非均质天然气藏的岩石物理模型及含气饱和度反演
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摘要
非均质气藏中,天然气一般呈"斑块状"分布于含水岩石内部,这种非均匀分布特征会导致地震波显著的频散与衰减现象.为发展适用于碳酸盐岩储层中流体检测的岩石物理模型,本文基于Biot-Rayleigh波动方程,实现了对非饱和岩石的多尺度理论建模,预测了不同尺度下波响应与岩性、流体间的定量联系.将此项建模技术应用于阿姆河右岸的灰岩气藏,给出了多尺度的岩石物理学图板.通过与实验数据、测井精细解释结果及地震数据的对比分析,本文论证了图板的正确性与可适用性.结合叠后波阻抗反演与叠前弹性参数反演,基于地震资料进行了储层含气饱和度与孔隙度的反演,反演结果与各井实际的产气情况吻合.
In heterogeneous natural gas reservoirs,generally gas forms countless small "patchy"-like packets embedded in the host matrix of water-saturated rocks.This heterogeneity feature(also called the "patchy-saturation") causes significant velocity dispersion and attenuation phenomena for seismic wave propagation.To build an appropriate rock physics model for the application of fluid identification in carbonate reservoirs,multi-scale theoretical modeling is performed for partially-saturated rocks and the quantitative relations between wave responses in different scales and basic properties of lithology and pore fluids are predicted.This approach of modeling is applied in limestone gas reservoirs of the right bank block of Amu Darya river.A multi-scale rock physics template is presented.Comparisons with experimental data,fine interpretation results of log data and seismic data have proved its validity and applicability.In combination with the methods of post-stack wave-impedance inversion and pre-stack elastic parameter inversion,seismic data is used to estimate rock porosity and gas saturation of the reservoirs.The results of estimate are in good agreement with the production status of the wells.
In heterogeneous natural gas reservoirs,generally gas forms countless small "patchy"-like packets embedded in the host matrix of water-saturated rocks.This heterogeneity feature(also called the "patchy-saturation") causes significant velocity dispersion and attenuation phenomena for seismic wave propagation.To build an appropriate rock physics model for the application of fluid identification in carbonate reservoirs,multi-scale theoretical modeling is performed for partially-saturated rocks and the quantitative relations between wave responses in different scales and basic properties of lithology and pore fluids are predicted.This approach of modeling is applied in limestone gas reservoirs of the right bank block of Amu Darya river.A multi-scale rock physics template is presented.Comparisons with experimental data,fine interpretation results of log data and seismic data have proved its validity and applicability.In combination with the methods of post-stack wave-impedance inversion and pre-stack elastic parameter inversion,seismic data is used to estimate rock porosity and gas saturation of the reservoirs.The results of estimate are in good agreement with the production status of the wells.
引文
[1]Gassmann F.ber die Elastizitt porser Medien.Vier.derNatur.Gesellschaft in Zürich,1951,96:1-23.
[2]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.
[3]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.
[4]White J E.Computed seismic speeds and attenuation in rockswith partial gas saturation.Geophysics,1975,40(2):224-232.
[5]Dutta N C,Seriff A J.On White’s model of attenuation inrocks with partial gas saturation.Geophysics,1979,44(11):1806-1812.
[6]Dutta N C,OdéH.Attenuation and dispersion ofcompressional waves in fluid-filled porous rocks with partialgas saturation(White model),Part I:Biot theory.Geophysics,1979,44(11):1777-1788.
[7]Johnson D L.Theory of frequency dependent acoustics inpatchy-saturated porous media.J.Acoust.Soc.Am.,2001,110(2):682-694.
[8]Müller 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.
[9]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.
[10]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.
[11]Dvorkin J,Nur A.Dynamic poroelasticity:A unified modelwith the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524-533.
[12]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),2004,47(6):1101-1105.
[13]Nie J X,Ba J,Yang D H,et al.BISQ model based on aKelvin-Voigt viscoelastic frame in a partially saturated porousmedium.Applied Geophysics,2012,9(2):213-222.
[14]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.
[15]刘炯,马坚伟,杨慧珠.周期成层Patchy模型中纵波的频散和衰减研究.地球物理学报,2009,52(11):2879-2885.Liu J,Ma J W,Yang H Z.Research on dispersion andattenuation of P wave in periodic layered-model with patchysaturation.Chinese J.Geophys.(in Chinese),2009,52(11):2879-2885.
[16]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.
[17]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.
[18]Ba J,Cao H,Yao F C,et al.Double-porosity rock modeland squirt flow in the laboratory frequency band.Appl.Geophys.,2008,5(4):261-276.
[19]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.
[20]Ba J,Yang H Z,Xie G Q.AGILD seismic modeling fordouble-porosity media.Piers Online,2008,4(3):doi:10.2529/PIERS071107235651.
[21]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.
[22]Ba J,Cao H,Yao F C.Velocity dispersion of P-waves insandstone and carbonate:Double-porosity and local fluid flowtheory.SEG Annual Meeting 2010,Denver,US,2010:2557-2563.
[23]巴晶,Carcione J M,曹宏等.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.地球物理学报,2012,55(1):219-231.Ba J,Carcione J M,Cao H,et al.Velocity dispersion andattenuation of P waves in partially-saturated rocks:Wavepropagation equations in double-porosity medium.Chinese J.Geophys.(in Chinese),2012,55(1):219-231.
[24]Sun W T,Ba J,Müller T M,et al.P-wave dispersion andattenuation in patchy-saturated Rocks.White,Dutta,Johnson and Biot-Rayleigh theories,The 74th EAGE2012inCopenhagen,2012,Copenhagen,Denmark.
[25]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J.Geophys.Res.,1995,100(B12):24611-24627.
[26]Berryman J G,Wang H F.Elastic wave propagation andattenuation in a double-porosity dual-permeability medium.Int.J.Rock Mech.Min.Sci.,2000,37(1-2):63-78.
[27]Santos J E,CorberóJ M,Douglas J.Static and dynamicbehavior of a porous solid saturated by a two-phase fluid.J.Acoust.Soc.Am.,1990,87(4):1428-1438.
[28]Santos J E,Douglas J,CorberóJ M,et al.A model for wavepropagation in a porous medium saturated by a two-phasefluid.J.Acoust.Soc.Am.,1990,87(4):1439-1448.
[29]赵海波.不相混气液饱和孔隙介质声场数值模拟与应用研究[博士论文].北京:中国科学院声学研究所,2007.Zhao H B.Numerical study of acoustic wavefield in porousmedia saturated with two immiscible fluids and its application[Ph.D.thesis](in Chinese).Beijing:Institute of Acoustics,Chinese Academy of Sciences,2007.
[30]Johnson D L,Koplik J,Dashen R.Theory of dynamicpermeability and tortuosity in fluid-saturated porous media.J.Fluid Mech.,1987,176:379-402.
[31]唐晓明.含孔隙、裂隙介质弹性波动的统一理论——Biot理论的推广.中国科学(地球科学),2011,41(6):784-785.Tang X M.A unified theory for elastic wave propagationthrough porous media containing cracks:An extension ofBiot′s poroelastic wave theory.Science China EarthSciences,2011,54(9):1441-1452.
[32]陈雪莲,唐晓明.孔、裂隙并存地层中的声波测井理论及多极子声场特征.地球物理学报,2012,55(6):2129-2140.Chen X L,Tang X M.Numerical study on the characteristicsof acoustic logging response in the fluid-filled boreholeembedded in crack-porous medium.Chinese J.Geophys.(inChinese),2012,55(6):2129-2140.
[33]Rayleigh L.On the pressure developed in a liquid during thecollapse of a spherical cavity.Philos.Mag.,1917,34(200):94-98.
[34]Xu S Y,White R E.A physical model for shear-wavevelocity prediction.Geophysical Prospecting,1995,44(4):687-717.
[35]Xu S Y,Payne M A.Modeling elastic properties in carbonaterocks.The Leading Edge,2009,28(1):66-74.
[36]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook-Tools for Seismic Analysis of Porous Media(2nded).New York:Cambridge University Press,2009.
[37]Norris A N.A differential scheme for the effective moduli ofcomposites.Mechanics of Materials,1985,4(1):1-16.
[38]Kuster G T,Toksz M N.Velocity and attenuation ofseismic waves in two-phase media:Part I.Theoreticalformulations.Geophysics,1974,39(5):587-606.
[39]Sams M S,Neep J P,Worthington M H,et al.Themeasurement of velocity dispersion and frequency-dependentintrinsic attenuation in sedimentary rocks.Geophysics,1997,62(5):1456-1464.
[40]徐光成,巴晶,李劲松等.阿姆河右岸麦捷让地区碳酸盐岩储层流体检测研究.地球物理学进展,2013,28(3),待刊.Xu G C,Ba J,Li J S,et al.A study on fluid detection inMetajan carbonate reservoirs in the right bank block of AmuDarya river.Progress in Geophys.(in Chinese),2013,28(3),in press.
[41]Adam L,Batzle M,Brevik I.Gassmann′s fluid substitutionand shear modulus variability in carbonates at laboratoryseismic and ultrasonic frequencies.Geophysics,2006,71(6):F13-F183.
[42]Cadoret T,Marion D,Zinszner B.Influence of frequency andfluid distribution on elastic wave velocities in partiallysaturated limestones.J.Geophys.Res.,1995,100(B6):9789-9803.
[2]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.
[3]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.
[4]White J E.Computed seismic speeds and attenuation in rockswith partial gas saturation.Geophysics,1975,40(2):224-232.
[5]Dutta N C,Seriff A J.On White’s model of attenuation inrocks with partial gas saturation.Geophysics,1979,44(11):1806-1812.
[6]Dutta N C,OdéH.Attenuation and dispersion ofcompressional waves in fluid-filled porous rocks with partialgas saturation(White model),Part I:Biot theory.Geophysics,1979,44(11):1777-1788.
[7]Johnson D L.Theory of frequency dependent acoustics inpatchy-saturated porous media.J.Acoust.Soc.Am.,2001,110(2):682-694.
[8]Müller 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.
[9]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.
[10]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.
[11]Dvorkin J,Nur A.Dynamic poroelasticity:A unified modelwith the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524-533.
[12]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),2004,47(6):1101-1105.
[13]Nie J X,Ba J,Yang D H,et al.BISQ model based on aKelvin-Voigt viscoelastic frame in a partially saturated porousmedium.Applied Geophysics,2012,9(2):213-222.
[14]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.
[15]刘炯,马坚伟,杨慧珠.周期成层Patchy模型中纵波的频散和衰减研究.地球物理学报,2009,52(11):2879-2885.Liu J,Ma J W,Yang H Z.Research on dispersion andattenuation of P wave in periodic layered-model with patchysaturation.Chinese J.Geophys.(in Chinese),2009,52(11):2879-2885.
[16]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.
[17]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.
[18]Ba J,Cao H,Yao F C,et al.Double-porosity rock modeland squirt flow in the laboratory frequency band.Appl.Geophys.,2008,5(4):261-276.
[19]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.
[20]Ba J,Yang H Z,Xie G Q.AGILD seismic modeling fordouble-porosity media.Piers Online,2008,4(3):doi:10.2529/PIERS071107235651.
[21]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.
[22]Ba J,Cao H,Yao F C.Velocity dispersion of P-waves insandstone and carbonate:Double-porosity and local fluid flowtheory.SEG Annual Meeting 2010,Denver,US,2010:2557-2563.
[23]巴晶,Carcione J M,曹宏等.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.地球物理学报,2012,55(1):219-231.Ba J,Carcione J M,Cao H,et al.Velocity dispersion andattenuation of P waves in partially-saturated rocks:Wavepropagation equations in double-porosity medium.Chinese J.Geophys.(in Chinese),2012,55(1):219-231.
[24]Sun W T,Ba J,Müller T M,et al.P-wave dispersion andattenuation in patchy-saturated Rocks.White,Dutta,Johnson and Biot-Rayleigh theories,The 74th EAGE2012inCopenhagen,2012,Copenhagen,Denmark.
[25]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J.Geophys.Res.,1995,100(B12):24611-24627.
[26]Berryman J G,Wang H F.Elastic wave propagation andattenuation in a double-porosity dual-permeability medium.Int.J.Rock Mech.Min.Sci.,2000,37(1-2):63-78.
[27]Santos J E,CorberóJ M,Douglas J.Static and dynamicbehavior of a porous solid saturated by a two-phase fluid.J.Acoust.Soc.Am.,1990,87(4):1428-1438.
[28]Santos J E,Douglas J,CorberóJ M,et al.A model for wavepropagation in a porous medium saturated by a two-phasefluid.J.Acoust.Soc.Am.,1990,87(4):1439-1448.
[29]赵海波.不相混气液饱和孔隙介质声场数值模拟与应用研究[博士论文].北京:中国科学院声学研究所,2007.Zhao H B.Numerical study of acoustic wavefield in porousmedia saturated with two immiscible fluids and its application[Ph.D.thesis](in Chinese).Beijing:Institute of Acoustics,Chinese Academy of Sciences,2007.
[30]Johnson D L,Koplik J,Dashen R.Theory of dynamicpermeability and tortuosity in fluid-saturated porous media.J.Fluid Mech.,1987,176:379-402.
[31]唐晓明.含孔隙、裂隙介质弹性波动的统一理论——Biot理论的推广.中国科学(地球科学),2011,41(6):784-785.Tang X M.A unified theory for elastic wave propagationthrough porous media containing cracks:An extension ofBiot′s poroelastic wave theory.Science China EarthSciences,2011,54(9):1441-1452.
[32]陈雪莲,唐晓明.孔、裂隙并存地层中的声波测井理论及多极子声场特征.地球物理学报,2012,55(6):2129-2140.Chen X L,Tang X M.Numerical study on the characteristicsof acoustic logging response in the fluid-filled boreholeembedded in crack-porous medium.Chinese J.Geophys.(inChinese),2012,55(6):2129-2140.
[33]Rayleigh L.On the pressure developed in a liquid during thecollapse of a spherical cavity.Philos.Mag.,1917,34(200):94-98.
[34]Xu S Y,White R E.A physical model for shear-wavevelocity prediction.Geophysical Prospecting,1995,44(4):687-717.
[35]Xu S Y,Payne M A.Modeling elastic properties in carbonaterocks.The Leading Edge,2009,28(1):66-74.
[36]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook-Tools for Seismic Analysis of Porous Media(2nded).New York:Cambridge University Press,2009.
[37]Norris A N.A differential scheme for the effective moduli ofcomposites.Mechanics of Materials,1985,4(1):1-16.
[38]Kuster G T,Toksz M N.Velocity and attenuation ofseismic waves in two-phase media:Part I.Theoreticalformulations.Geophysics,1974,39(5):587-606.
[39]Sams M S,Neep J P,Worthington M H,et al.Themeasurement of velocity dispersion and frequency-dependentintrinsic attenuation in sedimentary rocks.Geophysics,1997,62(5):1456-1464.
[40]徐光成,巴晶,李劲松等.阿姆河右岸麦捷让地区碳酸盐岩储层流体检测研究.地球物理学进展,2013,28(3),待刊.Xu G C,Ba J,Li J S,et al.A study on fluid detection inMetajan carbonate reservoirs in the right bank block of AmuDarya river.Progress in Geophys.(in Chinese),2013,28(3),in press.
[41]Adam L,Batzle M,Brevik I.Gassmann′s fluid substitutionand shear modulus variability in carbonates at laboratoryseismic and ultrasonic frequencies.Geophysics,2006,71(6):F13-F183.
[42]Cadoret T,Marion D,Zinszner B.Influence of frequency andfluid distribution on elastic wave velocities in partiallysaturated limestones.J.Geophys.Res.,1995,100(B6):9789-9803.
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