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The challenge Surrogate modelling Case studies Conclusion
Computationally e�cient surrogate based
multi-objective optimisation for PSA for Carbon
capture
Joakim Beck1 & Eric S Fraga2
1Department of Statistical Science2CPSE, Department of Chemical Engineering
University College London (UCL)
26 March 2015
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge: Surrogate modelling Case studies Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge: Surrogate modelling Case studies Conclusion
E�cient 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 e�ciency loss due to
carbon capture.
combined materials and
process design.
evaluation based on
experiments, detailed
modelling and process
simulation and optimisation.
EPSRC EP/G062129/1
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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 e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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
LightProduct
Purge LightProductPurge
Bed 1
Bed 2
FeedFeedHeavy Product
Heavy Product
Four step cycle:
FP: Feed pressurisation
F: Feed (adsorption)
CnD: Countercurrent
depressurisation
LR: Light re�ux
(desorption)
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge: Surrogate modelling Case studies Conclusion
Modelling I
Component mass balances (axial dispersed plug �ow model):
dc i
dt+
1− εbεb
dQi
dt+∂(uci)
∂z+∂Ji∂z
= 0
dQi
dt= εp
dcmidt
+ (1− εp)dqi
dt= k
pi
Ap
Vp
(ci − cmi )
Energy balance for the adsorbate in the gas phase:
εbdUf
dt= −(1− εb)
∂Up
∂t− εb
∂(Hf u)
∂z− ∂JT
∂z
−Nc∑i=1
∂(Ji Hi)
∂z− hw
Ac
Vc
(Tf − Tw )
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge: Surrogate modelling Case studies Conclusion
Modelling II
Energy balance for the adsorbate in the solid phase:
∂Up
∂t= εp
dUp,f
dt+ (1− εp)
dUp,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 e�ort is signi�cant.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge: Surrogate modelling Case studies Conclusion
Behaviour of objective function
Obje
ctiv
e f
unct
ion v
alu
e
Along a line in design space
⇒ motivates use of surrogate modelling (response surface
modelling, meta-modelling, . . . ).
G Fiandaca, ESF & S Brandani (2009), Engineering Optimization 41(9):833-854.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Surrogate model
a fast approximation of model's response y(x) : Rp → Rwhere 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
y(x) =
q∑k=1
βkhk(x) + ε(x)
with regressors hi(·) and a residual random process, ε(·).Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Kriging
A statistical interpolating approach used for approximatingdeterministic 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 e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Surrogate Based Optimisation I
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Surrogate Based Optimisation II
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling: Case studies Conclusion
Optimiser
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1
Pur
ity (
%)
λ
We use evolutionary stochastic methods to cater formulti-modality of objective function.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Case study 1: Dual Piston PSA
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Decision variables
Variables a b
tc Cycle time 1 20 sTb Bed temperature 15 70 ◦CVp1 Volume of piston chamber 1 0.5V0 15V0 m3
Vp2 Volume of piston chamber 2 0.5V0 15V0 m3
φp1 O�set angle of piston 1 0 2π radiansφp2 O�set angle of piston 2 0 2π radians
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
DP-PSA: Objective Function
Purity of CO2 (%) in piston chamber 1 at CSS:
100×
rtcuyCO2,p1dtr
tcu
∑j={CO2,N2}
yj ,p1dt
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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
Pur
ity (
%)
The number of detailed model evaluations
GASbGAEGO
J Beck, D Friedrich, S Brandani, S Guillas & ESF (2012), Proc. ESCAPE-22.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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
Var
iabl
e va
lues
(no
rmal
ised
)
Variables and objective
Initial dataIter 1
Iter 10Iter 50
Iter 100Iter 200
Best
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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
Var
iabl
e va
lues
(no
rmal
ised
)
Variables and objective
Dataset 1Dataset 2Dataset 3Dataset 4Dataset 5
Best
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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 e�ort large: 30-60
minutes per objective function
evaluation.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 64
0
20
40
60
80
100
0 20 40 60 80 100
Pur
ity (
%)
Recovery (%)
NSGA-IISbNSGA-IISbNSGA-II ALM
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 96
0
20
40
60
80
100
0 20 40 60 80 100
Pur
ity (
%)
Recovery (%)
NSGA-IISbNSGA-IISbNSGA-II ALM
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 176
0
20
40
60
80
100
0 20 40 60 80 100
Pur
ity (
%)
Recovery (%)
NSGA-IISbNSGA-IISbNSGA-II ALM
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Pareto front: n = 256
0
20
40
60
80
100
0 20 40 60 80 100
Pur
ity (
%)
Recovery (%)
NSGA-IISbNSGA-IISbNSGA-II ALM
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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
f1
f2
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies: Conclusion
Visualisation II
0
1
2
3
A �Zilinskas, ESF, J Beck & A Varoneckas (2015), J of Chemometrics 142:151-158.
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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The challenge Surrogate modelling Case studies Conclusion:
Topic
1 The challenge
2 Surrogate modelling
3 Case studies
4 Conclusion
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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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 e�ective in
optimal design.
suitable for multi-objective
optimisation.
now considering discrete functions
and uncertainty.
Acknowledgements
EPSRC EP/G062129/1, Prof Stefano Brandani & Dr DanielFriedrich (U of Edinburgh).
http://www.ucl.ac.uk/~ucecesf/
Computationally e�cient surrogate based multi-objective optimisation for PSA for Carbon capture
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