1 Rapid transition control of a CO 2 capture plant Håkon Dahl-Olsen and Sigurd Skogestad.
-
Upload
sage-densley -
Category
Documents
-
view
216 -
download
1
Transcript of 1 Rapid transition control of a CO 2 capture plant Håkon Dahl-Olsen and Sigurd Skogestad.
1
Rapid transition control of a CO2 capture plantHåkon Dahl-Olsen and Sigurd Skogestad
2
3
Control philosophy
Skogestad and Postlethwaite (2005): Multivariable feedback control – analysis and design, Wiley
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
Optimal steady-state operation
Minimize absorbent usage while maintaining y ≤ 0.5% (active)
12
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
13
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%
14
Implementation
15
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
16
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
17
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
18
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
19
CO
2 co
mp.
Performance check
Ab
sorb
ent
fee
d
Co
ntr
olle
d
vari
abl
e
20
Discussion