Fast and Efficient Mitigation of Coupled Axial-Torsional Drillstring Vibrations through State-Feedback Linear-Quadratic-Integral (LQI) Control

Summary In the exploitation of subsurface hydrocarbon and geothermal energy, more than 50% of total expenses are typically attributed to drilling and well completion. Coupled triaxial vibrations in the drilling system, excited by various mechanical, hydraulic, and geological sources, are major causes of premature downhole tool failures, excessive bit damage, compromised hole quality, reduced rate of penetration (ROP), and increased nonproductive time. Drillstring dynamic models, shock absorption tools, and controllers have been developed since the 1960s to understand and mitigate detrimental vibrations in the drilling system, aiming for smoother and more efficient operations. With advancements in measurement/logging while drilling technologies, rig equipment, mud pulse/wired pipe telemetry, and the digitalization of drilling engineering, a foundation has been established for proactive drilling vibration detection, analysis, and control to achieve efficient and safe drilling. In this study, a reduced-order axial-torsional drillstring dynamic model with soft string lateral contacts is first developed. Nonlinear drilling boundary conditions and inputs, such as bit-rock interactions (BRIs) with torque-on-bit (TOB) velocity-weakening effects, wellbore-drillstring contacts/friction, drillstring gravity, mud buoyancy, and more, are defined within the modeling framework. Equilibrium states and linearization of the model are derived for any given weight-on-bit (WOB) and rotational speed (RPM) setpoints, 3D well trajectories, and drillstring dimensions. A linear-quadratic-integral (LQI) controller is developed and tested for drillstring vibration suppression using a 6,562 ft (2000 m) drillstring model. In comparison to commercially available controllers for stick/slip mitigation, which are designed based on impedance matching and only address the decoupled drillstring torsional dynamics, the proposed state-feedback LQI controller emphasizes the coupling between the axial and torsional drillstring dynamics by simultaneously controlling WOB and RPM. Simulation results demonstrate that the LQI controller can suppress stick/slip and stabilize downhole WOB within 7 seconds, while a commercial drilling controller takes more than 35 seconds to achieve the same. Additionally, valuable insights and potential future directions for nonlinear drillstring vibration mitigation and drilling controller design are provided. With its fast drilling dysfunction stabilization time, small downhole RPM/WOB overshoots, minimal rig control inputs, robustness against drilling nonlinearities, and high efficiency, the proposed multi-input-multi-output state-feedback drilling controller holds great potential for application in proactive drilling vibration control, drilling automation, and real-time drilling optimization.