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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.

We design an adaptive observer for semi-linear 2 × 2 hyperbolic PDEs with parametric uncertainties in both state equations. The proposed method is an extension of a previous result where parametric uncertainties were only allowed in one of the system equation. We utilize partial state measurements of one of the distributed states to estimate the remaining unknown distributed state. The method can be applied to flow rate estimation in fluid flow systems where the pressure is measured.

An adaptive observer design for a system of n + 1 coupled 1-D linear hyperbolic partial differential equations with an uncertain boundary condition is presented, extending previous results by removing the need for sensing collocated with the uncertainty. This modification is important and motivated by applications in oil & gas drilling where information about the down-hole situation is crucial in order to prevent or deal with unwanted incidents. Uncertainties are usually present down-hole while measurements are available top-side at the rig, only. Boundedness of the state and parameter estimates is proved in the general case, while convergence to true values requires bounded system states and, for parameter convergence, persistent excitation. The central tool for analysis is the infinitedimensional backstepping method applied in two steps, the first of which is time-invariant, while the second is time-varying induced by the time-varying parameter estimates.

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.

Recently, the first result on backstepping-based adaptive control of a 1-D linear hyperbolic partial differential equation (PDE) with an uncertain transport speed was presented. The system also had an uncertain, constant in-domain coefficient, and the derived controller achieved convergence to zero in the L ∞ -sense in finite time. In this paper, we extend that result to systems with a spatially varying in-domain coefficient, achieving asymptotic convergence to zero in the L ∞ -sense. Additionally, for the case of having a constant in-domain coefficient, the new method is shown to have a slightly improved finite-time convergence time. The theory is illustrated 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.

Early kick/loss detection is a crucial part of safe well control, and it plays a major role in the reduction of risk and non-productive time in drilling. In conventional drilling, topside sensing is used for early kick/loss detection. Recently, Venturi flowmeter based online return flow estimation has been introduced for this purpose by the authors. In managed pressure drilling, both topside sensing and bottomside sensing can be used for kick/loss detection. Therefore, a topside return flow estimator with a bottomside well pressure and flow estimator is combined to provide a complete kick/loss detection and estimation scheme for managed pressure drilling systems. This allows improved kick/loss detection. In addition, a closed-loop kick/loss attenuation controller is used to illustrate the estimation scheme.

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.

A scheme for fast kick estimation in managed pressure drilling is presented. The reservoir pressure and production index are estimated by utilizing information in a fast traveling shock wave induced by an unexpected rise in reservoir pressure. A least squares estimation problem is formulated from an early-lumping approach based on a reduced order drift-flux model. The Levenberg-Marquardt scheme is applied to solve the non-linear least-squares problem. The estimation scheme is tested with simulated top-side flow measurements from a two-phase drift flux model. © 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 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.