Advanced Particle-Based 3D Modeling of Fuel Cell Electrodes
Antonio Bertei1,2, Vladimir Yufit2, Farid Tariq2, Nigel Brandon2
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
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
(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
Dimensionless distance from electrolyte / -
Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density
• 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
Dimensionless distance from electrolyte / -
Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density
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
Inhomogeneous current distribution
Current produced
Particle size distribution
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
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
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
(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
Dimensionless distance from electrolyte / -
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
Dimensionless distance from electrolyte / -
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
Dimensionless distance from electrolyte / -
Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density
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
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
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
(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
• 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
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
Dimensionless distance from electrolyte / -
Whole datasetParticles with current > 2 times analytical currentParticles with current < 1/2 times analytical currentAnalytical current density
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
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