Abstract: A reasonable well-path planning is the key to control well path successfully.It is expected to solve the problem about accurate,quick and reasonable design of three-dimensional well-path subject to various constraints.A general mathematical model for 3D well-path planning was established with given target position and direction of wellbore.The exact mathematical expressions of constraint variables and well-path calculation formulae were derived using space vectors theory.The new method has no need for solving the constraint equations group,and the design calculation is simple and accurate.The model was used to solve the difficult multi-constraint problems in complex 3D well-path planning successfully.This method can be widely used to plan all kinds of horizontal wells,directional wells and multiple target wells and may provide more accurate theory foundations for well-path control.

Key words: horizontal well, directional well, multiple target well, 3D well path, design, mathematical model, exact solution, calculation

摘要： 合理的井眼轨道设计是成功控制井眼轨道的关键.准确、快速、合理地设计多约条件下的三维井眼轨道是人们期待解决的问题.文中建立了给定目标点位置和井眼方向的三维轨道设计的一般数学模型,利用矢量分析理论得到了约束变量间的解析表达式和井眼轨道计算式.这种方法避免了求解多维非线性方程组,设计计算简单、精确.应用该模型成功地解决了复杂的多约束条件下的三维井眼轨道设计这一难题,具有普遍适用性,可广泛用于设计各种类型的水平井、定向井和多目标井,为井眼轨道控制提供了更为准确的理论依据.

关键词: 水平井, 定向井, 多目标井, 三维井眼轨道, 设计, 数学模型, 精确解, 计算