Florent Di Meglio

Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting (“heterodirectional”) transport PDEs with distributed local coupling and with controls at one or both boundaries. A recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport PDEs that convect at different speeds against the direction of the PDE whose boundary is actuated. In this paper we present a solution to the fully general case, in which the number of PDEs in either direction is arbitrary, and where actuation is applied on only one boundary (to all the PDEs that convect downstream from that boundary). To solve this general problem, we solve, as a special case, the problem of control of coupled “homodirectional” hyperbolic linear PDEs, where multiple transport PDEs convect in the same direction with arbitrary local coupling. Our approach is based on PDE backstepping and yields solutions to stabilization, by both full-state and observer-based output feedback, and trajectory tracking problems.

A first principle model for multiphase slugging flow in vertical risers

In this paper, we propose a simple model to represent the slugging flow regime appearing in vertical risers. We consider a one dimensional two-phase flow composed of a liquid phase and a gaseous compressible phase. The presented model can be applied to a wide class of systems, ranging from pure vertical risers to more complex geometries such as those found on actual sub sea petroleum facilities. Following ideas from the literature, we introduce a virtual valve located at the bottom of the riser. This allows us to reproduce observed periodic regimes. It also brings insight into the physics of the slugging phenomenon. Most importantly, this model reveals relatively easy to tune and seems suitable for control design. A tuning methodology is proposed along with a proof of the existence of a limit cycle under simplifying assumptions.

Reproducing slugging oscillations of a real oil well

This paper addresses the problem of reproducing oscillations generated by the well-known slugging phenomenon in multiphase flow. Reported investigations show how to determine the parameters of a recently proposed ordinary differential equations system, so that it captures the characteristics of actually observed slugging oscillations. A tuning procedure based on the mathematical properties of the model is presented. It is then applied to a test case consisting of a real oil well located in the North Sea. An observer using only topside measurements allows asymptotic reconstruction of critical variables such as the downhole pressure.

Model-based control of slugging flow: An experimental case study

In this paper, we compare two solutions for suppressing slug flow in pipes conveying a diphasic fluid by active feedback control of the outlet (production) choke. Conventionnaly, a non-collocated PI controller is used to stabilize the measured inlet pressure. Unfortunately, this method lacks robustness to changes in operating conditions and reveals difficult to calibrate. In this work, we propose a model-based approach to design a nonlinear state-feedback control law based on a first principles model of the slugging phenomenon. A theoretical proof of convergence of the closed-loop model is provided, as well as an experimental validation of these results on a mid-scale testbench.

Control-Oriented Drift-Flux Modeling of Single and Two-Phase Flow for Drilling

We present a simplified drift-flux model for gas-liquid flow in pipes. The model is able to handle single and two-phase flow thanks to a particular choice of empirical slip law. A presented implicit numerical scheme can be used to rapidly solve the equations with good accuracy. Besides, it remains simple enough to be amenable to mathematical and control-oriented analysis. In particular, we present an analysis of the steady-states of the model that yields important considerations for drilling practitioners. This includes the identification of 4 distinct operating regimes of the system, and a discussion on the occurrence of slugging in underbalanced drilling.Copyright

Minimum time control of heterodirectional linear coupled hyperbolic PDEs

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems. Considered systems feature an arbitrary number of coupled transport PDEs convecting in either direction. Using the backstepping approach, we derive a full-state feedback law and a boundary observer enabling stabilization by output feedback. Unlike previous results, finite-time convergence to zero is achieved in the theoretical lower bound for control time.

Fit-for-Purpose Modeling for Automation of Underbalanced Drilling Operations

Automation has the potential to improve efficiency, precision, and safety of pressure and flow control during underbalanced drilling (UBD). In addition, advanced estimation theory can be used to extract more information from existing measurements to increase knowledge of the downhole conditions during operation. An essential part of an advanced (model based) pressure control system is the hydraulic model. Even with high- bandwidth distributed downhole measurements, a calibrated hydraulic model is required to ensure robustness, e.g. to sensor loss, and obtain real time estimates of unmeasured quantities and reservoir characteristics. In UBD operations, in contrast to Managed-Pressure-Drilling (MPD) operations, the flow in the annulus is inherently a multiphase gas liquid flow, which severely complicates the modelling. Much effort has been put into developing multiphase flow models, however, to date; most of these are very complex, requires extensive configuration and are not well suited for real-time applications. Consequently, a major gap with respect to automation of UBD is the lack of a fit-for-purpose model capable of reproducing the main dynamics of the multiphase flow in the annulus, while being sufficiently robust and suitable for real-time applications. In this work, we present recent advances on the development of a simplified fit-for-purpose model of the distributed gas- liquid dynamics, suited for advanced control of UBD operations. Using an automated calibration procedure, the model is shown to retain accuracy in a realistic case study. It is also shown that its reduced complexity enables real time coupling with measurements to obtain estimates of unmeasured quantities such as gas distribution and perform reservoir characterization

Slugging in multiphase flow as a mixed initial-boundary value problem for a quasilinear hyperbolic system

This paper studies the multiphasis slugging flow phenomenon occurring in oil wells and flow lines. The main contribution is a low-dimensional distributed parameters model, comprising the gas mass fraction, the pressure, and gas velocity as states. Along with appropriate boundary conditions, on the one-dimensional space domain, it constitutes a well-posed mixed initial-boundary value problem for a quasilinear hyperbolic system. Numerical simulation results obtained with a presented characteristics method solver stress the validity of the approach and the fair representativeness of the model. In particular, the period of simulated oscillations and their overall shape is in accordance with reference results from the literature. Controllability and observability open problems are formulated for future works.

Boundary Estimation of Boundary Parameters for Linear Hyperbolic PDEs

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law.

Stabilization of coupled linear heterodirectional hyperbolic PDE–ODE systems

We solve the problem of stabilizing a linear ODE having a system of a linearly coupled hyperbolic PDEs in the actuating and sensing paths. The system is exponentially stabilized by mapping it to a target system with a cascade structure using a Volterra transformation.