Adaptive set-point regulation of linear 2x2 hyperbolic systems with application to the kick and loss problem in drilling
Peer reviewed, Journal article
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We study the kick and loss detection and attenuation problem in managed pressure drilling by modeling the well as a distributed parameter system. Two cases are considered, distinguished by whether down-hole pressure measurements are available or not. The main contribution of the paper is a theoretical result on adaptive stabilization and set-point regulation by boundary control for a general 2×2 linear hyperbolic system in the case of measurements taken at both boundaries, with stability proven in the L2-sense. The design is applied to the drilling system and shown to solve the kick and loss problem with sensing at both boundaries. An earlier result on adaptive set-point regulation for 2×2 hyperbolic systems is also applied to the drilling system and shown to solve a kick and loss problem with sensing restricted to the actuated boundary only. The two designs are compared in a simulation of a loss incident, showing a significant reduction in convergence time and total accumulated loss for the design with sensing allowed at both boundaries.