圆弧型井眼轨道设计问题的拟解析解理论

鲁港

鲁港. 圆弧型井眼轨道设计问题的拟解析解理论[J]. 石油钻探技术, 2014, 42(1): 26-32. DOI: 10.3969/j.issn.1001-0890.2014.01.005
引用本文: 鲁港. 圆弧型井眼轨道设计问题的拟解析解理论[J]. 石油钻探技术, 2014, 42(1): 26-32. DOI: 10.3969/j.issn.1001-0890.2014.01.005
shu
Lu Gang. Quasi-Analytic Solution Theory for Arc Type Well Trajectory Design[J]. Petroleum Drilling Techniques, 2014, 42(1): 26-32. DOI: 10.3969/j.issn.1001-0890.2014.01.005
Citation: Lu Gang. Quasi-Analytic Solution Theory for Arc Type Well Trajectory Design[J]. Petroleum Drilling Techniques, 2014, 42(1): 26-32. DOI: 10.3969/j.issn.1001-0890.2014.01.005
shu

圆弧型井眼轨道设计问题的拟解析解理论

  • 中国石油辽河油田分公司勘探开发研究院, 辽宁盘锦 124010

详细信息
    作者简介:

    鲁港（1963- ），男，辽宁锦州人，1985年毕业于复旦大学应用数学专业，2005年获大连理工大学软件工程专业硕士学位，高级工程师，长期从事石油钻探数学模型方面的研究工作。

  • 中图分类号: TE21

Quasi-Analytic Solution Theory for Arc Type Well Trajectory Design

  • Exploration & Development Research Institute of Liaohe Oilfield Company of PetroChina, Panjin, Liaoning, 124010, China

摘要

    摘要
  • 摘要: 为了快速、可靠地求解井眼轨道设计问题所形成的多元非线性方程组，基于数学机械化理论的思想和技术，经过复杂的数学公式推导，求出了该方程组的拟解析解，创建了拟解析解的完整理论体系。理论证明，从井眼轨道设计方程组出发可以推导出只含有一个未知数的特征多项式，而该方程组的所有未知数可以由该特征多项式的全部实数根和一组解析计算公式依序逐个计算出来。理论分析和实际计算表明，利用拟解析解方法可以快速判断该方程组是否有解，在有唯一解和多个解的情况下，能够快速、准确地计算出该唯一解或全部解。拟解析解方法克服了初值依赖性、收敛性、不能求多个解等数值迭代类算法的固有缺陷，它的计算精度只与特征多项式求实数根算法有关，是一种相对精确的算法。研究结果表明，拟解析解方法是求解井眼轨道设计方程组的快速、可靠、精确的先进计算技术，不仅是算法研究上的理论创新，而且在钻井软件开发上具有重要的实用价值。
    Abstract: To solve the system of multivariate nonlinear equations in well trajectory design quickly and reliably,the analytical solving method for the system of equations has been studied.Based on the theory and techniques of the mathematics and mechanics,a complete theoretical system of quasi-analytical solutions was created through complex mathematical formula derivation.It was proved theoretically that a characteristic polynomial containing only one unknown can be derived from the design equations,and all unknowns in designed equations can be calculated in sequence by all real roots of the characteristic polynomial and a group of analytical formula.The theoretical analysis and practical calculation showed that the quasi-analytical method can determine whether the system of equations are solvable,and calculate the solutions in the cases of the system of equations that have a unique solution or more.The quasi-analytical solution method completely overcomes inherent defects of numerical iteration methods such as initial dependence,convergence,and inability to solve multiple solutions etc.Its accuracy only depends on all real roots of characteristic polynomial,being an exact algorithm.The results showed that proposed method is a fast,reliable and accurate computing technique to solve the system of design equations.It is not only a theoretical innovation in algorithm research,but also has an important practical value in drilling software development.
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    • 参考文献(16)
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出版历程
  • 收稿日期:  2013-03-20
  • 修回日期:  2013-12-16
  • 刊出日期:  1899-12-31

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