Abstract

The Dusty Gas model (DGM), despite being arguably the most accurate representation of gas diffusion in electrodes, is not readily adopted in the literature as it entails relatively expensive numerical integration of differential equations for concentration polarization calculations. To address this issue, this article demonstrates an analytical procedure to solve the DGM equations in a fuel cell electrode setting. In the process, it highlights the differences with previous attempts in the literature and improves upon the shortcomings. This paper specifically provides explicit expressions of concentration overpotentials of anode-supported solid oxide fuel cells (SOFCs) for binary and ternary gas systems via the analytical solution of DGM equations in one dimension without considering the viscous effects. The model predictions match very well with the experimental data available in the open literature. This paper also provides a semi-analytical framework for higher-order multicomponent systems. Finally, the effect of the pore-size distribution in the porous electrode on the concentration polarization is thoroughly explored.

References

References
1.
Su
,
S.
,
Gao
,
X.
,
Zhang
,
Q.
,
Kong
,
W.
, and
Chen
,
D.
,
2015
, “
Anode- Versus Cathode-Supported Solid Oxide Fuel Cell: Effect of Cell Design on the Stack Performance
,”
Int. J. Electrochem. Sci.
,
10
, pp.
2487
2503
.
2.
Virkar
,
A. V.
,
Chen
,
J.
,
Tanner
,
C. W.
, and
Kim
,
J-W.
,
2000
, “
The Role of Electrode Microstructure on Activation and Concentration Polarizations in Solid Oxide Fuel Cells
,”
Solid State Ionics
,
131
(
1–2
), pp.
189
198
. 10.1016/S0167-2738(00)00633-0
3.
Zhang
,
S.
,
Bi
,
L.
,
Zhang
,
L.
,
Yang
,
C.
,
Wang
,
H.
, and
Liu
,
W.
,
2009
, “
Fabrication of Cathode Supported Solid Oxide Fuel Cell by Multi-Layer Tape Casting and Co-Firing Method
,”
Int. J. Hydrogen Energy
,
34
(
18
), pp.
7789
7794
. 10.1016/j.ijhydene.2009.07.081
4.
Ilbas
,
M.
, and
Kumuk
,
B.
,
2019
, “
Numerical Modeling of a Cathode Supported Solid Oxide Fuel Cell (SOFC) in Comparison With An Electrolyte-Supported Model
,”
J. Energy Inst.
,
92
(
3
), pp.
682
692
.
5.
Lanzini
,
A.
,
Leone
,
P.
,
Guerra
,
C.
,
Smeacetto
,
F.
,
Brandon
,
N. P.
, and
Santarelli
,
M.
,
2013
, “
Durability of Solid Oxide Fuel Cells (SOFC) Under Direct Dry-Reforming of Methane
,”
Chem. Eng. J.
,
220
, pp.
254
263
. 10.1016/j.cej.2013.01.003
6.
Papurello
,
D.
,
Lanzini
,
A.
,
Leone
,
P.
, and
Santarelli
,
M.
,
2016
, “
The Effect of Heavy Tars (toluene and Naphthalene) on the Electrochemical Perfomance of An Anode-Supported SOFC Running on Bio-Syngas
,”
Renew. Energy
,
99
, pp.
747
753
. 10.1016/j.renene.2016.07.029
7.
Yan
,
D.
,
Liang
,
L.
,
Yang
,
J.
,
Zhang
,
T.
,
Pu
,
J.
,
Chi
,
B.
, and
Li
,
J.
,
2017
, “
Performance Degradation and Analysis of 10-Cell Anode-Supported SOFC Stack With External Manifold Structure
,”
Energy
,
125
, pp.
663
670
. 10.1016/j.energy.2016.12.107
8.
Yakabe
,
H.
,
Hishinuma
,
M.
,
Uratani
,
M.
,
Matsuzaki
,
Y.
, and
Yasuda
,
I.
,
2000
, “
Evalualtion and Modeling of Performance of Anode-Supported Solid Oxide Fuel Cell
,”
J. Power Sources
,
86
(
1–2
), pp.
423
431
. 10.1016/S0378-7753(99)00444-9
9.
Suwanwarangkul
,
R.
,
Croiset
,
E.
,
Fowler
,
M. W.
,
Douglas
,
P. L.
,
Entchev
,
E.
, and
Douglas
,
M. A.
,
2003
, “
Performance Comparison of Fick’s, Dusty-Gas, and Stefan-Maxwell Models to Predict the Concentration Overpotential of a SOFC Anode
,”
J. Power Sources
,
122
(
1
), pp.
9
18
. 10.1016/S0378-7753(02)00724-3
10.
Chan
,
S. H.
,
Khor
,
K. A.
, and
Xia
,
Z. T.
,
2001
, “
A Compelete Polarization Model of a Solid Oxide Fuel Cell and Its Sensitivity to the Change of Cell Component Thickness
,”
J. Power Sources
,
93
(
1–2
), pp.
130
140
. 10.1016/S0378-7753(00)00556-5
11.
Vural
,
Y.
,
Ma
,
L.
,
Ingham
,
D. B.
, and
Pourkashanian
,
M.
,
2010
, “
Comparison of the Multicomponent Mass Transfer Models for the Prediction of the Concentration Overpotential for Solid Oxide Fuel Cell Anodes
,”
J. Power Sources
,
195
(
15
), pp.
4893
4904
. 10.1016/j.jpowsour.2010.01.033
12.
Bao
,
C.
,
Jiang
,
Z.
, and
Zhang
,
X.
,
2016
, “
Modeling Mass Transfer in Solid Oxide Fuel Cell Anode: I. Comparison Between Fickian, Stefan-Maxwell and Dusty-Gas Models
,”
J. Power Sources
,
310
, pp.
32
40
. 10.1016/j.jpowsour.2016.01.099
13.
Bao
,
C.
,
Jiang
,
Z.
, and
Zhang
,
X.
,
2016
, “
Modeling Mass Transfer in Solid Oxide Fuel Cell Anode: II. H2/CO Co-Oxidation and Surface Diffusion in Sysnthesis-Gas Operation
,”
J. Power Sources
,
324
, pp.
261
271
. 10.1016/j.jpowsour.2016.05.088
14.
Xu
,
H.
, and
Dang
,
Z.
,
2017
, “
Numerical Investigation of Coupled Mass Transport and Electrochemical Reactions in Porous SOFC Anode Microstructure
,”
Int. J. Heat Mass Transfer
,
109
, pp.
1252
1260
. 10.1016/j.ijheatmasstransfer.2017.02.090
15.
Ni
,
M.
,
Leung
,
D. Y. C.
, and
Leung
,
M. K. H.
,
2008
, “
Importance of Pressure Gradient in Solid Oxide Fuel Cell Electrodes
,”
J. Power Sources
,
183
(
2
), pp.
668
673
. 10.1016/j.jpowsour.2008.05.013
16.
Bertei
,
A.
, and
Nicolella
,
C.
,
2015
, “
Common Inconsistencies in Modeling Gas Transport in Porous Electrodes: The Dusty-Gas Model and the Fick Law
,”
J. Power Sources
,
279
, pp.
133
137
. 10.1016/j.jpowsour.2015.01.007
17.
Bertei
,
A.
, and
Nicolella
,
C.
,
2015
, “
Dusty-Gas Model With Uniform Pressure: A Numerical Study on the Impact of a Frequent Inconsistent Assumption in SOFC Electrode Modeling
,”
ECS Trans.
,
68
(
1
), pp.
2887
2895
. 10.1149/06801.2887ecst
18.
Tseronis
,
K.
,
Kookos
,
I. K.
, and
Theodoropoulos
,
C.
,
2008
, “
Modelling Mass Transport in Solid Oxide Fuel Cell Anodes: A Case for a Multidimensional Dusty Gas-Based Model
,”
Chem. Eng. Sci.
,
63
(
23
), pp.
5626
5638
. 10.1016/j.ces.2008.07.037
19.
Kong
,
W.
,
Zhu
,
H.
,
Fei
,
Z.
, and
Lin
,
Z.
,
2012
, “
A Modified Dusty Gas Model in the Form of a Fick’s Model for the Prediction of Multicomponent Mass Transport in a Solid Oxide Fuel Cell Anode
,”
J. Power Sources
,
206
, pp.
171
178
. 10.1016/j.jpowsour.2012.01.107
20.
García-Camprubí
,
M.
,
Sánchez-Insa
,
A.
, and
Fueyo
,
N.
,
2010
, “
Multimodal Mass Transfer in Solid-Oxide Fuel-Cells
,”
Chem. Eng. Sci.
,
65
(
5
), pp.
1668
1677
. 10.1016/j.ces.2009.11.006
21.
García-Camprubí
,
M.
,
Jasak
,
H.
, and
Fueyo
,
N.
,
2011
, “
CFD Analysis of Cooling Effects in H2-Fed Solid Oxide Fuel Cells
,”
Chem. Eng. Sci.
,
196
, pp.
7290
7301
.
22.
Jin
,
X.
,
Ku
,
A.
,
Verma
,
A.
,
Ohara
,
B.
,
Huang
,
K.
, and
Singh
,
S.
,
2018
, “
The Performance of Syngas-Fueled Solid Oxide Fuel Cell Predicted by a Reduced Order Model (ROM): Temperature and Fuel-Composition Effects
,”
J. Electrochem. Soc.
,
165
(
10
), pp.
F786
F798
. 10.1149/2.0511810jes
23.
Jin
,
X.
,
Singh
,
S.
,
Verma
,
A.
,
Ohara
,
B.
,
Ku
,
A.
, and
Huang
,
K.
,
2018
, “
The Performance of Syngas-Fueled Solid Oxide Fuel Cell Predicted by a Reduced Order Model (ROM): Pressurization and Flow-Pattern Effects
,”
J. Power Sources
,
404
, pp.
96
105
. 10.1016/j.jpowsour.2018.10.015
24.
Pisani
,
L.
,
2008
, “
Multi-Component Gas Mixture Diffusion Through Porous Media: A 1D Analytical Solution
,”
Int. J. Heat Mass Transfer
,
51
(
3–4
), pp.
650
660
. 10.1016/j.ijheatmasstransfer.2007.04.043
25.
Kerkhof
,
P. J. A. M.
,
1996
, “
A Modified Maxwell-Stefan Model for Transport Through Inert Membrane: The Binary Friction Model
,”
Chem. Eng. J.
,
64
(
3
), pp.
319
343
.
26.
Pant
,
L. M.
, and
M. Secanell
,
Mitra S. K.
,
2013
, “
A Generalized Mathematical Model to Study Gas Transport in PEMFC Porous Media
,”
Int. J. Heat Mass Transfer
,
58
(
1–2
), pp.
70
79
. 10.1016/j.ijheatmasstransfer.2012.11.023
27.
Das
,
S. K.
,
2019
, “
General Dusty Gas Model for Porous Media With a Specified Pore Size Distribution
,”
Chem. Eng. Sci.
,
203
, pp.
293
301
. 10.1016/j.ces.2019.03.085
28.
Fuller
,
E. N.
,
Schettler
,
P. D.
, and
Calvin Giddings
,
J.
,
1966
, “
A New Method for Prediction of Binary Gas-Diffusion Coefficients
,”
Ind. Eng. Chem.
,
58
, pp.
19
27
.
29.
Mason
,
E. A.
, and
Malinauskas
,
A. P.
,
1983
,
Gas Transport in Porous Media: The Dusty Gas Model
,
Elsevier
,
Amsterdam, The Netherlands
.
30.
Krishna
,
R.
, and
Wesselingh
,
J. A.
,
1997
, “
The Maxwell-Stefan Approach to Mass Transfer
,”
Chem. Eng. Sci.
,
52
(
6
), pp.
861
911
. 10.1016/S0009-2509(96)00458-7
31.
Ma
,
Z.
,
Blanchett
,
S.
,
Venkataraman
,
R.
,
Iaccarino
,
G.
, and
Moin
,
P.
,
2004
, “
Mathematical Modeling of an Internal-Reforming Carbonate Fuel Cell Stack
,”
2th International Conference on Fuel Cell Science, Engineering and Technology
,
Rochester, NY
,
June 14–16
, pp.
311
318
.
32.
Ma
,
Z.
,
Venkataraman
,
R.
, and
Farooque
,
M.
,
2010
, “
High Power Internal-Reforming Direct Carbonate Fuel Cell Stack Development Through Mathematical Modeling and Engineering Optimization
,”
ASME J. Fuel Cell Sci. Technol.
,
7
(
5
), p.
051003
. 10.1115/1.4000625
33.
Lu
,
X.
,
Tjaden
,
B.
,
Bertei
,
A.
,
Li
,
T.
,
Li
,
K.
,
Brett
,
D.
, and
Shearing
,
P.
,
2017
, “
3D Characterization of Diffusivites and Its Impact on Mass Flux and Concentration Overpotential in SOFC Anode
,”
J. Electrochem. Soc.
,
164
(
4
), pp.
F188
F195
. 10.1149/2.0111704jes
34.
Lu
,
X.
,
Taiwo
,
O. O.
,
Bertei
,
A.
,
Li
,
T.
,
Li
,
K.
,
Brett
,
D. J. L.
, and
Shearing
,
P. R.
,
2017
, “
Multi-Length Scale Tomography for the Determination and Optimization of the Effective Microstructural Properties in Novel Hierarchical Solid Oxide Fuel Cell Anodes
,”
J. Power Sources
,
367
, pp.
177
186
. 10.1016/j.jpowsour.2017.09.017
35.
Wejrzanowski
,
T.
,
Haj Ibrahim
,
S.
,
Cwieka
,
K.
,
Loeffler
,
M.
,
Milewski
,
J.
, and
Zschech
,
E.
,
2018
, “
Multi-Modal Porous Microstructure for High Temperature Fuel Cell Application
,”
J. Power Sources
,
373
, pp.
85
94
. 10.1016/j.jpowsour.2017.11.009
36.
Zhou
,
J.
,
Putz
,
A.
, and
Secanell
,
M.
,
2017
, “
A Mixed Wettability Pore Size Distribution Based Mathematical Model for Analyzing Two-Phase Flow in Porous Electrodes
,”
J. Electrochem. Soc.
,
164
(
6
), pp.
F530
F539
. 10.1149/2.0381706jes
You do not currently have access to this content.