直井和曲井内管柱非线性稳定性分析
摘要
近年来发展起来的大位移井技术中经常采用柔性管柱进行作业,管柱是否稳定直接关系到钻井的成败。因此现代石油钻采工程要求能够对管柱的屈曲行为有一个较为准确的了解,以此来优化钻井设计,降低钻探成本。到目前为止,分析井中管柱屈曲问题的理论和方法尚不完善,所以很有必要对受径向约束管柱的屈曲问题进行系统深入的研究。
本文先给出了井内管柱屈曲问题的研究现况,在深入了解和总结前人研究成果的基础上给出了本文的研究内容。然后,从空间弯扭杆的一般理论出发,通过引入井壁约束条件,推导出了三维井内受径向约束管柱的稳定平衡微分方程,经过退化得到了铅垂平面内曲井和直井中受径向约束管柱屈曲的平衡方程。
基于微分求积单元法和Newton-Raphson迭代法,构建了微分求积单元增量迭代法来求解受径向约束管柱的非线性屈曲问题。建立了微分求积直梁和曲梁单元,同时,给出了集成结构的微分求积方程的方法。提出了一种与以往不同的计算初值选取的方法,实践表明该方法减少了计算量,并提高了计算效率。所给出的基于微分求积单元法的计算策略和算法,拓展了微分求积单元法在工程中的应用范围。
编写了分析直井和曲井中管柱的线性和非线性屈曲问题的FORTRAN程序。研究了多个不同的算例,通过将计算结果与现有的有限元结果和试验结果的比较验证了所提出的算法和求解过程的正确性。通过数值计算和分析,着重考察了管柱的长度、重力线密度、井斜角、井眼曲率和轴向摩擦系数等对管柱屈曲载荷的影响规律,给出了一些有工程参考意义的结果。通过将本文的计算结果与前人实验研究结果的对比分析给出了井中管柱正弦屈曲和螺旋屈曲的定义和对应屈曲载荷的求解方法,正弦屈曲载荷可以通过求解管柱屈曲线性特征值问题得到的最低阶特征值得到,管柱的螺旋屈曲临界载荷可通过求解管柱屈曲非线性准静态加载问题得到,管柱首次出现脱离井壁(井壁约束力出现小于零)时的载荷即为螺旋屈曲临界载荷。
论文最后是全文的总结和展望,总结了全文的研究工作,指出了有创新意义的研究成果,并指出了需要进一步研究的一些内容。
Flexible tubular has been frequently used in extended reach wells, and the stability of the tubular is one of the key factors to be success in drilling engineering. It is required for us to understand the detailed buckling behavior of tubular in order to optimize the design of drilling assembles and to reduce the cost. Nowadays, theories and methods are, however, far more perfect for the analysis of tubular buckling in both straight and curved wells. Therefore, there is an urgent need for more comprehensive researches in this field.
Firstly, a literature study is performed. The research contents are determined based on the current status of the buckling of tubing in well-bores. Based on the general theory of the bending and twisting rod in space, the governing differential equilibrium equations of tubular subjected to radial constrains in 3D well-bore are obtained by introducing of the constraints of the well’s wall. Then, the equilibrium equations of tubular subjected to radial constraints in perpendicular plane-curved and straight wells are deduced.
After that, a differential quadrature element (DQE) incremental iteration method, based on the differential quadrature element method and Newton-Raphson iteration method, is proposed for obtaining solutions of the nonlinear buckling problem of tubular subjected to radial constrains. Straight and curved differential quadrature beam elements are established. The method for obtaining the structural differential quadrature equation is also given. A method for selecting initial iteration values, differing from the existing one, is proposed herein. It is shown that the proposed method reduces the computation effort and improves the computational efficiency. The proposed DQE-based computational tactics and algorithm extend the application range of the differential quadrature element method in engineering practice.
FORTRAN programs were written for linear and nonlinear buckling analyses of tubing within straight and curved wells. Various numerical examples are investigated. To verify the proposed method and solution procedures, numerical results are compared with existing finite element data and experimental results. The influence of tubing length, gravity, deviation angle of the well-bore, curvature, and axial frictions is investigated, and some results for engineering reference are given. The definition of lateral buckling and helical buckling of tubular in wells is presented based on the computational results and the test data, and the corresponding solution methods are given. The sinusoidal buckling load of tubing in well-bore, the lowest eigenvalue, can be obtained by solving an eigenvalue problem. The helical buckling load of tubing in well-bore can be obtained by directly solving the non-linear differential equations. The load is applied incrementally. When a negative constraint force appears which means that a small portion of the tube is no longer contact with the well wall, then, the load corresponding to the previous step is defined the helical buckling load.
Finally, the dissertation is ended by a summary. The research work is summarized. Some innovative research results are pointed out. And a few topics for further study are given for reference.
本文先给出了井内管柱屈曲问题的研究现况,在深入了解和总结前人研究成果的基础上给出了本文的研究内容。然后,从空间弯扭杆的一般理论出发,通过引入井壁约束条件,推导出了三维井内受径向约束管柱的稳定平衡微分方程,经过退化得到了铅垂平面内曲井和直井中受径向约束管柱屈曲的平衡方程。
基于微分求积单元法和Newton-Raphson迭代法,构建了微分求积单元增量迭代法来求解受径向约束管柱的非线性屈曲问题。建立了微分求积直梁和曲梁单元,同时,给出了集成结构的微分求积方程的方法。提出了一种与以往不同的计算初值选取的方法,实践表明该方法减少了计算量,并提高了计算效率。所给出的基于微分求积单元法的计算策略和算法,拓展了微分求积单元法在工程中的应用范围。
编写了分析直井和曲井中管柱的线性和非线性屈曲问题的FORTRAN程序。研究了多个不同的算例,通过将计算结果与现有的有限元结果和试验结果的比较验证了所提出的算法和求解过程的正确性。通过数值计算和分析,着重考察了管柱的长度、重力线密度、井斜角、井眼曲率和轴向摩擦系数等对管柱屈曲载荷的影响规律,给出了一些有工程参考意义的结果。通过将本文的计算结果与前人实验研究结果的对比分析给出了井中管柱正弦屈曲和螺旋屈曲的定义和对应屈曲载荷的求解方法,正弦屈曲载荷可以通过求解管柱屈曲线性特征值问题得到的最低阶特征值得到,管柱的螺旋屈曲临界载荷可通过求解管柱屈曲非线性准静态加载问题得到,管柱首次出现脱离井壁(井壁约束力出现小于零)时的载荷即为螺旋屈曲临界载荷。
论文最后是全文的总结和展望,总结了全文的研究工作,指出了有创新意义的研究成果,并指出了需要进一步研究的一些内容。
Flexible tubular has been frequently used in extended reach wells, and the stability of the tubular is one of the key factors to be success in drilling engineering. It is required for us to understand the detailed buckling behavior of tubular in order to optimize the design of drilling assembles and to reduce the cost. Nowadays, theories and methods are, however, far more perfect for the analysis of tubular buckling in both straight and curved wells. Therefore, there is an urgent need for more comprehensive researches in this field.
Firstly, a literature study is performed. The research contents are determined based on the current status of the buckling of tubing in well-bores. Based on the general theory of the bending and twisting rod in space, the governing differential equilibrium equations of tubular subjected to radial constrains in 3D well-bore are obtained by introducing of the constraints of the well’s wall. Then, the equilibrium equations of tubular subjected to radial constraints in perpendicular plane-curved and straight wells are deduced.
After that, a differential quadrature element (DQE) incremental iteration method, based on the differential quadrature element method and Newton-Raphson iteration method, is proposed for obtaining solutions of the nonlinear buckling problem of tubular subjected to radial constrains. Straight and curved differential quadrature beam elements are established. The method for obtaining the structural differential quadrature equation is also given. A method for selecting initial iteration values, differing from the existing one, is proposed herein. It is shown that the proposed method reduces the computation effort and improves the computational efficiency. The proposed DQE-based computational tactics and algorithm extend the application range of the differential quadrature element method in engineering practice.
FORTRAN programs were written for linear and nonlinear buckling analyses of tubing within straight and curved wells. Various numerical examples are investigated. To verify the proposed method and solution procedures, numerical results are compared with existing finite element data and experimental results. The influence of tubing length, gravity, deviation angle of the well-bore, curvature, and axial frictions is investigated, and some results for engineering reference are given. The definition of lateral buckling and helical buckling of tubular in wells is presented based on the computational results and the test data, and the corresponding solution methods are given. The sinusoidal buckling load of tubing in well-bore, the lowest eigenvalue, can be obtained by solving an eigenvalue problem. The helical buckling load of tubing in well-bore can be obtained by directly solving the non-linear differential equations. The load is applied incrementally. When a negative constraint force appears which means that a small portion of the tube is no longer contact with the well wall, then, the load corresponding to the previous step is defined the helical buckling load.
Finally, the dissertation is ended by a summary. The research work is summarized. Some innovative research results are pointed out. And a few topics for further study are given for reference.
引文
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