Treffer: 自然曲线井眼轨道设计点切条件下的数值求解方法.

The design of three-dimensional borehole trajectories using the natural curve approach under tangent-to-point conditions can be attributed to solving a system of multivariate highly nonlinear equations. Conventional numerical iterative methods often face challenges such as the inability to determine suitable initial iteration values. To overcome this issue in a stable and efficient manner, an univariate nonlinear equation (characteristic equation) was derived from this system. Once all real roots of the characteristic equation are determined, when the well deviation angle is prioritized, all the other variables can be calculated using a set of analytical formulas. In cases where the azimuth angle is prioritized, one of the other variables requires solving a simple trigonometric equation, while the remaining variables can be calculated using a set of analytical formulas. The characteristic function is a multimodal continuous function with numerous real roots. To enhance computational efficiency, the constraints were employed to define the maximum permissible interval for meaningful real roots, and the characteristic equation was solved within this interval using root separation and the bisection method. Numerical cases demonstrate that the proposed algorithm effectively and quickly solves the borehole trajectory design problem, eliminating the need for manually assigned initial iteration values. Moreover, it effectively addresses the issue of multiple solutions in a set of constraint equations. The results are fully consistent with those produced by Compass, a commercial drilling design software. This method is quite practical and can be integrated into the development of domestic and alternative drilling design software. [ABSTRACT FROM AUTHOR]

在点切条件下使用自然曲线法进行三维井眼轨道设计的问题, 可以归结为一个多元高度非线性方程组的求解, 而 使用常规的数值迭代法来求解面临着无法给定合适的迭代初始值等难题。为了稳健快速地求解多元非线性方程组, 从多元非 线性方程组推导出了一个只包含一个未知数的一元非线性方程 (特征方程)。求出特征方程全部实数根之后, 在井斜角先达 情况下, 其他所有未知数都可以通过一组解析计算公式来计算; 在方位角先达情况下, 其他未知数中的一个未知数需求解一个 简单的三角函数方程, 其余未知数也可以通过一组解析计算公式来计算。特征函数是一个多峰连续函数, 有非常多的实数根, 为了提高求解效率, 使用约束条件计算出了有意义实数根的最大允许区间, 在这个最大允许区间上使用实根分隔和二分法来 求解特征方程。数值算例表明, 本文算法可以快速地求解自然曲线井眼轨道设计问题, 并且无需给定人工迭代初始值, 可以很 好地处理约束方程组多解的情况; 计算结果与商用钻井设计软件 Compass 的计算结果完全相同。本文算法具有较高的应用价 值, 可以应用于钻井设计软件的国产化替代软件开发中。 [ABSTRACT FROM AUTHOR]

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