Establishment of Drill-String System Dynamic Model with PDM and Influence of PDM Parameters on Stick-Slip Vibration

Drill-string vibrations occur frequently during drilling. Stick-slip vibration, a common form of vibration, reduces the rate of penetration and leads to bit wear and drill-string failure. The positive-displacement motor (PDM), as an important downhole dynamic drilling tool, is increasingly widely used in the field of oil and gas drilling, using hydraulic energy to output torque and speed. Field data have demonstrated that the combined drilling method of a PDM and polycrystalline diamond compact (PDC) bits can effectively alleviate stick-slip vibration; however, the effect is uneven and no research has yet been conducted on the mechanism by which PDM suppresses stick-slip vibration. In this study, the research status of tools for suppressing downhole vibrations is reviewed. A dynamic model of a multi-degree-of-freedom drill-string system with PDM is established, and the structural parameters in the model are calculated. The Runge-Kutta method is used to solve the model, and the influence of the PDM on stick-slip vibration is analyzed. Research has indicated that the output parameters of the PDM have a positive role in suppressing stick-slip vibrations, and that there is a critical value for eliminating these vibrations. The critical value is influenced by the drilling and output parameters of the PDM: the greater weight on the bit (WOB) will lead to a higher critical value; the greater the output parameter of the PDM, the lower the critical value. In addition, the output parameters of the PDM significantly change the correlation between the response parameters of the bit, which is the key to eliminate stick-slip vibration.