Real-time estimation of the annular pressure profile is crucial for the planning and execution of well control operations, particularly while drilling wells in formations having narrow mud windows. Currently, the industry employs either simplified heuristic techniques, or complicated and often cost prohibitive commercial simulators, which are essentially "black boxes" with no options for further change by the user. Neither of the two approaches is particularly suitable for precise real-time well control analysis or design of robust automatic well control algorithms. Therefore, a simple transient multi-phase simulator amenable to real-time applications, which can represent essential dynamics with minimal cost and computational requirements, is highly desirable.

In this paper, we present a novel reduced Drift-Flux approach to model multi-phase well control situations. The model still preserves the transient multi-phase behavior of liquids and gas in the well. The proposed formulation consists of a lumped parameter model of the pressure dynamics, a transport equation for gas bubble migration, and the associated closure relations. Together, they form a system of coupled ordinary and partial differential equations with limited complexity. We then employ an explicit numerical solution algorithm that is fast and thereby reduces computational time and cost, making it suitable for control purposes.

The validity of the model is tested against experimental data from a test well with a simulated gas kick event. The model is also compared against a well control scenario generated by a commercial multi-phase flow simulator extensively used in the industry. There is good agreement between the results of the proposed model and the experimental data, on the one hand, and the commercial simulator results, on the other, thereby justifying the applicability of this model to real-world scenarios. The model provides a powerful tool to estimate and manage the surface pressures during a well control event for a given kick size and intensity. It has evident applications in well control analysis, automated Managed Pressure Drilling and well control management. As such, it has the potential to improve well control risk mitigation, enhance rig safety, and reduce non-productive time associated with well control-related trouble events.

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