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In under-balanced drilling, the bottom-hole pressure is kept below porepressure, causing pressure dependent influx of reservoir gas into the wellborethat makes the system unstable at low drawdowns. In this paper we propose afeedback controller which stabilizes the system around an arbitrary pressuresetpoint, using only topside measurement, and assuming unknown reservoirparameters. A particular challenge with this problem is the distributed andhighly nonlinear nature of the system dynamics. As the control model we use the``reduced Drift Flux Model'' which models gas-liquid flow as a nonlineartransport equation with a non-local integral source term. The observerestimates the distributed gas concentration, downhole pressure and reservoirparameters by solving the system dynamics backwards relative to how the gasrises in the well. The control inputs are then constructed by designing targetstates over the next sampling period and again solving reversed dynamics toobtain the required topside pressures. The resulting controller is implementedwith a 2 minute zero-order hold to accommodate the actuation limitationsituation on an actual drilling rig. The results are illustrated in simulationswith a industry standard Drift Flux formulation as the plant model.

Boundary Control and Estimation for Under-Balanced Drilling with Uncertain Reservoir Parameters