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.

[1]  N Petit,et al.  Model-based control of slugging flow: An experimental case study , 2010, Proceedings of the 2010 American Control Conference.

[2]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[3]  Florent Di Meglio,et al.  Reproducing slugging oscillations of a real oil well , 2010, IEEE Conference on Decision and Control.

[4]  A. Courbot.  Prevention of Severe Slugging in the Dunbar 16' Multiphase Pipeline , 1996 .

[5]  Espen Storkaas.  Stabilizing control and controllability. Control solutions to avoid slug flow in pipeline-riser systems , 2005 .

[6]  Wilco Sturm,et al.  Soft Sensing for Gas-Lift Wells , 2006 .

[7]  Ovadia Shoham,et al.  A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores , 1990 .

[8]  A. E. Dukler,et al.  Modelling flow pattern transitions for steady upward gas‐liquid flow in vertical tubes , 1980 .

[9]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[10]  Bjarne A. Foss,et al.  Stabilization of Gas-Distribution Instability in Single-Point Dual Gas Lift Wells , 2006 .

[11]  Florent Di Meglio,et al.  A first principle model for multiphase slugging flow in vertical risers , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Kjetil Havre,et al.  Automatic Control of Unstable Gas Lifted Wells , 1999 .

[13]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[14]  Emmanuel Duret.  Dynamique et contrôle des écoulements polyphasiques , 2005 .

[15]  F. P. Donohue.  Classification of Flowing Wells with Respect to Velocity , 1930 .

[16]  Erich Zakarian.  ANALYSIS OF TWO-PHASE FLOW INSTABILITIES IN PIPE-RISER SYSTEMS , 2000 .

[17]  Pierre Rouchon,et al.  Dynamics and solutions to some control problems for water-tank systems , 2002, IEEE Trans. Autom. Control..

[18]  A. R. Hasan,et al.  A Basic Approach to Wellbore Two-Phase Flow Modeling , 2007 .

[19]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[20]  Jinn-Chuang Yang,et al.  Characteristics method with cubic‐spline interpolation for open channel flow computation , 2004 .

[21]  Kjetil Havre,et al.  Active Feedback Control as a Solution to Severe Slugging , 2002 .

[22]  Georges Bastin,et al.  Boundary feedback control and Lyapunov stability analysis for physical networks of 2×2 hyperbolic balance laws , 2008, 2008 47th IEEE Conference on Decision and Control.

[23]  Miroslav Krstic,et al.  Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays , 2007, 2007 46th IEEE Conference on Decision and Control.

[24]  John-Morten Godhavn,et al.  New slug control strategies, tuning rules and experimental results , 2005 .

[25]  J. Coron.  Control and Nonlinearity , 2007 .

[26]  Bjarne A. Foss,et al.  STABILIZATION OF GAS LIFTED WELLS , 2002 .

[27]  Bjarne A. Foss,et al.  Stabilization of Gas Lifted Wells Based on State Estimation , 2004 .

[28]  Christopher E. Brennen,et al.  Fundamentals of Multiphase Flow , 2005 .