New Method for Geometric Nonlinear Analysis of Large Displacement Drill Strings
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摘要: 提出了基于实测的井深及相应的井斜角和方位角来获得确保井内钻柱参考构形长度不变的井眼轴线插值方法．当以空间大位移井的井眼轴线为钻柱的参考构形时，钻柱内的初始内力可以由井眼轴线的曲率和挠率确定．利用基于在空间自然坐标系下的包含所有单元刚体位移和常应变模式的位移函数，严格地按虚功原理推出了具有初始曲率和挠率的钻柱单元内由初始内力所引起的等效节点力计算公式，为大位移井钻柱的几何非线性处理提供了理论依据．澄清了钻柱有限元分析中的若干基本概念．为随后进行的以井眼轴线为参考构形的小变形分析，计算钻柱的自重和基于自然坐标系下的线性刚度矩阵及一致载荷列阵提供了保证．Abstract: Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state being consistent with well axis can be obtained from the curvatures and the tortuosity of well axis. By using the principle of virtual work, formula to compute the equivalent load vector of the initial stress was derived. In the derivation, natural (curvilinear) coordinate system was adopted since both the curvature and the tortuosity were generally not zero. A set of displacement functions fully reflecting the rigid body modes was used. Some basic concepts in the finite element analysis of drill string have been clarified. It is hoped that the proposed method would offer a theoretical basis for handling the geometry nonlinear problem of the drill string in a 3-D large displacement wellbore.
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Key words:
- finite element /
- geometric nonlinearity /
- numerical simulation /
- drill string
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