Computationally efficient surrogate based multi-objective optimisation for PSA for carbon capture

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


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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


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Integrating carbon capture

The project

considered both pre-

and post-combustion

capture.

This talk

concentrates on

post-combustion

alone.


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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)


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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 )


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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.


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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.


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The challenge Surrogate modelling: Case studies Conclusion

Topic

1 The challenge


3 Case studies

4 Conclusion


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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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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


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Surrogate Based Optimisation I


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Surrogate Based Optimisation II


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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.


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The challenge Surrogate modelling Case studies: Conclusion

Topic

1 The challenge


3 Case studies

4 Conclusion


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Case study 1: Dual Piston PSA


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dppsa.png


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


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DP-PSA: Objective Function

Purity of CO2 (%) in piston chamber 1 at CSS:

100×

rtcuyCO2,p1dtr

tcu

∑j={CO2,N2}

yj ,p1dt


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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.


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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


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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


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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.


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Pareto front: n = 64

0

20

40

60

80

100

0 20 40 60 80 100

Pur

ity (

%)

Recovery (%)

NSGA-IISbNSGA-IISbNSGA-II ALM


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0

20

40

60

80

100

0 20 40 60 80 100

Pur

ity (

%)

Recovery (%)



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0

20

40

60

80

100

0 20 40 60 80 100

Pur

ity (

%)

Recovery (%)



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0

20

40

60

80

100

0 20 40 60 80 100

Pur

ity (

%)

Recovery (%)



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Visualisation I

0 0.2 0.4 0.6 0.8

0.4

0.6

0.8

1

f1

f2


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Visualisation II

0

1

2

3

A �Zilinskas, ESF, J Beck & A Varoneckas (2015), J of Chemometrics 142:151-158.


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The challenge Surrogate modelling Case studies Conclusion:

Topic

1 The challenge


3 Case studies

4 Conclusion


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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/


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http://www.ucl.ac.uk/~ucecesf/

Computationally efficient surrogate based multi-objective optimisation for PSA for carbon capture

Design

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