二维圆弧型井眼轨道设计问题的通解

General Solution of 2D Arc Well Trajectory Design

二维圆弧型井眼轨道是常规定向井、水平井轨道设计优先考虑的剖面类型,应用比较广泛。但是由于井段组合形式很多,并且对于同一种井段组合还有很多种未知数求解组合,推导每种井段组合和求解组合情况下的解的计算公式的工作非常繁重和复杂。研究了任意井段组合和任意求解组合的通解问题,发现井眼轨道设计问题的约束方程组可以化归成线性代数方程组或者4种典型方程组之一;得到了4种典型方程组的实数解的计算公式,并给出了有实数解的判别条件。对于二维圆弧型井眼轨道设计问题的基础理论研究和计算机软件开发都有重要的意义。

2D arc well trajectory is considered with priority in conventional deviated and horizontal well design. However, because there are a lot of combination forms of hole sections and also a lot of resolution combinations of unknowns for the same hole section, the computation is very complicated to derive the computation formula for the solutions of each hole section combination and each solving combination. This paper studies the general solutions of arbitrary hole section combination and arbitrary solving combination, discovers that the constraint equation of hole trajectory design can be dissolved into linear algebra equation system or one of the four typical systems of equations. The computation formula of the real number solutions of the four typical equation systems is obtained and the discretion conditions of real number solution are given. This study has important significance for fundamental research and computer software development for 2D arc borehole trajectory design.