Real-time estimation of annular pressure profile and formation pressure is crucial for the execution and planning of a well control operation, especially when drilling formations with narrow pore and fracture pressure margins. A simple transient multi-phase simulator, capable of accurately representing gas and liquid dynamics while minimizing complexity and computational requirements, is highly desirable for real-time kick mitigation and control applications. Such a simulator is presented here in the form of a coupled ODE-PDE model composed of a first order ODE and a first order hyperbolic PDE. This model is shown to retain the dominating two-phase dynamics encountered during gas kick incidents. As a particular application, we demonstrate the use of the model in design of switched control algorithms for kick handling in a Managed Pressure Drilling setting. A Recursive Least Squares algorithm is employed for estimation of unknown model parameters.

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