非饱和岩石中的纵波频散与衰减:双重孔隙介质波传播方程
|
摘要
本文采用Rayleigh理论描述纵波激励下非饱和岩石中气泡的局域流体流动,从经典力学的哈密顿原理导出了双重孔隙介质中的波传播方程,即Biot-Rayleigh方程.方程的格式简洁,参数少,所有相关参数物理可测,因此,方程具有较好的物理可实现性.基于相同的岩石与前人理论对比,初步验证了本理论的有效性.对三个地区的砂岩储层进行了分析,结果显示:地震频段内纵波对储层是否含气非常敏感,但对含气饱和度指示性不佳,且随着孔隙度降低,纵波频散与衰减在中低频段更为显著;含甲烷与含二氧化碳的砂岩储层均呈第三类AVO响应特征,很难从叠前分析技术中鉴别;理论预测的纵波频散随饱和度与频率变化的趋势与特征,与多频段实验观测结果一致.
The dynamic process of P-wave-induced local fluid flow in partially-saturated rocks is described by introducing Rayleigh's theory into poroelastic equations.The wave propagation equations in double-porosity medium(Biot-Rayleigh Equations) are derived from Hamilton's principle of classic mechanics.This thoery benefits from concise mathematical expressions and fewer coefficients.All relevant coefficients in expressions can be determined by measuring rock fundamental properties,so that the Biot-Rayleigh equations are physically realizable.Comparisons with the former theories in literature have preliminarily proved the validity of this theory.An analysis on the sandstone reservoirs of the three districts shows: seismic-band P waves are sensitive to gas in reservoir,but are not so efficient to quantitatively indicate gas saturation,and P-wave dispersion and attenuation are more significant in seismic band for lower porosity sandstones;the CH4-saturated and CO2-saturated reservoirs share the same 3rd type of AVO characteristics and can hardly be discriminated based on the traditional pre-stack analysis;the theory successfully predicts the trends and the multi-frequency-band experimental observed characteristics of P wave velocity variation in relation to water saturation and frequency.
The dynamic process of P-wave-induced local fluid flow in partially-saturated rocks is described by introducing Rayleigh's theory into poroelastic equations.The wave propagation equations in double-porosity medium(Biot-Rayleigh Equations) are derived from Hamilton's principle of classic mechanics.This thoery benefits from concise mathematical expressions and fewer coefficients.All relevant coefficients in expressions can be determined by measuring rock fundamental properties,so that the Biot-Rayleigh equations are physically realizable.Comparisons with the former theories in literature have preliminarily proved the validity of this theory.An analysis on the sandstone reservoirs of the three districts shows: seismic-band P waves are sensitive to gas in reservoir,but are not so efficient to quantitatively indicate gas saturation,and P-wave dispersion and attenuation are more significant in seismic band for lower porosity sandstones;the CH4-saturated and CO2-saturated reservoirs share the same 3rd type of AVO characteristics and can hardly be discriminated based on the traditional pre-stack analysis;the theory successfully predicts the trends and the multi-frequency-band experimental observed characteristics of P wave velocity variation in relation to water saturation and frequency.
引文
[1]杨慧珠,巴晶,唐建侯等.油气勘探中常规地球物理勘探方法的发展.石油地球物理勘探,2006,41(2):231-236.Yang H Z,Ba J,Tang J H,et al.Development ofconventional geophysical methods in oil/gas exploration.OilGeophysical Prospecting(in Chinese),2006,41(2):231-236.
[2]地震勘探技术成为油气勘探主角.中国科技信息,doi:CNKI:SUN:XXJK.0.2007-18-003.The technology of seismic exploration has become theprotagonist in oil-gas exploration industry.China Science andTechnology Information,doi:CNKI:SUN:XXJK.0.2007-18-003.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.J.Acoust.Soc.Am.,1956,28(2):168-178.
[4]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range.J.Acoust.Soc.Am.,1956,28(2):179-191.
[5]Muller T M,Gurevich B,Lebedev M.Seismic waveattenuation and dispersion resulting from wave-induced flowin porous rocks-A review.Geophysics,2010,75(5):75A147-75A164.
[6]White J E.Computed seismic speeds and attenuation in rockswith partial gas saturation.Geophysics,1975,40(2):224-232.
[7]Dutta N C,Seriff A J.On White′s model of attenuation inrocks with partial gas saturation.Geophysics,1979,44(11):1806-1812.
[8]Gurevich B,Zyrianov V B,Lopatnikov S L.Seismicattenuation in finely layered porous rocks:Effects of fluidflow and scattering.Geophysics,1997,62(1):319-324.
[9]Shapiro S A,Müller T M.Seismic signatures of permeabilityin heterogeneous porous media.Geophysics,1999,64(1):99-103.
[10]Carcione J M,Picotti S.P-wave seismic attenuation by slowwave diffusion:Effects of inhomogeneous rock properties.Geophysics,2006,71(3):O1-O8.
[11]聂建新,杨顶辉,杨慧珠.基于非饱和多孔隙介质BISQ模型的储层参数反演.地球物理学报,2004,47(6):1101-1105.Nie J X,Yang D H,Yang H Z.Inversion of reservoirparameters based on the BISQ model in partially saturatedporous media.Chinese J.Geophys.(in Chinese),47(6):1101-1105.
[12]刘炯,马坚伟,杨慧珠.White球状Patchy模型中纵波传播研究.地球物理学报,2010,53(4):954-962.Liu J,Ma J W,Yang H Z.Research on P-wave's propagationin White's sphere model with patchy saturation.Chinese J.Geophys.(in Chinese),2010,53(4):954-962.
[13]Nie J X,Ba J,Yang D H,et al.BISQ model based onKelvin-Voigt viscoelastic frame in partially saturated porousmedium.Applied Geophysics,(in Press).
[14]Carcione J M,Morency C,Santos J E.Computationalporoelasticity-A review.Geophysics,2010,75(5):75A229-75A243.
[15]巴晶,卢明辉,胡彬等.黏弹双相介质中的松弛骨架模型.地球物理学报,2008,51(5):1527-1537.Ba J,Lu M H,Hu B,et al.The skeleton-relaxed model forporoviscoelastic media.Chinese J.Geophys.(in Chinese),2008,51(5):1527-1537.
[16]Dvorkin J,Nur A.Dynamic poroelasticity:A unified modelwith the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524-533.
[17]Pride S R,Berryman J G,Harris J M.Seismic attenuationdue to wave-induced flow.J.Geophys.Res.,2004,109:B01201,doi:10.1029/2003JB002639.
[18]Ba J,Carcione J M,Nie J X.Biot-Rayleigh theory of wavepropagation in double-porosity media.J.Geohpys.Res.,2011,116:B06202,doi:10.1029/2010JB008185.
[19]Liu J,Ba J,Ma J W,et al.An analysis of seismicattenuation in random porous media.Science China Physics,Mechanics&Astronomy,2010,53(4):628-637.
[20]Carcione J M,Helle H B,Pham N H.White′s model forwave propagation in partially saturated rocks:Comparisonwith poroelastic numerical experiments.Geophysics,2003,68(4):1389-1398.
[21]Berryman J G.Thoery of elastic properties of composite-materials.Appl.Phys.Lett.,1979,35(11):856-858.
[22]Rayleigh L.On the pressure developed in a liquid during thecollapse of a spherical cavity.Phil.Mag.,1917,34:94-98.
[23]Sato H,Fehler M.Seismic Wave Propagation and Scatteringin the Heterogeneous Earth.New York:Springer-Verlag,1998.
[24]Eshelby J D.The determination of the elastic field of anellipsoidal inclusion,and related problems.Proc.R.Soc.London,Ser.A,1957,241(1226):376-396.
[25]Kuster G T,Toksz M N.Velocity and attenuation of seismicwaves in two-phase media:I.Theoretical formulations.Geophysics,1974,39(5):587-606.
[26]Ba J,Nie J X,Cao H,et al.Mesoscopic fluid flowsimulation in double-porosity rocks.Geophys.Res.Lett.,2008,35:L04303,doi:10.1029/2007GL032429.
[27]Ba J,Yang H Z,Xie G Q.AGILD seismic modelling fordouble-porosity media.PIERS 2008in Hangzhou.Cambridge:The Electromagnetics Academy.2008.
[28]Ba J,Cao H,Yao F C,et al.Double-porosity rock modeland squirt flow in the laboratory frequency band.AppliedGeophysics,2008,5(4):261-276.
[29]Ba J,Cao H,Yao F C.Pore heterogeneity induces double-porosity in Guang′an sandstone.∥CPS/SEG Beijing.Beijing:Society of Petroleum Geophysics,2009.
[30]巴晶.双重孔隙介质波传播理论与地震响应实验分析.中国科学G辑,2010,40(11):1398-1409.Ba J.Wave propagation theory in double-porosity mediumand experimental analysis on seismic responses.ScientiaSinica Physica,Mechanica&Astronomica(in Chinese),2010,40(11):1398-1409.
[31]Ba J,Cao H,Yao F C.Velocity dispersion of P waves insandstone and carbonate:Double-porosity and local fluid flowtheory.SEG Expanded Abstracts,Denver,US,2010.
[32]Berryman J G,Wang H F.Double porosity modelling inelastic wave propagation for reservoir characterization.∥SPIE Conference on Mathematical Methods in GeophysicalImaging V.San Diego California:SPIE Press,1998.
[33]Johnson D L.Recent developments in the acoustic propertiesof porous media.∥Sette D.Frontiers in Physical AcousticsXCIII.New York:North Holland Elsevier.1987:255-290.
[34]Johnson D L.Theory of frequency dependent acoustics inpatchy saturated porous media.J.Acoust.Soc.Am.,2001,110(2):682-694.
[35]Toms J,Müller T M,Ciz R,et al.Comparative review oftheoretical models for elastic wave attenuation and dispersionin partially saturated rocks.Soil Dynamics and EarthquakeEngineering,2006,26(6-7):548-565.
[36]陈国俊,吕成福,王琪等.珠江口盆地深水区白云凹陷储层孔隙特征及影响因素.石油学报,2010,31(4):566-572.Chen G J,LüC F,Wang Q,et al.Characteristics of poreevolution and its controlling factors of Baiyun Sag indeepwater area of Pearl River Mouth Basin.Acta PetroleiSinica(in Chinese),2010,31(4):566-572.
[37]Tosaya C A.Acoustical properties of clay-bearing rocks[Ph.D.thesis].United States:Stanford University,1982.
[38]Batzle M L,Han D H,Hofmann R.Fluid mobility andfrequency-dependent seismic velocity-direct measurements.Geophysics,2006,71(1):N1-N9.
[2]地震勘探技术成为油气勘探主角.中国科技信息,doi:CNKI:SUN:XXJK.0.2007-18-003.The technology of seismic exploration has become theprotagonist in oil-gas exploration industry.China Science andTechnology Information,doi:CNKI:SUN:XXJK.0.2007-18-003.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.J.Acoust.Soc.Am.,1956,28(2):168-178.
[4]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range.J.Acoust.Soc.Am.,1956,28(2):179-191.
[5]Muller T M,Gurevich B,Lebedev M.Seismic waveattenuation and dispersion resulting from wave-induced flowin porous rocks-A review.Geophysics,2010,75(5):75A147-75A164.
[6]White J E.Computed seismic speeds and attenuation in rockswith partial gas saturation.Geophysics,1975,40(2):224-232.
[7]Dutta N C,Seriff A J.On White′s model of attenuation inrocks with partial gas saturation.Geophysics,1979,44(11):1806-1812.
[8]Gurevich B,Zyrianov V B,Lopatnikov S L.Seismicattenuation in finely layered porous rocks:Effects of fluidflow and scattering.Geophysics,1997,62(1):319-324.
[9]Shapiro S A,Müller T M.Seismic signatures of permeabilityin heterogeneous porous media.Geophysics,1999,64(1):99-103.
[10]Carcione J M,Picotti S.P-wave seismic attenuation by slowwave diffusion:Effects of inhomogeneous rock properties.Geophysics,2006,71(3):O1-O8.
[11]聂建新,杨顶辉,杨慧珠.基于非饱和多孔隙介质BISQ模型的储层参数反演.地球物理学报,2004,47(6):1101-1105.Nie J X,Yang D H,Yang H Z.Inversion of reservoirparameters based on the BISQ model in partially saturatedporous media.Chinese J.Geophys.(in Chinese),47(6):1101-1105.
[12]刘炯,马坚伟,杨慧珠.White球状Patchy模型中纵波传播研究.地球物理学报,2010,53(4):954-962.Liu J,Ma J W,Yang H Z.Research on P-wave's propagationin White's sphere model with patchy saturation.Chinese J.Geophys.(in Chinese),2010,53(4):954-962.
[13]Nie J X,Ba J,Yang D H,et al.BISQ model based onKelvin-Voigt viscoelastic frame in partially saturated porousmedium.Applied Geophysics,(in Press).
[14]Carcione J M,Morency C,Santos J E.Computationalporoelasticity-A review.Geophysics,2010,75(5):75A229-75A243.
[15]巴晶,卢明辉,胡彬等.黏弹双相介质中的松弛骨架模型.地球物理学报,2008,51(5):1527-1537.Ba J,Lu M H,Hu B,et al.The skeleton-relaxed model forporoviscoelastic media.Chinese J.Geophys.(in Chinese),2008,51(5):1527-1537.
[16]Dvorkin J,Nur A.Dynamic poroelasticity:A unified modelwith the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524-533.
[17]Pride S R,Berryman J G,Harris J M.Seismic attenuationdue to wave-induced flow.J.Geophys.Res.,2004,109:B01201,doi:10.1029/2003JB002639.
[18]Ba J,Carcione J M,Nie J X.Biot-Rayleigh theory of wavepropagation in double-porosity media.J.Geohpys.Res.,2011,116:B06202,doi:10.1029/2010JB008185.
[19]Liu J,Ba J,Ma J W,et al.An analysis of seismicattenuation in random porous media.Science China Physics,Mechanics&Astronomy,2010,53(4):628-637.
[20]Carcione J M,Helle H B,Pham N H.White′s model forwave propagation in partially saturated rocks:Comparisonwith poroelastic numerical experiments.Geophysics,2003,68(4):1389-1398.
[21]Berryman J G.Thoery of elastic properties of composite-materials.Appl.Phys.Lett.,1979,35(11):856-858.
[22]Rayleigh L.On the pressure developed in a liquid during thecollapse of a spherical cavity.Phil.Mag.,1917,34:94-98.
[23]Sato H,Fehler M.Seismic Wave Propagation and Scatteringin the Heterogeneous Earth.New York:Springer-Verlag,1998.
[24]Eshelby J D.The determination of the elastic field of anellipsoidal inclusion,and related problems.Proc.R.Soc.London,Ser.A,1957,241(1226):376-396.
[25]Kuster G T,Toksz M N.Velocity and attenuation of seismicwaves in two-phase media:I.Theoretical formulations.Geophysics,1974,39(5):587-606.
[26]Ba J,Nie J X,Cao H,et al.Mesoscopic fluid flowsimulation in double-porosity rocks.Geophys.Res.Lett.,2008,35:L04303,doi:10.1029/2007GL032429.
[27]Ba J,Yang H Z,Xie G Q.AGILD seismic modelling fordouble-porosity media.PIERS 2008in Hangzhou.Cambridge:The Electromagnetics Academy.2008.
[28]Ba J,Cao H,Yao F C,et al.Double-porosity rock modeland squirt flow in the laboratory frequency band.AppliedGeophysics,2008,5(4):261-276.
[29]Ba J,Cao H,Yao F C.Pore heterogeneity induces double-porosity in Guang′an sandstone.∥CPS/SEG Beijing.Beijing:Society of Petroleum Geophysics,2009.
[30]巴晶.双重孔隙介质波传播理论与地震响应实验分析.中国科学G辑,2010,40(11):1398-1409.Ba J.Wave propagation theory in double-porosity mediumand experimental analysis on seismic responses.ScientiaSinica Physica,Mechanica&Astronomica(in Chinese),2010,40(11):1398-1409.
[31]Ba J,Cao H,Yao F C.Velocity dispersion of P waves insandstone and carbonate:Double-porosity and local fluid flowtheory.SEG Expanded Abstracts,Denver,US,2010.
[32]Berryman J G,Wang H F.Double porosity modelling inelastic wave propagation for reservoir characterization.∥SPIE Conference on Mathematical Methods in GeophysicalImaging V.San Diego California:SPIE Press,1998.
[33]Johnson D L.Recent developments in the acoustic propertiesof porous media.∥Sette D.Frontiers in Physical AcousticsXCIII.New York:North Holland Elsevier.1987:255-290.
[34]Johnson D L.Theory of frequency dependent acoustics inpatchy saturated porous media.J.Acoust.Soc.Am.,2001,110(2):682-694.
[35]Toms J,Müller T M,Ciz R,et al.Comparative review oftheoretical models for elastic wave attenuation and dispersionin partially saturated rocks.Soil Dynamics and EarthquakeEngineering,2006,26(6-7):548-565.
[36]陈国俊,吕成福,王琪等.珠江口盆地深水区白云凹陷储层孔隙特征及影响因素.石油学报,2010,31(4):566-572.Chen G J,LüC F,Wang Q,et al.Characteristics of poreevolution and its controlling factors of Baiyun Sag indeepwater area of Pearl River Mouth Basin.Acta PetroleiSinica(in Chinese),2010,31(4):566-572.
[37]Tosaya C A.Acoustical properties of clay-bearing rocks[Ph.D.thesis].United States:Stanford University,1982.
[38]Batzle M L,Han D H,Hofmann R.Fluid mobility andfrequency-dependent seismic velocity-direct measurements.Geophysics,2006,71(1):N1-N9.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心