斜井、水平井双侧向测井响应三维有限元数值分析
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摘要
双侧向测井是电阻率测井方法中使用最广泛的方法之一,可以有效的评价地层的孔隙度和含油气饱和度及其产能,为油气藏的描述和油田地质情况的研究以及油层岩性的确定提供参考资料。
针对当前石油勘探开发过程中水平井和斜井应用的实际需求,按照双侧向测井仪器模型和工作方式,文章利用三维有限元方法成功模拟双侧向测井仪器在斜井和水平井中的响应,得到测井仪器在地层中的响应曲线,进而获得地层的电阻率分布,为斜井和水平井相应的解释工作提供参照根据。本文的创新点是采用三维网格加密技术完善了程序模拟复杂地层的能力,应用高阶基函数并结合优化后的边界条件,提高了三维有限元素法的计算效率和精度;本文提出的新算法同传统的三维有限元素法相比,能够在相同精度情况下,可以将计算效率提高一个数量级。
在第一章绪论部分,描述了本文的研究背景和国内外研究现状,并且对有限元素法进行了简单描述并给出了本文的主要研究贡献。
在第二章中,介绍了双侧向测井仪器的仪器的结构和工作原理。
在第三章中详细论述了利用有限元法进行双侧向测井数值分析的过程,从双侧向测井中电场满足的微分方程式出发,给出泛函表达式和边界条件,经过离散化求解泛函的极值达到求解边值问题。文中详细给出了网格划分和边界处理方法,最后通过前线解法求刚度矩阵,得到深浅侧向监督电极上的电压从而求出深浅侧向的仪器响应。文章通过改进网格划分方法,实现了斜井水平井多地层和侵入偏心模型的构造,提高了程序处理复杂地层的能力;通过改进电极处理方法,成功模拟B电极对测量结果和电流线分布的影响,定量的给出B电极对测量结果的影响。
在第四章中,针对三维有限元方法中线性插值基函数影响仿真效率和精度的问题,采用高阶基函数,使得在相对稀疏的网格下就可以得到具有较高精度的仿真结果,不仅节省了计算时间,而且还提高了程序的仿真精度,并且通过改进深侧向边界的处理条件,改进了深侧向结果的精确度。
第五章针对测井工作所遇到的常见地层和环境条件,开展了一系列模拟计算,对影响双侧向测井仪器响应的参数进行了详细研究。分析仪器不同几何结构对结果的影响;斜井中,通过分析不同角度对仪器响应结果的影响,给出了特定地层中的斜井的围岩校正图板;在水平井中通过分析地层中侵入、围岩、目的层等对仪器响应结果的影响,并制作了特定地层中的井孔上下距离校正图板、侵入校正图板和围岩层厚校正图板。
最后给出了本论文的总结和工作展望。作为本课题研究成果,三维有限元双侧向测井仿真程序能够快速仿真计算测井曲线,可用于解释石油测井曲线。
Lateral logging is one of the most popular methods in resistivity well logging, it is widely used to evaluate the porosity and saturation of oil and gas and its production. And can be used to give the description of reservoir and geological conditions and lithology of oil.
For the application of horizontal wells and deviate wells in the well logging process, the author simulations Lateral logging equipment response in deviate and horizontal well according to the mode it works by using three dimension finite element method. By using this method, We can get the equipment response curve and resistivity distribution of stratum, it helps to give the interpretation of logging. The innovation of this paper is adopt the remesh method to build model precisionly and in order to modeling dual laterolog response efficiently and accurately, high order basis function is adopted. The results show it has higher efficiency and precision compared with linear basis function. The architecture of this paper as follows:
The research of lateral logging domestic and abroad is given in chapter 1, and so is the finite element method and the main contribution of this paper.
In chapter 2, the mode of lateral logging equipment is given is given.
In chapter 3, the author discusses the process of numerical analysis of the lateral well logging using finite element method in detail. First of all, base the principle of finite element method, differential equations which the field of logging obeys is given, from which gives functional expression and boundary condition, finally, using frontal method to solve stiffness matrix and get the monitor electrode voltage, so we can get the deep and shallow equipment response. By improving the mesh method, multiple stratum in horizontal well and invaded eccentricity can be exitly modeled. the B-electrode also in consideration, results show that it will impact the deep lateral logging result and current.
In chapter 4, the auther improves process of simulation of lateral logging. In order to modeling lateral logging response efficiently and accurately, high order basis function is adopted. it shows the higher efficiency and precision compared with linear basis function. Furthermore, the anther optimized the mesh and the boundary condition to reduce the error caused by them.
In chapter 5, many simulation results in common environmental condition are given for research of response of lateral logging. By simulation the different electrode, different results and different electrode constant are given. Many conclusion and bed thinkness correction are given in deviate well with different angle and different condition; In horizontal well, different layer and invation is analysised and response curves are given, invasion correction chart and bed thickness correction chart are alse made.
Finally, the summarization and expectation of this paper is given. As one of the result of this research, the program of simulating the response of laterolog using 3D finite element method can give result quickly and exitly, it can be help to judge the interpretation of well logging response. The resistivity distribution of stratum which gotten by simulation is an important parameter in interpretation course. The results of this research have good prospects in logging interpretation.
针对当前石油勘探开发过程中水平井和斜井应用的实际需求,按照双侧向测井仪器模型和工作方式,文章利用三维有限元方法成功模拟双侧向测井仪器在斜井和水平井中的响应,得到测井仪器在地层中的响应曲线,进而获得地层的电阻率分布,为斜井和水平井相应的解释工作提供参照根据。本文的创新点是采用三维网格加密技术完善了程序模拟复杂地层的能力,应用高阶基函数并结合优化后的边界条件,提高了三维有限元素法的计算效率和精度;本文提出的新算法同传统的三维有限元素法相比,能够在相同精度情况下,可以将计算效率提高一个数量级。
在第一章绪论部分,描述了本文的研究背景和国内外研究现状,并且对有限元素法进行了简单描述并给出了本文的主要研究贡献。
在第二章中,介绍了双侧向测井仪器的仪器的结构和工作原理。
在第三章中详细论述了利用有限元法进行双侧向测井数值分析的过程,从双侧向测井中电场满足的微分方程式出发,给出泛函表达式和边界条件,经过离散化求解泛函的极值达到求解边值问题。文中详细给出了网格划分和边界处理方法,最后通过前线解法求刚度矩阵,得到深浅侧向监督电极上的电压从而求出深浅侧向的仪器响应。文章通过改进网格划分方法,实现了斜井水平井多地层和侵入偏心模型的构造,提高了程序处理复杂地层的能力;通过改进电极处理方法,成功模拟B电极对测量结果和电流线分布的影响,定量的给出B电极对测量结果的影响。
在第四章中,针对三维有限元方法中线性插值基函数影响仿真效率和精度的问题,采用高阶基函数,使得在相对稀疏的网格下就可以得到具有较高精度的仿真结果,不仅节省了计算时间,而且还提高了程序的仿真精度,并且通过改进深侧向边界的处理条件,改进了深侧向结果的精确度。
第五章针对测井工作所遇到的常见地层和环境条件,开展了一系列模拟计算,对影响双侧向测井仪器响应的参数进行了详细研究。分析仪器不同几何结构对结果的影响;斜井中,通过分析不同角度对仪器响应结果的影响,给出了特定地层中的斜井的围岩校正图板;在水平井中通过分析地层中侵入、围岩、目的层等对仪器响应结果的影响,并制作了特定地层中的井孔上下距离校正图板、侵入校正图板和围岩层厚校正图板。
最后给出了本论文的总结和工作展望。作为本课题研究成果,三维有限元双侧向测井仿真程序能够快速仿真计算测井曲线,可用于解释石油测井曲线。
Lateral logging is one of the most popular methods in resistivity well logging, it is widely used to evaluate the porosity and saturation of oil and gas and its production. And can be used to give the description of reservoir and geological conditions and lithology of oil.
For the application of horizontal wells and deviate wells in the well logging process, the author simulations Lateral logging equipment response in deviate and horizontal well according to the mode it works by using three dimension finite element method. By using this method, We can get the equipment response curve and resistivity distribution of stratum, it helps to give the interpretation of logging. The innovation of this paper is adopt the remesh method to build model precisionly and in order to modeling dual laterolog response efficiently and accurately, high order basis function is adopted. The results show it has higher efficiency and precision compared with linear basis function. The architecture of this paper as follows:
The research of lateral logging domestic and abroad is given in chapter 1, and so is the finite element method and the main contribution of this paper.
In chapter 2, the mode of lateral logging equipment is given is given.
In chapter 3, the author discusses the process of numerical analysis of the lateral well logging using finite element method in detail. First of all, base the principle of finite element method, differential equations which the field of logging obeys is given, from which gives functional expression and boundary condition, finally, using frontal method to solve stiffness matrix and get the monitor electrode voltage, so we can get the deep and shallow equipment response. By improving the mesh method, multiple stratum in horizontal well and invaded eccentricity can be exitly modeled. the B-electrode also in consideration, results show that it will impact the deep lateral logging result and current.
In chapter 4, the auther improves process of simulation of lateral logging. In order to modeling lateral logging response efficiently and accurately, high order basis function is adopted. it shows the higher efficiency and precision compared with linear basis function. Furthermore, the anther optimized the mesh and the boundary condition to reduce the error caused by them.
In chapter 5, many simulation results in common environmental condition are given for research of response of lateral logging. By simulation the different electrode, different results and different electrode constant are given. Many conclusion and bed thinkness correction are given in deviate well with different angle and different condition; In horizontal well, different layer and invation is analysised and response curves are given, invasion correction chart and bed thickness correction chart are alse made.
Finally, the summarization and expectation of this paper is given. As one of the result of this research, the program of simulating the response of laterolog using 3D finite element method can give result quickly and exitly, it can be help to judge the interpretation of well logging response. The resistivity distribution of stratum which gotten by simulation is an important parameter in interpretation course. The results of this research have good prospects in logging interpretation.
引文
[1]李鹏翔,林静,刘思.水平井测井解释研究的发展[J].江汉石油学院学报,1999,21(2):23-26.
[2]周灿灿,王昌学.水平井测井解释技术综述[J].地球物理学进展,2006,21(1):152-160.
[3]Koelman J M V A,et al.Interpretation of resistivity logs in horizontal wells:an application to complex reservoirs from 0-maniC].SPWLA 37th Annual Logging Symposium,1996,paper G.
[4]Bigelow E L,Cleneay C A.A new f rontier:log interpretation in horizontal wells[C].Houston,Texas,SPWLA 33th Annual Logging Symposium,1992,paper 00.
[5]王智.测井资料环境校正技术研究及应用[D].西南石油大学,2006.
[6]侯月明等.水平井生产测井解释方法研究,测井技术,2004,28,(1)
[7]张庚骥.电法测井(上册)[M].北京:石油工业出版社,1984.
[8]张庚骥.电法测井(下册)[M].北京:石油工业出版社,1986.
[9]张友生,魏斌,杨慧珠.双侧向测井仪器响应的数值分析[J].地球物理学进展,2002,17(4):671-676.
[10]范晓敏.吉林大学地球探测科技学[J],双侧向测井曲线形状与地层侵入关系研究,2007,22(1):142-146
[11]Towle G H.Electric log modeling with finite difference method[J].The Log Analyst,1988,16(3):184-195.
[12]Tamarchenko T,Druskin Y.Fast modeling of induction and resistivity logging in the model with mixed boundaries[C].SPWLA 34th Annual Logging Symposium,1993.
[13]聂在平,陈思渊.复杂介质环境中双侧向测井响应的高效数值分析[J].电子学报,1994,22(6):30-38.
[14]Fan G X,Liu Q H.3-D Numerical Mode-Matching(NMM)Method for Resistivity Well-logging tools[J].IEEE Transaction on Antennas and propagation,2000,48(10):1544-1553.
[15]Chemali R,Gianzero S,Su S M,The dual lateralog in commom complex situations[C],SPWLA 29th Annual Symposium,1988.
[16]谭永基,于泳.水平井和大斜度井的双侧向测井数值模拟[J].复旦大学学报(自然科学版),1997,36(6):633-638.
[17]朱大伟,邓少贵.大斜度井双侧向测井响应的数值模拟[J].测井技术,2005,29(3):208-211.
[18]汪涵明,张庚骥.倾斜地层的双侧向测井响应[J].测井技术,1994,18(6):408-412.
[19]陈亮,朱道平,方俊玲,等复杂地层中的双侧向测井数值模拟[J].测井技术,2007,16(6):527-528
[20]Wang H M,Shen L C,Zhang G J.Dual laterolog response in 3D environments[J].Petropbysics,2000,41(3):234-241.
[21]肖加奇,张庚骥.水平井和大斜度井中双侧向测井响应的正演[J].石油大学学报,1996,20(1):24-28
[22]曾余庚,徐国华.电磁场有限元素法[M],北京:科学出版社,1982.
[23]曲利岩.电磁场有限元分析技术的研究和实现[D],浙江大学,2002.
[24]冯启宁.测井仪器原理(电法测井仪器)[M],北京:石油工业出版社,1991.
[25]泥岩裂缝地层双侧向测井正演数值模拟[D],大庆石油学院,2002
[26]李大潜.有限元素法在电法测井中的应用[M],北京:石油工业出版社,1980.
[27]金建铭等,电磁场有限元方法[M],陕西:西安电子科技出版社,1998.
[28]王秉愚.有限元素法程序设计[M],北京:北京理工大学出版社,1991.
[29]胡斌杰,吴信宝.斯仑贝谢双侧向k值的理论研究[J].测井技术,1993,17(2):90-93
[30]高杰,谢然红.大斜度井侧向测井三维正演数值模拟及曲线快速校正方法研究[J].石油勘探与开发,2000,27(2):69-71.
[31]徐建华,高义兵等.斜度井的侧向测井围岩校正[J].江汉石油学院学报,1996,18(1):49-52.
[32]徐建华,唐开宁等.水平井中双侧向测井的侵入校正[J],测井技术,1996,2(20):113-116
[33]徐建华,朱德怀等.水平井中双侧向测井的围岩校正[J],江汉石油学院学报,1994,16(2):54-56
[34]Chemali,R.,Gianzero,S.et al.The shoulder bed effect on the dual laterolog and its variation with the resistivity of the borehole fluid[C].SPWLA 24th Annual Logging Symposium,1983,paper UU.
[35]Gianzero S,et al.Induction,resistivity and MWD tools in horizontal wells[C].SPWLA 30th Annual Logging Symposium,1989,paper N.
[2]周灿灿,王昌学.水平井测井解释技术综述[J].地球物理学进展,2006,21(1):152-160.
[3]Koelman J M V A,et al.Interpretation of resistivity logs in horizontal wells:an application to complex reservoirs from 0-maniC].SPWLA 37th Annual Logging Symposium,1996,paper G.
[4]Bigelow E L,Cleneay C A.A new f rontier:log interpretation in horizontal wells[C].Houston,Texas,SPWLA 33th Annual Logging Symposium,1992,paper 00.
[5]王智.测井资料环境校正技术研究及应用[D].西南石油大学,2006.
[6]侯月明等.水平井生产测井解释方法研究,测井技术,2004,28,(1)
[7]张庚骥.电法测井(上册)[M].北京:石油工业出版社,1984.
[8]张庚骥.电法测井(下册)[M].北京:石油工业出版社,1986.
[9]张友生,魏斌,杨慧珠.双侧向测井仪器响应的数值分析[J].地球物理学进展,2002,17(4):671-676.
[10]范晓敏.吉林大学地球探测科技学[J],双侧向测井曲线形状与地层侵入关系研究,2007,22(1):142-146
[11]Towle G H.Electric log modeling with finite difference method[J].The Log Analyst,1988,16(3):184-195.
[12]Tamarchenko T,Druskin Y.Fast modeling of induction and resistivity logging in the model with mixed boundaries[C].SPWLA 34th Annual Logging Symposium,1993.
[13]聂在平,陈思渊.复杂介质环境中双侧向测井响应的高效数值分析[J].电子学报,1994,22(6):30-38.
[14]Fan G X,Liu Q H.3-D Numerical Mode-Matching(NMM)Method for Resistivity Well-logging tools[J].IEEE Transaction on Antennas and propagation,2000,48(10):1544-1553.
[15]Chemali R,Gianzero S,Su S M,The dual lateralog in commom complex situations[C],SPWLA 29th Annual Symposium,1988.
[16]谭永基,于泳.水平井和大斜度井的双侧向测井数值模拟[J].复旦大学学报(自然科学版),1997,36(6):633-638.
[17]朱大伟,邓少贵.大斜度井双侧向测井响应的数值模拟[J].测井技术,2005,29(3):208-211.
[18]汪涵明,张庚骥.倾斜地层的双侧向测井响应[J].测井技术,1994,18(6):408-412.
[19]陈亮,朱道平,方俊玲,等复杂地层中的双侧向测井数值模拟[J].测井技术,2007,16(6):527-528
[20]Wang H M,Shen L C,Zhang G J.Dual laterolog response in 3D environments[J].Petropbysics,2000,41(3):234-241.
[21]肖加奇,张庚骥.水平井和大斜度井中双侧向测井响应的正演[J].石油大学学报,1996,20(1):24-28
[22]曾余庚,徐国华.电磁场有限元素法[M],北京:科学出版社,1982.
[23]曲利岩.电磁场有限元分析技术的研究和实现[D],浙江大学,2002.
[24]冯启宁.测井仪器原理(电法测井仪器)[M],北京:石油工业出版社,1991.
[25]泥岩裂缝地层双侧向测井正演数值模拟[D],大庆石油学院,2002
[26]李大潜.有限元素法在电法测井中的应用[M],北京:石油工业出版社,1980.
[27]金建铭等,电磁场有限元方法[M],陕西:西安电子科技出版社,1998.
[28]王秉愚.有限元素法程序设计[M],北京:北京理工大学出版社,1991.
[29]胡斌杰,吴信宝.斯仑贝谢双侧向k值的理论研究[J].测井技术,1993,17(2):90-93
[30]高杰,谢然红.大斜度井侧向测井三维正演数值模拟及曲线快速校正方法研究[J].石油勘探与开发,2000,27(2):69-71.
[31]徐建华,高义兵等.斜度井的侧向测井围岩校正[J].江汉石油学院学报,1996,18(1):49-52.
[32]徐建华,唐开宁等.水平井中双侧向测井的侵入校正[J],测井技术,1996,2(20):113-116
[33]徐建华,朱德怀等.水平井中双侧向测井的围岩校正[J],江汉石油学院学报,1994,16(2):54-56
[34]Chemali,R.,Gianzero,S.et al.The shoulder bed effect on the dual laterolog and its variation with the resistivity of the borehole fluid[C].SPWLA 24th Annual Logging Symposium,1983,paper UU.
[35]Gianzero S,et al.Induction,resistivity and MWD tools in horizontal wells[C].SPWLA 30th Annual Logging Symposium,1989,paper N.