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分析了轴向力和扭矩对钻柱弯曲变形的影响,推导出在井孔约束下水平井段钻柱的非线性静力分岔微分方程。采用Galerkin方法对其简化形式的研究表明,在钻井工程中,水平井段钻柱的静力分岔主要取决于钻压和井孔尺寸,扭矩产生的影响可以忽略。在不计扭矩情况下,用解析法求得的两端铰支模型钻柱的临界钻压与用能量法得到的结果相同。对铰-固模型钻柱静力分岔的研究表明,当钻柱屈曲后形成的半波数达到4以上时,两种模型计算的临界钻压差别很小。因此,对水平井段较长的钻柱可用比较简单的两端铰支模型计算其临界钻压。
The influence of axial force and torque on the bending deformation of drill string is analyzed, and the nonlinear static bifurcation differential equation of drill string in horizontal well section is derived. The simplified form study using Galerkin method shows that the static bifurcation of drill string in horizontal well depends on weight-on-bit and hole size, and the influence of torque can be ignored. Except for torque, the critical weight-on-bit of the drill string with hinged-end model determined by analytic method is the same as that obtained by energy method. The study on the static bifurcation of the hinge-solid model drill string shows that there is little difference between the two models when the half-wave number formed by the buckling of the drill string reaches more than 4. Therefore, the longer the horizontal section of the drill string can be relatively simple two-end hinge model to calculate the critical weight-on-bit.