三维井—地电位测井技术的正演模拟研究
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摘要
对于高含水期油田,注水分布和剩余油分布的研究是油气开发中的一个研究热点,也是一个研究难点。三维井-地电位测井作为国内外主要测井技术之一,是一种高效的勘探方法,为剩余油挖潜提供可靠的依据,在油田勘探和开发中能够大幅度提高钻探高效井的成功率,从而达到优化开发方案和提高最终原油采收率的目的。正演计算是我们认识地表电位的良好途径,井-地电位测井技术正演问题指的是已知井中地下介质的电阻率和电导率等参数的分布,求解井-地电位三维地电场的电位分布。本文研究三维井-地电位的正演,可为井-地电位反演成像的实现提供更加充分的正演支持。
对于垂直线电流源,由于源点上电压是奇异的,通常将总电位分离成正常电位和异常电位,采用解析法计算垂直线电流源在均匀大地条件下产生的正常电位;本文从异常电位满足的微分方程出发,采用有限差分方法计算地下异常体引起的异常电位,进一步求解得实际电位,从而实现了三维井-地电位的正演。对于有限差分方法求解过程中形成的线性方程组Aφ=S,对其进行直接解法的计算效率很低,本文引入了不完全Cholesky共轭梯度(ICCG)方法,由于方程组中的A是大型稀疏带状对称矩阵,可以充分利用A的稀疏性,结果计算速度有了很大提高,相反对于内存的要求则大大减少。
为了研究地下三维异常体引起的地表电位响应,本文对水平层状模型等进行了计算,并首次引入倾斜层状异常体以及三维球体异常体模型,最后给出了经过本文正演算法得到的图件。结果表明,本文采用的正演算法快速、精确,并且较准确地反映了地下三维异常体引起的电位响应,为进一步的三维反演研究奠定了基础,提供了约束条件。
The research of infused water distributing and remaining oil is a hot shot to high water cut producer in the industry of oil gas, also a hard nut. As one of main logging technologies in the world, three-dimensional borehole-to-surface logging technology is a valuable method, which can provide reliable basis for tapping the remaining oil, promote substantially success rates of finding efficient wells in the exploration process, finally to optimize development program and promote oil recovery. Forward modeling is a good way to get surface potential, the forward modeling of borehole-to-surface is actually computing potential distribution through the parameters of underground medium, such as conductivity, resistivity. In this paper, the forward with borehole-to-surface is studied and becomes the basis of inversion.
For vertical line source, the total potential is usually divided into normal potential and abnormal one because of voltage singularity in source. Normal potential produced in homogeneous half-space is calculated by analytic method. While for abnormal potential produced by underground anomalous body, Finite Difference Method (FDM) is used based on differential equation of abnormal potential. Further, the total potential is calculated and the forward is realized. The efficiency with direct method to solve the linear equation Aφ=S formed during FDM calculation process is quite slow, in which A is a large sparse band symmetric matrix. Accordingly, Incomplete Cholesky Conjugate Gradient (ICCG) is introduced in this paper, it converges more quickly while requires less memory.
To indicate potential distribution produced by underground anomalous body, models such as layer cake model are calculated in this paper. It is an initiation to introduce dipping bed model and sphericity model in this paper, then maps formed with FDM calculation are exhibited. It shows that forward modeling of this paper is fast in convergence and accurate, also images potential distribution more precisely, being the foundation of further inversion and providing constraints.
对于垂直线电流源,由于源点上电压是奇异的,通常将总电位分离成正常电位和异常电位,采用解析法计算垂直线电流源在均匀大地条件下产生的正常电位;本文从异常电位满足的微分方程出发,采用有限差分方法计算地下异常体引起的异常电位,进一步求解得实际电位,从而实现了三维井-地电位的正演。对于有限差分方法求解过程中形成的线性方程组Aφ=S,对其进行直接解法的计算效率很低,本文引入了不完全Cholesky共轭梯度(ICCG)方法,由于方程组中的A是大型稀疏带状对称矩阵,可以充分利用A的稀疏性,结果计算速度有了很大提高,相反对于内存的要求则大大减少。
为了研究地下三维异常体引起的地表电位响应,本文对水平层状模型等进行了计算,并首次引入倾斜层状异常体以及三维球体异常体模型,最后给出了经过本文正演算法得到的图件。结果表明,本文采用的正演算法快速、精确,并且较准确地反映了地下三维异常体引起的电位响应,为进一步的三维反演研究奠定了基础,提供了约束条件。
The research of infused water distributing and remaining oil is a hot shot to high water cut producer in the industry of oil gas, also a hard nut. As one of main logging technologies in the world, three-dimensional borehole-to-surface logging technology is a valuable method, which can provide reliable basis for tapping the remaining oil, promote substantially success rates of finding efficient wells in the exploration process, finally to optimize development program and promote oil recovery. Forward modeling is a good way to get surface potential, the forward modeling of borehole-to-surface is actually computing potential distribution through the parameters of underground medium, such as conductivity, resistivity. In this paper, the forward with borehole-to-surface is studied and becomes the basis of inversion.
For vertical line source, the total potential is usually divided into normal potential and abnormal one because of voltage singularity in source. Normal potential produced in homogeneous half-space is calculated by analytic method. While for abnormal potential produced by underground anomalous body, Finite Difference Method (FDM) is used based on differential equation of abnormal potential. Further, the total potential is calculated and the forward is realized. The efficiency with direct method to solve the linear equation Aφ=S formed during FDM calculation process is quite slow, in which A is a large sparse band symmetric matrix. Accordingly, Incomplete Cholesky Conjugate Gradient (ICCG) is introduced in this paper, it converges more quickly while requires less memory.
To indicate potential distribution produced by underground anomalous body, models such as layer cake model are calculated in this paper. It is an initiation to introduce dipping bed model and sphericity model in this paper, then maps formed with FDM calculation are exhibited. It shows that forward modeling of this paper is fast in convergence and accurate, also images potential distribution more precisely, being the foundation of further inversion and providing constraints.
引文
[1]林宏亮,金重熙.地球物理层析成像技术和三维成像的基本原理[J].地球物理学报,1986,29(2):185～196
[2]沈金松,佟文琪,房德斌.用跨井电磁波资料重现地下介质的电阻率分布[J].石油地球物理勘探,2000,35(6):741～750
[3]曹立斌,孟永良,周建兰.电阻率层析成像技术的回顾与展望[J].勘探地球物理进展,2004,27(3):170～173
[4] Lines L R, Jones F W. The perturbation of alternating geomagnetic fields by three-dimensional island structures [J]. Geophys J Roy Astr Soc, 1973, 32(2):133～154
[5] Zhdanov M S. The construction of effective methods for electromagnetic modeling [J]. Geophys J Roy AstrSoc, 1982, 68(5):589～607
[6] Mizunaga H, Ushijima K.流電電位法のデータ處理に關する研究[J].物理探查,1988,41(5):345～359
[7] Mizunaga H,Ushijima K.流電電位法の3次元モデリング[J].物理探查, 1991,44(4):215～226
[8]水永秀树,牛岛惠辅.流电电位法三维模拟[J].物理探查,1991,44(4):215-226.32(2):1～17
[9] Torres-Verdin,C.,and Habashy,T.M. Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation: Radio Science,1994,29,1051～1079
[10]徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994:178～193
[11]徐世浙,刘斌,阮百尧.电阻率法中求解异常电位的有限单元法[J].地球物理学报,1994,37(2):511～515
[12]周熙襄,钟本善.电法勘探数值模拟技术[M].成都:四川科学技术出版社,1986: 163～239
[13]吴小平,徐果明,李时灿.利用不完全Cholesky共轭梯度法求解点源三维电场[J].地球物理学报,1998,41(6):848～855
[14]吴小平,汪彤彤.利用共轭梯度算法的电阻率三维有限元正演[J].地球物理学报,2003,46(3):428～432
[15]王志刚,何展翔,等.井地直流电法三维数值模拟及异常规律研究[J].工程地球物理学报,2006,3(2):87～92
[16]徐凯军,李桐林.垂直有限线源三维地电场有限差分正演研究[J].吉林大学学报(地球科学版),2006, 36(1):137～141
[17]刘地渊,徐凯军,等.任意形状线电流源三维地电场研究[J].地球物理学进展,2006,21(2):395～399
[18]毛先进,鲍光淑,宋守根.半空间中多个三维体电阻率响应的边界积分方程模拟[J].地球物理学报,1996,39(6),823～834
[19]毛先进,鲍光淑. 2.5维问题电阻率正演的新方法[J].中南工业大学学报,1997,28(4),307～310
[20] Ranganayaki R P, Akturk S E, Fryer S M. Formation Resistivity Variation Due to Steam Flooding: A Log Study [J]. Geophysics, 1992, 57(3):488~494
[21] Mansure A J, Meldau R F, Weyland H V. Field Examples of Electrical Resistivity Changes During Steam-flooding [J]. SPE Formation Evaluation, 1993, 8(1):57~64
[22] Wilt M J, Morrison H f, Becker A and Tseng H W et al. A New Technology for Oil Field Characterization. The Leading Edge, 1995, 14, 173~177
[23] KAUFMAN A A and WIGHTMAN W E. Transmission-line model for electrical logging through casing [J]. Geophysics, 1993, 58(12):1739~1747
[24] SCHENKEL C J and MORRISON H F. Electrical resistivity measurement through metal casing [J]. Geophysics, 1994, 59(7):1072~1082
[25]张金成.电位法井间监测技术[J].地震地质,2001,23(2):292~300
[26]何展翔,贺振华,孔繁恕.非地震技术在油田开发中的应用综述[J].石油地球物理勘探,2001,36(增刊):1~4
[27]乔松,周锰钰,白朗.勘探电磁场论[M].中国矿业大学出版社,1991
[28] McGillivray P R, Oldenburg D W and Ellis R G et al . Calculation of Sensitivity for the Frequency - Domain Eletromagnetics. Geophys.J.Int., 1994, 116(1):1~4
[29]张胜业.应用地球物理学原理[M].中国地质大学出版社,2004
[30]傅良魁.应用地球物理教程:电法放射性地热[M].地质出版社,1991
[31] LE Masne, POIRMEUR A T, et al. Three-dimensional results for an electrical hole-to-surface method: application to the interpretation of field survey[J]. Geophysics, 1988, 52(4):85~103
[32] Coggon, J. H.. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971, v. 36.p. 132
[33]吴小平,徐果明.不完全Cholesky共轭梯度法及其在地电场计算中的应用.石油地球物理勘探,1998,33(1):89~94
[34]王世瑞,王金金,冯有前,等.计算方法[M].西安:电子科技大学出版社,1997,1:33~41
[35] PCGPAK User’s Guide( NEW Haven: Scientific Computing Associates, Inc)
[36] Bentley J. Programming Pearls(Reading, Ma: Addision-Wesley Publ Co), 1986
[37]舒继武,赵金熙,张德富.解大型稀疏线性方程组的一种有效并行ICCG法[J].计算机工程与应用,1999:30~34
[38]吴小平,徐果明.利用ICCG迭代技术加快电阻率三维正演计算[J].煤田地质与勘探,1999,27(3):62~65
[39] Meijerink J A, Van Der Vorst H A. An iterative solution method for linear system of which the coefficient matrix is a symmetric matrix. Math. Comp., 1977, 31(137):148~162
[40] Kershaw D S. The Incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J Comp Phys, 1978, 26:43~45
[41] Manteuffel T A. An incomplete factorization technique for positive definite linear systems. Math Comp, 1980, 34:473~497
[2]沈金松,佟文琪,房德斌.用跨井电磁波资料重现地下介质的电阻率分布[J].石油地球物理勘探,2000,35(6):741～750
[3]曹立斌,孟永良,周建兰.电阻率层析成像技术的回顾与展望[J].勘探地球物理进展,2004,27(3):170～173
[4] Lines L R, Jones F W. The perturbation of alternating geomagnetic fields by three-dimensional island structures [J]. Geophys J Roy Astr Soc, 1973, 32(2):133～154
[5] Zhdanov M S. The construction of effective methods for electromagnetic modeling [J]. Geophys J Roy AstrSoc, 1982, 68(5):589～607
[6] Mizunaga H, Ushijima K.流電電位法のデータ處理に關する研究[J].物理探查,1988,41(5):345～359
[7] Mizunaga H,Ushijima K.流電電位法の3次元モデリング[J].物理探查, 1991,44(4):215～226
[8]水永秀树,牛岛惠辅.流电电位法三维模拟[J].物理探查,1991,44(4):215-226.32(2):1～17
[9] Torres-Verdin,C.,and Habashy,T.M. Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation: Radio Science,1994,29,1051～1079
[10]徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994:178～193
[11]徐世浙,刘斌,阮百尧.电阻率法中求解异常电位的有限单元法[J].地球物理学报,1994,37(2):511～515
[12]周熙襄,钟本善.电法勘探数值模拟技术[M].成都:四川科学技术出版社,1986: 163～239
[13]吴小平,徐果明,李时灿.利用不完全Cholesky共轭梯度法求解点源三维电场[J].地球物理学报,1998,41(6):848～855
[14]吴小平,汪彤彤.利用共轭梯度算法的电阻率三维有限元正演[J].地球物理学报,2003,46(3):428～432
[15]王志刚,何展翔,等.井地直流电法三维数值模拟及异常规律研究[J].工程地球物理学报,2006,3(2):87～92
[16]徐凯军,李桐林.垂直有限线源三维地电场有限差分正演研究[J].吉林大学学报(地球科学版),2006, 36(1):137～141
[17]刘地渊,徐凯军,等.任意形状线电流源三维地电场研究[J].地球物理学进展,2006,21(2):395～399
[18]毛先进,鲍光淑,宋守根.半空间中多个三维体电阻率响应的边界积分方程模拟[J].地球物理学报,1996,39(6),823～834
[19]毛先进,鲍光淑. 2.5维问题电阻率正演的新方法[J].中南工业大学学报,1997,28(4),307～310
[20] Ranganayaki R P, Akturk S E, Fryer S M. Formation Resistivity Variation Due to Steam Flooding: A Log Study [J]. Geophysics, 1992, 57(3):488~494
[21] Mansure A J, Meldau R F, Weyland H V. Field Examples of Electrical Resistivity Changes During Steam-flooding [J]. SPE Formation Evaluation, 1993, 8(1):57~64
[22] Wilt M J, Morrison H f, Becker A and Tseng H W et al. A New Technology for Oil Field Characterization. The Leading Edge, 1995, 14, 173~177
[23] KAUFMAN A A and WIGHTMAN W E. Transmission-line model for electrical logging through casing [J]. Geophysics, 1993, 58(12):1739~1747
[24] SCHENKEL C J and MORRISON H F. Electrical resistivity measurement through metal casing [J]. Geophysics, 1994, 59(7):1072~1082
[25]张金成.电位法井间监测技术[J].地震地质,2001,23(2):292~300
[26]何展翔,贺振华,孔繁恕.非地震技术在油田开发中的应用综述[J].石油地球物理勘探,2001,36(增刊):1~4
[27]乔松,周锰钰,白朗.勘探电磁场论[M].中国矿业大学出版社,1991
[28] McGillivray P R, Oldenburg D W and Ellis R G et al . Calculation of Sensitivity for the Frequency - Domain Eletromagnetics. Geophys.J.Int., 1994, 116(1):1~4
[29]张胜业.应用地球物理学原理[M].中国地质大学出版社,2004
[30]傅良魁.应用地球物理教程:电法放射性地热[M].地质出版社,1991
[31] LE Masne, POIRMEUR A T, et al. Three-dimensional results for an electrical hole-to-surface method: application to the interpretation of field survey[J]. Geophysics, 1988, 52(4):85~103
[32] Coggon, J. H.. Electromagnetic and electrical modeling by the finite element method. Geophysics, 1971, v. 36.p. 132
[33]吴小平,徐果明.不完全Cholesky共轭梯度法及其在地电场计算中的应用.石油地球物理勘探,1998,33(1):89~94
[34]王世瑞,王金金,冯有前,等.计算方法[M].西安:电子科技大学出版社,1997,1:33~41
[35] PCGPAK User’s Guide( NEW Haven: Scientific Computing Associates, Inc)
[36] Bentley J. Programming Pearls(Reading, Ma: Addision-Wesley Publ Co), 1986
[37]舒继武,赵金熙,张德富.解大型稀疏线性方程组的一种有效并行ICCG法[J].计算机工程与应用,1999:30~34
[38]吴小平,徐果明.利用ICCG迭代技术加快电阻率三维正演计算[J].煤田地质与勘探,1999,27(3):62~65
[39] Meijerink J A, Van Der Vorst H A. An iterative solution method for linear system of which the coefficient matrix is a symmetric matrix. Math. Comp., 1977, 31(137):148~162
[40] Kershaw D S. The Incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J Comp Phys, 1978, 26:43~45
[41] Manteuffel T A. An incomplete factorization technique for positive definite linear systems. Math Comp, 1980, 34:473~497