基于沉积过程的数字岩石建模方法研究
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摘要
本文提出模拟地层沉积及成岩过程的矿物沉积算法,建立数字岩石模型,并通过对比Micro-CT扫描图像和数值模型的局部孔隙度及平均渗流概率函数分布特征,评价建模的准确性.结果表明,由二维扫描提取的粒径信息作为输入参数,模拟矿物沉积过程建模得到的三维数字岩石模型,能够准确重构原始岩心的非均质性及渗流特性,成功应用于泥质砂岩、碳酸盐岩、页岩等存在多矿物或多尺度孔隙的数字岩石建模中.数字岩石物理是正在兴起的重要技术.数字岩石采用超高分辨率先进成像装备,采集和表征微纳尺度岩石结构,在岩石弹性、电性、核磁、渗流特性等数值计算中发挥重要作用.但是,由于三维直接成像在有限视域内难以表征足够的岩石非均质性,提取二维结构统计特征,利用统计或地质过程法重构具有代表性的三维岩石结构成为十分有价值的研究课题,而且,对业界大量存在的岩石薄片及电镜高清二维图像的深度开发应用也具有重要的现实意义.本文发展的新方法,复原沉积过程,较好地解决了孔隙尺度岩石物理定量研究中数值建模与理论计算的技术瓶颈.
Digital Rock Physics(DRP)is widely used to accurately characterize pore structures and mineral distributions of hydrocarbon bearing rocks based on their three-dimensional(3D)images at micro-and nano-meter scales.It also plays an important role to numerically calculate rock elasticity,formation factor,permeability and simulate multi-phase flow properties etc.However,3D images are not always readily available for reservoir rocks and it is sometimes difficult to satisfy modeling requirements to cover heterogeneity due to limited rock volumes captured in 3D.Therefore,3D reconstruction methods become alternative approaches to model porous rocks.Comparing with statistical methods,geological process based reconstruction hasproved itself to be successful to reproduce sandstone structures.In this paper,we developed a method to improve the existing models with more realistic sedimentological processes and extend it to reconstruct shaly sandstone,carbonate rocks and shale by introducing more mechanism of diagenesis.The grain size distribution is extracted from a slice of 2D Micro-CT images using watershed segmentation algorithm;and then it is used as initial input information for the 3D reconstruction.The accuracy of modeling is evaluated by comparing their local porosity distributions and average percolation probability function distributions of the 3D digital rock images obtained by MicroCT imaging.The results show that our reconstruction can accurately reproduce heterogeneity and percolation characteristics of original Micro-CT images,which provide geologically realistic rock models for petrophysical studies.
Digital Rock Physics(DRP)is widely used to accurately characterize pore structures and mineral distributions of hydrocarbon bearing rocks based on their three-dimensional(3D)images at micro-and nano-meter scales.It also plays an important role to numerically calculate rock elasticity,formation factor,permeability and simulate multi-phase flow properties etc.However,3D images are not always readily available for reservoir rocks and it is sometimes difficult to satisfy modeling requirements to cover heterogeneity due to limited rock volumes captured in 3D.Therefore,3D reconstruction methods become alternative approaches to model porous rocks.Comparing with statistical methods,geological process based reconstruction hasproved itself to be successful to reproduce sandstone structures.In this paper,we developed a method to improve the existing models with more realistic sedimentological processes and extend it to reconstruct shaly sandstone,carbonate rocks and shale by introducing more mechanism of diagenesis.The grain size distribution is extracted from a slice of 2D Micro-CT images using watershed segmentation algorithm;and then it is used as initial input information for the 3D reconstruction.The accuracy of modeling is evaluated by comparing their local porosity distributions and average percolation probability function distributions of the 3D digital rock images obtained by MicroCT imaging.The results show that our reconstruction can accurately reproduce heterogeneity and percolation characteristics of original Micro-CT images,which provide geologically realistic rock models for petrophysical studies.
引文
Arns C H,Sheppard A P,Sok R M,et al.2007.NMR petrophysical predictions on digitized core images.Petrophysics,48(3):202-221.
Biswal B,Manwart C,Hilfer R,et al.1999.Quantitative analysis of experimental and synthetic microstructures for sedimentary rock.Physica A:Statistical Mechanics and Its Applications,273(3-4):452-475.
Chi L,Heidari Z.2015.Diffusional coupling between microfractures and pore structure and its impact on nuclear magnetic resonance measurements in multiple-porosity systems.Geophysics,80(1):D31-D42.
Dong H.2007.Micro-CT Imaging and pore network extraction[Ph.D.thesis].London:Imperial College.
Fang X W,Liu Z Y,Tan J R.2011.An algorithm for particle packing in 3D space by considering geometric and physical factors.Journal of Computer-Aided Design&Computer Graphics(in Chinese),23(7):1253-1262.
Guo J F,Xie R H,Zou Y L.2016.Simulation of NMR responses in sandstone and restricted diffusion.Chinese Journal of Geophysics(in Chinese),59(7):2703-2712,doi:10.6038/cjg20160733.
Hazlett R D.1997.Statistical characterization and stochastic modeling of pore networks in relation to fluid flow.Mathematical Geology,29(6):801-822.
Jiang Z,Chen W,Burkhart C.2013.Efficient 3Dporous microstructure reconstruction via Gaussian random field and hybrid optimization.Journal of Microscopy,252(2):135-148.
Jin G D,Patzek T W,Silin D B.2003.Physics-based reconstruction of sedimentary rocks.∥73rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Kameda A.2005.Permeability evolution in sandstone:digital rock approach[Ph.D.thesis].Stanford:Stanford University.
Liu X F,Sun J M,Wang H T.2009a.Reconstruction of 3-D digital cores using a hybrid method.Applied Geophysics(in Chinese),6(2):105-112.
Liu X F,Sun J M,Wang H T,et al.2009b.The accuracy evaluation on 3D digital cores reconstructed by sequence indicator simulation.Acta Petrolei Sinica(in Chinese),30(3):391-395.
Liu X F,Zhang W W,Sun J M.2013.Methods of constructing 3-Ddigital cores:a review.Progress in Geophysics(in Chinese),28(6):3066-3072,doi:10.6038/pg20130630.
Mehmani A.2015.Investigation of the petrophysical properties of unconventional rocks using multiscale network modeling[Ph.D.thesis].Austin:The University of Texas at Austin.
Mo X W,Zhang Q,Lu J A.2016.A complement optimization scheme to establish the digital core model based on the simulated annealing method.Chinese Journal of Geophysics(in Chinese),59(5):1831-1838,doi:10.6038/cjg20160526.
Nie X,Zou C C,Meng X H,et al.2016.3Ddigital core modeling of shale gas reservoir rocks:A case study of conductivity model.Natural Gas Geoscience(in Chinese),27(4):706-715.
Okabe H,Blunt M J.2004.Prediction of permeability for porous media reconstructed using multiple-point statistics.Physical Review E,70(6):066135,doi:10.1103/PhysRevE.70.066135.
?ren P E,Bakke S.2002.Process based reconstruction of sandstones and prediction of transport properties.Transport in Porous Media,46(2-3):311-343.
?ren P E,Bakke S.2003.Reconstruction of Berea sandstone and pore-scale modelling of wettability effects.Journal of Petroleum Science and Engineering,39(3-4):177-199.
Pilotti M.1998.Generation of realistic porous media by grains sedimentation.Transport in Porous Media,33(3):257-278.
Rabbani A,Jamshidi S,Salehi S.2014.An automated simple algorithm for realistic pore network extraction from microtomography images.Journal of Petroleum Science and Engineering,123:164-171.
Schwartz L M,Johnson D L,Mitchell J,et al.2013.Modeling twodimensional magnetic resonance measurements in coupled pore systems.Physical Review E,88(3):032813,doi:10.1103/PhysRevE.88.032813.
Sun H Q,Xie H P.2008.Fractal simulation of rock fracture surface.Rock and Soil Mechanics(in Chinese),29(2):347-352.
Torskaya T,Shabro V,Torres-Verdín C,et al.2014.Grain shape effects on permeability,formation factor,and capillary pressure from pore-scale modeling.Transport in Porous Media,102(1):71-90.
Wang C C.2013.Construction theory and method of dual pore network model in carbonate media[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum(East China).
Wang Y,Yue W Z,Zhang M.2016.Numerical research on the anisotropic transport of thermal neutron in heterogeneous porous media with micron X-ray computed tomography.Scientific Reports,6:27488.
Wu K,Nunan N,Crawford J W,et al.2004.An efficient Markov chain model for the simulation of heterogeneous soil structure.Soil Science Society of America Journal,68(2):346-351.
Xiong Q R,Baychev T G,Jivkov A P.2016.Review of pore network modelling of porous media:Experimental characterisations,network constructions and applications to reactive transport.Journal of Contaminant Hydrology,192:101-117.
Yan G L,Sun J M,Liu X F,et al.2013.Accuracy evaluation on 3Ddigital cores reconstruction by process-based method.Journal of Southwest Petroleum University(Science&Technology Edition)(in Chinese),35(2):71-76.
Yue W Z,Tao G.2013.A new non-Archie model for pore structure:numerical experiments using digital rock models.Geophysical JournalInternational,195(1):282-291.
Zhang T F.2015.MPS-driven digital rock modeling and upscaling.Mathematical Geosciences,47(8):937-954.
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.
Zhao J P,Sun J M,Liu X F,et al.2013.Numerical simulation of the electrical properties of fractured rock based on digital rock technology.Journal of Geophysics and Engineering,10(5):055009,doi:10.1088/1742-2132/10/5/055009.
Zhao X C,Yao J.2007.Construction of digital core and evaluation of its quality.Journal of Xi′an Shiyou University(Natural Science Edition)(in Chinese),22(2):16-20.
Zhu W,Yu W H,Chen Y.2012.Digital core modeling from irregular grains.Journal of Applied Geophysics,85:37-42.
方锡武,刘振宇,谭建荣.2011.几何与物理相结合的三维域颗粒堆积算法.计算机辅助设计与图形学学报,23(7):1254-1262.
郭江峰,谢然红,邹友龙.2016.砂岩核磁共振响应模拟及受限扩散.地球物理学报,59(7):2703-2712,doi:10.6038/cjg20160733.
刘学锋,孙建孟,王海涛.2009a.利用混合法构建三维数字岩心(英文).应用地球物理,6(2):105-112.
刘学锋,孙建孟,王海涛等.2009b.顺序指示模拟重建三维数字岩心的准确性评价.石油学报,30(3):391-395.
刘学锋,张伟伟,孙建孟.2013.三维数字岩心建模方法综述.地球物理学进展,28(6):3066-3072,doi:10.6038/pg20130630.
莫修文,张强,陆敬安.2016.模拟退火法建立数字岩心的一种补充优化方案.地球物理学报,59(5):1831-1838,doi:10.6038/cjg20160526.
聂昕,邹长春,孟小红等.2016.页岩气储层岩石三维数字岩心建模---以导电性模型为例.天然气地球科学,27(4):706-715.
孙洪泉,谢和平.2008.岩石断裂表面的分形模拟.岩土力学,29(2):347-352.
王晨晨.2013.碳酸盐岩介质双孔隙网络模型构建理论与方法[博士论文].青岛:中国石油大学(华东).
闫国亮,孙建孟,刘学锋等.2013.过程模拟法重建三维数字岩芯的准确性评价.西南石油大学学报(自然科学版),35(2):71-76.
赵秀才,姚军.2007.数字岩心建模及其准确性评价.西安石油大学学报(自然科学版),22(2):16-20.
Biswal B,Manwart C,Hilfer R,et al.1999.Quantitative analysis of experimental and synthetic microstructures for sedimentary rock.Physica A:Statistical Mechanics and Its Applications,273(3-4):452-475.
Chi L,Heidari Z.2015.Diffusional coupling between microfractures and pore structure and its impact on nuclear magnetic resonance measurements in multiple-porosity systems.Geophysics,80(1):D31-D42.
Dong H.2007.Micro-CT Imaging and pore network extraction[Ph.D.thesis].London:Imperial College.
Fang X W,Liu Z Y,Tan J R.2011.An algorithm for particle packing in 3D space by considering geometric and physical factors.Journal of Computer-Aided Design&Computer Graphics(in Chinese),23(7):1253-1262.
Guo J F,Xie R H,Zou Y L.2016.Simulation of NMR responses in sandstone and restricted diffusion.Chinese Journal of Geophysics(in Chinese),59(7):2703-2712,doi:10.6038/cjg20160733.
Hazlett R D.1997.Statistical characterization and stochastic modeling of pore networks in relation to fluid flow.Mathematical Geology,29(6):801-822.
Jiang Z,Chen W,Burkhart C.2013.Efficient 3Dporous microstructure reconstruction via Gaussian random field and hybrid optimization.Journal of Microscopy,252(2):135-148.
Jin G D,Patzek T W,Silin D B.2003.Physics-based reconstruction of sedimentary rocks.∥73rd Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Kameda A.2005.Permeability evolution in sandstone:digital rock approach[Ph.D.thesis].Stanford:Stanford University.
Liu X F,Sun J M,Wang H T.2009a.Reconstruction of 3-D digital cores using a hybrid method.Applied Geophysics(in Chinese),6(2):105-112.
Liu X F,Sun J M,Wang H T,et al.2009b.The accuracy evaluation on 3D digital cores reconstructed by sequence indicator simulation.Acta Petrolei Sinica(in Chinese),30(3):391-395.
Liu X F,Zhang W W,Sun J M.2013.Methods of constructing 3-Ddigital cores:a review.Progress in Geophysics(in Chinese),28(6):3066-3072,doi:10.6038/pg20130630.
Mehmani A.2015.Investigation of the petrophysical properties of unconventional rocks using multiscale network modeling[Ph.D.thesis].Austin:The University of Texas at Austin.
Mo X W,Zhang Q,Lu J A.2016.A complement optimization scheme to establish the digital core model based on the simulated annealing method.Chinese Journal of Geophysics(in Chinese),59(5):1831-1838,doi:10.6038/cjg20160526.
Nie X,Zou C C,Meng X H,et al.2016.3Ddigital core modeling of shale gas reservoir rocks:A case study of conductivity model.Natural Gas Geoscience(in Chinese),27(4):706-715.
Okabe H,Blunt M J.2004.Prediction of permeability for porous media reconstructed using multiple-point statistics.Physical Review E,70(6):066135,doi:10.1103/PhysRevE.70.066135.
?ren P E,Bakke S.2002.Process based reconstruction of sandstones and prediction of transport properties.Transport in Porous Media,46(2-3):311-343.
?ren P E,Bakke S.2003.Reconstruction of Berea sandstone and pore-scale modelling of wettability effects.Journal of Petroleum Science and Engineering,39(3-4):177-199.
Pilotti M.1998.Generation of realistic porous media by grains sedimentation.Transport in Porous Media,33(3):257-278.
Rabbani A,Jamshidi S,Salehi S.2014.An automated simple algorithm for realistic pore network extraction from microtomography images.Journal of Petroleum Science and Engineering,123:164-171.
Schwartz L M,Johnson D L,Mitchell J,et al.2013.Modeling twodimensional magnetic resonance measurements in coupled pore systems.Physical Review E,88(3):032813,doi:10.1103/PhysRevE.88.032813.
Sun H Q,Xie H P.2008.Fractal simulation of rock fracture surface.Rock and Soil Mechanics(in Chinese),29(2):347-352.
Torskaya T,Shabro V,Torres-Verdín C,et al.2014.Grain shape effects on permeability,formation factor,and capillary pressure from pore-scale modeling.Transport in Porous Media,102(1):71-90.
Wang C C.2013.Construction theory and method of dual pore network model in carbonate media[Ph.D.thesis](in Chinese).Qingdao:China University of Petroleum(East China).
Wang Y,Yue W Z,Zhang M.2016.Numerical research on the anisotropic transport of thermal neutron in heterogeneous porous media with micron X-ray computed tomography.Scientific Reports,6:27488.
Wu K,Nunan N,Crawford J W,et al.2004.An efficient Markov chain model for the simulation of heterogeneous soil structure.Soil Science Society of America Journal,68(2):346-351.
Xiong Q R,Baychev T G,Jivkov A P.2016.Review of pore network modelling of porous media:Experimental characterisations,network constructions and applications to reactive transport.Journal of Contaminant Hydrology,192:101-117.
Yan G L,Sun J M,Liu X F,et al.2013.Accuracy evaluation on 3Ddigital cores reconstruction by process-based method.Journal of Southwest Petroleum University(Science&Technology Edition)(in Chinese),35(2):71-76.
Yue W Z,Tao G.2013.A new non-Archie model for pore structure:numerical experiments using digital rock models.Geophysical JournalInternational,195(1):282-291.
Zhang T F.2015.MPS-driven digital rock modeling and upscaling.Mathematical Geosciences,47(8):937-954.
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.
Zhao J P,Sun J M,Liu X F,et al.2013.Numerical simulation of the electrical properties of fractured rock based on digital rock technology.Journal of Geophysics and Engineering,10(5):055009,doi:10.1088/1742-2132/10/5/055009.
Zhao X C,Yao J.2007.Construction of digital core and evaluation of its quality.Journal of Xi′an Shiyou University(Natural Science Edition)(in Chinese),22(2):16-20.
Zhu W,Yu W H,Chen Y.2012.Digital core modeling from irregular grains.Journal of Applied Geophysics,85:37-42.
方锡武,刘振宇,谭建荣.2011.几何与物理相结合的三维域颗粒堆积算法.计算机辅助设计与图形学学报,23(7):1254-1262.
郭江峰,谢然红,邹友龙.2016.砂岩核磁共振响应模拟及受限扩散.地球物理学报,59(7):2703-2712,doi:10.6038/cjg20160733.
刘学锋,孙建孟,王海涛.2009a.利用混合法构建三维数字岩心(英文).应用地球物理,6(2):105-112.
刘学锋,孙建孟,王海涛等.2009b.顺序指示模拟重建三维数字岩心的准确性评价.石油学报,30(3):391-395.
刘学锋,张伟伟,孙建孟.2013.三维数字岩心建模方法综述.地球物理学进展,28(6):3066-3072,doi:10.6038/pg20130630.
莫修文,张强,陆敬安.2016.模拟退火法建立数字岩心的一种补充优化方案.地球物理学报,59(5):1831-1838,doi:10.6038/cjg20160526.
聂昕,邹长春,孟小红等.2016.页岩气储层岩石三维数字岩心建模---以导电性模型为例.天然气地球科学,27(4):706-715.
孙洪泉,谢和平.2008.岩石断裂表面的分形模拟.岩土力学,29(2):347-352.
王晨晨.2013.碳酸盐岩介质双孔隙网络模型构建理论与方法[博士论文].青岛:中国石油大学(华东).
闫国亮,孙建孟,刘学锋等.2013.过程模拟法重建三维数字岩芯的准确性评价.西南石油大学学报(自然科学版),35(2):71-76.
赵秀才,姚军.2007.数字岩心建模及其准确性评价.西安石油大学学报(自然科学版),22(2):16-20.