Comparison of Linear and Nonlinear Methods for Robust Anti-Slug Regulation

1. Sammenligning av lineære og ulineære metoder for robust Anti-slug regulering Sigurd Skogestad og Essmaeil Jahanshahi Institutt for kjemisk prosessteknologi, NTNU SERVOMØTET, OKTOBER 2013 Two-phase pipe flow (liquid and vapor) Slug (liquid) buildup

2. Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

3. Experimental mini-loop (2003) Ingvald Bårdsen, Espen Storkaas, Heidi Sivertsen

4. z p2 p1 Experimental mini-loopValve opening (z) = 100% SLUGGING

5. z p2 p1 Experimental mini-loopValve opening (z) = 25% SLUGGING

6. z p2 p1 Experimental mini-loopValve opening (z) = 15% NO SLUG

7. z p2 p1 Experimental mini-loop:Bifurcation diagram No slug Valve opening z % Slugging

8. How to avoid slugging?

9. z p2 p1 Design change Avoid slugging:1. Close valve (but increases pressure) No slugging when valve is closed Valve opening z %

10. z p2 p1 Design change Avoid slugging:2. Design change to avoid slugging

11. z p2 p1 Design change Minimize effect of slugging:3. Build large slug-catcher • Most common strategy in practice

12. ref PC PT Avoid slugging:4. ”Active” feedback control z p1 Simple PI-controller

13. Anti slug control: Mini-loop experiments p1 [bar] z [%] Controller ON Controller OFF

14. Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

15. Summary anti slug control (2008)* • Stabilization of desired non-slug flow regime = $$$$! • Stabilization using downhole pressure simple • Stabilization using topside measurements difficult • Control can make a difference! • “Only” problem: Not sufficiently robust *Thanks to: Espen Storkaas + Heidi Sivertsen + Håkon Dahl-Olsen + Ingvald Bårdsen

16. 2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens New Experimental mini-rig 3m

17. 1st step: Developed new simple 4-state model*. Choke valve with opening Z x3, P2,VG2, ρG2 , HLT P0 wmix,out L3 x1, P1,VG1, ρG1, HL1 x4 L2 h>hc wG,lp=0 wL,in wG,in w x2 wL,lp h L1 hc θ State equations (mass conservations law): *Based on Storkaas model

18. New 4-state model. Comparison with experiments: Experiment Top pressure Subsea pressure

19. Linear Control Solutions

20. Experiment Solution 1: H∞controlbasedon linearizing new modelExperiment, mixed-sensitivity design

21. Experimental linear model (new approach) Fourth-order mechanistic model: Closed-loop step-response with P-control Hankel Singular Values: Model reduction: 4 parameters need to be estimated

22. y r u e Plant + _ Solution 2: IMC based on identifiedmodelIMC design Block diagram for Internal Model Control system IMC for unstable systems: Model: IMC controller:

23. Experiment Solution 2: IMC based on identifiedmodelExperiment

24. Experiment Solution 3: «Robustified» IMC using H∞ loop shaping

25. Comparinglinearcontrollers (subsea pressure) * *Controllers tuned at 30% valve opening

26. Fundamental limitation – top pressure Measuring topside pressure we can stabilize the system only in a limited range Unstable (RHP) zero dynamics of top pressure

27. Nonlinear Control Solutions

28. Nonlinear observer K State variables PT Solution 1: observer & state feedback uc uc Pt

29. High-Gain Observer

30. State Feedback Kc : linear optimal gain calculated by solving Riccati equation Ki : small integral gain (e.g. Ki = 10−3)

31. Experiment High-gain observer – top pressure measurement: topside pressurevalve opening: 20 %

32. Experiment High-gain observer – subsea pressure measurement: subsea pressurevalve opening: 20 % Not working ??!

33. Chain of Integrators • Fast nonlinear observer using subsea pressure: Not Working??! • Fast nonlinear observer (High-gain) acts like a differentiator • Pipeline-riser system is a chain of integrator • Measuring top pressure and estimating subsea pressure is differentiating • Measuring subsea pressure and estimating top pressure is integrating

34. Nonlinear observer and state feedbackSummary • Anti-slug control with top-pressure is possible using fast nonlinear observers • The operating range of top pressure is still less than subsea pressure • Surprisingly, nonlinear observer is not working with subsea pressure, but a (simpler) linear observer works very fine. *but only for small valve openings

35. Nonlinear controller PT PT Solution 2: feedback linearization Prt uc Jahanshahi, Skogestad and Grøtli, NOLCOS, 2013

36. Output-linearizing controllerStabilizing controller for riser subsystem System in normal form: : top pressure : riser-base pressure Linearizingcontroller: dynamics bounded Control signal to valve:

37. Experiment CV: riser-base pressure (y1), Z=60% Gain:

38. Solution 3: Adaptive PI Tuning Static gain: slope = gain is small for large valve openings Linear valve: PI Tuning:

39. Experiment Solution 3: Adaptive PI TuningExperiment Large valve opening: - Large controller gain - Large integral time

40. Solution 4: Gain-Scheduling IMC Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC controllers:

41. Experiment Solution 4: Gain-Scheduling IMCExperiment

42. Comparison of Nonlinear Controllers • Gain-scheduling IMC is the most robust solution • Adaptive PI controller is thesecond-best • Controllabilityremarks: • Fundamental limitation control: gain of the system goes to zero for fully open valve • Additional limitation top-side pressure: Inverse response (non-minimum-phase)

43. Conclusions • A new simplifiedmodelverified by OLGA simulations and experiments • Best: Anti-slug controlusing a subseavalveclosetoriser-base • New robust controllers have been developed • Main point: Increase controller gain for large valve openings Acknowledgements • Financial support from SIEMENS • Master students: Elisabeth Hyllestad, Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.