三段制圆弧轨道设计参数的谱集计算

Calculation of spectral sets of design parameters for three-section circular arc trajectory

为了解决井眼轨道设计中设计参数输入“试凑”问题,发展了设计参数谱集计算的数值算法。以二分法为基础,推导出了两个设计参数各自的整体允许范围的算法,以及当一个设计参数给定时另一个设计参数允许范围的算法,使用这些算法能有效地计算出谱集边界,从而绘制出设计参数谱集图形。进一步证明了谱集结构定理:三段制设计参数谱集由一个二维有界连通闭集或者不相交的多个二维有界连通闭集的并集组成。数值算例的计算结果表明,谱集计算算法能求出连通和不连通等各种情况的谱集边界。谱集计算算法在井眼轨道设计软件中可为软件用户提供可视化的设计参数选择数值范围,提高设计效率。

To solve the “cut-and-trial” problem of design parameter input in the wellbore trajectory design,numerical algorithms were developed for the calculation of design parameter spectral sets.Based on the bisection method,this study provides an algorithm in the overall allowable range of two design parameters and another in the allowable range of one design parameter when the other is set.These algorithms can effectively calculate the spectrum set boundaries,thus plotting the graphs of above spectral sets.The spectrum set structure theorem is proved as follows:the three-section design parameter spectral set is composed of a 2D bounded connected closed set or the union of several unconnected 2D bounded connected closed sets.Based on the results of numerical examples,it is indicated that the proposed algorithms can solve the boundaries of spectrum sets in various cases of being connected and disconnected.Therefore,the computation algorithm for spectral sets is highly valuable in wellbore trajectory design software,which can provide users with the visualized numerical ranges for design parameters,thus improving design efficiency.