Robust controller design for automated kick handling in managed pressure drilling. (November 2016) - Aarsnes, Ulf Jakob F.; Açıkmeşe, Behçet; Ambrus, Adrian; Aamo, Ole Morten
Abstract : Highlights: Distribute pressure dynamics is represented and then approximated. Effect of gas on is accounted for. High-frequency error introduced by simplifications is quantified. Actuation nonlinearity and gas uncertainty dealt with using polytopic LDI. High frequency uncertainty is dealt with using a norm-bounded LDI. Abstract: The problem considered in this paper is that of controlling downhole pressure during oil and gas well drilling, with a particular focus on handling gas kicks leading to two-phase gas–liquid flow conditions. We identify a first-order approximation to the infinite-dimensional system which captures the dominating mode of the pressure dynamics in the frequency range of interest, while the high-frequency pressure dynamics are represented by a multiplicative uncertainty. This approximation is then modified to accommodate the changes to the dynamics introduced by the two-phase flow. The linearized plant has an open-loop time constant which varies between 2 and 600 s depending on operating point and gas distribution in the well. Robust controller design is then performed using linear matrix inequalities (LMIs) via a polytopic norm-bounded description of both the high-frequency multiplicative, and the low-frequency parametric uncertainty. It is shown that, in order to achieve acceptable performance over such a large range of open loop time constants, a time-varying controller gain is required. The main contribution of the paper is to achieve this control objective systematically by formulating the control design problem as an LMI optimization problem. Then optimal solutions of the LMI problem can be obtained in polynomial time by using modern interior point method (IPM) numerical solution algorithms.