| Summary: | This thesis presents the results of applying modelling theory, estimation, and control for the efficient formulation of drilling system models for real-time implementation and analysis. Together with modern sensor devices, efficient mathematical models for online estimation and closedloop control during offshore drilling are becoming increasingly relevant. Therefore, the work in this thesis focuses on formulating models applicable to drilling performance optimization systems, where the models could act as virtual sensors to be used in a drilling control system. The thesis is organized as a collection of papers, including four journal papers, and a chapter containing theory for the purpose of exposition. This thesis presents an unscented Kalman Filter combined with a nonlinear model predictive controller developed for predicting downhole fluid friction forces during tripping while keeping bottom-hole and upper well section pressures within their limits. The results of comparing three offset-error mitigation methods implemented in the controller are presented. Two new lumped-parameter models of drill-string dynamics are proposed in this thesis. The first is derived by using Lagrangian mechanics and further structured into a component model with complete integral causality using the Bond Graph methodology. The assumed mode method is applied, reducing the dimension of the state-space while representing the distributed properties in terms of the number of modes included. The second proposed model is developed by using Kane’s method, with its basis in the Newton-Euler formulation. The dynamics of the discrete model is a perturbation of a parametric curve in space representing the well path. Extensive simulation studies are performed to analyze the model transient response in a deviated well. A numerical solver convergence study for the Runge Kutta order 4 method and Generalized-α method is performed, and the real-time properties of the model have been investigated. The thesis includes a stability analysis of a lumped-multi-element drill string model from previous work, described by axial and torsional dynamics. A nonlinear bit-rock model for predicting the dynamics of downhole drilling is included, and the stability margins of a decoupled axial system are presented for six common drill string configurations. Additionally, a simulation study is performed with a set of drill string configurations.
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