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Continuum Scale Modelling and Complementary Experimentation of Solid Oxide Cells

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Continuum Scale Modelling and Complementary Experimentation of Solid Oxide Cells Progress in Energy and Combustion Science 85 (2021) 100902 Contents lists available at ScienceDirect Progress in Energy and Combustion Science journal homepage: www.elsevier.com/locate/pecs Continuum scale modelling and complementary experimentation of solid oxide cells ∗ Steven B. Beale a,b, , Martin Andersson a,c, Carlos Boigues-Muñoz d, Henrik L. Frandsen e, Zijing Lin f, Stephen J. McPhail d, Meng Ni a,g, Bengt Sundén c, André Weber h, Adam Z. Weber i a Forschungszentrum Jülich GmbH, 52425 Jülich, Germany b Queen’s University, Kingston, ON K7L 3N6, Canada c Lund University, Lund 22100, Sweden d Italian National Agency for New Technologies, Energy and Sustainable Economic Development, 00123 Rome, Italy e Technical University of Denmark, 40 0 0 Roskilde, Denmark f University of Science and Technology of China, Hefei 230026, China g The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong China h Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany i Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States a r t i c l e i n f o a b s t r a c t Article history: Solid oxide cells are an exciting technology for energy conversion. Fuel cells, based on solid oxide tech- Received 16 April 2019 nology, convert hydrogen or hydrogen-rich fuels into electrical energy, with potential applications in sta- Accepted 19 December 2020 tionary power generation. Conversely, solid oxide electrolysers convert electricity into chemical energy, thereby offering the potential to store energy from transient resources, such as wind turbines and other Keywords: renewable technologies. For solid oxide cells to displace conventional energy conversion devices in the Solid oxide fuel cells marketplace, reliability must be improved, product lifecycles extended, and unit costs reduced. Math- Solid oxide electrolysers ematical models can provide qualitative and quantitative insight into physical phenomena and perfor- Mathematical modelling mance, over a range of length and time scales. The purpose of this paper is to provide the reader with a summary of the state-of-the art of solid oxide cell models. These range from: simple methods based on lumped parameters with little or no kinetics to detailed, time-dependent, three-dimensional solutions for electric field potentials, complex chemical kinetics and fully-comprehensive equations of motion based on effective transport properties. Many mathematical models have, in the past, been based on inaccu- rate property values obtained from the literature, as well as over-simplistic schemes to compute effective values. It is important to be aware of the underlying experimental methods available to parameterise mathematical models, as well as validate results. In this article, state-of-the-art techniques for measuring kinetic, electric and transport properties are also described. Methods such as electrochemical impedance spectroscopy allow for fundamental physicochemical parameters to be obtained. In addition, effective properties may be obtained using micro-scale computer simulations based on digital reconstruction ob- tained from X-ray tomography/focussed ion beam scanning electron microscopy, as well as percolation theory. The cornerstone of model validation, namely the polarisation or current-voltage diagram, pro- vides necessary, but insufficient information to substantiate the reliability of detailed model calculations. The results of physical experiments which precisely mimic the details of model conditions are scarce, and it is fair to say there is a gap between the two activities. The purpose of this review is to introduce the reader to the current state-of-the art of solid oxide analysis techniques, in a tutorial fashion, not only numerical and but also experimental, and to emphasise the cross-linkages between techniques. ©2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) ∗ Corresponding author at: Institute of Energy and Climate Research, IEK-14: Electrochemical Process Engineering, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. E-mail address: [email protected] (S.B. Beale). https://doi.org/10.1016/j.pecs.2020.100902 0360-1285/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) S.B. Beale, M. Andersson, C. Boigues-Muñoz et al. Progress in Energy and Combustion Science 85 (2021) 100902 Contents 1. Introduction . 3 1.1. Solid oxide cells: Pathway of technology development . 4 1.1.1. SOC history and state-of-the-art . 5 1.1.2. SOC basic principles . 5 1.1.3. Modelling and physical experiments . 7 1.2. Common analysis tools and techniques . 7 1.2.1. Global performance characterisation: Polarisation curves . 7 1.2.2. In-depth process characterisation: Electrochemical impedance spectroscopy . 8 1.2.3. Characterisation of state: Gas composition, pressure and temperature measurements. 10 1.2.4. In-situ characterisation: Segmented cells and local probing . 11 1.2.5. Optical in-situ characterisation . 11 1.3. History of continuum scale SOC modelling . 11 1.4. Model dimensionality and scale . 13 2. Current continuum scale cell models . 14 2.1. Basic thermodynamics . 14 2.2. Continuity and momentum. 16 2.3. Mass transport . 17 2.4. Charge transport . 19 2.5. Electrochemical reactions . 20 2.5.1. Electrochemical kinetics . 20 2.5.2. Electrochemically-active surface area . 21 2.6. Chemical reactions. 22 2.6.1. Methane steam reforming . 22 2.6.2. Water-gas-shift reaction . 22 2.7. Heat transfer. 22 2.7.1. Heat sources and sinks . 23 2.7.2. Porous media and stacks . 23 2.7.3. Thermal boundary conditions and contact resistance . 23 2.7.4. Heat transfer in solid oxide stacks . 24 2.7.5. Thermal radiation . 24 2.7.6. Surface radiation in internal fuel cell passages . 24 2.7.7. Participative radiation and radiative control . 24 2.7.8. External radiative exchange between cell stack and enclosure . 25 2.7.9. Cell and stack cooling. 25 2.8. Microstructural analysis of porous electrodes and transport layers . 25 2.8.1. Exchange coefficients in porous multiphase electrodes . 25 2.8.2. Structural property analysis of composite electrodes . 26 2.8.3. Structural properties and performance of infiltrated electrodes . 27 2.8.4. Numerical reconstruction of electrode microstructures. 27 2.9. Overpotentials . 28 2.9.1. Activation overpotential . ..
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