A comprehensive CFD model of anode-supported solid oxide fuel cells

The two-dimensional comprehensive CFD model of anode-supported SOFCs operating at intermediate temperature has been presented. This model provides transport phenomena of gas species with electrochemical characteristics and micro-structural properties, and predicts SOFC performance. The mathematical model solves conservation of electrons and ions, continuity equation, conservation of momentum, conservation of mass, and conservation of energy. A continuum micro-scale model based on statistical properties together with a mole-based conservation model was employed. CFD technique was used to solve the set of governing equations. The cell performance was decomposed with contributions of each overpotential and was presented at several operating temperatures with analysis of effective diffusivity. It was found that the contribution of potential gain due to temperature rising was considerably high. However it became non-significant at high operating temperature due to decreasing of effective diffusivity in AFL. These results showed that the performance and the distributions of current density, overpotentials, and mole fractions of gas species have a strong dependence upon temperature. From these results, it was concluded that the conservation of energy should be accommodated in comprehensive SOFC model. Also the useful information for the effect of parameters on cell performance and transport phenomena was provided.     

Mathematical Modelling of Proton‐Conducting Solid Oxide Fuel Cells and Comparison with Oxygen‐Ion‐Conducting Counterpart

Proton‐conducting solid oxide fuel cells (H‐SOFC), using a proton‐conducting electrolyte, potentially have higher maximum energy efficiency than conventional oxygen‐ion‐conducting solid oxide fuel cells (O‐SOFC). It is important to theoretically study the current–voltage (J–V) characteristics in detail in order to facilitate advanced development of H‐SOFC. In this investigation, a parametric modelling analysis was conducted. An electrochemical H‐SOFC model was developed and it was validated as the simulation results agreed well with experimental data published in the literature. Subsequently, the analytical comparison between H‐SOFC and O‐SOFC was made to evaluate how the use of different electrolytes could affect the SOFC performance. In addition to different ohmic overpotentials at the electrolyte, the concentration overpotentials of an H‐SOFC were prominently different from those of an O‐SOFC. H‐SOFC had very low anode concentration overpotential but suffered seriously from high cathode concentration overpotential. The differences found indicated that H‐SOFC possessed fuel cell characteristics different from conventional O‐SOFC. Particular H‐SOFC electrochemical modelling and parametric microstructural analysis are essential for the enhancement of H‐SOFC performance. Further analysis of this investigation showed that the H‐SOFC performance could be enhanced by increasing the gas transport in the cathode with high porosity, large pore size and low tortuosity.     

Microscale Modeling of an Anode‐Supported Planar Solid Oxide Fuel Cell

A microscale model of a solid oxide fuel cell (SOFC) involving the mass transfer together with the electrochemical reaction, the transportation of electrons and ions through the respective spherical shaped electron conducting and ion conducting particles inside the electrodes was mathematically developed. Couples of useful parameters were introduced in order to represent the characteristics of the cell. The predicted cell performance was showed according to various operating and design conditions. The effects of microscale electrode geometry on the cell performance were also taken into account. Parametric study according to the volumetric fraction of ionic and electronic conducting particles was conducted in order to examine the effects of operating conditions on the cell overpotentials. The study results substantiate the fact that SOFC overpotential could be effectively decreased by increasing the operating temperature as well as operating pressure. This present study reveals the working mechanisms of SOFC at the microscale level, while demonstrating the use of microscale relations to enhance the SOFC performance. The accuracy of the presented model was validated by comparing with already existing experimental results from the available literatures.     

Using electrochemical impedance spectroscopy to compensate for errors when measuring polarisation curves during three-electrode measurements of solid oxide fuel cell electrodes

The use of three-electrode techniques involving an independent reference electrode is invaluable in determining the overpotential losses at solid oxide fuel cell (SOFC) electrodes. However, there are numerous barriers to achieve the accurate measurement of such overpotentials in an SOFC. Furthermore electrochemical impedance spectroscopy (EIS) is commonly used to analyse the processes occurring on SOFC electrodes, and there has been considerable work in establishing viable three-electrode techniques for EIS experiments under open circuit conditions. However, the three-electrode techniques currently developed for EIS experiments are not well suited for conditions of high load, or changing gas compositions; either intentionally or under diffusion limiting conditions. This paper reports a solution for commonly used pellet cells, which mitigates these problems. The paper presents a method using EIS to correct for errors when measuring the working electrode overpotential during polarisation arising from a shift in the electrolyte current distribution from the primary to the secondary current distribution under load. This technique enables meaningful overpotentials to be calculated using experimentally simple cell geometries under conditions where they cannot normally be accurately measured.     

Electrochemical membranes: transport limitations for absorbed gases

The physics of a gas diffusion electrode–membrane cell is discussed and comparisons are made with experimental data. In particular, a second order expansion has been used to correlate the maximum current density data, valid for both small to large overpotentials and electrode specific surface areas. It is also demonstrated that the limiting or maximum current density for the diffusion limit can be predicted by assuming simple molecular diffusion across the membrane and the ion reference (open circuit) concentration in the cathode. An expression is also developed to account for differences in reactant gas concentrations and flowrates between reference and normal operating conditions. Comparisons are made between the theory and maximum current data for the absorption of H2S, CO2 and SO2. These comparisons suggest that the current density limitations of the cell are affected by electrochemical reaction rates on the cathode surface. Other possible limitations for electrochemical cell performance are discussed.     

管式固体氧化物燃料电池机理模型与性能分析

针对Siemens-Westinghouse公司阴极支撑型(AES)管式固体氧化物燃料电池,耦合电极内部离子传导、电子传导、气体扩散、热量传递及电化学反应过程,建立了全面考虑活化极化、欧姆极化与浓差极化损失的管式SOFC横截面方向二维微观机理模型。模型计算结果与文献中实验数据吻合较好,模拟结果表明：电池横截面方向的组分浓度和电流密度的分布与SOFC的运行工况密切相关。连接器的存在和尺寸对电池工作性能均有较强影响。对于所研究的阴极支撑型SOFC,电池性能会受到氧气在多孔阴极中扩散过程的限制,改善多孔电极的微观结构可有效提高电池运行性能。     

Current and voltage distributions in a tubular solid oxide fuel cell (SOFC)

One of the major obstacles to improving electrochemical performance of SOFCs is the limitation with respect to current collecting. The aim of this study is to examine these limitations on the basis of a model of a single cell of tubular SOFC. The simulation results allow us to understand and analyze the effects of ionic and electronic ohmic drops on cell performance. This paper describes a model using the CFD-Ace software package to simulate the behaviour of a tubular SOFC. Modelling is based on solving conservation equations of mass, momentum, energy, species and electric current by using a finite volume approach on 3D grids of arbitrary topology. The electrochemistry in the porous gas diffusion electrode is described using Butler-Volmer equations at the triple phase boundary. The electrode overpotential is computed at each spatial location within the catalyst layer by separately solving the electronic and ionic electric potential equations. The 3D presentation of the current densities and the electronic and ionic potentials allows analysis of the respective ohmic drops. The simulation results show that the principal limitations are at the cathodic side. The limitations due to ionic ohmic drops, classically considered to be the main restrictions, are confirmed. The particular interest of our study is that it also shows that, because of the cylindrical geometry, there is a significant electronic ohmic drop.     

Effects of Microstructural Functional Layers on Flat‐Tubular Solid Oxide Fuel Cells

The functional layer of a flat‐tubular solid oxide fuel cell (SOFC) is examined using a three‐dimensional microscale electrode model. SOFC electrodes essentially include two types of layers: a structural layer and a functional layer. The structural layers, which are the anode support layer and the cathode current collector layer, are composed of large particles with a high porosity that facilitates gas diffusion. The functional layers consist of small particles with a low porosity that increases the triple phase boundary (TPB) reaction area and reduces the activation overpotential. In the model, the particle diameter and functional layer thickness are adjusted and analyzed. The effects of the two parameters on the performance of the functional layer are monitored in the contexts of several multilateral approaches. Most reactions occurred near the electrode–electrolyte interface; however, an electrode design that included additional TPB areas improved the electrode performance. The role of the functional layer in a flat‐tubular SOFC is examined as a function of the functional layer particle size and thickness. The performance of a cell could be enhanced by preparing a functional layer using particles of optimal size and thickness, and by operating the device under conditions optimized for these parameters.     

Experimental and Analytical Study of an Anode-Supported Solid Oxide Electrolysis Cell

A 1-D electrochemical model for a solid oxide electrolysis cell (SOEC) is developed and validated using published experimental data. The model combines thermodynamics, kinetic, ohmic, and concentration overpotentials to predict cell performance. For the anode-supported SOEC, good agreement is obtained between the model and experimental data, with ohmic loss being the major contributor to the cell's total overpotential. Both kinetic and concentration losses are less significant due to high-temperature operation. Due to the dominating performance loss, reducing the anode thickness is effective in diminishing the cell potential. Overall, this simple 1-D model can be employed as a design tool to evaluate component design and estimate system performance for industrial applications.     

Modeling and experimental validation of overpotentials of a direct ethanol fuel cell

Direct ethanol fuel cell (DEFC) is a promising power source for future use in portable electronic equipments. In general, the power density obtained in DEFC is lower than that of direct methanol fuel cell. In the present study, various losses in DEFC are estimated by performing experiments with the prepared membrane electrode (MEA) to obtain current–voltage characteristics and comparing it with the prediction of mathematical model. MEA for the DEFC is prepared using Pt–Ru (40:20 by wt.%)/C as anode catalyst, Pt–black as cathode catalyst with 1 mg/cm² of loadings and cast Nafion^® (SE5112, DuPont) ionomer as proton exchange membrane. The mathematical model for DEFC is developed considering different overpotentials. The activation overpotential term is formulated considering ethanol electrooxidation mechanism proposed in literature and Butler–Volmer equation. The ohmic overpotential is modeled based on proton conductivity of Nafion^® membrane and ohmic losses at the electrodes, current collectors and electrode–current collector interfaces. The concentration overpotential is formulated using Fick's law, modified Butler–Volmer equation and transport process through electrodes and electrocatalyst layers. The experiment data on current–voltage characteristics is predicted by the model with reasonable agreement and the influence of ethanol concentration and temperature on the performance of DEFC is captured by the model.     

An evaluation of the macro-homogeneous and agglomerate model for oxygen reduction in PEMFCs

The kinetics of oxygen reduction reaction on platinum/carbon powders in a Nafion film were evaluated with rotating disk electrode and gas diffusion electrode. The effects of the activation, mass transport and ohmic overpotentials were simulated via an “effectiveness factor” approach. The macro-homogeneous model was suitable to simulate the ORR kinetics at the RDE. On the other hand, it was found that the macro-homogeneous model does not simulate the operation of a porous gas diffusion cathode in PEMFC. With this model, the diffusion overpotential in the cathode is considerably overestimated. Conversely, the good agreement between calculated and experimental Tafel plots demonstrates the validity of the agglomerate model, even though the active layers of the PEMFC electrodes were thin and contained no PTFE. These results provided evidence for a two step transport process in the active layer of PEMFC electrodes.     

Mathematical modeling of solid oxide fuel cells at high fuel utilization based on diffusion equivalent circuit model

Mass transfer and electrochemical phenomena in the membrane electrode assembly (MEA) are the core components for modeling of solid‐oxide fuel cell (SOFC). The general MEA model is simply governed with the Stefan‐Maxwell equation for multicomponent gas diffusion, Ohm's law for the charge transfer and the current‐overpotential equation for the polarization calculation. However, it has obvious discrepancy at high‐fuel utilization or high‐current density. An advanced MEA model is introduced based on the diffusion equivalent circuit model. The main purpose is to correct the real‐gas concentrations at the triple‐phase boundary by assuming that the resistance of surface diffusion is in series with that of the gaseous bulk diffusion. Thus, it can obtain good prediction of cell performance in a wide range by avoiding the decrement of effective gas diffusivity via unreasonable increment of the electrode tortuosity in the general MEA model. The mathematical model has been validated in the cases of H₂? H₂O, CO? CO₂ and H₂? CO fuel system. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

An Electrochemical Model of a Solid Oxide Steam Electrolyzer for Hydrogen Production

An electrochemical model was developed to simulate the J–V characteristics of a solid oxide steam electrolyzer (SOSE) used for hydrogen production. Activation, concentration, and ohmic overpotentials were considered as the main factors for voltage loss. The Butler‐Volmer equation, Fick's model, and Ohm's law were applied to determine the overpotentials of a SOSE cell. The simulation results were compared with experimental data from the literature and good agreement was obtained. Additionally, parametric modeling analyses were conducted to study how the operating temperature and gas composition affected the electrical characteristics. It was found that the voltage loss could be reduced by increasing the operating temperature and steam molar fraction. It was also observed that an anode‐supported SOSE cell exhibited a higher hydrogen production efficiency than electrolyte‐supported and cathode‐supported cells. The electrochemical model can be used to perform further analysis in order to further understand the principles of SOSE hydrogen production, and to optimize SOSE cell and system designs.     

Mathematical modeling of the coupled transport and electrochemical reactions in solid oxide steam electrolyzer for hydrogen production

A mathematical model was developed to simulate the coupled transport/electrochemical reaction phenomena in a solid oxide steam electrolyzer (SOSE) at the micro-scale level. Ohm's law, dusty gas model (DGM), Darcy's law, and the generalized Butler Volmer equation were employed to determine the transport of electronic/ionic charges and gas species as well as the electrochemical reactions. Parametric analyses were performed to investigate the effects of operating parameters and micro-structural parameters on SOSE potential. The results substantiated the fact that SOSE potential could be effectively decreased by increasing the operating temperature. In addition, higher steam molar fraction would enhance the operation of SOSE with lower potential. The effect of particle sizes on SOSE potential was studied with due consideration on the SOSE activation and concentration overpotentials. Optimal particle sizes that could minimize the SOSE potential were obtained. It was also found that decreasing electrode porosity could monotonically decrease the SOSE potential. Besides, optimal values of volumetric fraction of electronic particles were found to minimize electrode total overpotentials. In order to optimize electrode microstructure to minimize SOSE electricity consumption, the concept of “functionally graded materials (FGM)” was introduced to lower the SOSE potential. The advanced design of particle size graded SOSE was found effective for minimizing electrical energy consumption resulting in efficient SOSE hydrogen production. The micro-scale model was capable of predicting SOSE hydrogen production performance and would be a useful tool for design optimization.     

电沉积方法制备镍硫析氢电极及其电化学性能

采用恒电流电沉积方法制备Ni-S电极,通过极化曲线研究了硫脲质量浓度、电流密度、镀液温度、电沉积时间等对Ni-S电极析氢性能的影响,获得了较佳的制备工艺:NiSO4·6H2O187.2g/L,硫脲100g/L,H3BO340g/L,NaCl 20g/L,pH=4,电流密度30 mA/cm2,镀液温度55℃和电沉积时间1...     

Numerical Investigation into Thermofluidic and Electrochemical Characteristics of Tubular‐type SOFC

Three‐dimensional simulations based on a multi‐physics model are performed to examine the thermofluidic and electrochemical characteristics of a tubular, anode‐supported solid oxide fuel cell (SOFC). The simulations focus on the local transport characteristics of the cathode and anode gases and the distribution of the temperature field within the fuel cell. In addition, the electrochemical properties of the SOFC are systematically examined for a representative range of inlet gas temperatures and pressures. The validity of the numerical model is confirmed by comparing the results obtained for the correlation between the power density and the current density with the experimental results presented in the literature. Overall, the present results show that the performance of the tubular SOFC is significantly improved under pressurised conditions and a higher operating temperature.     

Three‐Dimensional Computational Fluid Dynamics Modeling of a Planar Solid Oxide Fuel Cell

A three‐dimensional computational fluid dynamics model was developed to study the performance of a planar solid oxide fuel cell (SOFC). The governing equations were solved with the finite volume method. The model was validated by comparing the simulation results with data from literature. Parametric simulations were performed to investigate the coupled heat/mass transfer and electrochemical reactions in a planar SOFC. Different from previous two‐dimensional studies the present three‐dimensional analyses revealed that the current density was higher at the center along the flow channel while lower under the interconnect ribs, due to slower diffusion of gas species under the ribs. The effects of inlet gas flow rate and electrode porosity on SOFC performance were examined as well. The analyses provide a better understanding of the working mechanisms of SOFCs. The model can serve as a useful tool for SOFC design optimization.     

Modeling of a Tubular‐SOFC: The Effect of the Thermal Radiation of Fuel Components and CO Participating in the Electrochemical Process

A mathematical model based on first principles is developed to study the effect of heat and electrochemical phenomena on a tubul solid oxide fuel cell (SOFC). The model accounts fordiffusion, inherent impedance, transport (momentum, heat and mass transfer) processes, internal reforming/shifting reaction, electrochemical processes, and potential losses (activation, concentration, and ohmic losses). Thermal radiation of fuel gaseous components is considered in detail in this work in contrast to other reported work in the literature. The effect of thermal radiation on SOFC performance is shown by comparing with a model without this factor. Simulation results indicate that at higher inlet fuel flow pressures and also larger SOFC lengths the effect of thermal radiation on SOFC temperature becomes more significant. In this study, the H₂ and CO oxidation is also studied and the effect of CO oxidation on SOFC performance is reported. The results show that the model which accounts for the electrochemical reaction ofCO results in better SOFC performance than other reported models. This work also reveals that at low inlet fuel flow pressures the CO and H₂ electrochemical reactions are competitive and significantly dependent on the CO/H₂ ratio inside the triple phase boundary.     

A validated multi‐scale model of a SOFC stack at elevated pressure

This paper presents a multi‐scale model of a solid oxide fuel cell (SOFC) stack consisting of five anode‐supported cells. A two‐dimensional isothermal elementary kinetic model is used to calculate the performance of single cells. Several of these models are thermally coupled to form the stack model. Simulations can be carried out at steady‐state as well as dynamic operation. The model is validated over a wide range of operating conditions including variation of temperature, gas composition (both on anode and cathode side), and pressure. Validation is carried out using polarization curves and impedance spectra. The model is then used to explain the pressure‐induced performance increase measured at constant fuel utilization of 40%. Results show that activation and concentration overpotentials are reduced with increasing pressure.     

Isothermal models for anode-supported tubular solid oxide fuel cells

Modeling of solid oxide fuel cells (SOFCs) has gained considerable significance in recent years. A detailed phenomenological model for SOFC can be used to understand performance limitations, optimization, in situ diagnostics and control. In this paper, we study the transport and various electrochemical phenomena in an anode-supported tubular SOFC using a steady-state model. In particular, we discuss the importance of modeling different phenomena vis-a-vis their impact on the prediction capability of the model. It is observed that even a reasonably simple model can be sufficiently predictive in a particular operating range. As the operating range of the cell is increased, the predictive capability of a model validated in a narrow range cannot be guarantied. It has also been observed that neglecting momentum conservation in the model for a tubular SOFC can affect the predictive capability of the model at higher overpotentials. An extensively validated model is used to study the percentage conversion of oxygen and oxygen concentration profile within a cell at different operating conditions. All of the simulation studies are supported by experimental data that spans a wide range of operation in terms of the DC polarization, reactant flow rates and operating temperatures.