Investigation on vibration characteristics and adaptive control of drill-string considering torsional-axial nonlinear coupling

During the process of deep oil and gas drilling, the frequent occurrence of drill-string vibration has become a key bottleneck restricting the efficient development of drilling and production engineering. To eliminate the problem of stick-slip and bit-bounce of drill-string, a three-degree-freedom torsional-axial nonlinear coupled vibration model of the drill-string was established by using the lumped mass method, and it was validated by a 5200 m example well. Based on this model, the influence of rotary table speed, bit characteristics, formation stiffness, and rock surface profile on the nonlinear coupled vibration characteristics of drill-string was investigated. Furthermore, an adaptive control scheme for the torsional-axial coupling vibration of the drill-string was proposed by using the fuzzy adaptive PID algorithm. The results indicate that, firstly, increasing the rotary table speed and bit blade can effectively reduce stick-slip vibration, but its axial vibration will increase, and even the bit-bounce phenomenon occurs, resulting in a certain impact load on the drill-string. Secondly, with the decrease of formation stiffness or the increase of rock surface profile, the stick-slip vibration is weakened, but its axial vibration is intensified, and the angular velocity shows a more obvious oscillation phenomenon. Therefore, the adaptive control strategy for coupled vibration under uncertain drilling conditions is particularly important. Thirdly, the proposed control scheme has good dynamic performance and adaptability under parameter perturbation. The angular velocity can be well tracked and kept at the desired velocity within 31 s, and the overshoot is controlled within 2.8 rad/s. It suppresses the coupled vibration of the drill-string under a wide range of operating conditions, achieving smooth drilling.