Multi-field coupling multiple nonlinear vibration model and fatigue crack propagation failure mechanism of tubing string in ultra-HPHT gas wells

Abstract In this work, a multiple nonlinear vibration model of drilling string system in ultra-HPHT oil & gas wells was established using finite element method, energy method and Lagrange equation, which considers multiple nonlinear factors such as the nonlinear effect of ultra-HPHT on the elastic modulus of the drill string, the nonlinear contact between the drill string and the borehole wall, and the longitudinal transverse torsional coupling vibration of the drill string structure. The incremental form Newmark and Newton Raphson joint iteration methods is proposed and the correctness of the model is verified by the field test data. Based on the mechanism of the torsion impact acceleration tool, corresponding motion equations are established and the main ways of acceleration were determined. Based on this, according to the parameters of YC ultra-HPHT well in South China Sea, the influence of the impact tool on the vibration characteristics and stick slip characteristics of the drill string were explored. It is found that, firstly, applying constant torque can effectively reduce the time for the drill string to stall and improve the mechanical drilling speed of the drill bit. The sine wave torque excitation has the best effect and can effectively improve the mechanical drilling speed. Secondly, with the increase of torque amplitude, the peak speed decreases significantly, the torsional vibration of the drill string becomes more stable, and the viscosity time of stick slip vibration also decreases significantly. Under the premise of meeting the safety of the acceleration tool, a torque amplitude of 4000 N·m can be used for acceleration, which has a better acceleration effect. Thirdly, the torque frequency increases, the peak speed shows a trend of first decreasing and then increasing, while the viscosity time also shows a trend of first decreasing and then increasing. This indicates that the optimal acceleration effect is achieved when the frequency of acceleration tool is selected to be around 20 Hz. The research results provide a theoretically guidance for designing and practically sound approach for effectively improving the mechanical speed in ultra-HPHT oil & gas wells.