三维圆弧型井眼轨道设计模型的拟解析解

doi:10.7623/syxb202012020

石油学报 ›› 2020, Vol. 41 ›› Issue (12): 1679-1685.DOI: 10.7623/syxb202012020

三维圆弧型井眼轨道设计模型的拟解析解

鲁港^1,2, 习伟东³, 来建强²

1. 中国石油辽河油田公司勘探开发研究院辽宁盘锦 124010;
2. 北京四利通控制技术股份有限公司北京 101102;
3. 中国石化中原石油工程有限公司装备处河南濮阳 457001

收稿日期:2020-04-27 修回日期:2020-11-09 出版日期:2020-12-25 发布日期:2021-01-06
通讯作者: 鲁港,男,1963年4月,1985年获复旦大学理学学士学位,2005年获大连理工大学软件工程专业硕士学位,现为中国石油天然气股份有限公司辽河油田分公司高级工程师,主要从事井眼轨道设计理论研究和智能钻井专家系统中定向井控制方面的研究工作。Email:Lugang1999@sina.com
基金资助:
国家科技重大专项"钻井压裂适度出砂油藏工程技术"（2008ZX05024-003）资助。

Q uasi-analytical solution of the design model of three-dimensional arc type well trajectory

Lu Gang^1,2, Xi Weidong³, Lai Jiangqiang²

1. Exploration&Development Research Institute, PetroChina Liaohe Oilfield Company, Liaoning Panjin 124010, China;
2. Beijing Sleton Control Technologies Co. Ltd., Beijing 101102, China;
3. Equipment Department, Sinopec Zhongyuan Petroleum Engineering Company, Henan Puyang 457001, China

Received:2020-04-27 Revised:2020-11-09 Online:2020-12-25 Published:2021-01-06

摘要/Abstract

摘要：

为了研究三维圆弧型井眼轨道设计方程组是否存在解析解以及如何有效求解，使用消去法从多元非线性方程组中推导出其中的某个未知数满足一个特征多项式方程，并且证明了该方程组的拟解析解可以由特征多项式方程的实数根和已知设计参数构成的解析公式计算得到；如果极点多项式非恒等于0，则当特征多项式次数不超过5时，如果有解则为解析解，否则为数值解。通过使用C++类实现多项式加减法、乘法的计算方法，提出了多项式实数根的分隔算法、并用二分法快速求解出多项式全部实数根的计算方案。该方法在数学上经严格推导，计算方案简洁、稳健，在三维井眼轨道设计、智能钻井定向控制中具有应用价值。

关键词: 定向钻井, 三维设计, 井眼轨道, 圆弧型, 拟解析解

Abstract:

To study whether there is an analytical solution to the design equation set of three-dimensional arc-shaped well trajectory and how to solve it effectively, this paper uses the elimination method to deduce an unknown number from the multivariate nonlinear equation set which satisfies a characteristic polynomial equation, and proves that the approximate analytical solution of the equation set can be calculated from the analytic formula including the real roots of characteristic polynomial equation and the known design parameters. If the polar polynomial is not identically vanishing, when the degree of the characteristic polynomial does not exceed 5, if there is a solution, it is an analytical solution. Otherwise, it is a numerical solution. The authors explore the methods of applying polynomial addition, subtraction and multiplication in computer programming using C++ classes, propose the real root insulating algorithm for the real number roots of a polynomial, and quickly determines the calculation scheme for all real roots of polynomials by dichotomy. The proposed method is rigorously deduced in mathematics, and the calculation scheme is simple and robust. It has application value in the three-dimensional well trajectory design and directional control of intelligent drilling.

Key words: directional drilling, three-dimensional design, well trajectory, arc type, approximate analytical solution

中图分类号:

TE243

鲁港, 习伟东, 来建强. 三维圆弧型井眼轨道设计模型的拟解析解[J]. 石油学报, 2020, 41(12): 1679-1685.

Lu Gang, Xi Weidong, Lai Jiangqiang. Q uasi-analytical solution of the design model of three-dimensional arc type well trajectory[J]. Acta Petrolei Sinica, 2020, 41(12): 1679-1685.

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三维圆弧型井眼轨道设计模型的拟解析解

Q uasi-analytical solution of the design model of three-dimensional arc type well trajectory

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