非直井迹最优控制模型、算法及应用
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摘要
本文以石油工程中的非直井(定向井、水平井、侧钻井、侧钻水平井、大位移井、分支井)轨迹控制为背景，研究了一类约束优化与最优控制问题。
本文主要研究内容及取得的成果可列为以下几款。
1．第一章简要介绍了非直井迹最优控制理论的工程背景，给出了文中将要用到参数的工程含义，回顾与总结了70年间非直井迹技术的发展概况。从系统论的角度指出本文研究的目的与意义在于如何综合运用已有的研究成果、硬件环境及技术人员的经验与直觉，使得井迹控制技术达到“整体最优”。
2．第二章在分析了目前非直井迹设计(计算)与施工中常用方法的特点与弊端之后，基于对非直井迹控制技术及约束优化思想与理论的理解，首次建立了多约束条件下的非直井迹优化模型——CORA模型，并论述了该模型的三种特例：二维模型(CORA-2D)、三维圆弧型模型(CORA-3A)、三维拟螺线型模型(CORA-3S)，以对应不同的井型与井迹的需要，CORA模型以井迹长度最短(对应了工程中低成本的要求)为目标函数，以造斜点、工具造斜能力、工具面角、井斜角和／或方位角等为设计变量，以中靶精度、绕障设计、工程中间参数、设计变量边界等为约束条件，第一次综合定量地考虑了影响非直井迹设计(计算)与控制的因素并将它们引入模型之中，经由CORA模型还可孵化出一系列有关井迹设计与计算的模型，可在涵盖目前几乎所有设计方法的基础上，提高井迹设计(计算)精度、简化设计(计算)过程。
3．第三章先将前一章中所建立的模型作数学上的统一化处理，依此构造了两类优化算法：一类为利用二次罚函数形式将非线性约束化入目标
大连理工大学博士学位论文：非直井迹最优控制模型、算法及应用 江胜宗，秋，200
函数中，保留约束集中的界式约束，采用工作集策略及妞S算法类的
Huang算法为代表，构造计算迭代格式并证明其收敛性．为提高算法
的收敛速度，对工作集算法中由ABS算法生成的约束阵进行了校正．
另一类是构造相应的Lagrange函数及其一种对偶算法的迭代格式，
讨论了修正Lagrange 函数的性质，并借助Banach扰动定理及
Bertsekas第H隐函数定理，及对修正Lagrange函数Hesse阵分析，
证明了该算法的收敛性．由于该算法不需要寻找初始可行点，因此比
可行方向法和其他需要初始可行点的算法具有更大的吸引力．
4．第四章分析了非直井迹控制系统的特性．建立了非直井迹的动力系
统模型，讨论了该模型的性质，以此为基础，建立了以满足终端约束
与最短并迹长度为性能指标的最优控制模型，讨论了该模型最优解存
在的必要条件．根据动态模型的特点，构造了以均匀设计方法与修正
N。。he－Jeeves方法为核。0的优化算法．数值结果表明所建立的动态
模型与算法的有效性．
5．本章介绍了基子非直井迹控制的动静态模型及相关算法编制的侧钻
水平轨迹控制软件系统的功能，及显现出的与目前常用的软件系统不
同之处．给出了具有代表性的1口水平井、2口高难度侧钻水平井的
计算结果．与进口的WellLead软件的比较说明了该软件系统的优越
性．
Well trajectory for non-straight wells, which includes directional wells, horizontal wells, siedtracking and /or horizontal wells, long-reach wells and multibranches, is one of key techniques in non-straight drilling.
The main results, obtained in this dissertation, may be summarized as follows.
1. Engineering background and some terms used in this dissertation are firstly introduced in Chapter One. Researches involved in this study are derived from reviewing and summarizing the history of well trajectory for non-straight wells.
2. Chapter Two presents an optimized model named CORA with multi-constraints based on analyzing and reviewing some conventional methods been used in petroleum industry nowadays. And three specific model such as CORA-2D, CORA-3A and CORA-3S induced respectively. Some constraints such as kick-off-point, build-up rate of bottom-hole assembly(BHA), toolface orientation, inclination and azimuth etc. are involved in this novel model quantitatively for the first time. Its high design efficiency and accuracy are validated after used in more 22 non-straight wells.
3. Two kinds of algorithms presented in Chapter Three: Working-set strategy based on Huang in ABS-class algorithms and Dual algorithm based on revised Lagrangian function. An convergence theorem proved and in order to speed convergence of working-set algorithm, constrained matrix derived from ABS in working-set method corrected. In latter part of Chapter Three, some exciting properties of the revised Lagrangian function discussed first, which leads to form a dual algorithm of CORA or COT. Convergence theorem proved by Banach perturbation theorem, Bertsekas implicit function theorem II and by analyzing Hesse matrix of revised
Largrangian function. Dual algorithm shows its advantage over other algorithms for its non-need for finding initial feasible point.
4. Chapter Four analyzes the characteristics of optimal control system. A dynamic model and then an optimal control model established, which regards the minimum length of well trajectory as the index of characteristic and meets the terminal conditions. And the necessary condition of optimal solutions for the optimal control system then discussed. A new method to solve this model developed based on uniform design method and revised Hooke-Jeeves method. Optimal control model and its algorithm validated by numerical tests.
5. A new software system with fine GUI and powerful functions and its applications introduced in Chapter Five. Then 3 typical case histories discussed hereinafter demonstrates its advantages and its leading rank with comparison to WellLead Software imported.
本文主要研究内容及取得的成果可列为以下几款。
1．第一章简要介绍了非直井迹最优控制理论的工程背景，给出了文中将要用到参数的工程含义，回顾与总结了70年间非直井迹技术的发展概况。从系统论的角度指出本文研究的目的与意义在于如何综合运用已有的研究成果、硬件环境及技术人员的经验与直觉，使得井迹控制技术达到“整体最优”。
2．第二章在分析了目前非直井迹设计(计算)与施工中常用方法的特点与弊端之后，基于对非直井迹控制技术及约束优化思想与理论的理解，首次建立了多约束条件下的非直井迹优化模型——CORA模型，并论述了该模型的三种特例：二维模型(CORA-2D)、三维圆弧型模型(CORA-3A)、三维拟螺线型模型(CORA-3S)，以对应不同的井型与井迹的需要，CORA模型以井迹长度最短(对应了工程中低成本的要求)为目标函数，以造斜点、工具造斜能力、工具面角、井斜角和／或方位角等为设计变量，以中靶精度、绕障设计、工程中间参数、设计变量边界等为约束条件，第一次综合定量地考虑了影响非直井迹设计(计算)与控制的因素并将它们引入模型之中，经由CORA模型还可孵化出一系列有关井迹设计与计算的模型，可在涵盖目前几乎所有设计方法的基础上，提高井迹设计(计算)精度、简化设计(计算)过程。
3．第三章先将前一章中所建立的模型作数学上的统一化处理，依此构造了两类优化算法：一类为利用二次罚函数形式将非线性约束化入目标
大连理工大学博士学位论文：非直井迹最优控制模型、算法及应用 江胜宗，秋，200
函数中，保留约束集中的界式约束，采用工作集策略及妞S算法类的
Huang算法为代表，构造计算迭代格式并证明其收敛性．为提高算法
的收敛速度，对工作集算法中由ABS算法生成的约束阵进行了校正．
另一类是构造相应的Lagrange函数及其一种对偶算法的迭代格式，
讨论了修正Lagrange 函数的性质，并借助Banach扰动定理及
Bertsekas第H隐函数定理，及对修正Lagrange函数Hesse阵分析，
证明了该算法的收敛性．由于该算法不需要寻找初始可行点，因此比
可行方向法和其他需要初始可行点的算法具有更大的吸引力．
4．第四章分析了非直井迹控制系统的特性．建立了非直井迹的动力系
统模型，讨论了该模型的性质，以此为基础，建立了以满足终端约束
与最短并迹长度为性能指标的最优控制模型，讨论了该模型最优解存
在的必要条件．根据动态模型的特点，构造了以均匀设计方法与修正
N。。he－Jeeves方法为核。0的优化算法．数值结果表明所建立的动态
模型与算法的有效性．
5．本章介绍了基子非直井迹控制的动静态模型及相关算法编制的侧钻
水平轨迹控制软件系统的功能，及显现出的与目前常用的软件系统不
同之处．给出了具有代表性的1口水平井、2口高难度侧钻水平井的
计算结果．与进口的WellLead软件的比较说明了该软件系统的优越
性．
Well trajectory for non-straight wells, which includes directional wells, horizontal wells, siedtracking and /or horizontal wells, long-reach wells and multibranches, is one of key techniques in non-straight drilling.
The main results, obtained in this dissertation, may be summarized as follows.
1. Engineering background and some terms used in this dissertation are firstly introduced in Chapter One. Researches involved in this study are derived from reviewing and summarizing the history of well trajectory for non-straight wells.
2. Chapter Two presents an optimized model named CORA with multi-constraints based on analyzing and reviewing some conventional methods been used in petroleum industry nowadays. And three specific model such as CORA-2D, CORA-3A and CORA-3S induced respectively. Some constraints such as kick-off-point, build-up rate of bottom-hole assembly(BHA), toolface orientation, inclination and azimuth etc. are involved in this novel model quantitatively for the first time. Its high design efficiency and accuracy are validated after used in more 22 non-straight wells.
3. Two kinds of algorithms presented in Chapter Three: Working-set strategy based on Huang in ABS-class algorithms and Dual algorithm based on revised Lagrangian function. An convergence theorem proved and in order to speed convergence of working-set algorithm, constrained matrix derived from ABS in working-set method corrected. In latter part of Chapter Three, some exciting properties of the revised Lagrangian function discussed first, which leads to form a dual algorithm of CORA or COT. Convergence theorem proved by Banach perturbation theorem, Bertsekas implicit function theorem II and by analyzing Hesse matrix of revised
Largrangian function. Dual algorithm shows its advantage over other algorithms for its non-need for finding initial feasible point.
4. Chapter Four analyzes the characteristics of optimal control system. A dynamic model and then an optimal control model established, which regards the minimum length of well trajectory as the index of characteristic and meets the terminal conditions. And the necessary condition of optimal solutions for the optimal control system then discussed. A new method to solve this model developed based on uniform design method and revised Hooke-Jeeves method. Optimal control model and its algorithm validated by numerical tests.
5. A new software system with fine GUI and powerful functions and its applications introduced in Chapter Five. Then 3 typical case histories discussed hereinafter demonstrates its advantages and its leading rank with comparison to WellLead Software imported.
引文
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