基于微增模型的海洋可控源电磁法三维非结构化矢量有限元数值模拟
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摘要
为了分析海洋中含金属矿的储油气砂层的成分、结构对于海洋可控源电磁场的影响特征,引入多相微增等效介质模型,结合非结构化网格实现了海洋可控源电磁三维矢量有限元正演.首先对多相微增模型进行了介绍,并分析不同参数影响下的等效电导率变化特征.而后,详细推导了频率域可控源电磁法非结构化矢量有限元方程.接着,利用预处理的IDR(s)迭代算法求解线性方程组.最后设计典型的海洋地电模型,通过正演计算,验证了本文算法的正确性和有效性,同时研究了海洋储油砂层中的金属矿的含量、孔隙度、含水饱和度等参数对于可控源电磁场响应特征的影响.
The aim of this study is to reveal characteristics of the three-dimensional marine electromagnetic field produced by a controlled source in pyrite-rich sedimentary rocks.We present an edge-based finite element method for 3 D marine controlled-source electromagnetic modeling in the frequency domain based on an unstructured grid and 4-phase incremental model.The theoretical incremental model is introduced firstly. Then the characteristics of the effective medium resistivity are analyzed considering the influence of different parameters.To avoid the source singularity problem for MCSEM modeling,we adopt a secondary field formulation.The sparse finite element system of equation is solved using an IDR(s)with incomplete LU decomposition results as a preconditioner to speed up the convergence.The effects of key parameters,i.e.,pyrite content,porosity,pyrite conductivity,grain aspect ratio and water saturation on theelectrical conductivity of pyrite-bearing sandstones and their corresponding CSEM responses are comprehensively studied.The results are expected to help the CSEM data interpretation when a pyrite-bearing sandstone reservoir is encountered in the future.
The aim of this study is to reveal characteristics of the three-dimensional marine electromagnetic field produced by a controlled source in pyrite-rich sedimentary rocks.We present an edge-based finite element method for 3 D marine controlled-source electromagnetic modeling in the frequency domain based on an unstructured grid and 4-phase incremental model.The theoretical incremental model is introduced firstly. Then the characteristics of the effective medium resistivity are analyzed considering the influence of different parameters.To avoid the source singularity problem for MCSEM modeling,we adopt a secondary field formulation.The sparse finite element system of equation is solved using an IDR(s)with incomplete LU decomposition results as a preconditioner to speed up the convergence.The effects of key parameters,i.e.,pyrite content,porosity,pyrite conductivity,grain aspect ratio and water saturation on theelectrical conductivity of pyrite-bearing sandstones and their corresponding CSEM responses are comprehensively studied.The results are expected to help the CSEM data interpretation when a pyrite-bearing sandstone reservoir is encountered in the future.
引文
Archie G E.1942.The electrical resistivity log as an aid in determining some reservoir characteristics.Transactions of the AIME,146(1):54-62.
Asami K.2002.Characterization of heterogeneous systems by dielectric spectroscopy.Progress in Polymer Science,27(8):1617-1659.
Bruggeman D A G.1935.Berechnung verschiedener physikalischer konstanten von heterogenen Substanzen.I.Dielektrizittskonstanten und Leitfhigkeiten der Mischk9rper aus isotropen Substanzen.Annalen Der Physik,416(7):636-664.
Bussian A E.1983.Electrical conductance in a porous medium.Geophysics,48(9):1258-1268.
Cai H Z,Xiong B,Zhdanov M.2015.Three-dimensional marine controlled-source electromagnetic modelling in anisotropic medium using finite element method.Chinese Journal of Geophysics(in Chinese),58(8):2839-2850,doi:10.6038/cjg20150818.
Chen G B,Wang H N,Yao J J,et al.2009.Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method.Acta Physica Sinica(in Chinese),58(6):3848-3857.
Clennell M B,Josh M,Esteban L,et al.2010.The influence of pyrite on rock electrical properties:A case study from NW Australian gas reservoirs.∥SPWLA 51st Annual Logging Symposium.Perth:Society of Petrophysicists and Well-Log Analysts.
Constable S,Srnka L J.2007.An introduction to marine controlledsource electromagnetic methods for hydrocarbon exploration.Geophysics,72(2):WA3-WA12.
Guo N N,Chang Y J,Jia H T.2011.Influences of induced polarization on marine controlled-source electromagnetic survey(in Chinese).∥The 10th China International Geo-Electromagnetic Workshop.Nanchang:Chinese Geophysical Society,392-395.
Han T C,Clennell M B,Josh M,et al.2015.Determination of effective grain geometry for electrical modeling of sedimentary rocks.Geophysics,80(4):D319-D327.
Hanai T.1960a.Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions.KolloidZeitschrift,171(1):23-31.
Hanai T.1960b.A remark on the“Theory of the dielectric dispersion due to the interfacial polarization”.Kolloid-Zeitschrift,175(1):61-62.
He Z X,Wang X B.2007.Geo-electrical anomalous pattern of reservoir and oil/gas detection by electromagnetic survey.Oil Geophysical Prospecting(in Chinese),42(1):102-106.
JahandariH,Farquharson C G.2015.Finite-volume modelling of geophysical electromagnetic data on unstructured grids using potentials.Geophysical Journal International,202(3):1859-1876.
Jin J.2002.Finite Element Method in Electromagnetic.New York:Wiley-IEEE Press.
Key K,Ovall J.2011.A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling.Geophysical Journal International,186(1):137-154.
Li Y,Key K.2007.2D marine controlled-source electromagnetic modeling:Part 1-An adaptive finite-element algorithm.Geophysics,72(2):WA51-WA62.
Liu C S,Everett M E,Lin J,et al.2010.Modeling of seafloor exploration using electric-source frequency-domain CSEM and the analysis of water depth effect.Chinese Journal of Geophysics(in Chinese),53(8):1940-1952,doi:10.3969/j.issn.0001-5733.2010.08.020.
Liu Y,Li Y G.2011.A Paralleled adaptive finite element modeling for 2D marine controlled-source electromagnetic forward modeling(in Chinese).∥The 10th China International Geo-Electromagnetic Workshop.Nanchang:Chinese Geophysical Society.
Liu Y,Li Y G.2015.Marine controlled-source electromagnetic fields of an arbitrary electric dipole over a layered an isotropic medium.Oil Geophysical Prospecting(in Chinese),50(4):755-765.
Manning M J,Athavale K A.1986.Dielectric properties of pyrite samples at 1100 Mhz.Geophysics,51(1):172-182.
Puzyrev V,Koldan J,De La Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693,doi:10.1093/gii/ggt027.
Schwarzbach C,B9rner R U,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geoelectromagnetics-a marine CSEM example.Geophysical Journal International,187(1):63-74,doi:10.1111/j.1365-246X.2011.05127.x.
Shen J S,Sun W B.2009.Numerical simulation of marine controlledsource electromagnetic(MCSEM)response to 2-D seabed formation.Geophysical Prospecting for Petroleum(in Chinese),48(2):187-194.
Sternberg B K.1991.A review of some experience with the inducedpolarization/resistivity method for hydrocarbon surveys:Successes and limitations.Geophysics,56(10):1522-1532.
Tang J T,Ren Z R,Hua X R.2007.Theoretical analysis of geoelectromagnetic modeling on Coulomb gauged potentials by adaptive finite element method.Chinese Journal of Geophysics(in Chinese),50(5):1584-1594.
Tang J T,Zhang L C,Gong J Z,et al.2014.3Dfrequency domain controlled source electromagnetic numerical modeling with coupled finite-infinite element method.Journal of Central South University(Science and Technology)(in Chinese),45(4):1252-1260.
Ulrich C,Slater L.2004.Induced polarization measurements on unsaturated,unconsolidated sands.Geophysics,69(3):762-771.
Unsworth M J,Travis B,Chave A D.1993.Electromagnetic induction by a finite electric dipole source over a 2-D earth.Geophysics,58(2):198-214.
Veeken P C H,Legeydo P J,Davidenko Y A,et al.2009.Benefits of the induced polarization geoelectric method to hydrocarbon exploration.Geophysics,74(2):B47-B59.
Yang B,Xu Y X,He Z X,et al.2012.3Dfrequency-domain modeling of marine controlled source electromagnetic responses with topography using finite volume method.Chinese Journal of Geophysics(in Chinese),55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.
Yin C C,Ben F,Liu Y H,et al.2014.MCSEM 3D modeling for arbitrarily anisotropic media.Chinese Journal of Geophysics(in Chinese),57(12):4110-4122,doi:10.6038/cjg20141222.
蔡红柱,熊彬,Zhdanov M.2015.电导率各向异性的海洋电磁三维有限单元法正演.地球物理学报,58(8):2839-2850,doi:10.6038/cjg20150818.
陈桂波,汪宏年,姚敬金等.2009.各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟.物理学报,58(6):3848-3857.
郭宁宁,昌彦君,贾慧涛.2011.激电效应对海洋可控源电磁测量的影响.∥第十届中国国际地球电磁学术讨论会论文集.南昌:中国地球物理学会,392-395.
何展翔,王绪本.2007.油气藏电性异常模式与电磁法油气检测.石油地球物理勘探,42(1):102-106.
刘长胜,Everett M E,林君等.2010.海底电性源频率域CSEM勘探建模及水深影响分析.地球物理学报,53(8):1940-1952,doi:10.3969/j.issn.0001-5733.2010.08.020.
刘颖,李予国.2011.海洋可控源电磁场2D自适应有限元正演模拟并行算法分析.∥第十届中国国际地球电磁学术讨论会论文集.南昌:中国地球物理学会.
刘颖,李予国.2015.层状各向异性介质中任意取向电偶源的海洋电磁响应.石油地球物理勘探,50(4):755-765.
沈金松,孙文博.2009.二维海底地层可控源海洋电磁响应的数值模拟.石油物探,48(2):188-194.
汤井田,任政勇,化希瑞.2007.Coulomb规范下地电磁场的自适应有限元模拟的理论分析.地球物理学报,50(5):1584-1594.
汤井田,张林成,公劲喆等.2014.三维频率域可控源电磁法有限元-无限元结合数值模拟.中南大学学报(自然科学版),45(4):1252-1260.
杨波,徐义贤,何展翔等.2012.考虑海底地形的三维频率域可控源电磁响应有限体积法模拟,地球物理学报,55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04035.
殷长春,贲放,刘云鹤等.2014.三维任意各向异性介质中海洋可控源电磁法正演研究.地球物理学报,57(12):4110-4122,doi:10.6038/cjg20141222.
Asami K.2002.Characterization of heterogeneous systems by dielectric spectroscopy.Progress in Polymer Science,27(8):1617-1659.
Bruggeman D A G.1935.Berechnung verschiedener physikalischer konstanten von heterogenen Substanzen.I.Dielektrizittskonstanten und Leitfhigkeiten der Mischk9rper aus isotropen Substanzen.Annalen Der Physik,416(7):636-664.
Bussian A E.1983.Electrical conductance in a porous medium.Geophysics,48(9):1258-1268.
Cai H Z,Xiong B,Zhdanov M.2015.Three-dimensional marine controlled-source electromagnetic modelling in anisotropic medium using finite element method.Chinese Journal of Geophysics(in Chinese),58(8):2839-2850,doi:10.6038/cjg20150818.
Chen G B,Wang H N,Yao J J,et al.2009.Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method.Acta Physica Sinica(in Chinese),58(6):3848-3857.
Clennell M B,Josh M,Esteban L,et al.2010.The influence of pyrite on rock electrical properties:A case study from NW Australian gas reservoirs.∥SPWLA 51st Annual Logging Symposium.Perth:Society of Petrophysicists and Well-Log Analysts.
Constable S,Srnka L J.2007.An introduction to marine controlledsource electromagnetic methods for hydrocarbon exploration.Geophysics,72(2):WA3-WA12.
Guo N N,Chang Y J,Jia H T.2011.Influences of induced polarization on marine controlled-source electromagnetic survey(in Chinese).∥The 10th China International Geo-Electromagnetic Workshop.Nanchang:Chinese Geophysical Society,392-395.
Han T C,Clennell M B,Josh M,et al.2015.Determination of effective grain geometry for electrical modeling of sedimentary rocks.Geophysics,80(4):D319-D327.
Hanai T.1960a.Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions.KolloidZeitschrift,171(1):23-31.
Hanai T.1960b.A remark on the“Theory of the dielectric dispersion due to the interfacial polarization”.Kolloid-Zeitschrift,175(1):61-62.
He Z X,Wang X B.2007.Geo-electrical anomalous pattern of reservoir and oil/gas detection by electromagnetic survey.Oil Geophysical Prospecting(in Chinese),42(1):102-106.
JahandariH,Farquharson C G.2015.Finite-volume modelling of geophysical electromagnetic data on unstructured grids using potentials.Geophysical Journal International,202(3):1859-1876.
Jin J.2002.Finite Element Method in Electromagnetic.New York:Wiley-IEEE Press.
Key K,Ovall J.2011.A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling.Geophysical Journal International,186(1):137-154.
Li Y,Key K.2007.2D marine controlled-source electromagnetic modeling:Part 1-An adaptive finite-element algorithm.Geophysics,72(2):WA51-WA62.
Liu C S,Everett M E,Lin J,et al.2010.Modeling of seafloor exploration using electric-source frequency-domain CSEM and the analysis of water depth effect.Chinese Journal of Geophysics(in Chinese),53(8):1940-1952,doi:10.3969/j.issn.0001-5733.2010.08.020.
Liu Y,Li Y G.2011.A Paralleled adaptive finite element modeling for 2D marine controlled-source electromagnetic forward modeling(in Chinese).∥The 10th China International Geo-Electromagnetic Workshop.Nanchang:Chinese Geophysical Society.
Liu Y,Li Y G.2015.Marine controlled-source electromagnetic fields of an arbitrary electric dipole over a layered an isotropic medium.Oil Geophysical Prospecting(in Chinese),50(4):755-765.
Manning M J,Athavale K A.1986.Dielectric properties of pyrite samples at 1100 Mhz.Geophysics,51(1):172-182.
Puzyrev V,Koldan J,De La Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693,doi:10.1093/gii/ggt027.
Schwarzbach C,B9rner R U,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geoelectromagnetics-a marine CSEM example.Geophysical Journal International,187(1):63-74,doi:10.1111/j.1365-246X.2011.05127.x.
Shen J S,Sun W B.2009.Numerical simulation of marine controlledsource electromagnetic(MCSEM)response to 2-D seabed formation.Geophysical Prospecting for Petroleum(in Chinese),48(2):187-194.
Sternberg B K.1991.A review of some experience with the inducedpolarization/resistivity method for hydrocarbon surveys:Successes and limitations.Geophysics,56(10):1522-1532.
Tang J T,Ren Z R,Hua X R.2007.Theoretical analysis of geoelectromagnetic modeling on Coulomb gauged potentials by adaptive finite element method.Chinese Journal of Geophysics(in Chinese),50(5):1584-1594.
Tang J T,Zhang L C,Gong J Z,et al.2014.3Dfrequency domain controlled source electromagnetic numerical modeling with coupled finite-infinite element method.Journal of Central South University(Science and Technology)(in Chinese),45(4):1252-1260.
Ulrich C,Slater L.2004.Induced polarization measurements on unsaturated,unconsolidated sands.Geophysics,69(3):762-771.
Unsworth M J,Travis B,Chave A D.1993.Electromagnetic induction by a finite electric dipole source over a 2-D earth.Geophysics,58(2):198-214.
Veeken P C H,Legeydo P J,Davidenko Y A,et al.2009.Benefits of the induced polarization geoelectric method to hydrocarbon exploration.Geophysics,74(2):B47-B59.
Yang B,Xu Y X,He Z X,et al.2012.3Dfrequency-domain modeling of marine controlled source electromagnetic responses with topography using finite volume method.Chinese Journal of Geophysics(in Chinese),55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.
Yin C C,Ben F,Liu Y H,et al.2014.MCSEM 3D modeling for arbitrarily anisotropic media.Chinese Journal of Geophysics(in Chinese),57(12):4110-4122,doi:10.6038/cjg20141222.
蔡红柱,熊彬,Zhdanov M.2015.电导率各向异性的海洋电磁三维有限单元法正演.地球物理学报,58(8):2839-2850,doi:10.6038/cjg20150818.
陈桂波,汪宏年,姚敬金等.2009.各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟.物理学报,58(6):3848-3857.
郭宁宁,昌彦君,贾慧涛.2011.激电效应对海洋可控源电磁测量的影响.∥第十届中国国际地球电磁学术讨论会论文集.南昌:中国地球物理学会,392-395.
何展翔,王绪本.2007.油气藏电性异常模式与电磁法油气检测.石油地球物理勘探,42(1):102-106.
刘长胜,Everett M E,林君等.2010.海底电性源频率域CSEM勘探建模及水深影响分析.地球物理学报,53(8):1940-1952,doi:10.3969/j.issn.0001-5733.2010.08.020.
刘颖,李予国.2011.海洋可控源电磁场2D自适应有限元正演模拟并行算法分析.∥第十届中国国际地球电磁学术讨论会论文集.南昌:中国地球物理学会.
刘颖,李予国.2015.层状各向异性介质中任意取向电偶源的海洋电磁响应.石油地球物理勘探,50(4):755-765.
沈金松,孙文博.2009.二维海底地层可控源海洋电磁响应的数值模拟.石油物探,48(2):188-194.
汤井田,任政勇,化希瑞.2007.Coulomb规范下地电磁场的自适应有限元模拟的理论分析.地球物理学报,50(5):1584-1594.
汤井田,张林成,公劲喆等.2014.三维频率域可控源电磁法有限元-无限元结合数值模拟.中南大学学报(自然科学版),45(4):1252-1260.
杨波,徐义贤,何展翔等.2012.考虑海底地形的三维频率域可控源电磁响应有限体积法模拟,地球物理学报,55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04035.
殷长春,贲放,刘云鹤等.2014.三维任意各向异性介质中海洋可控源电磁法正演研究.地球物理学报,57(12):4110-4122,doi:10.6038/cjg20141222.