非均匀介质中的电磁感应和低频电磁传播问题研究
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摘要
随着越来越多的油田进入中后期开发，为了探测出更为隐蔽的油气层，钻井和测井技术得到了快速的发展，随之也出现了一些新的挑战，如大斜度井、水平井的感应测井响应特征分析，各向异性的影响和各向异性层电阻率的测量，新型测井仪器的评估和设计等。事实表明通过非均匀介质中场的仿真和测井实验的研究能为这些问题的解决提供有效的途径。
本文的工作正是基于上述背景而开展的，研究内容不仅包括非均匀介质中电磁感应和电磁波传播测井问题的正演和反演方法，也包括新型的多分量感应测井仪器的实验研究。所涉及的正向建模方法不仅有三维建模的数值方法，也包括快速的一维解析方法和二维半解析半数值方法，三种方法各具优缺点，在数值仿真分析中针对实际问题可以选择性地使用。
本文首先推导了平面分层和柱面分层各向异性介质中场的格林函数，并应用于一维分层地层中感应测井响应的建模。其优点是求解速度快、精度高，能用于任意方向的激励，特别能用于各向异性的倾斜地层。另外，还介绍了用于二维非均匀介质中感应和电磁波传播测井响应计算的数值模式匹配法。
针对复杂的三维模型，本文研究了两种数值方法，有限元法和体积分方程法。并结合电磁测井问题的特点在建模过程中进行了一定的创新，从而能节省未知量，提高求解速度。在三维的有限元建模中采用了混合阶的基函数并结合了线性方程的快速求解方法，一次的方程求解能得到多个测量点的值。在三维电磁测井问题的积分方程求解上提出了一种快速有效的求解方法。
在上述工作的基础上，分别对两种具有代表性的随钻电磁波测井和多分量感应测井仪器进行了建模分析，特别是对多分量感应测井仪器的响应特性进行了全面的仿真分析，重点考查横向线圈与轴向线圈受环境影响的区别和它们的探测特性，并给出了减小井眼和围岩影响的相关方法。上述的分析对测井数据的解析和新型感应测井仪器的优化设计具有参考价值。
本文还对多分量感应测井数据的反演技术进行了初步的研究，给出了基于解析解作为正向建模的快速反演方法。反演方法中引入了线性搜索来加快反演的收敛速度。
在结合上述理论分析的基础上对多分量感应测井实验进行了设计研究，包括实验井模型的设计、线圈系结构的设计、测量方法和测量系统的设计，最后实验结果与仿真结果进行了对比验证，说明上述设计方法的正确可行性。另外还将上述的反演技术应用到了实验数据的反演中，说明了通过多分量感应测井数据的反演能够得到各向异性地层的水平和垂直电阻率。
With more and more oilfields being developed in the middle and later period, in order to detect subtle reservoir of oil and gas, the technology of drilling and well logging has undergone rapid progress. However, some new challenges also arise, such as the response characteristic analysis of induction logging tools in highly deviated or horizontal wells, the electric anisotropic effect on the response of well logging, the measurement of the anisotropic resistivity of formation, the evaluation and design of new types of well logging sonde, etc. It has been shown that the numerical simulation and experiment research of logging tool can serve as an efficient tool to solve these problems.
This paper is just carried out in the above-mentioned background, whose content includes forward modeling method and inversion method, and also the experiment research of multicomponet induction logging tool. The forward modeling method includes three-dimensional numerical method and also one-dimensional analytic method and two-dimensional semi-analytical and semi-numerical method. These three methods have its own advantages and disadvantages, and we could selectively use them in accordance with the reality in numerical simulation analysis.
Firstly, Green's Functions for planar and cylindrical layered electric anisotropic media are derived in this paper, and they are applied to the modeling of induction logging problems in one-dimensional layered formation. Its advantage is fast and accurate, and is able to model excited source of any direction, and is especially applicable to deviated anisotropic formatiom. In addition, we introduce the numerical mode method (NMM) to simulate the response of induction and propagation logging in two-dimensional inhomogeneous media.
In this paper, we study two kinds of numerical methods used to simulate the response of induction and electromagnetic propagation logging tools in three-dimensional complex media: finite element method and volume integral equation method. Considering the characteristics of electromagnetic logging model, some innovations are made in the modeling, which is helpful for decreasing the unknowns and accelerating the solution speed. Mixed order basis function is applied in three-dimensional finite element modeling, and a fast method of solving linear equation is incorporated into the implementation of the FEM algorithm. The results of multiple measure points can be got by solving linear equation only once. A fast and effective numerical computational method is developed to deal with the volume integral equation used in the modeling of three-dimensional electromagnetic logging problems.
Based on the above studies, we simulate and analyze two kinds of representative electromagnetic logging tools: Logging-while-drilling (LWD) electromagnetic wave propagation logging tool and multicomponent induction logging tool. Especially, the response of multicomponent induction logging tool is simulated and analyzed comprehensively. Differences of response in axial and transversal coils as well as the detective characteristics of axial and transversal coils are investigated. Some methods for decreasing the borehole and shoulder effects on the response of multicomponent induction logging are gived. The above analysis is useful for the explanation of logging data and optimal design of new induction logging tools.
We preliminarily study the inversion technology of multicomponent induction logging data, and put forward the fast inversion method based on the forward modeling with the analytic formulae. Linear search is incorporated into the inversion method to improve the speed of the convergence rate of inversion.
Based on the above theories, the experiment of multicomponent induction logging is designed, which includes the designs of well model, coils-array configuration, method of measurement and system of measurement. Finally, the comparision of experimental result and simulated result illustrates that the experiment design is correct and feasible. In addition, the inversion method above is applied to experimental data inversion, and the results show that the horizontal and vertical resistivity of anisotropic formation can be obtained by data inversion of multicomponent induction logging.
本文的工作正是基于上述背景而开展的，研究内容不仅包括非均匀介质中电磁感应和电磁波传播测井问题的正演和反演方法，也包括新型的多分量感应测井仪器的实验研究。所涉及的正向建模方法不仅有三维建模的数值方法，也包括快速的一维解析方法和二维半解析半数值方法，三种方法各具优缺点，在数值仿真分析中针对实际问题可以选择性地使用。
本文首先推导了平面分层和柱面分层各向异性介质中场的格林函数，并应用于一维分层地层中感应测井响应的建模。其优点是求解速度快、精度高，能用于任意方向的激励，特别能用于各向异性的倾斜地层。另外，还介绍了用于二维非均匀介质中感应和电磁波传播测井响应计算的数值模式匹配法。
针对复杂的三维模型，本文研究了两种数值方法，有限元法和体积分方程法。并结合电磁测井问题的特点在建模过程中进行了一定的创新，从而能节省未知量，提高求解速度。在三维的有限元建模中采用了混合阶的基函数并结合了线性方程的快速求解方法，一次的方程求解能得到多个测量点的值。在三维电磁测井问题的积分方程求解上提出了一种快速有效的求解方法。
在上述工作的基础上，分别对两种具有代表性的随钻电磁波测井和多分量感应测井仪器进行了建模分析，特别是对多分量感应测井仪器的响应特性进行了全面的仿真分析，重点考查横向线圈与轴向线圈受环境影响的区别和它们的探测特性，并给出了减小井眼和围岩影响的相关方法。上述的分析对测井数据的解析和新型感应测井仪器的优化设计具有参考价值。
本文还对多分量感应测井数据的反演技术进行了初步的研究，给出了基于解析解作为正向建模的快速反演方法。反演方法中引入了线性搜索来加快反演的收敛速度。
在结合上述理论分析的基础上对多分量感应测井实验进行了设计研究，包括实验井模型的设计、线圈系结构的设计、测量方法和测量系统的设计，最后实验结果与仿真结果进行了对比验证，说明上述设计方法的正确可行性。另外还将上述的反演技术应用到了实验数据的反演中，说明了通过多分量感应测井数据的反演能够得到各向异性地层的水平和垂直电阻率。
With more and more oilfields being developed in the middle and later period, in order to detect subtle reservoir of oil and gas, the technology of drilling and well logging has undergone rapid progress. However, some new challenges also arise, such as the response characteristic analysis of induction logging tools in highly deviated or horizontal wells, the electric anisotropic effect on the response of well logging, the measurement of the anisotropic resistivity of formation, the evaluation and design of new types of well logging sonde, etc. It has been shown that the numerical simulation and experiment research of logging tool can serve as an efficient tool to solve these problems.
This paper is just carried out in the above-mentioned background, whose content includes forward modeling method and inversion method, and also the experiment research of multicomponet induction logging tool. The forward modeling method includes three-dimensional numerical method and also one-dimensional analytic method and two-dimensional semi-analytical and semi-numerical method. These three methods have its own advantages and disadvantages, and we could selectively use them in accordance with the reality in numerical simulation analysis.
Firstly, Green's Functions for planar and cylindrical layered electric anisotropic media are derived in this paper, and they are applied to the modeling of induction logging problems in one-dimensional layered formation. Its advantage is fast and accurate, and is able to model excited source of any direction, and is especially applicable to deviated anisotropic formatiom. In addition, we introduce the numerical mode method (NMM) to simulate the response of induction and propagation logging in two-dimensional inhomogeneous media.
In this paper, we study two kinds of numerical methods used to simulate the response of induction and electromagnetic propagation logging tools in three-dimensional complex media: finite element method and volume integral equation method. Considering the characteristics of electromagnetic logging model, some innovations are made in the modeling, which is helpful for decreasing the unknowns and accelerating the solution speed. Mixed order basis function is applied in three-dimensional finite element modeling, and a fast method of solving linear equation is incorporated into the implementation of the FEM algorithm. The results of multiple measure points can be got by solving linear equation only once. A fast and effective numerical computational method is developed to deal with the volume integral equation used in the modeling of three-dimensional electromagnetic logging problems.
Based on the above studies, we simulate and analyze two kinds of representative electromagnetic logging tools: Logging-while-drilling (LWD) electromagnetic wave propagation logging tool and multicomponent induction logging tool. Especially, the response of multicomponent induction logging tool is simulated and analyzed comprehensively. Differences of response in axial and transversal coils as well as the detective characteristics of axial and transversal coils are investigated. Some methods for decreasing the borehole and shoulder effects on the response of multicomponent induction logging are gived. The above analysis is useful for the explanation of logging data and optimal design of new induction logging tools.
We preliminarily study the inversion technology of multicomponent induction logging data, and put forward the fast inversion method based on the forward modeling with the analytic formulae. Linear search is incorporated into the inversion method to improve the speed of the convergence rate of inversion.
Based on the above theories, the experiment of multicomponent induction logging is designed, which includes the designs of well model, coils-array configuration, method of measurement and system of measurement. Finally, the comparision of experimental result and simulated result illustrates that the experiment design is correct and feasible. In addition, the inversion method above is applied to experimental data inversion, and the results show that the horizontal and vertical resistivity of anisotropic formation can be obtained by data inversion of multicomponent induction logging.
引文
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