几种岩石骨架模型的适用性研究
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摘要
在地震岩石物理中,Biot-Gassmann理论通常用来研究饱和流体对岩石地震特征的影响以及描述地震响应与岩石物性之间的关系.然而Biot-Gassmann理论并没有阐述多孔岩石的骨架与基质之间的关系,因此出现了各种各样的岩石骨架模型分别从不同的角度建立了岩石骨架与岩石基质之间的关系,如Krief模型、Nur模型(临界孔隙度模型)和Pride模型等都是广泛使用的岩石骨架模型.本文将这些常见的岩石骨架模型应用于Biot-Gassmann理论中,进行理论模型正演、速度预测以及Biot系数计算等,并与实验室测量数据对比,分析发现Pride模型比Krief模型和Nur模型的适用范围更广,以及Krief模型和Nur模型不能适用于低压、低孔岩石的特点.
In the study of seismic rock physics,Biot-Gassmann theory is one of the most classic and practical instruments which is used to calculate the effect of fluid saturation on seismic properties and to predict the relation between the elastic velocities and the physical properties of porous rocks.But Biot-Gassmann theory does not illuminate the relation between the moduli of the dry frame and that of the matrix.There are several models which illustrate the relation from different aspects,such as the Krief model,Nur model (critical porosity model),Pride model,etc.They are the most popular models.We have applied the Krief model,Nur model and Pride model to Biot-Gassmann theory,through forward modelling,predicting velocity and calculating Biot coefficient,compared with core samples measured in laboratory,to check their accuracy and applicability.We found that the Pride model could work well consistently;while the Krief model and Nur model could only exhibit their applicability under normal conditions and fail in other conditions;and more importantly,the last two models could not work well when the porosity of rocks is low or the effective pressure is low.
In the study of seismic rock physics,Biot-Gassmann theory is one of the most classic and practical instruments which is used to calculate the effect of fluid saturation on seismic properties and to predict the relation between the elastic velocities and the physical properties of porous rocks.But Biot-Gassmann theory does not illuminate the relation between the moduli of the dry frame and that of the matrix.There are several models which illustrate the relation from different aspects,such as the Krief model,Nur model (critical porosity model),Pride model,etc.They are the most popular models.We have applied the Krief model,Nur model and Pride model to Biot-Gassmann theory,through forward modelling,predicting velocity and calculating Biot coefficient,compared with core samples measured in laboratory,to check their accuracy and applicability.We found that the Pride model could work well consistently;while the Krief model and Nur model could only exhibit their applicability under normal conditions and fail in other conditions;and more importantly,the last two models could not work well when the porosity of rocks is low or the effective pressure is low.
引文
[1] Avseth P,Mukerji T,Mavko G.Quantitative seismic interpretation:applying rock physics tools to reduce interpretation risk[M].Cambridge University Press,1998．
[2] Wang Z J.Fundamentals of seismic rock physics[J].Geophysics,2001,66(2) :398～412．
[3] Biot M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,I,Low-frequency range;Ⅱ,higher frequency range[J].Journal of Acoustical Society of America,1956,28:168～191．
[4] Geertsma J,Smit J C.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophysics,1961,26:169～181．
[5] Gassmann F.Uber die elastizitat poroser medien:verteljahrsschrift der naturforschenden gesellschaft in zurich[J].1951,96:1～23．
[6] Digby P J.The effective elastic moduli of porous granular rocks[J].Journal of Applied Mechanics,1981,48:803～808．
[7] Murphy W FIII.Acoustic measures of partial gas saturation in tight sandstones[J].Journal of Geophysical Research,1984,89:11549～11559．
[8] Winkler K W.Contact stiffness in granular porous materials-Comparison between theory and experiment[J].Geophysical Research Letters,1983,10:1073～1076．
[9] Pickett G R.Acoustic character logs and their applications in formation evaluation[J].Journal of Petroleum Technology,1963,15:650～667．
[10] Raymer L L,Hunt E R,Gardner J S.An improved sonic transit time-to-porosity transform[J].21st Ann.Logg.Symp.,SPWLA.1980(p).
[11] Krief M,Garat J,Stellingwerff J,et al.A petrophysical interpretation using the velocities of P and S waves (full-waveform sonic)[J].The Log Analyst,1990,31:355～369．
[12] Nur A.Critical porosity and the seismic velocities in rocks[J].EOS,Trans.Am.Geophys.Union,1992,73:43～66．
[13] Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-induced flow[J].Journal of Geophysical Research,2004,109,No.B1,B01201．
[14] Lee M W.A simple method of predicting S-wave velocity[J].Geophysics,2006,69(5) :161～164．
[15] Gregory A R.Fluid saturation effects on dynamic elastic properties of sedimentary rocks[J].Geophysics,1976,41:895～921．
[16] Coyner K B.Effects of stress,pore pressure,and pore fluids on bulk strain,velocity and permeability in rocks[D].Ph.D.dissertation,Massachusetts Institute of Technology.1984．
[17] Domenico S N.Elastic properties of unconsolidated porous sandreservoirs[J].Geophysics,1977,42:1339～1368．
[18] Han D H,Nur A,Morgan D.Effects of porosity and clay content on wave velocities[J].Geophysics,1986,51:2093～2107．
[19] Jizba D L.Mechanical and acoustic properties of sandstones and shales[D].Ph.D.dissertation,Stanford University,1991．
[20] Freund D.Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity,clay content,and confining pressure[J].Geophysical Journal International,1992,108:125～135．
[21] Hill R.The elastic behavior of crystalline aggregate[J].Proceedings of the Physical Society,London,1952,A65:349～354．
[22] Voigt W.Lehrbuch der kristallphysik[J].Teubner,1928．
[23] Reuss A.Berechnung der fliessgrenze von mischkristallen auf grund der Plastizit? tsbedingungen für einkristalle[J].Zeitschrift für Angewandte Mathematic undMechanik,1929,9:49～58．
[24] Mavko G,Mukerji T,Dvoskin J.The rock physics handbook[M].Cambridge University Press,1998．
[25] Wang Z J.Dynamic versus static elastic properties of reservoir rocks[J].Seismic and Acoustic Velocities in Reservoir Rocks,Society of Exploration Geophysics,Tulsa,2000,19:531～539．
[26] 马中高,解吉高.岩石的纵横波速度与密度的规律研究[J].地球物理学进展,2005,20(4) :905～910． Ma Z G,Xie J G.Relationship among compressional wave,shear wave velocities and density of rocks[J].Progress in Geophysics (inChinese),2005,20(4) :905～910．
[27] 孙福利,杨长春,麻三怀,等.横波速度预测方法[J].地球物理学进展,2008,23(2) :470～474． Sun F L,Yang C C,Ma S H,et al.An S-wave velocity predicted method[J].Progress in Geophysics,2008,23 (2) :470～474．
[28] 徐胜峰,李勇根,曹宏,等.地震岩石物理研究概述[J].地球物理学进展,2009,24(2) :680～691． Xu S F,Li Y G,Cao H,et al.A review of seismic rock physics.Progress in Geophysics (in Chinese),2009,24(2) :680～691．
[2] Wang Z J.Fundamentals of seismic rock physics[J].Geophysics,2001,66(2) :398～412．
[3] Biot M A.Theory of propagation of elastic waves in a fluidsaturated porous solid,I,Low-frequency range;Ⅱ,higher frequency range[J].Journal of Acoustical Society of America,1956,28:168～191．
[4] Geertsma J,Smit J C.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophysics,1961,26:169～181．
[5] Gassmann F.Uber die elastizitat poroser medien:verteljahrsschrift der naturforschenden gesellschaft in zurich[J].1951,96:1～23．
[6] Digby P J.The effective elastic moduli of porous granular rocks[J].Journal of Applied Mechanics,1981,48:803～808．
[7] Murphy W FIII.Acoustic measures of partial gas saturation in tight sandstones[J].Journal of Geophysical Research,1984,89:11549～11559．
[8] Winkler K W.Contact stiffness in granular porous materials-Comparison between theory and experiment[J].Geophysical Research Letters,1983,10:1073～1076．
[9] Pickett G R.Acoustic character logs and their applications in formation evaluation[J].Journal of Petroleum Technology,1963,15:650～667．
[10] Raymer L L,Hunt E R,Gardner J S.An improved sonic transit time-to-porosity transform[J].21st Ann.Logg.Symp.,SPWLA.1980(p).
[11] Krief M,Garat J,Stellingwerff J,et al.A petrophysical interpretation using the velocities of P and S waves (full-waveform sonic)[J].The Log Analyst,1990,31:355～369．
[12] Nur A.Critical porosity and the seismic velocities in rocks[J].EOS,Trans.Am.Geophys.Union,1992,73:43～66．
[13] Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-induced flow[J].Journal of Geophysical Research,2004,109,No.B1,B01201．
[14] Lee M W.A simple method of predicting S-wave velocity[J].Geophysics,2006,69(5) :161～164．
[15] Gregory A R.Fluid saturation effects on dynamic elastic properties of sedimentary rocks[J].Geophysics,1976,41:895～921．
[16] Coyner K B.Effects of stress,pore pressure,and pore fluids on bulk strain,velocity and permeability in rocks[D].Ph.D.dissertation,Massachusetts Institute of Technology.1984．
[17] Domenico S N.Elastic properties of unconsolidated porous sandreservoirs[J].Geophysics,1977,42:1339～1368．
[18] Han D H,Nur A,Morgan D.Effects of porosity and clay content on wave velocities[J].Geophysics,1986,51:2093～2107．
[19] Jizba D L.Mechanical and acoustic properties of sandstones and shales[D].Ph.D.dissertation,Stanford University,1991．
[20] Freund D.Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity,clay content,and confining pressure[J].Geophysical Journal International,1992,108:125～135．
[21] Hill R.The elastic behavior of crystalline aggregate[J].Proceedings of the Physical Society,London,1952,A65:349～354．
[22] Voigt W.Lehrbuch der kristallphysik[J].Teubner,1928．
[23] Reuss A.Berechnung der fliessgrenze von mischkristallen auf grund der Plastizit? tsbedingungen für einkristalle[J].Zeitschrift für Angewandte Mathematic undMechanik,1929,9:49～58．
[24] Mavko G,Mukerji T,Dvoskin J.The rock physics handbook[M].Cambridge University Press,1998．
[25] Wang Z J.Dynamic versus static elastic properties of reservoir rocks[J].Seismic and Acoustic Velocities in Reservoir Rocks,Society of Exploration Geophysics,Tulsa,2000,19:531～539．
[26] 马中高,解吉高.岩石的纵横波速度与密度的规律研究[J].地球物理学进展,2005,20(4) :905～910． Ma Z G,Xie J G.Relationship among compressional wave,shear wave velocities and density of rocks[J].Progress in Geophysics (inChinese),2005,20(4) :905～910．
[27] 孙福利,杨长春,麻三怀,等.横波速度预测方法[J].地球物理学进展,2008,23(2) :470～474． Sun F L,Yang C C,Ma S H,et al.An S-wave velocity predicted method[J].Progress in Geophysics,2008,23 (2) :470～474．
[28] 徐胜峰,李勇根,曹宏,等.地震岩石物理研究概述[J].地球物理学进展,2009,24(2) :680～691． Xu S F,Li Y G,Cao H,et al.A review of seismic rock physics.Progress in Geophysics (in Chinese),2009,24(2) :680～691．
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