Public PhD defence

1. Public PhD defence Control Solutions for Multiphase FlowLinear and nonlinear approaches to anti-slug control PhD candidate: EsmaeilJahanshahi Supervisors: Professor SigurdSkogestad Professor Ole JørgenNydal PhD Defence – October 18th 2013, NTNU, Trondheim

2. Outline • Modeling • Control structure design • Controlled variable selection • Manipulated variable selection • Linear controlsolutions • H∞mixed-sensitivity design • H∞ loop-shaping design • IMC control (PIDF) basedonidentifiedmodel • PI Control • Nonlinear controlsolutions • State estimation & state feedback • Feedback linearization • Adaptive PI tuning • Gain-scheduling IMC

3. Introduction * figure from Statoil

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

5. Introduction • Anti-slug solutions • Conventional Solutions: • Choking (reduces the production) • Design change (costly) : Full separation, Slug catcher • Automatic control: The aim is non-oscillatory flow regime together with the maximum possible choke opening to have the maximum production

6. Modeling

7. Modeling: Pipeline-riser case study OLGA sample case: 4300 m pipeline 300 m riser 100 m horizontal pipe 9 kg/s inflow rate

8. Modeling: Simplified 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):

9. Simple model compared to OLGA

10. Experimental rig 3m

11. Simple model compared to experiments Experiment Top pressure Subsea pressure

12. Modeling: Well-pipeline-riser system OLGA sample case: 3000 m vertical well 320 bar reservoir pressure 4300 m pipeline 300 m riser 100 m horizontal pipe

13. Modeling: 6-state simplified model Prt , m,rt ,L,rt Pwh Pbh Pin win wout Qout Prb Z1 Z2 Two new states: mGw: mass of gas in well mLw: mass of liquid in well

14. Model fitting using bifurcation diagrams simplified model olga simulations

15. Control Structure Design

16. Control Structure What to control? using which valve? • Candidate Manipulated Variables (MV): • Z1 : Wellhead choke valve • Z2 : Riser-base choke valve • Z3 : Topside choke valve • Candidate Controlled Variables (CVs): • Pbh: Pressure at bottom-hole • Pwh: Pressure at well-head • Win: Inlet flow rate to pipeline • Pin: Pressure at inlet of the pipeline • Pt: Pressure at top of the riser • Prb:Pressure at base of the riser • Pr:Pressure drop over the riser • Q: Outlet Volumetric flow rate • W: Outlet mass flow rate • m:Density of two-phase mixture • L:Liquid volume fraction • Disturbances (DVs): • WGin: Inlet gas flow (10% around nominal) • WLin: Inlet liquid flow (10% around nominal) P2 L m Q W Win Pwh Prb Pin Pbh

17. Control Structure Design: Method Input-output pairs Experiment or detailed model Simulations withLinearized Model bad Model fitting SimplifiedModel good ComparingResults Simulations withNonlinear Model bad ControllabilityAnalysis good ComparingResults bad Experiment good Robust input-output pairing

18. Controllability Analysis • The state controllability is not considered in this work. We use the input-output controllability concept as explained by Skogestad and Postlethwaite (2005) • Chapter 5, Chapter 6

19. Minimum achievable peaks of S and T Top pressure: Fundamentally difficult to control With large valve opening

20. Control Structure: Suitable CVs • Good CVs • Bottom-hole pressure or subsea pressures • Outlet flow rate • Top-side pressure combined with flow-rate or density (Cascade) • Bad CVs • Top-side pressure • Liquid volume fraction

21. Experiment Control Structure: Suitable MVs Using top-side valve Using riser-base valve Wellhead valvecannot stabilizethe system

22. Experiment Nonlinearity of system Process gain = slope

23. Linear Control Solutions

24. Solution 1: H∞controlbasedonmechanisticmodelmixed-sensitivity design WP: Performance WT: Robustness Wu: Input usage Small γmeans a bettercontroller, but itdependson design specificationsWu, WT and WP

25. Solution 1: H∞controlbasedonmechanisticmodelmixed-sensitivity design Controller:

26. Experiment Solution 1: H∞controlbasedonmechanisticmodelExperiment, mixed-sensitivity design

27. Solution 2: H∞controlbasedonmechanisticmodelloop-shaping design Controller:

28. Experiment Solution 2: H∞controlbasedonmechanisticmodelExperiment - loop-shaping design

29. Solution 3: IMC based on identifiedmodelModel identification First-order unstable with time delay: Closed-loop stability: Steady-state gain: First-order model is not a good choice

30. Solution 3: IMC based on identifiedmodelModel identification Fourth-order mechanistic model: Hankel Singular Values: Model reduction: 4 parameters need to be estimated

31. y r u e Plant + _ Solution 3: IMC based on identifiedmodelIMC design Bock diagram for Internal Model Control system IMC for unstable systems: Model: IMC controller:

32. Solution 3: IMC based on identifiedmodelPID and PI tuning based on IMC IMC controller can be implemented as a PID-F controller ---- IMC/PID-F ---- PI PI tuning from asymptotes of IMC controller

33. Experiment Solution 3: IMC based on identifiedmodelExperiment Closed-loop stable: Open-loop unstable: IMC controller:

34. Experiment Solution 3: IMC based on identifiedmodelExperiment PID-F controller: PI controller:

35. Comparinglinearcontrollers • IMC controllerdoes not needanymechanisticmodel • IMC controller is easier to tune usingthe filter time constant • H∞loop-shaping controllerresults in a faster controllerthatstabilizesthe system up to a largervalveopening

36. Experimentsonmedium-scale S-riser Open-loop unstable: IMC controller:

37. Experiment Experimentsonmedium-scale S-riser PID-F controller: PI controller:

38. Nonlinear Control Solutions

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

40. High-Gain Observer

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

42. Control signal Nonlinear observer and state feedbackOLGA Simulation

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

44. Fundamental limitation – top pressure Measuring topside pressure we can stabilize the system only in a limited range RHP-zero dynamics of top pressure

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

46. 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

47. 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.

48. Nonlinear controller PT PT Solution 2: feedback linearization Prt uc

49. Solution 2: feedback linearizationCascade system

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