钻井轨道设计问题的有解判别图研究

在求解钻井轨道设计问题的各种数值迭代算法中,不仅计算量大、计算速度慢,而且难以准确判断设计问题是否有解,有几个解。为了解决这个问题,提出了使用拟解析解方法来绘制有解判别图的图示法,通过计算设计方程组的特征多项式的全部实数根,绘制出设计方程组某些正约束未知数的连续变化曲线。通过对比这些连续变化曲线与特征多项式全部实数根的相对位置关系,可以直观地对轨道设计问题解的情况的程序判断结果进行交叉验证。通过对实际设计算例的有解判别图的分析,证实了有解判别图对于设计问题解的存在性判断的正确性。在轨道设计的计算机软件中,有解判别图可以以图形方式直观地向用户展示特征多项实数根与设计问题真解之间的内在关系,有助于用户对设计问题解的存在性做出正确判断。

Application of Discriminant Chart with Solution to Drilling Trajectory Design

Numerical iterative algorithms are applied to solving the problems of drilling trajectory design ,but calculated task is hard,computing velocity is slow and it is hard to judge one,more or none solution.In order to solve these problems,quasi-analytical solution method is proposed to map discriminant chart with solution.After all real roots of proper polynomial in design equation set are calculated,curves of continuous variation of some positive constraints in the design equation set are mapped.Relative position between these curves and all real roots may verify the judgment result of the solution for the trajectory design directly.The discriminant chart with solution can judge the existence of the solution for the trajectory design correctly, which is proved by the analysis of actual cases.Among computer softwares of the trajectory design,the discriminant chart with solution can illustrate the inner relation between the real roots and the true solution for the trajectory design to the customer,which will help the customer to do correct judgment on the solution for the trajectory design.