Numerical investigation of the chemical and electrochemical characteristics of planar solid oxide fuel cell with direct internal reforming

Abstract

A fully three-dimensional mathematical model of a planar solid oxide fuel cell (SOFC) with complete direct internal steam reforming was constructed to investigate the chemical and electrochemical characteristics of the porous-electrode-supported (PES)-SOFC developed by the Central Research Institute of Electric Power Industry of Japan. The effective kinetic models developed over the Ni/YSZ anode takes into account the heat transfer and species diffusion limitations in this porous anode. The models were used to simulate the methane steam reforming processes at the co- and counter-flow patterns. The results show that the flow patterns of gas and air have certain effects on cell performance. The cell at the counter-flow has a higher output voltage and output power density at the same operating conditions. At the counter-flow, however, a high hotspot temperature is observed in the anode with a non-fixed position, even when the air inlet flow rate is increased. This is disadvantageous to the cell. Both cell voltage and power density decrease with increased air flow rate.

Keywords

planar solid oxide fuel cell (SOFC) / direct internal reforming / chemical reaction / methane / electrochemical

Introduction

The increasing pressure of identifying suitable energy sources and protecting the environment pose great challenges to a world burdened by problems on economic growth, energy conservation, and emission reduction. The solid oxide fuel cell (SOFC) is a promising energy conversion unit that produces electric power and heat from hydrocarbon fuels with high efficiency, low noise, and low pollutant emission, especially when its hybrid power generation is combined with a gas turbine. It is superior to other fuel cells in that the hydrocarbon can be converted directly on the anode side because of relatively high operating temperatures of approximately 700-1000°C [1-4]. The high operating temperature also maintains the high oxygen ion conduction of the solid oxide electrolyte, accelerates electrochemical reaction with non-precious metal catalysts, and produces high-quality by-product heat for cogeneration or for use in a bottoming cycle [1,5,6]. Therefore, a high-temperature SOFC offers a wide range of potential applications, flexible fuel options, and the possibility of operations with internal reforming [1,7].

After direct internal steam reforming on the Ni-YSZ anode side, natural gas, LPG, methanol, coal gasified gas, biomass gas, or other oil derivatives can serve as anode feed. The uses of these alternative fuels in SOFCs have been widely investigated [8-10], but methane appears to be the most promising fuel for the SOFC system as it is abundant in natural gas (80%-95% CH₄). The H₂/CO-rich gas produced by catalytic-heated methane steam reforming on porous anode is eventually used to generate electrical energy and heat in the SOFC system [11]. Methane steam reforming is widely used in industry. Compared with other fuel processing technologies, its main advantages are high thermal efficiency and high hydrogen concentration in the produced mixed gas. The direct internal reforming technique also lowers the requirement for cell cooling and presents many advantages with regard to cost and efficiency.

Although methane steam reforming technology is a relatively well-established commercial process for the production of hydrogen and synthetic gas, it is quite complex. It not only involves the transfer and diffusion of reactants and products between bulk flow and the catalyst surface, as well as within the catalyst, but also involves several simultaneous reactions in parallel or in series [12]. Two major problems require resolution before SOFCs can be routinely operated with the direct feed of alternative fuels other than hydrogen. One is the carbon deposition on the anode, which causes loss of active sites as well as poor cell performance and durability [13]. The other is the internal stress in cell components; this stress arises from non-homogeneous temperature distributions.

A goal in SOFC development is to create more economical systems. Advancements in cell manufacture and design can lower capital costs. An increase in power density is also a major technical approach to cost reduction. The SOFC system involves complex multi-component transport, chemical, and electrochemical processes, and its operating performance is strongly affected by corresponding transport resistances and activation barriers [14]. These polarizations are represented as concentration, activation, and ohmic over-potentials, and are functions of both the operating conditions and the physical properties of cell components. The operating conditions include temperature, pressure, and fuel and oxidizer concentrations. The cell properties involve materials, the macro- and micro-structures of the electrolyte and composite electrodes (including the porosity, tortuosity, permeability, and thickness of the anode and cathode), the ionic conductivity and thickness of the electrolyte, and the active area and activity of the electrode-electrolyte interface. Furthermore, the temperature distribution in a single cell is determined by the operating conditions and the physical properties of cell components in a complicated manner. In particular, direct internal steam reforming causes a sharp change in the local temperature on the anode because of the large amount of heat for endothermic reaction. This temperature change not only causes larger internal stress and increases the difficulty of sealing, but also raises the possibility of carbon formation.

The performance of planar SOFC should be studied in detail to understand chemical and electrochemical processes, as well as various resistances, and to optimize cell design and enhance cell performance. The new structure of the porous electrode-supported (PES)-SOFC cell was designed and optimized by the Central Research Institute of Electric Power Industry (CRIEPI) of Japan. The performance of the hydrogen-fuelled PES-SOFC was studied by experimental and numerical analyses [15]. The performance of methane steam reforming over the Ni/YSZ porous anode was studied, and effective kinetic models over this anode was developed under heat/mass transfer and species diffusion limitations [16].

In the present study, a fully three-dimensional mathematical model for the planar PES-SOFC with complete direct internal steam reforming was constructed. The model is designed to simulate flow, heat, and mass transfer characteristics, as well as chemical and electrochemical reactions at different operation conditions. The model, created using a commercial CFD software (CFX4.4), was based on the above-mentioned cell structure and the physical properties of cell components, as well as on a developed routine for investigating mass diffusion and heat transfer in the porous electrode, electrochemical processes, current field, and methane steam reforming. A more detailed spatial variation of temperature, chemical species, local over-potential, electric potential, and current density was obtained using Darcy’s gas model with constant porosity and permeability, the temperature-dependent physical property of cell components, and a voltage-to-current algorithm. The results were used to evaluate the overall performance of the PES-SOFC stack with direct internal steam reforming, and significantly optimize design and operation for practical applications.

Computational model

In the SOFC, the fluid consists of multiple components: oxygen and nitrogen in the cathode channel, and hydrogen, methane, carbon dioxide, carbon monoxide, and water vapor in the anode channel. Heat and mass transfer are coupled.

Flow and heat/mass transfer

The basic set of equations for flow and heat/mass transfer comprises the equations for the conservation of mass, momentum, energy, and concentration, known as the three-dimensional Navier-Stokes equations. The effect of turbulence is represented by the k-ϵ model. In this model, wall functions are used to resolve the flow near wall surfaces. The following time-averaged equations are used for the steady state in compressible gases [15,17]:

(1)\nabla \cdot \left(\rho \overline{U}\varphi -{\Gamma }_{\varphi }\nabla \varphi \right)=S_{\varphi },

where \varphi represents \overline{U}, k, ϵ, H, and Y.

The model commonly used for flow in a porous medium is a generalization of the Navier-Stokes equations and Darcy’s law, with constant porosity and permeability. Mass diffusion coefficients are required whenever species transport equations in multi-component flows are solved. Diffusion in a porous medium is usually described by molecular diffusion or Knudsen diffusion. Because of the tortuous nature and constrictions of the pore, the diffusivity is corrected by tortuosity factor {{\tau }_{}}_p and porosity of porous medium {{ϵ}_{}}_p. The overall effective diffusion coefficient is given by

(2)D_{i,\text{e}}={\displaystyle \frac{{{ϵ}_{}}_p}{{{\tau }_p}_{}}}{\left({\displaystyle \frac{\mathrm{1}}{D_{i,m}}}+{\displaystyle \frac{\mathrm{1}}{{D_k}_{}}}\right)}^{-\mathrm{1}},

where D_{i,m} is the mass diffusion coefficient for species i in the mixture [18] and {D_{}}_k is the Knudsen diffusion [19,20].

To take into account the heat conduction of a porous solid, the effective thermal conductivity in the porous medium is computed as the volume average of the fluid conductivity and the solid conductivity by

(3)\lambda ={{ϵ}_p}_{}{{\lambda }_{}}_g+(\mathrm{1}-{{ϵ}_p}_{}){{\lambda }_{}}_s\text{},

where {\lambda }_g is the thermal conductivity of a multi-component mixture, whose computational formula and coefficient can be found in Ref. [18]; {{\lambda }_s}_{} is the isotropic constant, listed in Table 1.

Steam reforming reactions and kinetic models

The overall reactions of methane and steam in forming hydrogen, carbon monoxide, carbon dioxide, and carbon are presented by the equations listed in Table 2 [12,21]. CO₂ reforming (reactions 4 and 5) is a linear combination of the methane steam reforming reaction (reactions 1 and 3) and the water shift reaction (reaction 2). The rates of reactions 4, 5, and 9-11 can be quite slow in terms of thermodynamics. Therefore, they are not considered to occur from the perspective of kinetic analysis [12]. Methane cracking (reaction 6), Boudard reaction (reaction 7), and reaction 8 are the reactions that most probably lead to carbon formation and gasification; hence, they are used to analyze carbon deposition and gasification. The methane cracking and Boudard reaction are the major pathways for carbon formation at high operating temperatures. Given the exothermic nature of the water shift reaction, the amount of CO becomes significant at high temperatures.

The heat/mass transfer and diffusion limitations in the porous anode are considerable. Different manufacturing methods can create only a part of the catalyst in the porous anode contributing to the reforming process. Therefore, these effects must be considered. In a previous work, on the basis of the kinetic models of methane steam reforming developed by Xu and Froment, the effective kinetic models of methane steam reforming over the Ni/YSZ anode for the planar SOFC in the present study was developed through experimental and the computational results [16]; the results are summarized in Table 3. The reaction rate parameters determined by Xu and Froment [21] were applied. The effective factor (C_e) is 5 × 10^-4.

Electrochemical model

The electrochemical model calculates the current power output and the molar compositions of the cathode and anode flows for each control volume. The fuel consists of H₂, H₂O, CH₄, CO, and CO₂ on the anode side, and the oxidizer (air) is modeled as an O₂/N₂ mixture on the cathode side. The fuel and air run at co- and counter-flows. The electrochemical reaction occurring at the interface of the cathode/electrolyte is expressed as

(4){\text{O}}_2+4{\text{e}}^{-}\to 2{\text{O}}^{\text{2}-}

Then, the oxygen ion is transported through the electrolyte into the active anode. The electrochemical reaction occurring at the interface of the anode/electrolyte is expressed as

(5){\text{H}}_2+{\text{O}}^{2-}\to {\text{H}}_2\text{O}+2{\text{e}}^{-}

The electromotive force yielded by the oxidation of H₂ is a local quantity as it depends on gas composition and temperature, and can be determined by the well-known Nernst equation, as follows [1].

(6)E_{\text{TPB}}=\frac{-\Delta G}{2F}=\frac{-\Delta G^{\circ }}{2F}+\frac{RT}{2F}\ln \left(\frac{P_{{\text{H}}_{\text{2}}\text{,TPB}}{P}_{{\text{O}}_{\text{2}}\text{,TPB}}^{0.5}}{P_{{\text{H}}_{\text{2}}\text{O,TPB}}}\right).

Concentration over-potentials appear when mass transport hinders electrode reaction. The main factors that contribute to concentration polarization are the diffusion of gases through porous media and the dissolution of reactants and products in solution. Along with the consumption and production of gas species in fuel and air flows, the molar fraction of reactants and products from the electrochemical reactions also vary with the flow stream of fuel and air. In Eq. (6), the Nernst electromotive force obtained includes the over-potential incurred by the component diffusion, caused by the use of species concentrations at the three-phase boundary, i.e., considering the mass diffusion of multi-component flow in porous medium. This yields the localized electromotive force (E_TPB) over the electrolyte layer, which generates the localized ionic transfer rate through the electrolyte layer, as shown in the equation

(7)i=\frac{E_{\text{TPB}}-{\eta }^{\text{act}}-\left(V^{\text{c}}-V^{\text{a}}\right)}{R_{\text{Ohm}}^{\text{e}}}.

Activation polarization

Activation polarization is controlled by the electrode kinetics at the electrode surfaces. This polarization is directly related to the activation barrier that must be overcome by the reacting species in order for the electrochemical reaction to occur. The activation over-potential (η_act) incurred by the activation polarization reflects the kinetics of reactions and occurs at both the anode and cathode. It is often represented by the nonlinear Butler-Volmer equation, which relates the current density drawn to the activation over-potential, and for a first-order charge transfer-controlled electrochemical reaction, is given by

(8)\frac{j}{j_0}=\exp \left(\alpha \frac{zF{\eta }^{\text{act}}}{RT}\right)-\exp \left(-(1.0-\alpha )\frac{zF{\eta }^{\text{act}}}{RT}\right),

where j₀ is the exchange current density, given by [22]

(9)j_0^a=5.5\times {10}^8\left(\frac{P_{{\text{H}}_{\text{2}}}}{P_{\text{Ref}}}\right)\left(\frac{P_{{\text{H}}_{\text{2}}\text{O}}}{P_{\text{Ref}}}\right)\exp \left(-\frac{100\times {10}^3}{RT}\right),

(10)j_0^c=7.0\times {10}^8{\left(\frac{P_{{\text{O}}_{\text{2}}}}{P_{\text{Ref}}}\right)}^{0.25}\exp \left(-\frac{120\times {10}^3}{RT}\right).

The Butler-Volmer equation is solved numerically in the present work. The most commonly used method for solving non-linear equations is the Newton-Raphson method.

Ohmic losses

Ohmic losses are caused by resistance to the conduction of ions (through the electrolyte) and electrons (through the electrodes and interconnector) and by contact resistance between cell components. This voltage drop is important in all types of cells and is essentially linear and proportional to current density. Given that the ionic flow in the electrolyte and the electronic flow in the electrodes obey Ohm’s law, the ohmic losses can be expressed by

(11){\eta }^{\text{ohm}}=R_{\text{ohm}}\times i.

The ohmic resistance is calculated according to the second Ohm’s law:

(12)R_{\text{ohm}}={\rho }_i\frac{\delta }{A},

where ρ_i is the corresponding material resistivity, calculated with a temperature-dependent relationship (Table 1).

In the present study, the current calculation in the electrolyte is of one dimension, along with the thickness direction, because of the very small thickness, and is of three dimensions in the anode and cathode. Applying Kirchhoff’s current law, the potential and current in each calculating volume are obtained, as shown in Eq. (13).

(13){\displaystyle \sum _{j=\mathrm{1}}^{\mathrm{6}}{i}_j}=\mathrm{0.0},

where i_j = (V_j – V_P) / R_{j, P}, P is the present calculating volume, and j indicates six neighborhood volumes at the x-, y-, and z-axes.

Because the potential difference between two interconnectors is the cell terminal voltage, the potential on the outside surface of the interconnector in contact with the anode is assumed to be zero. Thus, the potential at the outside surface of the interconnector in contact with the cathode will be the terminal voltage of the fuel cell. Once all the local electromotive forces are obtained from Eq. (6), only two unknown conditions will exist: the total current flowing out from the cell and the potential at the interconnector in contact with the cathode. Therefore, either must be specified as the initial condition. In the present study, the total current is specified according to the average current density and total reacting area of the cell.

Results and discussion

The schematic view of the simulated planar PES-SOFC is illustrated in Fig. 1. The layer of the electrolyte is laminated onto the diffusible porous electrode. In a practical planar SOFC stack, many planar cells are mounted on a container. Each of most of the planar cells mounted serially is connected to two others. Therefore, most of the single planar SOFCs very likely work under the same operating conditions. This makes it possible to obtain results that are very useful for evaluating the performance of a cell stack through the analysis of the heat/mass transfer and electrochemical performance of a single cell and its controllable area. The cell size and the physical properties of the cell components measured by CRIEPI are listed in Table 1. The operating conditions are presented in Table 4. The outside surfaces of two interconnectors are specified to the periodic boundary because most of the single planar SOFCs work under the same operating conditions. This indicates that the heat exchange between the cells is the same. In the calculation, the no-electrochemical-reaction extended region (4 mm) at the inlet and outlet of the cell exists.

Cell performance

Figure 2 illustrates the predicted cell voltage and power density as a function of current density. Under these operating conditions, high cell voltage and power density are observed at the counter-flow. The cell voltage decreases with increased current density, especially when the current density is larger than 4000 A/m². The power density initially increases and then decreases with current density. The power density reaches a peak value of 0.23 W/cm² at the counter-flow (0.22 W/cm² at the co-flow) when the current density is approximately 4000 A/m², and the current cell output voltage is 0.568 V at the counter-flow (0.547 V at the co-flow).

The maximum (max) and minimum (min) temperatures in the cell and the outlet gas temperatures plotted against current density at the same inlet flow rate are shown in Fig. 3. On the whole, all these temperatures increase with the enhancement of current density because of the release of more heat from the electrochemical reaction. Furthermore, the difference between the max and min temperatures increases, indicating that larger internal stress is imposed on the components at a higher current density. Under all operating conditions, the min temperature is lower than or closer to the inlet gas temperature. At the co-flow, the outlet temperatures of air and fuel are almost the same (the outlet fuel temperature is slightly higher). At the counter-flow, however, the air and fuel outlet temperatures are very different, and the fuel outlet temperature is higher. At a lower current density, the air and fuel outlet temperatures are lower than the inlet temperature. This low temperature indicates that the heat released from the electrochemical reaction is insufficient for reforming reaction. For the co-flow, the outlet gas temperature is equal to the inlet temperature when the current density is approximately 2500 A/m², whereas that for the counter-flow is still approximately 3200 A/m².

Detailed spatial distribution of parameters

A more detailed spatial variation of temperature, chemical species, local electric potential, and current density is given when the current density is 4000 A/m². In Figs. 4-6, the midsection of the pipe indicates the center section of the pipe on the porous electrodes.

Distribution of temperature

Figure 4 shows the temperature field at the midsection of the pipe of the porous electrode when the current density is 4000 A/m². The fuel in the anode channel is first cooled down because of the endothermic methane reforming reaction, and then progressively heated by the heat generated by the entropy change in the electrochemical reaction at the interface of the anode and electrolyte. In the anode channel, the gas flow rate is small, so that its velocity is very low, especially in the porous medium. The small gas flow rate is caused by the large resistance force. The thermal conductivity of the solid electrode, relative to the gas, is larger. Therefore, the temperature distribution in the porous electrode is mainly determined by heat conduction. In the cathode channel, the gas temperature is lower than that in the porous medium because of the larger air flow rate. Because of the different thermal conductivities of different cell components, larger temperature drops occur on the interface between different cell components. In accordance with the flow arrangement, the hotspot position of the cell at the co-flow must occur at the outlet end of the anode near the electrolyte. However, at the counter-flow, the hotspot position is not fixed and occurs after the methane reforming reaction is completed. Its position is determined by the cell structure and operating conditions in a complex manner.

Distribution of chemical species

The molar fraction of chemical species in the electrode channels is given in Fig. 5. The molar fraction of O₂ decreases along the air flow direction because of the O₂ reduction reaction. The contour shape of O₂ also indicates a relatively large difference in the O₂ molar fractions between the bulk flow and the cathode/electrolyte interface. Given the higher inlet temperature, no H₂ feed, and active catalyst, the methane steam reforming reaction occurs rapidly at the inlet end of the porous anode. Thus, the molar fraction of H₂ and CO increases sharply, but decreases along the fuel stream because H₂ and CO consumption occurs at the anode/electrolyte interface. Corresponding to this H₂ situation, the molar fraction of H₂O first decreases and then gradually increases. The shape of the contour lines of H₂ and H₂O is initially very sharp and then becomes relatively flat from the anode/electrolyte interface to the anode/interconnector interface. This result indicates a larger species diffusion over-potential at the anode. The molar fraction of CO₂ gradually increases along the anode channel.

Distribution of current field

Figure 6 shows the electric potential distribution at the midsection along the flow direction. In the anode, the electric potential has a negative value because of the assumption that the potential on the outside surface of the interconnector in contact with the anode is zero. The electric potential decreases from the outside surface of the interconnector to the anode/electrolyte interface. The absolute value of the anode material (i.e., the ohmic over-potential of the anode) is small because of the high electrical conductivity. In the cathode, the electric potential is positive, and decreases from the cathode/electrolyte interface to the outside surface of the interconnector in contact with the cathode. The electric potential at this location is the cell output voltage. The current through the region between the two pipes of the porous electrodes is relatively large, which leads to denser contour lines (i.e., a large drop in electric potential occurs). The ohmic over-potential of the cathode (the difference in the electric potentials of the cathode/electrolyte interface and the outside surface of the interconnector in contact with the cathode) is larger than that of the anode. The potential and current in this pipe region is zero because there is no electronic conductor in the hollow pipes of the porous electrodes.

Figure 7 illustrates the distribution of the electromotive force (i.e., the Nernst potential with species diffusion polarization taken into account) at the co-flow. Because of the sharp concentration enhancement in H₂ and CO produced from the methane reforming reaction (Fig. 5), the Nernst potential rapidly reaches the maximum from the anode inlet, and then slightly decreases owing to the progressive consumption of H₂ and CO from the electrochemical reaction. When the methane steam reforming reaction is thoroughly completed, the Nernst potential is quickly reduced because of the decrease in H₂ and CO. The different diffusion levels of species in the pipes and porous region of the porous electrodes cause variations in the Nernst potential along the x-axis.

Distribution of current density

The distribution of current density through the electrolyte is demonstrated in Fig. 8. According to Eq. (7), the current density distribution is determined by many parameters, such as temperature, species concentrations, activation over-potential, etc. As the methane steam reforming and electrochemical reactions proceed, the temperature first decreases and then increases from the inlet to the outlet of the cell. The ionic resistance of the electrolyte initially increases and then decreases because the ohmic resistance is a function of temperature. Given the stronger heat exchange in the pipes of the porous cathode, there is a lower temperature at the regions of the electrolyte corresponding to these pipes (i.e., higher ionic resistance occurs at these areas). There are also higher electric potentials in these areas (Fig. 7). Therefore, the distribution of current density through the electrolyte presents the wave variation along the x-axis.

Effect of air flow rate on cell performance

To prevent the cell from overheating, the air flow rate must be enhanced to maintain the temperature at a maximum level. The max and min temperatures in the channels and the outlet gas temperature plotted against the air flow rate at a current density of 4000 A/m² are presented in Fig. 9. As the air flow rate increases, the temperature in the cell gradually decreases. At the co-flow, the maximum temperature in the cell, as well as the air and fuel outlet temperatures, decreases rapidly, whereas the minimum temperature decreases only slightly. However, at the counter-flow, the decrement of the outlet fuel temperature is the largest. The outlet air temperature and the min temperature both increase first and then decline slowly. The smaller decrement of the max temperature at the counter-flow means that there is a higher hotspot temperature in the cell, although the air inlet flow rate is larger. This result is disadvantageous to the cell.

The cell output voltage and power density as a function of the air flow rate is shown in Fig. 10. The cell output voltage and the power density both decrease with increased air flow rate because the reduction of the temperature in the cell caused by the larger air flow rate increases the ohmic resistance of all the components. However, the decrements of cell output voltage and power density gradually decline because the larger air flow rate also increases the local oxygen concentration.

Conclusions

A fully three-dimensional mathematical model of a planar PES-SOFC with complete direct internal steam reforming was constructed to simulate the chemical and electrochemical characteristics and the multi-species/heat transport at the steady state. The spatial variation of chemical species concentration, temperature, potential, current, and current density for various PES-SOFCs with different geometries were studied at the co- and counter-flows. The following conclusions are drawn.

1) The cell output voltage and power density at the counter-flow are higher than those at the co-flow under the same operating conditions, but there is a larger hotspot temperature in the cell at the counter-flow. The hotspot temperature at the counter-flow also increases with the enhancement in air flow rate, which is disadvantageous to the cell. Therefore, the cell performs better at the co-flow.

2) The difference between the max and min temperatures increases as the current density increases, indicating that larger internal stress is imposed on the components at a higher current density. Therefore, the catalyst of methane steam reforming in the anode must be controlled to reduce the temperature difference.

3) The temperature in the cell is determined by the operating conditions, especially the inlet flow rate of methane and air. The gas flow is first cooled down and then progressively heated with the flow stream. A hotspot is located at the end of the anode near the electrolyte at the co-flow. On the other hand, a hotspot at the counter-flow with a non-fixed position is observed. This hotspot is formed after the completion of the methane reforming reaction, and is determined by the cell structure and operating conditions in a complex manner.

4) The concentrations of hydrogen and carbon monoxide generated by the complete direct internal reforming reaction of the methane in the anode channel are low, especially at a high S/C ratio. Therefore, the output voltage is also low relative to the condition in which hydrogen is used as fuel [15].

5) The cell temperature, voltage, and power density decrease with increased air flow rate.

References

[1] .National Energy Technology Laboratory. Fuel Cell Handbook. 7th Ed. Technical Report DOE/NETL 2004/1206, Morgantown, WV (2002); available at:

[2] Bavarsad P G. Energy and exergy analysis of internal reforming solid oxide fuel cell-gas turbine hybrid system. International Journal of Hydrogen Energy, 2007, 32(17): 4591-4599

[3] Aguiar P, Adjiman C S, Brandon N P. Anode-supported intermediate temperature direct internal reforming solid oxide fuel cell. I: Model-based steady-state performance. Journal of Power Sources, 2004, 138(1-2): 120-136

[4] Colpan C O, Dincer I, Hamdullahpur F. Thermodynamic modeling of direct internal reforming solid oxide fuel cells operating with syngas. International Journal of Hydrogen Energy, 2007, 32(7): 787-795

[5] Boder M, Dittmeyer R. Catalytic modification of conventional SOFC anodes with a view to reducing their activity for direct internal reforming of natural gas. Journal of Power Sources, 2006, 155(1): 13-22

[6] Haseli Y, Dincer I, Naterer G F. Thermodynamic modeling of a gas turbine cycle combined with a solid oxide fuel cell. International Journal of Hydrogen Energy, 2008, 33(20): 5811-5822

[7] Sangtongkitcharoen W, Assabumrungrat S, Pavarajarn V, Laosiripojana N, Praserthdam P. Comparison of carbon formation boundary in different modes of solid oxide fuel cells fueled by methane. Journal of Power Sources, 2005, 142(1): 75-80

[8] Wang Q S, Li L J, Wang C. Numerical study of thermoelectric characteristics of a planar solid oxide fuel cell with direct internal reforming of methane. Journal of Power Sources, 2009, 186(2): 399-407

[9] Finnerty C M, Ormerod R M. Internal reforming over nickel/zirconia anodes in SOFCS oparating on methane: influence of anode formulation, pre-treatment and operating conditions. Journal of Power Sources, 2000, 86(1-2): 390-394

[10] Peters R, Dahl R, Klüttgen U, Palm C, Stolten D. Internal reforming of methane in solid oxide fuel cell systems. Journal of Power Sources, 2002, 106(1-2): 238-244

[11] Seo Y S, Shirley A, Kolaczkowski S T. Evaluation of thermodynamically favourable operating conditions for production of hydrogen in three different reforming technologies. Journal of Power Sources, 2002, 108(1-2): 213-225

[12] Hou K, Hughes R. The kinetics of methane steam reforming over a Ni/α-Al₂O catalyst. Chemical Engineering Journal, 2001, 82(1-3): 311-328

[13] Clarke S H, Dicks A L, Pointon K, Smith T A, Swann A. Catalytic aspects of the steam reforming of hydrocarbons in internal reforming fuel cells. Catalysis Today, 1997, 38(4): 411-423

[14] Zhu H Y, Kee R J. A general mathematical model for analyzing the performance of fuel-cell membrane-electrode assemblies. Journal of Power Sources, 2003, 117(1-2): 61-74

[15] Wang Y Z, Yoshiba F, Watanabe T, Weng S L. Numerical analysis of electrochemical characteristics and heat/species transport for planar porous-electrode-supported SOFC. Journal of Power Sources, 2007, 170(1): 101-110

[16] Wang Y Z, Yoshiba F, Kawase M, Watanabe T. Performance and effective kinetic models of methane steam reforming over Ni/YSZ anode of planar SOFC. International Journal of Hydrogen Energy, 2009, 34(9): 3885-3893

[17] Wang Y Z, Li Y X, Weng S L, Wang Y H. Numerical simulation of counter-flow spray saturator for humid air turbine cycle. Energy, 2007, 32(5): 852-860

[18] Todd B, Young J B. Thermodynamic and transport properties of gases for use in solid oxide fuel cell modelling. Journal of Power Sources, 2002, 110(1): 186-200

[19] Chan S H, Khor K A, Xia Z T. A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness. Journal of Power Sources, 2001, 93(1-2): 130-140

[20] Hwang J J, Chen C K, Lai D Y. Computational analysis of species transport and electrochemical characteristics of a MOLB-type SOFC. Journal of Power Sources, 2005, 140(2): 235-242

[21] Xu J, Froment G F. Methane steam reforming machination and water gas shift-I. Intrinsic kinetics. American Institute of Chemical Engineers, 1989, 35(1): 88-96

[22] Costamagna P, Selimovic A, Del M B, Agnew G. Electrochemical model of the integrated planar solid oxide fuel cell (IP-SOFC). Chemical Engineering Journal, 2004, 102(1): 61-69

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg