CAJ | 학술논문

为了快速、精确地求解阶梯形水平井段等曲率双圆弧形三维井眼轨道设计问题，对设计约束方程组的解析求解方法进行了研究。利用三维井眼轨道设计问题的拟解析解理论，推导了圆弧曲率相等且同为未知数时的特征多项式的数学表示式；利用C＋＋面向对象编程语言，实现了多项式的数值计算。利用构造理论模型计算出该模型的各种关键数据，再以此为已知设计数据、以圆弧曲率为未知数进行求解验证；设计约束方程组的解析法不仅能够正确区分出真解与增解，而且真解与已知数据完全相同。求出了阶梯形水平井段等曲率双圆弧形三维井眼轨道设计问题的解析解，解决了该问题有解、无解的判定问题，以及快速求解的问题。研究结果表明，设计约束方程组的解析法是一种可以用计算机实现的新算法，计算速度快、结果精确、可靠性高，可应用于钻井设计软件开发。
위료쾌속、정학지구해계제형수평정단등곡솔쌍원호형삼유정안궤도설계문제，대설계약속방정조적해석구해방법진행료연구。이용삼유정안궤도설계문제적의해석해이론，추도료원호곡솔상등차동위미지수시적특정다항식적수학표시식；이용C＋＋면향대상편정어언，실현료다항식적수치계산。이용구조이론모형계산출해모형적각충관건수거，재이차위이지설계수거、이원호곡솔위미지수진행구해험증；설계약속방정조적해석법불부능구정학구분출진해여증해，이차진해여이지수거완전상동。구출료계제형수평정단등곡솔쌍원호형삼유정안궤도설계문제적해석해，해결료해문제유해、무해적판정문제，이급쾌속구해적문제。연구결과표명，설계약속방정조적해석법시일충가이용계산궤실현적신산법，계산속도쾌、결과정학、가고성고，가응용우찬정설계연건개발。
This study investigated the design constraints on the analytical method of solving equations for quickly and accurately solving the system of restricted equations for the design problem of hyperboloi‐dal arch type trajectory of equal curvature for step‐horizontal sections .An explicit formulation of the char‐acteristic polynomial was given by taking advantage of the known result of the theory of quasi‐analytic so‐lution for three dimensional trajectory design .An implementation strategy for polynomial numerical calcu‐lation was given by taking advantage of object‐oriented C+ + programming techniques .To test the correct‐ness of the analytic solution formulation ,a theoretical model was constructed ,and the key data of trajectory was calculated using this model ,then they solved the system of restricted equations in which the equal cur‐vature was one of the unknowns and above key data were known .The analytic solution method was not on‐ly able to discriminate exactly the true solution from pseudo solution ,but also giving the true solution the same to known data .An analytic solution formulation for the solution's existence was given for the trajecto‐ry design problem ,and could be used for quick calculation .The result showed that the analytic method was a new programmable algorithm for solving the system of restricted equations of trajectory design ,w hich had the advantages of quickness ,accuracy ,reliability ,and usefulness in drilling software development .