Calculation of spectral sets of design parameters for three-section circular arc trajectory

doi:10.7623/syxb202404008

Acta Petrolei Sinica ›› 2024, Vol. 45 ›› Issue (4): 708-717.DOI: 10.7623/syxb202404008

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Calculation of spectral sets of design parameters for three-section circular arc trajectory

Wang Haitao¹, Zheng Peng², Deng Qingshan³, Sun Liwei⁴, Lu Gang¹, Meng Qing'an¹, Qin Ji¹

1. Kunlun Digital Technology Co., Ltd., Beijing 100043, China;
2. Directional Well Service Company, CNPC Bohai Drilling Engineering Company Limited, Tianjin 300280, China;
3. No.3 Drilling Company, CNPC Bohai Drilling Engineering Company Limited, Tianjin 300280, China;
4. Engineering Technology Research Institute, CNPC Great Wall Drilling Engineering Co., Ltd., Liaoning Panjin 124010, China

Received:2023-07-03 Revised:2024-02-18 Online:2024-04-25 Published:2024-05-08

三段制圆弧轨道设计参数的谱集计算

王海涛¹, 郑鹏², 邓青山³, 孙立伟⁴, 鲁港¹, 孟庆安¹, 覃吉¹

1. 昆仑数智科技有限责任公司北京 100043;
2. 中国石油渤海钻探工程有限公司定向井技术服务分公司天津 300280;
3. 中国石油渤海钻探工程有限公司第三钻井工程分公司天津 300280;
4. 中国石油长城钻探工程有限公司工程技术研究院辽宁盘锦 124010

通讯作者: 鲁港,男,1963年4月生,1985年获复旦大学数学系应用数学专业理学学士学位,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
作者简介: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
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。

Abstract

Abstract: To solve the "cut-and-trial" problem of design parameter input in the wellbore trajectory design, numerical algorithms were developed for the calculation of design parameter spectral sets. Based on the bisection method, this study provides an algorithm in the overall allowable range of two design parameters and another in the allowable range of one design parameter when the other is set. These algorithms can effectively calculate the spectrum set boundaries, thus plotting the graphs of above spectral sets. The spectrum set structure theorem is proved as follows:the three-section design parameter spectral set is composed of a 2D bounded connected closed set or the union of several unconnected 2D bounded connected closed sets. Based on the results of numerical examples, it is indicated that the proposed algorithms can solve the boundaries of spectrum sets in various cases of being connected and disconnected. Therefore, the computation algorithm for spectral sets is highly valuable in wellbore trajectory design software, which can provide users with the visualized numerical ranges for design parameters, thus improving design efficiency.

Key words: directional drilling, hole trajectory, three-section system, spectral set, bisection method

摘要： 为了解决井眼轨道设计中设计参数输入“试凑”问题,发展了设计参数谱集计算的数值算法。以二分法为基础,推导出了两个设计参数各自的整体允许范围的算法,以及当一个设计参数给定时另一个设计参数允许范围的算法,使用这些算法能有效地计算出谱集边界,从而绘制出设计参数谱集图形。进一步证明了谱集结构定理:三段制设计参数谱集由一个二维有界连通闭集或者不相交的多个二维有界连通闭集的并集组成。数值算例的计算结果表明,谱集计算算法能求出连通和不连通等各种情况的谱集边界。谱集计算算法在井眼轨道设计软件中可为软件用户提供可视化的设计参数选择数值范围,提高设计效率。

关键词: 定向钻井, 井眼轨道, 三段制, 谱集, 二分法

CLC Number:

TE22

Wang Haitao, Zheng Peng, Deng Qingshan, Sun Liwei, Lu Gang, Meng Qing'an, Qin Ji. Calculation of spectral sets of design parameters for three-section circular arc trajectory[J]. Acta Petrolei Sinica, 2024, 45(4): 708-717.

王海涛, 郑鹏, 邓青山, 孙立伟, 鲁港, 孟庆安, 覃吉. 三段制圆弧轨道设计参数的谱集计算[J]. 石油学报, 2024, 45(4): 708-717.

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Calculation of spectral sets of design parameters for three-section circular arc trajectory

三段制圆弧轨道设计参数的谱集计算

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[2]	Hong Difeng, Tang Xueping, Gao Wenkai, Lü Haichuan. Comprehensive solving method for arc-type well-path planning model [J]. Acta Petrolei Sinica, 2021, 42(2): 226-232.
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