Modeling and control of drillstring dynamics for vibration suppression

Drill-string vibrations could cause fatigue failure to downhole tools, bring damage to the wellbore, and decrease drilling efficiency; therefore, it is important to understand the drill-string dynamics through accurately modeling of the drill-string and bottom-hole assembly (BHA) dynamics, and then develop controllers to suppress the vibrations. Modeling drill-string dynamics for directional drilling operation is highly challenging because the drill-string and BHA bend with large curvatures. In addition, the interaction between the drill-string and wellbore wall could occur along the entire well. This fact complicates the boundary condition of modeling of drill-string dynamics. This dissertation presents a finite element method (FEM) model to characterize the dynamics of a directional drill-string. Based on the principle of virtual work, the developed method linearizes the drill-string dynamics around the central axis of a directional well, which significantly reduced the computational cost. In addition, a six DOF curved beam element is derived to model a curved drill-string. It achieves higher accuracy than the widely used straight beam element in both static and dynamic analyses. As a result, fewer curved beam elements are used to achieve the same accuracy, which further reduces the computational cost. During this research, a comprehensive drill-string and wellbore interaction model is developed as the boundary condition to simulate realistic drilling scenarios. Both static and dynamic analyses are carried out using the developed modeling framework. The static simulation can generate drill-string internal force as well as the drilling torque and drag force. The dynamic simulation can provide an insight of the underlying mechanism of drilling vibrations. Top drive controllers are also incorporated as torsional boundary conditions. The guidelines for tuning the control parameters are obtained from dynamic simulations. Drill-string vibrations can be suppressed through BHA configuration optimization. Based on the developed modeling framework, the BHA dynamic performance is evaluated using vibration indices. With an objective to minimize these indices, a genetic algorithm is developed to optimize the BHA stabilizer location for vibration suppression. After optimization, the BHA strain energy and the stabilizer side force, two of the vibration indices, are significantly reduced compared to the original design, which proves the BHA optimization method can lead to a significant reduction of undesirable drilling dynamics. At the end of this dissertation, reduced order models are also discussed for fast simulation and control design for real time operation