Quantitative evaluation of solid oxide fuel cell porous anode microstructure based on focused ion beam and scanning electron microscope technique and prediction of anode overpotentials

A three-dimensional microstructure of a solid oxide fuel cell (SOFC) anode is directly observed by a focused ion beam and scanning electron microscope (FIB-SEM) technique. Microstructural parameters, which are closely related to transport phenomena and electrochemical reaction in a porous anode, are quantitatively evaluated, such as volume fraction, percolation probability, tortuosity factor, surface-to-volume ratio, and three-phase boundary density. A random-walk-based diffusion simulation is effectively used for quantification. As an application of the quantified parameters, 1D numerical simulation of a SOFC anode is conducted. The predicted anode overpotential agrees well with the experimental counterparts in the condition of 3.0% H₂O-97% H₂, 1273 K, while it is overestimated at high humidified and low temperature conditions.     

Pore-scale investigation of mass transport and electrochemistry in a solid oxide fuel cell anode

The development and validation of a model for the study of pore-scale transport phenomena and electrochemistry in a Solid Oxide Fuel Cell (SOFC) anode are presented in this work. This model couples mass transport processes with a detailed reaction mechanism, which is used to model the electrochemical oxidation kinetics. Detailed electrochemical oxidation reaction kinetics, which is known to occur in the vicinity of the three-phase boundary (TPB) interfaces, is discretely considered in this work. The TPB regions connect percolating regions of electronic and ionic conducting phases of the anode, nickel (Ni) and yttria-stabilized zirconia (YSZ), respectively; with porous regions supporting mass transport of the fuel and product. A two-dimensional (2D), multi-species lattice Boltzmann method (LBM) is used to describe the diffusion process in complex pore structures that are representative of the SOFC anode. This diffusion model is discretely coupled to a kinetic electrochemical oxidation mechanism using localized flux boundary conditions. The details of the oxidation kinetics are prescribed as a function of applied activation overpotential and the localized hydrogen and water mole fractions. This development effort is aimed at understanding the effects of the anode microstructure within TPB regions. This work describes the methods used so that future studies can consider the details of SOFC anode microstructure.     

Modeling of gas transport through a tubular solid oxide fuel cell and the porous anode layer

A design model is a necessary tool to understand the gas transport phenomena that occurs in a tubular solid oxide fuel cell (SOFC). This paper describes a computational model, which studies the gas flow through an anode-supported tubular SOFC and the subsequent diffusion of gas through its porous anode. The model is a numerical solution for the gas flow through a plug flow reactor with a diffusion layer, which includes the activation, ohmic, and concentration polarizations. Gas diffusion is modeled using the dusty-gas equations which include Knudsen diffusion. Mercury intrusion porosimetry (MIP) is used to experimentally determine micro-structural parameters such as porosity, tortuosity and effective diffusion coefficients, which are used in the diffusion equations for the porous anode layer. It was found that diffusion in the anode plays a key role in the performance of a tubular SOFC. The concentration gradient of hydrogen and water results in a lower concentration of hydrogen and a higher concentration of water at the reactive triple phase boundary (TPB) than in the fuel stream which both lead to a lower cell voltage. The gas diffusion determines the limiting current density of the cell where a higher concentration drop of hydrogen results in a lower limiting current density. The model validates well with experimental data and is used to improve micro-tubular solid oxide fuel cell designs.     

Two-dimensional numerical study of temperature field in an anode supported planar SOFC: Effect of the chemical reaction

In the present work the effect of the chemical reaction on the temperature field in an anode supported planar SOFC is numerically studied by the aid of a two-dimensional mathematical model. For the model development the mass transport phenomena, the energy conservation, the species flow governed by Darcy’s law and the electrochemistry are coupled. The finite difference method is used to solve numerically the system of the equations.The temperature field within each component of the SOFC (interconnection, cathode, anode and electrolyte) is calculated via the mathematical model which is implemented in FORTRAN language. The model results demonstrate the effect of different expressions of the chemical heat source, expressed in terms of enthalpy and entropy, on the temperature field and the location of the higher temperatures that occur within the SOFC during its operation.     

Micro-scale modelling of solid oxide fuel cells with micro-structurally graded electrodes

A mathematical model was developed for modelling the performance of solid oxide fuel cell (SOFC) with functionally graded electrodes at the micro-scale level. The model considered all forms of overpotentials and was able to capture the coupled electrochemical reactions and mass transfer involved in the SOFC operation. The model was validated by comparing the simulation results with experimental data from the literature. Additional modelling analyses were conducted to gain better understanding of the SOFC working mechanisms at the micro-scale level and to quantify the performance of micro-structurally graded SOFC. It was found that micro-structural grading could significantly enhance the gas transport but had negligible effects on the ohmic and activation overpotentials, especially for thick electrodes. However, for thin electrodes with large particles, too much grading should be avoided as the increased activation overpotentials may result in higher overall overpotentials at a medium or low current density. Among all the cases tested in the present study, the micro-structurally graded SOFC showed significantly higher power density than conventional SOFC of uniform porosity and particle size. The difference between micro-structurally graded SOFC and conventional SOFC is more pronounced for smaller electrode–electrolyte (EE) interfacial particles. Particle size grading is generally more effective than porosity grading and it can increase the maximum power density by one-fold in comparison with conventional SOFC. The present study reveals the working mechanisms of SOFC at the micro-scale level and demonstrates the promise of the use of micro-structural grading to enhance the SOFC performance.     

Modeling of a planar solid oxide fuel cell based on proton‐conducting electrolyte

A 2D computational fluid dynamics (CFD) model is developed to study the performance of an advanced planar solid oxide fuel cell based on proton conducting electrolyte (SOFC‐H). The governing equations are solved with the finite volume method (FVM). Simulations are conducted to understand the transport phenomena and electrochemical reaction involved in SOFC‐H operation as well as the effects of operating/structural parameters on SOFC‐H performance. In an SOFC based on oxygen ion conducting electrolyte (SOFC‐O), mass is transferred from the cathode side to the anode side. While in an SOFC‐H, mass is transferred from the anode to the cathode, which causes different velocity fields of the fuel and oxidant gas channels and influences the distributions of temperature and gas composition in the cell. It is also found that increasing the inlet gas velocity leads to an increase in the local current density and a slight decrease in the SOFC‐H temperature due to stronger cooling effect of the gas species at a higher velocity. Another finding is that the electrode structure does not significantly affect the heat and mass transfer in an SOFC‐H at typical operating voltages. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of different current collecting modes of anode supported micro-tubular SOFC through mathematical modeling

A two-dimensional model comprising fuel channel, anode, cathode and electrolyte layers for anode-supported micro-tubular solid oxide fuel cell (SOFC), in which momentum, mass and charge transport are considered, has been developed. By using the model, tubular cells operating under three different modes of current collection, including inlet current collector (IC), outlet current collector (OC) and both inlet and outlet collector (BC), are proposed and simulated. The transport phenomena inside the cell, including gas flow behavior, species concentration, overpotential, current density and current path, are analyzed and discussed. The results depict that the model can well simulate the diagonal current path in the anode. The current collecting efficiency as a function of tube length is obtained. Among the three proposed modes, the BC mode is the most effective mode for a micro-tubular SOFC, and the IC mode generates the largest current density variation at z-direction.     

Physics-based modeling of a low-temperature solid oxide fuel cell with consideration of microstructure and interfacial effects

The main objective of this paper is to develop a physical model for the simulation of heat/mass transport and electrochemical process in a solid oxide fuel cell. The model is then used to evaluate the effects of lowering the operating temperature for a solid oxide fuel cell. This model consists of two submodels, i.e., a micro-scale submodel and a macro-scale submodel. The macro-scale submodel is based on the continuum conservation laws. The micro-scale submodel addresses the complex relationships among the transport phenomena in the electrodes and electrolyte, which includes the transport of electron, ion, and gas molecules through the composite electrodes, electrolyte, and triple-phase boundary region. After integrating the two submodels, the dependence of electrochemical performance on the temperature, global geometrical parameter, and microstructures (porosity, volume fraction and composite ratio, etc.) were assessed.Results demonstrate that for a reduced-temperature solid oxide fuel cell with composite electrodes, its performance is also lowered due to a higher ohmic loss in electrolyte and a slower electrochemical kinetics in the cathode. Among the various microstructure parameters for electrodes, the particle size and TPB length are the most important factors that dominate the performance of a reduced-temperature SOFC. In addition, optimal thicknesses for the electrodes exist. It is believed that the current work will provide a valuable model approach, which can be used to help understand the complex transport phenomena in electrodes and optimize the design of a reduced-temperature solid oxide fuel cell.     

Numerical modeling and parametric analysis of solid oxide fuel cell button cell testing process

In laboratory studies of solid oxide fuel cell (SOFC), performance testing is commonly conducted upon button cells because of easy implementation and low cost. However, the comparison of SOFC performance testing results from different labs is difficult because of the different testing procedures and configurations used. In this paper, the SOFC button cell testing process is simulated. A 2‐D numerical model considering the electron/ion/gas transport and electrochemical reactions inside the porous electrodes is established, based on which the effects of different structural parameters and configurations on SOFC performance testing results are analyzed. Results show that the vertical distance (H) between the anode surface and the inlet of the anode gas channel is the most affecting structure parameter of the testing device, which can lead to up to 18% performance deviation and thus needs to be carefully controlled in SOFC button cell testing process. In addition, the current collection method and the configuration of gas tubes should be guaranteed to be the same for a reasonable and accurate comparison between different testing results. This work would be helpful for the standardization of SOFC button cell testing.     

DMFC performance and methanol cross-over: Experimental analysis and model validation

A combined experimental and modelling approach is proposed to analyze methanol cross-over and its effect on DMFC performance. The experimental analysis is performed in order to allow an accurate investigation of methanol cross-over influence on DMFC performance, hence measurements were characterized in terms of uncertainty and reproducibility. The findings suggest that methanol cross-over is mainly determined by diffusion transport and affects cell performance partly via methanol electro-oxidation at the cathode. The modelling analysis is carried out to further investigate methanol cross-over phenomenon. A simple model evaluates the effectiveness of two proposed interpretations regarding methanol cross-over and its effects. The model is validated using the experimental data gathered. Both the experimental analysis and the proposed and validated model allow a substantial step forward in the understanding of the main phenomena associated with methanol cross-over. The findings confirm the possibility to reduce methanol cross-over by optimizing anode feeding.     

Elementary reaction kinetic model of an anode-supported solid oxide fuel cell fueled with syngas

In this paper, a detailed one-dimension transient elementary reaction kinetic model of an anode-supported solid oxide fuel cell (SOFC) operating with syngas based on button cell geometry is developed. The model, which incorporates anodic elementary heterogeneous reactions, electrochemical kinetics, electrodes microstructure and complex transport phenomena (momentum, mass and charge transport) in positive electrode|electrolyte|negative electrode (PEN), is validated with experimental performance for various syngas compositions at 750, 800 and 850 °C. The comparisons show that the simulation results agree reasonably well with the experimental data. Then the model is applied to analyze the effects of temperature and operation voltage on polarizations in each component of PEN, electronic current density in both electrodes and species concentrations distributions in anode. The numerical results of carbon deposition simulation indicate that higher temperature and lower operation voltage are helpful to reduce the possibility of carbon deposition on Ni surfaces by Bouduard reactions. Furthermore, a sensitivity analysis of cell performance on syngas composition is performed for the typical syngas from entrained-flow coal gasifier and natural methane thermochemical reforming processes. The cell performance increases with the increasing of effective compositions (e.g. H₂ and CO) in syngas and the large N₂ content introduced by using air as oxidant leads to significant deterioration of performance.     

Effect of characteristic lengths of electron,ion, and gas diffusion on electrode performance and electrochemical reaction area in a solid oxide fuel cell

A precise evaluation of the active reaction zone in the electrodes is important to design an effective solid oxide fuel cell (SOFC). A scale analysis and one‐dimensional numerical simulations are conducted to obtain a better understanding of the electrochemical reaction zone in a SOFC anode. In the scale analysis, the characteristic lengths of the electron, oxide ion, and gas transports are evaluated from their conservation equations. Relative comparisons of the characteristic lengths show that the transport phenomena in the SOFC anode are primarily governed by the oxide‐ion conduction under standard operating conditions. The gas diffusion may affect the extent and the location of the active reaction zone at high temperature and/or low reaction gas concentration conditions. The one‐dimensional numerical simulations for an anode provided detailed information such as the electric potential of electron‐ and ion‐conducting phases, the gas concentration, and local charge‐transfer current distributions. It is found that the electrochemical reaction actively occurs in the vicinity of the anode–electrolyte interface. The effective thickness increases as the characteristic length of the ion conduction is increased resulting in better power generation performance. The effective thickness is also increased when the gas‐diffusion length is short. The cell performance is, however, lowered in this case because the low gas diffusivity yields the increase of the ohmic loss of ion conduction as well as the concentration overpotential. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20373     

Modeling of two-phase transport in the diffusion media of polymer electrolyte fuel cells

A three-dimensional model of polymer electrolyte fuel cells (PEFCs) is developed to investigate multiphase flows, species transport, and electrochemical processes in fuel cells and their interactions. This two-phase model consists of conservation principles of mass, momentum, species concentration and charges, and elucidates the key physicochemical mechanisms in the constituent components of PEFCs that govern cell performance. Efforts are made to formulate two-phase transport in the anode diffusion media and its coupling with cathode flooding as well as the interaction between single- and two-phase flows. Numerical simulations are carried out to investigate multiphase flow, electrochemical activity, and transport phenomena and the intrinsic couplings of these processes inside a fuel cell at low humidity. The results indicate that multiphase flows may exist in both anode and cathode diffusion media at low-humidity operation, and two-phase flow emerges near the outlet for co-flow configuration while is present in the middle of the fuel cell for counter-flow one. The validated numerical tools can be applied to investigate vital issues related to anode performance and degradation arising from flooding for PEFCs.     

Mechanistic modelling of a cathode-supported tubular solid oxide fuel cell

A two-dimensional mechanistic model of a tubular solid oxide fuel cell (SOFC) considering momentum, energy, mass and charge transport is developed. The model geometry of a single cell comprises an air-preheating tube, air channel, fuel channel, anode, cathode and electrolyte layers. The heat radiation between cell and air-preheating tube is also incorporated into the model. This allows the model to predict heat transfer between the cell and air-preheating tube accurately. The model is validated and shows good agreement with literature data. It is anticipated that this model can be used to help develop efficient fuel cell designs and set operating variables under practical conditions. The transport phenomena inside the cell, including gas flow behaviour, temperature, overpotential, current density and species concentration, are analysed and discussed in detail. Fuel and air velocities are found to vary along flow passages depending on the local temperature and species concentrations. This model demonstrates the importance of incorporating heat radiation into a tubular SOFC model. Furthermore, the model shows that the overall cell performance is limited by O₂ diffusion through the thick porous cathode and points to the development of new cathode materials and designs being important avenues to enhance cell performance.     

Continuum-level solid oxide electrode constriction resistance effects

Continuum-level mass and electronic transport through solid oxide cell electrodes, inclusive of ribbed interconnects, are modeled employing analytical solutions of the 2D Laplace equation. These analytical solutions describe localized mass and electronic transport phenomena in solid oxide fuel cell (SOFC) anodes and localized mass transport phenomena in SOFC cathodes. Two-dimensional constriction resistance effects created by reductions in active transport area are shown to significantly increase internal cell resistances by increasing transport path lengths within a cross-sectional region of the cell. Furthermore, these effects can alter cell performance with respect to fuel depletion phenomena and create a competition of losses between mass and electronic transport resistances. Fuel depletion is shown to occur at a current density lower than the traditionally defined limiting current density. An analytical expression for this fuel depletion current density is proposed based upon the models developed. The competition between mass transfer and electronic resistance effects arising from solid oxide cell interconnect geometry is also characterized through parametric studies based on a design of experiments (DOEs) approach. These studies demonstrate the benefits of smaller SOFC unit cell geometry.     

A simple electric circuit model for proton exchange membrane fuel cells

A simple and novel dynamic circuit model for a proton exchange membrane (PEM) fuel cell suitable for the analysis and design of power systems is presented. The model takes into account phenomena like activation polarization, ohmic polarization, and mass transport effect present in a PEM fuel cell. The proposed circuit model includes three resistors to approach adequately these phenomena; however, since for the PEM dynamic performance connection or disconnection of an additional load is of crucial importance, the proposed model uses two saturable inductors accompanied by an ideal transformer to simulate the double layer charging effect during load step changes. To evaluate the effectiveness of the proposed model its dynamic performance under load step changes is simulated. Experimental results coming from a commercial PEM fuel cell module that uses hydrogen from a pressurized cylinder at the anode and atmospheric oxygen at the cathode, clearly verify the simulation results.     

Micro modeling of solid oxide fuel cell anode based on stochastic reconstruction

A novel modeling scheme of SOFC anode based on the stochastic reconstruction technique and the Lattice Boltzmann Method (LBM) is proposed and applied to the performance assessment and also to the optimization of anode microstructures. A cross-sectional microscopy image is exploited to obtain a two-dimensional phase map (i.e., Ni, YSZ and pore), of which two-point correlation functions are used to reconstruct a three-dimensional model microstructure. Then, the polarization resistance of the reconstructed anode is obtained by the LBM simulation. The predicted anodic polarization resistance for a given microstructure and its sintering temperature dependence are in good agreement with the literature data. Three-dimensional distributions of potential and current can be obtained, while and the effect of working temperature is discussed. The proposed method is considered as a promising tool for designing SOFC anodes.     

Numerical modelling of methane-powered micro-tubular, single-chamber solid oxide fuel cell

An experimentally validated, two-dimensional, axisymmetric, numerical model of micro-tubular, single-chamber solid oxide fuel cell (MT-SC-SOFC) has been developed. The model incorporates methane full combustion, steam reforming, dry reforming and water-gas shift reaction followed by electrochemical oxidation of produced hydrogen within the anode. On the cathode side, parasitic combustion of methane along with the electrochemical oxygen reduction is implemented. The results show that the poor performance of single-chamber SOFC as compared to the conventional (dual-chamber) SOFC (in case of micro-tubes) is due to the mass transport limitation on the anode side. The gas velocity inside the micro-tube is far too low when compared to the gas-chamber inlet velocity. The electronic current density is also non-uniform over the cell length, mainly due to the short length of the anode current collector located at the cell outlet. Furthermore, the higher temperature near the cell edges is due to the methane combustion (very close to the cell inlet) and current collection point (at the cell outlet). Both of these locations could be sensitive to the silver current collecting wire as silver may rupture due to cell overheating.     

Review on modeling development for multiscale chemical reactions coupled transport phenomena in solid oxide fuel cells

A literature study is performed to compile the state-of-the-art, as well as future potential, in SOFC modeling. Principles behind various transport processes such as mass, heat, momentum and charge as well as for electrochemical and internal reforming reactions are described. A deeper investigation is made to find out potentials and challenges using a multiscale approach to model solid oxide fuel cells (SOFCs) and combine the accuracy at microscale with the calculation speed at macroscale to design SOFCs, based on a clear understanding of transport phenomena, chemical reactions and functional requirements. Suitable methods are studied to model SOFCs covering various length scales. Coupling methods between different approaches and length scales by multiscale models are outlined. Multiscale modeling increases the understanding for detailed transport phenomena, and can be used to make a correct decision on the specific design and control of operating conditions. It is expected that the development and production costs will be decreased and the energy efficiency be increased (reducing running cost) as the understanding of complex physical phenomena increases. It is concluded that the connection between numerical modeling and experiments is too rare and also that material parameters in most cases are valid only for standard materials and not for the actual SOFC component microstructures.