数字岩心逆建模理论下的储层参数定量预测方法
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摘要
数字岩心微观孔隙结构十分复杂,有限元模拟物性参数与弹性参数之间关系是非线性的,直接反演其物性参数准确度低、稳定性差.本文发展了一种数字岩石物理逆建模方法,实现了基于数字岩心的储层参数有效预测.从数字岩心基函数的构建出发,基于有限元方法,计算了一系列具有等间距物性参数值(孔隙度、泥质含量和含水饱和度)的数字岩心弹性参数(体积模量、剪切模量和密度),通过插值算法建立了数字岩心弹性参数三维数据集,从而实现了弹性模量的有限元数值解的快速构建;然后搜索弹性参数的单值等值面,通过等值面的空间交会得到交点,完成储层参数预测.测试结果表明:基于数字岩心逆建模理论的储层参数预测结果与实际模型一致,具有可行性,并且可以通过增加插值点数目提高预测的准确性;孔隙度和泥质含量预测结果稳定性很好,而含水饱和度对噪声的加入较为敏感.
The microstructure of the digital core is complex and the relationship between reservoir parameters and elastic parameters is nonlinear.Therefore,it is difficult to calculate the reservoir parameters directly.This paper apply the inverse rock physics modeling method to the digital core to estimate the reservoir properties.The elastic parameters of digital core with equal spacing reservoir parameters are calculated by finite element method.Then,an improved Lagrange interpolation algorithm is used to fit the calculation formula of the elastic parameters of digital cores.Based on the digital core basis function,we establish the digital core dataset in 3-D spatial domain to determine the link between the geophysical parameters and reservoir parameters,which constructs the finite element numerical solution of elastic modulus quickly.The digital core inverse modeling is to search the single value isosurface of the elastic parameters(K,μ,ρ)in 3-D database,intersect the isosurface and get the coordinates of the intersection point,which are the values of the reservoir parameters.Tests show that,the inverse digital rock physics modeling method for reservoir parameter prediction of digital cores is feasible,and the accuracy of the prediction can be improved by increasing the number of interpolation points.The prediction results ofporosity and shale content are very stable,while water saturation is more sensitive to noise.
The microstructure of the digital core is complex and the relationship between reservoir parameters and elastic parameters is nonlinear.Therefore,it is difficult to calculate the reservoir parameters directly.This paper apply the inverse rock physics modeling method to the digital core to estimate the reservoir properties.The elastic parameters of digital core with equal spacing reservoir parameters are calculated by finite element method.Then,an improved Lagrange interpolation algorithm is used to fit the calculation formula of the elastic parameters of digital cores.Based on the digital core basis function,we establish the digital core dataset in 3-D spatial domain to determine the link between the geophysical parameters and reservoir parameters,which constructs the finite element numerical solution of elastic modulus quickly.The digital core inverse modeling is to search the single value isosurface of the elastic parameters(K,μ,ρ)in 3-D database,intersect the isosurface and get the coordinates of the intersection point,which are the values of the reservoir parameters.Tests show that,the inverse digital rock physics modeling method for reservoir parameter prediction of digital cores is feasible,and the accuracy of the prediction can be improved by increasing the number of interpolation points.The prediction results ofporosity and shale content are very stable,while water saturation is more sensitive to noise.
引文
Arns C H,Knackstedt M A,Pinczewski W V,et al.2002.Computation of linear elastic properties from microtomographic images:methodology and agreement between theory and experiment.Geophysics,67(5):1396-1405.
Blunt M J.2001.Flow in porous media-pore-network models and multiphase flow.Current Opinion in Colloid&Interface Science,6(3):197-207.
Bohn R B,Garboczi E J.2003.User manual for finite element difference programs:A parallel version of NISTIR 6269.Gaithersburg,MD:National Institute of Standards and Technology Internal Report 6997.
Bredesen K,Jensen E H,Johansen T A,et al.2015.Seismic reservoir and source-rock analysis using inverse rock-physics modeling:A Norwegian Sea demonstration.The Leading Edge,34(11):1350-1355.
Garboczi E J,Day A R.1995.An algorithm for computing the effective linear elastic properties of heterogeneous materials:Three-dimensional results for composites with equal phase Poisson ratio.Journal of the Mechanics and Physics of Solids,43(9):1349-1362.
Grechka V,Vasconcelos I,Kachanov M.2006.The influence of crack shape on the effective elasticity of fractured rocks.Geophysics,71(5):D153-D160.
Johansen T A,Spikes K,Dvorkin J.2004.Strategy for estimation of lithology and reservoir properties from seismic velocities and density.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1726-1729.
Johansen T A,Jensen E H,Mavko G,et al.2013.Inverse rock physics modeling for reservoir quality prediction.Geophysics,78(2):M1-M18.
Knackstedt M A,Arns C H,Pinczewski W V.2003.Velocityporosity relationships,1:accurate velocity model for clean consolidated sandstones.Geophysics,68(6):1822-1834.
Liu Q,Yin X Y,Li C.2016.Quantitative prediction of reservoir characteristics based on inverse modeling theory.Chinese Journal of Geophysics(in Chinese),59(9):3491-3502,doi:10.6038/cjg20160931.
Liu Q,Dong N,Ji Y X.2017.Reservoir parameter prediction based on a constrained inverse rock physics modeling method.∥CGS/SEG Expanded Abstracts,1225-1228.
Liu X F.2010.Numerical simulation of elastic and electrical properties of rock based on digital cores[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum.
Liu X J,Zhu H L,Liang L X.2014.Digital rock physics of sandstone based on micro-CT technology.Chinese Journal of Geophysics(in Chinese),57(4):1133-1140,doi:10.6038/cjg20140411.
Mavko G,Mukerji T,Dvorkin J.1998.The Rock Physics Handbook:Tools for Seismic Analysis in Porous Media.Cambridge:Cambridge University Press.
Moyano B,Jensen E H,Johansen T A.2011.Improved quantitative calibration of rock physics models.Petroleum Geoscience,17(4):345-354.
Moyano B,Jensen E H,Johansen T A.2015.Spatial constrained inverse rock physics modelling.Geophysical Prospecting,63(1):183-191.
Saenger E H,Gold N,Shapiro S A.2000.Modeling the propagation of elastic waves using a modified finite-difference grid.Wave Motion,31(1):77-92.
Saenger E H,Shapiro S A.2002.Effective velocities in fractured media:a numerical study using the rotated staggered finitedifferenced grid.Geophysical Prospecting,50(2):183-194.
Saenger E H,Krüger O S,Shapiro S A.2004.Numerical considerations of fluid effects on wave propagation:Influence of the tortuosity.Geophysical Research Letters,31(21):L21613,doi:10.1029/2004GL020970.
Saenger E H,Enzmann F,Keehm Y,et al.2011.Digital rock physics:Effect of fluid viscosity on effective elastic properties.Journal of Applied Geophysics,74(4):236-241.
Sain R.2010.Numerical simulation of pore-scale heterogeneity and its effects on elastic,electrical and transport properties[Ph.D.thesis].Stanford:Stanford University.
Yin X Y,Zong Z Y,Wu G C.2015.Research on seismic fluid identification driven by rock physics.Science China Earth Sciences,58(2):159-171,doi:10.1007/s11430-014-4992-3.
Yin X Y,Zheng Y,Zong Z Y.2017.Research on the equivalence between digital core and rock physics models.Journal of Geophysics and Engineering,14(3):666-674.
Zhang J Y,Sun J M.2012.Rock elastic properties determined by using digital rock and effective medium model.Journal of Oil and Gas Technology(in Chinese),34(2):65-70.
Zhang Y,Toks9z M N.2012.Impact of the cracks lost in the imaging process on computing linear elastic properties from 3Dmicrotomographic images of Berea sandstone.Geophysics,77(2):R95-R104.
Zong Z Y,Yin X Y,Wu G C.2015.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion.Surveys in Geophysics,36(5):659-681.
Zong Z Y,Yin X Y.2017.Model parameterization and p-wave AVA direct inversion for Young′s impedance.Pure and Applied Geophysics,174(5):1965-1981.
刘学锋.2010.基于数字岩心的岩石声电特性微观数值模拟研究[博士论文].青岛:中国石油大学.
刘向君,朱洪林,梁利喜.2014.基于微CT技术的砂岩数字岩石物理实验.地球物理学报,57(4):1133-1140,doi:10.6038/cjg20140411.
刘倩,印兴耀,李超.2016.基于逆建模理论的储层特征定量预测方法.地球物理学报,59(9):3491-3502,doi:10.6038/cjg20160931.
印兴耀,宗兆云,吴国忱.2015.岩石物理驱动下地震流体识别研究.中国科学:地球科学,45(1):8-21.
张晋言,孙建孟.2012.应用数字岩心和有效介质模型研究岩石弹性性质.石油天然气学报,34(2):65-70.
Blunt M J.2001.Flow in porous media-pore-network models and multiphase flow.Current Opinion in Colloid&Interface Science,6(3):197-207.
Bohn R B,Garboczi E J.2003.User manual for finite element difference programs:A parallel version of NISTIR 6269.Gaithersburg,MD:National Institute of Standards and Technology Internal Report 6997.
Bredesen K,Jensen E H,Johansen T A,et al.2015.Seismic reservoir and source-rock analysis using inverse rock-physics modeling:A Norwegian Sea demonstration.The Leading Edge,34(11):1350-1355.
Garboczi E J,Day A R.1995.An algorithm for computing the effective linear elastic properties of heterogeneous materials:Three-dimensional results for composites with equal phase Poisson ratio.Journal of the Mechanics and Physics of Solids,43(9):1349-1362.
Grechka V,Vasconcelos I,Kachanov M.2006.The influence of crack shape on the effective elasticity of fractured rocks.Geophysics,71(5):D153-D160.
Johansen T A,Spikes K,Dvorkin J.2004.Strategy for estimation of lithology and reservoir properties from seismic velocities and density.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1726-1729.
Johansen T A,Jensen E H,Mavko G,et al.2013.Inverse rock physics modeling for reservoir quality prediction.Geophysics,78(2):M1-M18.
Knackstedt M A,Arns C H,Pinczewski W V.2003.Velocityporosity relationships,1:accurate velocity model for clean consolidated sandstones.Geophysics,68(6):1822-1834.
Liu Q,Yin X Y,Li C.2016.Quantitative prediction of reservoir characteristics based on inverse modeling theory.Chinese Journal of Geophysics(in Chinese),59(9):3491-3502,doi:10.6038/cjg20160931.
Liu Q,Dong N,Ji Y X.2017.Reservoir parameter prediction based on a constrained inverse rock physics modeling method.∥CGS/SEG Expanded Abstracts,1225-1228.
Liu X F.2010.Numerical simulation of elastic and electrical properties of rock based on digital cores[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum.
Liu X J,Zhu H L,Liang L X.2014.Digital rock physics of sandstone based on micro-CT technology.Chinese Journal of Geophysics(in Chinese),57(4):1133-1140,doi:10.6038/cjg20140411.
Mavko G,Mukerji T,Dvorkin J.1998.The Rock Physics Handbook:Tools for Seismic Analysis in Porous Media.Cambridge:Cambridge University Press.
Moyano B,Jensen E H,Johansen T A.2011.Improved quantitative calibration of rock physics models.Petroleum Geoscience,17(4):345-354.
Moyano B,Jensen E H,Johansen T A.2015.Spatial constrained inverse rock physics modelling.Geophysical Prospecting,63(1):183-191.
Saenger E H,Gold N,Shapiro S A.2000.Modeling the propagation of elastic waves using a modified finite-difference grid.Wave Motion,31(1):77-92.
Saenger E H,Shapiro S A.2002.Effective velocities in fractured media:a numerical study using the rotated staggered finitedifferenced grid.Geophysical Prospecting,50(2):183-194.
Saenger E H,Krüger O S,Shapiro S A.2004.Numerical considerations of fluid effects on wave propagation:Influence of the tortuosity.Geophysical Research Letters,31(21):L21613,doi:10.1029/2004GL020970.
Saenger E H,Enzmann F,Keehm Y,et al.2011.Digital rock physics:Effect of fluid viscosity on effective elastic properties.Journal of Applied Geophysics,74(4):236-241.
Sain R.2010.Numerical simulation of pore-scale heterogeneity and its effects on elastic,electrical and transport properties[Ph.D.thesis].Stanford:Stanford University.
Yin X Y,Zong Z Y,Wu G C.2015.Research on seismic fluid identification driven by rock physics.Science China Earth Sciences,58(2):159-171,doi:10.1007/s11430-014-4992-3.
Yin X Y,Zheng Y,Zong Z Y.2017.Research on the equivalence between digital core and rock physics models.Journal of Geophysics and Engineering,14(3):666-674.
Zhang J Y,Sun J M.2012.Rock elastic properties determined by using digital rock and effective medium model.Journal of Oil and Gas Technology(in Chinese),34(2):65-70.
Zhang Y,Toks9z M N.2012.Impact of the cracks lost in the imaging process on computing linear elastic properties from 3Dmicrotomographic images of Berea sandstone.Geophysics,77(2):R95-R104.
Zong Z Y,Yin X Y,Wu G C.2015.Geofluid discrimination incorporating poroelasticity and seismic reflection inversion.Surveys in Geophysics,36(5):659-681.
Zong Z Y,Yin X Y.2017.Model parameterization and p-wave AVA direct inversion for Young′s impedance.Pure and Applied Geophysics,174(5):1965-1981.
刘学锋.2010.基于数字岩心的岩石声电特性微观数值模拟研究[博士论文].青岛:中国石油大学.
刘向君,朱洪林,梁利喜.2014.基于微CT技术的砂岩数字岩石物理实验.地球物理学报,57(4):1133-1140,doi:10.6038/cjg20140411.
刘倩,印兴耀,李超.2016.基于逆建模理论的储层特征定量预测方法.地球物理学报,59(9):3491-3502,doi:10.6038/cjg20160931.
印兴耀,宗兆云,吴国忱.2015.岩石物理驱动下地震流体识别研究.中国科学:地球科学,45(1):8-21.
张晋言,孙建孟.2012.应用数字岩心和有效介质模型研究岩石弹性性质.石油天然气学报,34(2):65-70.