Design for segmented-in-series solid oxide fuel cell through mathematical modeling

The segmented-in-series solid oxide fuel cell comprising fuel channel, anode, cathode and electrolyte layers has been evaluated by developing a two-dimensional model, in which the equations have been solved numerically through finite element methods. The results indicate that the voltage of each membrane electrode assembly (MEA) exhibits a parabola-like curve and is higher than the appointed voltage of unit cell (0.7 V). From fuel inlet to outlet, the voltage of each MEA deceases due to the decreasing local H₂ concentration. When both the interconnector and electrolyte gap lengths are fixed, the cell module with 5 mm long anode gives the maximal power density for the SS-SOFC. Higher power densities can be achieved through increasing the cathode thickness.     

Monte-Carlo simulation and performance optimization for the cathode microstructure in a solid oxide fuel cell

A 3D micro-scale model is developed to simulate the transport and electrochemical reaction in a composite cathode. This model takes into account the details of the specific cathode microstructure such as random pore structure, active TPB (three phase boundary) site distribution, particle size and composition and their interrelationship to the charge transfer and mass transport processes. Especially, the pore structure and mass diffusion were incorporated into this model. Influence of the microsturcture parameters on the performance was investigated by numerical simulations.     

An error in solid oxide fuel cell stack modeling

This paper points out an error in the literature and analyzes its effect on electrochemical models of solid oxide fuel cell stacks. A correction is presented.     

Thermal stress modeling of anode supported micro-tubular solid oxide fuel cell

An anode-supported micro-tubular solid oxide fuel cell (SOFC) is analyzed by a two-dimensional axisymmetric numerical model, which is validated with the experimental I-V data. The temperature distribution generated by the thermo-electrochemical model is used to calculate the thermal stress field in the tubular SOFC. The results indicate that the current transport in the anode is the same at every investigated position. The stress of the micro-tubular cell occurs mainly because of the residual stress due to the mismatch between the coefficients of thermal expansion of the materials of the membrane electrode assembly. The micro-tubular cell can operate safely, but if there is an interfacial defect or a high enough tensile stress applied at the electrolyte, a failure can arise.     

Three-dimensional thermo-fluid and electrochemical modeling of anode-supported planar solid oxide fuel cell

This paper presents a three-dimensional model of an anode-supported planar solid oxide fuel cell with corrugated bipolar plates serving as gas channels and current collector above the active area of the cell. Conservation equations of mass, momentum, energy and species are solved incorporating the electrochemical reactions. Heat transfer due to conduction, convection and radiation is included. An empirical equation for cell resistance with measured values for different parameters is used for the calculations. Distribution of temperature and gas concentrations in the PEN (positive electrode/electrolyte/negative electrode) structure and gas channels are investigated. Variation of current density over the cell is studied. Furthermore, the effect of radiation on the temperature distribution is studied and discussed. Modeling results show that the relatively uniform current density is achieved at given conditions for the proposed design and the inclusion of thermal radiation is required for accurate prediction of temperature field in the single cell unit.     

Heat-up and start-up modeling of direct internal reforming solid oxide fuel cells

In this paper, a transient heat transfer model to simulate the heat-up and start-up periods of co- and counter-flow direct internal reforming solid oxide fuel cells is developed and presented. In this comprehensive model, all the heat transfer mechanisms, i.e. conduction, convection, and radiation, and all the polarization nodes, i.e. ohmic, activation, and concentration, are considered. The heat transfer model is validated using the results of a benchmark test and two numerical studies obtained from the literature. After validating the model, the heat-up, start-up, and steady-state behaviors of the cell are investigated. In addition, the first principal thermal stresses are calculated to find the probability of failure of the cell during its operation. The results of the present model are in good agreement with the literature data. It is also shown for the given input data that counter-flow case yields a higher average current density and power density, but a lower electrical efficiency of the cell. For the temperature controlled heat-up and start-up strategy, the maximum probability of failure during the operation of the cell is found to be 0.068% and 0.078% for co- and counter-flow configurations, respectively.     

Three-dimensional modeling of pressure effect on operating characteristics and performance of solid oxide fuel cell

A three-dimensional (3-D) model for planar, anode-supported, solid oxide fuel cell (SOFC) is developed to investigate the effect of operating pressure on cell characteristics. The results show that the elevated operating pressure can improve cell performance by increasing open circuit voltage and reducing activation overpotential, and enhance the electrochemical reaction in the vicinity of electrolyte. Besides, the high pressure can also change the distributions of species and internal reforming reactions. Compared to the case using syngas as fuel, the operating pressure has more significant effects on temperature gradient along flow direction when partly pre-reformed gas is supplied. In addition, efficient control of cell temperature could be achieved by decreasing fuel utilization in the case of partly pre-reformed gas, but this is achieved at the expense of cell efficiency, especially under high pressure condition. Another way to reduce the temperature gradient is to adopt higher air ratio. Moreover, when partly pre-reformed gas is used, the counter-flow configuration has a better performance due to the higher overall temperature.     

Power generation enhancement of solid oxide fuel cell by cathode-electrolyte interface modification in mesoscale assisted by level set-based optimization calculation

To explore potential for the power density enhancement of solid oxide fuel cells by controlling the cathode-electrolyte interface in mesoscale, two-dimensional numerical simulations were conducted. In the simulation, a level set-based topology optimization technique was successfully coupled with the SOFC simulation based on a microscale model and was applied for the local optimization of the interface shape. The numerical results showed that the optimized shape of the cathode-electrolyte interface varied depending on the simulation conditions and that the cell performance could be improved by applying non-flat design to the cathode-electrolyte interface for the same amount of cathode/electrolyte materials.     

Thermodynamic modeling of direct internal reforming solid oxide fuel cells operating with syngas

In this paper a direct internal reforming solid oxide fuel cell (DIR-SOFC) is modeled thermodynamically from the energy point of view. Syngas produced from a gasification process is selected as a fuel for the SOFC. The modeling consists of several steps. First, equilibrium gas composition at the fuel channel exit is derived in terms mass flow rate of fuel inlet, fuel utilization ratio, recirculation ratio and extents of steam reforming and water–gas shift reaction. Second, air utilization ratio is determined according to the cooling necessity of the cell. Finally, terminal voltage, power output and electrical efficiency of the cell are calculated. Then, the model is validated with experimental data taken from the literature. The methodology proposed is applied to an intermediate temperature, anode-supported planar SOFC operating with a typical gas produced from a pyrolysis process. For parametric analysis, the effects of recirculation ratio and fuel utilization ratio are investigated. The results show that recirculation ratio does not have a significant effect for low current density conditions. At higher current densities, increasing the recirculation ratio decreases the power output and electrical efficiency of the cell. The results also show that the selection of the fuel utilization ratio is very critical. High fuel utilization ratio conditions result in low power output and air utilization ratio but higher electrical efficiency of the cell.     

Three-dimensional modeling of planar solid oxide fuel cells and the rib design optimization

Three-dimensional (3D) multi-physics models of co-, counter- and cross-flow planar solid oxide fuel cell (SOFC) stack units are described. The models consider electronic conduction in the electrodes, ionic conduction in the electrolyte, mass transport in the porous electrodes and electrochemical reactions on the three phase boundaries. Based on the analysis of the ionic conducting equation for the thin electrolyte layer, a mathematically equivalent method is proposed to scale the electrolyte thickness with the corresponding change in the ionic conductivity to moderate the thin film effect in the meshing step and decrease the total number of degrees of freedom in the 3D numerical models. Examples of applications are given with typical physical fields illustrated and the characteristic features discussed for co-, counter- and cross-flow designs. The 3D models are also used to optimize the rib widths in SOFC stacks as a function of interconnect–electrode contact resistance.     

Experimental characterization and mechanistic modeling of carbon monoxide fueled solid oxide fuel cell

The paper presents an elementary reaction based solid oxide fuel cell (SOFC) model coupled with anodic elementary heterogeneous reactions and electrochemical charge transfer reactions for CO/CO₂ fuel based on an anode supported button cell. The model is calibrated and validated using experimental data obtained for various CO/CO₂ fuel compositions at 750, 800 and 850 °C. The comparison shows that the modeling results agree well with the experimental data. The effects of operating conditions on the cell performance and the detailed species concentration distribution are predicted. Then, the carbon deposition on the SOFC anode with CO/CO₂ fuel is experimentally measured and simulated using the elementary reaction model. The results indicate that lower temperature and lower operation voltage are helpful to reduce the possibilities of carbon deposition on Ni particle surfaces.     

Multi-objective optimization of biogas systems producing hydrogen and electricity with solid oxide fuel cells

The design of solid oxide fuel cells (SOFC) using biogas for distributed power generation is a promising alternative to reduce greenhouse gas emissions in the energy and waste management sectors. Furthermore, the high efficiency of SOFCs in conjunction with the possibility to produce hydrogen may be a financially attractive option for biogas plants. However, the influence of design variables in the optimization of revenues and efficiency has seldom been studied for these novel cogeneration systems. Thus, in order to fulfill this knowledge gap, a multi-objective optimization problem using the NSGA-II algorithm is proposed to evaluate optimal solutions for systems producing hydrogen and electricity from biogas. Moreover, a mixed-integer linear optimization routine is used to ensure an efficient heat recovery system with minimal number of heat exchanger units. The results indicate that hydrogen production with a fuel cell downstream is able to achieve high exergy efficiencies (65–66%) and a drastic improvement in net present value (1346%) compared with sole power generation. Despite the additional equipment, the investment costs are estimated to be quite similar (12% increase) to conventional steam reforming systems and the levelized cost of hydrogen is very competitive (2.27 USD/kgH₂).     

Performance analysis of solid oxide fuel cell using reformed fuel

Fuelling SOFC with reformed fuel can be beneficial due to it being cheaper compared to pure hydrogen. A biomass fuel can be easily modeled as a reformed fuel, as it can be converted into H₂ and CO using gasification or biodegradation, the main composition of product from a reformer. Hence in this study it is assumed that feed to the fuel cell contains only H₂ and CO. A closed parametric model is formulated. Performance is analyzed with changes in temperature, pressure and fuel ratio; considering the possible voltage losses, like ohmic, activation, mass transfer and fuel crossover. Performance curves consisting of operating voltage, fuel utilization, efficiency, power density and current density are developed for both pure hydrogen and mixture of CO and H₂. Variations of open circuit voltage with temperature, power density with current density, operating voltage with current density and maximum power density with fuel utilization are also evaluated.     

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.     

Combined micro-scale and macro-scale modeling of the composite electrode of a solid oxide fuel cell

The design of a cathode inter-layer is important to the high performance of a solid oxide fuel cell (SOFC). In this paper, the processes of electrochemical reactions, electronic and ionic conductions and gas transports in an SOFC are discussed in detail. An analysis shows that the current conduction and electrochemical processes can be replicated by an equivalent circuit model. A corresponding macro-scale model using the Butler-Volmer equation for electrochemical reactions, Ohm's law for current conduction and the Dusty-gas model for gas transport is described. A percolation theory based micro-model is used to obtain the effective electrode properties in the macro-model from the microstructure parameters of the porous electrode. Experimental I-V relations can be accurately accounted for by the proposed theory. The macro- and micro-models are then combined to systematically examine the effects of various parameters on the performance of a composite cathode inter-layer. The examined parameters include the thickness, effective electronic and ionic conductivities, exchange current density, operating temperature, output current density, electrode- and electrolyte-particle radii, composition and porosity of the cathode inter-layer. The comprehensive study shows conclusively that a cathode inter-layer thickness in a range of 10-20 μm is optimal for all practical material choices and microstructure designs.     

Multiscale modeling of degradation of full solid oxide fuel cell stacks

Limiting the degradation of solid oxide fuel cells is an important challenge for their widespread use and commercialization. The computational expense of long-term simulation of a full stack with conventional models is immense. In this study, we present a multiscale three-dimensional model of a degrading full stack of solid oxide cells, where we integrate degradation phenomena of nickel particle coarsening in the anode electrode, chromium poisoning of the cathode electrode, and oxidation of the interconnect into a multiscale model of the stack. This approach makes this type of simulation computationally feasible, and 38 thousand hours of the stack operation can be simulated in 1 h and 15 min on a high-end workstation. Hereby one can start to explore the optimum operating conditions for a range of parameters. The model is validated with experimental data from an 18-cell Jülich Mark-F stack experiment and predicts common trends reported in the literature for evolutions of the stack performance, degradation phenomena, and the related model variables. Moreover, it captures how different regimes in the full stack degrades at different rates and how the various degradation phenomena interact over time. The model is used to investigate the effects of galvanostatic and potentiostatic operation modes, operating conditions, and flow configurations on the long-term performance of the stack. Results demonstrate, as expected, that potentiostatic operation mode, moderate temperature, lower load current, and counter-flow configuration improve the long-term performance of the stack.     

Transient modeling of anode-supported solid oxide fuel cells

An isothermal 2-D transient model is developed for an anode-supported solid oxide fuel cell. The model takes into account the transient effects of both charge migration and species transport in PEN assembly. Due to the lack of transient experimental data, the transient model, under steady state operating conditions, is validated using experimental results from open literature. Numerical results show that the cell can obtain very quick transient current response when subjected to a step voltage change, followed by a slow current transient period due to species diffusion effects within porous electrodes. It is also found that the transient response of the cell current is sensitive to oxygen concentration change at cathode/channel interface, whereas the current response is slow when step change of hydrogen concentration is applied at anode/channel interface. The cell transient performance can be improved by increasing porosity or decreasing tortuosity of electrodes.     

Thermodynamic modeling of an integrated biomass gasification and solid oxide fuel cell system

An integrated process of biomass gasification and solid oxide fuel cells (SOFC) is investigated using energy and exergy analyses. The performance of the system is assessed by calculating several parameters such as electrical efficiency, combined heat and power efficiency, power to heat ratio, exergy destruction ratio, and exergy efficiency. A performance comparison of power systems for different gasification agents is given by thermodynamic analysis. Exergy analysis is applied to investigate exergy destruction in components in the power systems. When using oxygen-enriched air as gasification agent, the gasifier reactor causes the greatest exergy destruction. About 29% of the chemical energy of the biomass is converted into net electric power, while about 17% of it is used to for producing hot water for district heating purposes. The total exergy efficiency of combined heat and power is 29%. For the case in which steam as the gasification agent, the highest exergy destruction lies in the air preheater due to the great temperature difference between the hot and cold side. The net electrical efficiency is about 40%. The exergy combined heat and power efficiency is above 36%, which is higher than that when air or oxygen-enriched air as gasification agent.     

Fabrication of hydrogen electrode supported cell for utilized regenerative solid oxide fuel cell application

A utilized regenerative solid oxide fuel cell (URSOFC) provides the dual function of performing energy storage and power generation, all in one unit. When functioning as an energy storage device, the URSOFC acts like a solid oxide electrolyzer cell (SOEC) in water electrolysis mode; whereby the electric energy is stored as (electrolyzied) hydrogen and oxygen gases. While hydrogen is useful as a transportation fuel and in other industrial applications, the URSOFC also acts as a solid oxide fuel cell (SOFC) in power generation mode to produce electricity when needed. The URSOFC would be a competitive technology in the upcoming hydrogen economy on the basis of its low cost, simple structure, and high efficiency. This paper reports on the design and manufacturing of its anode support cell using commercially available materials. Also reported are the resulting performance, both in electrolysis and fuel cell modes, as a function of its operating parameters such as temperature and current density. We found that the URSOFC performance improved with increasing temperature and its fuel cell mode had a better performance than its electrolysis mode due to a limited humidity inlet causing concentration polarization. In addition, there were great improvements in performance for both the SOFC and SOEC modes after the first test and could be attributed to an increase in porosity within the oxygen electrode, which was beneficial for the oxygen reaction.