THERMODYNAMIC MODELING OF DIRECT INTERNAL REFORMING SOLID OXIDE FUEL CELLS OPERATING WITH SYNGAS

Transcription

1 THERMODYNAMIC MODELING O DIRECT INTERNAL REORMING SOLID OXIDE UEL CELLS OPERATING WITH SYNGAS C. Ozgur Colpan 1, Ibrahm Dncer, erdun Hamdullahpur 3 1,3 Mechancal and Aerospace Engneerng Department, Carleton Unversty 115 Colonel By Drve, Ottawa, Ontaro, Canada K1S 5B6 E-mal: cocolpan@connect.carleton.ca, ferdun_hamdullahpur@carleton.ca aculty of Engneerng and Appled Scence, Unversty of Ontaro Insttute of Technology 000 Smcoe Street North, Oshawa, Ontaro, Canada L1H 7L7 E-mal: Ibrahm.Dncer@uot.ca ABSTRACT In ths paper a drect nternal reformng sold ode fuel cell (DIR-SOC) s modeled thermodynamcally. Syngas produced from a gasfcaton process s selected as a fuel for SOCs. The modelng conssts of several steps. rst, ulbrum gas composton at the fuel channel et s derved n terms mass flow rate of fuel nlet, fuel utlzaton rato, recrculaton rato and etents of steam reformng and water-gas shft reacton. Second, ar utlzaton rato s determned accordng to the coolng necessty of the cell. nally, termnal voltage, power output and electrcal effcency of the cell are calculated. Then, the model s valdated wth epermental data taken from the lterature. The methodology developed s appled to an ntermedate temperature, anode-supported planar SOC operatng wth a typcal gas produced from a pyrolyss process. or parametrc analyss, the effects of recrculaton rato and fuel utlzaton rato are nvestgated. The results show that recrculaton rato does not have a sgnfcant effect for low current densty condtons. At hgher current denstes, ncreasng the recrculaton rato decreases the power output and electrcal effcency of the cell. The results also show that the selecton of the fuel utlzaton rato s very crtcal. Hgh fuel utlzaton rato condtons result n low power output and ar utlzaton rato but hgher electrcal effcency of the cell. INTRODUCTION SOC s a sold state energy converson devce that contans an ode on-conductng electrolyte made from a ceramc materal and operates at temperatures from 500 to 1000 C. The basc deas and materals were proposed by Nernst and hs colleagues at the end of the nneteenth century. A detaled hstory of SOCs s gven by Snghal and Kendall (00). SOCs may be classfed accordng to ther temperature level, cell and stack desgn and reformng type; whch s shown n Table 1. Table 1. Classfcaton of sold ode fuel cells Classfcaton crtera Types 1. Low temperature SOC (LT-SOC) Temperature level. Intermedate temperature SOC (IT-SOC) 3. Hgh temperature SOC (HT-SOC) 1. Planar SOC Cell and stack desgn. Tubular SOC 3. Monolthc SOC 1. Eternal reformng Reformng. Drect nternal reformng SOC (DIR-SOC) 3. Indrect nternal reformng (IIR-SOC) Detaled descrptons of these dfferent types of SOCs, advantages and dsadvantages of each type over another, etc. may be found n lterature (Snghal, 000; Snghal, 00; Snghal and Kendall, 00; Larmne and Dcks, 003). One of the key advantages of SOCs s ts fuel fleblty. There are many optons for choosng the fuel of SOCs. Among these fuel optons, H and CO are electrochemcally odzed at the anode. The remanng ones are reformed nto H and/or CO and then electrochemcally reacted. Methane, hgher hydrocarbons, methanol, ethanol, landfll gas, bomass produced gas, ammona, hydrogen sulfde, etc. may be fuel optons for SOCs. Many studes, manly nvestgatng the thermodynamc feasblty of these fuels to be used n SOCs, may be found n lterature (e.g., Assabumrungrat et.al., 004; Assabumrungrat et.al., 005; Lu and Schaefer, 004; Van herle et.al., 004; Wojck et.al., 003; Y et.al., 005; Yn et.al., 004).

2 Two key ponts for thermodynamc modelng of SOCs are determnng the et gas composton and thermal management. There are dfferent approaches for calculatng the et gas composton of the anode secton of a SOC n lterature. In a fuel cell handbook by EGG (004), a smple approach to calculate the SOC effluent composton s gven for a SOC operatng wth 100% methane whch s assumed to be completely reformed wthn the fuel cell. The mosture rured for the reformng s suppled by nternal recrculaton. In ther approach, frst, an ntermedate soluton s found by takng nto account the combned fuel cell and steam reformng reacton for the part of the fuel that s utlzed, and the steam reformng reacton for the part of the fuel that s not utlzed. Then, the true et gas composton s determned by consderng the effect of the water gas shft ulbrum. Accordng to the approach of Achenbach and Rensche (1994), steam reformng of methane reacton s knetcally controlled. An uaton s proposed for the reformng knetcs n the form of the Arrhenus-type ndependence of the H O partal pressure and proportonal to the CH 4 partal pressure. On the other hand, n many studes (e.g., Massardo and Lubell, 000; Ghosh and De, 003; Lu and Schaefer, 004), the steam reformng and water gas shft reactons are consdered n ulbrum, and, accordng to the reformng type, electrochemcal reacton may or may not occur smultaneously wth these reactons. In most of these studes, t s consdered that hydrogen s the gas that s electrochemcally odzed snce the CO odaton rates are much lower than hydrogen, and CO s converted nto H by water gas shft reacton. Thermal management of SOCs s mportant due to operatng the fuel cell safely, and thermodynamcally and economcally more effcent. In a SOC operatng wth a gas mture contanng hydrocarbon, the heat s generated nsde a SOC due to electrochemcal reacton, polarzatons and water gas shft reacton. Some of the heat generated s used by steam reformng reacton. The utlzaton of the remanng heat may be used n several ways: Yoshda and Iwa (005) have consdered a SOC system havng the same nlet and outlet temperatures. In ths system, the ecess heat s utlzed by a combustor whch s postoned n close thermal contact wth SOC. It s also possble to operate the SOC wthn a dstnct temperature range. However, hgh temperature gradents are not desrable wthn a SOC. So, mamum temperature dfference between fuel cell nlet and et becomes a desgn crteron. The coolng of the fuel cell s provded by usng ecess ar at the cathode nlet. On the other hand, t s also mportant to mantan a unform temperature gradent along the cell n mnmzng the stresses n cell components (Snghal and Kendall, 00). Snce the stresses are developed due to msmatch n coeffcents of thermal epansons when there s a temperature dfference between the fuel cell and the envronment, the system should be nsulated. The prmary purpose of ths study s to develop a model for DIR-SOC takng nto account the effect of recrculaton rato of the anode et gas whch s mportant especally for supplyng water for ntatng the chemcal reactons and preventng carbon deposton. In addton, a method for calculatng the ar utlzaton rato s developed. THERMODYNAMIC MODEL Operaton Prncple A unt cell s shown n gure 1. Syngas mes wth recrculated gas mture and enters the fuel channel. Steam reformng of methane, water-gas shft and electrochemcal reactons occur smultaneously at the anode. The gas mture etng the fuel channel has, generally, hgh water content. So, some porton of t may be recrculated snce the chemcal reactons need water as reactant. The odant, taken as ar n ths study, enters from the ar channel. The oygen molecules n the ar react wth the electrons, whch are produced at the anode and cycled va the load. Ode ons are produced at the cathode and they dffuse to the anode through the electrolyte. The gas mture, havng less oygen content than the ar enterng, ets the ar channel. Electrc current s produced by the flow of electrons and t effectuates work on the load. Assumptons The followng assumptons are made n the analyss: Syngas conssts of the followng gas speces. ={CH 4, CO, CO, H O, H, N } Ar conssts of 79% N and 1% O. j={o, N } uel cell operates at steady state. Gas mture at the fuel channel et s at chemcal ulbrum. Pressure drops along the fuel cell are neglected. Temperature at the channel nlets s same ( Ty Tf 3 Ta1 ). Also, temperature at the channel ets s same ( Tz Tf 4 Ta ).

3 Temperature of the sold structure s mdway between the nlet and et temperatures (Omosun et.al., 004). uel cell s nsulated whch means that there s no heat nteracton wth envronment. Only hydrogen s electrochemcally reacted. CO s converted to CO and H by water-gas shft reacton. Contact resstances are gnored. Radaton transfer between sold structure and gas channels s gnored. f f3 UEL CHANNEL f4 f5 ANODE ELECTROLYTE CATHODE e - e - LOAD a1 AIR CHANNEL a gure 1. Schematc of the DIR-SOC Input Data The volumetrc gas composton at state s chosen as a typcal composton obtaned from a pyrolyss process. In dry bass, the composton s as follows (Brdgwater, 1995): 1% CH 4, 40% H, 0% CO, 18% CO, 1% N. Other fed nput parameters are shown n Table. Among them, echange current densty depends on temperature and materal. or the temperature used n ths study and common SOC materals, these values are obtaned from lterature (Chan et. al., 00). Effectve dffusvty through the anode and cathode depends on materal thckness and temperature. In ths study, the cell s assumed to be an anodesupported cell and sutable values are chosen accordng the data gven by Snghal and Kendall (00). uel utlzaton rato, recrculaton rato and current densty are chosen as varyng nput parameters. Current densty s taken n a range from 0.1 to a close value to ts mamum value. Recrculaton rato s taken as 0.1, 0. and 0.3. When the effect of fuel utlzaton s nvestgated, t s fed at 0.. uel utlzaton rato s taken as 0.65, 0.75 and When the effect of recrculaton rato s nvestgated, t s fed at Table. Input values that are fed throughout the study Input Value Temperature of the et (T z ) 850 C Temperature dfference between et and nlet (ΔT) 100 C Pressure of the cell (P cell ) 1 bar Actve surface area (A) 100 cm Echange current densty of anode ( oa ) 0.65 A/cm Echange current densty of cathode ( oc ) 0.5 A/cm Effectve gaseous dffusvty through the anode (D aeff ) 0. cm /s Effectve gaseous dffusvty through the cathode (D ceff ) 0.05 cm /s Thckness of anode (L a ) 500 μm Thckness of electrolyte (L e ) 10 μm Thckness of cathode (L c ) 50 μm Calculaton of the Equlbrum Gas Mture Composton at the uel Channel Et Here the frst step s the calculaton of the ulbrum gas composton at the fuel channel et. We derve the uatons n terms of total molar or mass flow rate of gas speces at state. Snce, t s more convenent to adjust the mass flow rate for a system operator; the uatons are gven n terms of mass flow rate of state. In ths regard, the molar flow rate of gas speces at state may be gven n terms of mass flow rate as follows:

4 mf N 1 (1) M Here, the states f, f4 and f5 have the same molar compostons. The composton of gas speces at these states s shown by. Then, the molar flow rate of gas speces at the state f3 becomes N N N N N N r N ) () f 3 f f ( f 4 The steam reformng reacton for methane, water-gas shft reacton and electrochemcal reactons, whch are shown n Eqs.(3)-(5), respectvely, occur smultaneously at the cell as follows: CH 4 H O CO 3H (3) CO H O H CO (4) 1 H O H O (5) Let the etents of reactons shown by Eqs.(3)-(5) be a, b and c, respectvely. The molar flow rate of state f4 s gven as f N 4 f 3 d (6) N where d CH 4 a (6.1) d O a b c (6.) d CO a b (6.3) d CO b (6.4) d H 3a b c (6.5) N d 0 (6.6) Here, c s also the molar flow rate of hydrogen utlzed n the fuel cell whch can also be defned as follows: c ( N 3a b) U (7) H f 3 We obtan the followng uaton by summng molar flow rate of gas speces at state f4 by usng Eqs.(6)- (6.6) and combnng wth Eq.(): N N r.( N a) (8) f 3 f 3 The total molar flow rate of state f3 s gven as N f 3 N f 1 ar 1 r (9) Combnng Eqs.(6)-(6.6), (8) and (9), the ulbrum molar gas composton at the fuel channel et results n N N f 4 f 4 N N d a (10) The molar flow rate of hydrogen utlzed, c, s redefned by combnng Eqs.(6.5) and (7)-(10) as

5 ( N c H 3a b) 1 r r U U (11) Hence, usng Eqs.(6)-(6.6), (10) and (11), the ulbrum gas composton at the fuel channel et s found as CH 4 N f N CH 1 4 a a H ( N 3a b) ( 1 r )( 1 U N r r U f a 1 1 N CO a b N a N CO b N a H ) CO CO HO N N HO N N N a H ( N 3a b) U a b 1 r r U N a (1) (13) (14) (15) (16) (17) Here, a, b, and molar flow rates of gas speces at state whch are a functon of are unknown. So, we need three uatons to be solved smultaneously to fnd a, b and m. These are the chemcal ulbrum uatons correspondng to the steam reformng and water-gas shft reactons, and the relaton between electrcal current and molar flow rate of hydrogen utlzed; whch are shown n Eqs.(18)-(0), respectvely. K K r s CO 3 ( ) ( ) P ep Δg r / RTz (18) HO CH4 ( )( ) P ep Δg s / RT z H ( ( ( N I A c CO ) ( )( H CO HO ) ) H 3a b) 1 r r U U The temperature dependent ulbrum constant s solved by the classcal method n whch the change n Gbbs free energy of the reactons s used. However, ulbrum constants for steam reformng and watergas shft reactons may also be found by usng a smple relaton and ulbrum constant coeffcents (Bossel, 199). On the other hand, nstead of dong calculatons based on ulbrum constant, a more drect procedure whch s based on mnmzaton of the total Gbbs free energy may be used. In ths method, t s not necessary to know the chemcal reactons. Only, gas speces that are present n the system, moles of speces n the ntal unreacted state, temperature and pressure should be known to calculate the ulbrum composton. Soluton s found by usng Lagrange multplers. urther nformaton on ths may be found n Perry and Green (1997). Calculaton of Ar Utlzaton, Termnal Voltage, Power output and Cell Effcency The cell analyzed n ths study s assumed to be nsulated, and the heat produced n the cell s carred away by sendng ecess ar. Also, the mamum temperature dfference s taken as 100 C as to be determned as an nput parameter to adjust the mass flow rate of ar enterng the ar channel. Hence, the ar utlzaton rato s calculated accordng to the coolng necessty of the fuel cell. The molar flow rates of gas speces at the ar channel nlet and et are defned as follows: m (19) (0)

6 O c N a1 (1) U o N c c N a1 () U 1 4 U o o O c c c 1 N a 1 (3) Uo Uo N c N 79 a (4) 4 U o The gas composton at the ar channel et s calculated usng the followng: O a N N N a 1 O a a 1 Uo 100 / 1 U O a o (6) (5) Here the Nernst voltage s calculated as HO Δg ( T z ) RTz VN ln H O a P P (7) Here, three types of polarzatons, e.g., ohmc, actvaton and concentraton, are consdered and calculated through Eqs.(8-3). The ohmc polarzaton s caused by the resstance to the flow of ode ons through the electrolyte and resstance to the flow of electrons. The actvaton polarzaton s the voltage drop due to the sluggshness of reactons occurrng at the electrode-electrolyte nterfaces (Snghal and Kendall, 00). If we assume that charge transfer coeffcent for anode and cathode s 0.5 and substtute ths value n the Butler- Volmer uaton, ths uaton takes the form as shown n Eq. (9) (Chan et.al., 00). The concentraton polarzaton s caused by the resstance to mass transport through the electrodes and nterfaces (Km et.al., 1999). V V ohm act Rcontact ρk L k (8) k V act RT s 1 RT s, a Vact, c snh snh o, a 1 H a c RT z RT z pf 4 RTz Vconc Vconc Vconc ln 1 ln 1 ln 1 (30) H O as pf as 4 4 cs where as cs H f 4 P RT 4 P P P D L z a O Pa O a aeff D ceff RT z L c The electrcal resstvty of cell components, ρ, s the nverse of electrcal conductvtes. The formulatons for electrcal conductvtes of cell components, as a functon of temperature of sold structure, for common SOC materals are gven by Bossel (00). The termnal voltage and power output of the cell are gven by V V V V V (33) N ohm act con, o c (9) (31) (3)

7 I V (34) W C Here, the enthalpy flow rate of state '' s calculated usng an energy balance around the control volume enclosng the juncton pont by Eq.(35). The temperature of ths state s then found by teraton. N h T ) N h ( T ) N h ( T ) (35) H ( f 3 y f z or the nsulated fuel cell, the energy balance around the control volume enclosng the fuel cell s wrtten as j j j j h N h W N h N h (36) N a1 C f 5 a Here the ar utlzaton s calculated through an teratve soluton method usng Eq.(36). After obtanng ar utlzaton by teraton, termnal voltage and power output of the cell s found usng Eqs.(33) and (34). nally, the electrcal effcency of the cell s calculated as W C el, cell (37) N LHV f 1 The flowchart of the MathCAD program used for the model s shown n gure. Valdaton of the Model The epermental works for DIR-SOCs lack n the lterature n terms of usage of dfferent fuels and nformaton about the nput parameters used for the eperment. In the present model, takng the channel nlet and et temperatures dfferent, takng the fuel cell as nsulated, and usng a syngas make t dffcult to fnd data for comparson purpose from lterature. However, epermental data wth methane as fuel presented by Tao et al. (005) are used for comparson wth the model results as gven n Table 3. Table 3. Comparson of the model created wth epermental data (The values are taken as appromate values) gven by Tao.et.al.(005). Current densty (A/cm ) Cell voltage of the model (V) Cell voltage of the eperment (V) Power densty of the model (W/cm ) Power densty of the eperment (W/cm ) It s seen that the dfference s n the range of 1% for the voltage and 8% for the power output whch sort of valdates the model. Ths dfference s manly due to the assumptons consdered n the model and the comparson.

8 gure. low chart of the MathCAD program RESULTS AND DISCUSSION In ths study, formulatons to fnd the et gas composton of the anode secton are derved for a gas mture ncludng water vapor as fuel. If there s enough amount of water vapor n the ntal gas mture, t may not be necessary to recrculate the anode et gas stream. However, f we consder a more general case n whch, for eample, a dry gas mture s used as the fuel, recrculaton s necessary for a DIR-SOC to ntate the steam reformng and water gas shft reactons. Hydrogen produced by these reactons s utlzed by the electrochemcal reacton smultaneously, and more amount of water vapor than the amount of that necessary for ntatng the reactons s produced. Ths study s smplfed by consderng the cell as a whole whch may be regarded as a zero dmensonal modelng approach. Due to ths fact, t s not possble to track

9 the change of gas composton along the cell. An mproved method may be dvdng the cell nto several sectons to analyze the change of gas composton along the cell. If such a method s appled, the effect of ntal water vapor amount may be seen more clearly. In lterature, t may be seen that dfferent nput and output parameters are used n dfferent thermodynamc models of SOCs. or eample, fuel utlzaton may be consdered as an nput parameter n one study and an output parameter n another study. In ths study, nput parameters are determned accordng to the recrculaton and thermal management consderatons. Due to ths, mass flow rate and temperature of the nlet fuel are consdered as output. These parameters may be adjusted by the system operator accordngly. The recrculaton rato adjusts the steam to carbon rato enterng the anode secton. In many studes n lterature, t s seen that carbon deposton problem s related wth ths rato. However, ths problem s not consdered n ths study; rather, ts effect on system performance s nvestgated. Hgh recrculaton ratos ncrease the system s complety whch s generally undesrable. The effect of ths rato on output parameters s shown n gure 3. It may be observed from the fgures that ts effect s not very sgnfcant for low current denstes. or hgh current denstes, as recrculaton rato ncreases, mass flow rate of fuel, ar utlzaton rato, termnal voltage, power output, and electrcal effcency of the cell decrease. Havng a lower ar utlzaton rato means hgher mass flow rate of ar enterng from the cathode sectons; whch n turn ncreases the cost of the system. However, the mass flow rate of fuel decreases n ths condton whch decreases the operaton cost. Ar utlzaton rato (a) Power output [W] (c) r= Current densty (A/cm ) r=0. r= Current densty (A/cm ) r=0.3 r=0.1 r=0. Termnal voltage (V) (b) Electrcal effcency (d) r= r=0.3 r= Current densty (A/cm ) r= r= r= Current densty (A/cm ) gure 3. Effect of recrculaton rato and current densty on (a) ar utlzaton rato; (b) termnal voltage; (c) power output; (d) electrcal effcency; for fuel utlzaton rato of It s known that there s always some unused hydrogen and that the degree of the utlzaton of hydrogen s determned by the fuel utlzaton rato. gure 4 shows the effect of fuel utlzaton rato on output parameters. Unlke recrculaton rato, ts effect s more sgnfcant. It may be observed from the fgures that a wder range of current densty may be selected for lower fuel utlzaton ratos. As fuel utlzaton rato ncreases, mass flow rate of fuel, ar utlzaton rato, termnal voltage, and power output of the cell decrease; whereas

10 electrcal effcency of the cell ncreases. It may be consdered controversal to have low power output and hgh electrcal effcency at the same tme. Ths s due to the fact that less mass flow rate of fuel s needed for hgher fuel utlzaton ratos. Hence, t s seen that ncreasng ths rato mproves the system thermodynamcally and decreases the cost of fuel; but also ncreases the cost of the ar flow enterng the cathode secton. Ar utlzaton rato (a) Power output [W] (c) U f = U f =0.85 U f = Current densty (A/cm ) U f = U f = U f = Current densty (A/cm ) Termnal voltage (V) (b) Electrcal effcency (d) U f = U f =0.85 U f = Current densty (A/cm ) U f= U f= U f = Current densty (A/cm ) gure 4. Effect of fuel utlzaton rato and current densty on (a) ar utlzaton rato; (b) termnal voltage; (c) power output; (d) electrcal effcency; for recrculaton rato of 0.. CONCLUSIONS In ths study, a DIR-SOC operatng wth syngas has been modeled thermodynamcally. The recrculaton of the anode et gas stream s taken nto account n the model to obtan a formulaton vald for gas mtures contanng dfferent gas compostons. The effect of recrculaton rato and fuel utlzaton rato s also nvestgated. The condtons that are thermodynamcally effectve and economcally effectve are dentfed and dscussed. uture study wll concentrate on the thermoeconomc optmzaton of the DIR-SOC and enhancement of the present model ncludng the carbon deposton usng the fnte control volume method. NOMENCLATURE a etent of steam reformng reacton for methane, mole/s A actve surface area, cm b etent of water gas shft reacton, mole/s c etent of electrochemcal reacton, mole/s D aeff effectve gaseous dffusvty through the anode, cm /s D ceff effectve gaseous dffusvty through the cathode, cm /s faraday constant, C h specfc molar enthalpy, J/mole H enthalpy flow rate, W current densty, A/cm

11 oa echange current densty of anode, A/cm oc echange current densty of cathode, A/cm as anode-lmtng current densty, A/cm cs cathode-lmtng current densty, A/cm I current, A K ulbrum constant L thckness of a cell component, μm LHV lower heatng value, J/mole m mass flow rate, g/s M molecular weght, g/mole N molar flow rate, mole/s r recrculaton rato P pressure, bar R unversal gas constant, J/mole-K T temperature, K U fuel utlzaton rato U o ar (odant) utlzaton rato V voltage, V W C power output of the cell, W molar concentraton Greek Letters ρ electrcal resstvty of cell components, ohm-cm η, electrcal effcency of the fuel cell el cell Δ g change n specfc molar gbbs free energy, J/mole Subscrpts a anode act actvaton c cathode conc concentraton e electrolyte ulbrum ohm ohmc r steam reformng reacton for methane s water gas shft reacton; sold structure N nernst Superscrpts a anode c cathode o standard state REERENCES Achenbach, E. and E. Rensche Methane/steam reformng knetcs for sold ode fuel cells. Journal of Power Sources. 5:83-88 Assabumrungrat, S., V. Pavarajarn, S. Charojrochkul, and N. Laosrpojana Thermodynamc analyss for a sold ode fuel cell wth drect nternal reformng fueled by ethanol. Chemcal Engneerng Scence. 59: Assabumrungrat, S., N. Laosrpojana, V. Pavarajarn, W. Sangtongktcharoen, A. Tangjtmatee, and P. Praserthdam. 005.Thermodynamc analyss of carbon formaton n a sold ode fuel cell wth a drect nternal reformer fuelled by methanol. Journal of Power Sources. 139:55-60 Bossel, U.G nal Report on SOC Data acts and gures. Berne, CH:Swss ederal Offce of Energy Brdgwater, A.V The techncal and economc feasblty of bomass gasfcaton for power generaton. uel. 74(5): Chan, S.H., C.. Low, and O.L. Dng. 00. Energy and eergy analyss of smple sold-ode fuel-cell power

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