A General Mechanistic Model of Solid Oxide Fuel Cells

TSINGHUA SCIENCE AND TECHNOLOGY I S S N 1 0 0 7 - 0 2 1 4 1 0 / 1 5 p p 7 0 1 -711 Volume 11, Number 6, December 2006

A General Mechanistic Model of Solid Oxide Fuel Cells SHI Yixiang (史翊翔), CAI Ningsheng (蔡宁生)** Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China Abstract: A comprehensive model considering all forms of polarization was developed. The model considers the intricate interdependency among the electrode microstructure, the transport phenomena, and the electrochemical processes. The active three-phase boundary surface was expressed as a function of electrode microstructure parameters (porosity, coordination number, contact angle, etc.). The exchange current densities used in the simulation were obtained by fitting a general formulation to the polarization curves proposed as a function of cell temperature and oxygen partial pressure. A validation study shows good agreement with published experimental data. Distributions of overpotentials, gas component partial pressures, and electronic/ionic current densities have been calculated. The effects of a porous electrode structure and of various operation conditions on cell performance were also predicted. The mechanistic model proposed can be used to interpret experimental observations and optimize cell performance by incorporating reliable experimental data. Key words: solid oxide fuel cell; porous electrode; transport phenomena; mechanistic model

Introduction In recent years, increasing attention has been paid to application of fuel cell technology in both the automotive and power industries. Compared to conventional energy conversion technologies, fuel cells promise power generation with high efficiency and low environmental impact. In particular, solid oxide fuel cells (SOFCs), which usually operate at 650-1000℃, allow conversion of a wide range of fuels, including syngas, biogas, and various hydrocarbon fuels. The relatively high operating temperature can result in highly efficient conversion to power and heat either for cogeneration or for a bottoming cycle[1]. Some demonstrations have indicated that the SOFC hybrid systems can have a higher efficiency and have both less pollutant Received: 2005-06-08; revised: 2005-10-24

﹡﹡ To whom correspondence should be addressed. E-mail: [email protected]; Tel: 86-10-62789955

emissions and lower greenhouse gas emissions than other alternatives[2]. With rising fuel prices and stricter emission control regulations, these capabilities make SOFC even more attractive. However, there are still numerous issues that need to be addressed before commercialization is possible. Since experimental studies on SOFC are expensive, time-consuming, and labor-intensive, quantitative mechanistic models are useful for SOFC scientists and developers, as they can help to elucidate the processes within the cell and allow optimization of materials, cells, stacks, and systems. SOFC porous electrodes are usually composed of electronic and ionic conductor particles. The operation of each cell involves complex chemical, electrochemical, and transport processes, with the performance strongly affected by charge transfer rates, conductivity of electronic/ionic conductor, and the transport resistances. Figure 1 illustrates the phenomena taking place in the SOFC electrodes, where subscripts “c”, “e”, and “a” are cathode, electrolyte, and anode, respectively.

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Fig. 1 Illustration of SOFC cathode, electrolyte, and anode

Many researchers have studied these complex transport and reaction processes through either experimental or numerical modeling[3-8]. However, due to a lack in our understanding of the electrochemical reactions, the intricacy transport processes, and the complex electrode structure, it is still frequently difficult to predict how material properties and geometry (e.g., porosity, tortuosity, particle size, electrode thickness, etc.) affect the polarization, even if the corresponding parameters of the elementary electrochemical reaction steps are known. The existing electrode models in the open literature can be divided into continuum level, manyparticle level, local current density distribution level, and chemical kinetics level models[9]. The choice of a suitable model level depends on the required accuracy. Sunde[10] used the Monte Carlo method to simulate composite electrodes, based on random resistor networks. Costamagana et al.[11] used a random packing sphere model, based on the particle coordination number and percolation theory. Tanner et al.[12] calculated the effective charge transfer resistance of an electrode as a function of electrode, intrinsic charge transfer resistance, the ionic conductivity of the electrolyte, and the electrode thickness. In order to predict the concentration polarization in detail, Virkar et al.[7] and Kim et al.[13] developed porous media gas phase transport models to predict concentration overpotentials, and used Tanner’s method to calculate activation overpotentials. Chan et al.[14,15] developed micro electrode models taking molecular and Knudsen diffusion as well as pressure-driven Darcy flow into account. However, none of the models have been validated using

reliable experimental data. In this paper we present a mechanistic model that couples structural assumptions, the intricate interdependency among the ionic conduction, electronic conduction, gas transport phenomena, and electrochemical processes. All polarization forms, including Ohmic polarization, activation polarization, concentration polarization, as well as leak overpotential, have been considered. To improve the general ability of the model, the active three-phase boundary (TPB) surface was expressed as a function of electrode microstructure parameters (porosity, coordination number, contact angle, etc.). The exchange current densities used in the simulation were obtained by fitting a general formulation to the polarization curves proposed as a function of cell temperature and oxygen partial pressure.

1

Model Description

1.1

Model assumptions

To simplify the calculation, it is necessary to make the following assumptions: (1) Steady state conditions apply. (2) The active surface area, and the temperature and total pressure distributions in the electrode are uniform. (3) The two conducting phases are considered as continuous and homogeneous. (4) The gas concentration and current density are uniform in the fuel channel. This assumption is acceptable because the length of the fuel channel is usually very small[16].

SHI Yixiang (史翊翔) et al：A General Mechanistic Model of Solid Oxide …

Thus, the model could be simplified to onedimension in the x direction along the electrode thickness. 1.2

Charge transfer

The charge transfer along the electronic and ionic conductive phases, and the transfer current between the electronic and ionic conductors can be modeled on the basis of the Ohm’s law. For the electronic conductor, (1) ∇Vel + ρ eleff iel = 0 For the ionic conductor, ∇Vio + ρioeff iio = 0

(2)

where Vel , Vio , iel, and iio are the voltages and current densities due to electronic transfer and ionic transfer. ρ eleff and ρioeff are the effective resistivities of the electronic conductor[11]. Within the electrodes, electrochemical reactions take place near the TPB and form the electron sink or source and the ion source or sink. These processes can be described by charge balance equations. In a onedimensional coordinate system, they can be simplified as diel (3) = − St i dx diio di = − el dx dx

(4)

where St is the TPB active area per unit volume of the electrode. This parameter has been formulated by some researchers by using the particle coordination number, together with the percolation theory as follows[7,9,11]: (5) S t = π sin 2 θ rel 2 nt nel nio Z el Z io Pel Pio / Z where rel is the average radius of the electronic conductor particle; θ is the contact angle between two different particles; nt is the total number of particles per unit volume; nel and nio are the fraction numbers of electronic conductor and ionic conductor particles; Zel and Zio are the coordination numbers; and Pel and Pio are the whole range connection probabilities of the same kinds particles. These parameters are discussed in detail by Costamagana et al.[11] and Chan et al.[14,15] In Eq. (3) i is the transfer current density. This value can be calculated by using the general current overpotential equation:

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⎛c n Fη ⎞ ⎞ ⎛ n Fη ⎞ crd ⎛ i = i0 ⎜ ox exp ⎜ α e − I exp ⎜ -（1 − α ) e ⎟ ⎟ I RT ⎠ crd RT ⎟⎠ ⎠ ⎝ ⎝ ⎝ cox (6) where α is the charge transfer coefficient, F is the Faraday constant, R is the gas constant, and η is the local polarization, defined as follows[11,14,15]: η = (Vioeq − Veleq ) − (Vio − Vel ) (7) di di d 2η = ρioeff io − ρeleff el =（ρeleff + ρioeff ) St i 2 dx dx dx

(8)

where Vioeq − Veleq is the equilibrium potential of the electrode, calculated on the basis of thermodynamic considerations, and cox , coxI , crd, and crdI are the oxidant and reductant concentrations at the reaction active site and at the electrode/channel interface. The oxidant and reductant concentrations can be simplified as the concentration of reactants and products at the anode: cox pH2O crd pH2 = I , I = I (9) I cox pH2O crd pH2

At the cathode, by assuming that the reductant concentration at the reactive sites is equal to that at electrode/channel interface, we can write cox pO2 = I , crd = crdI (10) I cox pO2

The exchange current density i0 is a very important parameter. It is defined as the current density of the charge-transfer reaction at the dynamic equilibrium potential. Under this circumstance, the forward and reverse current densities are equal at i0. Thus i0 is a measure of the electrocatalytic activity at the electrodeelectrolyte interface or the TPB for a given electrochemical reaction[17]. In fact, the exchange current density usually determines the activation overpotentials. A high exchange current density means that a high electrochemical reaction rate and good fuel cell performance can be expected[18]. It is very difficult to obtain a general expression for i0 as its value may depend both on the operating conditions and on the porous electrode structures. Some researchers have, however, proposed adapted models for calculating the exchange current density[19,20]. Reference [19] suggests that the general for mulation for i0 is

Tsinghua Science and Technology, December 2006, 11(6): 701-711

704 m

i0 =

β RT ⎛ −∆Gact ⎞ ⎛ cox ⎞ ⎛ crd ⎞ exp ⎜ ⎟⎜ I ⎟ ⎜ I ⎟ (2 + α ) F ⎝ RT ⎠ ⎝ cox ⎠ ⎝ crd ⎠

n

(11)

where β is a constant, ∆G is the electrochemical reaction activation energy of the electrodes, and m and n are exponential coefficients that differ among different authors. In this paper, the parameters used by Nagata et al.[19] are selected, with a few modifications made to the electrochemical activation energy in order to match experimental data. Another important parameter is the effective conductivity. It is calculated by correcting conductivity[14]:

σ eff = kσ

(12)

where k is an adjustable parameter of the model, usually taken as 0.5. The conductivity σ can be represented as a function of temperature according published data[19]. It should be noted that in the electrolyte layer, there is no current source or sink. Consequently, only the Ohm polarization exists in the electrolyte: dη (13) = ρ eeff I dx where ρ

eff e

is the effective resistivity of the yttria sta-

bilized zirconia (YSZ) electrolyte. 1.3

Gas transport

There are four types of major transport processes in porous electrodes. They are molecular diffusion, Knudsen diffusion, surface diffusion, and Darcy’s viscous flow[17]. A mass transport model must be applied to estimate gas concentrations inside the electrode. Darcy’s viscous flow can usually be neglected since its effects on cell performance is not significant, especially in binary fuel systems[14,21]. Surface diffusion may become dominant when the current density is high or when the effective gas component concentration is low. In this study, however, only the molecular diffusion and Knudsen diffusion are considered. The incorporation of surface diffusion into the model is left as further work. In general, gas transport inside a porous electrode can be described using either the extended Fick’s law or a dusty-gas model. Both models take into account molecular diffusion and Knudsen diffusion. The main difference between the two models is that the flux ratio in the dusty-gas model depends on the square-root of the gas molecular weight. A large number of studies

on gas transport phenomena are based on Fick’s law, as it allows the analytic expressions of the mass flux[5,8,9,14,15]. Some researchers[19], however, have used the Stefan-Maxwell model for mass transport calculations. Suwanwarangkul et al.[16] has compared these three models, and found that the dusty-gas model was the most accurate model, especially for conditions of high current density, low reactant concentration, and small pore size. In addition, Veldsink et al.[21] argued that although the reactant fluxes predicted by Fick’s model are in reasonable agreement with the dusty-gas model, the direction of product flow and the motion through the porous media are not predicted correctly. In the dusty-gas model the diffusive transport is described by the Stefan-Maxwell diffusion equations, and the convective motion is implemented in the flux equations directly[21]. The flux expression Ni for a single species i in a one-dimensional coordinate system according to the dusty-gas model results in an expression of the form: n (y N − y N ) Ni i j j i − = ∑ eff Di j pDi ,K eff j =1 j ≠i

y B0 p 1 dyi dp + i (1 + ) RT dx PRT µmix Di ,K eff dx

(14)

where yi is the mole fraction of gas species; Di ,K eff , and Di j eff are effective Knudsen and molecular diffusion coefficients, respectively; B0 is the permeability coefficient; and µmix is the dynamic viscosity of the gas mixture. In general, it is impossible to derive an explicit expression for the diffusion flux. Hence, most early studies using the dusty-gas model made a few approximations in order to solve the mass balance equations[21]. For binary diffusion and neglecting the pressure gradient in the porous electrode, the diffusion flux can be simplified as

N ⎛ 1 − yA − B yA ⎜ NA 1 1 ⎜ NA = + eff eff RT ⎜ DA-B DA,K ⎜ ⎝

－1

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

dpA dx

(15)

where subscripts A, B denote the gas components; for the SOFC anode they are H2 and H2O, and for the cathode they are O2 and N2. By assuming the gas mixture to be ideal, Dalton’s law of partial pressures and Graham’s law can be used: pi = yi p0 (16)

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SHI Yixiang (史翊翔) et al：A General Mechanistic Model of Solid Oxide …

NA = NB

MB MA

(17)

where M denotes the molar mass. The diffusion flux thus reduces to

collector interface are expressed as follows: dη = − ρ eleff I dx

－1

p M ⎡ ⎤ 1 − A (1+( A )0.5 ) ⎢ p0 MB 1 1 ⎥ ⎢ ⎥ + NA = eff eff RT ⎢ DA-B DA,K ⎥ ⎢ ⎥ ⎣ ⎦

dpA (18) dx

The relation between mass transport and electrochemical reaction can be expressed by Faraday’s law: N A = i /(ne F ) (19) where ne is the number of electrons transferred per reaction. The Knudsen and molecular diffusion coefficients are effective diffusivities correlated to material properties and can be calculated as[22]

Di ,K eff =

ε ε Di ,K = 97.0r τ τ

T Mi

(20)

eff DA-B =

ε DA-B τ

(21) where V is the diffusion volume, ε denotes the porosity of the electrode, τ is the porous tortuosity of the porous media, and r denotes the average pore radius. 1.4

Governing equation system and boundary conditions

By combining Eqs. (6), (8), (18) and (19), the equations for the electrode model systems can be rewritten as Eqs. (22)-(24). d 2η = ( ρeleff ＋ρioeff )i dx 2 ⎛c ne Fη ⎞ ⎞ ⎛ n Fη ⎞ crd ⎛ Sti0 ⎜ ox exp ⎜ α e ⎟ − c I exp ⎜ −(1 − α ) RT ⎟ ⎟ I c RT ⎝ ⎠ rd ⎝ ⎠⎠ ⎝ ox

(26)

dpA = pAI dx

(27)

where I is the total current density, including the electronic current density and the ionic current density. Once the local polarization distributions are determined, the total electrode polarization ηi can be calculated by assuming that the overpotentials at the electrode/electrolyte interface and the electrode/current collector interface are ηe-e and ηe-c[15]

ηi =

τ p (V 1/ 3 + V 1/3 )2 a A B

diel =I dx

The boundary condition at the electrode/electrolyte interface is expressed as follows: dη (28) = − ρioeff I dx

1/ 2

⎛ 1 1 ⎞ + ⎜ ⎟ MB ⎠ ε M = 0.001 01T 1.75 ⎝ A

(25)

ρeleffηe-c + ρeleff ρioeff ILi + ρioeffηe-e ρeleff + ρioeff

(29)

The total Ohm polarization on the electrolyte can then be solved analytically, eff ηelectrolyte,i = ρelectrolyte ILelectrolyte

1.5

(30)

Nernst potential

In order to predict the unit cell voltage, the cell open circuit voltage must be specified based on a chemical potential balance at open circuit. The expression for the Nernst potential can be simplified for the case of a fuel: pO0.52 ,c pH2 ,a RT (31) E = E0 − ln 2F pH2 O,a

(22)

where E0 is the ideal Nernst potential and can be calculated as ∆G 0 (32) E0 = − ne F

p M ⎡ ⎤ 1 − A (1+( A )0.5 ) ⎢ ⎥ p0 MB dpA RT 1 ⎢ = ＋ eff ⎥ iel eff DA-B DA,K ⎥ dx ne F ⎢ ⎢ ⎥ ⎣ ⎦

(23)

where ∆G0 is the change of standard-state Gibbs free energy between the products and the reactants.

diel 1 dη = − eff eff dx ρel ＋ρio dx 2

(24)

2

Solution Algorithm

2

The boundary conditions at the electrode/current

The model is solved by calculating the total current density I to determine the cell voltage. The cell real potential can be expressed as

Tsinghua Science and Technology, December 2006, 11(6): 701-711

706

Er = E − ηa − ηc − ηe − ηleak

(33)

Equations (22)-(24) are strongly nonlinear ordinary differential equations (ODEs) involving boundary value problems (BVP). The commercial software MATLAB was used as the solution platform. The solution procedure includes the following steps: (1) Calculation of the Nernst potential, which depends on the temperature and composition of both fuel and oxidizer; (2) Calculation of the anode and cathode polarization by solving governing Eqs. (22)-(24) based on appropriate boundary conditions given the total current density; (3) Evaluation of the electrolyte Ohmic polarization; (4) Evaluation of the cell voltage by considering all overpotentials. The steps described above only predict one cell voltage value for each total current density. To generate the full voltage-current plot, the above procedure is repeated over a range of current densities to calculate the corresponding cell voltages.

3

Results and Discussion

3.1

Model validation

Since it is almost impossible to control the distributions

of local overpotentials, gas component partial pressure, and electronic/ionic current density through experiment, a model validation was carried out on macro level. Figure 2 shows the calculated open circuit voltage and the experimental open circuit voltage as a function of water vapor partial pressure at 800℃ with air serving as the cathode gas. The results indicate that the calculated open circuit voltage exhibits the same trend as that of the experimental data, though the model values are a little higher than the experimental values. In this paper, we treat this as a so called “leak overpotential” denoted by ηleak. The leak overpotential was kept constant for all other calculations. The calculated polarizations of the anode, cathode and electrolyte are compared with published experimental data from Virkar[23] in Fig. 3. For the comparison, the fuel composition is taken as 97% H2, 3% H2O, while the oxidizer composition is 21% O2, 79% N2. The electrolyte thickness, Le, is 10 µm; the operating pressure, p, is 101 325 Pa; the operating temperature, T, is 800℃; and the leak overpotential, ηleak, is 0.05 V. The other relevant parameters are listed in Table 1. Most of these parameters are taken

Table 1 Parameters of electrode used in the SOFC mechanistic model Value

Parameter

Anode

Cathode

Electronic conductor particle size, rel (µm)

0.1-2

[23]

0.1-2 [23]

Ionic conductor particle size, rio (µm)

0.1-2 [23]

0.1-2 [23]

Average pore size, r (µm)

(rio+rel)/2

(rio+rel)/2

[23]

0.25[23]

[23]

0.5[23]

0.5

Electronic conductor mole fraction, nio Porosity, ε

0.5

Tortuosity, τ

5

Electronic conductor conductivity, σel (S/m)

5[1]

Ionic conductor conductivity, σio (S/m) Electrode thickness, L (µm) Hydrogen partial pressure, pH 2 (Pa)

5 103[1]

10 4

3.34×10 exp (−10 300/T)

[1]

4

3.34×10 exp (−10 300/T)[1]

1300 [23]

60 [23]

97 000

2[19]

α

2

2

β

5.5×108[19]

1.047×106[19]

M

0

0

N ∆Gact (J/mol)

[19]

0.133

75 000

0.5[19] 147 000

SHI Yixiang (史翊翔) et al：A General Mechanistic Model of Solid Oxide …

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Fig. 4 Experimental[23] and calculated cell voltage and power density as functions of current density Fig. 2 Calculated and experimental open circuit voltage as a function of pH2O for H2-H2O at 800℃

Fig. 5 Cathode overpotential as a function of current density with varying temperatures Fig. 3 Comparison of calculated anode, cathode, and electrolyte polarizations with experimental data[23]

from published sources though some others such as activation energy and tortuosity are fitted to the experimental data. The results show that the experimental values of anode, cathode, and electrolyte Ohm overpotentials can be represented well by our mechanistic model through fitting the activation energy used for calculation of i0 to the experimental data. The relative deviations between the experiment data and the calculated voltages are no larger than 1%. By incorporating the Nernst potential and the leak overpotential, the voltage-current plot and power-current plot can be created, as shown in Fig. 4. The relative deviation between the experimental data and the calculated voltages are no larger than 2%. The model can predict the cell voltage and power density accurately particularly for low current densities. Figure 5 shows a detailed comparison of the cathode overpotential-current plot at 650℃. Then data were created without changing any of the other parameters in the model.

Although the relative deviation at higher current densities between the experimental data and the calculated overpotentials reaches about 20%, the simulation results are much closer to the experimental data than the model without exchange current density modification. This shows that the present numerical model is quite reliable. The parameters used in the model are however not general and can not be used for other unit cells with different geometry or materials. In addition to bringing many valuable insights into the unit cell operator and to its use in interpreting experimental observations, this new mechanistic model can also be used in cell performance optimization 3.2

Parameter distributions

For convenience, the parameter distributions are plotted as functions of dimensionless thickness (the cathode is in the region between 0 and 1 in the x coordinate; the electrolyte is between 1 and 2; and the anode is between 2 and 3). For the calculations, the total current density was set at 30 kA/m2. The values of Lc, Le, and

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La are listed in Table 1. Figure 6 gives the oxygen partial pressure distributions at the cathode, and the water vapor partial pressure distributions at the anode. Both sharply decrease at the electrode/electrolyte interface, especially for small particle sizes (e.g., 0.1 µm). In general, the smaller the particle size, the smaller the pore size will be. If the average pore size is smaller than the mean-free path of the diffusion species, Knudsen diffusion resistance will become dominant in the mass diffusion process.

reactions mainly occur at the electrode/electrolyte interface. It should be noted that with decreasing electrode pore size, it becomes more difficult for the reactant gas to diffuse close to the anode/electrolyte interface. Thus the reaction will occur at a position further from the anode/electrolyte interface. In fact, the reactions always occur at the sites where the total resistances, including mass transport resistance, electrochemical activation resistance, and also the charge transfer resistance, reach the minimum[14]. It should be remembered, however, that the particle size in a real SOFC electrode is not uniform, whereas in our model we use a fixed value to simplify the analysis. 3.3

Influence of the particle size and electrode thickness on electrode performance

Figures 8 and 9 present the anode overpotential and cathode overpotential, respectively, as a function of the electrode thickness and the particle size. Fig. 6 Distributions of oxygen partial pressure on the cathode and the water vapor pressure on the anode (cc/ca, ca/el, el/an, and an/cc mean the interfaces of current collect and cathode, cathode and electrolyte, electrolyte and anode, and anode and current collect, respectively.)

Figure 7 gives the electronic current density and ionic current density distributions at the anode, cathode, and electrolyte. Most of the electrons are generated near the electrode/electrolyte interface where ions are eliminated. The calculations suggest that the electrochemical

Fig. 7 Distributions of electronic and ionic current density at the cathode, electrolyte, and anode

Fig. 8 Anode overpotential as a function of both anode thickness and particle size

Fig. 9 Cathode overpotential as a function of both cathode thickness and particle size

SHI Yixiang (史翊翔) et al：A General Mechanistic Model of Solid Oxide …

The results indicate that adopting a thin electrode with small particle size electrode could optimize electrode performance. If small particles are used, the electrode thickness should be reduced, otherwise, the electrode performance will deteriorate significantly. This result has been shown experimentally by Virkar et al.[7] In addition, if the particle size is large, the variation of electrode thickness has a relatively small impact on electrode performance. The impact of the particle size on the electrode performance at the anode is much smaller than that at the cathode. However, the electrode thickness and particle size are both limited by manufacturing techniques, and usually should be selected carefully to achieve good cell performance. 3.4

Impact of the gas component partial pressure on the electrode performance

Figure 10 shows the effect of the water vapor partial pressure in the fuel on the anode overpotential for different particle sizes. Since the sum of water vapor and hydrogen partial pressure remains constant (p0, 101 325 Pa), the figure also reflects the impact of hydrogen partial pressure on anode performance. The total current density was set at 30 kA/m2. The anode overpotential drops quickly as the water vapor partial pressure initially increases. After a certain water vapor content, the overpotential begins to increase. The nature of the polarization indicates that when the current density is relatively high, the forward reaction speed is much faster than the backward reaction speed. At certain high hydrogen concentrations, the effect of the concentration variation on the forward reaction speed is significant, whereas at relatively low hydrogen concentration, the effect of the concentration variation on the backward reaction speed is significant. Both of the cases will lead to an increase of the polarization. The results suggest that adding about 20% to 40% water vapor in the fuel for a particle size around 1 µm should optimize the anode performance. However, if a smaller particle size is used (e.g., 0.5 µm), the water vapor content optimized region is in the vicinity of 10% and is narrower. In the actual SOFC operation the water vapor content is significantly higher in the fuel channel downstream, especially in the case of higher fuel utilization and large current density. Thus, the cell voltage decreases along the fuel flow direction. This is the reason why some engineers have proposed the hybrid generation system, into which a bottom cycle is integrated

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Fig. 10 Anode overpotential as a function of water vapor partial pressure with different particle size

to maintain relatively low fuel utilization. Figure 11 gives the cathode overpotential as a function of oxygen partial pressure for different current densities. For low values of the oxygen partial pressure, the impact of the oxygen partial pressure on the cathode performance is relatively significant. In the actual SOFC operation the air utilization is relatively low, because there is usually an excess amount of air, or account of the fact that it serves as both the oxidant gas and cooling gas. However, at high current densities (>16 kA/m2), the cathode overpotential increases much more significantly as the oxygen partial pressure decreases. This dependency suggests that the air utilization should be carefully selected when the current density is high.

Fig. 11 Cathode overpotential as a function of the oxygen partial pressure and current density

4

Conclusions

A mechanistic model has been developed in this paper. The model shows the interactions between ionic

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Tsinghua Science and Technology, December 2006, 11(6): 701-711

conduction, electronic conduction, transport phenomenon, and electrochemical processes as well as electrode microstructure. The model has been applied to generate performance curves and polarization curves for certain cell configurations and specified operating conditions. This was appropriate in model validation. Numerical simulations were conducted mainly in the experimental data of Virkar[23]. The model results agree satisfactorily with the experimental data. It was found that reactions mainly occur at the electrode/electrolyte interface, where each parameter changes rapidly, particularly for small particle sizes. The impact of the particle size, and electrode thickness on electrode performance provides some insights for electrode microstructure optimization. The results indicate that the overall electrode polarization reaches a minimum at certain particle size depending on the thickness and the microstructure of the electrode. The electrode performance should be optimized by adopting a thin electrode layer with small particle size. However at present both the electrode thickness and particle size are limited by the available manufacturing techniques. The impact of gas composition on electrode performance was strong. Results also show that addition of a certain amount of water vapor into the fuel can reduce the anode overpotential. At the cathode, although the impact of the oxygen partial pressure on the cathode overpotential is relatively small, air utilization should be carefully selected when the current density is high. Finally, we note that it is still necessary to consider both competitive adsorption and surface diffusion in transport processes. The model should therefore be further improved and used to study the performance of SOFC systems using syngas or natural gas, both of which are more commonly used in actual SOFC applications. These developments will be the subject of further study. References

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[10] Sunde S. Monte Carlo simulations of conductivity of composite electrodes for solid oxide fuel cells. Journal of Electrochemical Society, 1996, 43: 1123-1132. [11] Costamagana P, Costa P, Antonucci V. Micro-modeling of solid oxide fuel cell electrodes. Electrochimica Acta, 1998, 43(3-4): 375-394. [12] Tanner C W, Fung K Z, Virkar A V. The effect of porous composite electrode structure on solid oxide fuel cell performance, I. Theoretical analysis. J. Electrochem. Soc., 1997, 144: 21-30. [13] Kim J W, Virkar A V, Fung K Z, et al. Polarization effects in intermediate temperature, anode-supported solid oxide fuel cells. Journal of the Electrochemical Society, 1999, 146: 69-78. [14] Chan S H, Xia Z T. Anode micro model of solid oxide fuel cell. Journal of the Electrochemical Society, 2001, 148(4): A388-A394. [15] Chan S H, Chen X J, Khor K A. Cathode micromodel of solid oxide fuel cell. Journal of the Electrochemical Society, 2004, 151(1): A164-A172. [16] Suwanwarangkul R, Croiset E, Fowler M W, et al. Performance comparison of Fick’s, dusty-gas and Stefan-

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SHI Yixiang (史翊翔) et al：A General Mechanistic Model of Solid Oxide … Maxwell models to predict the concentration overpotential

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Professor Wang Xiaoyun Awarded Qiushi Outstanding Scientist Prize Tsinghua Professor Wang Xiaoyun was awarded the Qiushi Outstanding Scientist Prize at the 2006 annual meeting of the China Association for Science and Technology, held in the Great Hall of the People on September 16, 2006. Professor Andrew Chi-chih Yao, the Turing Award Winner, gave an introduction to Professor Wang. Professor C. N. Yang, the Nobel Prize Winner, awarded the certification of honors to Professor Wang in recognition of her achievements in cryptology studies. Professor Wang Xiaoyun was born in 1966 in Shandong Province. She got her Ph.D. in Mathematics in Shandong University in 1993 and was a Professor of Shandong University before she came to Tsinghua. In 2005, Professor Wang was invited as a C. N. Yang Professor of the Center of Advanced Study, Tsinghua University. She is also the Changjiang Scholar specially appointed professor of Tsinghua. Professor Wang was renowned for breaking two international crypto system standards for electronic communications, MD5 and SHA-1, finding weakness. Five faculty members at Tsinghua University received the Qiushi Outstanding Youth Technology Transfer Award at the meeting.

（From http://news.tsinghua.edu.cn）