence of the elastic propertiesof a porous rock on the compressibility of a pore fluid.Geophysics,1975;40:608—616
8 Berryman J G,Milton G W.Exact results for generalized Gassmann’sequation in composite porous media with two constituents.Geophys-ics,1991;56(12):1950—1960
9 Berryman J G.Origin of Gassmann’s equations.Geophysics,1999;64(5):1627—1629
10 Carcione J M,Helle H B,Santos J E,et al.A constitutive equationand generalized Gassmann modulus for multimineral porous media.Geophysics,2005;70(2):N17—N26
11 Niu Binhua,Sun Chunyan,Yan Guojing,et al.Linear numericalcalculation method for obtaining critical point,pore fluid,andframework parameters of gas bearing media.Applied Geophysics,2009;6(4):319—326
12董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000;43(6):856—864
13董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999;34(1):45—56
14牛滨华,孙春岩,李明.各向同性固体连续介质与地震波传波.石油工业出版社,2002
15牛滨华,孙春岩.半空间介质与地震波传播.北京:石油工业出版社,2002
16牛滨华,孙春岩.半空间均匀各向同性单相固体弹性介质与地震波传播.北京:地质出版社,2005
17牛滨华,孙春岩.半空间均匀各向同性单相固体黏弹性介质与地震波传播.北京:地质出版社,2007
18 Nur A,Mavko G,Dvorkin Je,t al.Critical porosity:a key to rela-ting physical properties to porosity in rocks.The Leading Edge,1998;17:357—362
19郭自强.固体中的波.北京:地震出版社,1982
20戈革.弹性波动力学.北京:石油工业出版社,1980
2 Biot M A.Theory of propagation of elastic waves in a fluid-saturatedporous solid.1.higher-frequency range J Acoust Soc Am,1956;28:179—191
3 Biot M A.Mechanics deformation and acoustic propagation in porousmedia.J Appl Phys,1962;33:1482—1498
4 Biot M A.Generalized theory of acoustic propagation in porous dissi-pative media.J Acoust Soc Am,1962;34:1254—1264
5 Gassmann F.Uber die elastizitat poroser medien:verteljahrsschrift dernaturforschenden gesellschaft in zurich,1951;96:1—21
6 Gassmann F.Elastic waves through a packing of spheres.Geophysics,1951;16(4):673—685
7 Brown R J S,Korringa J.On the dependence of the elastic propertiesof a porous rock on the compressibility of a pore fluid.Geophysics,1975;40:608—616
8 Berryman J G,Milton G W.Exact results for generalized Gassmann’sequation in composite porous media with two constituents.Geophys-ics,1991;56(12):1950—1960
9 Berryman J G.Origin of Gassmann’s equations.Geophysics,1999;64(5):1627—1629
10 Carcione J M,Helle H B,Santos J E,et al.A constitutive equationand generalized Gassmann modulus for multimineral porous media.Geophysics,2005;70(2):N17—N26
11 Niu Binhua,Sun Chunyan,Yan Guojing,et al.Linear numericalcalculation method for obtaining critical point,pore fluid,andframework parameters of gas bearing media.Applied Geophysics,2009;6(4):319—326
12董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000;43(6):856—864
13董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999;34(1):45—56
14牛滨华,孙春岩,李明.各向同性固体连续介质与地震波传波.石油工业出版社,2002
15牛滨华,孙春岩.半空间介质与地震波传播.北京:石油工业出版社,2002
16牛滨华,孙春岩.半空间均匀各向同性单相固体弹性介质与地震波传播.北京:地质出版社,2005
17牛滨华,孙春岩.半空间均匀各向同性单相固体黏弹性介质与地震波传播.北京:地质出版社,2007
18 Nur A,Mavko G,Dvorkin Je,t al.Critical porosity:a key to rela-ting physical properties to porosity in rocks.The Leading Edge,1998;17:357—362
19郭自强.固体中的波.北京:地震出版社,1982
20戈革.弹性波动力学.北京:石油工业出版社,1980
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