Adaptive set-point regulation of linear 2 × 2 hyperbolic systems with application to the kick and loss problem in drilling

Abstract

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.