advanced particle-based 3d modeling of fuel cell electrodes€¦ · advanced particle-based 3d...

Advanced Particle-Based 3D Modeling of Fuel Cell Electrodes

Antonio Bertei1,2, Vladimir Yufit2, Farid Tariq2, Nigel Brandon2

[email protected]

1Department of Civil and Industrial Engineering, University of Pisa (IT)2Department of Earth Science and Engineering, Imperial College London (UK)

Solid Oxide Fuel Cells

Main characteristics•Electricity from H2 and air

•Solid electrolyte

•600-1000°C

•Porous composite electrodes

Efficiency and degradation

½O2 + 2e- O2- H2 + O2- H2O + 2e-

*picture taken from H. Zhu, R.J. Kee, J. Electrochem. Soc. 155 (2008) B715-B729**picture taken from V.A.C. Haanappel et al., J. Power Sour. 141 (2005) 216-226

*

**

2

3D tomography & electrode microstructure

FIB-SEM

X-ray nano-CT*

*picture adapted from Shearing et al., J. Eur. Ceram. Soc. 30 (2010) 1809

3

Averaged results from 3D modelling

Simulating physics and electrochemistry within the 3D microstructure

*

**

*picture adapted from Carraro et al., Electrochim. Acta 77 (2012) 315**picture adapted from Häffelin et al., J. Electrochem. Soc. 160 (2013) F867

Full 3D microstructural details to get… averaged electrochemical response

...which can be predicted by continuum models too

4

Motivation

• 3D simulations must go beyond what 1D macro-homogeneous models can do

• 3D simulations should assess:o heterogeneous distributionso hot spots which may trigger localized degradation phenomenao truly three-dimensional properties

There is the need to exploit the full potential of simulations combined with 3D tomography

5

A novel approach to fully exploit 3D data

Tomographic microstructure

3D electrochemical model

Resolve individual particles*

0k kD C 0V 1

0k

F FRT RT

TPB kk

i i p e e

linking electrochemical behavior to individual particles*Quiq3D by IQM Elements, London

6

Workflow

1. Produce the mesh (Synopsys Simpleware)

2. Solve the model (Comsol Multiphysics)

3. Export and process the results (Comsol Multiphysics + Matlab)

7

1) Mesh in Synopsys Simpleware

8

INPUT = segmented microstructural dataset

PROCEDURE1.Assign isolated islands smaller than 125 voxels to the adjacent phase

2.Produce the mesh (smart mask smoothing, coarseness factor -15)

OUTPUT = Nastran mesh file (~ 40 M mesh elements)

2) Model in Comsol

9

INPUT = Nastran mesh file

PROCEDURE1.Import the mesh2.Define geometric entities (Boolean operations)

2) Model in Comsol

10

PROCEDURE3. Set the physics (General Form PDE Interface)

Ni:

ScSZ:

Pore:

4. Set the reaction rate as an edge source5. Select stationary solver (segregated)6. OPTIONAL: Reduce element order7. Solve in cluster (> 150 GB RAM)

0 eI Niee VI

0 OI ScSZOO VI

0 HN HHH yRTPDN

H2(g) + O2-(ScSZ) H2O(g) + 2e-

(Ni)

3) Export data (Comsol + Matlab)

11

INPUT = solved model (field variables within the domains)

PROCEDURE*1.Export data in Gauss points

2.Use an in-house Matlab code to interpolate values in Gauss points to a regular grid

OUTPUT = Field variables in grid to be overlaid with microstructure & particles

*Letting Comsol export as a regular grid is too slow.

Inhomogeneous current distribution

0

2

4

6

8

10

12

14

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8Particle equivalent diameter / m

Num

ber f

requ

ency

(Ni)

/ %

Ni

0

2

4

6

8

10

12

14


Num

ber f

requ

ency

(ScS

Z) /

% ScSZ

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14Number Ni-Ni neighbors / -

Ni

Num

ber f

requ

ency

(Ni)

/ %

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14

ScSZ

Number ScSZ-ScSZ neighbors / -

Num

ber f

requ

ency

(ScS

Z) /

%

Current transferred

Particle size distribution

Particle connectivity

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0Ni e

lect

roni

c cu

rren

t den

sity

/ A m

-2

Dimensionless distance from electrolyte / -

Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0

ScSZ

ioni

c cu

rren

t den

sity

/ A m

-2



• Inhomogeneous distribution of current transferred by particles• Good particles have more connections, bad particles are disconnected

Ni/ScSZ anode

12

Localized Joule heating and particle dispersion

Particle dispersion

The wider the particle dispersion, the more inhomogeneous the

current distribution

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0Ni e

lect

roni

c cu

rren

t den

sity

/ A m

-2



Localized Joule heating

8 % of particles experience more current than what continuum

models predict

Hot spots and localized Joule heating

13

From particle statistics to design indications

• Good particle for transferring current have connections but small reaction sites• Good particles for producing current have reaction sites but small connections• Particles which excel in both functions are a tiny fraction (~1 % of the total)

Connections and reaction sites (TPBs) are mutually exclusive conditions an advanced design is required by decoupling the functionalities

0

5

10

15

20

0 10 20 30 40

Num

ber N

i-Ni n

eigh

bors

/ -

Active TPB length per particle volume / m m-3

Ni

Particles transferring more

current than average

Particles producing more current than

average

Particles transferring and producing more

current than average

14

Conclusions

•3D tomography + physically-based simulation + resolving particles

• Comsol coupled with Synopsys Simpleware and Matlab

• Some tricks to handle big models… a lot of room for improvement!

• There is more 3D information in outliers than in mean trends

15

Acknowledgements

This project has received funding from :1) the European Union’s Horizon 2020 research and innovation programme under the Marie

Skłodowska-Curie grant agreement No 6549152) the EPSRC grant agreements EP/M014045/1 and EP/M009521/1

Have a look at the paper!!!

16

Backup slides


Current produced


TPB length per particle

• Inhomogeneous distribution of current produced by particles• Good particles have more TPBs, bad particles have less or no TPB

0

2

4

6

8

10

12

14


Num

ber f

requ

ency

(Ni)

/ %

Ni

0

2

4

6

8

10

12

14


Num

ber f

requ

ency

(ScS

Z) /

% ScSZ

0

5

10

15

20

25

0.2 2.0 20.0 200.0Active TPB length per particle volume / m m-3

Ni

Num

ber f

requ

ency

(Ni)

/ %

0

5

10

15

20

25

0.2 2.0 20.0 200.0Active TPB length per particle volume / m m-3

ScSZ

Num

ber f

requ

ency

(ScS

Z) /

%

0

0

0

0

0

0.0 0.2 0.4 0.6 0.8 1.0

Ni T

PB c

urre

nt d

ensi

ty/ A

m

-3


Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density at TPB

10-8

10-9

10-10

10-11

10-12

0

0

0

0

0

0.0 0.2 0.4 0.6 0.8 1.0

ScSZ

TPB

cur

rent

den

sity

/ A

m-3


Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density at TPB

10-8

10-9

10-10

10-11

10-12

8

Localized Joule heating and particle dispersion

Particle dispersion

The wider the particle dispersion, the more inhomogeneous the

current distribution

Coarsening may induce further coarsening

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0Ni e

lect

roni

c cu

rren

t den

sity

/ A m

-2



Localized Joule heating

8 % of particles experience more current than what continuum

models predict

Hot spots and localized Joule heating

10

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0 4,000 8,000 12,000

Volta

ge [V

]

Current density [A/m2]

T [°C]825800775

Macro-homogeneous modelling

Gas transport

Phase-resolved Continuum

Charge transport

Electrochem. reaction

vg TPB TPB

k kg k

i LD CF

vsTPB TPB

s

V i L

Averaged microstructural properties to get averagedelectrochemical response

CH2 [mol/m3]3 4 5 6 7 8

*

*picture adapted from Bertei et al., Int. J. Hydrog. Energy 41 (2016) 22381


0

2

4

6

8

10

12

14


Num

ber f

requ

ency

(Ni)

/ %

Ni

0

2

4

6

8

10

12

14


Num

ber f

requ

ency

(ScS

Z) /

% ScSZ

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14Number Ni-Ni neighbors / -

Ni

Num

ber f

requ

ency

(Ni)

/ %

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14

ScSZ

Number ScSZ-ScSZ neighbors / -

Num

ber f

requ

ency

(ScS

Z) /

%

Current transferred


Particle connectivity

• Inhomogeneous distribution of current transferred by particles• Good particles have more connections, bad particles are disconnected

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0Ni e

lect

roni

c cu

rren

t den

sity

/ A m

-2



1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0

ScSZ

ioni

c cu

rren

t den

sity

/ A m

-2



Electrochemical modelling approach

Fabrication

Characterization

Modelling

Model-based design approach

VALIDATION DESIGN

3D tomography:microstructure

-1012345

5 7 9 11 13 15

-ZIm

[c

m2 ]

ZRe [cm2]

Impedance spectroscopy:electrochemistry

Physically-based model

-2

0

2

4

6

8

10

0 2 4 6 8 10 12 14 16 18 20

-ZIm

[c

m2 ]

ZRe [cm2]

exp.sim.

6

4

2

0

650°C 600°C

11 13 15 17 19 21 23 25 27 29 31750°C 700°C2

0

-2

Simulation & validation(1)

(1) Bertei et al., Int. J. Hydrogen En. 41 (2016) 22381-22393

Advanced microstructural characterisation tools

0

10

20

30

40

50

0 200 400 600 800 1000 1200 1400

frequ

ency

[%]

Ni-Ni neck equivalent radius [nm]

x19_initial

x19_degraded

Particle analysis (proprietary)•Watershed algorithm to identify particles•Statistics of neighbours, contact areas, TPB, etc.

Tortuosity factor (open-source)*•Solves Fick law in 3D voxels•Segmented or gray-scale datasets•Extended to diffusion impedance

* S.J. Cooper et al., SoftwareX 5 (2016) 203-210

advanced particle-based 3d modeling of fuel cell electrodes€¦ · advanced particle-based 3d...

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