# Modeling of mass and charge transport in a solid oxide fuel cell anode structure by a 3D lattice Boltzmann approach

- 680 Downloads
- 2 Citations

## Abstract

A 3D model at microscale by the lattice Boltzmann method (LBM) is proposed for part of an anode of a solid oxide fuel cell (SOFC) to analyze the interaction between the transport and reaction processes and structural parameters. The equations of charge, momentum, heat and mass transport are simulated in the model. The modeling geometry is created with randomly placed spheres to resemble the part of the anode structure close to the electrolyte. The electrochemical reaction processes are captured at specific sites where spheres representing Ni and YSZ materials are present with void space. This work focuses on analyzing the effect of structural parameters such as porosity, and percentage of active reaction sites on the ionic current density and concentration of H_{2} using LBM. It is shown that LBM can be used to simulate an SOFC anode at microscale and evaluate the effect of structural parameters on the transport processes to improve the performance of the SOFC anode. It was found that increasing the porosity from 30 to 50 % decreased the ionic current density due to a reduction in the number of reaction sites. Also the consumption of H_{2} decreased with increasing porosity. When the percentage of active reaction sites was increased while the porosity was kept constant, the ionic current density increased. However, the H_{2} concentration was slightly reduced when the percentage of active reaction sites was increased. The gas flow tortuosity decreased with increasing porosity.

## Keywords

Solid Oxide Fuel Cell Lattice Boltzmann Method Ionic Current Density Knudsen Diffusion Porous Domain## List of symbols

*AV*Surface area to volume (m

^{2}/m^{3})*b*Particle distribution function, ion/electron transport

*C*Concentration (mol/m

^{3})*D*_{e}Effective diffusivity (m

^{2}/s)*D*_{eff}Average effective diffusivity (m

^{2}/s)*D*_{Keff}Effective Knudsen diffusivity (m

^{2}/s)*d*_{p}Particle diameter (m)

**e**Base velocity in the lattice Boltzmann model

*E*Activation energy (kJ/mol)

*E*Actual voltage (V)

*E*^{eq}Equilibrium voltage (V)

*f*Particle distribution function, momentum transport

*F*Faraday’s constant (96,485 A s/mol)

*g*Particle distribution function, mass transport

*h*Particle distribution function, heat transport

*i*Current density (A/m

^{2})*L*Porous domain length (m)

- M
Molecular weight (g/mol)

*p*Pressure (atm)

*Q*Heat flow (J/s)

- R
Gas constant [8.3145 J/(mol K)]

*Re*Reynolds number (–)

*R*_{j}Reaction rate (mol/s)

*S*Entropy (J/mol K)

*T*Temperature (K)

*t*Time (s)

**u**Velocity vector (m/s)

*u, v*Velocity (m/s)

*x, y, z*Position (m)

## Greek symbols

*α*Lattice direction (–)

*β*Transfer coefficient in the Butler–Volmer equation (–)

*ε*Porosity (–)

*η*Polarization (V)

*ρ*Density (kg/m

^{3})*σ*Conductivity (S/m) or characteristic length (Å)

*τ*Relaxation time (–)

*ν*Kinematic viscosity (m

^{2}/s)*ϕ*Electric potential (V)

*Ω*Collision operator (–)

*Ω*_{D}Dimensionless collision integral (–)

## Abbreviations

- BGK
Bhatnagar, Gross, Krook (method, collision operator)

- CFD
Computational fluid dynamics

- FEM
Finite element method

- FDM
Finite difference method

- FIB
Focused ion beam

- FVM
Finite volume method

- LBM
Lattice Boltzmann method

Particle distribution function

- SEM
Scanning electron microscopy

- SOFC
Solid oxide fuel cell

- TPB
Three-phase boundary

- YSZ
Yttria-stabilized zirconia

## Chemical formula

- H
_{2} Hydrogen

- H
_{2}O Water

- Ni
Nickel

- O
_{2} Oxygen

- O
^{2−} Oxygen ions

## Subscripts

- act
Activation

- conc
Concentration

- e
Electronic, electrochemical

- io
Ionic

- j
Species index

- k
Species index

- ohm
Ohmic

- r
Reaction

## Notes

### Acknowledgments

The Swedish Research Council (VR-621-2010-4581) and the European Research Council (ERC-226238-MMFCs) are gratefully acknowledged for the financial support of this research work. Also, the authors want to acknowledge the Swedish National Infrastructure for Computing (SNIC) for the use of the computer cluster Lunarc.

## References

- 1.Andersson M, Yuan J, Sundén B (2012) SOFC modeling considering electrochemical reactions at the active three phase boundaries. Int J Heat Mass Transf 55:773–788CrossRefzbMATHGoogle Scholar
- 2.Kakaç S, Pramuanjaroenkij A, Zhou XY (2007) A review of numerical modeling of solid oxide fuel cells. J Hydrog Energy 32:761–786CrossRefGoogle Scholar
- 3.Doraswami U, Shearing P, Droushiotis N, Li K, Brandon NP, Kelsall GH (2011) Modeling the effects of measured anode triple-phase boundary densities on the performance of micro-tubular hollow fiber SOFCs. Solid State Ion 192:494–500CrossRefGoogle Scholar
- 4.Grew KN, Joshi AS, Peracchio AA, Chiu WKS (2010) Pore-scale investigation of mass transport and electrochemistry in a solid oxide fuel cell anode. J Power Sources 195:2331–2345CrossRefGoogle Scholar
- 5.Nam JH, Jeon DH (2006) A comprehensive micro-scale model for transport and reaction in intermediate temperature solid oxide fuel cells. Electrochim Acta 51:3446–3460CrossRefGoogle Scholar
- 6.Joshi AS, Peracchio AA, Grew KN, Chiu WKS (2007) Lattice Boltzmann method for multi-component mass diffusion in complex 2D geometries. J Phys D Appl Phys 40:2961–2971CrossRefGoogle Scholar
- 7.Virkar AV, Chen J, Tanner CW, Kim J (2000) The role of electrode microstructure on activation and concentration polarizations in solid oxide fuel cells. Solid State Ion 131:189–198CrossRefGoogle Scholar
- 8.Suzue Y, Shikazono N, Kasagi N (2008) Micro modeling of solid oxide fuel cell anode based on stochastic reconstruction. J Power Sources 184:52–59CrossRefGoogle Scholar
- 9.Iwai H, Shikazono N, Matsui T, Teshima H, Kishimoto M, Kishida R, Hayashi D, Matsuzaki K, Kanno D, Saito M, Muroyama H, Eguchi K, Kasagi N, Yoshida H (2010) Quantification of SOFC anode microstructure based on dual beam FIB-SEM technique. J Power Sources 195:955–961CrossRefGoogle Scholar
- 10.Kanno D, Shikazono N, Takagi N, Matsuzaki K, Kasagi N (2011) Evaluation of SOFC anode polarization simulation using three-dimensional microstructures reconstructed by FIB tomography. Electrochim Acta 56:4015–4021CrossRefGoogle Scholar
- 11.Dawson SP, Chen S, Doolen GD (1993) Lattice Boltzmann computations for reaction-diffusion equations. J Chem Phys 98:1514–1523CrossRefGoogle Scholar
- 12.Xu Y-S, Zhong Y-J, Huang G-X (2004) Lattice Boltzmann method for diffusion-reaction-transport processes in heterogeneous porous media. Chin Phys Lett 21Google Scholar
- 13.Aguiar P, Adjiman CS, Brandon NP (2004) Anode-supported intermediate temperature direct internal reforming solid oxide fuel cell I: model-based steady-state performance. J Power Sources 132:113–126CrossRefGoogle Scholar
- 14.Bessler WG, Warnatz J, Goodwin DG (2007) The influence of equilibrium potential on hydrogen oxidation kinetics of SOFC anodes. Solid State Ion 177:3371–3383CrossRefGoogle Scholar
- 15.Newman J, Thomas-Alyea KE (2004) Electrochemical systems, 3rd edn. Wiley-Interscience, HobokenGoogle Scholar
- 16.Nsofor EC, Adebiyi GA (2001) Measurement of the gas-particle heat transfer coefficient in a packed bed for high-temperature energy storage. Exp Therm Fluid Sci 24:1–9CrossRefGoogle Scholar
- 17.Reid RC, Prausnitz JM, Poling BE (1987) The properties of gases and liquids, 4th edn. McGraw Hill, New YorkGoogle Scholar
- 18.Chen S, Dawson SP, Doolen GD, Janecky DR, Lawniczak A (1995) Lattice methods and their applications to reacting systems. Comput Chem Eng 19:617–646CrossRefGoogle Scholar
- 19.Kang QJ, Lichtner PC, Janecky DR (2010) Lattice Boltzmann method for reacting flows in porous media. Adv Appl Math Mech 5:545–563MathSciNetGoogle Scholar
- 20.Joshi AS, Grew KN, Izzo JR Jr, Peracchio AA, Chiu WKS (2010) Lattice Boltzmann modeling of three-dimensional, multicomponent mass diffusion in a solid oxide fuel cell anode. ASME J Fuel Cell Sci Technol 7:1–8CrossRefGoogle Scholar
- 21.Kandhai D, Vidal DJ-E, Hoekstra AG, Hoefsloot H, Iedema P, Sloot PMA (1999) Lattice-Boltzmann and finite element simulations of fluid flow in a SMRX static mixer reactor. Int J Numer Methods Fluids 31:1019–1033CrossRefzbMATHGoogle Scholar
- 22.Geller S, Krafczyk M, Tölke J, Turek S, Hron J (2006) Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows. Comput Fluids 35:888–897CrossRefzbMATHGoogle Scholar
- 23.Zheng HW, Shu C, Chew YT, Sun JH (2008) Three-dimensional lattice Boltzmann interface capturing method for incompressible flows. Int J Numer Methods Fluids 56:1653–1671MathSciNetCrossRefzbMATHGoogle Scholar
- 24.Yoshida H, Nagaoka M (2010) Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J Comput Phys 229:7774–7795MathSciNetCrossRefzbMATHGoogle Scholar
- 25.Breyiannis G, Valougeorgis D (2004) Lattice kinetic simulation in three-dimensional magnet hydrodynamics. Phys Rev E 69:065702CrossRefGoogle Scholar
- 26.Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511–525CrossRefzbMATHGoogle Scholar
- 27.Shan X, Doolen G (1996) Diffusion in a multicomponent lattice Boltzmann equation model. Phys Rev E 54:3614–3620CrossRefGoogle Scholar
- 28.Huber C, Parmigiani A, Chopard B, Manga M, Bachmann O (2008) Lattice Boltzmann model for melting with natural convection. Int J Heat Fluid Flow 29:1469–1480CrossRefGoogle Scholar
- 29.Kang Q, Litchner PC, Zhang D (2007) An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale. Water Resour Res 43:W12S14Google Scholar
- 30.Chiu WKS, Joshi AS, Grew KN (2009) Lattice Boltzmann model for multi-component mass transfer in a solid oxide fuel cell anode with heterogeneous internal reformation and chemistry. Eur Phys J Spec Top 171:159–165CrossRefGoogle Scholar
- 31.Latt J (2007) Hydrodynamic limit of the lattice Boltzmann equations. PhD Thesis, University of GenevaGoogle Scholar
- 32.Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models. An introduction. Springer, BerlinCrossRefzbMATHGoogle Scholar
- 33.Dardis O, McCloskey J (1998) Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media. Phys Rev E 57:4834–4837CrossRefGoogle Scholar
- 34.He X, Li N (2000) Lattice Boltzmann simulation of electrochemical systems. Comput Phys Commun 129:158–166MathSciNetCrossRefzbMATHGoogle Scholar
- 35.Paradis H, Sundén B (2012) Evaluation of lattice Boltzmann method for reaction-diffusion process in a porous SOFC anode microstructure. In: Proceedings of the ASME 2012 10th international conference on nanochannels, microchannels and minichannels, ICNMM2012-73163, Puerto Rico, USAGoogle Scholar
- 36.Ghassemi A, Pak A (2011) Pore scale study of permeability and tortuosity for flow through particulate media using lattice Boltzmann method. Int J Numer Anal Methods Geomech 35:886–901CrossRefzbMATHGoogle Scholar
- 37.Yang S, Chen T, Wang Y, Peng Z, Wang WG (2013) Electrochemical analysis of an anode-supported SOFC. Int J Electrochem Sci 8:2330–2344Google Scholar
- 38.Rogers WA, Gemmen RS, Johnson C, Prinkey M, Shahnam M (2003) Validation and application of a CFD based model for solid oxide fuel cells and stacks. ASME J Fuel Cell Sci Technol 1762:517–520Google Scholar