Adaptive Boundary Observer for Nonlinear Hyperbolic Systems: Design and Field Testing in Managed Pressure Drilling

Abstract

The present paper develops an adaptive boundary observer for systems modeled by nonlinear hyperbolic PDEs with limited number of measurements. The design is based on the backstepping method and relies only on one boundary measurement. The observer gains are obtained through solving a first-order hyperbolic system of Goursat-type PDEs. The design is implemented in an estimation problem in managed pressure drilling (MPD), where a state observer and an update-law are used to estimate the annular downhole pressure and the rate of lost circulation, respectively. The design is tested against a field scale flow-loop test in Stavanger, Norway by Statoil. The results show that the state observer converges to the actual flow and pressure values and that the update-law accurately estimates the rate of lost circulation.