岩石三维微观结构定量研究方案与应用实例
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摘要
微观CT技术可以提供微米(或更小)分辨率的三维高精度数字图像,为研究岩石内部结构提供了强有力的技术支持。微观CT数据的定量分析主要包含三个方面:(1)图像数据中岩石微观结构的定量表征;(2)流体力学代表性体元的确定和流体力学参数计算;(3)固体力学代表性体元的确定及固体力学参数计算。简要介绍了三个方面定量分析的实施方案,并将可视化技术作为数据分析的辅助手段。给出了糜棱岩、砂岩和灰岩三个不同样品的计算分析实例。岩石微观三维CT数据量大,尤其是包含了时间序列的四维CT数据量更为巨大,其中包含了丰富且独特的信息,处理过程复杂多变,构成了地学大数据的一个重要组成部分。
Microtomography provides digital images at microns or sub-micron resolution and enables the study of rock microstructures.Quantitative analyses of microtomographic data mainly include three parts:(1)characterizing rock microstructures;(2)determining representative volume element(RVE)size and pore-scale fluid simulation for extracting fluid transport properties;and(3)determining mechanical RVE size and extracting mechanical properties.Here,we briefly introduced the implementing schemes of quantitative analyses of microtomography,using visualization methods to assistant data analyses.We analyzed three typical samples—a mylonite,a synthetic sandstone and a carbonate sample-to illustrate the procedure and validity of our method.Microtomographic data are voluminous,vary at different processing stages,and contain plentiful yet specific information,thus they are important components of geoscience big-data.
Microtomography provides digital images at microns or sub-micron resolution and enables the study of rock microstructures.Quantitative analyses of microtomographic data mainly include three parts:(1)characterizing rock microstructures;(2)determining representative volume element(RVE)size and pore-scale fluid simulation for extracting fluid transport properties;and(3)determining mechanical RVE size and extracting mechanical properties.Here,we briefly introduced the implementing schemes of quantitative analyses of microtomography,using visualization methods to assistant data analyses.We analyzed three typical samples—a mylonite,a synthetic sandstone and a carbonate sample-to illustrate the procedure and validity of our method.Microtomographic data are voluminous,vary at different processing stages,and contain plentiful yet specific information,thus they are important components of geoscience big-data.
引文
[1] DESRUES J,VIGGIANI G,BESUELLE P.Advances in Xray tomography for geomaterials[M].London:ISTE Ltd,2010.
[2] JERRAM D A,HIGGINS M D.3D analysis of rock textures:quantifying genius microstructures[J].Elements,2007,3:239-245.
[3] STAUFFER D,AHARONY A.Introduction to percolation theory[M].2nd ed.London:Taylor and Francis,1994.
[4] SPANNE P,THOVERT J F,JACQUIN C J,et al.Synchrotron computed microtomography of porous media:topology and transports[J].Physical Review Letters,1994,73(14):2001.
[5] ARNS C H,KNACKSTEDT M A,PINCZEWSKI M V,et al.Accurate estimation of transport properties from microtomographic images[J].Geophysical Research Letters,2001,28(17):3361-3364.
[6] FREDRICH J T,DIGIOVANNI A A,NOBLE D R.Predicting macroscopic transport properties using microscopic image data[J].Journal of Geophysical Research:Solid Earth,2006,111:B03201.
[7] KNACKSTEDT M A,ARNS C H,SAADATFAR M,et al.Elastic and transport properties of cellular solids derived from three-dimensional tomographic images[J].Proceedings Mathematical Physical&Engineering Sciences,2006,462(2073):2833-2862.
[8] ARNS C H,KNACKSTEDT M A,PINCZEWSK W V,et al.Computation of linear elastic properties from microtomographic images:methodology and agreement between theory and experiment[J].Geophysics,2002,67(5):1396-1405.
[9] ROBERTS A P,GARBOCZI E J.Elastic properties of model random three-dimensional open-cell solids[J].Journal of the Mechanics&Physics of Solids,2002,50(1):33-55.
[10]姚军,赵秀才,衣艳静,等.数字岩心技术现状及展望[J].油气地质与采收率,2005,12(6):52-54.
[11]姚军,赵秀才,衣艳静,等.储层岩石微观结构性质的分析方法[J].中国石油大学学报(自然科学版),2007,31(1):80-86.
[12]赵秀才,姚军.数字岩心建模及其准确性评价[J].西安石油大学学报(自然科学版),2007,22(2):16-20.
[13] FUSSEIS F,XIAO X,SCHRANK C,et al.A brief guide to synchrotron radiation-based microtomography in(structural)geology and rock mechanics[J].Journal of Structural Geology,2014,65(3):1-16.
[14] LIU J,REGENAUER-LIEB K,HINES C,et al.Applications of microtomography to multi-scale system dynamics:visualization,characterization and high performance computation[M].Berlin:Springer-Verlag,2013:653-674.
[15]屈乐,孙卫,杜环虹,等.基于CT扫描的三维数字岩心孔隙结构表征方法及应用:以莫北油田116井区三工河组为例[J].现代地质,2014,28(1):190-196.
[16]赵静,冯增朝,杨栋,等.基于三维CT图像的油页岩热解及内部结构变化特征分析[J].岩石力学与工程学报,2014,33(1):112-117.
[17]郭雪晶,何顺利,陈胜,等.基于纳米CT及数字岩心的页岩孔隙微观结构及分布特征研究[J].中国煤炭地质,2016,28(2):28-34.
[18] BULTREYS T,BOEVER W D,CNUDDE V.Imaging and image-based fluid transport modeling at the pore scale in geological materials:apractical introduction to the current state-of-the-art[J].Earth-Science Reviews,2016,155:93-128.
[19] ALMQVIST B S,MAINPRICE D,MADONNA C,et al.Application of differential effective medium,magnetic pore fabric analysis,and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates[J].Journal of Geophysical Research:Solid Earth,2011,116:1-17.
[20]孙建孟,闫国亮,姜黎明,等.基于数字岩心研究流体性质对裂缝性低渗透储层弹性参数的影响规律[J].中国石油大学学报(自然科学版),2014,38(3):39-44.
[21]刘向君,朱洪林,梁利喜.基于微CT技术的砂岩数字岩石物理实验[J].地区物理学报,2014,57(4):1133-1140.
[22] LIU J,SAROUT J,ZHANG M,et al.Computational upscaling of Drucker-Prager plasticity from micro-CT images of synthetic porous rock[J].Geophysical Journal International,2018,212(1):151-163.
[23]杨振琦,王述红,孟嫣然,等.基于CT扫描的花岗岩三维数值试件重构模型及应用[J].固体力学学报,2017(6):591-600.
[24] SAENGER E H,CIZ R,KRGER O S,et al.Finitedifference modeling of wave propagation on microscale:a snapshot of the work in progress[J].Geophysics,2007,72(5):293.
[25]刘学锋.基于数字岩心的岩石声电特性微观数值模拟研究[D].东营:中国石油大学(华东),2010.
[26] PIANE C D,SAROUT J,MADONNA C,et al.Frequencydependent seismic attenuation in shales:experimental results and theoretical analysis[J].Geophysical Journal International,2014,198(1):351-367.
[27]朱伟,单蕊.虚拟岩石物理研究进展[J].石油地球物理勘探,2014,49(6):1138-1146.
[28]孔强夫,周灿灿,张艳,等.基于数字岩心岩石电性数值模拟方法综述[J].地球物理学进展,2015,30(2):718-724.
[29] BLUNT M J,JACKSON M D,PIRI M,et al.Detailed physics,predictive capabilities and macroscopic consequences for pore-network models of multiphase flow[J].Advances in Water Resources,2002,25:1069-1089.
[30] CNUDDE V,BOONE M N.High-resolution X-ray computed tomography in geosciences:a review of the current technology and applications[J].Earth-Sciences Reviews,2013,123(4):1-17.
[31] FUSSEIS F,SCHRANK C,LIU J,et al.Pore formation during dehydration of a polycrystalline gypsum sample observed and quantified in a time-series synchrotron X-ray microtomography experiment[J].Solid Earth,2012,3:71-86.
[32] FUSSEIS F,SCHRANK C,LIU J.Thermal damage in Westerly granite investigated by means of synchrotron radiation based microtomography[C]∥EGU General Assembly.Vienna:EGU,2012:P-9555.
[33] SCHRANK C,FUSSEIS F,KARRECH A,et al.Thermalelastic stresses and the criticality of the continental crust[J].Geochemistry,Geophysics,Geosystems,2013,13(9):Q09005.
[34] KETCHAM R A.Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[J].Journal of Structural Geology,2005,27:1217-1228.
[35] LIU J,REGENAUER-LIEB K,HINES C,et al.Improved estimates of percolation and anisotropic permeability from3-D X-ray microtomography using stochastic analyses and visualization[J].Geochemistry,Geophysics,Geosystems,2009,10(5):323-328.
[36] LIU J,PEREIRA G,LIU Q,et al.Computational challenges in the analyses of petrophysics using microtomography and upscaling:a review[J].Computers&Geosciences,2016,89:107-117.
[37] NAKASHIMA Y,KAMIYA S.Mathematica programs for the analysis of three-dimensional pore connectivity and anisotropic tortuosity of porous rocks using X-ray computed tomography image data[J].Journal of Nuclear Science and Technology,2007,44:1233-1247.
[38] PROVIS J L,MYERS R J,WHITE C E,et al.X-ray microtomography shows pore structure and tortuosity in alkaliactivated binders[J].Cement&Concrete Research,2012,42(6):855-864.
[39] PLUYMAKERS A,KOBCHENKO M,RENARD F.How microfracture roughness can be used to distinguish between exhumed cracks and in-situ flow paths in shales[J].Journal of Structural Geology,2017,94:87-97.
[40] DONG H,BLUNT M J.Pore-network extraction from micro-computerized-tomography images[J].Physical Review E,2009,80(2):036307.
[41] WANG L L,BORNERT M,HERIPRE E,et al.Microscale insight into the influence of humidity on the mechanical behavior of mudstones[J].Journal of Geophysical Research:Solid Earth,2015,120:1-14.
[42] MARCKE P V,VERLEYE B,CARMELIET J,et al.An improved pore network model for the computation of the saturated permeability of porous rock[J].Transport in Porous Media,2010,85(2):451-476.
[43] PENG S,MARONE F,DULTZ S.Resolution effect in Xray microcomputed tomography imaging and small pore's contribution to permeability for a Berea sandstone[J].Journal of Hydrology,2014,510:403-411.
[44]姚军,赵建林,张敏,等.基于格子Boltzmann方法的页岩气微观流动模拟[J].石油学报,2015,36(10):1280-1289.
[45]张磊,姚军,孙海,等.基于数字岩心技术的气体解析/扩散格子Boltzmann模拟[J].石油学报,2015,36(3):361-365.
[46] KANIT T,FOREST S,GALLIET I,et al.Determination of the size of the representative volume element for random composites:statistical and numerical approach[J].International Journal of Solids and Structures,2003,40:3647-3679.
[47] RAEINI A Q,BLUNT M J,BIJELJIC B.Modelling twophase flow in porous media at the pore scale using the volume-of-fluid method[J].Journal of Computational Physics,2012,231(17):5653-5668.
[48] PEREIRA G G,DUPUY P M,CLEARY P W,et al.Comparison of permeability of model porous media between SPH and LB[J].Progress in Computational Fluid Dynamics,2012,12:176-186.
[49] PAN C X,LUO L S,MILLER C T.An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers&Fluids,2006,35:898-909.
[50] CHAI Z H,SHI B C,LIU J H,et al.Non-Darcy flow in disordered porous media:a lattice Boltzmann study[J].Computers&Fluids,2010,39:2069-2077.
[51] NARVAEZ A,ZAUNER T,RAISCHEL F,et al.Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations[J].Journal of Statistical Mechanics Theory&Experiment,2010,11:1363-1378.
[52] AXNER L,BERNSDORF J,ZERSER T,et al.Performance evaluation of a parallel sparse lattice Boltzmann solver[J].Journal of Computational Physics,2008,227(10):4895-4911.
[53] ZUDROP J,MASILAMANI K,ROLLER S,et al.A robust lattice Boltzmann method for parallel simulations of multicomponent flows in complex geometries[J].Computers&Fluids,2017,153:20-33.
[54] TERADA K,HORI M,KYOYA T,et al.Simulation of the multi-scale convergence in computational homogenization approaches[J].International Journal of Solid and Structures,2000,37:2285-2311.
[55] REGENAUER-LIEB K,VEVEAKIS M,POULET T,et al.Multiscale coupling and multiphysics approaches in earth science:theory[J].Journal of Coupled Systems and Multiscale Dynamics,2013,1(1):49-73.
[56] REGENAUER-LIEB K,KARRECH A,HUI T C,et al.Time-dependent,irreversible entropy production and geodynamics[J].Philosophical Transactions Mathematical Physical&Engineering Sciences,2010,368(1910):285-300.
[57] LIU J,FREIJ-AYOUB R,REGENAUER-LIEB K.Rock plasticity from microtomography and upscaling[J].Journal of Earth Science,2015,26(1):053-059.
[58] SHULAKOVA V,PERVUKHINA M,MLLER TM,et al.Computational elastic up-scaling of sandstone on the basis of X-ray micro-tomographic images[J].Geophysical Prospecting,2013,61(2):287-301.
[59] LIU J,FREIJ-AYOUB R,REGENAUER-LIEB K.Determination of the plastic strength of carbonates from microtomography and upscaling using percolation theory[C]∥Proceeding of ECCOMAS 2012.Vienna,Austria,2012.
[60] FUSSEIS F,REGENAUER-LIEB K,LIU J,et al.Creep cavitation can establish a dynamic granular fluid pump in ductile shear zones[J].Nature,2009,459:974-977.
[61] LIU J,REGENAUER-LIEB K.Application of percolation theory to microtomography of structured media:percolation threshold,critical exponents and upscaling[J].Physical Review E,2011,83,016106.
[62] SUNGKORN R,MORCOTE A,CARPIO G,et al.Multiscale and upscaling of digital rock physics with a machine that can learn about rocks[C]∥St.John's Newfoundland and Labrador,Canada:International Symposium of the Society of Core Analysts 2015(SCA2015-026),2015.
[2] JERRAM D A,HIGGINS M D.3D analysis of rock textures:quantifying genius microstructures[J].Elements,2007,3:239-245.
[3] STAUFFER D,AHARONY A.Introduction to percolation theory[M].2nd ed.London:Taylor and Francis,1994.
[4] SPANNE P,THOVERT J F,JACQUIN C J,et al.Synchrotron computed microtomography of porous media:topology and transports[J].Physical Review Letters,1994,73(14):2001.
[5] ARNS C H,KNACKSTEDT M A,PINCZEWSKI M V,et al.Accurate estimation of transport properties from microtomographic images[J].Geophysical Research Letters,2001,28(17):3361-3364.
[6] FREDRICH J T,DIGIOVANNI A A,NOBLE D R.Predicting macroscopic transport properties using microscopic image data[J].Journal of Geophysical Research:Solid Earth,2006,111:B03201.
[7] KNACKSTEDT M A,ARNS C H,SAADATFAR M,et al.Elastic and transport properties of cellular solids derived from three-dimensional tomographic images[J].Proceedings Mathematical Physical&Engineering Sciences,2006,462(2073):2833-2862.
[8] ARNS C H,KNACKSTEDT M A,PINCZEWSK W V,et al.Computation of linear elastic properties from microtomographic images:methodology and agreement between theory and experiment[J].Geophysics,2002,67(5):1396-1405.
[9] ROBERTS A P,GARBOCZI E J.Elastic properties of model random three-dimensional open-cell solids[J].Journal of the Mechanics&Physics of Solids,2002,50(1):33-55.
[10]姚军,赵秀才,衣艳静,等.数字岩心技术现状及展望[J].油气地质与采收率,2005,12(6):52-54.
[11]姚军,赵秀才,衣艳静,等.储层岩石微观结构性质的分析方法[J].中国石油大学学报(自然科学版),2007,31(1):80-86.
[12]赵秀才,姚军.数字岩心建模及其准确性评价[J].西安石油大学学报(自然科学版),2007,22(2):16-20.
[13] FUSSEIS F,XIAO X,SCHRANK C,et al.A brief guide to synchrotron radiation-based microtomography in(structural)geology and rock mechanics[J].Journal of Structural Geology,2014,65(3):1-16.
[14] LIU J,REGENAUER-LIEB K,HINES C,et al.Applications of microtomography to multi-scale system dynamics:visualization,characterization and high performance computation[M].Berlin:Springer-Verlag,2013:653-674.
[15]屈乐,孙卫,杜环虹,等.基于CT扫描的三维数字岩心孔隙结构表征方法及应用:以莫北油田116井区三工河组为例[J].现代地质,2014,28(1):190-196.
[16]赵静,冯增朝,杨栋,等.基于三维CT图像的油页岩热解及内部结构变化特征分析[J].岩石力学与工程学报,2014,33(1):112-117.
[17]郭雪晶,何顺利,陈胜,等.基于纳米CT及数字岩心的页岩孔隙微观结构及分布特征研究[J].中国煤炭地质,2016,28(2):28-34.
[18] BULTREYS T,BOEVER W D,CNUDDE V.Imaging and image-based fluid transport modeling at the pore scale in geological materials:apractical introduction to the current state-of-the-art[J].Earth-Science Reviews,2016,155:93-128.
[19] ALMQVIST B S,MAINPRICE D,MADONNA C,et al.Application of differential effective medium,magnetic pore fabric analysis,and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates[J].Journal of Geophysical Research:Solid Earth,2011,116:1-17.
[20]孙建孟,闫国亮,姜黎明,等.基于数字岩心研究流体性质对裂缝性低渗透储层弹性参数的影响规律[J].中国石油大学学报(自然科学版),2014,38(3):39-44.
[21]刘向君,朱洪林,梁利喜.基于微CT技术的砂岩数字岩石物理实验[J].地区物理学报,2014,57(4):1133-1140.
[22] LIU J,SAROUT J,ZHANG M,et al.Computational upscaling of Drucker-Prager plasticity from micro-CT images of synthetic porous rock[J].Geophysical Journal International,2018,212(1):151-163.
[23]杨振琦,王述红,孟嫣然,等.基于CT扫描的花岗岩三维数值试件重构模型及应用[J].固体力学学报,2017(6):591-600.
[24] SAENGER E H,CIZ R,KRGER O S,et al.Finitedifference modeling of wave propagation on microscale:a snapshot of the work in progress[J].Geophysics,2007,72(5):293.
[25]刘学锋.基于数字岩心的岩石声电特性微观数值模拟研究[D].东营:中国石油大学(华东),2010.
[26] PIANE C D,SAROUT J,MADONNA C,et al.Frequencydependent seismic attenuation in shales:experimental results and theoretical analysis[J].Geophysical Journal International,2014,198(1):351-367.
[27]朱伟,单蕊.虚拟岩石物理研究进展[J].石油地球物理勘探,2014,49(6):1138-1146.
[28]孔强夫,周灿灿,张艳,等.基于数字岩心岩石电性数值模拟方法综述[J].地球物理学进展,2015,30(2):718-724.
[29] BLUNT M J,JACKSON M D,PIRI M,et al.Detailed physics,predictive capabilities and macroscopic consequences for pore-network models of multiphase flow[J].Advances in Water Resources,2002,25:1069-1089.
[30] CNUDDE V,BOONE M N.High-resolution X-ray computed tomography in geosciences:a review of the current technology and applications[J].Earth-Sciences Reviews,2013,123(4):1-17.
[31] FUSSEIS F,SCHRANK C,LIU J,et al.Pore formation during dehydration of a polycrystalline gypsum sample observed and quantified in a time-series synchrotron X-ray microtomography experiment[J].Solid Earth,2012,3:71-86.
[32] FUSSEIS F,SCHRANK C,LIU J.Thermal damage in Westerly granite investigated by means of synchrotron radiation based microtomography[C]∥EGU General Assembly.Vienna:EGU,2012:P-9555.
[33] SCHRANK C,FUSSEIS F,KARRECH A,et al.Thermalelastic stresses and the criticality of the continental crust[J].Geochemistry,Geophysics,Geosystems,2013,13(9):Q09005.
[34] KETCHAM R A.Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[J].Journal of Structural Geology,2005,27:1217-1228.
[35] LIU J,REGENAUER-LIEB K,HINES C,et al.Improved estimates of percolation and anisotropic permeability from3-D X-ray microtomography using stochastic analyses and visualization[J].Geochemistry,Geophysics,Geosystems,2009,10(5):323-328.
[36] LIU J,PEREIRA G,LIU Q,et al.Computational challenges in the analyses of petrophysics using microtomography and upscaling:a review[J].Computers&Geosciences,2016,89:107-117.
[37] NAKASHIMA Y,KAMIYA S.Mathematica programs for the analysis of three-dimensional pore connectivity and anisotropic tortuosity of porous rocks using X-ray computed tomography image data[J].Journal of Nuclear Science and Technology,2007,44:1233-1247.
[38] PROVIS J L,MYERS R J,WHITE C E,et al.X-ray microtomography shows pore structure and tortuosity in alkaliactivated binders[J].Cement&Concrete Research,2012,42(6):855-864.
[39] PLUYMAKERS A,KOBCHENKO M,RENARD F.How microfracture roughness can be used to distinguish between exhumed cracks and in-situ flow paths in shales[J].Journal of Structural Geology,2017,94:87-97.
[40] DONG H,BLUNT M J.Pore-network extraction from micro-computerized-tomography images[J].Physical Review E,2009,80(2):036307.
[41] WANG L L,BORNERT M,HERIPRE E,et al.Microscale insight into the influence of humidity on the mechanical behavior of mudstones[J].Journal of Geophysical Research:Solid Earth,2015,120:1-14.
[42] MARCKE P V,VERLEYE B,CARMELIET J,et al.An improved pore network model for the computation of the saturated permeability of porous rock[J].Transport in Porous Media,2010,85(2):451-476.
[43] PENG S,MARONE F,DULTZ S.Resolution effect in Xray microcomputed tomography imaging and small pore's contribution to permeability for a Berea sandstone[J].Journal of Hydrology,2014,510:403-411.
[44]姚军,赵建林,张敏,等.基于格子Boltzmann方法的页岩气微观流动模拟[J].石油学报,2015,36(10):1280-1289.
[45]张磊,姚军,孙海,等.基于数字岩心技术的气体解析/扩散格子Boltzmann模拟[J].石油学报,2015,36(3):361-365.
[46] KANIT T,FOREST S,GALLIET I,et al.Determination of the size of the representative volume element for random composites:statistical and numerical approach[J].International Journal of Solids and Structures,2003,40:3647-3679.
[47] RAEINI A Q,BLUNT M J,BIJELJIC B.Modelling twophase flow in porous media at the pore scale using the volume-of-fluid method[J].Journal of Computational Physics,2012,231(17):5653-5668.
[48] PEREIRA G G,DUPUY P M,CLEARY P W,et al.Comparison of permeability of model porous media between SPH and LB[J].Progress in Computational Fluid Dynamics,2012,12:176-186.
[49] PAN C X,LUO L S,MILLER C T.An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers&Fluids,2006,35:898-909.
[50] CHAI Z H,SHI B C,LIU J H,et al.Non-Darcy flow in disordered porous media:a lattice Boltzmann study[J].Computers&Fluids,2010,39:2069-2077.
[51] NARVAEZ A,ZAUNER T,RAISCHEL F,et al.Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations[J].Journal of Statistical Mechanics Theory&Experiment,2010,11:1363-1378.
[52] AXNER L,BERNSDORF J,ZERSER T,et al.Performance evaluation of a parallel sparse lattice Boltzmann solver[J].Journal of Computational Physics,2008,227(10):4895-4911.
[53] ZUDROP J,MASILAMANI K,ROLLER S,et al.A robust lattice Boltzmann method for parallel simulations of multicomponent flows in complex geometries[J].Computers&Fluids,2017,153:20-33.
[54] TERADA K,HORI M,KYOYA T,et al.Simulation of the multi-scale convergence in computational homogenization approaches[J].International Journal of Solid and Structures,2000,37:2285-2311.
[55] REGENAUER-LIEB K,VEVEAKIS M,POULET T,et al.Multiscale coupling and multiphysics approaches in earth science:theory[J].Journal of Coupled Systems and Multiscale Dynamics,2013,1(1):49-73.
[56] REGENAUER-LIEB K,KARRECH A,HUI T C,et al.Time-dependent,irreversible entropy production and geodynamics[J].Philosophical Transactions Mathematical Physical&Engineering Sciences,2010,368(1910):285-300.
[57] LIU J,FREIJ-AYOUB R,REGENAUER-LIEB K.Rock plasticity from microtomography and upscaling[J].Journal of Earth Science,2015,26(1):053-059.
[58] SHULAKOVA V,PERVUKHINA M,MLLER TM,et al.Computational elastic up-scaling of sandstone on the basis of X-ray micro-tomographic images[J].Geophysical Prospecting,2013,61(2):287-301.
[59] LIU J,FREIJ-AYOUB R,REGENAUER-LIEB K.Determination of the plastic strength of carbonates from microtomography and upscaling using percolation theory[C]∥Proceeding of ECCOMAS 2012.Vienna,Austria,2012.
[60] FUSSEIS F,REGENAUER-LIEB K,LIU J,et al.Creep cavitation can establish a dynamic granular fluid pump in ductile shear zones[J].Nature,2009,459:974-977.
[61] LIU J,REGENAUER-LIEB K.Application of percolation theory to microtomography of structured media:percolation threshold,critical exponents and upscaling[J].Physical Review E,2011,83,016106.
[62] SUNGKORN R,MORCOTE A,CARPIO G,et al.Multiscale and upscaling of digital rock physics with a machine that can learn about rocks[C]∥St.John's Newfoundland and Labrador,Canada:International Symposium of the Society of Core Analysts 2015(SCA2015-026),2015.
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