摆线型大位移井剖面设计的数值计算

Numerical Calculation of Design for Cycloid Extended Reach Well Trajectory

摘要:

摆线型大位移井轨道由“直井段—圆弧井段—摆线井段—稳斜井段”构成，与其他类型的大位移井轨道相比，摆线型大位移井具有最小的或很小的摩阻和摩阻力矩。摆线型大位移井轨道设计问题归结为求解一个二元方程组，当未知设计参数为摆线井段初始井斜角或稳斜井段井斜角时，该方程组为非线性方程组，没有解析解。通过数学变换和化简，得到了等价的三角函数方程，根据区间搜索和二分法提出了求该三角函数方程近似解的数值迭代算法。算例表明，该算法具有很好的迭代稳定性，计算精度高、速度快。新算法可用于大位移井轨道设计的计算机软件开发，对于提高软件的适用性和稳定性具有较大的帮助。

Abstract:

The trajectory of cycloid extended reach well consists of straight section-arc section-cycloid section-steady inclined section with the minimum or very small friction and friction moment. The design comes down to solution for system of two elements equations, when the unknown design parameters are according to the initial well deviation angle of cycloid section or deviation angle of remained inclined section, the equations are nonlinear without analytical solution. The equivalent triangle function equation is obtained by mathematical transformation and simplification; numerical iterative algorithm for triangle function equation approximate solution is put forward by interval query and bisection method. The numerical examples show the algorithm has high calculation accuracy and quick operation with good iterative stability. This new algorithm can be applied in the development of computer software to improve the applicability.