大位移井悬链线剖面设计的数值计算

悬链线剖面是大位移井轨道的经典类型，在进行设计时需要求解一个以悬链线初始井斜角为未知数的非线性方程。由于未知数包含在多个三角函数和对数函数中，计算工作量较大，而且常用的迭代求解方法存在一些问题。通过数学变换将该方程转换成一个只包含对数函数和多项式函数的新方程，对新方程的函数性态做了几何分析，进而提出了寻找求解区间的步长搜索算法和自适应步长搜索算法。利用二分法在求解区间上能够快速求出新方程的数值解。利用大位移井设计实例验证了本文算法的有效性，并对圆弧井段井眼曲率与方程解的关系进行了讨论。本文提出的算法可用于大位移井轨道设计的计算机软件开发中。

Numerical Calculation on Design of Catenary Shape Profile for Extended Reach Well

Catenary shape profile is a classical type of extended reach well; a nonlinear equation with the initial well oblique angle as unknown factor should be solved for its design. As this unknown factor exists in several triangular functions and logarithmic functions, large amount of calculation is required; and common-used interative solution method is not so ideal. The nonlinear equation is changed to a new one only with logarithmic function and polynomial function, to which geometric analysis is made on the function character, and step search algorithm and adaptive step search algorithm are proposed for solution interval. Numerical solution of new equation can be got rapidly in solution interval by dichotomy. The effectiveness of the above algorithm was proved by the design case of extended reach well, and relationship between hole curvature in arc well section and equation solution was discussed. The algorithm introduced in this paper can be applied in the development of computer software for the design on extended reach well trajectory.