石油钻探技术
石油鑽探技術
석유찬탐기술
PETROLEUM DRILLING TECHNIQUES
2014年
1期
26-32
,共7页
钻井设计%井眼轨道%方程组%拟解析解%多项式%实数根
鑽井設計%井眼軌道%方程組%擬解析解%多項式%實數根
찬정설계%정안궤도%방정조%의해석해%다항식%실수근
drilling design%wellbore trajectory%system of equations%quasi-analytic solutions%polynomi-al%real root
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。
為瞭快速、可靠地求解井眼軌道設計問題所形成的多元非線性方程組，基于數學機械化理論的思想和技術，經過複雜的數學公式推導，求齣瞭該方程組的擬解析解，創建瞭擬解析解的完整理論體繫。理論證明，從井眼軌道設計方程組齣髮可以推導齣隻含有一箇未知數的特徵多項式，而該方程組的所有未知數可以由該特徵多項式的全部實數根和一組解析計算公式依序逐箇計算齣來。理論分析和實際計算錶明，利用擬解析解方法可以快速判斷該方程組是否有解，在有唯一解和多箇解的情況下，能夠快速、準確地計算齣該唯一解或全部解。擬解析解方法剋服瞭初值依賴性、收斂性、不能求多箇解等數值迭代類算法的固有缺陷，它的計算精度隻與特徵多項式求實數根算法有關，是一種相對精確的算法。研究結果錶明，擬解析解方法是求解井眼軌道設計方程組的快速、可靠、精確的先進計算技術，不僅是算法研究上的理論創新，而且在鑽井軟件開髮上具有重要的實用價值。
위료쾌속、가고지구해정안궤도설계문제소형성적다원비선성방정조，기우수학궤계화이론적사상화기술，경과복잡적수학공식추도，구출료해방정조적의해석해，창건료의해석해적완정이론체계。이론증명，종정안궤도설계방정조출발가이추도출지함유일개미지수적특정다항식，이해방정조적소유미지수가이유해특정다항식적전부실수근화일조해석계산공식의서축개계산출래。이론분석화실제계산표명，이용의해석해방법가이쾌속판단해방정조시부유해，재유유일해화다개해적정황하，능구쾌속、준학지계산출해유일해혹전부해。의해석해방법극복료초치의뢰성、수렴성、불능구다개해등수치질대류산법적고유결함，타적계산정도지여특정다항식구실수근산법유관，시일충상대정학적산법。연구결과표명，의해석해방법시구해정안궤도설계방정조적쾌속、가고、정학적선진계산기술，불부시산법연구상적이론창신，이차재찬정연건개발상구유중요적실용개치。
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 character-istic polynomial containing only one unknow n can be derived from the design equations ,and all unknow ns 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-analyti-cal method can determine w hether 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 ,conver-gence ,and inability to solve multiple solutions etc .Its accuracy only depends on all real roots of characteris-tic polynomial ,being an exact algorithm .The results showed that proposed method is a fast ,reliable and ac-curate 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 .
