三维七段制圆弧型井眼轨道设计的拟解析解

doi:10.7623/syxb202309011

石油学报 ›› 2023, Vol. 44 ›› Issue (9): 1545-1551.DOI: 10.7623/syxb202309011

三维七段制圆弧型井眼轨道设计的拟解析解

鲁港¹, 王海涛¹, 李杉², 李雪松¹, 杨志国¹, 王建华¹, 邱晨¹

1. 昆仑数智科技有限责任公司北京 100043;
2. 中国石油集团渤海钻探工程有限公司定向井技术服务分公司天津 300280

收稿日期:2022-06-20 修回日期:2023-06-25 出版日期:2023-09-25 发布日期:2023-10-09
通讯作者: 王海涛,男,1984年5月生,2004年获中国地质大学(武汉)学士学位,现为昆仑数智科技有限责任公司钻井咨询顾问,主要从事钻完井软件研发与信息化系统建设工作。Email:wanghaitao05@cnpc.com.cn
作者简介:鲁港,男,1963年4月生,1985年毕业于复旦大学数学系应用数学专业,现为昆仑数智科技有限责任公司特聘专家、高级工程师,主要从事定向钻井轨迹计算方面的研究工作。Email:Lugang1999@sina.com
基金资助:
国家科技重大专项"钻井工程一体化软件"(2016ZX05020-006)资助。

Quasi-analytical solution for the design of 3D 7-section arc-type well trajectory

Lu Gang¹, Wang Haitao¹, Li Shan², Li Xuesong¹, Yang Zhiguo¹, Wang Jianhua¹, Qiu Chen¹

1. Kunlun Digital Technology Co. Ltd., Beijing 100043, China;
2. Directional Well Company, CNPC Bohai Drilling Engineering Company Limited, Tianjin 300280, China

Received:2022-06-20 Revised:2023-06-25 Online:2023-09-25 Published:2023-10-09

摘要/Abstract

摘要： 为了求解七段制圆弧型井眼轨道设计约束方程组,使用数学消去技巧,先将稳斜段井眼方向矢量消去,再将狗腿角消去,然后化简,最终得到只含有一个未知数的特征方程,该方程在大部分情况下是多项式方程。通过求解该特征方程,得到全部实数根,并在数学上严格证明了设计方程组的解可以用包含特征方程实数根的一组解析计算公式快速计算。该算法可以判断设计问题是否有解以及有几个解,在有多个解的情况下可以一次性同时计算出这些解。算法涵盖七段制设计问题45种有意义的未知数组合情况,较好地解决了七段制圆弧型井眼轨道设计问题的数值求解难题。数值算例验证了算法的有效性和快速求解性。配合多项式类的编程技术,可以用于钻井工程井眼轨道设计类计算机软件的开发。

关键词: 定向钻井, 井眼轨道, 七段制, 拟解析解, 数值求解

Abstract: To solve the constraint equations of 7-section arc-type well trajectory design, mathematical elimination technique is used to eliminate the vector of angle holding section in well direction, and also the dog-leg angle, then simplify the conditions, and finally obtain the characteristic equation containing only one unknown (in most cases, it is a polynomial equation). All the real roots of the characteristic equation are obtained by solving the characteristic equation. It is mathematically proved that the the designed equations can be quickly solved by a set of analytical formulas containing the real roots of the characteristic equation. The algorithm can determine whether the design problem has a solution and how many solutions it has. In case of multiple solutions, these solutions can be obtained at the same time. The algorithm covers 45 meaningful combinations of unknowns about design problem in the 7-section system, and basically solves the numerical problem of the seven-section arc-type well trajectory design. Numerical examples prove that the algorithm is effective and can quickly get the solutions. The programming technique with polynomial classes can be used in the development of computer software for well trajectory design in drilling engineering.

Key words: directional drilling, well trajectory, 7-section system, quasi-analytical solution, numerical solution

中图分类号:

TE22

鲁港, 王海涛, 李杉, 李雪松, 杨志国, 王建华, 邱晨. 三维七段制圆弧型井眼轨道设计的拟解析解[J]. 石油学报, 2023, 44(9): 1545-1551.

Lu Gang, Wang Haitao, Li Shan, Li Xuesong, Yang Zhiguo, Wang Jianhua, Qiu Chen. Quasi-analytical solution for the design of 3D 7-section arc-type well trajectory[J]. Acta Petrolei Sinica, 2023, 44(9): 1545-1551.

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三维七段制圆弧型井眼轨道设计的拟解析解

Quasi-analytical solution for the design of 3D 7-section arc-type well trajectory

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