Modeling of Proton-Conducting Solid Oxide Fuel Cells Fueled with Syngas

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1 Energes 2014, 7, ; do: /en Artcle OPEN ACCESS energes ISSN Modelng of Proton-Conductng Sold Oxde Fuel Cells Fueled wth Syngas Meng N 1, *, Zongpng Shao 2 and Kwong Yu Chan Department of Buldng and Real Estate, the Hong Kong Polytechnc Unversty, Hung Hom, Kowloon, Hong Kong, Chna State Key Laboratory of Materals-Orented Chemcal Engneerng, College of Chemstry & Chemcal Engneerng, Nanjng Unversty of Technology, No. 5 Xn Mofan Road, Nanjng , Chna; E-Mal: shaozp@njtech.edu.cn Department of Chemstry, the Unversty of Hong Kong, Pokfulam Road, Hong Kong, Chna; E-Mal: hrsccky@hku.hk * Author to whom correspondence should be addressed; E-Mal: bsmengn@polyu.edu.hk; Tel.: ; Fax: Receved: 25 Aprl 2014; n revsed form: 27 June 2014 / Accepted: 3 July 2014 / Publshed: 9 July 2014 Abstract: Sold oxde fuel cells (SOFCs) wth proton conductng electrolyte (H-SOFCs) are promsng power sources for statonary applcatons. Compared wth other types of fuel cells, one dstnct feature of SOFC s ther fuel flexblty. In ths study, a 2D model s developed to nvestgate the transport and reacton n an H-SOFC fueled wth syngas, whch can be produced from conventonal natural gas or renewable bomass. The model fully consders the flud flow, mass transfer, heat transfer and reactons n the H-SOFC. Parametrc studes are conducted to examne the physcal and chemcal processes n H-SOFC wth a focus on how the operatng parameters affect the H-SOFC performance. It s found that the presence of CO dlutes the concentraton of H 2, thus decreasng the H-SOFC performance. Wth typcal syngas fuel, addng H 2 O cannot enhance the performance of the H-SOFC, although water gas shft reacton can facltate H 2 producton. Keywords: proton-conductng sold oxde fuel cells; mathematcal modelng; coupled transport and reacton; syngas; water gas shft reacton; computatonal flud dynamcs; electrochemstry

2 Energes 2014, Introducton Sold oxde fuel cells (SOFCs) are promsng electrochemcal energy converson devces due to ther hgh effcency, low polluton, fuel flexblty, and potental for co-generaton or mult-generaton [1]. To realze commercal SOFC applcatons, t s very mportant to further reduce ther cost and mprove ther long-term stablty. One effectve way s to lower the very hgh operatng temperature from about 1273 K to an ntermedate range ( K). Ths s because lower cost nterconnectng materals can be used at a reduced temperature [2]. In addton, the coarsenng of porous electrodes can be greatly slowed down wth decreasng temperature, whch n turn enhances long-term durablty. However, the SOFC performance decreases wth decreasng temperature, partly due to the ncreased Ohm s loss at the electrolyte. The ohmc loss at the electrolyte can be reduced by fabrcatng a thn flm electrolyte. Large-scale fabrcaton of SOFCs requres a conventonal ceramc processng method (.e., tape castng), whch lmts the electrolyte thckness to about 10 µm [3]. Alternatvely, the ohmc loss can be decreased by developng new materals wth hgh onc conductvtes. Proton-conductng ceramcs have been recognzed as a promsng electrolyte materal for SOFCs operatng at reduced temperature due to ther good onc conductvtes at a temperature range of K [4]. Expermental studes have demonstrated good performance of SOFCs based on proton-conductng electrolytes (H-SOFCs). Several mathematcal models have also been developed to understand the transport and reacton n H-SOFCs [5 7]. However, the majorty of the models only consder H 2 or NH 3 as fuel n the H-SOFC [5 8]. The use of hydrocarbon fuels or syngas has been rarely studed. As the fuel flexblty s a dstnct feature of SOFC, t s very mportant to examne how a H-SOFC performs wth alternatve fuels. In the near term, both conventonal coal and renewable bomass wll be mportant energy sources. These fuels can be converted to syngas contanng H 2 and CO, whch can be subsequently used n SOFCs for power generaton [9 11]. Consderng the mportance of syngas for power generaton n SOFCs, ths study s purposely desgned to nvestgate the syngas fueled H-SOFC. 2. Model Development The workng prncples of a syngas fueled H-SOFC and the computatonal doman are shown n Fgure 1. The computatonal doman ncludes nterconnect, ar channel, porous cathode, dense proton-conductng electrolyte, porous anode, and fuel channel. In operaton, syngas (a mxture of H 2 and CO) s suppled to the fuel channel whle ar s suppled to the ar channel. When H 2 O s ncluded n the fuel stream, the water gas shft reacton (WGSR, Equaton (1)) wll occur n the porous anode, generatng CO 2 and H 2 : CO H2O CO2 H2 (1) H 2 molecules dffuse through the porous anode to the trple-phase boundary (TPB) at the anode-electrolyte nterface, where they are splt nto protons and electrons (Equaton (2)). The protons are transported through the dense electrolyte to the cathode. The electrons are transported va the electronc network of the porous anode to the anode surface, where they are collected by the current collector (nterconnect). Subsequently, electrons flow through the external crcut to the cathode sde, where they react wth oxygen molecules and protons to produce steam (Equaton (3)).

3 Energes 2014, H 2H 2e (2) 2 2H 0.5O 2e H O (3) 2 2 Both the electrochemcal reactons and WGSR are exothermc. The overpotental loss n SOFC also contrbutes to heat generaton. Thus, the H-SOFC fueled wth syngas nvolves heat transfer, flud flow, mass transfer, chemcal reacton (f H 2 O s ncluded), and electrochemcal reactons. A numercal model s developed to smulate all these processes. The model conssts of three sub-models: (1) an electrochemcal model for determnng the electrochemcal reacton rates and related heat generaton; (2) a chemcal model for calculatng the rate of WGSR f H 2 O s ncluded n the fuel stream; and (3) a computatonal flud dynamcs (CFD) model for smulatng the flud flow, heat transfer and mass transfer n the cell. Fgure 1. Workng prncple of syngas fueled H-SOFC and the computatonal doman. The followng assumptons are adopted n the model: (1) The model s 2D, neglectng the 3D effect; (2) Heat radaton s assumed to be neglgble; (3) The flow n the gas channels s lamnar due to low velocty and small dmenson; (4) Electrochemcal reactons are assumed to take place at the electrode-electrolyte nterface only Electrochemcal Model In the H-SOFC, only H 2 can partcpate n the electrochemcal reacton to produce protons and electrons. Electrochemcal oxdaton of CO can occur n a SOFC wth an oxygen on conductng electrolyte (O-SOFC), but cannot occur n H-SOFC due to the lack of oxygen ons at the anode. In a SOFC, the electrcal conductvty of nterconnect s usually qute hgh and thus the electrcal potental along the flow channel can be consdered as unform. The operatng potental (V) can be determned as [12]:

4 Energes 2014, V Eact, a act, c ohmc (4) RT P E T ln 2F P I I, C H2 O2 IC, PHO 2 where E s the equlbrum potental and the subscrpts; T s temperature (K). R s the unversal gas constant ( J mol 1 K 1 ). F s the Faraday constant (96,485 C mol 1 I ). P H 2 s the partal pressure I, C I, C of H 2 at the anode-electrolyte nterface. P and P are the partal pressure of O 2 and H 2 O at the O2 cathode-electrolyte nterface, respectvely. Thus, the concentraton overpotentals at the electrodes are ncluded n the Nernst potental (Equaton (5)). η ohmc s the ohmc overpotental of the electrolyte and can be determned as: 1 ohmc JL (6) where L s the thckness (m) of the electrolyte and σ onc s the onc conductvty (Ω 1 m 1 ). J s the current densty (A m 2 ). Accordng to Matsumoto [13], the proton conductvty of the BaCe0.8Y0.2O 3-α electrolyte s about 2.6 S m 1 at 973 K and 3.5 S m 1 at 1073 K. Thus, the proton conductvty (σ onc, S m 1 ) can be approxmated as: HO 2 onc onc 0.009T (7) η act,a and η act,c are the actvaton overpotentals wth the subscrpt a and c referrng to the anode and cathode, respectvely. As expermental studes suggests lnear relatonshp between current densty and the actvaton overpotental [14], η act can be determned as: act, 0 nfj 0.5 (5) RTJ (8) 0 where J s the exchange current denstes (A m 2 ) whch ndcates the actvty of the electrode. n s the number of electrons nvolved n the electrochemcal reacton. Based on the prevous studes, the exchange current denstes for anode and cathode are 5300 A m 2 and 2000 A m 2, respectvely [15] Chemcal Model The reacton rate and reacton heat of WGSR are calculated n the chemcal model. The reacton rate for WGSR (R WGSR, mol m 3 s 1 ) can be calculated wth the Haberman and Young formula [16]: k sf RWGSR ksf phop 2 CO p p K H2 CO2 ps exp RT (mol m 3 Pa s 1 ) (10) K Z Z Z 3 2 ps exp (11) (9) 1000 Z 1 T( K) (12)

5 Energes 2014, The heat generaton from the exothermc WGSR (H WGSR, J mol 1 ) can be approxmated usng the enthalpy change of the WGSR reacton as [17]: HWGSR 2.3. Computatonal Flud Dynamc (CFD) Model T (13) The lamnar flud flow, heat and mass transfer processes are modeled wth the CFD model. The local thermal equlbrum s adopted assumng a neglgble temperature dfference between the sold structure and the gas stream n the porous electrodes [18]. The governng equatons n the CFD model are summarzed below [19]: U V x y S UU VU P U U S x y x x x y y UV VV P V V S x y y x x y y cut P cvt P T T k k S x y x x y y UY VY Y Y m, m, x y x x y y eff eff D D Ssp U and V are the velocty n x and y drectons, respectvely. ρ s the effectve densty of gas mxture and can be determned as: 1 N Y 1 where ρ and Y are the densty and mass fracton of gas speces. The effectve vscosty of the gas mxture (µ) can be calculated as [20]: n y n 1 y j1 / j j m T y x (14) (15) (16) (17) (18) (19) (20) M j 1 j j (21) M where M s molecular weght of speces (kg kmol 1 ). In the porous anode and cathode, the effectve heat conductvty (k) and the effectve heat capacty (c p ) can be calculated as [21]: k kf 1 ks (22) cp cp, f 1 cp, s (23)

6 Energes 2014, In the gas channel, the effectve dffuson coeffcent eff D only ncludes the molecular dffuson m, whle both molecular dffuson and Knudsen dffuson are consdered n the porous electrodes. The eff value of D can thus be calculated as [20]: m, 1 D eff m, X j j Dj 3 M, n porous electrodes 1X 2rp 8RT X j j Dj, n gas channels 1 X (24) D j T 1.5 2MM j j p M j M 2 2 D (25) D kt kt b b kt kt b b exp exp , j, j, j, j (26) where ξ/ε s the rato of tortuosty to porosty of the electrodes. r p s the average radus of pores; D j s the bnary/molecular dffuson coeffcent; σ s the mean characterstc length of speces; Ω D s a dmensonless dffuson collson term; k b s the Boltzmann s constant ( J K 1 ). The values of σ and ε j are summarzed n Table 1 [20]. X s the molar fracton of spece. The mass fracton (Y ) can be converted from the molar fracton as: Y X N 1 M X M (27) Table 1. Values of σ and ε /k for calculatng the dffuson coeffcents [20]. CO CO 2 H 2 O 2 N 2 H 2 O σ (A) ε /k (K 2 J 1 ) In the momentum equaton, Darcy s law s used as source terms so that the momentum equatons can be appled to both gas channels and the porous electrodes: S x U B (28) g V S y B (29) g

7 Energes 2014, where B g s the permeablty (m 2 ). Typcal value of B g of m 2 s used for the SOFC porous electrodes whle m 2 s used for the gas channels. The source term (S T, W m 3 ) n the energy equaton (Equaton (17)) represents the heat generaton from the WGSR reacton, electrochemcal reactons, and rreversble overpotental losses. Thus, the source term S T can be wrtten as [12]: S T RWGSRHWGSR, n porous anode JTS Jt, n electrolyte 2FL L (30) where S s the entropy change for electrochemcal reacton. η t s the total overpotental loss. The source term (S sp, kg m 3 s 1 ) n the speces equaton (Equaton (18)) s caused by the chemcal and electrochemcal reactons. For H 2, the source term ( S ) can be wrtten as: H 2 S RWGSRMH, n porous anode 2 JM, at the anode-electrolyte nterface 2Fy H2 H2 (31) where y s the control volume wdth n y-drecton (Fgure 1) at the anode-electrolyte nterface. 3. Numercal Methodologes The fnte volume method (FVM) s adopted to dscretze and solve the governng equatons presented n the prevous sectons. The central dfference and upwnd schemes are used to treat the dffusve and convectve terms. The SIMPLEC algorthm s used to lnk the pressure and the velocty. The algebrac equatons are solved teratvely. The detals on the boundary condtons can be found from our prevous publcatons [22]. The program starts from ntalzaton ntal velocty feld, temperature feld, and gas composton are specfed over the whole computatonal doman. Then the electrochemcal model s solved to calculate the current densty along the flow channel. Subsequently, the chemcal model s solved to determne the rate of WGSR. Based on the electrochemcal model and chemcal model, the source terms for CFD model can be determned. After the CFD model s solved, the flow feld, temperature feld, the pressure feld, and the gas composton n the cell can be updated. Computaton s repeated usng the updated data, untl convergence s acheved. The program s wrtten n FORTRAN and has been valdated. Detals on the valdaton of the model can be found n the prevous publcatons [22] and not reported here. 4. Results and Analyss In ths secton, smulatons are performed to nvestgate the effect of varous operatng parameters on the performance of the syngas fueled H-SOFC. The values of model parameters are summarzed n Table 2. As the cell n the smulaton s short, both the fuel utlzaton and energy effcency are expected to be low [23]. The practcal consderaton of the gas recyclng s also not consdered as the focus of the study s on the fundamental processes occurrng n the cell.

8 Energes 2014, Table 2. Parameters used n smulaton. Parameter Value Operatng temperature, T (K) 1073 Operatng pressure, P (bar) 1.0 Electrode porosty, ε 0.4 Electrode tortuosty, ξ 3.0 Average pore radus, r p (μm) 0.5 Anode-supported electrolyte: - Anode thckness d a (μm) 500 Electrolyte thckness, L (μm) 100 Cathode thckness, d c (μm) 100 Heght of gas flow channel (mm) 1.0 Length of the planar SOFC (mm) 40 Thckness of nterconnector (mm) 0.5 Inlet velocty at anode: U 0 (m s 1 ) 1.0 Cathode nlet gas molar rato: O 2 /N 2 / 0.18/0.79/0.03 Anode nlet gas molar rato: H 2 /CO (Syngas) 3/1 SOFC operatng potental (V) 0.7 Thermal conductvty of SOFC component (W m 1 K 1 ) - Anode 11.0 Electrolyte 2.7 Cathode 6.0 Interconnect Effect of Syngas Composton In practce, CH 4 can be steam reformed to produce syngas wth a H 2 /CO molar fracton rato of 3/1 (Equaton (32)). Alternatvely, CO 2 reformng of CH 4 can produce a gas mxture of 50% H 2 and 50% CO (Equaton (33)): CH4 H2O CO 3H2 (32) CH4 CO2 2CO2 2H2 (33) Thus, the molar fracton rato of H 2 /CO can range from 1/1 to 3/1. In ths secton, the local current densty n syngas fueled H-SOFC s shown n Fgure 2a. As can be seen, the local current densty ncreases consderably wth an ncrease n molar fracton of H 2. Ths s because only H 2 s nvolved n the electrochemcal reacton thus the exstence of CO only dlutes the concentraton of H 2, whch n turn decreases the Nernst potental of the cell (Fgure 2b). To better understand the coupled transport and reacton n the SOFC, the gas composton, temperature and velocty rato (U/U 0 ) are studed. As can be seen from Fgure 3a,c, the molar fractons of H 2 and O 2 decrease along the channel as the electrochemcal reactons consume the fuel and oxdant. The varaton n O 2 molar fracton s smaller than that of H 2, as the flow rate n the cathode s three tmes that of the anode. For comparson, the CO molar fracton s slghtly ncreased (Fgure 3b). As CO s not nvolved n electrochemcal reacton, ts total amount s unchanged but ts molar fracton s ncreased due to decreased amount of H 2 n the anode. Ths s dfferent from O-SOFC, n whch both

9 Energes 2014, H 2 and CO are electrochemcally consumed n the anode [12]. Due to the heat generaton from the electrochemcal reactons and the overpotental losses, the temperature n the SOFC s found to ncrease consderably along the channel (Fgure 4). In the present smulaton, the temperature at the outlet of the SOFC s about 45 K hgher than that at the nlet, ndcatng an average temperature gradent of about 11 K/cm along the channel. The velocty contours n the anode and cathode are plotted n Fgure 5. As can be seen, the velocty profles n SOFC channels are smlar to conventonal fully developed duct flows. The velocty n the porous electrodes s very low, ndcatng the mass transport s manly by means of dffuson. Fgure 2. Effect of syngas composton on the performance of H-SOFC (a) current densty dstrbuton; (b) Nernst potental dstrbuton. (a) (b)

10 Energes 2014, Fgure 3. Gas composton n syngas fueled SOFC (a) H 2 ; (b) CO; and (c) O 2. (a) (b) (c)

11 Energes 2014, Fgure 4. Temperature n SOFC. Fgure 5. Velocty contours n H-SOFC Effect of Operatng Temperature For a SOFC, temperature s a crtcal parameter affectng the performance, durablty and cost. As there s a trend to lower the operatng temperature down to an ntermedate level, the nlet temperature s purposely decreased to 973 K n the present study. As can be seen from Fgure 6a, a reducton n temperature consderably decreases the current densty of H-SOFC. Ths s because the total overpotental loss ncreases wth decreasng temperature, although the Nernst potental ncreases (Fgure 6b).

12 Energes 2014, Fgure 6. Effect of nlet temperature on H-SOFC performance (a) local current densty; and (b) local Nernst potental. (a) 4.3. Effect of Steam Addton (b) Snce the exstence of CO n H-SOFC decreases the cell performance, steam s purposely ncluded n the fuel stream to ntate the WGSR reacton wth an am to produce more H 2. Smulatons are performed for fuel stream wth vared steam addton. As can be seen from Fgure 7, addton of steam does not enhance the electrcal performance of the H-SOFC.

13 Energes 2014, Fgure 7. Effect of steam addton on performance of syngas fueled H-SOFC (a) syngas wth H 2 /CO molar rato of 3/1; and (b) syngas wth H 2 /CO molar raton of 1/1. (a) (b) Ths s because addton of steam tends to dlute the H 2 concentraton on the one hand, and tends to ncrease H 2 concentraton va the WGSR on the other hand. In the present smulatons, the decreased current densty wth H 2 O addton ndcates that the dluton effect domnates. Ths s because the H 2 molar fracton n the syngas s hgh (no less than 50%) whle the molar fracton of CO s relatvely low. Thus the H 2 generated from the WGSR s nsuffcent to offset the dluton effect. However, t s expected that wth ncreasng CO concentraton, the addton of steam wll become necessary. For example, f pure CO s suppled to the bh-sofc, the power output wthout H 2 O addton s 0, thus H 2 O s needed to produce H 2 for power generaton. 5. Conclusons A 2D numercal model s developed for a syngas fueled H-SOFC. The model consders the flud flow, heat transfer, mass transfer, as well as reactons n the H-SOFC. Parametrc smulatons are performed to nvestgate the effect of operatng parameters on H-SOFC performance. Wth typcal

14 Energes 2014, syngas fuel, the CO dlutes the H 2 concentraton and decreases the performance of the H-SOFC. The electrcal output of the H-SOFC s ncreased wth ncreasng temperature, although the Nernst potental s decreased. Addng H 2 O to the syngas fuel facltates H 2 generaton from WGSR. However, t decreases the H-SOFC performance as the dluton effect domnates. Acknowledgments Ths research s supported by a fund from The Research Grant Councl (RGC) of Hong Kong (Project No: PolyU 5326/12E). Author Contrbutons Meng N contrbuted to the model development and smulaton. Zongpng Shao and Kwong Yu Chan contrbuted to analyss and paper revson. Nomenclature B g Permeablty of the porous electrode (m 2 ) c p Heat capactty (J kg 1 K 1 ) d a Thckness of anode (µm) d c Thckness of cathode (µm) eff D Effectve dffuson coeffcent of speces n gas mxture (cm 2 s 1 ) m, D,k Knudsen dffuson coeffcent of (cm 2 s 1 ) D,j Bnary dffuson coeffcent of and j (cm 2 s 1 ) E Equlbrum potental (V) E 0 Reversble potental at standard condton (V) F Faraday constant ( C mol 1 ) H WGS Heat generaton from water gas shft reacton (J mol 1 ) J Current densty (A m 2 ) k Thermal conductvty (W m 1 K 1 ) L Thckness of the electrolyte (m) M Molecular weght of speces (kg mol -1 ) n Number of electrons transferred P Operatng pressure (bar) P I Partal pressure (bar) of speces at electrode-electrolyte nterface R WGSR Rate of water gas shft reacton (mol m 3 s 1 ) r p Mean pore radus of electrode (µm) R Unversal gas constant ( J mol 1 K 1 ) S Entropy change of electrochemcal reactons (kj kg 1 K 1 ) S m Source term n contnuty equaton (kg m 3 s 1 ) S x, S y Source terms n momentum equatons (kg m 2 s 2 ) S T Source terms n energy equatons (W m 3 ) S sp Source terms n speces equatons (kg m 3 s 1 )

15 Energes 2014, T Operatng temperature (K) U Velocty n x drecton (m s 1 ) U 0 Gas velocty at the SOFC nlet (m s 1 ) V SOFC operatng potental (V); Velocty n y drecton (m s 1 ) X Molar fracton of speces Y Mass fracton of speces ε Electrode porosty ξ Electrode tortuosty σ,j Mean characterstc length of speces and j (Å) σ onc Ionc conductvty of the electrolyte (Ω 1 m 1 ) Ω D Dmensonless dffuson collson ntegral ρ Densty of the gas mxture (kg m 3 ) µ Vscosty of gas mxture (kg m 1 s 1 ) η act,a Actvaton overpotental at anode (V) η act,c Actvaton overpotental at cathode (V) η ohmc Ohmc overpotental of the electrolyte (V) Conflcts of Interest The authors declare no conflcts of nterest. References 1. Wachsman, E.D.; Lee, K.T. Lowerng the temperature of sold oxde fuel cells. Scence 2011, 334, Lee, K.T.; Yoon, H.S.; Wachsman, E.D. The evoluton of low temperature sold oxde fuel cells. J. Mater. Res. 2012, 27, Wang, Z.R.; Qan, J.; Cao, J.; Wang, S.R.; Wen, T.L. A study of multlayer tape castng method for anode-supported planar type sold oxde fuel cells (SOFCs). J. Alloys Compd. 2007, 437, Iwahara, H. Hgh temperature protonc conductors and ther applcatons. Sold State Ion. 1992, Lu, H.; Akhtar, Z.; L, P.W.; Wang, K. Mathematcal modelng analyss and optmzaton of key desgn parameters of proton-conductve sold oxde fuel cells. Energes 2014, 7, N, M.; Leung, D.Y.C.; Leung, M.K.H. An mproved electrochemcal model for the NH 3 fed proton conductng sold oxde fuel cells at ntermedate temperatures. J. Power Sources 2008, 185, N, M.; Leung, M.K.H.; Leung, D.Y.C. Mathematcal modelng of proton-conductng sold oxde fuel cells and comparson wth oxygen on conductng counterpart. Fuel Cells 2007, 7, N, M. The effect of electrolyte type on performance of sold oxde fuel cells runnng on hydrocarbon fuels. Int. J. Hydrog. Energy 2013, 38, Andersson, M.; Yuan, J.L.; Sunden, B. SOFC modelng consderng hydrogen and carbon monoxde as electrochemcal reactants. J. Power Sources 2013, 232,

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