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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 trajectory design is a newly proposed method for designing a large-displacement well trajectory. Because numerical integration is required to calculate the increment of the well section, it is difficult to design the numerical solution of the constrained equations. The original function of the incremental integral of vertical depth is obtained, and the analytic formula of the vertical increment is obtained. Using this analytical formula, an approximate solution to the constrained design equations is obtained, which can be used as the initial value of the iterative method to solve the system of equations. Using this analytical formula, it is also proved that the length and catenary There is a linear correlation between the line characteristic parameters, and this linear correlation is used to reduce the dimensionality of the design constraint equations, so that the original design constraint equations with three independent unknowns can be simplified to have two independent unknowns Reduce the difficulty of solving the system of equations. The droop increment formula is also used to simplify the consequent calculation of implicit unknowns in the process of solving an equation set, greatly reducing the computational complexity of numerical integration. Using the number theory mesh iterative method to solve the design constrained equations after dimension reduction, not only the calculation process is stable and reliable, but also easy to implement by computer programming.