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Rapid transition control of a CO2 capture plantHåkon Dahl-Olsen and Sigurd Skogestad

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Control philosophy

Skogestad and Postlethwaite (2005): Multivariable feedback control – analysis and design, Wiley

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Maximum gain rule

( )

0

min ( ( ))

( , ), (0)

fu tJ x t

x f x u x x

Optimal control problem:

NCO:( ) ( ) ( ( ), ( ))

, ( ) ( )

( ) 0.

T

x f x f

u

H t t f x t u t

H t J t

H t

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Maximum gain rule

Hamiltonian Loss:*( ) ( ( )) ( )HL t H u t H t

A second-order approximation yields:

*

* 1

1( ) ( ) ( ) ( ),

21

( ) ( ) ( ) ( ) ( )2

TH uu

T TH uu

L t u t H t u t

L y t G t H t G t y t

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P2P Gains – Simple• Look at step responses for the time-scale that is

relevant for economic control:

*

,

( | ) ( )i b j i bi j

y t u y tg

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Cyclic operation of a CO2 removal plant

20.00

35.00

50.00

01.06.2008 11.06.2008 21.06.2008

Ener

gy p

rice

[€/M

Wh]

Trading day (Nord Pool Power Exchange)

NG EL Profit margin

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Lean absorbent L

Sour gas feed

Purified gasyCO2 ≤ 0.005

CaCO3 (s), H2O, Ca(OH)2 (aq)

TCTC

0.02 ≤ yCO2 ≤ 0.06 Rich absorbent, LN

Power plant

Power plant

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Modeling

2 3 22CO (g) Ca OH (aq) CaCO (s)+H O(l)

VLE described by Henry’s law for

CO2/water system: 2 2CO COy Hx

Reaction in water phase:

Assumed first-order kinetics:

2 2CO CORr k C

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Modeling1i i iN L L

2 2 2 2 2 2

1CO , CO , 1 CO , CO , 1 CO , CO ,

ii i i i i i

i i

L HVx x x x x kx

N N

i iL N

X L V N H k θ

Mole fraction in water phase

Liquid flow

Vapor flow (feed)

Tray holdup (moles)

Henry’s law constant

Reaction constant

Tray hydraulics parameter

Variable definitions

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Optimal steady-state operation

Minimize absorbent usage while maintaining y ≤ 0.5% (active)

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Optimal transition paths• Objectives: minimum time and limited absorbent

usage

2*100 2 2*

0

*( ) 2HTSS LTSS SHTSJ L L Lt V tL d

• Constraint y < 0.5% at all times• This constraint is active for the transition phase• Constraint not measureable

• Can measure dissolved CO2, but threshold on x = 5 ppm

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Optimal transition paths

1012141618202224

0 20 40 60

L [km

ol/m

in]

Time [min]

d = 2% d = 4 %

d = 6%

1

1.2

1.4

1.6

1.8

2

0 20 40 60

V [k

mol

/min

]

Time [min]

d = 2% d = 4 %d = 6%

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Implementation

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Scorecard 1: Direct measurement

Output Optimal variation

Implementation error (assumed)

Span P2P Gain Scaled gain

X14 2.23 ppm 1 ppm 3.23 ppm 0.435 0.134

X15 2.59 ppm 1 ppm 3.59 ppm 0.431 0.120

N1 44.9 kmol 5 kmol 49.9 kmol 10.0 0.219

N2 44.9 kmol 5 kmol 49.9 kmol 9.94 0.217

… … … … … …

N9 32.3 kmol 5 kmol 43.7 kmol 6.26 0.120

L 4.45 kmol/min

1 kmol/min 5.45 kmol 1 0.183

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Can we use ratio control to limit the span of the CV?• Approximate span propagation by

linearization

1

2

yc

y* 1 1 2

22 2

yc c

y y

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Output108 x

Optimal variation

Implementation error (linear app.)

Span P2P Gain Scaled gain

X14/N1 0.14 0.030 0.17 5.53 32.5

X14/N2 0.14 0.031 0.17 5.53 32.5

x15/N1 0.13 0.053 0.23 5.90 25.6

X15/N2 0.13 0.064 0.25 6.12 24.5

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Loss evaluation(Constant set point policy)

Candidate CV Average absorbent usage

Loss [%]

X14/N1 1609 1.9

X14/N2 1659 5.0

X15/N1 1610 2.0

X15/N2 1660 5.1

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CO

2 co

mp.

Performance check

Ab

sorb

ent

fee

d

Co

ntr

olle

d

vari

abl

e

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