| Drill string vibration is an important reason for the failure of the drill string, which can seriously affect the drilling safety and cost. Stick-slip vibration is a kind of severe torsional vibration, while whirl is a kind of serious lateral vibration. These two are the main reasons for the failure of the BHA, the drilling bit especially the PDC bit during the modern drilling process.This paper established the torsional vibration model of drill string system, deduced the stability condition of the torsional vibration through the stability analyzing. The stick-slip model of the drill string system has been built up and worked out, and the general rule of the stick-slip which contains frequency and bit rotation speed is obtained, the frequency of stick-slip increases in inverse proportion to the string length and proportion to the rotation speed. Based on the dimensionless, stick-slip equation was simplified, deduced critical damping and critical damping ratio while the stick-slip vibration occurs, verified the rationality of the method that raise the rotation speed to cure stick-slip vibration. Based on the Routh-Hurwitz criterion, the stability of drilling string axial vibration and coupled torsional vibration are analyzed, and the condition of the stability of the coupled vibration is deduced. According to the PDC bit and the rock interaction model, analyzed the influence of the parameters of PDC bit to the stick-slip vibration. According to the energy method, the formulas of the critical drilling pressure are deduced, which proposed the method of controlling the stick-slip by adjusting the drilling pressure. Divided the relationship between the BHA and the borehole into3types, respectively, without contact, pure rolling, slipping contact, and analyzed the whirl motion of each situation, deduced the vortex speed of the drill string system in the event of a bifurcation moving, and analyzed the impact of the fluid damping and structural damping on the eddy of drill string system. |
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