基于时域有限差分法的随钻电磁波测井响应数值计算研究
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摘要
地层电各向异性是目前电法测井研究的重要领域,电各向异性介质中的电磁波传播特性国内外研究的很少。本文应用时域有限差分方法研究了随钻电磁波测井在电各向异性地层中的响应特性和瞬态传播特性,主要包括以下几个方面。
首先,在分析地层电各向异性特点和随钻电磁波测井原理的基础上,推导建立了磁偶极子源在电各向异性介质中产生的电磁场的三维FDTD计算公式,分析了稳定性和边界条件,编程实现了相应的计算程序。
其次,推导了电各向异性地层中的波动方程,指出三个方向的电导率不同,相应的幅度衰减和相移不同,电磁波相速也不同,导致各个方向的传播特性不一样。应用FDTD方法分析了电磁波在电各向异性介质中的瞬态特性,观察到经过3个周期后信号才能变为稳定的等幅振荡。通过引入升余弦函数使信号在1个周期就达到稳定状态。计算分析了单轴和双轴电各向异性地层中的瞬态传播特性,结果表明,单轴电各向异性地层中垂直电导率的变化对测量得到的磁场值不产生影响;双轴电各向异性地层中σ_x＞σ_y与σ_x＜σ_y的传播不同,前者的磁场Hz幅度小。研究了电各向异性地层中不同发射频率情况下电磁波传播特性,发射频率越大,电磁波衰减快,受趋肤效应影响大。
最后,重点研究了FDTD方法在随钻电磁波测井响应数值模拟中的应用。计算比较了垂直和水平磁偶极子源在电各向同性和单轴地层中的仪器响应特性。水平磁偶极子源的仪器响应受趋肤影响小,线性好。列表分析了径向三层地层中两种侵入深度下电各向异性电导率不同时的垂直磁偶极子源的响应特性。分析了目的层为单轴电各向异性地层的纵向三层地层中垂直磁偶极子源在不同位置时的响应特性。研究成果为随钻电磁波测井在电各向异性地层中的响应解释提供了理论基础。
The conductivity anisotropy of formation is the key study field in the conductivityal logging. There are a few researches about the electromagnetic wave propagation in the conductivity anisotropic formation both at home and abroad. This dissertation studies the response characteristic of the electromagnetic wave propagation resistivity logging (EPRL) and transient characteristic of the electromagnetic wave in the conductivity anisotropic formation by using the finite-difference time-domain method (FDTD). The contents include the follow three topics.
Firstly, based on the analysis of the feature of conductivity anisotropic formation and the theory of EPRL, the three dimensional FDTD formulae of the conductivity anisotropic formation in Cartesian coordinate system are derived. The source is the magnetic poles. At the same time, the stability and absorbing boundary conditions are given, and the code is designed.
Secondly, the wave equation in the conductivity anisotropic formation is derived. When conductivity in three directions is different, the corresponding amplitude attenuation, phase shift and phase velocity are all different, thus the propagation characteristics in three directions are different. The FDTD is applied to analyze the transient characteristic f the electromagnetic wave. We observe that signal can reach the steady oscillation after there periods. By introducing the up cosine function, the signal can reach the steady of scillation after one period. The transient characteristics of the electromagnetic wave in single and dual axis conductivity anisotropic formation are calculated. The results show that the change of the vertical conductivity has no effect on the magnetic field in the single axis conductivity anisotropic formation; the amplitude of magnetic field whenσ_x >σ_y is less than that whenσ_x <σ_y in the dual axis conductivity anisotropic formation. Further more, the transient characteristics of the electromagnetic wave at different transmitting frequency is analyzed. The results show that the higher frequency, the attenuation of the wave is faster and the skin effect is more serious.
Finally, FDTD method is used to calculate the response of EPRL in the various formations. The tool response characteristics in the isotropic and single axis formation are compared. The source is vertical or horizontal magnetic pole. The response of the horizontal magnetic pole is linear and has weaker skin effect. The response characteristics of vertical magnetic pole in the formation with three layers in radial direction are concluded by table. There are two invasion depth, and different isotropic conductivities. The response characteristics of vertical magnetic pole in different positions are analyzed when target formation is the single axis anisotropy and other two adjacent layers are isotropic. All above results will provide the theoretical foundation for the abnormal response interpretation of EPRL in the conductivity anisotropic formation.
首先,在分析地层电各向异性特点和随钻电磁波测井原理的基础上,推导建立了磁偶极子源在电各向异性介质中产生的电磁场的三维FDTD计算公式,分析了稳定性和边界条件,编程实现了相应的计算程序。
其次,推导了电各向异性地层中的波动方程,指出三个方向的电导率不同,相应的幅度衰减和相移不同,电磁波相速也不同,导致各个方向的传播特性不一样。应用FDTD方法分析了电磁波在电各向异性介质中的瞬态特性,观察到经过3个周期后信号才能变为稳定的等幅振荡。通过引入升余弦函数使信号在1个周期就达到稳定状态。计算分析了单轴和双轴电各向异性地层中的瞬态传播特性,结果表明,单轴电各向异性地层中垂直电导率的变化对测量得到的磁场值不产生影响;双轴电各向异性地层中σ_x＞σ_y与σ_x＜σ_y的传播不同,前者的磁场Hz幅度小。研究了电各向异性地层中不同发射频率情况下电磁波传播特性,发射频率越大,电磁波衰减快,受趋肤效应影响大。
最后,重点研究了FDTD方法在随钻电磁波测井响应数值模拟中的应用。计算比较了垂直和水平磁偶极子源在电各向同性和单轴地层中的仪器响应特性。水平磁偶极子源的仪器响应受趋肤影响小,线性好。列表分析了径向三层地层中两种侵入深度下电各向异性电导率不同时的垂直磁偶极子源的响应特性。分析了目的层为单轴电各向异性地层的纵向三层地层中垂直磁偶极子源在不同位置时的响应特性。研究成果为随钻电磁波测井在电各向异性地层中的响应解释提供了理论基础。
The conductivity anisotropy of formation is the key study field in the conductivityal logging. There are a few researches about the electromagnetic wave propagation in the conductivity anisotropic formation both at home and abroad. This dissertation studies the response characteristic of the electromagnetic wave propagation resistivity logging (EPRL) and transient characteristic of the electromagnetic wave in the conductivity anisotropic formation by using the finite-difference time-domain method (FDTD). The contents include the follow three topics.
Firstly, based on the analysis of the feature of conductivity anisotropic formation and the theory of EPRL, the three dimensional FDTD formulae of the conductivity anisotropic formation in Cartesian coordinate system are derived. The source is the magnetic poles. At the same time, the stability and absorbing boundary conditions are given, and the code is designed.
Secondly, the wave equation in the conductivity anisotropic formation is derived. When conductivity in three directions is different, the corresponding amplitude attenuation, phase shift and phase velocity are all different, thus the propagation characteristics in three directions are different. The FDTD is applied to analyze the transient characteristic f the electromagnetic wave. We observe that signal can reach the steady oscillation after there periods. By introducing the up cosine function, the signal can reach the steady of scillation after one period. The transient characteristics of the electromagnetic wave in single and dual axis conductivity anisotropic formation are calculated. The results show that the change of the vertical conductivity has no effect on the magnetic field in the single axis conductivity anisotropic formation; the amplitude of magnetic field whenσ_x >σ_y is less than that whenσ_x <σ_y in the dual axis conductivity anisotropic formation. Further more, the transient characteristics of the electromagnetic wave at different transmitting frequency is analyzed. The results show that the higher frequency, the attenuation of the wave is faster and the skin effect is more serious.
Finally, FDTD method is used to calculate the response of EPRL in the various formations. The tool response characteristics in the isotropic and single axis formation are compared. The source is vertical or horizontal magnetic pole. The response of the horizontal magnetic pole is linear and has weaker skin effect. The response characteristics of vertical magnetic pole in the formation with three layers in radial direction are concluded by table. There are two invasion depth, and different isotropic conductivities. The response characteristics of vertical magnetic pole in different positions are analyzed when target formation is the single axis anisotropy and other two adjacent layers are isotropic. All above results will provide the theoretical foundation for the abnormal response interpretation of EPRL in the conductivity anisotropic formation.
引文
[1]徐莉莉,夏克文,朱军.测井学[M].北京:石油工业出版社,1998,283-285.
[2]时程鹏,随钻测井技术在我国石油勘探开发中的应用[J].测井技术,2002,26(6),441-445.
[3]Electrical Logging[J].The Oil Weekly,July 15,1935.
[4]Baad Bargach,et al.Real-Time LWD:Logging for Drilling[J].Oilfieid Review,Autumn,2000.
[5]张辛耘,郭彦军,王敬农.随钻测井的昨天,今天和明天[J].测井技术,2006,30(6),487-488.
[6]郭彦军,张辛耘,王敬农.对我国发展随钻测井技术和装备的思考[J].石油仪器,2007,21(2),1-4.
[7]Zhou,Q,etal.Update Survey of MWD Resisitivity Tools[EB/OL].http://www.spwla.org/MWD tool summary/July 2005.
[8]张建华,刘振华,仵杰.电法测井原理与应用[M].西北大学出版社,2002,63-65.
[9]Kunz,K S and Moran J H.Some effects of formation anisotropy on restivity measurements in boreholes[J].Geophysics,1958,23,770-794.
[10]Moran J H and Gianzero S.Effects of formation anisotropy of resistivity logging measurements[J].Geophysics,1979,44(7):1266-1286.
[11]Chemali,R,Gianzero,S,and Su,S M.The effect of shale anisotropy on focused resistivity devices[C].SPWLA 28th Annual Logging Symposium,1987,Paper H.
[12]L(u|¨)ling,M G,and Shray,F.Processing and modeling 2-MHz resistivity tools in dipping,laminated,anisotropic formations[C].SPWLA 35th Annual Logging Symposium,June 19-22,1994.
[13]Anderson,B I,Barber,T D and Luling,M G.The response of induction tools to dipping,anisotropic formations[C].SPWLA 36th Annual Logging Symposium,June 26-29,1995.
[14]Moran,J H,and Gianzero,S,Effects of formation anisotropy of resistivity logging measurements[J].Geophysics,1979,vol.44,no.7,p.1266-1286.
[15]Bittar,M S,and Rodney,P F.The effects of rock anisotropy on MWD electromagnetic wave resistivity Sensors[J].The Log Analyst,January-February 1996.
[16]Graciet,S,Shen,L C.Theory and numerical simulation of induction and resistivity tools in anisotropic dipping bed[J].The Log Analyst,January-February 1998.
[17]Wang Tsili and Fang S.3-D electromagnetic anisotropy modeling using finite differences[J].Geophysics,2001,66(5):1386-1396.
[18]Newman G A and Alumbaugh D L.Three dimensional induction logging problems,Part 2:A finite difference solution[J].Geophysics,2002,67(5).
[19]Weiss C J and Newman G A.Electromagnetic induction in a fully 3D anisotropy earth[J].Geophysics,2002,67(4):1104-1114.
[20]Weiss C J and Newman G A.Electromagnetic induction in a generalized 3D anisotropy earth,part2:the LIN preconditioner[J].Geophysics,2003,68(3):922-930.
[21]Fang Sheng,Gao Guozhong,Torres-Verdin Carlos.Efficient 3-D electromagnetic modeling in the presence of anisotropic conductive media using integral equation[J].3DEMIII Worshop,2003,February.
[22]Gao Guozhong,Torres-Verdin,Carlos and Fang Sheng.Fast 3D modeling of borehole induction measurements in dipping and anisotropic formations using a novel approximation technique[J].Petrophysics,2004,45(4):335-349.
[23]王昌学,杨韦华,覃世银,陶果,沈金松,何宝庆.垂直井中三分量感应测井的大型三维有限差分模拟[J].测井技术,2003,27(6),459-452.
[24]沈金松.用有限差分法计算各向异性介质中多分量感应测井的响应[J].地球物理学进展,2004,19(1),101-107.
[25]覃世银,王昌学,杨韦华,陶果,沈金松.各向异性地层中电磁散射响应的计算及应用[J].测井技术,2004,28(3),191-195.
[26]陈峰,安金珍,廖椿庭.原始电阻率各向异性原始电阻率变化的方向性[J].地球物理学报,2003,46(2),271-280.
[27]Yee K S.Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media.IEEE Trans Antennas Propagat.1966-5,AP-14(3):302-307.
[28]葛德彪,闫玉波,电磁波时域有限差分方法[M].西安电子科技大学出版社,2002,19-24.
[29]Rodney P F,Wisler M M.Electromagnetic wave resisitivity MWD tool[J].S P E Drilling Engineering,1986,10,337-346.
[30]达耶夫.高频电磁测井方法[M].北京:石油工业出版社,1981,34-35.
[31]张善成,杨荣,王秋月.感应及MWD电阻率测井仪在各向异性倾斜地层中的相应与数值模拟[J].世界石油工业.1999,6(4),17-21.
[2]时程鹏,随钻测井技术在我国石油勘探开发中的应用[J].测井技术,2002,26(6),441-445.
[3]Electrical Logging[J].The Oil Weekly,July 15,1935.
[4]Baad Bargach,et al.Real-Time LWD:Logging for Drilling[J].Oilfieid Review,Autumn,2000.
[5]张辛耘,郭彦军,王敬农.随钻测井的昨天,今天和明天[J].测井技术,2006,30(6),487-488.
[6]郭彦军,张辛耘,王敬农.对我国发展随钻测井技术和装备的思考[J].石油仪器,2007,21(2),1-4.
[7]Zhou,Q,etal.Update Survey of MWD Resisitivity Tools[EB/OL].http://www.spwla.org/MWD tool summary/July 2005.
[8]张建华,刘振华,仵杰.电法测井原理与应用[M].西北大学出版社,2002,63-65.
[9]Kunz,K S and Moran J H.Some effects of formation anisotropy on restivity measurements in boreholes[J].Geophysics,1958,23,770-794.
[10]Moran J H and Gianzero S.Effects of formation anisotropy of resistivity logging measurements[J].Geophysics,1979,44(7):1266-1286.
[11]Chemali,R,Gianzero,S,and Su,S M.The effect of shale anisotropy on focused resistivity devices[C].SPWLA 28th Annual Logging Symposium,1987,Paper H.
[12]L(u|¨)ling,M G,and Shray,F.Processing and modeling 2-MHz resistivity tools in dipping,laminated,anisotropic formations[C].SPWLA 35th Annual Logging Symposium,June 19-22,1994.
[13]Anderson,B I,Barber,T D and Luling,M G.The response of induction tools to dipping,anisotropic formations[C].SPWLA 36th Annual Logging Symposium,June 26-29,1995.
[14]Moran,J H,and Gianzero,S,Effects of formation anisotropy of resistivity logging measurements[J].Geophysics,1979,vol.44,no.7,p.1266-1286.
[15]Bittar,M S,and Rodney,P F.The effects of rock anisotropy on MWD electromagnetic wave resistivity Sensors[J].The Log Analyst,January-February 1996.
[16]Graciet,S,Shen,L C.Theory and numerical simulation of induction and resistivity tools in anisotropic dipping bed[J].The Log Analyst,January-February 1998.
[17]Wang Tsili and Fang S.3-D electromagnetic anisotropy modeling using finite differences[J].Geophysics,2001,66(5):1386-1396.
[18]Newman G A and Alumbaugh D L.Three dimensional induction logging problems,Part 2:A finite difference solution[J].Geophysics,2002,67(5).
[19]Weiss C J and Newman G A.Electromagnetic induction in a fully 3D anisotropy earth[J].Geophysics,2002,67(4):1104-1114.
[20]Weiss C J and Newman G A.Electromagnetic induction in a generalized 3D anisotropy earth,part2:the LIN preconditioner[J].Geophysics,2003,68(3):922-930.
[21]Fang Sheng,Gao Guozhong,Torres-Verdin Carlos.Efficient 3-D electromagnetic modeling in the presence of anisotropic conductive media using integral equation[J].3DEMIII Worshop,2003,February.
[22]Gao Guozhong,Torres-Verdin,Carlos and Fang Sheng.Fast 3D modeling of borehole induction measurements in dipping and anisotropic formations using a novel approximation technique[J].Petrophysics,2004,45(4):335-349.
[23]王昌学,杨韦华,覃世银,陶果,沈金松,何宝庆.垂直井中三分量感应测井的大型三维有限差分模拟[J].测井技术,2003,27(6),459-452.
[24]沈金松.用有限差分法计算各向异性介质中多分量感应测井的响应[J].地球物理学进展,2004,19(1),101-107.
[25]覃世银,王昌学,杨韦华,陶果,沈金松.各向异性地层中电磁散射响应的计算及应用[J].测井技术,2004,28(3),191-195.
[26]陈峰,安金珍,廖椿庭.原始电阻率各向异性原始电阻率变化的方向性[J].地球物理学报,2003,46(2),271-280.
[27]Yee K S.Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media.IEEE Trans Antennas Propagat.1966-5,AP-14(3):302-307.
[28]葛德彪,闫玉波,电磁波时域有限差分方法[M].西安电子科技大学出版社,2002,19-24.
[29]Rodney P F,Wisler M M.Electromagnetic wave resisitivity MWD tool[J].S P E Drilling Engineering,1986,10,337-346.
[30]达耶夫.高频电磁测井方法[M].北京:石油工业出版社,1981,34-35.
[31]张善成,杨荣,王秋月.感应及MWD电阻率测井仪在各向异性倾斜地层中的相应与数值模拟[J].世界石油工业.1999,6(4),17-21.