Microstructure Simulation of Solid Oxide Fuel Cells under Carbon Deposition Using Phase-Field Modeling

Solid Oxide Fuel Cells (SOFCs) represent one of the most promising technologies for clean and efficient energy conversion due to their high efficiency and fuel flexibility [1]. However, carbon deposition, which can occur due to the reaction of hydrocarbons in the fuel within the anode, leads to significant reduction of durability. Understanding the mechanisms of carbon-induced degradation is critical for improving the long-term stability and performance of SOFCs. Currently, some studies have conducted experimental tests on the microstructure of anode under carbon deposition [2,3] or simulated the deformation of electrode materials under long-term operation [4-7], but there is still a lack of microstructure simulation considering carbon deposition reaction kinetics. In this study, we employed a phase-field modeling (PFM) approach to investigate the carbon evolution in the nickel-based anode and combined it with a one-dimensional transient elementary reaction kinetic model. The PFM model incorporates a set of coupled partial differential equations, which describe the growth and diffusion of carbon species in the anode material. The PFM model accounts for the interactions between the carbon and Ni-YSZ crystal grains, using a free energy functional that includes the bulk free energy and gradient energy. The time evolution of the system is governed by the time-dependent Ginzburg-Landau equation and Cahn-Hilliard equations. The kinetic model incorporates the coupling effect of heterogeneous elementary chemical and electrochemical reactions, the electrode microstructure and the charge and mass transport processes. The carbon deposition source term is calculated by the heterogeneous elementary chemical reactions using methane and water as fuels. Then to ensure the accuracy and reliability, the model is validated by experimental I-V curves. After validation, the size and distribution of carbon, the porosity of the anode, and the three phase boundary area can be analyzed under different temperatures and fuel compositions. This study provides valuable insights into the mechanisms of carbon-induced degradation in SOFCs and offers a predictive tool for optimizing operating conditions to enhance the long-term stability of SOFCs. References: [1] Faro M L, Antonucci V, Antonucci P L, et al. Fuel flexibility: A key challenge for SOFC technology[J]. Fuel, 2012, 102: 554-559. [2] Sciazko A, Komatsu Y, Nakamura A, et al. 3D microstructures of solid oxide fuel cell Ni-YSZ anodes with carbon deposition[J]. Chemical Engineering Journal, 2023, 460: 141680. [3] Wang R, Wang T, Ma Y, et al. Control of carbon deposition over methane-fueled SOFCs through tuning the O/C ratio at the anode/electrolyte interface[J]. Journal of Power Sources, 2022, 544: 231854. [4] Li Q, Liang L, Gerdes K, et al. Phase-field modeling of three-phase electrode microstructures in solid oxide fuel cells[J]. Applied Physics Letters, 2012, 101(3). [5] Vijay P, Tadé M O, Shao Z. Model based evaluation of the electrochemical reaction sites in solid oxide fuel cell electrodes[J]. International Journal of Hydrogen Energy, 2019, 44(16): 8439-8459. [6] Wang Y, Wu C, Du Q, et al. Morphology and performance evolution of anode microstructure in solid oxide fuel cell: A model-based quantitative analysis[J]. Applications in Energy and Combustion Science, 2021, 5: 100016. [7] Jiao Z, Shikazono N. Prediction of nickel morphological evolution in composite solid oxide fuel cell anode using modified phase field model[J]. Journal of The Electrochemical Society, 2018, 165(2): F55.