Two-dimensional mechanistic Solid Oxide Fuel Cell model with revised detailed methane reforming mechanism

Electrochimica Acta 249 (2017) 216–226

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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta

Two-dimensional mechanistic Solid Oxide Fuel Cell model with revised detailed methane reforming mechanism Jingde Li, Guihua Liu, Eric Croiset* Department of Chemical Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

A R T I C L E I N F O

Article history: Received 9 June 2017 Received in revised form 1 August 2017 Accepted 4 August 2017 Available online 7 August 2017 Keywords: Solid Oxide Fuel Cell Two-dimensional Modeling Elementary reactions Carbon deposition

A B S T R A C T

A revised mechanistic SOFC model is presented with two main important modifications compared to the current state-of-the-art mechanistic SOFC models: 1) current models are all developed based on the “CH4 adsorption mechanism”; this is one of the most critical reactions but studies have indicated that CH4 adsorbed dissociatively on nickel, which is considered in the present revised model; and 2) kinetic data in the current models are fitted, in particular those for critical reactions such as CH4 cracking, CO and CO2 surface reactions; in the present work, the activation energies for those reactions are taken from DFT calculations, while the pre-exponential factors are still fitted to experimental data. The results show that carbon distribution predicted by the revised model fits better the experimental observations reported in the literature and thus the proposed revised model represents a more realistic SOFC model operating with CH4 or CO fuel gas. Furthermore, the revised model was used to investigate the distributions of gas/ surface species concentration and temperature effects under humidified CH4. The results show that Ni surface is covered mainly by H(s) and CO(s) where the electrochemical reactions take place, whereas there is a very high coverage of C(s) where electrochemical reactions are absent. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction As a promising energy conversion device, solid oxide fuel cell (SOFC) powered by carbon-containing fuels (e.g. hydrocarbon) is gaining global wide attention in power generation industries [1,2]. Compared with H2 powered SOFC, it bypasses the technological hurdle associated with the practical generation and storage of H2 [3,4]. However, the reforming and electrochemical oxidation of hydrocarbon fuel within the SOFC anode are very complex [5]. For example, the dissociation of hydrocarbon produces many intermediate species that can electrochemically oxidized to H2O, CO and CO2 [6]. At the same time, hydrocarbon dissociation reactions can lead to carbon deposition at the anode catalyst [7,8]. Moreover, all these reactions are coupled together with ionic/electronic conduction and multiple gas transport processes in SOFC. As compared to experimental approaches, numerical approaches, pending reliable models, are more effective to investigate the underlying mechanisms of these complex coupled processes. In fact, many mathematical models have been developed to study the CH4 reforming in Ni based SOFC anode [9–13], but, most of these models consider only global reactions [14–18].

* Corresponding author. E-mail address: [email protected] (E. Croiset). http://dx.doi.org/10.1016/j.electacta.2017.08.017 0013-4686/© 2017 Elsevier Ltd. All rights reserved.

Although the models’ predictions agree well with experiments under different operating conditions, elementary reaction kinetic based model would provide more insights in revealing the reaction mechanism and processes in SOFC, in particular with respect to carbon deposition. Such SOFC models, however, are quite sophisticated. They require detailed description of the elementary heterogeneous and electrochemical reactions within the cell [13,19–25], which would be very difficult to implement in a model aimed at describing a full industrial SOFC stack. Instead, application of this model would be particularly suited to simulate isothermal SOFC button cells, which can be, in many instances, experimentally validated. Although many efforts have been made in the development of more sophisticated button cell SOFC models [19–27], most of these models are 1D models [13,19–22], which are not capable of modeling the fuel/air flow at the channels of SOFC. There are only a few 2D SOFC models with detailed CH4 reforming heterogeneous catalysis and electrochemical reactions reported in the open literature [23–27]. The reforming mechanism in the above 2D mechanistic models are the same. It consists of a total of 21 reversible elementary reactions and starts with CH4 adsorption and desorption on Ni catalyst surface [28]. Herein, it is referred as ‘CH4 adsorption mechanism’. However, experimental studies have reported that CH4 adsorption on Ni surface is more likely an activated dissociative chemisorption process [29,30]. Density Functional

J. Li et al. / Electrochimica Acta 249 (2017) 216–226

Nomenclature Am ci Em F G J k lTPB P R s T z

pre-exponential factor for reaction m (cm, mol, s) concentration of species i (mol m
3 or mol m
2) activation energy (J mol
1) Faraday constant (C mol
1) Gibbs free energy (J mol
1) current density (A cm
2) rate constant (m2 mol
1 s
1 or m3 mol
1 s
1) volume-specific TPB length of the composite electrode (m m
3) pressure (Pa) gas constant (J mol
1 K
1) species production rate (mol m
2 s
1) temperature (K) number of electrons transferred in the electrochemical

Greek symbols a symmetry factor of charge transfer reaction b temperature factor u surface coverage h overpotential (V) v stoichiometric coefficient s conductivity (S m
1) t tortuosity G area-specific density of Ni (mol m
2) e porosity Subscripts an anode ca cathode CT charge transfer reaction ele electron elyte electrolyte g gas i gas or surface species ion ionic m reaction Superscripts eff effective coefficient

Theory (DFT) studies also suggest that the catalytic CH4 reforming or cracking reactions starts with CH4 dissociative adsorption [31– 36]. Moreover, the reaction kinetics obtained from DFT are quite different from the empirical regressed values in the CH4 adsorption mechanism. For example, in the CH4 adsorption mechanism, the forward and backward energy barrier for the adsorbed CH4(s) dissociation reaction is reported as 57.7 and 58.83 kJ/mol, respectively [26]. The DFT calculated barriers for the forward and backward CH4 dissociative adsorption reactions are 109.995 and 62.717 kJ/mol, respectively [37]. The difference in forward and backward energy barriers can result in opposite trends of equilibrium constant changes for the reaction as function of temperature. According to the Arrhenius reaction rate equation, high temperature will accelerate reactions with high energy barrier more than that with low barrier. Therefore, one can expect that the forward CH4 dissociation reaction will be promoted as the temperature increases in the CH4 dissociative adsorption mechanism. In the CH4 adsorption mechanism, however, higher temperatures will favor CH4 production. It is well-know that higher temperature promotes CH4 reforming and cracking towards C and H2 production. This has been proven by both experimental

217

observations and thermodynamic calculations [38–41]. Therefore, the CH4 dissociative adsorption mechanism should be considered in the mechanistic model of SOFC instead of the CH4 adsorption mechanism. In addition, there are a significant disparities between DFT and empirically fitted kinetics of C

O bond formation reactions in CO and CO2 production (see Tables 1 and 2 reactions (14) and (15)). Therefore, the energy barriers of these key reactions obtained from DFT calculation should be evaluated in the model of SOFC. In the present study, 2D mechanistic models (orgModel and revModel) considering CH4 adsorption mechanism and CH4 dissociative adsorption mechanism, respectively, were developed for nickel/yttria-stabilized zirconia (Ni/YSZ) SOFC button cell system. In revModel, the energy barriers for CH4 dissociative adsorption, CO and CO2 formation on Ni catalyst surface are obtained from DFT. The corresponding pre-exponential factors are fitted from experimental polarization data. The rest of the reactions and their kinetic parameters are kept the same as that in orgModel. These detailed catalytic, electrochemical elementary reactions are coupled together with gas transport in the chambers and porous electrode and with the charge transfer processes. Prediction of carbon deposition using the two models are compared under different carbon-containing fuel, such as humidified CH4 and CO at various operating conditions. To have a better understanding of the reactions in a fuel cell and improve the cell performance, the distributions of gas/surface phase species concentration and operating temperature effects are also investigated. Moreover, a sensitivity analysis of the predicted carbon surface coverage and gas species concentration on the fitted preexponential factor Am of the critical elementary steps in revModel are also performed. 2. Model development 2.1. Model description Fig. 1a illustrates the schematic of the modelled anodesupported Ni-YSZ SOFC button cell test stand. The fuel gas is supplied to the anode electrode via a small ceramic tube located at the center of the large vertical tube, and the surplus gas and reaction products flow out from the large tube. The cathode electrode is exposed to the ambient air. A furnace is utilized to control the temperature of the cell test stand. Fig. 1b shows the computational domain of the 2D model used for the present study. The model assumptions are: i) the model is isothermal; ii) the gas mixtures are assumed to be ideal gases; iii) heterogeneous elementary reactions occur on the Ni surface and the active reaction sites are assumed to be uniformly distributed. Herein, the area located at the left side of the anode that is in contact with the electrolyte is referred as electrochemical reaction zone, whereas the other part of the anode is referred as the chemical reaction zone. 2.2. Chemical and electrochemical kinetics The global aspects of reforming, that involves CH4 cracking water–gas shift and Boudouard reaction, on the Ni catalyst is usually describe by the ‘CH4 adsorption’ mechanism [26,28]. It consists of 42 reactions which involve 6 gas phase species and 12 surface adsorbed species (Table 1). However, as mentioned above, both experimental and DFT studies have reported that CH4 adsorption on Ni surface is an activated dissociative chemisorption process [29–36]. Moreover, there is a significant disparity between DFT and empirically fitted kinetics of key elementary reactions, e.g. the first C

H cleavage in CH4, C

O bond formation in CO and CO2 production. These reactions are important because the first C

H

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Table 1 Surface reactions mechanism [23,26] in orgModel.

b

Em or DGCT (kJ mol
1)

No.

Reaction

Am or kf ;CT (cm, mol, s)

adsorption/desorption 1 2 3 4 5 6

H2(g) + 2*(s) ? H(s) + H(s) O2(g) + 2*(s) ? O(s) + O(s) H2O(g) + *(s) ? H2O(s) CO(g) + *(s) ? CO (s) CO2(g) + *(s) ? CO2(s) CH4(g) + *(s) ? CH4(s)

10
2; 2.545  10+19 10
2; 2.508  10+23 10
1; 3.732  10+12 10
2; 4.041 10+11 1 10
5; 9.334  10+7 8  10
3; 5.302  10+15

0; 0; 0; 0; 0; 0;

surface reaction 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

CH4(s) + *(s) ? CH3(s) + H(s) CH4(s) + O(s) ? CH3(s) + OH(s) CH3(s) + *(s) ? CH2(s) + H(s) CH2(s) + *(s) ? CH(s) + H(s) CH(s) + *(s) ? C(s) + H(s) O(s) + H(s) ? OH(s) + *(s) OH(s) + H(s) ? H2O(s) + *(s) C(s) + O(s) ? CO(s) + *(s) CO(s) + O(s) ? CO2(s) + *(s) CH3(s) + O(s) ? CH2(s) + OH(s) CH2(s) + O(s) ? CH(s) + OH(s) CH (s) + O(s) ? C (s) + OH(s) OH (s) + OH(s) ? H2O (s) + O(s) CO (s) + H(s) ? HCO (s) + *(s) CH (s) + O(s) ? HCO (s) + *(s)

3.7  1021; 4.438  10+21 1.7  1024; 8.178  10+22 3.7  1024; 9.513  10+22 3.7  1024; 3.008  10+24 3.7  1021; 4.4  10+22 5.0  1022; 1.781 10+21 3.0  1020; 2.271 10+21 5.2  1023; 1.418  10+22 2  1019; 3.214  10+23 3.7  1024; 3.815  10+21 3.7  1024; 1.206  10+23 3.7  1021; 1.764  10+21 3.0  1021; 6.373  10+23 2.338  1020; 3.7  10+21 7.914  1020; 3.7  10+24

0; 0 0; 0 0; 0 0; 0 0; 0 0; 0 0; 0 0;-3 0;-1 0; 0 0; 0 0; 0 0; 0 -1; 0 0;
3

0

Ni/YSZ-surface (Charge transfer reactions) 
22 O2
YSZ þ NiðsÞ ! OðsÞ þ V YSZ þ 2e 23 OðsÞ þ V  þ 2e
! O2
þ NiðsÞ YSZ

a,b

0 0 0 0 0 0

6.8  10+11

0; 0; 0; 0; 0; 0;

81.21 470.39 60.79 112.85a 28.80 33.15

57.7; 58.83 88.3; 28.72 100; 52.58 97.1; 76.43 18.8; 160.49 97.9; 36.09 42.7; 91.76 148.1; 115.97a 123.6a; 86.5 130.1; 21.97 126.8; 45.42 48.1; 129.08 100; 210.86 127.98; 0b 114.22; 95.8

74.00 (Em) -79.826 (DGCT)

YSZ

In addition to the Em, a coverage dependent activation energy ekm of
50 kJ mol
1 and 50 kJ mol
1 were used, respectively.

Table 2 Revised reactions mechanism and kinetics from DFT [37,45] used in revModel.

a

No.

Reaction

Am or kf ;CT (cm, mol, s)

6&7 14 15

CH4(g) + 2*(s) ? CH3(s) + H(s) C(s) + O(s) ? CO(s) + *(s) CO(s) + O(s) ? CO2(s) + *(s)

1.397  10+15; 2.338  10+13 2.2  1021; 3.3  10+23 9  1020; 6  10+17

0

b

Em (kJ mol
1)

-1.5; 0 0;
1 0; 0

109.995; 62.717 153.414; 290.43a 146.66a; 54.033

In addition to the Em, a coverage dependent activation energy ekmof
50 kJ mol
1 was used.

breaking is usually reported as the rate determining step in CH4 dissociation [43,44], whereas the C

O bond formation are the elementary steps producing CO and CO2. As discussed in Section 1, the disparity between DFT and empirical reaction kinetics can make a significant difference in the predicted reaction behavior as function of temperature. Table 1 shows the reported heterogeneous chemistry reactions and kinetics that were used in

orgModel. In revModel, the CH4 adsorption (R6) and dissociation (R7) reactions (Table 1) are replaced by CH4 dissociative adsorption (R6&7) (Table 2). The energy barriers for CH4 dissociative adsorption, CO and CO2 formation on Ni catalyst surface obtained from DFT are implemented in revModel (Table 2). The rest of the reactions and their kinetics are kept the same as that in orgModel.

Fig. 1. a) Schematic of SOFC button cell test stand and b) the axisymmetric 2D model used for the present study [36].

J. Li et al. / Electrochimica Acta 249 (2017) 216–226

Regarding the electrochemical reactions in the SOFC electrodes, the oxygen gas (O2,gas) “catches” e
at the cathode side and is

219

Eact f :CT

!

    DGCT ð1
aÞzF exp han exp
RT RT

converted into oxygen ion (O2
YSZ Þ on the surface of YSZ ionic conductor, according to Eq. (1):

kr;CT ¼ kf ;CT exp


1 O2;gas þ 2e
þ ðYSZ Þ ! O2
YSZ 2

where kf ;CT is the pre-exponential factor; Eact is the thermal

RT

ð6Þ

0

ð1Þ

The O2
YSZ ion is then conducted toward the anode gas/ceramic/ catalyst triple phase boundaries (TPBs) sites, where O2
YSZ is released from OXYSZ and charge transfer reactions take place. In the present elementary model, electrochemical reactions are assumed to take place at TPB and in a single-step reversible oxygen-spillover charge transfer (CT) process [20,46]: 
O2
YSZ þ NiðsÞ$OðsÞ þ V YSZ þ 2e

0

ð2Þ

activation energies, DGCT is the Gibbs free energy change of the charge transfer reaction, z is the number of electrons transferred in the electrochemical reaction (z = 2), a is the symmetry factor of charge-transfer reaction, han is the anodic overpotential which will be described later, and F is the Faraday constant (96,487 C mol
1). Detailed information about the kinetic rate expressions and the source of the faradic current (Q) derived from electrochemical reactions in the electrodes can be found in [42] The local overpotentials at anode han and cathode hca are defined as

The adsorption rate constant, kads, of a gas molecule onto Ni surface was calculated as: rffiffiffiffiffiffiffiffiffiffiffiffi   Am RT Em kads ¼ g T b exp
ð3Þ 2pW RT G

han ¼ V elec;an
V ion;an
V ref ;an

ð7Þ

hca ¼ V elec;ca
V ion;ca
V ref ;ca

ð8Þ

where, Am is the sticking coefficient, W is the molecular weight of the gas-phase species; g is the number of surface sites involved in the adsorption. In the present study, g equals to 1 for adsorption; b is the temperature factor; G is the area-specific density of Ni (mol m
2); Em is the activation energy. For all other surface reactions (including dissociative adsorption), their rate constants are expressed in Arrhenius rate form as [23]:

where Velec and Vion are the electron and ionic potentials of the conductor phases at the electrodes, respectively; Vref,an is the anode reference potential and was set to zero; Vref,ca is the cathode reference potential, which can be determined by Nernst equation as [47]: ! Pca RT O2 ln an ð9Þ V ref ;ca ¼ 4F P O2

   Ks  Em Y ekm ui km km ¼ Am T b exp
um exp
RT k¼1 i RT

ca where Pan O2 and P O2 an are the equilibrium O2 partial pressures in

ð4Þ

where km is the rate constant for the mth reaction, Am is preexponential factor, mkm and ekm are parameters modeling the coverage dependency of rate constant ui is the surface coverage of ith surface species, which is defined as u i ¼ CGi , where ci is surface concentration. For the CT reaction occurring in the anode, the reaction rate coefficients kf,CT and kr,CT for reaction 23 and 24 (Table 1) can be represented as [42], !   Eact azF f :CT 0 han ð5Þ kf ;CT ¼ kf ;CT exp
exp RT RT

anode and cathode, respectively. Pan O2 is determined by the elementary reactions mechanism when iteratively solving the model. 2.3. Numerical implementation and setup The finite element commercial software COMSOL MULTIPHSICS V4.3b was used to carry out the simulations in the presents study. Due to the symmetricity of the cell and flow conditions, a 2D computational domain is used to represent a complete SOFC cell (Fig. 1b). The inner fuel channel has a radius of 3.0  10
3 m. The radius for the outer fuel channel is 7.5  10
3 m. The thickness of the wall in between the inner and outer fuel channel is 1.0  10
3 m. Regarding the air channel, it has a radius of

Table 3 Configuration and material properties of the anode, electrolyte and cathode [42]. Parameters

Value

Units

Anode Thickness, radius Porosity (e) Tortuosity(t) Ni electronic conductivity(s Ni) Surface site density of Ni (G)

5.0  10
4, 7.5  10
3 0.4 1.2 ð3:27e6
1060:3½1=K   T Þ

m

Volumetric TPB length

7:2  1011

m m
3

Electrolyte Thickness, radius YSZ ionic conductivity (s YSZ)

2.5  10
5, 7.5  10
3

m s m
1

Cathode Thickness, radius Porosity (e) Tortuosity(t) LSM electronic conductivity(s LSM) Volumetric TPB length

3.0  10
5, 3.0  10
3 0.35 3.5 4:2e7½S  K=m=T  expð
1150½K =T Þ

5:1  10
5

3:34  104 expð
10300=T Þ

4:4  1010

s m
1 mol m
2

m

s m
1 m m
3

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J. Li et al. / Electrochimica Acta 249 (2017) 216–226

9.5  10
3 m. The configuration and material properties of the anode, electrolyte and cathode, e.g. dimension, ionic/electronic conductivities, are listed in Table 3. Note that, the ionic/electronic conductivities of the electrodes in the table are for pure material. For porous composite electrodes, effective electronic or ionic

revModel

should be used [48–51]. In the present study,

seff i is calculated using the statistical properties of random packing systems of binary spherical particles, e.g., percolation probability [51]. The 2D domain was discretized into triangular mesh elements with “Extra fine” element size. The complete mesh consists of approximate 12500 domain elements. The simulations were carried out using multifrontal massively parallel sparse (MUMPS) Direct and Fully Coupled nodes together with the stationary solver. Gas transport in the fuel/gas supply channel is simulated using laminar flow model. The momentum conservation in the fuel/gas supply channel and porous electrodes are described by the compressible Brinkman equation and the Darcy’s law, respectively. Charge balances were formulated using generic Ohm’s law. A detailed introduction of these governing equations can be found in a previous study [42]. Convergence was determined when the estimated relative error in Newton iterations is smaller than the specified tolerance of 10
3.

1.0 0.8 0.6 0.4 0.2 0.0

0.5

1.0

2.0

2.5

3.0

Current Density (A/cm ) Fig. 2. Comparisons between simulation and experimental polarization curve for humidified CH4 fuel gas (97%CH4–3%H2O) at different temperatures from reference [47].

0.8

Voltage (V)

revModel o 600 C 700oC 800oC

orgModel 600oC 700oC 800oC

1.0

2.5. Model validation

1.5

2

2.4. Boundary conditions To solve the partial differential equations used in the multiphysics transport processes, boundary conditions are applied to the computational domain in Fig. 1b and are listed in Table 4. The inlet fuel gas are humidified methane (97%CH4–3%H2O) and pure CO. The cathode is fed with air. The operating pressure is 1 atm. The velocity (or flow rate) of the inlet fuel and ambient air at the fuel and air channel was set to 0.15 and 0.05 m s
1, respectively. The operating temperatures are in the range of 600–800  C. The cell voltage are specified at the cathode/channel interface. In the boundary conditions, “Insulation” mean that the partial derivative of the electron and ionic potentials (Velec and Vion) at the boundary are zero. “Wall” represents the velocity is zero. All other boundaries in the 2D domain that are not mentioned in Table 4 are “Insulation” for electronic/ionic charge transfer, “No flux” for mass transfer, and “Wall” for momentum transfer process.

Exp600oC o Exp700 C Exp800oC

orgModel 1.2

Voltage (V)

conductivitiess

ef f i

1.4

0.6

0.4

0.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Current Density (A/cm2) Fig. 3. The polarization curve for pure CO fuel gas predicted by the orgModel and revModel at different temperatures.

The current density and gas/surface species concentration distributions were calculated under different operating conditions, such as voltage, fuel gas composition, temperature. The polarization curves predicted by orgModel and revModel are compared with the experimental measurement reported by Liu et al. [52]. The experiments were carried out using fuel gas composed of 97% CH4 and 3% H2O and with ambient oxygen as the oxidant under different operating temperatures. A comparison of experimental and simulated polarization curves is shown in Fig. 2. The results indicate that the SOFC polarization performances of both orgModel and revModel are very similar and they reasonably well reproduced the experimental observations. Note that the preexponential factors in Table 2 (used in revModel) are fitted to

reproduce experimental measured current density at 0.8 V and 700 C. Then, the parameters were fixed and used to predict the current density at other voltages and temperatures. Also, it should be mentioned that revModel cannot converge at low current density especially at high temperatures (Fig. 2). This is due to the high carbon deposition coverage predicted in the chemical reaction zone by revModel at steady-state as discussed in section 4.3. The validated model is then used for further simulation studies. When using pure CO as fuel gas, the simulated polarization curves by revModel is slightly higher than that of orgModel especially at higher temperatures (Fig. 3). This might result from the CO2(s) formation/dissociation (R15) energy barriers used in the

Table 4 Boundary conditions. Air channel inlet

Cathode/channel

Cathode/electrolyte

Ionic charge Electronic charge Mass Momentum

N/A N/A Air composition Pressure/velocity

Insulation Cell voltage Continuity Continuity

Continuity Insulation No flux Wall

Anode/electrolyte

Channel/anode

Fuel channel inlet

Continuity Insulation No flux Wall

Insulation 0 Continuity Continuity

N/A N/A Fuel composition Pressure/velocity

J. Li et al. / Electrochimica Acta 249 (2017) 216–226

two models. The revModel has a higher activation energy (146.66 kJ mol
1) for the CO2(s) formation than that in orgModel (123.6 kJ mol
1). For CO2(s) dissociation reaction, however, revModel has a lower energy barrier (54.033 kJ mol
1) than that in orgModel (86.5 kJ mol
1). As a result, CO2(s) formation will be more favored in revModel than orgModel at higher temperature. This can promote the consumption of O(s) in revModel and the electrochemical reactions as well. 3. Results and discussion 3.1. Temperature effect on surface carbon distribution within the anode Fig. 4 shows the surface carbon coverage u CðsÞ distribution within the SOFC anode using humidified CH4 as fuel gas predicted by the orgModel and revModel. In all cases, it is observed that uCðsÞ gradually decreases from fuel channel/anode interface towards the electrolyte. Fig. 4a show the temperature effect of uCðsÞ distribution at a current density of 0.25A/cm2. As the temperature increases from 600 to 700  C, both the orgModel and revModel predict an increase of uCðsÞ . But, the u CðsÞ increase more rapidly in revModel than orgModel. Since the revModel did not converge at 800  C and 0.25A/cm2, the u CðsÞ distribution from 700 to 800  C was studied at a higher current density J = 0.50A/cm2 (Fig. 4b). The results show that, in orgModel, uCðsÞ at T = 800  C is slightly higher than that at T = 700  C. In revModel, however, uCðsÞ increases significantly when

221

temperature increases from 700 to 800  C. The carbon deposition behavior predicted by revModel is closer to the experimental observations, in which carbon deposition was found to increases rapidly with increasing temperature on Ni/YSZ anode when the cell is operating under a same current density [39,53]. Therefore, the effect of temperature on uCðsÞ distribution is not as important for orgModel as for revModel. As discussed in section 1, this results from the two different methane cracking mechanisms and corresponding energy barriers implemented in the models. The forward CH4 dissociation reaction in revModel has a much higher activation energy barrier (109.995 kJ mol
1) than that in orgModel (57.7 kJ mol
1). Therefore, temperature will have a more significant effect on the prediction for revModel than for orgModel. The temperature effect on surface carbon coverage u CðsÞ distribution using pure CO as fuel gas was also investigated. Fig. 4c and d show u CðsÞ distribution at J = 0.25A/cm2 predicted by orgModel and revModel, respectively. Different from that observed in humidified CH4, opposite trends were observed for uCðsÞ from CO fuel: carbon deposition increases as the temperature decreases. This is consistent with what is reported experimentally [39,54]. Moreover, Fig. 4c and d shows that uCðsÞ in revModel drops more rapidly in the direction of gas/anode interface to the electrolyte than that in orgModel. In fact, the revModel prediction using humidified CH4 and CO agrees well with what is reported by Sumi et al. [55]. For example, their experimental study found that carbon deposition mainly occurs near the anode surface in CO-CO2 fuel and less amount of carbon was observed near the anode/

Fig. 4. Surface carbon coverage uCðsÞ distribution along the distance from gas/anode to anode/electrolyte interface at cell axis-symmetric line for humidified CH4 fuel gas (97%CH4-3%H2O) and pure CO fuel gas at different temperatures: a) @0.25A/cm2 and b) 0.50A/cm2 under humidified CH4; c) @0.25A/cm2 under pure CO with orgModel and d) 0.25A/cm2 under pure CO with revModel.

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electrolyte interface, suggesting that CO disproportionation proceeds mainly near the anode surface. On the other hand, carbon was deposited more evenly throughout the anode in humidified CH4. When comparing the uCðsÞ profile, the results from revModel much better describe the experimental observations by Sumi et al. regarding carbon deposition for the cases of humidified CH4 and CO feed than the results from orgModel. In the rest of the paper, the focus is in describing the surface and gas species distributions predicted from revModel, which are not easily accessible experimentally. 3.2. Distribution of gas species Fig. 5 shows the molar fraction distributions of gas species CH4, H2, H2O, CO, CO2 and O2 within the gas channels and porous electrodes predicted by revModel. The operating temperature for the simulation is 700  C. The cell voltage is set at 0.6 V under humidified CH4 fuel gas and oxidant air. It can be seen that the molar fraction of CH4 decreases from the inlet toward the anode/ electrolyte interface (Fig. 5a). In the anode, CH4 was converted into H2, H2O, CO and CO2 by electrochemical oxidation. The molar fractions of H2, H2O, CO and CO2 show opposite trend and increases towards the gas flow direction with H2O and CO2 mainly exist in the anode area close to the anode/electrolyte interface (Fig. 5b–e). Fig. 5f shows the molar fraction profile of O2 at the cathode side and there is a slight decrease of O2 concentration toward the cathode/electrolyte interface. Similar trends were observed in the orgModel for the gas phase distribution from fuel inlet toward the anode/electrolyte interface (Fig. S1 in Supplementary Information). As compared with the revModel, the orgModel also predicts similar gas species concentration (CH4, H2, CO, CO2 and H2O) in the outlet stream. But, they predict different gas concentration distribution in the electrochemical and chemical reaction zones. The revModel predicts a slightly higher CH4 concentration and lower CO and H2 concentrations in the electrochemical reaction zone than in the chemical reaction zone. However, in the orgModel, a lower CH4 concentration and higher CO and H2

concentrations are observed. This suggests that: i) in revModel, the electrochemical reaction is mainly contributed by H(s) oxidation. This can also be supported by the high H2O concentration in the electrochemical reaction zone (Fig. 5c), ii) In orgModel, the electrochemical reaction is mainly governed by CH4(s) and C(s) oxidation, producing more CO and less H2O in the electrochemical reaction zone than that in revModel. This might also result from the two different CH4 cracking reaction mechanisms and their kinetics in revModel and orgModel. In the orgModel, the CH4(g) first adsorbs on the Ni surface CH4(s); then, it can dissociate into CH3(s) and H(s) or reacts with O(s) through R7 and R8 (Table 1), respectively. In revModel, however, CH4(g) will directly dissociates into CH3(s) and H(s) and there is no CH4(s). Therefore, as compared with revModel, the ‘CH4 adsorption mechanism’ in orgModel provide an important CH4(s) oxidation pathway. Moreover, in orgModel, H(s) and O(s) reaction (R12) rate constants are about 50 times that of the C(s) and O(s) reaction (R14) rate. But, it becomes 23000 in revModel indicating that H2O production is more favored in this model than in orgModel. 3.3. Distribution of adsorbed surface species within the anode Fig. 6 illustrates the distribution of the major adsorbed surface intermediates species within the anode for the case humidified CH4 fuel gas, oxidant air, 700  C and cell voltage of 0.6 V. The results show that, in the electrochemical reaction zone, surface coverage (u ) of oxidation productions, e.g. H2O(s), CO(s), CO2(s) and O(s) increase from the channel/anode interface toward the anode/ electrolyte interface, whereas uH slightly deceases toward the anode/electrolyte interface. Moreover, Fig. 6 also shows that the electrochemical reaction zone are mainly covered by H(s) (15%) and CO(s) (8%), the remaining being vacant sites. In the chemical reaction zone, however, there is a very high coverage of C(s) (70%) (Fig. 6e). The corresponding current density is 0.55 A/cm2. One can expect that when the current density is even lower, the C(s) coverage in the chemical reaction zone will be keep increases. This might be the reason that causes the convergence problem in

Fig. 5. The molar fraction distribution of bulk gas species within electrodes predicted by revModel: a) CH4; b) H2; c) H2O; d) CO; e) CO2 @anode and (f) O2@cathode. Operational condition: humidified CH4 fuel gas (97%CH4-3%H2O), oxidant air, 700  C and cell voltage at 0.6 V.

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223

Fig. 6. Surface coverage distribution of adsorbed surface species within the anode predicted by revModel: a) H(s), b) H2O(s), c) CO(s), d) CO2(s), e) C(s), and f) O(s). Operational condition: humidified CH4 fuel gas (97%CH4-3%H2O), oxidant air, 700  C and cell voltage at 0.6 V.

revModel at low current density. An important difference between revModel and orgModel is that the orgModel predicts that the uH increases from anode/channel to the anode/electrolyte interface and, more importantly, that the u CðSÞ at the chemical reaction zone is less than 1% (Fig. S2 in Supplementary materials). 3.4. Effect of operating temperature on the surface species distribution The operating temperature can significantly affect the surface reaction and transport processes in SOFC. Herein, we further investigated the effect of temperature on the surface species distribution within SOFC anode using humidified CH4 fuel gas at 0.6 V cell potential. Fig. 7 shows the distributions of the major surface species (H, O, H2O and CO) along the axial-symmetrical line of the cell (r = 0) at temperatures of 600  C, 700  C and 800  C. The results show that the surface coverage of H(s) increases as the temperature increase from 600  C to 700  C, and then decreases when temperature is increased to 800  C. The surface coverage of O (s) follows the opposite trends: it decreases first and then increase when the temperature increases from 600  C to 800  C. This might results from the reaction rate acceleration disparity between CH4 dissociative adsorption (Rre6,f), OH(s), CO(s), CO2(s) formation (R12, R14, R15, respectively) and electrochemical reaction (R22) at different temperatures. It was found that, as the temperature increases from 600  C to 700  C, higher reaction rate constant acceleration of Rre6,f (4.07), R12 (3.95), R14 (8.77) and R15 (7.96) are observed than that of R22 (2.85). This indicates that the H(s) production and O(s) consumption rate are more accelerated than O (s) production when the temperature increases. As a result, uHðsÞ will increase as the temperature increases from 600  C to 700  C, whereas uOðsÞ shows opposite trend. When the temperature increase from 700  C to 800  C, the acceleration of reaction rate constant will drops for Rre6,f (24.08%), R12 (22.78%), R14 (33.18%), R15 (32.16%) and R22 (17.54%), respectively. The acceleration rate of H(s)

production (Rre6,f) and O(s) consumption (R12, R14, R15) drops more than O(s) production (R22). This will favors O(s) production more than H(s) production. Therefore, one can expect that uOðsÞ will increase as the temperature increases from 700  C to 800  C, whereas u HðsÞ will drops. Despite the rate acceleration competition between the production and consumption of H(s) and O(s) surface species, they will eventually react with each other and form H2O(s) and CO(s). Thus, the production of H2O(s) and CO(s) always increases as the temperature increases from 600  C to 800  C (Fig. 7c and 7d). As compared with the revModel, the orgModel predicts an opposite trend for the temperature effect on uHðsÞ , uOðsÞ anduH2OðsÞ . Details can be found in the Supplementary Information (Fig. S3). 3.5. Sensitivity on the kinetic parameters in revModel As discussed in section 2, the energy barriers for key reaction steps in revModel were obtained from DFT calculations. However, the pre-exponential factors Am was tuned to fit the experimental polarization curves at different temperatures (Fig. 2). The uncertainties in Am can translate into variability in the predicted surface coverage and gas species concentration. To examine the sensitivity of the predicted surface coverage and gas species concentration on Am used in revModel, the uncertainty associated with Am in the selected key elementary steps was studied. Those key elementary steps in revModel are show in Table 2: i) CH4 dissociative adsorption (Rre6), which is usually considered as the rate determining step for CH4 dissociation on Ni, producing intermediate precursors for C and H atoms; ii) CO(s) and CO2(s) formation (R14 and R15). To evaluate the sensitivity of the predicted C(s) surface coverage, the current density J and CH4(g), CO(g) and CO2(g) concentrations on the values of pre-exponential factor of the key reactions considered in Table 2, the Am for those reactions were varied by 50%. Note that the kinetic parameters for all the other

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H(s)

O(s)

0.0025

0.17

a)

b)

600oC 700oC 800oC

0.16

600o C o 700 C 800o C

0.0020

0.15 0.0015

Surface species coverage

0.14 0.13

0.0010 0.12 0.0005

0.11 0

100

200

300

400

500

0

100

200

H2O(s)

c) 0.0010

0.09

0.0006

0.06

0.0004

0.03

0.0002

300

400

500

600 C o 700 C 800oC

0.12

0.0008

500

o

d)

o

600 C 700oC o 800 C

400

CO(s)

0.15

0.0012

300

0.00 0

100

200

300

400

500

0

100

200

Distance from gas/anode to anode/eletrolyte interface ( m) Fig. 7. Effects of operating temperature on adsorbed species along the distance from gas/anode to anode/electrolyte interface at cell axis-symmetric line predicted by revModel: a) H(s); b) O(s); c) H2O(s); d) CO(s). Fuel gas: humidified CH4 (97%CH4-3%H2O) at 0.6 V cell potential.

elementary steps were kept constant in the analysis. Fig. 8a shows the simulation results obtained while using different Am,re6,f for the forward CH4 dissociative adsorption (Rre6) reaction under

2.5 humidify CH4

Ratio to reference value

2.0

+50% on Am,re6,f -50% on Am,re6,f

1.5 1.0 0.5 0.0 2.5 2.0

C(s)

J

CO(g)

CH4(g)

+50% on Am,14,f

+50% on Am,15,f

-50% on Am,14,f

-50% on Am,15,f

CO2(g)

1.5 1.0

humidify CH4

pure CO

0.5

humidified CH4 (97%CH4–3%H2O). The results show that uCðsÞ , J, CO(g) and CO2(g) are all sensitive to Am,re6,f, especially uCðsÞ, i.e., an increase or decrease of Am,re6,f will double or reduce by half the uCðsÞ . This indicates that CH4 dissociative adsorption is an essential step for CH4 reforming on Ni. Same analysis was applied on Am,re6, b for the backward reaction of CH4 dissociative adsorption. The results show that deviation ( 50%) of Am,re6,b has no effects on uCðsÞ , J, CH4(g), CO(g) and CO2(g) concentrations. Therefore, this effect is not show in Fig. 8. Moreover, the analysis also show that deviation ( 50%) of Am,14,f and Am,15,f in the CO(s) and CO2(s) formation reaction can only affect uCðsÞ and CO2(g) concentration (Fig. 8b). A 50% deviation of Am for their backward reactions has no observable effects on the surface species coverage and gas species concentration. Note that the purposed of this sensitivity analysis is to study the effect of the fitted Am parameters (Table 2) on the revModel’s predictions. Although a 50% deviation of preexponential factors is small, it clearly shows that revModel is sensitive to Am,re6,f, Am,14,f and Am,15,f, indicating the corresponding reactions are important in the SOFC modeling feed with humidified CH4 and CO.

0.0

C(s)

CO2(g)

C(s)

CO2(g)

Fig. 8. Sensitivity of the C(s) surface coverage and gas species concentration at the electrochemical reaction zone, e.g. CH4(g), CO(g) and CO2(g), on the pre-exponential factor Am in revModel at T = 700  C and 0.6 V cell potential: a) for the Rre6 forward reaction under humidified CH4 (97%CH4-3%H2O); b) for the R14, R15 forward reaction under humidified CH4 (97%CH4-3%H2O) and pure CO;.

4. Conclusions In the present study, two 2D mechanistic SOFC models (orgModel and revModel) that cover global aspects of reforming, water–gas shift and Bouduard reaction were developed using an anode-supported Ni-YSZ button cell system. Two multi-step

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heterogeneous reaction mechanisms were considered: i) CH4 adsorption mechanism (orgModel); ii) CH4 dissociative adsorption mechanism (revModel). In revModel, the energy barriers for CH4 dissociative adsorption, CO and CO2 formation on Ni catalyst surface are obtained from DFT. The corresponding pre-exponential factors are fitted from the experimental polarization data, whereas the other reactions and their kinetics are kept same as that in orgModel. Their prediction on carbon deposition was compared under different carbon-containing fuel, such as humidified CH4 and CO at various operating conditions. The results show that, as compared with orgModel, the uCðsÞ distribution predicted by revModel fits better with the experimental observations reported in the literature. The revModel represents a more realistic model to describe the temperature effect on carbon deposition in SOFC, and could be used to simulate larger non-isothermal cells (whether planar or tubular) and possibly stack, where large temperature differences exist. To have a better understanding of the reactions in a fuel cell, the distributions of gas/surface phase species concentration and operating temperature effects were studied using revModel. Results show that Ni catalyst surface is covered mainly by H(s) and CO(s) in the electrochemical reaction zone, whereas there is a very high coverage of C(s) in chemical reaction zone. Moreover, sensitivity analysis the fitted exponential factor Am in revModel shows that the C(s) surface coverage, current density J and CH4(g), CO(g) and CO2(g) concentration are sensitive to Am,re6,f, Am,14,f and Am,15,f, especially Am,re6,f for the forward CH4 dissociative adsorption (Rre6) reaction. This indicates that CH4 dissociative adsorption is an essential step for CH4 reforming on Ni.

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Acknowledgments [23]

The authors gratefully acknowledge the financial support from the Natural Science and Engineering Research Council of Canada (NSERC) (RGPIN[HYPHEN]2014[HYPHEN]04370). Appendix A. Supplementary data

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[25]

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. electacta.2017.08.017.

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