Stabilization of severe slugging based on a lowdimensional

Stabilization of severe slugging based on a low-dimensional nonlinear model Presented at AICh. E Annual Meeting in Indianapolis, USA November 7 th, 2002 Espen Storkaas and Sigurd Skogestad Dep. of Chemical Engineering Norwegian University of Science and Technology 1 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Outline • Introduction / Problem Description • Model Description • Case • Controllability analysis • Controller configurations and design • Summary and conclusion 2 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Slug cycle 1. Liquid blocking 2. Slug growth/pressure buildup 3. Liquid Production 4. Gas production/Liquid fallback 4 www. chemeng. ntnu. no/~espensto/ 1 2 4 3 9/26/2020

Slug cycle (2) Experiments performed by the Multiphase Laboratory, NTNU 5 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Objectives • Avoid slug behavior (open loop stable) • Obtain stationary behavior (open loop unstable) • Issues – Impossible/existence? – Modeling – Control • Previous Work – Hedne & Linga (1990) – Henriot et al. (1999) – Havre et al. (2000) 6 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Modeling basis • Three states • Continuous • Description of both slug- and ”stationary” flow regime 7 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Model • Upstream gas volume (1 state) – – Holdup gas Constant volume Ideal gas law No liquid dynamics • Riser (2 states) – – Holdup of liquid and gas Stationary pressure balance Pressure-flow relationship for gas Entrainment of liquid • Choke valve – Simplified gas valve 8 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Case • Test case for slug-flow in OLGA • Constant feed • Valve closing time : 1 min • Downstream pressure: 50 Bar 11 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Model tuning • Based on bifurcation chart from OLGA simulations • Tuning based on Hopf point (purely imaginary poles) • Amplitude/freque ncy • Focus on stabilizable area 12 www. chemeng. ntnu. no/~espensto/ Stable slug Unstable stationary 9/26/2020

Poles and Zeros • Unstable (RHP) poles need feedback for stabilization • Imposes lower limit on bandwidth • RHP zeros limit performance • Imposes upper limit on bandwidth • RHP poles combined with RHP zeros may render stabilizing control impossible if the zero is close to the pole 13 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Poles and zeros FT ρT Operation points: P 1 z 0. 175 70. 05 0. 25 69 DP Poles 1. 94 -6. 11 0. 0008± 0. 0067 i 0. 96 -6. 21 0. 0027± 0. 0092 i DP P 1 Zeros: y z P 1 [Bar] DP[Bar] ρT [kg/m 3] -0. 0034 3. 2473 0. 0142 -0. 0004 0. 0048 -4. 5722 -0. 0032 -0. 0004 -7. 6315 -0. 0004 0 -0. 0034 3. 4828 0. 0131 -0. 0004 0. 0048 -4. 6276 -0. 0032 -0. 0004 -7. 7528 -0. 0004 0 0. 175 0. 25 15 www. chemeng. ntnu. no/~espensto/ FQ [m 3/s] FW [kg/s] 9/26/2020

Stabilization using P 1 • Easy • Gain K = 0. 5 Bar-1 • Integral time τI=500 s • MS = 1. 02, MT = 1. 04 • Bandwidth = 0. 15 s-1 PC ref PT 17 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Stabilization using P 1 (2) 18 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Stabilization using downstream measurements (1) • Difficult • Stabilizing controller: Volumetric flow in slave controller – K = 8 s/m 3, τI = 40 s z ref ZC FC ZT • Cascade: Valve position reset – K = 0. 01 m 3/s, τI = 750 s • MS = 1. 37, MT = 1. 47 • Bandwidth (outer loop) = 0. 001 s-1 20 www. chemeng. ntnu. no/~espensto/ FT 9/26/2020

Stabilization using downstream measurements (2) 21 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Summary and conclusions • Stabilization of desired flow regime • Simple, physically motivated model for control purposes – Useful for measurement selection – Choice of control configuration • Stabilization using upstream pressure simple • Stabilization using downstream measurements possible 23 www. chemeng. ntnu. no/~espensto/ 9/26/2020

Acknowledgements • Norwegian Research Council for financial support • ABB and Statoil for supervision and collaboration References Havre, K. , Stornes, K. and Stray, H. Taming Slug Flow in pipelines, ABB Review 4 (2000), p. 55 -63. Hedne, P. And Linga, H. Suppression of terrain slugging with automatic and manual riser choking, Advances in Gas-Liquid Flows (1990), p. 453 -469 Henriot, V. , Courbot, A. , Heintze, E. And Moyeux, L. Simulation of process to control severe slugging: Application to Dunbar pipeline, SPE Annual Conference and Exhibition, Huston, Texas(1999). SPE 56461 24 www. chemeng. ntnu. no/~espensto/ 9/26/2020