Modeling and simulation of solid oxide fuel cell based on the volume–resistance characteristic modeling technique

Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The real-time dynamic simulation of SOFC is still a challenge up to now. This paper develops a one-dimensional mathematical model for direct internal reforming solid oxide fuel cell (DIR-SOFC). The volume–resistance (V–R) characteristic modeling technique is introduced into the modeling of the SOFC system. Based on the V–R modeling technique and the modular modeling idea, ordinary differential equations meeting the quick simulation are obtained from partial differential equations. This model takes into account the variation of local gas properties. It can not only reflect the distributed parameter characteristics of SOFC, but also meet the requirement of the real-time dynamic simulation. The results indicate that the V–R characteristic modeling technique is valuable and viable in the SOFC system, and the model can be used in the quick dynamic and real-time simulation.     

Two-dimensional dynamic simulation of a direct internal reforming solid oxide fuel cell

This study presents a two-dimensional mathematical model of a direct internal reforming solid oxide fuel cell (DIR-SOFC) stack which is based on the reforming reaction kinetics, electrochemical model and principles of mass and heat transfer. To stimulate the model and investigate the steady and dynamic performances of the DIR-SOFC stack, we employ a computational approach and several cases are used including standard conditions, and step changes in fuel flow rate, air flow rate and stack voltage. The temperature distribution, current density distribution, gas species molar fraction distributions and dynamic simulation for a cross-flow DIR-SOFC are presented and discussed. The results show that the dynamic responses are different at each point in the stack. The temperature gradients as well as the current density gradients are large in the stack, which should be considered when designing a stack. Further, a moderate increase in the fuel flow rate improves the performances of the stack. A decrease in the air flow rate can raise the stack temperature and increase fuel and oxygen utilizations. An increased output voltage reduces the current density and gas utilizations, resulting in a decrease in the temperature.     

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.     

Thermal field under the effect of the chemical reaction of a direct internal reforming solid oxide fuel cell DIR-SOFC

The effects of direct internal reforming in a fuel cell solid oxide (SOFC) on thermal fields are studied by mathematical modeling. This study presents the thermal fields of a standard fuel cell (Ni-YSZ/YSZ/LSM) anode supported. This study is also made in the perpendicular plane at the flow of gases. The fuel cell is powered by air and fuel, CH₄, H₂, CO₂, CO and H₂O hence the birth of the phenomenon of direct internal reforming (DIR-SOFC). It is based on reforming chemical reactions, steam reforming reaction and water–gas shift reaction. The main purpose of this work is the visualization of temperature fields under the influence of global chemical reactions and the confirmation of the thermal behavior of this chemical reaction. The thermal fields are obtained by a computer program (FORTRAN).     

A reduced 1D dynamic model of a planar direct internal reforming solid oxide fuel cell for system research

A reduced 1D dynamic model of a planar direct internal reforming SOFC (DIR-SOFC) is presented in this paper for system research by introducing two simplifications. The two simplification strategies employed are called Integration and Average, respectively. The present model is evaluated with a detailed 1D SOFC model, which does not introduce the two simplifications, and a lumped parameter (i.e., 0D) SOFC model. Results show that under the operating conditions investigated the accuracy of the reduced model is not significantly compromised by the two simplifications in prediction of the outlet gas flow rates and molar fractions, the outlet temperatures, and the cell voltage, while its computational time is significantly decreased by them. Moreover, it is quite simple in form. Therefore, the reduced SOFC model is attractive for system research. Compared with the lumped model, the reduced SOFC model is an improvement with regard to accuracy because it takes into account the spatially distributed nature of SOFCs to a certain extent. The discretized node number for solving the reduced model can be taken as an adjustable parameter in modeling, and is determined according to specific modeling requirements.     

Yttria-stabilized zirconia (YSZ) supported Ni–Co alloys (precursor of SOFC anodes) as catalysts for the steam reforming of ethanol

Bioethanol is an attractive fuel for direct internal reforming SOFC (DIR-SOFC). The aim of this work is to investigate the activity of Ni–YSZ, used as precursor for the preparation of SOFC anodes and as catalyst of the ethanol steam reforming reaction. The effect of the addition of cobalt is also studied, as the best performance is given by Ni–Co (25:25)/YSZ catalyst. This achieves total conversion of ethanol around 670 K, at which temperature the H₂ yield is 65%. The addition of Co results in the inhibition of the dehydration reaction as well as of methane production. Furthermore, Co also has an effect on the hydrogen yield, by increasing it and thus apparently favouring methane steam reforming.     

天然气水蒸气重整与SOFC耦合应用

固体氧化物燃料电池（SOFC）系统具有高能源效率和使用可再生燃料的可能性,将在未来的可持续能源系统中发挥重要作用。过去几年燃料电池的发展很快,但在成本、稳定性和市场份额方面,该技术仍处于早期发展阶段。在以天然气为燃料的SOFC系统中,燃料的重整过程和燃料利用水平都可能影响系统运行的稳定性、热量和能量平衡,从而影响系统的使用寿命、输出功率和效率。因此,对燃料重整过程的设计与控制对有效的SOFC电池运行具有重要意义。对天然气在SOFC系统中的重整器配置方式（包括外重整和内重整）、重整参数和重整燃料利用方式进行了详细的综述分析,并对未来天然气SOFC系统的发展进行了展望。     

Part-load,startup, and shutdown strategies of a solid oxide fuel cell-gas turbine hybrid system

Current work on the performance of a solid oxide fuel cell (SOFC) and gas turbine hybrid system is presented. Each component model developed and applied is mathematically defined. The electrochemical performance of single SOFC with different fuels is tested. Experimental results are used to validate the SOFC mathematical model. Based on the simulation model, a safe operation regime of the hybrid system is accurately plotted first. Three different part-load strategies are introduced and used to analyze the part-load performance of the hybrid system using the safe regime. Another major objective of this paper is to introduce a suitable startup and shutdown strategy for the hybrid system. The sequences for the startup and shutdown are proposed in detail, and the system responses are acquired with the simulation model. Hydrogen is used instead of methane during the startup and shutdown process. Thus, the supply of externally generated steam is not needed for the reforming reaction. The gas turbine is driven by complementary fuel and supplies compressed air to heat up or cool down the SOFC stack operating temperature. The dynamic simulation results show that smooth cooling and heating of the cell stack can be accomplished without external electrical power.     

The impact of sulfur on the performance of a solid oxide fuel cell (SOFC) system operated with hydrocarboneous fuel gas

The impact of thiophene in the fuel gas of a commercial solid oxide fuel cell (SOFC) system is investigated for concentrations up to 400 ppmV. Based on the measured voltage–current curves, an empiric correlation for the estimation of the expectable power output of the investigated SOFC system when operated with sulfur containing fuel gases is derived. An interrelation between the open circuit voltage (OCV) and the sulfur concentration of the investigated hydrocarboneous fuel gas is presented and discussed based on corresponding model simulations. The reduction of the steam reforming (STR) activity of the anode cermet material and of the catalytic partial oxidation catalyst used for the fuel gas processing in the investigated SOFC system are found important factors regarding the power output reduction induced by sulfur traces in the fuel gas of SOFCs.     

天然气重整SOFC/MGT混合分布式供能系统性能分析

针对固体氧化物燃料电池(SOFC)与微型燃气轮机(MGT)构成的混合分布式供能系统,首先建立了一种管式SOFC准二维数值模型,优化了辐射计算,提高了热传递模型的准确性;考虑了CO及H2同时作为燃料参加电化学反应,并完善了损失计算模型;最后采用所发展的系统性能预测模型,分别在内部重整和外部重整情况下,预测比较了两种SOFC/MGT混合系统的性能,结果表明外部重整系统在系统输出功率、CO2排放以及热应力分布方面都比内部重整系统具有优势,然而这种轻微的优势是需要额外增加外部重整器的设备投资换取的。     

Fault-tolerant control for steam fluctuation in SOFC system with reforming units

Faults of solid oxide fuel cell (SOFC) systems can affect the characteristics of the stack and inhibit SOFC system commercialization. It has been found that the temperature fluctuation of the burner caused by fluctuation of steam flow rate would greatly affect the temperature of SOFC system and even exceed the safe operation range. Firstly, this paper introduces a mathematical model for the process of steam and natural gas reforming in a real SOFC system. Secondly, the cause of the burner temperature fluctuation is analyzed, and the model to simulate this faulty situation is established. Then, the Bayesian regularization neural network is used for fault diagnosis and good test results are obtained. Finally, fuzzy fault-tolerant control strategy is designed for the thermal safety problem of SOFC system. The simulation results validate the effectiveness of the proposed fault-tolerant control strategy.     

The effect of fuel feeding method on performance of SOFC–PEFC system

We evaluate two kinds of solid-oxide-fuel-cell (SOFC)–polymer-electrolyte-fuel-cell (PEFC) combined systems by numerical simulation to investigate the effect of the fuel feeding method. In one, fuel for the system is reformed by using exhaust heat from the SOFC and is separately supplied to the SOFC and PEFC (parallel SOFC–PEFC system). In the other, fuel is fed to the SOFC first and then SOFC exhaust fuel is fed to the PEFC (series SOFC–PEFC system). The quality of the fuel gas in the SOFC is better in the latter system, whereas the quality of the fuel gas in the PEFC is better in the former. We demonstrate that larger PEFC output can be obtained in the parallel SOFC–PEFC system, since more steam, which is included in the SOFC anode exhaust gas, can be used for the reforming of the fuel for the PEFC. We show that the series SOFC–PEFC system provides higher electrical efficiency because the fuel gas quality has a stronger influence on the electromotive force in the SOFC than in the PEFC.     

Development of a fuel feeder for a solid oxide fuel cell test station

Solid oxide fuel cells (SOFC) can utilize various fuels, such as natural gas, hydrogen and biogas, but often, it is sensible to use a pre‐reformer that converts the fuel into a hydrogen‐rich gas stream. Relevant testing conditions, including the fuel to be used in SOFC systems, are important because cell performance depends on test conditions, such as fuel composition. Still, a majority of the reported single‐cell and short stack tests are performed with pure hydrogen or synthetic reformate mixed from gas bottles. In this article, the development of a fuel feeder used to pre‐reform natural gas for a single cell SOFC test station is presented. To mimic SOFC system conditions, natural gas is taken from the grid, desulfurized with commercial sulfur sorbent and reformed with a commercial precious metal catalyst. The fuel feeder is designed to be a versatile and efficient research tool, capable to be used in a wide temperature and gas flow range and with different reforming techniques, such as steam reforming, catalytic partial oxidation and simulated anode off‐gas recycling. The construction, operation and characterization of the fuel feeder as well as methods of avoiding carbon formation are discussed. The performance is evaluated by comparing measured outlet temperatures and compositions against equilibrium values. All measured gas compositions matched closely with the calculated equilibrium values, and the identified deviations were small and to no harm in practical use. The operator can control the product gas composition by setting the fuel feeder heater to the temperature corresponding to the targeted composition. Results show that the fuel feeder design can be used as such for single‐cell testing or scaled to fit larger stack test stations. Copyright © 2015 John Wiley & Sons, Ltd.     

SOFC cogeneration system for building applications, part 1: Development of SOFC system-level model and the parametric study

A thermal and electrochemical model is developed for the simulation of Solid Oxide Fuel Cell (SOFC) cogeneration system in this study. The modeling algorithms of electrochemical and thermal models are described. Since the fuel cell stack itself is only a single component within the whole SOFC system, the modeling of the balance-of-plant (BOP) components is also performed to assess the system-level performance. Using the new model, a parametric analysis is carried out to investigate the effects of fuel flow rate, extent of methane gas pre-reforming, fuel utilization factor, recycling rate of cathode gas and cell voltage on the overall system performance. As a result of the parametric study, fuel flow rate, cell voltage, fuel utilization and recycling rate of cathode gas turned out to improve system power output. In addition, the internal reforming turned out to have advantage over external reforming in terms of system power supply.     

Catalytic steam reforming of methane,methanol, and ethanol over Ni/YSZ: The possible use of these fuels in internal reforming SOFC

This study investigated the possible use of methane, methanol, and ethanol with steam as a direct feed to Ni/YSZ anode of a direct internal reforming Solid Oxide Fuel Cell (DIR-SOFC). It was found that methane with appropriate steam content can be directly fed to Ni/YSZ anode without the problem of carbon formation, while methanol can also be introduced at a temperature as high as 1000 °C. In contrast, ethanol cannot be used as the direct fuel for DIR-SOFC operation even at high steam content and high operating temperature due to the easy degradation of Ni/YSZ by carbon deposition. From the steam reforming of ethanol over Ni/YSZ, significant amounts of ethane and ethylene were present in the product gas due to the incomplete reforming of ethanol. These formations are the major reason for the high rate of carbon formation as these components act as very strong promoters for carbon formation.     

Efficiency analyses of ethanol-fueled solid oxide fuel cell power system

In this study, the balance of plant (BOP) of an ethanol-fueled SOFC is analyzed using the GCTool software package developed by Argonne National Laboratory (ANL). The effects of the excess air ratio and fuel utilization on the electric and heat efficiencies of the SOFC are systematically examined for two reforming methods (steam reforming and auto-thermal reforming) and two flow sheets (BOP A and BOP B). In BOP A, the cathode off-gas is passed directly to the afterburner together with the unreacted fuel, and the hot flue gas exiting the burner is then used to provide the thermal energy required for the ethanol reforming process. In BOP B, the cathode off-gas is passed through a heat exchanger in order to heat the ethanol fuel prior to the reforming process, and is then flowed into the burner with the unreacted fuel. The results show that given an SOFC inlet temperature of 650 °C, a fuel utilization of 70.2% and excess air ratios of 4, 6 and 7, respectively, the overall system efficiency is equal to 74.9%, 72.3% and 71.0%. In general, the results presented in this study provide a useful starting point for the design and development of practical ethanol-fueled SOFC test systems.     

Comparison between two methane reforming models applied to a quasi-two-dimensional planar solid oxide fuel cell model

Up to recently 2-D solid oxide fuel cell (SOFC) modelling efforts were based on global kinetic approaches for the methane steam reforming and water gas shift reactions (WGS) or thermodynamic equilibrium. Lately detailed models for elementary heterogeneous chemical kinetics of reforming (HCR) over Ni–YSZ anode became available in literature. Both approaches were employed in a quasi 2-D model of a planar high temperature electrolyte supported (ESC) SOFC and simulations were carried out for three different fuel gas compositions: pre-reformed natural gas (high CH₄ content), and two different biomass derived producer gases (low CH₄ content). The results show that the HCR predicts much slower reforming rates which leads to a more evenly distributed solid temperature but smaller power output and thus electrical efficiency. The two models result into predictions that differ greatly if high methane content fuels are used and for such cases the decision upon the modelling scheme to follow should be based on experimental investigations.     

Thermodynamic model and parametric analysis of a tubular SOFC module

Solid oxide fuel cells (SOFCs) have been considered in the last years as one of the most promising technologies for very high-efficiency electric energy generation from natural gas, both with simple fuel cell plants and with integrated gas turbine-fuel cell systems. Among the SOFC technologies, tubular SOFC stacks with internal reforming have emerged as one of the most mature technology, with a serious potential for a future commercialization. In this paper, a thermodynamic model of a tubular SOFC stack, with natural gas feeding, internal reforming of hydrocarbons and internal air preheating is proposed. In the first section of the paper, the model is discussed in detail, analyzing its calculating equations and tracing its logical steps; the model is then calibrated on the available data for a recently demonstrated tubular SOFC prototype plant. In the second section of the paper, it is carried out a detailed parametric analysis of the stack working conditions, as a function of the main operating parameters. The discussion of the results of the thermodynamic and parametric analysis yields interesting considerations about partial load SOFC operation and load regulation, and about system design and integration with gas turbine cycles.     

Dynamic modeling of a SOFC/MGT hybrid power system based on modified OIF Elman neural network

Solid oxide fuel cell (SOFC) integrated into micro gas turbine (MGT) cycle is a promising power‐generation technology. This article proposes a modified output–input feedback (OIF) Elman neural network model to describe the nonlinear temperature and power dynamic properties of the SOFC/MGT hybrid system. A physics‐based mathematical model of a 220 kW SOFC/MGT hybrid power system is used to generate the data required for the training and prediction of the modified OIF Elman neural network identification model. Compared with the conventional Elman neural network, the simulation results show that the modified OIF Elman identification model can follow the temperature and power response of the SOFC/MGT hybrid system with higher prediction accuracy and faster convergent speed. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance comparison of cocurrent and countercurrent flow solid oxide fuel cells

Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The flowing configuration of fuel and oxidants in the fuel cell will greatly affect the performance of the fuel cell stack. Based on the developed mathematical model of direct internal reforming SOFC, this paper established a distributed parameters simulation model for cocurrent and countercurrent types of SOFC based on the volume-resistance characteristic modeling method. The steady-state distribution characteristics and dynamic performances were compared and were analyzed for cocurrent and countercurrent types of SOFCs. The results indicate that the cocurrent configuration of SOFC is more suitable with regard to performance and safety.