Horizontal well is one of the main measures to improve oil and gas production capacity. However, with the extension of horizontal section, the risk of pipe string buckling will be increased. In the quasi-static finite element calculation, it is difficult to identify the contact with the cylindrical wellbore due to the jumping changes of the sinusoidal and helical buckling configurations of the pipe string. Therefore, this method is difficult to solve the calculation convergence problem, especially with the increase of horizontal pipe string length and greater flexibility, this problem becomes particularly prominent. We propose a finite element calculation strategy, namely, using the dynamic relaxation method, to transform the static buckling of the horizontal pipe string into a virtual dynamic problem. We put forward the identification methods of sinusoidal and helical post buckling modes, as well as their critical load determination methods. The research results show that the use of large damping in the dynamic relaxation method can significantly restrain the vibration phenomenon of alternating contact and separation between the horizontal pipe string and the cylinder wall, reduce the response time to reach the stable buckling mode, and also can significantly improve the calculation efficiency. The change trend of critical load is the same when the length of horizontal pipe string is extended for a certain length. Within the extended length range, the horizontal pipe string has the same half sine wave or helix number, and the critical loads of sine and helix buckling will gradually decrease with the extension of the string length, and eventually tend to be constant. This trend is more obvious when the number of half sine waves or helixes of horizontal pipe string is more. The dimensionless critical loads of sinusoidal and helical buckling tend to 1.00 and $\sqrt{2}$ respectively, and the corresponding dimensionless string lengths are 3.73π and 6.21π, respectively. However, other researchers underestimated the effect of length on the critical load of helical buckling. We have verified the critical loads for sinusoidal and helical buckling of short and long pipe strings. The results of this paper are practical for post-buckling analysis of horizontal wells with various lengths of pipe string.

水平井是提高油气产能的主要措施之一。但随着水平段的延伸，管柱屈曲的风险会增加。在准静态有限元计算中，由于管柱正弦和螺旋屈曲构型的跳跃变化，很难识别与圆柱形井筒的接触。因此，该方法难以解决计算收敛问题，特别是随着水平管柱长度的增加和柔性的增大，该问题显得尤为突出。我们提出了一种有限元计算策略，即使用动力松弛法，将水平管柱的静态屈曲转化为虚拟动力问题。我们提出了正弦和螺旋后屈曲模式的识别方法，以及它们的临界载荷确定方法。研究结果表明，动力松弛法中采用大阻尼能够显着抑制水平管柱与筒壁交替接触和分离的振动现象，缩短达到稳定屈曲模态的响应时间，并且能够显着提高计算效率。水平管柱延长一定长度后临界载荷变化趋势相同。在延长长度范围内，水平管柱具有相同的半正弦波或螺旋数，正弦和螺旋屈曲的临界载荷会随着管柱长度的延长而逐渐减小，并最终趋于恒定。当水平管柱的半正弦波或螺旋数较多时，这种趋势更为明显。正弦和螺旋屈曲的无量纲临界载荷趋向于 1.00 和$\sqrt{\mathrm{2个}}$分别对应的无量纲弦长分别为 3.73π 和 6.21π。然而，其他研究人员低估了长度对螺旋屈曲临界载荷的影响。我们已经验证了短管柱和长管柱的正弦曲线和螺旋屈曲的临界载荷。本文结果对不同管柱长度水平井的后屈曲分析具有实用价值。