张昊, 雷雨辰, 高云飞, 张维维, 闫启方, 刘林超. 分数黏弹性可压缩油气井管杆准静态响应分析[J]. 信阳师范学院学报(自然科学版), 2021, 34(2): 331-338,344. DOI: 10.3969/j.issn.1003-0972.2021.02.026
引用本文: 张昊, 雷雨辰, 高云飞, 张维维, 闫启方, 刘林超. 分数黏弹性可压缩油气井管杆准静态响应分析[J]. 信阳师范学院学报(自然科学版), 2021, 34(2): 331-338,344. DOI: 10.3969/j.issn.1003-0972.2021.02.026
ZHANG Hao, LEI Yuchen, GAO Yunfei, ZHANG Weiwei, YAN Qifang, LIU Linchao. Quasi-static Response Analysis of Fractional Viscoelastic Compressible Oil and Gas Well Pipe Rod[J]. Journal of Xinyang Normal University (Natural Science Edition), 2021, 34(2): 331-338,344. DOI: 10.3969/j.issn.1003-0972.2021.02.026
Citation: ZHANG Hao, LEI Yuchen, GAO Yunfei, ZHANG Weiwei, YAN Qifang, LIU Linchao. Quasi-static Response Analysis of Fractional Viscoelastic Compressible Oil and Gas Well Pipe Rod[J]. Journal of Xinyang Normal University (Natural Science Edition), 2021, 34(2): 331-338,344. DOI: 10.3969/j.issn.1003-0972.2021.02.026

分数黏弹性可压缩油气井管杆准静态响应分析

Quasi-static Response Analysis of Fractional Viscoelastic Compressible Oil and Gas Well Pipe Rod

  • 摘要: 将水平油气井管杆简化为受弹性约束的黏弹性圆柱管模型,采用分数阶黏弹性理论描述管杆的本构关系,并结合弹性力学理论,建立了可压缩黏弹性管杆平衡方程,求解得到了可压缩管杆体的黏弹性应力位移解析解.数值算例的分析结果表明:分数阶导数数值越大,所对应的管杆内壁处的初始应力越大,圆柱管内壁处的径向和环向应力值越大,所对应的竖向应力的上升段越大,管杆的竖向应力稳定值越大;外围套管泊松比越大,径向位移值越小,所对应的径向应力值越小,泊松比的大小对环向应力的影响并不明显,会对径向应力产生显著影响;套管的弹性模量对径向位移的影响较小;模型常数比越大,所对应的径向和环向应力值越大;外围套管的厚度对柱管内壁处的环向应力的影响很小,厚度越大,内壁所受的径向应力越大,竖向应力值会减小.

     

    Abstract: The horizontal oil and gas well pipe rod is simplified as a viscoelastic cylindrical pipe model with elastic constraints. The fractional derivative viscoelastic theory is used to describe the constitutive relationship of the pipe rod. Combined with the theory of elastic mechanics, the equilibrium equations of compressible viscoelastic pipe rod are established, and the analytical solutions of viscoelastic stress and displacement of compressible pipe rod are obtained. The numerical results show that the larger the order of the fractional derivative, the larger the initial stress at the inner wall of the corresponding pipe rod, the larger the radial and circumferential stress at the inner wall of the cylindrical pipe, the larger the rising section of the corresponding vertical stress, and the larger the stable value of the vertical stress of the pipe rod. When the the Poisson's ratio of the outer casing increases, the radial displacement and stress will be smaller. The influence of Poisson's ratio on the circumferential stress is not obvious, but the influence on radial stress is more significant. The elastic modulus of casing has little effect on the radial displacement. The larger the model constant ratio, the larger the radial and circumferential stresses. The thickness of the outer casing has little influence on the circumferential stress at the inner wall of the column pipe. When the thickness of the outer casing increases, the radial stress will also increase, and the vertical stress value will decrease.

     

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