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Modeling of Solid Oxide Electrolysis Cells

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High Temperature Electrolysis

Part of the book series: Lecture Notes in Energy ((LNEN,volume 95))

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Abstract

The practical operation of solid oxide electrolysis cell (SOEC) involves complex physicochemical coupling processes between “multi-physics fields” at “multiple scales”. Mathematical simulation and modeling can explain the inherent connections and influencing mechanisms of multi-physics fields at different scales, which are crucial for the study of SOEC’s basic electrochemical characteristics and the development of engineering applications. In this chapter, we mainly summarize different simulation techniques for SOEC from the perspective of spatial scale categories. Models related to single cells and stacks are mainly based on the continuum hypothesis, and the macroscopic characteristics such as the distribution of multi-physics fields, input/output power, and cell efficiency inside single cells/stacks are obtained through traditional computational fluid dynamics using finite volume method or finite element method. This article first introduces the relevant conservation equations and modeling methods of macroscopic models based on the continuum hypothesis. Then, numerical simulation methods for heterogeneous electrode structures at the electrode scale are introduced, including the lattice Boltzmann method, kinetic Monte Carlo method, and phase field method. Finally, we also introduce the application of machine learning methods in SOEC simulation and provide prospects for future research.

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Abbreviations

C :

Conserved order parameters

\(C_{i}\) :

Molar concentration of species i (mol m-3)

d p :

Average diameter of pore (μm)

D i,k :

Knudsen diffusion coefficients (m2 s-1)

D i,j :

Binary diffusion coefficients (m2 s-1)

E act :

Activation energy (J mol-1)

F :

The Faraday constant (C mol-1)

F total :

Total free energy of the system

f 0 :

Bulk free energy density

J :

Electrochemical reaction rate (A m-3 s-1)

j 0 :

Exchange current density (A m-3)

K :

Permeability (m2)

K pr :

Equilibrium constant of MSR

K ps :

Equilibrium constant of WGSR

k rf :

Forward reaction rate constant for MSR

k sf :

Forward reaction rate constant for WGSR

M :

Average molar mass (kg mol-1)

M C :

Mobility of conserved order parameters

n e :

Number of electrons transferred per reaction

P :

Pressure (Pa)

p :

Partial pressure (Pa)

r p :

Pore diameter (m)

T :

Temperature (K)

V i :

Special Fuller diffusion volume (cm-3 mol-1)

W ca :

Wettability parameter

φ :

Electric potential (V）

η i :

Non-conserved order parameters

η act :

Activation overpotential

κ :

Gradient energy coefficients

κ eff :

Effective thermal conductivity (W m-1 K-1)

σ :

Conductivity (S m-1)

ρ :

Density (kg m-3)

μ :

Dynamic viscosity (N s m-2)

ε :

Porosity

ω i :

Weight coefficients

τ :

Tortuosity

τ i :

Relaxation coefficients

act:

Activation

bulk:

Bulk diffusion

conc:

Concentration

ele:

Electron

ion:

Ion

N:

Ni

ohm:

Ohmic

Y:

YSZ

P:

Pore

References

  • Bi L, Boulfrad S, Traversa E (2014) Steam electrolysis by solid oxide electrolysis cells (SOECs) with proton-conducting oxides. Chem Soc Rev 43:8255–8270

    Article  Google Scholar 

  • Birnbaum K, Steinberger-Wilkens R, Zapp P (2013) Solid oxide fuel cells, sustainability aspects. Fuel Cells, Springer, pp 731–790

    Google Scholar 

  • Chen L, Kang QJ, Mu YT, He YL, Tao WQ (2014) A critical review of the pseudopotential multiphase lattice Boltzmann model: methods and applications. Int J Heat Mass Transf 76:210–236

    Article  Google Scholar 

  • Da Y, Jiao Z, Zhong Z (2021) Phase field modeling of cubic to tetragonal transformation in YSZ and its effect on ionic conductivity degradation and mechanical damages. In: ECS meeting abstracts, IOP Publishing, pp 247

    Google Scholar 

  • Damm DL, Fedorov AG (2005) Spectral radiative heat transfer analysis of the planar SOFC. J Fuel Cell Sci Technol 2:258–262

    Article  Google Scholar 

  • Durlofsky L, Brady JF (1987) Analysis of the Brinkman equation as a model for flow in Porous-media. Phys Fluids 30:3329–3341

    Article  MATH  Google Scholar 

  • Gayon-Lombardo A, Mosser L, Brandon NP, Cooper SJ (2020) Pores for thought: generative adversarial networks for stochastic reconstruction of 3D multi-phase electrode microstructures with periodic boundaries. Npj Comput Mater 6

    Google Scholar 

  • Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. Adv Neural Info Process Syst 27(Nips 2014), 27:2672–2680

    Google Scholar 

  • Hasanabadi A, Baniassadi M, Abrinia K, Safdari M, Garmestani H (2016) Optimization of solid oxide fuel cell cathodes using two-point correlation functions. Comput Mater Sci 123:268–276

    Article  Google Scholar 

  • Hsu T, Epting WK, Kim H, Abernathy HW, Hackett GA, Rollett AD, Salvador PA, Holm EA (2021) Microstructure generation via generative adversarial network for heterogeneous, topologically complex 3D materials. Jom 73:90–102

    Article  Google Scholar 

  • Jiao ZJ, Shikazono N (2016) Simulation of the reduction process of solid oxide fuel cell composite anode based on phase field method. J Power Sour 305:10–16

    Article  Google Scholar 

  • Jordan MI, Mitchell TM (2015) Machine learning: trends, perspectives, and prospects. Science 349:255–260

    Article  MathSciNet  MATH  Google Scholar 

  • Li Z, Yang M, Zhang YW (2016) Lattice Boltzmann method simulation of 3-D natural convection with double MRT model. Int J Heat Mass Transf 94:222–238

    Article  Google Scholar 

  • Li R, Liu XM, He GZ, Hu PF, Zhen Q, Liu JBL, Bashir S (2021) Green catalytic synthesis of ammonia using solid oxide electrolysis cells composed of multicomponent materials. Catal Today 374:102–116

    Article  Google Scholar 

  • Luo Y, Shi YX, Li WY, Cai NS (2015) Dynamic electro-thermal modeling of co-electrolysis of steam and carbon dioxide in a tubular solid oxide electrolysis cell. Energy 89:637–647

    Article  Google Scholar 

  • Ma R, Yang T, Breaz E, Li ZL, Briois P, Gao F (2018) Data-driven proton exchange membrane fuel cell degradation predication through deep learning method. Appl Energy 231:102–115

    Article  Google Scholar 

  • Mogensen MB, Hauch A, Sun X, Chen M, Tao Y, Ebbesen SD, Hansen KV, Hendriksen PV (2017) Relation between Ni particle shape change and Ni migration in Ni-YSZ electrodes—a hypothesis. Fuel Cells 17:434–441

    Article  Google Scholar 

  • Mogensen MB, Chen M, Frandsen HL, Graves C, Hauch A, Hendriksen PV, Jacobsen T, Jensen SH, Skafte TL, Sun XF (2021) Ni migration in solid oxide cell electrodes: review and revised hypothesis. Fuel Cells 21:415–429

    Google Scholar 

  • Monaco F, Hubert M, Vulliet J, Ouweltjes JP, Montinaro D, Cloetens P, Piccardo P, Lefebvre-Joud F, Laurencin J (2019) Degradation of Ni-YSZ electrodes in solid oxide cells: impact of polarization and initial microstructure on the Ni evolution. J Electrochem Soc 166:F1229–F1242

    Article  Google Scholar 

  • Nabiollahi N, Moelans N, Gonzalez M, De Messemaeker J, Wilson CJ, Croes K, Beyne E, De Wolf I (2015) Microstructure simulation of grain growth in Cu through silicon vias using phase-field modeling. Microelectron Reliab 55:765–770

    Article  Google Scholar 

  • Nelson GJ, Grew KN, Izzo JR, Lombardo JJ, Harris WM, Faes A, Hessler-Wyser A, Van Herle J, Wang S, Chu YS, Virkar AV, Chiu WKS (2012) Three-dimensional microstructural changes in the Ni-YSZ solid oxide fuel cell anode during operation. Acta Mater 60:3491–3500

    Article  Google Scholar 

  • Patil MA, Tagade P, Hariharan KS, Kolake SM, Song T, Yeo T, Doo S (2015) A novel multistage support vector machine based approach for Li ion battery remaining useful life estimation. Appl Energy 159:285–297

    Article  Google Scholar 

  • Prokop TA, Berent K, Iwai H, Szmyd JS, Brus G (2018) A three-dimensional heterogeneity analysis of electrochemical energy conversion in SOFC anodes using electron nanotomography and mathematical modeling. Int J Hydrogen Energy 43:10016–10030

    Article  Google Scholar 

  • Riazat M, Tafazoli M, Baniassadi M, Safdari M, Faraji G, Garmestani H (2017) Investigation of the property hull for solid oxide fuel cell microstructures. Comput Mater Sci 127:1–7

    Article  Google Scholar 

  • Sanyal J, Goldin GM, Zhu HY, Kee RJ (2010) A particle-based model for predicting the effective conductivities of composite electrodes. J Power Sour 195:6671–6679

    Article  Google Scholar 

  • Tafazoli M, Shakeri M, Baniassadi M, Babaei A (2017) Investigation of the geometric property hull for infiltrated solid oxide fuel cell electrodes. Int J Energy Res 41:2318–2331

    Article  Google Scholar 

  • Trini M, Hauch A, De Angelis S, Tong X, Hendriksen PV, Chen M (2020) Comparison of microstructural evolution of fuel electrodes in solid oxide fuel cells and electrolysis cells. J Power Sour 450

    Google Scholar 

  • Wang Y, Du YM, Ni M, Zhan RB, Du Q, Jiao K (2020a) Three-dimensional modeling of flow field optimization for co-electrolysis solid oxide electrolysis cell. Appl Therm Eng 172

    Google Scholar 

  • Wang Y, Seo B, Wang B, Zamel N, Jiao K, Adroher XC (2020b) Fundamentals, materials, and machine learning of polymer electrolyte membrane fuel cell technology. Energy and AI 1:100014

    Article  Google Scholar 

  • Wang Y, Wu C, Du Q, Ni M, Jiao K, Zu B (2021a) Morphology and performance evolution of anode microstructure in solid oxide fuel cell: a model-based quantitative analysis. Appl Energy and Combustion Sci 5:100016

    Google Scholar 

  • Wang Y, Wu C, Zu B, Han M, Du Q, Ni M, Jiao K (2021b) Ni migration of Ni-YSZ electrode in solid oxide electrolysis cell: an integrated model study. J Power Sour 516:230660

    Article  Google Scholar 

  • Wang Y, Zhan RB, Qin YZ, Zhang GB, Du Q, Jiao K (2018) Three-dimensional modeling of pressure effect on operating characteristics and performance of solid oxide fuel cell. Int J Hydrogen Energy 43:20059–20076

    Article  Google Scholar 

  • Wang Y, Zu B, Zhan R, Du Q, Ni M, Jiao K (2020c) Three-dimensional modeling and performance optimization of proton conducting solid oxide electrolysis cell. Fuel Cells 20:701–711

    Article  Google Scholar 

  • Wu C, Wang Y, Hou Y, Li X, Peng Z, Du Q, Ni M, Jiao K (2022) Reconstruction and optimization of LSCF cathode microstructure based on kinetic Monte Carlo method and Lattice Boltzmann method. Chem Eng J 436:132144

    Article  Google Scholar 

  • Xu HR, Ma JB, Tan P, Wu Z, Zhang YX, Ni M, Xuan J (2021) Enabling thermal-neutral electrolysis for CO2-to-fuel conversions with a hybrid deep learning strategy. Energy Convers Managem 230

    Google Scholar 

  • Yan Z, He A, Hara S, Shikazono N (2019) Modeling of solid oxide fuel cell (SOFC) electrodes from fabrication to operation: Microstructure optimization via artificial neural networks and multi-objective genetic algorithms. Energy Convers Managem 198

    Google Scholar 

  • Yuan JL, Sunden B (2014) On mechanisms and models of multi-component gas diffusion in porous structures of fuel cell electrodes. Int J Heat Mass Transf 69:358–374

    Article  Google Scholar 

  • Zhang JH, Lei LB, Liu D, Zhao FY, Ni M, Chen FL (2018) Mathematical modeling of a proton-conducting solid oxide fuel cell with current leakage. J Power Sour 400:333–340

    Article  Google Scholar 

  • Zhang QP, Guo YX, Ding JW, Xia SH (2019) Hole conductivity in the electrolyte of proton-conducting SOFC: mathematical model and experimental investigation. J Alloy Compd 801:343–351

    Article  Google Scholar 

  • Zheng KQ, Ni M (2016) Reconstruction of solid oxide fuel cell electrode microstructure and analysis of its effective conductivity. Sci Bulletin 61:78–85

    Article  Google Scholar 

  • Zheng Y, Wang JC, Yu B, Zhang WQ, Chen J, Qiao JL, Zhang JJ (2017) A review of high temperature co-electrolysis of H2O and CO2 to produce sustainable fuels using solid oxide electrolysis cells (SOECs): advanced materials and technology. Chem Soc Rev 46:1427–1463

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Building and Real Estate, Research Institute for Sustainable Urban Development (RISUD) and Research Institute for Smart Energy (RISE), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Yang Wang & Meng Ni

  2. State Key Laboratory of Engines, Tianjin University, Tianjin, China

    Chengru Wu, Kui Jiao & Qing Du

Authors
  1. Yang Wang
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  2. Chengru Wu
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  3. Kui Jiao
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  4. Qing Du
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  5. Meng Ni
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Corresponding author

Correspondence to Meng Ni .

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Editors and Affiliations

  1. Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC—Universidad de Zaragoza, Zaragoza, Spain

    Miguel Angel Laguna-Bercero

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Wang, Y., Wu, C., Jiao, K., Du, Q., Ni, M. (2023). Modeling of Solid Oxide Electrolysis Cells. In: Laguna-Bercero, M.A. (eds) High Temperature Electrolysis. Lecture Notes in Energy, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-031-22508-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-22508-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22507-9

  • Online ISBN: 978-3-031-22508-6

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