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SummaryWe deploy an adaptive observer recently developed for general hyperbolic partial differential equation (PDE) systems to detect and diagnose various drilling incidents. The well is modeled by a distributed PDE which, contrary to lumped models, preserves fundamental properties of well-flow dynamics enabling faster and more accurate incident detection and estimation. Wired drillpipe technology with pressure sensors is needed to locate and isolate incidents. Four realistic simulation case studies demonstrating various properties of the observer are presented. Drilling incidents treated in the simulation case studies include packoff in the annulus, formation in-flows, loss of circulation, and various combinations of these. Although simulation results show that the developed observers successfully estimate properties of the incidents that they are tailored for, they do not constitute an incident-detection system for drilling. However, they provide a part of the data on which an overall incident-detection system can rely.

A model based method for kick and loss detection and attenuation in Managed Pressure Drilling is presented. The drilling system is modeled as a distributed parameter system combined with a reservoir flow equation containing reservoir pressure and the so-called productivity index as uncertain parameters. A swapping-based design for state and parameter estimation utilizing bottom-hole pressure measurements available via wired drill pipe is combined with a closed loop controller for kick and loss attenuation. The performance of the proposed method is compared to earlier results on kick attenuation in a simulation, showing significant improvement. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd.

We solve an adaptive boundary control problem for an 1-D linear hyperbolic partial differential equation (PDE) with an uncertain in-domain source parameter and uncertain transport speed using boundary sensing only. Convergence of the parameters to their true values is achieved in finite-time. Since linear hyperbolic PDEs are finite-time convergent in the non-adaptive case, finite-time parameter convergence leads to the system state converging in finite-time. This is achieved by combining a recently derived transport speed estimation scheme using boundary sensing only, with the swapping scheme for hyperbolic PDEs and a least-squares identifier of an event-triggering type. The method is demonstrated in simulations. © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We design an adaptive model-based observer for state and parameter estimation in 2 × 2 semi-linear hyperbolic systems with uncertain parameters where we assume that one of the two distributed states is available through distributed sensing. The uncertainties appear in the equation for the unmeasured distributed state and may be non-linear in the unmeasured state, although linearly parameterized. The adaptive law is designed using a Lyapunov approach and expressed in terms of known signals by utilizing the specific model structure which gives rise to a general solution strategy valid for a large class of non-linear source terms. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2 × 2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well–reservoir interactions in oil and gas drilling where properties of the reservoir are unknown. Boundedness of the system states in the L 2 -norm, and convergence to a steady state profile satisfying a control objective relevant to the drilling application, are proved. The state estimation error is shown to converge to zero in the L 2 -norm and one of the boundary parameter estimates (modelling the reservoir pressure in the drilling application) is shown to converge to the true parameter value. The design is illustrated in a simulation example.

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 L 2 -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.

We design an adaptive controller for a 2 × 2 linear hyperbolic PDE with uncertain boundary parameters where measurements are taken at both boundaries, while only one boundary is actuated. The uncertainty, which appears in the un-actuated boundary, is in a bilinear form, which allows us to use bilinear adaptive laws for which parameter estimate convergence is guaranteed under a simple, a priori verifiable, persistence of excitation criterion. The control objective is boundary set-point regulation where the set-point is dependent on one of the unknown parameters. Stability is proved in the L 2 -sense and all signals in the closed loop are shown to be bounded. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, an adaptive control law that stabilizes a 2 × 2 linear hyperbolic system and achieves set-point regulation is derived. Sensing is restricted to be collocated with the control and anti-collocated with two uncertain parameters in an affine boundary condition. Proof of L 2 -boundedness for all signals in the closed loop is given, along with convergence to the set-point in the sense of an appropriate objective. The theory is demonstrated in a simulation.