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

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1 DOI: /fuce Mathematical Modelling of Proton- Conducting Solid Oxide Fuel Cells and Comparison with Oxygen-Ion- Conducting Counterpart M. Ni 1,M.K.H.Leung 1 *,andd.y.c.leung 1 1 Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China Received November 24, 2006; accepted May 2, 2007 Abstract Proton-conducting solid oxide fuel cells (H-SOFC), using a proton-conducting electrolyte, potentially have higher maximum energy efficiency than conventional oxygen-ion-conducting solid oxide fuel cells (O-SOFC). It is important to theoretically study the current voltage (J V) characteristics in detail in order to facilitate advanced development of H-SOFC. In this investigation, a parametric modelling analysis was conducted. An electrochemical H-SOFC model was developed and it was validated as the simulation results agreed well with experimental data published in the literature. Subsequently, the analytical comparison between H-SOFC and O-SOFC was made to evaluate how the use of different electrolytes could affect the SOFC performance. In addition to different ohmic overpotentials at the electrolyte, the concentration overpotentials of an H-SOFC were prominently different from those of an O-SOFC. H-SOFC had very low anode concentration overpotential but suffered seriously from high cathode concentration overpotential. The differences found indicated that H-SOFC possessed fuel cell characteristics different from conventional O-SOFC. Particular H-SOFC electrochemical modelling and parametric microstructural analysis are essential for the enhancement of H-SOFC performance. Further analysis of this investigation showed that the H-SOFC performance could be enhanced by increasing the gas transport in the cathode with high porosity, large pore size and low tortuosity. Keywords: Mass Transport, Overpotential Losses, Porous Media, Proton-Conducting Electrolyte, SOFC 1 Introduction Solid oxide fuel cell (SOFC), identified as a promising technology for clean and efficient power generation to alleviate environmental burdens, has attracted increasing interests in recent years [1 6]. Operating at high temperature (400 1,000 C), SOFC eliminates the need for noble catalyst and, thus, is more cost-effective. In addition, high temperature enables direct reforming of hydrocarbons in SOFC, resulting in more flexible fuel choices [7 12]. Furthermore, the hightemperature waste heat can be effectively recovered for power generation by driving an integrated gas turbine to enhance the overall energy efficiency [13 16]. The conventional type of SOFC is oxygen-ion-conducting SOFC (O-SOFC) of which the electrolyte is commonly made of an oxygen-ion-conducting material, such as yttria-stabilised zirconia (YSZ). Extensive research studies have been conducted for the development of novel materials that can improve the electrochemical reactivity and withstand high operating temperature. Meanwhile, electrochemical mechanical models have been developed to characterise the O-SOFC performance [17 31]. These models in both micro- and macrolevels provide useful information on the working mechanisms of SOFC and can effectively facilitate robust O-SOFC design optimisation [32 34]. Besides O-SOFC, SOFC can be built with a protonconducting electrolyte to form a more advanced protonconducting SOFC (H-SOFC). H-SOFC is advantageous because complete hydrogen utilisation is highly plausible. [ * ] Corresponding author, mkhleung@hku.hk FUEL CELLS 07, 2007, No. 4, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 269

2 H-SOFC does not need any complicated gas separation process, which is, however, a requirement for O-SOFC. Furthermore, the Nernst potential of H-SOFC can be higher than that of O-SOFC, resulting in a higher open-circuit cell potential. Recent studies have shown that H-SOFC, using hydrogen, methanol or ethanol as a fuel, has higher maximum energy efficiency than O-SOFC [35 38]. Presently, experimental and analytical thermodynamic works done on H-SOFC are limited. As the proton conductivity is generally low, a lot of efforts are made to search for suitable proton conductors with high proton conductivity and long-term stability. Presently, the BaCeO 3 -based ceramics with proper doping, i.e. Nd, Y, Gd, Sm-doped BaCeO 3, exhibit moderate proton conductivity and have been widely used in H-SOFC [39]. Moreover, the ohmic loss of the electrolyte can be minimised by reducing its thickness to enhance the H-SOFC performance. It has been demonstrated that reducing the thickness of the protonic electrolyte from 500 to 50 lm, the achievable H-SOFC power density can be increased from 1,000 to 3,400 Wm 2 [40]. Besides some thermodynamics analyses on H-SOFC [35 38], none of the H-SOFC studies reported in the literature is related to electrochemical modelling. Thus, the gas transport behaviours and detailed overpotential losses are not clearly understood. For this reason, an H-SOFC electrochemical model was developed in the present study and quantitative analyses for the J V characteristics were conducted. The determinations of Nernst potential, ohmic overpotential and activation overpotentials of H-SOFC were accomplished based on the similarity to O-SOFC. The concentration overpotentials of H-SOFC, prominently different from the O-SOFC counterparts, were newly derived in this study. The comparison between H-SOFC and O-SOFC was made to investigate how the use of different electrolyte type could affect the electrical performance of SOFC. Finally, methods to enhance the H-SOFC performance were examined. 2 Model Development 2.1 Operation Mechanisms of H-SOFC The fundamental operation mechanisms of conventional O-SOFC and advanced H-SOFC are illustrated in Figures 1a and 1b for easy comparison. In a conventional O-SOFC, hydrogen fuel is fed to the anode and oxidant air (mixture of oxygen and nitrogen) is supplied to the cathode, oxygen ion flows through the electrolyte, and steam is formed as a byproduct and transported out of the anode. As the molar hydrogen consumption rate is equal to the molar steam generation rate, the gas pressure within the anode is invariant. Thus, the transport of hydrogen and steam in the anode is entirely by means of diffusion. On the other hand, the consumption of oxygen in the cathode electrolyte interface causes both gas pressure gradient and concentration gradient in the cathode; Fig. 1 Mechanisms of O-SOFC and H-SOFC. thus, oxygen is transported in the cathode by means of both permeation and diffusion. In an H-SOFC, hydrogen is also fed to the anode. At the anode electrolyte interface, H 2 is oxidised to H + and e. The electrons flow through an external load in the form of useful electricity, while the protons are transported through the proton-conducting electrolyte to the cathode. The consumption of hydrogen at the anode electrolyte interface causes a pressure gradient in the anode. Thus, hydrogen will continue to flow to the anode by permeation. At the cathode, O 2 is transported to the cathode electrolyte interface and reacts with H + and e to form H 2 O. The generated H 2 O is then transported to the cathode surface and leaves the fuel cell. As the oxygen molar consumption rate is half of the steam molar generation rate, both the pressure gradient and gas concentration gradient are established in the porous cathode. Therefore, gas transport in the cathode is by means of both diffusion and permeation. As the pressure at the cathode electrolyte interface is higher than that at the cathode surface, the pressure gradient exerts a negative effect on the transport of O 2 from the cathode surface to the cathode electrolyte interface WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 07, 2007, No. 4,

3 2.2 H-SOFC Potential Similar to conventional O-SOFC, the external voltage (V) of an H-SOFC can be determined by the equilibrium voltage minus the activation overpotentials, ohmic overpotential and the concentration overpotentials at both electrodes. The equilibrium voltage, the activation overpotentials and the ohmic overpotential of an H-SOFC can be obtained by Nernst, Butler-Volmer and Ohm s equations, respectively, similar to their O-SOFC counterpart [41]. However, the gas transport mechanisms of H-SOFC are prominently different from O- SOFC and thus, their derivations are the focus of this paper. 2.3 Concentration Overpotentials of an H-SOFC According to their definition, the concentration overpotentials of an H-SOFC can be expressed in the Nernst form as:! g conc;a ˆ RT 2F ln P0 H 2 P I H 2 and g conc;c ˆ RT 2F ln P0 O 2 1=2! P I H 2 O P I O 2 1=2 P 0 H 2 O where P I H 2, P I O 2 and P I H 2 O represent the pressure of hydrogen at the anode electrolyte interface, partial pressure of oxygen at the cathode electrolyte interface and partial pressure of steam at the cathode electrolyte interface, respectively. It is assumed that the electrochemical reactions take place at the electrode electrolyte interfaces. In a steady state, the transport of each participating component is determined by the local conservation of mass [42]: N i ˆ 0 (3 where N i is the flux of mass transfer of species i. In the anode of H-SOFC, H 2 is the only component present in the porous electrode layer. The transport of H 2 by means of permeation can be determined by Darcy s law [43]: N H2 ˆ P H 2 B g RTl H2 P H2 (4 where l H2 is the dynamic viscosity of H 2 and B g is the permeation coefficient, which can be determined by a sixth-order polynomial function developed by Todd and Young [44] and the Kozeny Carman relationship [45, 46], respectively. Substituting Eq. (4) into Eq. (3), the controlling equation for H 2 permeation in the porous anode can be obtained as: " x P # H 2 B g P H2 ˆ 0 (5 RTl H2 x (1 (2 where x is measured from the electrode surface and is applicable to both anode and cathode. At the anode electrolyte interface (x = d a, the thickness of anode), the rate of H 2 transport to the interface, which is equal to the H 2 consumption rate under steady-state condition, is governed by the electrical current density: J 2F ˆ P H 2 B g RTl H2 P H2 x (6 xˆda The Dirichlet boundary condition can be applied to the anode surface: P H2 j ˆ P 0 H 2 (7 xˆ0 Integrating Eq. (5) with boundary conditions of Eqs. (6) and (7), the analytical expression of P H2 at the anode electrode interface can be derived by: P I H 2 s ˆ P 0 H 2 2 JRTl H 2 d a FB g The anode concentration overpotential can thus be expressed as: 0r 1 g conc;a ˆ RT P 0 H 2F ln 2 2 JRTl H 2 d a FB B g A (9 P 0 H 2 On the cathode side, the mass transfer phenomena become more complex as three components (i.e. O 2,H 2 O and N 2 ) are presented within the porous electrode. In addition, both diffusion driven by the concentration gradient and permeation driven by the pressure gradient occur simultaneously. In the present study, the dusty gas model (DGM) is employed to characterise the mass transfer within the porous cathode. Considering both diffusion and permeation, the DGM can be written as [47, 48]: N i D eff Xn i;k jˆ1;j i 1 RT y j N i y i N j ˆ D eff ij " P dy i dx y dp i 1 B!# (10 gp dx D eff i;k l m where D eff i;k is the effective Knudsen diffusion coefficient of species i; D eff ij represents the effective binary diffusion coefficient of species i and j; y i represents molar fraction of species i; P the local total pressure within cathode and l m the dynamic viscosity of gas mixture (O 2, H 2 O and N 2 ). The determination of molecular diffusion and Knudsen diffusion coefficients can be found in the literature [42]. The gas mixture viscosity can be obtained by Wilke s method [49]. (8 FUEL CELLS 07, 2007, No. 4, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 271

4 Based on Eqs. (3) and (10), the mass transport of multicomponent gas species (i.e. O 2, H 2 O and N 2 ) inside the H-SOFC cathode can be determined. However, no analytical expressions can be obtained and an iterative scheme has to be used. Details of calculation are presented in the subsequent section. 2.4 Computation Procedures The Nernst potential, activation overpotentials and ohmic overpotentials are implicitly formulated in analytical forms by the Nernst equation, Butler Volmer equation and Ohm s equation, respectively. The anode concentration overpotential can be calculated directly by the newly derived analytical expression (Eq. (9)). The mass transport of gas species in the porous cathode is described by the DGM. The unknown parameters are molar fractions of each gas components (y O2, y H2 O and y N2 ) and the local total pressure P. The values of y O2, y H2 O, y N2 and P at the cathode surface serve as boundary conditions for the governing equations. In practical operation of SOFC, the molar fraction of H 2 O product is generally kept small to prevent considerable concentration overpotential, typically around 3% [35, 50, 51]. In a SOFC operating with air (79% N 2 ) as the oxidant, the values of y O2, y H2 O, y N2 and P at the cathode surface were set to 18, 3, 79% and 1 atmospheric pressure (atm), respectively. The governing equations were discretised by the finite difference method. An iteration approach is employed to obtain distributions of gas composition and total pressure. Computation is executed until convergence is attained. Substituting the final partial pressures of O 2 and H 2 O at the cathode electrolyte interface into Eq. (2), the concentration overpotential of the cathode can be calculated. Combining the calculated Nernst potential, activation overpotentials at both electrodes, concentration overpotentials at both electrodes and ohmic overpotential at electrolyte, the J V relationship of H-SOFC under steady-state operation can be obtained. and anode were made of Sm-doped BaCeO 3 (BCSO), Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3 x -BCSO and Ni-BCSO, respectively. The thicknesses of electrolyte, cathode and anode were 50, 35 and 650 lm, respectively. Tests were conducted under 1 atm and temperature from 773 to 973 K. The conductivities of electrolyte at 773, 873 and 973 K were 0.416, and siemens m 1, respectively. However, in subsequent parametric analyses, the typical electrolyte conductivity of 1.0 siemens m 1 was adopted [39, 50]. In Peng et al s experiments, oxygen, instead of air, was used as the oxidant. Therefore, in the simulation, y N2 and N N2 are eliminated from the calculation. In the theoretical simulation, the values of the input parameters are summarised in Table 1. The J V characteristics of H-SOFC are shown in Figure 2a. The effect of current density on power density is presented in Figure 2b. The cell potential decreased as the current density increased, while the power density reached the maximum at an optimal current density of about 7,000 A m 2. In Figures 2a and 2b, the simulated results agree well with experimental data by Peng et al. [40]., V / V 2.5 Concentration Overpotentials of O-SOFC The analytical formulae derived by Chan et al. [19, 20] can be employed to determine the concentration overpotentials of an O-SOFC. Detailed derivation and descriptions can be found in the literature [19, 20]. 3 Model Validation The above model was used to simulate experimental results published in the literature for model validation. Peng et al. s experimental work in H-SOFC was selected because the laboratory setup and test procedures were clearly reported in the literature [40]. In Peng et al. s experiments, the J V characteristics of power generation by anode-supported H-SOFC were measured. The electrolyte, cathode Fig. 2 Comparison between simulation results and experimental data [40] J V characteristics of H-SOFC under steady-state operation and effect of current density on H-SOFC power density WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 07, 2007, No. 4,

5 4 Results and Discussion Parametric analyses using the validated model were performed in this section. The input values of the case studies are summarised in Table Selection of H-SOFC Support An H-SOFC can be anode-supported, cathode-supported or electrolyte-supported. The overpotential losses of the three H-SOFC types are plotted in Figures 3a 3c. It is noted that activation overpotentials are not shown in Figures 3b and 3c because the values are same as those in Figure 3a. By inspection, electrolyte-supported H-SOFC configuration will be ruled out because thick electrolyte (500 lm) of low proton conductivity has very high ohmic overpotential (Figure 3c). As shown in Figures 3a and 3b, for both anode-supported and cathode-supported H-SOFC configurations, the limiting currents are caused by the cathode concentration overpotentials. This observation implies that the transport of O 2 with multiple species in the porous cathode is much lower than that of H 2 as a single component in the anode. Therefore, anode-supported H-SOFC using a thinner cathode yields a lower cathode concentration loss and a higher limiting current density. Additional quantitative comparisons of the power density are shown in Figure 3d. The maximum power Table 1 Values of input parameters used in the present study. Parameter Value Operating temperature, T /K For model validation 973 For parametric analyses 873 Operating pressure, P / atm 1.0 Gas composition at cathode surface For model validation (molar ratio of H 2 O/O 2 ) 0.03:0.97 For parametric analyses (molar ratio of H 2 O/O 2 /N 2 ) 0.03:0.18:0.79 Exchange current density at anode, J 0,a /Am 2 4,000 Exchange current density at cathode, J 0,c /Am 2 1,300 Electrode porosity, e 0.4 Electrode pore radius, r / lm 0.5 Electrode tortuosity, f 5.0 Electrolyte thickness, L / lm For model validation 50 Anode-supported H-SOFC 50 Cathode-supported H-SOFC 50 Electrolyte-supported H-SOFC 500 Anode thickness, d a / lm For model validation 650 Anode-supported H-SOFC 500 Cathode-supported H-SOFC 50 Electrolyte-supported H-SOFC 50 Cathode thickness, d c / lm For model validation 35 Anode-supported H-SOFC 50 Cathode-supported H-SOFC 500 Electrolyte-supported H-SOFC 50 (c) / V / V (d) / V Fig. 3 Selection of proper support for H-SOFC Overpotentials of anode-supported H-SOFC; cathode-supported H-SOFC; (c) electrolyte support and (d) power densities of H-SOFC with different support configurations. FUEL CELLS 07, 2007, No. 4, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 273

6 density of an electrolyte-supported H-SOFC (500 lm electrolyte, 50 lm cathode, 50 lm anode) is 500 Wm 2, which is consistent with the published experimental measurements [52 54]. A cathode-supported H-SOFC (50 lm electrolyte, 500 lm cathode, 50 lm anode) has a higher maximum power density of 1,000 Wm 2. An anode-supported H-SOFC (50 lm electrolyte, 50 lm cathode, 500 lm anode) exhibits the highest cell potential and power density of 3,400 Wm 2. As a result, the anode-support is apparently the most desirable configuration for H-SOFC. Although the electrolyte is thin (50 lm thick) in the anodesupported H-SOFC, the ohmic overpotential still dominates the loss among other overpotentials, except under operation near the limiting current condition [Figure 3]. Therefore, the development of novel electrolyte materials with high proton conductivity is of paramount importance to reduce ohmic overpotential. Alternatively, advanced materials or fabrication processes leading to the making of thinner ion conducting electrolyte will also reduce the ohmic overpotential. For reference, based on present technology, the oxygen-ion-conducting electrolyte of conventional O-SOFC can be made as thin as 8 lm [51]. 4.2 Effect of Operating Parameters on H-SOFC Performance In this section, the effects of operating parameters on the H-SOFC performance are discussed. Figure 4a shows the effect of temperature on H-SOFC J V characteristics. The cell potential increases significantly with increase in temperature because of higher proton conductivity of the electrolyte at a higher temperature. As a result, almost 100% increase in maximum power density can be obtained for temperature increased from 773 to 973 K, as shown in Figure 4b. The effect of the operating pressure on the H-SOFC J V curve is shown in Figure 4c. Similar to O-SOFC, the cell potential of H-SOFC increases with increase in pressure. As the gas density increases with increase in pressure, the molar diffusion rate can be enhanced at a higher pressure, leading to lower concentration overpotential. As a result, both cell potential and power density can be improved by increasing the pressure (Figures 4c and 4d). / K / K, V / V / atm / atm, V / V (c) (d) Fig. 4 Effect of operating parameters on H-SOFC performance effect of temperature on J V characteristics; effect of temperature on power density; (c) effect of pressure on J V characteristics and (d) effect of pressure on power density WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 07, 2007, No. 4,

7 4.3 Comparison of Concentration Overpotentials between H-SOFC and O-SOFC The theoretical model developed by Chan et al. [20, 21] was employed to calculate the concentration overpotentials at O-SOFC electrodes. The same electrode microstructures were used for H-SOFC as well. Figure 5 compares the anode concentration overpotentials between H-SOFC and conventional O-SOFC. At the anode of conventional O-SOFC, H 2 is the reactant and H 2 O is the product. The counterdiffusion of heavier H 2 O molecules slows down the diffusion of H 2 molecules to the reaction sites, resulting in a high concentration overpotential. For H-SOFC, H 2 is the only gas in the porous anode. The transport of small H 2 molecules by means of permeation is faster resulting in low concentration overpotential and high limiting current density. On the contrary, the cathode concentration overpotential of H-SOFC is more pronounced than that of O-SOFC, as shown in Figure 5b. In an H-SOFC using air as an oxidant, the reactant O 2 molecules are transported to the cathode electrolyte interface while the product H 2 O molecules are transported from the reaction site to the surface of cathode. The countertransport of H 2 O inhibits the transport of O 2. Furthermore, as the H 2 O molar generation rate is twice as much as the O 2 molar consumption rate, the pressure at the reaction site is higher than that at the cathode surface, inhibiting the transport of O 2. As a result, the overall resistance to the transport of O 2 is high, leading to high concentration overpotential. In an O-SOFC, H 2 O is produced at the anode site, eliminating the negative effect of H 2 O countertransport. In addition, the consumption of O 2 at the reaction sites causes a pressure gradient, which is beneficial for O 2 transport. Therefore, conventional O-SOFC has relatively lower cathode concentration overpotential than that of H-SOFC. The above analyses signify the difference in concentration overpotentials between H-SOFC and O-SOFC and also imply that the existing models for O-SOFC cannot be directly applied to H-SOFC. Thus, more modelling studies are needed for the optimisation of H-SOFC. As the cathode concentration overpotential of H-SOFC is more serious and limits the cell performance, it is more important to enhance the microstructure of the cathode to increase the H-SOFC performance. / V / V Fig. 5 Comparison between H-SOFC and O-SOFC anode concentration overpotentials and cathode concentration overpotentials. 4.4 Effect of Electrode Structural Parameters on H-SOFC Performance Figure 6a shows the effects of electrode porosity on the H- SOFC performance. The transport of O 2 and H 2 O is based on both diffusion and permeation. Increasing electrode porosity means higher void fraction that is favourable to gas transport and, in turn, increases both diffusion and permeation. Therefore, the cathode concentration overpotential decreases considerably, which further leads to increase in cell potential and enhanced power output. The effect of the pore size on the H-SOFC performance is shown in Figure 6b. The diffusion process in the porous cathode is based on both Knudsen diffusion and molecular diffusion. Increase in the pore size can facilitate the Knudsen diffusion process. In addition, the permeation process is also enhanced with increase in the pore size. Therefore, gas transport is facilitated with increase in the pore size, leading to decrease in cathode concentration overpotential and enhanced H-SOFC performance. Figure 6c shows the effect of electrode tortuosity on the H- SOFC performance. The cell power output increases with decrease in electrode tortuosity because low tortuosity of porous electrode implies short tortuous path for the gas transport and thus low resistance to transport of reactant O 2 and product H 2 O through the porous layer. Consequently, the concentration overpotential decreases and power density increases. The effects of the electrode structural parameters on the performance of a conventional O-SOFC are presented in Figures 7a c in order to discuss the difference between H-SOFC and O-SOFC. Both H-SOFC and O-SOFC are similar as their performance can be improved by increasing the electrode porosity, increasing the pore size or decreasing the electrode tortuosity. As shown in Figure 5, a conventional O-SOFC has FUEL CELLS 07, 2007, No. 4, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 275

8 a low limiting current density (<15,000 A m 2 ) for both anode and cathode. Thus, reduction in the gas transport resistance in both O-SOFC electrodes can yield significant improvement in the O-SOFC performance (Figures 7a c). On the other / µm hand, an H-SOFC has a low limiting current density for the cathode (Figure 5b) but a high limiting current density for the anode (Figure 5a). The H-SOFC performance can be improved by, primarily, modification of the cathode. / µm (c) Fig. 6 Effect of electrode microstructure on H-SOFC performance porosity effect; pore size effect and (c) effect of electrode tortuosity on cell performance. (c) Fig. 7 Effect of electrode microstructure on O-SOFC performance porosity effect; pore size effect and (c) tortuosity effect WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 07, 2007, No. 4,

9 4.5 Alternative Fuels for H-SOFC There is an increasing interest in using alternative fuels for SOFC. It is therefore useful to consider the effect of fuel type on the H-SOFC performance. As CO is one of the main products of coal/biomass gasification processes, synthesis gas (CO + H 2 ) is used as a typical fuel for O-SOFC. In the anode of an O-SOFC, CO and H 2 can be converted to CO 2 and H 2 O, respectively. However, since there is no O 2 available in the anode of an H-SOFC, H 2 O must be added to convert CO to CO 2 via water gas shift reaction [55]. As CO and H 2 O have higher molecular weight than H 2, the use of synthesis gas (CO + H 2 ) in H-SOFC is expected to cause a higher anode concentration overpotential, in comparison with the use of pure H 2 fuel. A higher CO content in the fuel requires more H 2 O supply, resulting in a higher anode concentration overpotential. Furthermore, other chemicals, such as methane, ethanol and ammonia, can also be used as fuels in an H-SOFC [36 38]. Similar to synthesis gas (CO + H 2 ), the use of other fuels will involve complex gas transport and chemical reactions. It will be fruitful to conduct further modelling study of the electrochemical behaviours of using different fuel types in H-SOFC. 5 Conclusion An electrochemical model was developed to study the J V characteristics of H-SOFC with an emphasis on the concentration overpotentials. The anode concentration overpotentials were calculated using the newly derived analytical expression. The cathode concentration overpotentials were obtained by the numerical method. Simulation results were compared with experimental data from the literature and good agreement was found. Subsequently, parametric analyses were performed to identify the key sources of voltage loss and to evaluate the effect of electrolyte type on the SOFC performance. Ohmic overpotential is found to be the major source of energy loss. Concentration overpotential at the cathode becomes a limiting factor of the H-SOFC at a high current density. The present study also reveals the significant difference in concentration overpotentials between H-SOFC and O-SOFC. In comparison with O-SOFC, H-SOFC has very small anode concentration overpotential but suffers from more serious cathode concentration overpotential. The prominent difference indicates the need for more modelling studies on H- SOFC. The considerable cathode concentration overpotential of H-SOFC can be minimised by increase in the electrode porosity and pore size or decrease in the electrode tortuosity. Acknowledgement The work described in this paper was part of an ongoing project supported by a grant from the Research Grants Council of Hong Kong, P. R. China (HKU7150/05E). References [1] T. Hibino, A. Hashimoto, T. Inoue, J. Tokuno, S. Yoshida, M. Sano, Science 2000, 288, [2] S. D. Park, J. M. 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