Axial-torsional coupling vibration model and nonlinear behavior of drill string system in oil and gas wells

In response to the failure problem of axial-torsional coupling vibration of drill string in oil & gas wells, an axial-torsional coupling nonlinear vibration model of drill string is established using the finite element method, which can effectively simulate the coupling vibration of actual wellbore drill string multi-body systems and the real-time rock breaking effect. Moreover, the correctness and effectiveness of the theoretical model verified by a similar experiment of tubing vibration. Finally, the influences of feed rate and rotary drilling speed on the nonlinear behavior of the vibration of the drill string are investigated. The results obtained demonstrate that, the axial vibration response of the drill string system shows an overall trend of quasi-periodic-chaotic change with the increase of feed rate, and the torsional vibration of the drill string shows the trend of quasi periodic-chaotic. When the feed rate is high, the vibration of the drill string system is mainly for the irregular and complex hybrid motion. Therefore, the appropriate reduction of feed speed can increase the stability of the drill string on-site, and reduce the jump drilling and stick-slip vibration of the drill string. When the rotary drilling speed is 90–210 rpm, the torsional vibration response of the drill string shows a chaotic-quasi-periodic trend and the complexity of the torsional vibration of the drill string decreases with the increase of rotary drilling speed. The axial vibration response of the drill string shows a chaotic-quasi-periodic-chaotic trend with the increase of the rotary drilling speed. When the rotary drilling speed increases to 400–410 rpm, the axial vibration of the drill string becomes a quasi-periodic motion. Therefore, increasing the rotary drilling speed within a certain range can reduce the complexity of the vibration of the drill string and reduce the skip and stick-slip vibration of the drill string.