A Control-Oriented Lumped Parameter Drillstring Dynamic Model for Real-Time Vibration Mitigation and Drilling Optimization

Drilling is an essential operation for subsurface hydrocarbon/geothermal energy extraction or underground waste fluid/gas storage. Efficient drilling is the key to an economically viable operation. Axial, torsional, and lateral oscillations that are excited in the drillstring by various surface/downhole sources (like the application of the weight-on-bit (WOB), rock cutting process, bottom-hole-assembly (BHA) resonance, downhole tool operation, drilling fluid dynamics, etc.), are the prime causes of downhole tool failure, material fatigue, bit wear/damage, and insufficient surface-to-bottom energy transfer. Since the 1960s, a wide variety of models have been developed to analyze drillstring dynamics and optimize the well/drillstring design. With the advance of drilling engineering, sensor technology, and data science, a fast and comprehensive drilling system dynamic model is in need for real-time drilling optimization and automation. In this study, a control-oriented physics-based lumped parameter model (LPM) is developed to investigate the fully coupled drillstring dynamics in all three directions. Various boundary conditions (wellbore-drillstring interaction, bit-rock interaction, presence of stabilizers/centralizers) and system input actuations (surface WOB/hookload, surface rotational speed (RPM)/torque, mud motor operational parameters, etc.) are defined in the modeling framework. Simulations are run for different drillstring scenarios in a vertical and an actual L-shaped wellbore configuration. System dynamic responses illustrate various amplitudes, frequencies, and modes of fully coupled drillstring vibrations at different depths when simulated with different drilling parameters. Another significant observation is the emergence, propagation, and transition of lateral vibration modes between forward, backward, and chaotic whirl patterns. Based on the tradeoff between accuracy and complexity, the proposed dynamic model can be adapted for real-time model-based control, and can also be deployed for well design purposes or digital twinning applications.