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Methane Steam Reforming over an Ni-YSZ Solid Oxide Fuel Cell Anode in StackConfiguration

Mogensen David Grunwaldt Jan-Dierk Hendriksen Peter Vang Nielsen Jens Ulrik Dam-JohansenKimPublished inJournal of Chemistry

Link to article DOI1011552014710391

Publication date2014

Document VersionPublishers PDF also known as Version of record

Link back to DTU Orbit

Citation (APA)Mogensen D Grunwaldt J-D Hendriksen P V Nielsen J U amp Dam-Johansen K (2014) Methane SteamReforming over an Ni-YSZ Solid Oxide Fuel Cell Anode in Stack Configuration Journal of Chemistry 2014[710391] DOI 1011552014710391

Research ArticleMethane Steam Reforming over an Ni-YSZ Solid Oxide Fuel CellAnode in Stack Configuration

D Mogensen1 J-D Grunwaldt12 P V Hendriksen3 J U Nielsen4 and K Dam-Johansen1

1 Department of Chemical and Biochemical Engineering Technical University of Denmark Soltofts Plads Building 2292800 Kongens Lyngby Denmark

2 Institute for Chemical Technology and Polymer Chemistry Karlsruhe Institute of Technology (KIT)Engesserstraszlige 20 76131 Karlsruhe Germany

3Department of Energy Conversion and Storage Technical University of Denmark DTU Risoe Campus Frederiksborgvej 3994000 Roskilde Denmark

4Topsoe Fuel Cell Nymoslashllevej 66 2800 Kongens Lyngby Denmark

Correspondence should be addressed to D Mogensen damogengmailcom

Received 17 February 2014 Accepted 20 April 2014 Published 24 June 2014

Academic Editor Subrata Mondal

Copyright copy 2014 D Mogensen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The kinetics of catalytic steam reforming of methane over an Ni-YSZ anode of a solid oxide fuel cell (SOFC) have been investigatedwith the cell placed in a stack configuration In order to decrease the degree of conversion a single cell stack with reduced area wasused Measurements were performed in the temperature range 600ndash800∘C and the partial pressures of all reactants and productswere varied The obtained rates could be well fitted with a power law expression (119903 prop 11987507CH4 ) A simple model is presented which iscapable of predicting the methane conversion in a stack configuration from intrinsic kinetics of the anode support material Thepredictions are compared with the stack measurements presented here and good agreement is observed

1 Introduction

The major advantage of partial internal steam reforming inan SOFC is that the waste heat from the electrochemicalreactions and the joule heat are used to supply the energy forthe endothermic reforming reaction (Reaction (1)) which hasa reaction enthalpy of 206 kJmol at 25∘CTheoverall reactionis still strongly endothermic when taking into account alsothe exothermic water gas shift reaction (Reaction (2)) havinga reaction enthalpy of minus41 kJmol at 25∘C [1]

CH4+H2O 999445999468 3H

2+ CO (1)

CO +H2O 999445999468 CO

2+H2

(2)

A further advantage of internal reforming is the decreasedneed for cooling via air flow at the cathode side which cansignificantly increase system efficiency

The rate of catalytic steam reforming of methane over anindustrial SOFC anode is very high [2] This is caused by

the combined effect of high operating temperature a highlyactive catalyst material and a high nickel catalyst contentThe Ni content and particle size are optimised to meetelectrochemical and electrical needs and not for optimizingthe steam reforming rate The result is a rapid cooling dueto the reaction enthalpy at the anode inlet giving largetemperature gradients which decreases the stack efficiencyand in the worst case can result in mechanical failure ofthe cells due to thermal stresses [3] So in order to achieveoptimal operation of SOFC systems with internal steamreforming it is necessary to have a good understanding andpossibly control the amount reforming taking place in thecell This in turn requires a good model representation of thestack which has also received much attention lately [4ndash11]The accuracy of such models depends on the accuracy of thekinetic expression used to predict the steam reforming rateand the purpose of this work is to obtain such an expressionmeasured directly in a stack configuration Furthermore it ishighly advantageous to be able to predict the reforming rate in

Hindawi Publishing CorporationJournal of ChemistryVolume 2014 Article ID 710391 8 pageshttpdxdoiorg1011552014710391

2 Journal of Chemistry

different stack configurations In rigorous models describingboth the flow in the gas channels and the diffusion throughthe anode the observed reforming rate can be predictedby using an intrinsic kinetic expression Such a model willhowever require heavy computations if used at stack level InSection 4 a very simple method for predicting the reformingrate in a stack is presented and validated

2 Experimental

The setup used in these investigations is an ldquoEvaluator C50rdquofrom FuelCon [12] which has undergone somemodificationsto fit the purpose of these experiments Dry gas flows are con-trolled with mass flow controllers (MFC) of the type ldquoLOWΔ119875 FLOWrdquo and ldquoEL-FLOWrdquo from Bronkhorst HI-TECwhich were calibrated using a Gilibrator 2 soap bubble flowmeter from Gilian with a specified measuring range of 20ndash6000mLmin Water vapour is added by bubbling nitrogenthrough a bubble flask at 90∘C Temperature measurementswere made with K-type thermocouples

Two IR analyzers of the type NGA 2000 Analyzer fromFisher-Rosemount were used interchangeably to measure theCO and CO

2content in the gas streams The contents of the

remaining species were calculated from themass balanceThefact that this is a trustworthy method was verified in someselected cases where a gas chromatograph was used to deter-mine the concentration of all species (except H

2O) present at

both inlet and outlet (CH4 CO2 CO and H

2) The analyzers

have a measurement error of 1 of the given measuringlimit

The stackswere reduced by the following procedure heat-ing to 860∘C in N

2 At 860∘C the gas was changed to 20 H

2

in N2for at least 4 hours hereafter the sample was cooled to

the test temperature and measurements were startedThe first attempt ofmeasuring the steam reforming kinet-

ics was made on a 5-cell SOFC 10 cm times 10 cm standard stackfrom Topsoe Fuel Cell It was found that the methane wascompletely converted even at the highest flows that the setupcould deliver

Therefore a special stack was provided by Topsoe FuelCell with only a single crossflow cell Three quarters of thecell was cut away so that a number of the cathode flow chan-nels were removed and the length of the anode flow channelswas shortened as illustrated in Figure 1

A further decrease in cell area would have been preferredbut removing part of the cell significantly reduced therobustness of the cells and several modified cells crackedunder conditions that a normal stack could easily withstandFurthermore removing more than 34 of the cell could resultin a gas flowpattern significantly different from that of the fullcell

Four thermocouples were placed in the gas distributionplates close to the flow channels in order to monitor thetemperature gradient one at each corner of the fuel inlet sideone at the corner with fuel outlet and air inlet and finally oneat the fuel outlet and halfway through the air channel Thetemperature used in later calculations is an average of thesefour measurements The cathode side was only fed with

Cathode flowAnode flow

Cell areaRemoved cell area

Figure 1 Illustration of the orientation of the quarter cell withrespect to flow directions

Table 1 Overview of the gas composition at standard conditionsand the range each gas is varied in

Gas StandardkPa

RangekPa

CH4 12 12ndash30H2O 56 45ndash70H2 7 7ndash18CO 0 0ndash6CO2 0 0ndash9

nitrogen both in order to avoid mixing of air with the anodegas and to avoid electrochemical reactions in the cell Itis desired to avoid the electrochemical reactions since thesteam reforming reaction can be studied better when noother reactions are taking place

The rate measurements on this cell were performed atflows much higher than what is used during normal opera-tion of an SOFC with a total flow of approximately 2Nlminand a methane flow of up to 05Nlmin This was donein order to decrease the degree of conversion of methaneThe supplied methane flow is enough to sustain a currentof 70A which corresponds to a current density of 3 Acm2The specific current density where the SOFC is expectedto operate depends on the specific application as well ason the area specific resistance Normal current densitiesapplied in long-termdurability testing of SOFC at the presentdevelopment stage lie in the range between 025Acm2 and1Acm2 The pressure and temperature were 119879 = 600ndash700∘Cand 119875 = 11ndash125 atm

Table 1 shows the standard gas composition as well as therange in which each gas species was varied in the inlet

3 Results

During the rate measurements it was observed that thecatalytic activity of the anode had a slow approach to

Journal of Chemistry 3

8

7

6

5

4

3

2

1

00 50 100 150 250200 300 350 400

COCO2

Shutdown for two weeks

Con

cent

ratio

n (m

ole

)

Time (hr)

Figure 2 Startup curve for a half-cell stack at 119879 = 600∘C 119875CH4 =20 kPa 119875H2O = 59 kPa 119875H2 = 4 kPa and 119875N2 = 36 kPa

steady state after startup and after changes in temperatureor hydrogen partial pressure An example of this is shown inFigure 2 Possible explanation for such a decrease in activity ischanges in the anode microstructure carbon deposition andpoisoning All experiments were conducted under conditionswhere carbon formation should not be possible and no signsof carbon formationwere observed after the experimentsThedynamic behaviour is ascribed to microstructural changes inthe anode however it is not possible to conclusively rule outppb levels of poisoning An important note on this dynamicbehavior is that if the activation energy is examined withoutwaiting for steady state after each temperature change thevalue will be underestimated with a factor 2-3 All measure-ments reported in this paper are obtained after steady statehas been achieved at the relevant temperature

Figures 3 and 4 show the influence on the reaction rateof varying the inlet gas composition at 650∘C and 750∘Crespectively The measurements of the reaction rate depen-dence on the CO concentration at 650∘C were not completeddue to problems with the equipment

The observed reaction order of all species exceptmethaneis seen to be close to zero in agreement with the majorityof the expressions reported in the literature [2ndash15] A weakdependence on 119875H

2

minus02 at 650∘C and 01 at 750∘C isobserved This could be due to restructuring of the catalystThe influence of methane partial pressure has been testedat several temperatures and the observed rate orders areshown in Table 2 A power law expression was fitted to themeasured data using a methane rate order of 07 It shouldbe noted that this rate expression is only intended as a directdescription of the observed conversions and as such masstransport limitations and temperature gradients have notbeen taken into account Such effects will be discussed inthe next section That is the rate constant is calculated from(3) The change in methane concentration through the cell is

Table 2 Measured rate order of CH4 at different temperatures

119879 [∘C] Reaction order

600 063625 056650 075675 080725 063750 065775 071800 073

taken into account by using a logarithmic mean of the inletand outlet concentrations even though this is only accuratewhen there is a first order dependency

119896 = (119903obs)

times (119860ano lowast (119875CH4in minus 119875CH

4out

log (119875CH4in) minus log (119875CH

4out)

)

07

)

minus1

(3)

where 119903obs is the observed rate and 119860ano is the geometricanode area (asymp23 cm2) An Arrhenius plot of the rate constantfor this kinetic expression is shown in Figure 5 resulting inthe rate expression in

119903 = 2 sdot 104molesm2 Pa

exp(minus1661 (kJmole) 119877

119892

119879

)11987507

CH4

(4)

4 Predicting the Reaction Rate fromIntrinsic Kinetics

Kinetic measurements in a stack configuration are subjectto mass transport limitations and temperature gradients andconditions vary significantly over the cell area This meansthat a rate expression obtained on a stack is not necessarilyvalid for a stack with a different configuration In detailedmodels with a complete description ofmass and energy trans-port this problem can be avoided by using intrinsic kineticsThis type ofmodel requiresmassive computations and as suchis not viable for flow sheetmodels Here a simple approach topredicting steam reforming kinetics in a stack from intrinsickinetics is presented and validated against the stack mea-surements The cellstack is described by the design equationfor a packed bed reactor as shown in (5) [16] The differ-ential equation is solved using ode45 in MATLAB takinginto account the change in gas composition through the stack

119889119883CH4

119889119882cat=

119903eff119873CH

4in (5)

4 Journal of Chemistry

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 075

PH2O = 512 plusmn 041kPaPH2

= 693 plusmn 035kPa

(a) Dependency on CH4

times10minus3

5

45

4

35

3

25

2

15

1

05

0

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

0 10 20 30 40 50

Rate order = minus00577

PCH4= 12 plusmn 029 kPa

PH2= 675 plusmn 016 kPa

(b) Dependency on H2O

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus0207

PCH4= 12 plusmn 0038kPa

PH2O = 512 plusmn 0098kPa

(c) Dependency on H2

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00547

PCH4= 119 plusmn 0063kPa

PH2O = 511 plusmn 023 kPa

PH2= 714 plusmn 01kPa

(d) Dependency on CO2

Figure 3 Reaction rate of the internal steam reforming as function of the gas concentration of CH4

H2

O H2

and CO2

in a quarter cell stackat 650∘C

where119883CH4

is the degree of conversion ofmethane119882cat is thecatalyst weight119873CH

4in is themolar inlet flowofmethane and

119903eff is the effective reaction rate described by

119903eff = 120578 lowast 119903int (6)

where 120578 describes how big a fraction of the available catalystmaterial that is being fully used is that is an efficiency factor= 1 corresponds to full usage of the catalyst [17]

120578 =

tanh (120601)120601

(7)

where 120601 is the Thiele modulus which for first order kineticsis

120601 = 119871radic119896

119863

(8)

where119871 is the anode thickness 119896 is the rate constant (sminus1) and119863 is the effective diffusion coefficient (m2 sminus1) of methaneThe gas composition is a multicomponent mixture and thepore size of the anode support (04ndash1 120583m) is in the rangewhere Knudsen diffusion must be taken into account Forthis case it is not trivial to estimate the effective diffusioncoefficient We will in the analysis of the data first treat it asa fitting parameterThe expression used here for determining120578 is valid for systems where pore diffusion is dominant that

Journal of Chemistry 5

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Rate order = 0649

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PH2O = 482 plusmn 21 kPa

PH2= 14 plusmn 31kPa

(a) Dependency on CH4

007

006

005

004

003

002

001

00 10 20 30 40 50

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus00248

PH2= 129 plusmn 036kPa

PCH4= 103 plusmn 019 kPa

(b) Dependency on H2O

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 00104

PCH4= 103 plusmn 0086 kPa

PH2O = 489 plusmn 021 kPa

(c) Dependency on H2

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PCH4= 104 plusmn 014 kPa

PH2O = 483 plusmn 031kPa

PH2= 133 plusmn 022 kPa

Rate order = minus00619

(d) Dependency on CO

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00298

PH2O = 489 plusmn 041kPa

PH2= 129 plusmn 036kPa

PCH4= 102 plusmn 0091kPa

(e) Dependency on CO2

Figure 4 Corresponding measured rates and dependencies of the different gas species over the quarter cell stack at 750∘C

6 Journal of Chemistry

minus8

minus9

minus10

minus11

minus12

minus13

minus14

minus1509 1 11 12

times10minus3

A = 199e + 004mols m2 Pa07

Ea = 1661 kJmol

1T (1K)

ln(K

)

Figure 5 Arrhenius plot for measured rate constants on the quartercell stack

is intermediate values of 120601 At high and low values of 120601 otherestimations should be used

The intrinsic rate (119903int) is calculated from an expressionobtained in a plug-flow reactor under differential conversionand without mass transfer limitations The expression isshown in

119903int

= (100

moleg s Pa

exp(minus195 (kJmole)119877119879

)

times119875CH4

(1 minus

119876sr119870sr))

times ((1 + 46 sdot 10minus7Paminus1 exp(32 (kJmole)

119877119879

)119875CO)2

)

minus1

(9)

Themajority of the kinetic expressions reported in the lit-erature for steam reforming over Ni-YSZ report an activationenergy in the range 58ndash135 kJmol [4 13ndash15 20ndash22] and onlya few report values around 200 kJmol [23ndash25]

The high activation energy both in (9) and (4) is a resultof waiting for the slow approach to steady state at each tem-perature which has not been reported in the previous studiesThe expressions presented here are consequently not a goodrepresentation of the steam reforming rate in a stack justafter startup or a temperature change Instead they describethe reforming rate in a stack operating at steady state forlong periods of time

Figure 6 shows a comparison of the measured conversionin the ldquostackrdquo experiment and the conversion predicted fromthe expression of the intrinsic kinetics (9) ldquocorrectedrdquo formass transfer limitations (6)ndash(8) and differentiated across theanode (5) Figure 6(a) shows the entire range of obtainedvalues while Figure 6(b) shows a zoom at low conversion

The line in the figures correspond to ideal fit between themeasured value and the predicted value

Considering the simplicity of themodel it gives a surpris-ingly good agreement of themeasured conversion in the stackand the estimate deduced from the intrinsic kinetics via themodelNote that the only inputs are the inlet gas compositionthe effective diffusion coefficient and the temperature Bestagreement is observed for an effective diffusion coefficientof 10minus5m2 sminus1 (note that any temperature dependence of thediffusion coefficient has been neglected) It can furthermorebe seen from the figures that the major deviations are atlow conversion while higher conversions result in a betterfit The measurements that deviate most from the model inFigure 6(b) are withmethane concentration changes at 675∘C(four points overestimated by model) and 625∘C (four pointsunderestimated bymodel) It is also these fourmeasurementsat 625∘C that deviate from the trend in the Arrhenius plot inFigure 5This deviance could be an indication that the surfacestructure at low temperatures is substantially different fromthe structure in the majority of the measurements presentedhere However the deviation does not seem to be systematicand for the scope of this study it is ascribed to experimentaluncertainty

The value of the diffusion coefficient that gave thebest description was 10minus5m2 sminus1 resulting in an efficiencyfactor close to 1 at 600∘C and asymp05 at 800∘C This valuecorresponds to 004 times the binary diffusion coefficientof a steammethane gas mixture at 750∘C calculated asdescribed in appendix The strong reduction as comparedto the free gas value is due to the hindering effect ofthe anode support Assuming a porosity of 30 and atortuosity of 3 a reduction of the binary gas diffusion ofa factor of 10 should be expected Moreover the effectivediffusion coefficient is further reduced due to a small sizeof the pores Hence a reduction by a factor of 20 does notseem unfeasible In a study of mass transport limitationson the electrochemical conversion of hydrogen in a similarbut slightly less porous anode structure Hendriksen et al[26] reported values of the effective diffusion coefficient onthe order of 05ndash1 of the binary diffusion coefficients

The results are given high credibility from the fact thatthemeasurements can be correlatedwithmeasurements froma plug-flow reactor through a simple description of theexpected mass transport in the stack

5 Conclusion

The rate of methane steam reforming over an SOFC Ni-YSZ anode has been measured in the temperature range600ndash800∘C and with variations in the partial pressure of allreactants and products The activity was observed to have along-term dynamic behavior Furthermore a simple methodfor predictingmethane conversion in a stack froman intrinsicexpression was presented The method was validated againstthe quarter stack measurements and was found to give asurprisingly good representation of the observed methaneconversion The simplicity of this method makes it ideal forsimple SOFC stack models for flow sheeting purposes

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

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Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 3

8

7

6

5

4

3

2

1

00 50 100 150 250200 300 350 400

COCO2

Shutdown for two weeks

Con

cent

ratio

n (m

ole

)

Time (hr)

Figure 2 Startup curve for a half-cell stack at 119879 = 600∘C 119875CH4 =20 kPa 119875H2O = 59 kPa 119875H2 = 4 kPa and 119875N2 = 36 kPa

steady state after startup and after changes in temperatureor hydrogen partial pressure An example of this is shown inFigure 2 Possible explanation for such a decrease in activity ischanges in the anode microstructure carbon deposition andpoisoning All experiments were conducted under conditionswhere carbon formation should not be possible and no signsof carbon formationwere observed after the experimentsThedynamic behaviour is ascribed to microstructural changes inthe anode however it is not possible to conclusively rule outppb levels of poisoning An important note on this dynamicbehavior is that if the activation energy is examined withoutwaiting for steady state after each temperature change thevalue will be underestimated with a factor 2-3 All measure-ments reported in this paper are obtained after steady statehas been achieved at the relevant temperature

Figures 3 and 4 show the influence on the reaction rateof varying the inlet gas composition at 650∘C and 750∘Crespectively The measurements of the reaction rate depen-dence on the CO concentration at 650∘C were not completeddue to problems with the equipment

The observed reaction order of all species exceptmethaneis seen to be close to zero in agreement with the majorityof the expressions reported in the literature [2ndash15] A weakdependence on 119875H

2

minus02 at 650∘C and 01 at 750∘C isobserved This could be due to restructuring of the catalystThe influence of methane partial pressure has been testedat several temperatures and the observed rate orders areshown in Table 2 A power law expression was fitted to themeasured data using a methane rate order of 07 It shouldbe noted that this rate expression is only intended as a directdescription of the observed conversions and as such masstransport limitations and temperature gradients have notbeen taken into account Such effects will be discussed inthe next section That is the rate constant is calculated from(3) The change in methane concentration through the cell is

Table 2 Measured rate order of CH4 at different temperatures

119879 [∘C] Reaction order

600 063625 056650 075675 080725 063750 065775 071800 073

taken into account by using a logarithmic mean of the inletand outlet concentrations even though this is only accuratewhen there is a first order dependency

119896 = (119903obs)

times (119860ano lowast (119875CH4in minus 119875CH

4out

log (119875CH4in) minus log (119875CH

4out)

)

07

)

minus1

(3)

where 119903obs is the observed rate and 119860ano is the geometricanode area (asymp23 cm2) An Arrhenius plot of the rate constantfor this kinetic expression is shown in Figure 5 resulting inthe rate expression in

119903 = 2 sdot 104molesm2 Pa

exp(minus1661 (kJmole) 119877

119892

119879

)11987507

CH4

(4)

4 Predicting the Reaction Rate fromIntrinsic Kinetics

Kinetic measurements in a stack configuration are subjectto mass transport limitations and temperature gradients andconditions vary significantly over the cell area This meansthat a rate expression obtained on a stack is not necessarilyvalid for a stack with a different configuration In detailedmodels with a complete description ofmass and energy trans-port this problem can be avoided by using intrinsic kineticsThis type ofmodel requiresmassive computations and as suchis not viable for flow sheetmodels Here a simple approach topredicting steam reforming kinetics in a stack from intrinsickinetics is presented and validated against the stack mea-surements The cellstack is described by the design equationfor a packed bed reactor as shown in (5) [16] The differ-ential equation is solved using ode45 in MATLAB takinginto account the change in gas composition through the stack

119889119883CH4

119889119882cat=

119903eff119873CH

4in (5)

4 Journal of Chemistry

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 075

PH2O = 512 plusmn 041kPaPH2

= 693 plusmn 035kPa

(a) Dependency on CH4

times10minus3

5

45

4

35

3

25

2

15

1

05

0

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

0 10 20 30 40 50

Rate order = minus00577

PCH4= 12 plusmn 029 kPa

PH2= 675 plusmn 016 kPa

(b) Dependency on H2O

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus0207

PCH4= 12 plusmn 0038kPa

PH2O = 512 plusmn 0098kPa

(c) Dependency on H2

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00547

PCH4= 119 plusmn 0063kPa

PH2O = 511 plusmn 023 kPa

PH2= 714 plusmn 01kPa

(d) Dependency on CO2

Figure 3 Reaction rate of the internal steam reforming as function of the gas concentration of CH4

H2

O H2

and CO2

in a quarter cell stackat 650∘C

where119883CH4

is the degree of conversion ofmethane119882cat is thecatalyst weight119873CH

4in is themolar inlet flowofmethane and

119903eff is the effective reaction rate described by

119903eff = 120578 lowast 119903int (6)

where 120578 describes how big a fraction of the available catalystmaterial that is being fully used is that is an efficiency factor= 1 corresponds to full usage of the catalyst [17]

120578 =

tanh (120601)120601

(7)

where 120601 is the Thiele modulus which for first order kineticsis

120601 = 119871radic119896

119863

(8)

where119871 is the anode thickness 119896 is the rate constant (sminus1) and119863 is the effective diffusion coefficient (m2 sminus1) of methaneThe gas composition is a multicomponent mixture and thepore size of the anode support (04ndash1 120583m) is in the rangewhere Knudsen diffusion must be taken into account Forthis case it is not trivial to estimate the effective diffusioncoefficient We will in the analysis of the data first treat it asa fitting parameterThe expression used here for determining120578 is valid for systems where pore diffusion is dominant that

Journal of Chemistry 5

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Rate order = 0649

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PH2O = 482 plusmn 21 kPa

PH2= 14 plusmn 31kPa

(a) Dependency on CH4

007

006

005

004

003

002

001

00 10 20 30 40 50

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus00248

PH2= 129 plusmn 036kPa

PCH4= 103 plusmn 019 kPa

(b) Dependency on H2O

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 00104

PCH4= 103 plusmn 0086 kPa

PH2O = 489 plusmn 021 kPa

(c) Dependency on H2

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PCH4= 104 plusmn 014 kPa

PH2O = 483 plusmn 031kPa

PH2= 133 plusmn 022 kPa

Rate order = minus00619

(d) Dependency on CO

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00298

PH2O = 489 plusmn 041kPa

PH2= 129 plusmn 036kPa

PCH4= 102 plusmn 0091kPa

(e) Dependency on CO2

Figure 4 Corresponding measured rates and dependencies of the different gas species over the quarter cell stack at 750∘C

6 Journal of Chemistry

minus8

minus9

minus10

minus11

minus12

minus13

minus14

minus1509 1 11 12

times10minus3

A = 199e + 004mols m2 Pa07

Ea = 1661 kJmol

1T (1K)

ln(K

)

Figure 5 Arrhenius plot for measured rate constants on the quartercell stack

is intermediate values of 120601 At high and low values of 120601 otherestimations should be used

The intrinsic rate (119903int) is calculated from an expressionobtained in a plug-flow reactor under differential conversionand without mass transfer limitations The expression isshown in

119903int

= (100

moleg s Pa

exp(minus195 (kJmole)119877119879

)

times119875CH4

(1 minus

119876sr119870sr))

times ((1 + 46 sdot 10minus7Paminus1 exp(32 (kJmole)

119877119879

)119875CO)2

)

minus1

(9)

Themajority of the kinetic expressions reported in the lit-erature for steam reforming over Ni-YSZ report an activationenergy in the range 58ndash135 kJmol [4 13ndash15 20ndash22] and onlya few report values around 200 kJmol [23ndash25]

The high activation energy both in (9) and (4) is a resultof waiting for the slow approach to steady state at each tem-perature which has not been reported in the previous studiesThe expressions presented here are consequently not a goodrepresentation of the steam reforming rate in a stack justafter startup or a temperature change Instead they describethe reforming rate in a stack operating at steady state forlong periods of time

Figure 6 shows a comparison of the measured conversionin the ldquostackrdquo experiment and the conversion predicted fromthe expression of the intrinsic kinetics (9) ldquocorrectedrdquo formass transfer limitations (6)ndash(8) and differentiated across theanode (5) Figure 6(a) shows the entire range of obtainedvalues while Figure 6(b) shows a zoom at low conversion

The line in the figures correspond to ideal fit between themeasured value and the predicted value

Considering the simplicity of themodel it gives a surpris-ingly good agreement of themeasured conversion in the stackand the estimate deduced from the intrinsic kinetics via themodelNote that the only inputs are the inlet gas compositionthe effective diffusion coefficient and the temperature Bestagreement is observed for an effective diffusion coefficientof 10minus5m2 sminus1 (note that any temperature dependence of thediffusion coefficient has been neglected) It can furthermorebe seen from the figures that the major deviations are atlow conversion while higher conversions result in a betterfit The measurements that deviate most from the model inFigure 6(b) are withmethane concentration changes at 675∘C(four points overestimated by model) and 625∘C (four pointsunderestimated bymodel) It is also these fourmeasurementsat 625∘C that deviate from the trend in the Arrhenius plot inFigure 5This deviance could be an indication that the surfacestructure at low temperatures is substantially different fromthe structure in the majority of the measurements presentedhere However the deviation does not seem to be systematicand for the scope of this study it is ascribed to experimentaluncertainty

The value of the diffusion coefficient that gave thebest description was 10minus5m2 sminus1 resulting in an efficiencyfactor close to 1 at 600∘C and asymp05 at 800∘C This valuecorresponds to 004 times the binary diffusion coefficientof a steammethane gas mixture at 750∘C calculated asdescribed in appendix The strong reduction as comparedto the free gas value is due to the hindering effect ofthe anode support Assuming a porosity of 30 and atortuosity of 3 a reduction of the binary gas diffusion ofa factor of 10 should be expected Moreover the effectivediffusion coefficient is further reduced due to a small sizeof the pores Hence a reduction by a factor of 20 does notseem unfeasible In a study of mass transport limitationson the electrochemical conversion of hydrogen in a similarbut slightly less porous anode structure Hendriksen et al[26] reported values of the effective diffusion coefficient onthe order of 05ndash1 of the binary diffusion coefficients

The results are given high credibility from the fact thatthemeasurements can be correlatedwithmeasurements froma plug-flow reactor through a simple description of theexpected mass transport in the stack

5 Conclusion

The rate of methane steam reforming over an SOFC Ni-YSZ anode has been measured in the temperature range600ndash800∘C and with variations in the partial pressure of allreactants and products The activity was observed to have along-term dynamic behavior Furthermore a simple methodfor predictingmethane conversion in a stack froman intrinsicexpression was presented The method was validated againstthe quarter stack measurements and was found to give asurprisingly good representation of the observed methaneconversion The simplicity of this method makes it ideal forsimple SOFC stack models for flow sheeting purposes

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

4 Journal of Chemistry

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 075

PH2O = 512 plusmn 041kPaPH2

= 693 plusmn 035kPa

(a) Dependency on CH4

times10minus3

5

45

4

35

3

25

2

15

1

05

0

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

0 10 20 30 40 50

Rate order = minus00577

PCH4= 12 plusmn 029 kPa

PH2= 675 plusmn 016 kPa

(b) Dependency on H2O

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus0207

PCH4= 12 plusmn 0038kPa

PH2O = 512 plusmn 0098kPa

(c) Dependency on H2

times10minus3

5

45

4

35

3

25

2

15

1

05

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00547

PCH4= 119 plusmn 0063kPa

PH2O = 511 plusmn 023 kPa

PH2= 714 plusmn 01kPa

(d) Dependency on CO2

Figure 3 Reaction rate of the internal steam reforming as function of the gas concentration of CH4

H2

O H2

and CO2

in a quarter cell stackat 650∘C

where119883CH4

is the degree of conversion ofmethane119882cat is thecatalyst weight119873CH

4in is themolar inlet flowofmethane and

119903eff is the effective reaction rate described by

119903eff = 120578 lowast 119903int (6)

where 120578 describes how big a fraction of the available catalystmaterial that is being fully used is that is an efficiency factor= 1 corresponds to full usage of the catalyst [17]

120578 =

tanh (120601)120601

(7)

where 120601 is the Thiele modulus which for first order kineticsis

120601 = 119871radic119896

119863

(8)

where119871 is the anode thickness 119896 is the rate constant (sminus1) and119863 is the effective diffusion coefficient (m2 sminus1) of methaneThe gas composition is a multicomponent mixture and thepore size of the anode support (04ndash1 120583m) is in the rangewhere Knudsen diffusion must be taken into account Forthis case it is not trivial to estimate the effective diffusioncoefficient We will in the analysis of the data first treat it asa fitting parameterThe expression used here for determining120578 is valid for systems where pore diffusion is dominant that

Journal of Chemistry 5

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Rate order = 0649

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PH2O = 482 plusmn 21 kPa

PH2= 14 plusmn 31kPa

(a) Dependency on CH4

007

006

005

004

003

002

001

00 10 20 30 40 50

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus00248

PH2= 129 plusmn 036kPa

PCH4= 103 plusmn 019 kPa

(b) Dependency on H2O

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 00104

PCH4= 103 plusmn 0086 kPa

PH2O = 489 plusmn 021 kPa

(c) Dependency on H2

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PCH4= 104 plusmn 014 kPa

PH2O = 483 plusmn 031kPa

PH2= 133 plusmn 022 kPa

Rate order = minus00619

(d) Dependency on CO

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00298

PH2O = 489 plusmn 041kPa

PH2= 129 plusmn 036kPa

PCH4= 102 plusmn 0091kPa

(e) Dependency on CO2

Figure 4 Corresponding measured rates and dependencies of the different gas species over the quarter cell stack at 750∘C

6 Journal of Chemistry

minus8

minus9

minus10

minus11

minus12

minus13

minus14

minus1509 1 11 12

times10minus3

A = 199e + 004mols m2 Pa07

Ea = 1661 kJmol

1T (1K)

ln(K

)

Figure 5 Arrhenius plot for measured rate constants on the quartercell stack

is intermediate values of 120601 At high and low values of 120601 otherestimations should be used

The intrinsic rate (119903int) is calculated from an expressionobtained in a plug-flow reactor under differential conversionand without mass transfer limitations The expression isshown in

119903int

= (100

moleg s Pa

exp(minus195 (kJmole)119877119879

)

times119875CH4

(1 minus

119876sr119870sr))

times ((1 + 46 sdot 10minus7Paminus1 exp(32 (kJmole)

119877119879

)119875CO)2

)

minus1

(9)

Themajority of the kinetic expressions reported in the lit-erature for steam reforming over Ni-YSZ report an activationenergy in the range 58ndash135 kJmol [4 13ndash15 20ndash22] and onlya few report values around 200 kJmol [23ndash25]

The high activation energy both in (9) and (4) is a resultof waiting for the slow approach to steady state at each tem-perature which has not been reported in the previous studiesThe expressions presented here are consequently not a goodrepresentation of the steam reforming rate in a stack justafter startup or a temperature change Instead they describethe reforming rate in a stack operating at steady state forlong periods of time

Figure 6 shows a comparison of the measured conversionin the ldquostackrdquo experiment and the conversion predicted fromthe expression of the intrinsic kinetics (9) ldquocorrectedrdquo formass transfer limitations (6)ndash(8) and differentiated across theanode (5) Figure 6(a) shows the entire range of obtainedvalues while Figure 6(b) shows a zoom at low conversion

The line in the figures correspond to ideal fit between themeasured value and the predicted value

Considering the simplicity of themodel it gives a surpris-ingly good agreement of themeasured conversion in the stackand the estimate deduced from the intrinsic kinetics via themodelNote that the only inputs are the inlet gas compositionthe effective diffusion coefficient and the temperature Bestagreement is observed for an effective diffusion coefficientof 10minus5m2 sminus1 (note that any temperature dependence of thediffusion coefficient has been neglected) It can furthermorebe seen from the figures that the major deviations are atlow conversion while higher conversions result in a betterfit The measurements that deviate most from the model inFigure 6(b) are withmethane concentration changes at 675∘C(four points overestimated by model) and 625∘C (four pointsunderestimated bymodel) It is also these fourmeasurementsat 625∘C that deviate from the trend in the Arrhenius plot inFigure 5This deviance could be an indication that the surfacestructure at low temperatures is substantially different fromthe structure in the majority of the measurements presentedhere However the deviation does not seem to be systematicand for the scope of this study it is ascribed to experimentaluncertainty

The value of the diffusion coefficient that gave thebest description was 10minus5m2 sminus1 resulting in an efficiencyfactor close to 1 at 600∘C and asymp05 at 800∘C This valuecorresponds to 004 times the binary diffusion coefficientof a steammethane gas mixture at 750∘C calculated asdescribed in appendix The strong reduction as comparedto the free gas value is due to the hindering effect ofthe anode support Assuming a porosity of 30 and atortuosity of 3 a reduction of the binary gas diffusion ofa factor of 10 should be expected Moreover the effectivediffusion coefficient is further reduced due to a small sizeof the pores Hence a reduction by a factor of 20 does notseem unfeasible In a study of mass transport limitationson the electrochemical conversion of hydrogen in a similarbut slightly less porous anode structure Hendriksen et al[26] reported values of the effective diffusion coefficient onthe order of 05ndash1 of the binary diffusion coefficients

The results are given high credibility from the fact thatthemeasurements can be correlatedwithmeasurements froma plug-flow reactor through a simple description of theexpected mass transport in the stack

5 Conclusion

The rate of methane steam reforming over an SOFC Ni-YSZ anode has been measured in the temperature range600ndash800∘C and with variations in the partial pressure of allreactants and products The activity was observed to have along-term dynamic behavior Furthermore a simple methodfor predictingmethane conversion in a stack froman intrinsicexpression was presented The method was validated againstthe quarter stack measurements and was found to give asurprisingly good representation of the observed methaneconversion The simplicity of this method makes it ideal forsimple SOFC stack models for flow sheeting purposes

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 5

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Rate order = 0649

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PH2O = 482 plusmn 21 kPa

PH2= 14 plusmn 31kPa

(a) Dependency on CH4

007

006

005

004

003

002

001

00 10 20 30 40 50

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = minus00248

PH2= 129 plusmn 036kPa

PCH4= 103 plusmn 019 kPa

(b) Dependency on H2O

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

Rate order = 00104

PCH4= 103 plusmn 0086 kPa

PH2O = 489 plusmn 021 kPa

(c) Dependency on H2

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2)

PCH4= 104 plusmn 014 kPa

PH2O = 483 plusmn 031kPa

PH2= 133 plusmn 022 kPa

Rate order = minus00619

(d) Dependency on CO

007

006

005

004

003

002

001

00 5 10 15 20 25 30 35 40

Partial pressure (kPa)

Reac

tion

rate

(mol

s m

2) Rate order = minus00298

PH2O = 489 plusmn 041kPa

PH2= 129 plusmn 036kPa

PCH4= 102 plusmn 0091kPa

(e) Dependency on CO2

Figure 4 Corresponding measured rates and dependencies of the different gas species over the quarter cell stack at 750∘C

6 Journal of Chemistry

minus8

minus9

minus10

minus11

minus12

minus13

minus14

minus1509 1 11 12

times10minus3

A = 199e + 004mols m2 Pa07

Ea = 1661 kJmol

1T (1K)

ln(K

)

Figure 5 Arrhenius plot for measured rate constants on the quartercell stack

is intermediate values of 120601 At high and low values of 120601 otherestimations should be used

The intrinsic rate (119903int) is calculated from an expressionobtained in a plug-flow reactor under differential conversionand without mass transfer limitations The expression isshown in

119903int

= (100

moleg s Pa

exp(minus195 (kJmole)119877119879

)

times119875CH4

(1 minus

119876sr119870sr))

times ((1 + 46 sdot 10minus7Paminus1 exp(32 (kJmole)

119877119879

)119875CO)2

)

minus1

(9)

Themajority of the kinetic expressions reported in the lit-erature for steam reforming over Ni-YSZ report an activationenergy in the range 58ndash135 kJmol [4 13ndash15 20ndash22] and onlya few report values around 200 kJmol [23ndash25]

The high activation energy both in (9) and (4) is a resultof waiting for the slow approach to steady state at each tem-perature which has not been reported in the previous studiesThe expressions presented here are consequently not a goodrepresentation of the steam reforming rate in a stack justafter startup or a temperature change Instead they describethe reforming rate in a stack operating at steady state forlong periods of time

Figure 6 shows a comparison of the measured conversionin the ldquostackrdquo experiment and the conversion predicted fromthe expression of the intrinsic kinetics (9) ldquocorrectedrdquo formass transfer limitations (6)ndash(8) and differentiated across theanode (5) Figure 6(a) shows the entire range of obtainedvalues while Figure 6(b) shows a zoom at low conversion

The line in the figures correspond to ideal fit between themeasured value and the predicted value

Considering the simplicity of themodel it gives a surpris-ingly good agreement of themeasured conversion in the stackand the estimate deduced from the intrinsic kinetics via themodelNote that the only inputs are the inlet gas compositionthe effective diffusion coefficient and the temperature Bestagreement is observed for an effective diffusion coefficientof 10minus5m2 sminus1 (note that any temperature dependence of thediffusion coefficient has been neglected) It can furthermorebe seen from the figures that the major deviations are atlow conversion while higher conversions result in a betterfit The measurements that deviate most from the model inFigure 6(b) are withmethane concentration changes at 675∘C(four points overestimated by model) and 625∘C (four pointsunderestimated bymodel) It is also these fourmeasurementsat 625∘C that deviate from the trend in the Arrhenius plot inFigure 5This deviance could be an indication that the surfacestructure at low temperatures is substantially different fromthe structure in the majority of the measurements presentedhere However the deviation does not seem to be systematicand for the scope of this study it is ascribed to experimentaluncertainty

The value of the diffusion coefficient that gave thebest description was 10minus5m2 sminus1 resulting in an efficiencyfactor close to 1 at 600∘C and asymp05 at 800∘C This valuecorresponds to 004 times the binary diffusion coefficientof a steammethane gas mixture at 750∘C calculated asdescribed in appendix The strong reduction as comparedto the free gas value is due to the hindering effect ofthe anode support Assuming a porosity of 30 and atortuosity of 3 a reduction of the binary gas diffusion ofa factor of 10 should be expected Moreover the effectivediffusion coefficient is further reduced due to a small sizeof the pores Hence a reduction by a factor of 20 does notseem unfeasible In a study of mass transport limitationson the electrochemical conversion of hydrogen in a similarbut slightly less porous anode structure Hendriksen et al[26] reported values of the effective diffusion coefficient onthe order of 05ndash1 of the binary diffusion coefficients

The results are given high credibility from the fact thatthemeasurements can be correlatedwithmeasurements froma plug-flow reactor through a simple description of theexpected mass transport in the stack

5 Conclusion

The rate of methane steam reforming over an SOFC Ni-YSZ anode has been measured in the temperature range600ndash800∘C and with variations in the partial pressure of allreactants and products The activity was observed to have along-term dynamic behavior Furthermore a simple methodfor predictingmethane conversion in a stack froman intrinsicexpression was presented The method was validated againstthe quarter stack measurements and was found to give asurprisingly good representation of the observed methaneconversion The simplicity of this method makes it ideal forsimple SOFC stack models for flow sheeting purposes

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

6 Journal of Chemistry

minus8

minus9

minus10

minus11

minus12

minus13

minus14

minus1509 1 11 12

times10minus3

A = 199e + 004mols m2 Pa07

Ea = 1661 kJmol

1T (1K)

ln(K

)

Figure 5 Arrhenius plot for measured rate constants on the quartercell stack

is intermediate values of 120601 At high and low values of 120601 otherestimations should be used

The intrinsic rate (119903int) is calculated from an expressionobtained in a plug-flow reactor under differential conversionand without mass transfer limitations The expression isshown in

119903int

= (100

moleg s Pa

exp(minus195 (kJmole)119877119879

)

times119875CH4

(1 minus

119876sr119870sr))

times ((1 + 46 sdot 10minus7Paminus1 exp(32 (kJmole)

119877119879

)119875CO)2

)

minus1

(9)

Themajority of the kinetic expressions reported in the lit-erature for steam reforming over Ni-YSZ report an activationenergy in the range 58ndash135 kJmol [4 13ndash15 20ndash22] and onlya few report values around 200 kJmol [23ndash25]

The high activation energy both in (9) and (4) is a resultof waiting for the slow approach to steady state at each tem-perature which has not been reported in the previous studiesThe expressions presented here are consequently not a goodrepresentation of the steam reforming rate in a stack justafter startup or a temperature change Instead they describethe reforming rate in a stack operating at steady state forlong periods of time

Figure 6 shows a comparison of the measured conversionin the ldquostackrdquo experiment and the conversion predicted fromthe expression of the intrinsic kinetics (9) ldquocorrectedrdquo formass transfer limitations (6)ndash(8) and differentiated across theanode (5) Figure 6(a) shows the entire range of obtainedvalues while Figure 6(b) shows a zoom at low conversion

The line in the figures correspond to ideal fit between themeasured value and the predicted value

Considering the simplicity of themodel it gives a surpris-ingly good agreement of themeasured conversion in the stackand the estimate deduced from the intrinsic kinetics via themodelNote that the only inputs are the inlet gas compositionthe effective diffusion coefficient and the temperature Bestagreement is observed for an effective diffusion coefficientof 10minus5m2 sminus1 (note that any temperature dependence of thediffusion coefficient has been neglected) It can furthermorebe seen from the figures that the major deviations are atlow conversion while higher conversions result in a betterfit The measurements that deviate most from the model inFigure 6(b) are withmethane concentration changes at 675∘C(four points overestimated by model) and 625∘C (four pointsunderestimated bymodel) It is also these fourmeasurementsat 625∘C that deviate from the trend in the Arrhenius plot inFigure 5This deviance could be an indication that the surfacestructure at low temperatures is substantially different fromthe structure in the majority of the measurements presentedhere However the deviation does not seem to be systematicand for the scope of this study it is ascribed to experimentaluncertainty

The value of the diffusion coefficient that gave thebest description was 10minus5m2 sminus1 resulting in an efficiencyfactor close to 1 at 600∘C and asymp05 at 800∘C This valuecorresponds to 004 times the binary diffusion coefficientof a steammethane gas mixture at 750∘C calculated asdescribed in appendix The strong reduction as comparedto the free gas value is due to the hindering effect ofthe anode support Assuming a porosity of 30 and atortuosity of 3 a reduction of the binary gas diffusion ofa factor of 10 should be expected Moreover the effectivediffusion coefficient is further reduced due to a small sizeof the pores Hence a reduction by a factor of 20 does notseem unfeasible In a study of mass transport limitationson the electrochemical conversion of hydrogen in a similarbut slightly less porous anode structure Hendriksen et al[26] reported values of the effective diffusion coefficient onthe order of 05ndash1 of the binary diffusion coefficients

The results are given high credibility from the fact thatthemeasurements can be correlatedwithmeasurements froma plug-flow reactor through a simple description of theexpected mass transport in the stack

5 Conclusion

The rate of methane steam reforming over an SOFC Ni-YSZ anode has been measured in the temperature range600ndash800∘C and with variations in the partial pressure of allreactants and products The activity was observed to have along-term dynamic behavior Furthermore a simple methodfor predictingmethane conversion in a stack froman intrinsicexpression was presented The method was validated againstthe quarter stack measurements and was found to give asurprisingly good representation of the observed methaneconversion The simplicity of this method makes it ideal forsimple SOFC stack models for flow sheeting purposes

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 7

08

07

06

05

04

03

02

01

00 02 04 06 08

Mod

el co

nver

sion

Measured conversion

(a) Results with measured temperature

01

008

006

004

002

00 002 004 006 008 01

Mod

el co

nver

sion

Measured conversion

(b) Representation of the data in Figure 6(a) only at low conversion

Figure 6 Comparison of measured conversion and the conversion predicted by the model using data from a plug-flow reactor

Table 3 Constants used for determining the binary diffusioncoefficients [18 19]

120590 120598k 119872

A K gmolO2 3433 113 31999N2 3667 998 28013H2 2915 38 2016H2O 2641 8091 18016CO 3590 110 28010CO2 3996 190 44010CH4 3780 154 16040

Appendix

Estimation of Diffusion Coefficient

TheChapman-Enskog expression (A1) is used to determinebinary diffusion coefficients (119863

119894119895)

119863119894119895= 00018583radic119879

3

(

1

119872119894

+

1

119872119895

)

1

1198751205902

119894119895

Ω119863119894119895

(A1)

where119872 is the molar mass of the denoted species and Ω isthe dimensionless collision integral which is a function ofthe dimensionless temperature 120581119879120598

119894119895 The parameters 120590 and

120598120581 can be found as tabulated values for each species and thevalue for each pair of species can be estimated by [18]

120590119894119895=

120590119894+ 120590119895

2

120598119894119895= radic120598119894120598119895

(A2)

The tabulated values of120590 and 120598 that are used in this projectare shown in Table 3

Equation (A4) given by Reid et al [19] is used to calculateΩ119863119894119895

119910 = 1199094

+ 4

= (1199092

+ 2)

2

minus 41199092

le (1199092

+ 2)

2

(A3)

Ω119863119894119895

=

119860

(119879lowast

)119861

+

119862

exp (119863119879lowast)+

119864

exp (119865119879lowast)+

119866

exp (119867119879lowast)

(A4)

where 119879lowast = 120581119879120598119894119895is the dimensionless temperature and the

constants 119860 minus119867 are given below

119860 = 106036

119861 = 015610

119862 = 019300

119863 = 047635

119864 = 103587

119865 = 152996

119866 = 176474

119867 = 389411

The method described here should give the binary diffu-sion coefficients within 10

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

8 Journal of Chemistry

References

[1] J R Rostrup-Nielsen J Sehested and J K Noslashrskov ldquoHydrogenand synthesis gas by steam- and C02 reformingrdquo Advances inCatalysis vol 47 pp 65ndash139 2002

[2] D Mogensen J-D Grunwaldt P V Hendriksen K Dam-Johansen and J U Nielsen ldquoInternal steam reforming in solidoxide fuel cells status and opportunities of kinetic studies andtheir impact on modellingrdquo Journal of Power Sources vol 196no 1 pp 25ndash38 2011

[3] P Hendriksen ldquoModel studies of internal steam reforming inSOFC stacksrdquo in Proceedings of the 5th International Symposiumon Solid Oxide Fuel Cells (SOFC rsquo97) pp 1319ndash1328 1997

[4] H Timmermann W Sawady R Reimert and E Ivers-TiffeeldquoKinetics of (reversible) internal reforming of methane in solidoxide fuel cells under stationary and APU conditionsrdquo Journalof Power Sources vol 195 no 1 pp 214ndash222 2010

[5] T X Ho P Kosinski A C Hoffmann and A Vik ldquoEffects ofheat sources on the performance of a planar solid oxide fuelcellrdquo International Journal of Hydrogen Energy vol 35 no 9 pp4276ndash4284 2010

[6] N Akhtar S P Decent and K Kendall ldquoNumerical modellingofmethane-poweredmicro-tubular single-chamber solid oxidefuel cellrdquo Journal of Power Sources vol 195 no 23 pp 7796ndash7807 2010

[7] T F Petersen N Houbak and B Elmegaard ldquoA zero-dimensional model of a 2nd generation planar SOFC using cal-ibrated parametersrdquo International Journal of Thermodynamicsvol 9 no 4 pp 161ndash169 2006

[8] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFC-gas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003

[9] M Sucipta S Kimijima and K Suzuki ldquoPerformance analysisof the SOFC-MGT hybrid system with gasified biomass fuelrdquoJournal of Power Sources vol 174 no 1 pp 124ndash135 2007

[10] K Nikooyeh A A Jeje and J M Hill ldquo3D modeling of anode-supported planar SOFC with internal reforming of methanerdquoJournal of Power Sources vol 171 no 2 pp 601ndash609 2007

[11] F P Nagel T J Schildhauer S M A Biollaz and S StuckildquoCharge mass and heat transfer interactions in solid oxide fuelcells operated with different fuel gasesmdasha sensitivity analysisrdquoJournal of Power Sources vol 184 no 1 pp 129ndash142 2008

[12] httpwwwfuelconcom[13] D L King J J Strohm X Wang et al ldquoEffect of nickel

microstructure onmethane steam-reforming activity ofNi-YSZcermet anode catalystrdquo Journal of Catalysis vol 258 no 2 pp356ndash365 2008

[14] M Boder and R Dittmeyer ldquoCatalytic modification of con-ventional SOFC anodes with a view to reducing their activityfor direct internal reforming of natural gasrdquo Journal of PowerSources vol 155 no 1 pp 13ndash22 2006

[15] E Achenbach and E Riensche ldquoMethanesteam reformingkinetics for solid oxide fuel cellsrdquo Journal of Power Sources vol52 no 2 pp 283ndash288 1994

[16] S Fogler Elements of Chemical Reaction Engineering PrenticeHall New York NY USA 1999

[17] I Chorkendorff and J Niemantsverdriet Concepts of ModernCatalysis and Kinetics Wiley-VCH Weinheim Germany

[18] R Bird W Stewart and E Lightfoot Transport PhenomenaJohn Wiley amp Sons New York NY USA 2nd edition 2002

[19] R Reid J Prausnitz and B PolingThe Properties of Gases andLiquids McGraw-Hill New York NY USA 5th edition 2001

[20] A L Lee R F Zabransky andW J Huber ldquoInternal reformingdevelopment for solid oxide fuel cellsrdquo Industrials and Engineer-ing Chemistry Research vol 29 no 5 pp 766ndash773 1990

[21] R Odegard E Johnsen and H Karoliussen ldquoMethane reform-ing on Nizirconia SOFC anodesrdquo in Proceedings of the 4thInternational Symposium on Solid Oxide Fuel Cells (SOFC rsquo95)pp 810ndash819 1995

[22] K Ahmed and K Foger ldquoKinetics of internal steam reformingof methane on NiYSZ-based anodes for solid oxide fuel cellsrdquoCatalysis Today vol 63 no 2ndash4 pp 479ndash487 2000

[23] S Bebelis A Zeritis C Tiropani and S G NeophytidesldquoIntrinsic kinetics of internal steam reforming of CH4 over aNi-YSZ-cermet catalyst-electroderdquo Industrial and EngineeringChemistry Research vol 39 no 12 pp 4920ndash4927 2000

[24] H Yakabe T Ogiwara M Hishinuma and I Yasuda ldquo3-Dmodel calculation for planar SOFCrdquo Journal of Power Sourcesvol 102 no 1-2 pp 144ndash154 2001

[25] R Leinfelder Reaktionskinetische Untersuchung zur Methan-Dampf-Reformierung und Shift-Reaktion an Anoden oxid-keramischer Brennstoffzellen [PhD thesis] Der TechnischenFakultat der Universitat Erlangen-Nurnberg 2004

[26] P Hendriksen S Koch M Mogensen Y L Liu and P HLarsen ldquoBreak down of losses in thin electrolyte SOFCsrdquo inPro-ceedings of the 8th International Symposium on Solid Oxide FuelCells (SOFC rsquo20) Paris France April-May 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chromatography Research International

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Analytical ChemistryInternational Journal of

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