三维侧位抛物线型方位漂移轨道设计的数值算法

Numerical Algorithm for the Design of 3D Lateral Parabola Azimuth Drift Well-path

摘要:

考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组，需要使用数值迭代法才能求出其数值解。给出了解析形式的垂深增量公式，利用约束方程组中的垂深方程，将3个独立未知数中的一个未知数表示成其他2个未知数的函数，并用之对设计约束方程组进行降维处理。剖析了隐含未知数的计算细节，给出了隐含未知数的递推算法。提出了降维后的约束方程组的数值求解算法——缩半网格法，该算法可以快速、可靠地求出设计问题的数值解，适用于在开发计算机软件时编程实现。

Abstract:

The design constrained equations of azimuth drift is a nonlinear one that contains 3 independent and several hidden unknowns, the numerical iteration method should be used to get the numerical solution. The vertical depth increasing equation was provided, by using vertical depth increasing equation of the constrained equations, one of the 3 independent unknowns was expressed as functions of the other 2 unknowns, which were used for dimension reduction of the design constraint equations. The paper analyzed the calculation details of hidden unknowns and gave the recursive algorithm for hidden unknowns. The numerical value arithmetic of constrained equations after dimension reduction was also put forward, that was half- shrinkage grid method, which could be applied to quickly and reliably find the numerical solutions of design, especially for programming computer software.