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In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled by the assumed mode method, representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper can aid in developing system simulation case studies and parameter identification for offshore drilling operations.

In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled with mode shape functions representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper will aid in developing simulation case studies and parameter identification for offshore drilling operations.

In this paper, an unscented Kalman filter (UKF) coupled with a nonlinear model-predictive controller (NMPC) for a hydraulic wellbore model with multi-variable control and tracking is presented. In a wellbore, high drill string velocities in operational sequences such as tripping might result in surge and swab pressures in the annular section of the wellbore. To overcome these challenges, a controller incorporating safety and actuator limits should be used. A second-order model is used to predict axial drill string velocity downhole. With a NMPC specifying the block position trajectory, choke flow reference, desired backpressure pump flowrate and stand-pipe pressure, we can automatically supervise and control the pressure in the wellbore. To compensate for unmeasured states, an estimator is designed to predict the frictional pressure forces in the wellbore and filter noisy measurements. A stochastic approach for the hydraulic model is taken, including variance of the average fluctuations for the flow and pressure states. Comparing three NMPC configurations, the result of using an integration of the tracking error in the prediction model gave best offset-free tracking of the bottom-hole pressure. The controller compensates for the unknown fluctuations, and is shown to be robust towards model mismatch. Including the mechanical system in the NMPC prediction model, we can effectively constrain the predicted axial drill string velocity to reduce the pressure oscillations and achieve tracking of bottom hole pressure and choke differential pressure. The outcome is shown through extensive simulations to be an effective control strategy, reducing the pressure spikes while tripping.