扭矩和边界约束对水平井钻柱静力分岔的影响

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。

Effects of torque and boundary constraints on static bifurcation of drilstring in horizontal section

Based on an analysis of the effect of axial force and torque on bending deformation of a drillstring, a differential equation for the non linear static bifurcation of the drillstring constrained by the borehole in a horizontal section is derived. A study of its simplified form by Galerkin Method shows that the static bifurcation of the drillstring depends mainly on the weight on bit(WOB) and the diameter of the borehole. The effect of the torque on static bifurcation can be neglected in oil drilling engineering. When torque is not considered, the critical WOB for the hinged hinged model obtained here is the same as the previous results got from the energy method. It is also noticed that the difference between the critical WOB calculated by the hinged hinged model and that calculated by the hinged fixed model is very small when the number of half waves of buckled drillstring is larger than 4. In this case the critical WOB on the drillstring in longer horizontal sections can be determined by the simpler hinged hinged model.