三维悬链线轨道设计的改进算法

Modified Algorithm of Three-dimensional Catenary Profile Design

三维悬链线轨道设计是新近提出的一种大位移井轨道设计新方法,由于需要使用数值积分法来计算井段增量,设计约束方程组的数值求解比较困难。求出了垂深增量积分式的原函数,得到了垂深增量的解析计算公式。使用该解析公式,求出了约束设计方程组的一个近似解,可以将它作为求解该方程组的迭代法的初始值;使用该解析公式,还证明了稳斜井段的段长与悬链线特征参数之间存在线性相关性,并将这种线性相关性用于设计约束方程组的降维处理,使得原来的具有3个独立未知数的设计约束方程组简化为具有2个独立未知数,从而降低了该方程组的求解难度。垂深增量公式还被用于简化方程组求解过程中的隐含未知数的递序计算,大量减少了数值积分的计算量。使用数论网格迭代法求解降维后的设计约束方程组,不仅计算过程稳定、可靠,而且易于计算机编程实现。

Three-dimensional catenary profile design is a new method for the extended reach well in recent years.For numerical integration method is needed for hole section increment calculation,numerical computation by constraint equation set is difficult to design.Primary function with increment integration of vertical depth is gained,and analytical formula of the increment of the vertical depth as well.This analytical formula has two usages.That is,an approximate solution of the constraint equation set is solved,which may be considered as the starting value of interative method of the formula.The other is,linear correlation appears between length of hole-angle section and catenary characteristic parameter,which may be used to dimension dropping treatment of the equation set.Three independent unknown will be simplified to two independent unknown,and the difficulty of the solution with the equation set will be reduced.The increment formula of the vertical depth is also applied to simplify recursive sequence calculation of implied unknown during the resolution of the equation set,which makes less calculation of the numerical integration at large scale.The interative method of number theory framework is applied to solute the designed constraint equation set after dimension dropping with the result of stable and reliable computation process and easier programming by computer.