Presentation given at the CCS forum in Athens 26 March 2015.

1. The challenge Surrogate modelling Case studies Conclusion
Computationally ecient surrogate based
multi-objective optimisation for PSA for Carbon
capture
Joakim Beck1 Eric S Fraga2
1Department of Statistical Science
2CPSE, Department of Chemical Engineering
University College London (UCL)
26 March 2015
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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2. The challenge: Surrogate modelling Case studies Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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3. The challenge: Surrogate modelling Case studies Conclusion
Ecient carbon capture
Identification
of solvent or
nanoporous
material
Detailed
process modelling
Try
again
Process
integration
Molecular modelling
and/or experiments
Done
Yes
Yes
Yes
No
No
No
Evaluation
reduce eciency loss due to
carbon capture.
combined materials and
process design.
evaluation based on
experiments, detailed
modelling and process
simulation and optimisation.
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Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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4. The challenge: Surrogate modelling Case studies Conclusion
Integrating carbon capture
The project
considered both pre-
and post-combustion
capture.
This talk
concentrates on
post-combustion
alone.
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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5. The challenge: Surrogate modelling Case studies Conclusion
Pressure Swing Adsorption (PSA)
FP F CnD LR
Feed Feed Heavy
Product
Heavy
Product
CnD LR FP F
Light
Product
Purge Light
ProductPurge
Bed 1
Bed 2
FeedFeed
Heavy
Product
Heavy
Product
Four step cycle:
FP: Feed pressurisation
F: Feed (adsorption)
CnD: Countercurrent
depressurisation
LR: Light reux
(desorption)
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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6. The challenge: Surrogate modelling Case studies Conclusion
Modelling I
Component mass balances (axial dispersed plug ow model):
dci
dt
+
1 − b
b
d ¯Qi
dt
+
∂(uci)
∂z
+
∂Ji
∂z
= 0
d ¯Qi
dt
= p
dcm
i
dt
+ (1 − p)
d¯qi
dt
= kp
i
Ap
Vp
(ci − cm
i )
Energy balance for the adsorbate in the gas phase:
b
d ˆUf
dt
= −(1 − b)
∂ ˆUp
∂t
− b
∂(ˆHf u)
∂z
−
∂JT
∂z
−
Nc
i=I
∂(Ji ˆHi)
∂z
− hw
Ac
Vc
(Tf − Tw)
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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7. The challenge: Surrogate modelling Case studies Conclusion
Modelling II
Energy balance for the adsorbate in the solid phase:
∂ ˆUp
∂t
= p
d ˆUp,f
dt
+ (1 − p)
d ˆUp,s
dt
= hp
Ap
Vp
(Tf − Tp)
Energy balance in the bed wall:
ρwCp,w
∂Tw
∂t
= −hw
Ac
Vw
(Tw − Tf ) − Uαwl(Tw − T∞)
and so on.
As simulation must reach cyclic steady state,
⇒ computational eort is signicant.
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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8. The challenge: Surrogate modelling Case studies Conclusion
Behaviour of objective function
Objectivefunctionvalue
Along a line in design space
⇒ motivates use of surrogate modelling (response surface
modelling, meta-modelling, ...).
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Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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9. The challenge Surrogate modelling: Case studies Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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10. The challenge Surrogate modelling: Case studies Conclusion
Surrogate model
a fast approximation of model's response y(x) : Rp → R
where X ⊂ Rp is the space with p design variables.
suitable for black box optimisation models as the surrogate
model is non-intrusive.
based on training data: a set of known design points.
Most surrogates have form
ˆy(x) =
q
k=I
βkhk(x) + (x)
with regressors hi(·) and a residual random process, (·).
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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11. The challenge Surrogate modelling: Case studies Conclusion
Kriging
A statistical interpolating approach used for approximating
deterministic models.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
y(x)
x
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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12. The challenge Surrogate modelling: Case studies Conclusion
Surrogate Based Optimisation I
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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13. The challenge Surrogate modelling: Case studies Conclusion
Surrogate Based Optimisation II
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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14. The challenge Surrogate modelling: Case studies Conclusion
Optimiser
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1
Purity(%)
λ
We use evolutionary stochastic methods to cater for
multi-modality of objective function.
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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15. The challenge Surrogate modelling Case studies: Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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16. The challenge Surrogate modelling Case studies: Conclusion
Case study 1: Dual Piston PSA
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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17. The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Decision variables
Variables a b
tc Cycle time 1 20 s
Tb Bed temperature 15 70 ◦
C
VpI Volume of piston chamber 1 0.5VH 15VH mQ
VpP Volume of piston chamber 2 0.5VH 15VH mQ
φpI Oset angle of piston 1 0 2π radians
φpP Oset angle of piston 2 0 2π radians
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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18. The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Objective Function
Purity of COP (%) in piston chamber 1 at CSS:
100 × tc
uyCO2,pIdt
tc
u
j={CO2,N2}
yj,pIdt
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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19. The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Objective Function
Evolution
0
20
40
60
80
100
0 100 200 300 400 500 600 700 800
Purity(%)
The number of detailed model evaluations
GA
SbGA
EGO
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Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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20. The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Design Evolution
0
0.2
0.4
0.6
0.8
1
tc φp1 φp2 Vp1 Vp2 Tb Purity
Variablevalues(normalised)
Variables and objective
Initial data
Iter 1
Iter 10
Iter 50
Iter 100
Iter 200
Best
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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21. The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Diversity
0
0.2
0.4
0.6
0.8
1
tc φp1 φp2 Vp1 Vp2 Tb Purity
Variablevalues(normalised)
Variables and objective
Dataset 1
Dataset 2
Dataset 3
Dataset 4
Dataset 5
Best
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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22. The challenge Surrogate modelling Case studies: Conclusion
Case study 2: 6 step, 2 bed PSA
Bed
1
Bed
2
Vaccum
Tank
V1
V2
V4
V5
V7
V3 V6
Vent tank
Vent
Feed tank
Feed
BH
BH
BH
BH
6 design variables.
3 objective functions: recovery,
purity and power (but will illustrate
2).
computational eort large: 30-60
minutes per objective function
evaluation.
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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23. The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 64
0
20
40
60
80
100
0 20 40 60 80 100
Purity(%)
Recovery (%)
NSGA-II
SbNSGA-II
SbNSGA-II ALM
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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24. The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 96
0
20
40
60
80
100
0 20 40 60 80 100
Purity(%)
Recovery (%)
NSGA-II
SbNSGA-II
SbNSGA-II ALM
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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25. The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 176
0
20
40
60
80
100
0 20 40 60 80 100
Purity(%)
Recovery (%)
NSGA-II
SbNSGA-II
SbNSGA-II ALM
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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26. The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 256
0
20
40
60
80
100
0 20 40 60 80 100
Purity(%)
Recovery (%)
NSGA-II
SbNSGA-II
SbNSGA-II ALM
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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27. The challenge Surrogate modelling Case studies: Conclusion
Visualisation I
0 0.2 0.4 0.6 0.8
0.4
0.6
0.8
1
f
1
f
2
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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28. The challenge Surrogate modelling Case studies: Conclusion
Visualisation II
0
1
2
3
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Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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29. The challenge Surrogate modelling Case studies Conclusion:
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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30. The challenge Surrogate modelling Case studies Conclusion:
Summary
Identification
of solvent or
nanoporous
material
Detailed
process modelling
Try
again
Process
integration
Molecular modelling
and/or experiments
Done
Yes
Yes
Yes
No
No
No
Evaluation
surrogate modelling eective in
optimal design.
suitable for multi-objective
optimisation.
now considering discrete functions
and uncertainty.
Acknowledgements
EPSRC EP/G062129/1, Prof Stefano Brandani Dr Daniel
Friedrich (U of Edinburgh).
http://www.ucl.ac.uk/~ucecesf/
Computationally ecient surrogate based multi-objective optimisation for PSA for Carbon capture
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