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This paper presents a nonlinear model predictive control scheme for stabilizing the well pressure during oil well drilling. While drilling, a fluid is pumped through the drill string and the drill bit, and is returning through the annulus between the drilled well and the drill string. Varying reservoir conditions and fluctuation in circulation flow rates cause sudden variations in the pressure conditions along the well. To compensate for these pressure fluctuations, the annulus choke valve opening can be adjusted. The proposed control scheme is based on a first-principles two-phase flow model using spatial discretization of the complete well. The optimal future choke settings are found using the Levenberg–Marquardt optimization algorithm. This control scheme is evaluated against two other control methods, a manual control scheme and a standard feed-back PI-control scheme of the choke valve with feed-forward control of …