Sammenligning av linere og ulinere metoder for robust Anti-slug - - PDF document

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Sammenligning av linere og ulinere metoder for robust Anti-slug - - PDF document

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Sammenligning av linere og ulinere metoder for robust Anti-slug regulering Sigurd Skogestad og Essmaeil Jahanshahi Institutt for kjemisk prosessteknologi, NTNU SERVOMTET, OKTOBER 2013 Two-phase pipe flow (liquid and vapor) Slug (liquid)

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SLIDE 1

1

Sammenligning av lineære og ulineære metoder for robust Anti-slug regulering

Slug (liquid) buildup Two-phase pipe flow (liquid and vapor)

Sigurd Skogestad og Essmaeil Jahanshahi Institutt for kjemisk prosessteknologi, NTNU

SERVOMØTET, OKTOBER 2013 2

Slug cycle (stable limit cycle)

Experiments performed by the Multiphase Laboratory, NTNU

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SLIDE 2

3

Experimental mini-loop (2003)

4

p1 p2 z

Experimental mini-loop Valve opening (z) = 100% SLUGGING

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SLIDE 3

5

p1 p2 z

Experimental mini-loop Valve opening (z) = 25% SLUGGING

6

p1 p2 z

Experimental mini-loop Valve opening (z) = 15% NO SLUG

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SLIDE 4

7

p1 p2 z

Experimental mini-loop: Bifurcation diagram

Valve opening z %

No slug Slugging

8

How to avoid slugging?

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SLIDE 5

9

p1 p2 z

Avoid slugging:

  • 1. Close valve (but increases pressure)

Valve opening z %

No slugging when valve is closed

Design change 10

Avoid slugging:

  • 2. Design change to avoid slugging

p1 p2 z

Design change

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SLIDE 6

11

Minimize effect of slugging:

  • 3. Build large slug-catcher
  • Most common strategy in practice

p1 p2 z

Design change 12

Avoid slugging:

  • 4. ”Active” feedback control

PT PC ref

Simple PI-controller p

1

z

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SLIDE 7

13

Anti slug control: Mini-loop experiments

Controller ON Controller OFF

p1 [bar] z [%]

14

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

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SLIDE 8

15

Avoid slugging:

  • 5. ”Active” feedback control with topside

measurement?

PC ref

Control is difficult (Inverse reponse = Unstable zero dynamics) p

2

z

16

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

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SLIDE 9

17

2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens

New Experimental mini-rig

Pump Buffer Tank Water Reservoir Seperator Air to atm. Mixing Point safety valve P1 Pipeline Riser Subsea Valve Top-side Valve Water Recycle FT water FT air P3 P4 P2

3m

18

1st step: Developed new simple 4-state model*

State equations (mass conservations law):

θ 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

1 , , G G in G lp

m w w   

1 , , L L in L lp

m w w   

2 , , G G lp G out

m w w   

2 , , L L lp L out

m w w   

1 : mass of gas in the pipeline G

m

1 : mass of liquid in the pipeline L

m

2 : mass of gas in the riser G

m

2 : mass of liquid in the riser L

m

*Based on Storkaas model

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SLIDE 10

19

New 4-state model. Comparison with experiments:

Top pressure Subsea pressure

Experiment

20

Linear Control Solutions

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SLIDE 11

21

2 4 6 8 10 12 14 16 18 20 15 20 25 30 35 40

  • pen-loop stable
  • pen-loop unstable

inlet pressure (controlled variable) Pin [kpa] t [min]

2 4 6 8 10 12 14 16 18 20 20 40 60 80 Controller Off Controller On Controller Off

  • pen-loop stable
  • pen-loop unstable

Zm [%] t [min] actual valve position (manipulated variable)

Experiment

Solution 1: H∞ control based on linearizing new model

Experiment, mixed-sensitivity design

min ( ) ,

u T K P

W KS N K N W T W S

          

22

Experimental linear model (new approach)

Fourth-order mechanistic model: Hankel Singular Values: Model reduction: 4 parameters need to be estimated Closed-loop step-response with P-control

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SLIDE 12

23

Solution 2: IMC based on identified model

IMC design Block diagram for Internal Model Control system IMC for unstable systems:

y u e r + _

Plant

( ) C s

Model: IMC controller:

24

2 4 6 8 10 12 14 16 18 20 15 20 25 30 35 40

  • pen-loop stable
  • pen-loop unstable

inlet pressure (controlled variable) Pin [kpa] t [min]

2 4 6 8 10 12 14 16 18 20 20 40 60 80 Controller Off Controller On Controller Off

  • pen-loop stable
  • pen-loop unstable

Zm [%] t [min] actual valve position (manipulated variable)

Experiment

Solution 2: IMC based on identified model

Experiment

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SLIDE 13

25

5 10 15 20 15 20 25 30 35

  • pen-loop stable
  • pen-loop unstable

inlet pressure (controlled variable) Pin [kpa] t [min]

5 10 15 20 20 40 60 80 Controller Off Controller On Controller Off

  • pen-loop stable
  • pen-loop unstable

Zm [%] t [min] actual valve position (manipulated variable)

Experiment

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

26

Comparing linear controllers (subsea pressure)

*Controllers tuned at 30% valve opening

*

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SLIDE 14

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Fundamental limitation – top pressure

,min 1

p

N i S i i

z p M z p

  

Z = 20% Z = 40% Ms,min 2.1 7.0

Measuring topside pressure we can stabilize the system only in a limited range

Unstable (RHP) zero dynamics of top pressure

  • 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

  • 0.2
  • 0.15
  • 0.1
  • 0.05

0.05 0.1 0.15 Real axis Imaginary axis Z=5% Z=95% Z=5% Z=95% Z=15% Z=20% Z=30% Z=45% Z=60% Z=95% Z=15% Z=20% Z=30% Z=45% Z=60% Z=95% RHP-Zeros RHP-poles

28

Nonlinear Control Solutions

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SLIDE 15

29

PT

Nonlinear

  • bserver

K

State variables

uc uc Pt

Solution 1: observer & state feedback

30

High-Gain Observer

1 1 2 2 3 3 4 4

ˆ ˆ ( ) ˆ ˆ ( ) 1 ˆ ˆ ˆ ( ) ( ) ˆ ˆ ( )

m

z f z z f z z f z y y z f z           

1 : mass of gas in the pipeline (

)

gp

z m

2 : mass of liquid in the pipeline (

)

lp

z m

3 ,

: pressure at top of the riser ( )

r t

z P

4 : mass of liquid in the riser (

)

lr

z m

,

( )

g r Lr G r r r t l

RT m M m V P   

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SLIDE 16

31

State Feedback

ˆ ˆ ( ) ( ( ) ) ( ( ) )

t c ss i in

u t K x t x K P r d       

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

32

High-gain observer – top pressure

measurement: topside pressure valve opening: 20 %

Experiment

5 10 15 20 25 30 35 20 30 40 time [min] P1 [kpa gauge]

subsea pressure (estimated by observer)

Open-Loop Stable Open-Loop Unstable

actual

  • bserver

set-point 5 10 15 20 25 30 35 5 10 15 time [min] P2 [kpa gauge]

top-side pressure (measurement used by observer)

Open-Loop Stable Open-Loop Unstable

actual

  • bserver

5 10 15 20 25 30 35 20 40 60 Controller Off Controller On Controller Off

Open-Loop Stable Open-Loop Unstable

time [min] Zm [%]

top-side valve actual position

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SLIDE 17

33

High-gain observer – subsea pressure

measurement: subsea pressure valve opening: 20 %

Experiment

2 4 6 8 10 20 30 40

Open-Loop Stable Open-Loop Unstable

time [min] P1 [kpa gauge]

subsea pressure (measurement used by observer)

actual

  • bserver

2 4 6 8 10 5 10 15

Open-Loop Stable Open-Loop Unstable

time [min] P2 [kpa gauge]

top-side pressure (estimated by observer)

actual

  • bserver

2 4 6 8 10 20 40 60 Controller Off

Open-Loop Stable Open-Loop Unstable

time [min] Zm [%]

top-side valve actual position

Not working ??!

34

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

2( )

f x

1( )

f x

rt

P

in

P

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SLIDE 18

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  • Anti-slug control with top-pressure is possible using fast nonlinear
  • bservers
  • 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.

Subsea pressure Top Pressure Nonlinear Observer Not Working !? Working* Linear Observer Working Not Working PI Control Working Not Working

  • Max. Valve

60% 20%

Nonlinear observer and state feedback

Summary

*but only for small valve openings

36

Solution 2: feedback linearization

PT PT

Nonlinear controller

uc Prt

Jahanshahi, Skogestad and Grøtli, NOLCOS, 2013

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SLIDE 19

37

Solution 2: feedback linearization

Cascade system

38

Output-linearizing controller

Stabilizing controller for riser subsystem System in normal form: Linearizing controller: Control signal to valve:

dynamics bounded : riser-base pressure : top pressure

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SLIDE 20

39

5 10 15 20 10 20 30 40

t [min] Prb [kPa] riser-base pressure (controlled variable)

  • pen-loop stable
  • pen-loop unstable

set-point measurement 5 10 15 20 5 10 15

  • pen-loop stable
  • pen-loop unstable

topside pressure (measurement used by controller) t [min] Prt [kPa]

5 10 15 20 50 100 Controller Off Controller On Controller Off

  • pen-loop stable
  • pen-loop unstable

t [min] Zm [%] actual valve position (manipulated variable)

Experiment

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50

Z1 [%] Pin [kpa]

min & max steady-state

Gain:

CV: riser-base pressure (y1), Z=60%

40

Solution 3: Adaptive PI Tuning

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50

Z1 [%] Pin [kpa]

min & max steady-state

Static gain: Linear valve:

PI Tuning:

slope = gain

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SLIDE 21

41

Experiment

Solution 3: Adaptive PI Tuning

Experiment

5 10 15 20 25 30 15 20 25 30 35 40

  • pen-loop stable
  • pen-loop unstable

inlet pressure (controlled variable) Pin [kpa] t [min]

5 10 15 20 25 30 20 40 60 80

  • pen-loop stable
  • pen-loop unstable

Zm [%] t [min] actual valve position (manipulated variable)

5 10 15 20 25 30

  • 100
  • 50
  • pen-loop stable

Kc [-] t [min] proportional gain

5 10 15 20 25 30 200 400 600

I [sec] t [min] integral time

42

Solution 4: Gain-Scheduling IMC

Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC controllers:

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SLIDE 22

43

Solution 4: Gain-Scheduling IMC

Experiment

5 10 15 20 15 20 25 30 35 40

  • pen-loop stable
  • pen-loop unstable

inlet pressure (controlled variable) t [min] Pin [kPa]

5 10 15 20 5 10 15

  • pen-loop stable
  • pen-loop unstable

topside pressure t [min] Prt [kPa]

5 10 15 20 50 100

  • pen-loop stable
  • pen-loop unstable

t [min] Zm [%] actual valve position (manipulated variable)

Experiment

44

Comparison of Nonlinear Controllers

  • Gain-scheduling IMC is the most robust solution
  • Adaptive PI controller is the second-best
  • 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)

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SLIDE 23

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Conclusions

  • A new simplified model verified by OLGA simulations and experiments
  • Best: Anti-slug control using a subsea valve close to riser-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.