Multiple nonlinear vibration model of drilling string and mechanism of drilling speed increase in ultra-HPHT oil & gas wells

In the drilling process of ultra-HPHT oil & gas wells, the drill string is more susceptive to tends to stick slip, whirl, jump and other harmful movements, which will lead to a decrease in drilling efficiency. Therefore, a multiple nonlinear vibration model of drilling string system in ultra-HPHT oil & gas wells is established using energy method and Lagrange equation, which considers multiple nonlinear factors including the nonlinearity of drill string geometry, contact collision of drill string-casing, and high temperature and high pressure on drill string viscous resistance. The correctness of the model is verified by the field test data and the simulation test results. Based on the mechanism of the torsion impact acceleration tool, corresponding motion equations are established and the main ways of acceleration are determined. Based on this, the influence of the impact tool on the vibration characteristics and stick slip characteristics of the drill string are explored. It is found that, firstly, applying constant torque can effectively improve the mechanical drilling speed of the drill bit. The sine wave torque excitation can effectively improve the mechanical drilling speed. Secondly, with the increase of torque amplitude, the peak speed decreases significantly, and the torsional vibration of the drill string becomes more stable. 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 and the viscosity time shows a trend of first decreasing and then increasing. The optimal acceleration effect is achieved when the frequency of acceleration tool is selected as 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.