限定井眼方向待钻轨道设计的代数法

限定了井眼方向的待钻井眼轨道设计问题需要求解一个7元非线性方程组，通常使用的数值迭代方法有许多固有的缺点，提出了一个新方法──代数法：将原始非线性方程组化简成一个三元多项式方程组，再进一步归结为求一个10次多项式方程全部正实数解问题和一个二元线性代数方程组问题。给出了代数法的计算机实现方法，具有计算速度快、数值稳定性好、存储需求小等特点。代数法具有与解析法相近的良好数学性质，能够对问题是否有解做出事前判断；在问题存在多个解的情况下，能够正确求出全部的解。所使用的数学化简技巧能够推广应用到求解定向井、水平井的井眼轨道设计问题中，有重要的理论价值和应用前景。

AN ALGEBRAIC METHOD OF BOREHOLE TRAJECTORY DESIGN WITH DEFINED BOREHOLE DIRECTION

The borehole trajectory design to be drilled well with defined direction needs to solve a set of 7-element nonlinear equations.To the generally used numerical iterative process，there are many intrinsic disadvantages.A new method，algebraic method，is presented to simplify the primitive equations into a set of 3-element polynomial equations，and is further resolved into solving all the positive real numbers of a 10-degree polynomial equation and a set of 2-element linear algebraic equations.The computer realization of algebraic method is provided.It is fast in computation speed and requires little memory.The algebraic method has similar mathematical nature with analytical method，and can give judgment for whether a problem has solution and correctly solving all the solutions when a problem has multiple solutions.The method can be applied to solve the problems in trajectory design of directional and horizontal wells，thereby its theoretical importance and application future are proved.