Abstract: To reduce the operation difficulties of three-dimensional horizontal wells in shale oil and gas fields,this paper proposes a design model of the seven-section well-path with constant tool face angle.According to the engineering design requirements,the design parameters are grouped into 3 categories and 18 parameter combinations.Since the parameter constraint equations are multivariate nonlinear systems of equations,which are difficult to be solved analytically,numerical solution methods are explored for this purpose.Firstly,the corresponding three-dimensional circular arc well-path model is solved,and the result is used as the initial value for the model of well-path with constant tool face angle,and then the model is solved using the quasi-Newton method.Based on the three-dimensional circular arc well-path model and its analytical formula,an algorithm flow has been designed for the common parameter combination of the model of well-path with constant tool face angle,and the difficulty in solving the three-dimensional constant tool face angle design model is finally solved.The case study shows that the solution method is simple and effective,characterized with high computational accuracy and easy implementation of programming,which provides options and technical support for three-dimensional horizontal well-path design and the optimal and fast drilling of three-dimensional horizontal cluster wells in shale oil and gas fields.

Key words: horizontal well, three-dimensional well-path, constant tool face angle, numerical model, design method

摘要： 为降低页岩油气田三维水平井的施工难度,提出了七段制恒工具面角轨道设计模型。根据工程设计需求,将设计参数归为3类18种求解组合。由于参数约束方程为多元非线性方程组,难以解析求解,为此探索了数值求解方法。首先求解对应的三维圆弧轨道模型,将其结果作为恒工具面角轨道模型的初值,进而采用拟牛顿法进行求解。基于三维圆弧轨道模型及其解析公式,设计了恒工具面角轨道模型常用求解组合算法流程,解决了三维恒工具面角设计模型求解难题。算例研究表明,模型求解方法简单、有效,计算精度高,易于编程实现,可以为三维水平井轨道设计以及页岩油气田三维丛式水平井优快钻井提供新选择以及相应的技术支持。

关键词: 水平井, 三维轨道, 恒工具面角, 数值模型, 设计方法