Dynamic Model of an Oilwell Drillstring with Stick-Slip and Bit-Bounce Interaction

摘要

Oilwell drillstrings sometimes vibrate severely and can twist off in hard rock drilling. Stick-slip particularly predominates when drilling with polycrystalline diamond compact (PDC) bits, which may also excite severe axial and lateral vibrations in the bottom hole assembly, causing damage to the drillstrings and downhole equipment. Controlling these vibrations is essential to improving the efficiency and minimizing the cost of drilling. A bond graph model of a drillstring has been developed that predicts axial vibration, torsional vibration, and coupling between axial and torsional vibration due to bit-rock interaction. Axial and torsional submodels use a lumped-segment approach, with each submodel having a total of 21 segments to capture vibration of the kelly, drill pipes, and drill collars. In addition, the model incorporates viscous damping, hydrodynamic damping, and hydraulic forces due to drilling mud; an empirical treatment of rock-bit interaction, and top drive motor dynamics. The model predicts the expected coupling between weight on bit (WOB), bit speed, and rock-bit interface conditions; and their effect on stick-slip. Low bit speed and high WOB cause stick-slip. Mitigating open-loop measures used in the drilling industry (increasing rotary speed and decreasing WOB through changing derrick cable tension) were applied to the model, and successfully eliminated stick-slip. A linear quadratic regulator (LQR) controller was then implemented which controlled stick slip and eliminated bit bounce.