Single solid oxide fuel cell modeling and optimization

In this paper a dynamic model of a single solid oxide fuel cell (SOFC) is developed using a volume element methodology. It consists of a set of algebraic and ordinary differential equations derived from physical laws (e.g., the first law of thermodynamics, Fick's law, and Fourier's law), which allow for the prediction of the temperature and pressure spatial distribution inside the single SOFC, as functions of geometric and operating parameters. The thermodynamic model is coupled with an electrochemical model that is capable of determining the voltage, current, and power output. Based on the simulation results, the internal configuration (structure of the positive electrode-electrolyte-negative electrode assembly) and the operating conditions (air stoichiometric ratio and fuel utilization factor), as well as their impact on the performance of the single SOFC are discussed. Optimal geometric and operating parameters are obtained so that electrical power of the single SOFC at the nominal operating point is maximized. The method used is general and the fundamental optimization results are sharp, showing up to a 357% single SOFC performance variation within the studied parameters’ range, therefore these findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.     

A quasi-two-dimensional electrochemistry modeling tool for planar solid oxide fuel cell stacks

A quasi-two-dimensional numerical model is presented for the efficient computation of the steady-state current density, species concentration, and temperature distributions in planar solid oxide fuel cell stacks. The model reduction techniques, engineering approximations, and numerical procedures used to simulate the stack physics while maintaining adequate computational speed are discussed. The results of the model for benchmark cases with and without on-cell methane reformation are presented with comparisons to results from other research described in the literature. Simulations results for a multi-cell stack have also been demonstrated to show capability of the model on simulating cell to cell variation. The capabilities, performance, and scalability of the model for the study of large multi-cell stacks are then demonstrated.     

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.     

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.     

Modeling and optimization of electrode structure design for solid oxide fuel cell

A comprehensive steady-state model is developed to investigate the effects of electrode structure on the performance of solid oxide fuel cell, considering detailed heat and mass transfer processes, as well as electronic and ionic charge transport. The percolation theory is used to evaluate the effective transport properties in electrode. The uniform and non-uniform distributions of electronic/ionic conducting materials in anode/cathode function layer (AFL/CFL) are comprehensively compared. The effects of function layer thickness and particle sizes are found to be different in anode and cathode. The optimal AFL thickness is increased with the increment of particle sizes. The results show that the optimal AFL thickness ranges from 5 μm to 30 μm with relatively small particle sizes (<0.4 μm), while the cell performance keeps increasing with relatively large particle radius when the AFL grows thicker. Although there exists slight performance drop in condition of non-uniform distribution, the structure reduces ionic-conducting material dosage and fabrication difficulty and it provides another alternative microstructural design which is meaningful to fuel cell optimization.     

Control relevant modeling of planer solid oxide fuel cell system

This paper provides two types of control relevant models of planer solid oxide fuel cell system with different details. Dynamic models of system components which include heat exchanger, reformer and after-burner are also provided along with the necessary formulation of a fuel cell connected in parallel with a capacitor. Steady-state and dynamic simulations of fuel cell system for both types of models are performed. The results indicate that both models are comparable in predicting stack voltage at lower current load. But, the discrepancy in the stack voltage, power and temperature of different components become more prominent at higher current load.     

Diagnosis methodology and technique for solid oxide fuel cells: A review

The present study aims to identify and recollect the articles existing in literature that deal malfunction or failure causes of SOFC cells and relative diagnostic systems. This work is motivated by the increasing demand for diagnostic techniques aimed at both increasing durability and fully exploiting SOFC benefits throughout system lifetime. This paper reviews SOFC cells degradation phenomena and relevant fault detection methodologies already available, having found a gap in literature, above all relative to SOFC electrode microstructural degradation related, specifically, to sintering of the electrode microstructure, poisoning of the cathode microstructure with chromium products outgassed from the interconnect plates, carbon deposition in the anode, anode sulfur poisoning and boron SOFC cathodes' poisoning. It is therefore encouraged a future effort of the research activity in this specific sector.     

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.     

Geometrical modeling of microstructure of solid oxide fuel cell composite electrodes

A model based on random packing of electron and ion conductor particles is developed to study the microstructure performance relationship of solid oxide fuel cell electrodes. This three-dimensional model takes into account special variations of triple phase boundary (TPB) by keeping track of all particles in the packing. Porosity of the media can be controlled and is set to 30%. Effect of particle size, electrode thickness, electrode composition and particle size ratio on the length of TPB line has been studied. The study shows that unlike what models based on percolation theory suggest, the electrode media is not homogeneous for electrochemical reaction. While increasing the thickness increases the length of the TPB to some extent, beyond that little or no improvement was observed. The study also revealed that adding a current collector layer made of electron conductors can increase the TPB line by at least 4%. While for particles of the same size maximum length of TPB was observed at equal volume percent of electron and ion conductor particles, for size ratio of particles other than one the maximum TPB tends to occur above or below 50% depending on the size ratio.     

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.     

Static and dynamic modeling of solid oxide fuel cell using genetic programming

Modeling of solid oxide fuel cell (SOFC) systems is a powerful approach that can provide useful insights into the nonlinear dynamics of the system without the need for formulating complicated systems of equations describing the electrochemical and thermal properties. Several algorithmic approaches have in the past been reported for the modeling of solid oxide fuel cell stacks. However, all of these models have their limitations. This paper presents an efficient genetic programming approach to SOFC modeling and simulation. This method, belonging to the computational intelligence paradigm, is shown to outperform the state-of-the-art radial basis function neural network approach for SOFC modeling. Both static (fixed load) and dynamic (load transient) analyses are provided. Statistical tests of significance are used to validate the improvement in solution quality.     

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.     

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.     

Importance of pressure gradient in solid oxide fuel cell electrodes for modeling study

The pressure gradients in the electrodes of a solid oxide fuel cell (SOFC) are frequently neglected without any justification in calculating the concentration overpotentials of the SOFC electrodes in modeling studies. In this short communication, a comparative study has been conducted to study the effect of pressure gradients on mass transfer and the resulting concentration overpotentials of an SOFC running on methane (CH₄) fuel. It is found that the pressure gradients in both anode and cathode are significant in the fuel cell electrochemical activities. Neglecting the anode pressure gradient in the calculation can lead to underestimation of the concentration overpotential by about 20% at a typical current density of 5000 A m⁻² and at a temperature of 1073 K. The deviation can be even larger at a higher temperature. At the cathode, neglecting the pressure gradient can result in overestimation of the concentration overpotential by about 10% under typical working conditions.     

Performance comparison of three solid oxide fuel cell power systems

An energy analysis of three typical solid oxide fuel cell (SOFC) power systems fed by methane is carried out with detailed thermodynamic model. Simple SOFC system, hybrid SOFC‐gas turbine (GT) power system, and SOFC‐GT‐steam turbine (ST) power system are compared. The influences of air ratio and operative pressure on the performance of SOFC power systems are investigated. The net system electric efficiency and cogeneration efficiency of these power systems are given by the calculation model. The results show that internal reforming SOFC power system can achieve an electrical efficiency of more than 49% and a system cogeneration efficiency including waste heat recovery of 77%. For SOFC‐GT system, the electrical efficiency and cogeneration efficiency are 61% and 80%, respectively. Although SOFC‐GT‐ST system is more complicated and has high investment costs, the electrical efficiency of it is close to that of SOFC‐GT system. Copyright © 2013 John Wiley & Sons, Ltd.     

High temperature creep strength design and optimization of solid oxide fuel cell

In order to improve product design efficiency and guarantee the high temperature structural integrity during the long-term creep of solid oxide fuel cell (SOFC), the creep strength design method is studied by using the finite element method (FEM) and the response surface method (RSM) with considering the interaction between the geometric parameters. A multi-regression model representing the correlation between the sealant failure probability and the geometric parameters is established for rapid estimation of creep strength and optimization design of geometric dimensions. The sealant failure probability is decreased from 0.994 to 0.015 by the optimization of SOFC geometrical size. And the error between results predicted by the FEM and results predicted by the multi-regression model is less than 10%. Therefore, the multi-regression model is proven to be an excellent tool for creep failure prediction and structural design optimization, reducing research costs and time, and improving design efficiency.     

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.     

A review of numerical modeling of solid oxide fuel cells

The solid oxide fuel cell (SOFC) is one of the most promising fuel cells for direct conversion of chemical energy to electrical energy with the possibility of its use in co-generation systems because of the high temperature waste heat. Various mathematical models have been developed for three geometric configurations (tubular, planar, and monolithic) to solve transport equations coupled with electrochemical processes to describe the reaction kinetics including internal reforming chemistry in SOFCs. In recent years, considerable progress has been made in modeling to improve the design and performance of this type of fuel cells. The numbers of the contributions on this important type of fuels have been increasing rapidly. The objective of this paper is to summarize the present status of the SOFC modeling efforts so that unresolved problems can be identified by the researchers.     

System modeling of an air-independent solid oxide fuel cell system for unmanned undersea vehicles

To examine the feasibility of a solid oxide fuel cell (SOFC)-powered unmanned undersea vehicle (UUV), a system level analysis is presented that projects a possible integration of the SOFC stack, fuel steam reformer, fuel/oxidant storage and balance of plant components into a 21-in. diameter UUV platform. Heavy hydrocarbon fuel (dodecane) and liquid oxygen (LOX) are chosen as the preferred reactants. A maximum efficiency of 45% based on the lower heating value of dodecane was calculated for a system that provides 2.5 kW for 40 h. Heat sources and sinks have been coupled to show viable means of thermal management. The critical design issues involve proper recycling of exhaust steam from the fuel cell back into the reformer and effective use of the SOFC stack radiant heat for steam reformation of the hydrocarbon fuel.     

Composite electrode modelling and optimization for solid oxide fuel cells

In a solid oxide fuel cell (SOFC), the electrode is a composite porous structure, which can be considered to be made of ionic conductor material, electronic conductor material and pores that function as channels for the flow of reacting gases. This article proposes a model for the composite electrode of an SOFC, suitable for optimization. The model can be used to study the effects on fuel cell performance of pore diameter, porosity and tortuosity, electrical conductivity, ionic conductivity, electrode temperature, inlet reacting gas pressure, diffusivity and activation energy for the reaction. The article illustrates the use of the proposed model to find an optimal thickness of the active reaction layer by the minimization of total potential losses, or alternatively by the maximization of the fuel cell net power output. A three‐way single SOFC optimization was conducted with respect to the active reaction layer thicknesses at both electrodes, operating temperature and electrode porosity, showing that the SOFC net power density varies approximately by factor of 2, which stresses the importance of the developed model for SOFC design and optimization. This work provides a way to incorporate aspects of the electrode composition and microstructure in the evaluation of the fuel cell performance. For the ranges of electrode active reaction layer thicknesses studied in this article, the variation of net power density reached 16% at T = 973 K and 11% at T = 1173 K in the two‐way optimization. Regarding porosity, in the three‐way optimization, the net power density variation reached 10% at T = 1073 K. Therefore, the cumulative effects in the three‐way optimization for a fixed temperature show that net power density can vary approximately by 20%. Copyright © 2012 John Wiley & Sons, Ltd.