Modeling of Two-Phase Flow for Estimation and Control of Drilling Operations
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Modern approaches to process monitoring, optimization and control promise enhanced robustness and performance through the merger of process knowledge encoded in mathematical models with real-time measurements from the process. Such design techniques, often referred to as model-based estimation and control, require a mathematical model with the right balance between complexity and fidelity: i.e. the complexity must be limited to facilitate the use of established mathematical analysis and design techniques, while the qualitative response of the process is retained. Finding such models amenable for estimation and control of two-phase flow in drilling is particularly challenging due to the relative complexity of both the mathematical models and the dynamics to be represented. In particular the timescale separation between dominating dynamic effects, distributed nature of important transport phenomena and the nonlinear coupling between them entails very rich dynamics with modes over a broad frequency range and bifurcations between potential operating points. This thesis uses the classical transient drift flux model as a starting point for heuristically distinguishing between three qualitatively different dynamic effects, each of which dominates the transient response in a given frequency range: ~ 10 seconds, the distributed pressure dynamics, ~ 1- 10 minutes, a slow compressional pressure mode, and finally ~ 10 minutes to hours, the advection of a two-phase void wave. Since the distributed pressure waves operate in a high-frequency range, it is of little impact for operations concerned with slower phenomena. This insight is employed to develop simplified model descriptions of the slow pressure mode, and void wave advection, which are amenable for certain model-based control and estimation applications. In particular the description is used to develop an RLS estimator of reservoir pressure during a gas in flux. The heuristic for characterizing the dominating effect after frequency range (or timescale) is also used to develop a robust pressure controller using an automatically controlled back-pressure choke. The approach retains the dominating dynamic effect in the frequency range of interest (the slow pressure mode) while ensuring robustness to the discarded high-frequency pressure waves. The thesis gives examples from the industry to problems and processes which can be dealt with through use of model-based estimation and control techniques and provides a framework for designing such algorithms.