1. Public PhD defence
Control Solutions for Multiphase Flow Linear and nonlinear approaches to anti-slug control
PhD candidate: Esmaeil Jahanshahi
Supervisors: Professor Sigurd Skogestad
Professor Ole Jørgen Nydal
The thematic content of the series:
1 Facts
Revenue from the last two years; Localization; History and surroundings
2 Research
Six strategic areas; Three Centres of Excellence; Laboratories; Cooperation with SINTEF;
3 Education and student activities
Study areas and programmes of study; Quality Reform; Further- and continuing education; Internationalization
4 Innovation and relationships with business and industry
Innovative activities; Agreements with the public and private sectors
5 Dissemination
Publications, events and the mass media
Museum of Natural History and Archaeology, NTNU Library
6 Organization and strategy
Board and organization; Vision, goal and strategies;
For more on terminology, see (“terminologiliste”)
See also (”Selected administrative terms with translations”)
PhD Defence – October 18th 2013, NTNU, Trondheim

2. Outline Modeling Control structure design Linear control solutions
Controlled variable selection
Manipulated variable selection
Linear control solutions
H∞ mixed-sensitivity design
H∞ loop-shaping design
IMC control (PIDF) based on identified model
PI Control
Nonlinear control solutions
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 modelθ h L2 hc
wmix,out
x1, P1,VG1, ρG1, HL1
x3, P2,VG2, ρG2 , HLT P0
Choke valve with opening Z x4
h>hc
wG,lp=0
wL,lp L3
wL,in
wG,in w x2 L1
State equations (mass conservations law):

9. Simple model compared to OLGA

10. Experimental rig 3m

11. Simple model compared to experiments
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
Two new states:
mGw: mass of gas in well
mLw: mass of liquid in well
Pwh
Pbh
Pin
Prt , m,rt , L,rt
win
wout
Qout
Prb Z1 Z2

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) L P2 m Q W
Win
Pwh
Pin
Prb
Pbh

17. Control Structure Design: Method
Input-output pairs
Experiment or detailed model
bad
Simulations with Linearized Model
Model fitting
good
Simplified Model
Comparing Results
bad
Simulations with Nonlinear Model
good
Controllability Analysis
Comparing Results
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. Control Structure: Suitable MVs
Experiment
Control Structure: Suitable MVs
Using riser-base valve
Using top-side valve
Wellhead valve cannot stabilize the system

22. Nonlinearity of system
Experiment
Nonlinearity of system
Process gain = slope

23. Linear Control Solutions

24. Solution 1: H∞ control based on mechanistic model mixed-sensitivity design
WP: Performance
WT: Robustness
Wu: Input usage
Small γ means a better controller, but it depends on design specifications Wu, WT and WP

25. Solution 1: H∞ control based on mechanistic model mixed-sensitivity design
Controller:

26. Experiment
Solution 1: H∞ control based on mechanistic model Experiment, mixed-sensitivity design

27. Solution 2: H∞ control based on mechanistic model loop-shaping design
Controller:

28. Experiment
Solution 2: H∞ control based on mechanistic model Experiment - loop-shaping design

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

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

32. Solution 3: IMC based on identified model PID 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. Solution 3: IMC based on identified model Experiment
Closed-loop stable:
Open-loop unstable:
IMC controller:

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

35. Comparing linear controllers
IMC controller does not need any mechanistic model
IMC controller is easier to tune using the filter time constant
H ∞ loop-shaping controller results in a faster controller that stabilizes the system up to a larger valve opening

36. Experiments on medium-scale S-riser
Open-loop unstable:
IMC controller:

37. Experiments on medium-scale S-riser
PID-F controller:
PI controller:

38. Nonlinear Control Solutions

39. Solution 1: observer & state feedbackPT
Nonlinear observer K
State
variables 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. Nonlinear observer and state feedback OLGA Simulation
Control signal

43. High-gain observer – top pressure
Experiment
High-gain observer – top pressure
measurement: topside pressure valve 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
Z = 20%
Z = 40%
Ms,min
2.1
7.0

45. High-gain observer – subsea pressure
Experiment
High-gain observer – subsea pressure
measurement: subsea pressure valve 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 feedback Summary
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.
Method \ CV
Subsea pressure
Top Pressure
Nonlinear Observer
Not Working !?
Working
Linear Observer
Not Working
PI Control
Max. Valve
60%
20%

48. Solution 2: feedback linearizationPT
Nonlinear controller uc
Prt

49. Solution 2: feedback linearization Cascade system

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

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

52. CV: topside pressure (y2), Z=20%
Experiment
CV: topside pressure (y2), Z=20%
y2 is non-minimum phase

53. Solution 3: Adaptive PI Tuning
Static gain:
slope = gain
Linear valve:
PI Tuning:

54. Solution 3: Adaptive PI Tuning Experiment

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

56. Solution 4: Gain-Scheduling IMC Experiment

57. Comparison of Nonlinear Controllers
Gain-scheduling IMC is the most robust solution
Gain-scheduling IMC does not need any mechanistic model
Adaptive PI controller is the second controller, and it is based on a simple model for static gain
Controllability remarks:
Fundamental limitation control: gain of the system goes to zero for fully open valve
Additional limitation top-side pressure: Inverse response (non-minimum-phase)

58. Conclusions
A new simplified model verified by OLGA simulations and experiments
Suitable CVs and MVs for stabilizing control were identified
Anti-slug control using a subsea valve close to riser-base
Online PID and PI tuning rules for anti-slug control
New linear and nonlinear control solutions were developed and tested experimentally
We showed that …
Simple methods work better for process control
Fundamental controllability limitations are idependant from control design

59. Thank you! Acknowledgements SIEMENS: Funding of the project
Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.
Thank you!