Abstract: This paper first discusses some trajectory-design methods that are commonly used,then develops new mathematical model for designing 3-D trajectory in re-entry horizontal drilling based on optimization theory and the trajectory-control characteristics.The new model regards the length of curve section as its objective,in which main factors affecting 3-D trajectory design &control are considered quantitatively.Theoretical analysis and more than 10 case studies show that the new model has many advantages comparison with traditional design methods.It embodies the features of trajectory design &control,can greatly simplify the design process and hit the prescribed point or target with much higher accuracy.

Key words: re-entry, horizontal well, three dimensions, trajectory, optimal design, mathematical model

摘要： 对目前几种轨道设计方法进行了讨论.结合侧钻水平井轨道控制技术的特点,依据数学优化理论,建立了侧钻水平井轨道三维优化设计的数学模型.该模型以最短曲线段长度为目标函数,定量地考虑了影响轨道设计与控制的主要因素.理论分析与10多口井的验证表明,与常规轨道设计方法相比,该模型真实地反映了侧钻水平井轨道控制的规律,提高了轨道设计的科学性,避免了重复调整设计的缺点,极大地简化了轨道三维设计的过程.另外,该模型具有中靶精度可调、精确中靶定位的功能.

关键词: 侧钻, 水平井, 三维, 轨道, 优化设计, 数学模型