三维悬链线井眼轨迹模型的数值计算

Numerical calculation of 3D catenary borehole trajectory model

在三维悬链线轨道设计问题的非线性方程组的数值求解算法中,悬链线井段的坐标增量是使用数值积分法来计算的,由于数值积分嵌套在迭代算法中,数值积分的计算成为影响设计方程组求解效率的主要因素。通过一些数学技巧推导出了垂深增量和水平投影长度增量的解析计算公式,从而在设计方程组的迭代算法中不必再使用数值积分法来计算垂深和水平投影长度增量。使用积分变量替换将北、东坐标增量的积分计算式简化成了另一种等价形式,使用这种新形式来计算数值积分,可以比原来的数值积分法节省三分之一的三角函数运算次数,从而显著提高整个设计方程组迭代算法的计算效率。

In the 3D catenary borehole trajectory design of nonlinear equations numerical algorithm,the coordinates increment of catenary section is calculated by numerical integral.As the numerical integral is nested in the iteration algorithm,the calculation of numerical integral method is the main factor influencing the design equation.Through some math skills,the increment of vertical depth and length increment of horizontal projection have been derived,thus in the design of the equations of iterative algorithm,the numerical integral method can not be taken to calculate vertical and horizontal length increment deep projection.By using integration variable displacement,the integral formula of northern and eastern coordinates is simplified to another equivalent form.With this new kind of numerical calculation,one third of the triangle function number operations can be saved compared with the original save.Thus the iterative algorithm computation efficiency of the whole design equations is obviously improved.