an investigation of direct hydrocarbon (propane) fuel cell...

Research ArticleAn Investigation of Direct Hydrocarbon (Propane) Fuel CellPerformance Using Mathematical Modeling

Bhavana Parackal123 Hamidreza Khakdaman 4

Yves Bourgault5 and Marten Ternan 126

1Department of Chemical and Biological Engineering University of Ottawa 161 Louis-Pasteur Ottawa ON Canada K1N 6N52Center for Catalysis Research and Innovation University of Ottawa 30 Marie-Curie Street Ottawa ON Canada K1N 6N53Clara Pontoppidans Vej 16 1 tv 2500 Copenhagen Denmark4ExxonMobil Corporation Process Fundamentals Global Chemical Research BTEC-W-3144 5200 Bayway Drive TX 77520 USA5Department of Mathematics and Statistics University of Ottawa 585 King Edward Avenue Ottawa ON Canada K1N 6N56EnPross Incorporated 147 Banning Road Ottawa ON Canada K2L 1C5

Correspondence should be addressed to Marten Ternan ternanbellnet

Received 1 June 2018 Revised 26 August 2018 Accepted 5 September 2018 Published 2 December 2018

Academic Editor Sheng S Zhang

Copyright copy 2018 Bhavana Parackal et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

An improved mathematical model was used to extend polarization curves for direct propane fuel cells (DPFCs) to larger currentdensities than could be obtained with any of the previous models DPFC performance was then evaluated using eleven differentvariables The variables related to transport phenomena had little effect on DPFC polarization curves The variables that hadthe greatest influence on DPFC polarization curves were all related to reaction rate phenomena Reaction rate phenomena weredominant over the entireDPFCpolarization curve up to 100mAcm2 which is a value that approaches the limiting current densitiesof DPFCs Previously it was known that DPFCs are much different than hydrogen proton exchangemembrane fuel cells (PEMFCs)This is the first work to show the reason for that difference Reaction rate phenomena are dominant in DPFCs up to the limitingcurrent density In contrast the dominant phenomenon in hydrogen PEMFCs changes from reaction rate phenomena to protonmigration through the electrolyte and to gas diffusion at the cathode as the current density increases up to the limiting currentdensity

1 Introduction

The characteristics of direct hydrocarbon fuel cells (DHFCs)are different than those of hydrogen fuel cells (H2FCs)H2FCs have current densities (reaction rates) that arenormally two orders of magnitude greater than DHFCsConsequently much more research has been performed onH2FCs than on DHFCs That research has produced manyimprovements since the initial H2FC experiment performedbyGrove [1] in 1839There are now commercially viableH2FCproducts available such as materials handling equipment(fork lifts) and fuel cell systems that generate stand-byelectrical power Furthermore fuel cell powered automobilescan now be purchased in several countries Perry and Fuller[2] and Eisler [3] have documented some of the history ofH2FC development

In spite of the success enjoyed by H2FCs there areseveral factors that favor DHFCs over H2FCs (a) Existinginfrastructure makes hydrocarbon fuels (natural gas lique-fied petroleum gas [LPG] or propane gasoline diesel fuel)available almost everywhere In contrast infrastructure tosupply hydrogen fuel does not exist inmost placesThe cost ofmanufacturing hydrogen varies with the energy source usedto make it The lowest cost hydrogen is obtained from hydro-carbons (eg natural gas) using complex processes involvingthe steam reforming reaction high and low temperaturewater gas shift reactions and hydrogen purification Moreexpensive hydrogen can be produced from renewable energy(solar or wind technologies) followed by water electrolysis(b) Many hydrocarbons can be stored as liquids The hydro-gen storage options are a high pressure gas a cryogenic liquid

HindawiInternational Journal of ElectrochemistryVolume 2018 Article ID 5919874 18 pageshttpsdoiorg10115520185919874

2 International Journal of Electrochemistry

( ndash 252∘C) or a metal hydride All of the hydrogen storageoptions are more expensive than liquid storage (c) Theenergy density of hydrocarbons is much greater than that ofhydrogen (d)The electrochemical reactions of hydrocarbonshave fractional theoretical energy efficiencies of 092ndash096[4] In contrast that for hydrogen is 063 (a combination of083 [4] for the electrochemical energy efficiency and 075 forthe energy efficiency of the endothermic hydrocarbon steamreforming reaction) Every carbon atom used in a DHFCor in a combination of a process to make hydrogen fromhydrocarbons and a H2FC will produce one carbon dioxidemolecule The above difference in their theoretical energyefficiencies indicates that the amounts of carbon dioxideemitted to the atmosphere per unit of energy generated couldbe smaller for DHFCs than for H2FCs

Grove performed the first DHFC experiment [5] in 1845Early research on DHFCs by Becquerel Jablochkof JacquesBorchers Liebenow and Stresser Haber and Hofmann hasbeen documented by Ketelaar [6] who concluded that ldquofuelcell development had reached a relatively low level duringthe first 100 years of researchrdquo In the 1960s a concentratedresearch effort on DHFCs was funded in the USA Resultsfrom that program have been reported in three reviews [47 8] Sporadic DHFC research has been performed sincethat time In our laboratory a phosphoric acid fuel cell wasused for experiments that included a commercial low-sulphurdiesel fuel at 200∘C [9] Although the current densities wereextremely small the results were encouraging in that steady-state operation was demonstrated for 15 hours with each offour different diesel fuels

Recently there have been several more encouragingDHFC studies using high temperature direct hydrocarbonsolid oxide electrolyte fuel cells (SOFCs) In those studies aninternal reforming catalyst layer had been added to the anodecatalyst layer Its purpose was to convert the hydrocarbon tohydrogen before it reached the adjacent anode catalyst layerLee and coworkers [10] added aNi-Fe reforming catalyst layerto an anode layer consisting of NiOndashYSZ (yttria stabilizedzirconia) in experiments with methane at 750∘C Later [10]they reported a 1000 h continuous fuel cell operation usinga ceria coated Ni reforming catalyst in experiments withmethane at 610∘C Liu and coworkers [11] added a reformingcatalyst layer containing Ni YSZ and BaZr(1minus119883) Y119883O(3minus120575)in experiments with iso-octane at 750∘C Zhang et al [12]showed that direct propane solid oxide fuel cells havingelectrodes composed of a blend of silver and gadoliniumdoped ceria maintained a stable performance for 160 h time-on-stream However experiments with a nickel-gadoliniumdoped ceria experienced serious deactivation after 40 h oftime-on-stream In all of the above reports on SOFCs thecurrent densities were slightly smaller but of the same orderof magnitude as those in H2FCs

Propanewas the fuel chosen for this work for two reasonsPropane is used to provide space heating in rural areasTherefore the infrastructure for direct propane fuel cells(DPFCs) in rural areas is already in place Second the cost foran electrical utility to deliver electrical power in rural areas ismuch greater than in urban areas even though the price of

electrical power in rural and urban areas is similar Thereforeelectrical power from a fuel cell system in a rural locationmaybe cost competitive with rural electrical power costs even if itis too expensive for urban areas

Results with low temperature proton exchange mem-brane fuel cells (PEMFCs) operating on propane have beenless encouraging Some of the most promising results withpropane from the 1960s were obtained with a phosphoricacid electrolyte Grubb and Michalske [13] and with ahydrofluoric acid electrolyte Cairns [14] However in recentyears only a limited amount of work has been reported onDPFCs Examples are the propane work using Nafion andpolybenzimidazole electrolyte membranes by Savadogo andVarela [15] and using a polybenzimidazole membrane byCheng et al [16]

Our long-term objective is to seek DPFC characteristics(processing conditions materials and equipment config-urations) for which the performance of low temperatureDPFCswould become competitivewithH2FCs Two steps arenecessary to achieve this objective (a) identifying the limitingphenomena that are responsible for small current densitiesin DPFCs and (b) identifying the DPFC characteristics thatwould remove those limitations

To contribute to the first step in this work we haveused mathematical modeling to examine the effect of severalvariables that influence DPFC performance Experimentsare always more definitive than models However thereare some variables that are extremely difficult to measureexperimentally An example would be the pressure gradientacross the electrolyte layer In contrast they can sometimes becomputed precisely using models By studying large changesin each of the variables it should be possible to identify thosevariables having the greatest potential to improve fuel cellperformance

Mathematical models of fuel cells have been used todescribe a wide range of physical chemical electrochemicaland mass transfer phenomena There were several earlymodels Verbrugge and Hill [17] used dilute solution theoryto describe the migration of protons in a fuel cell having aperfluorosulfonate ionomer membrane Springer et al [18]developed one of the first models for a hydrogen fuel cellIt predicted a ratio of water flux to proton flux in a Nafion117 membrane that was consistent with the experimentalvalue Bernardi and Verbrugge [19] modeled the transportmechanisms of several species within a PEMFC and foundthat the diffusion of dissolved gases to the catalyst limited fuelcell performance Since then models of various complexitieshave been developed from simple (analytical models) Kim etal [20] to more complex (mechanistic models) Amphlett etal [21] and numerical models Weber and Newman [22] Anextremely large body of literature describing fuel cell modelsnow exists Some recent reviews are those by Jarauta andRyzhakov [23] Salomov et al [24] and Zhang and Jiao [25]

The first mathematical model of a direct propane fuelcell (DPFC) was developed by Psofogiannakis et al 2006[26] It was a one-dimensional computational fluid dynamics(CFD) model It used a phosphoric acid electrolyte andPt anode catalyst Overpotential was found to control fuelcell performance Subsequently Khakdaman et al [27 28]

International Journal of Electrochemistry 3

developed a two-dimensional mathematical model based ona proton exchange membrane and a Pt anode catalyst Itcorrectly described the transport of charged species Theelectrons (negatively charged) migrated from the anode tothe cathode in response to an electrical potential differenceThe protons (positively charged) diffused from the anode tothe cathode in response to a proton concentration differenceRecently Danilov et al [29] described a tank-in-series reactormodel to describe a direct propane fuel cell

In this work a two-dimensional direct propane fuel cellmodel is described which is an improvement over themodels of Khakdaman et al [28] Aprogressive time-steppingmethodwas used to improve convergence so that polarizationcurves could be predicted over a greater range of currentdensities The model was used to investigate an array ofvariablesThe variables were placed in two groups One groupof variables affected mass transport processes The othergroup of variables was related to phenomena that occur onthe electrochemical catalyst surfaces and therefore affectedthe reaction rate

An overview of this work can be summarized in twostatements The main aim of the work described here was toidentify the limiting phenomena that might be responsiblefor the small current densities observed in DPFCs Thenovelty of the results reported is that all of the computationswere consistent with a single phenomenon limiting theperformance of DPFCs

2 Model Description

The model is based on the following desirable reactionsoccurring in the fuel cell The reaction between propane andwater at the anode

C3H8 + 6H2O = 3CO2 + 20H+ + 20endash 120601A = 0136 V (1)

and the reaction between oxygen in air with protons andelectrons at the cathode

5O2 + 20H+ + 20endash = 10H2O 120601C = 1229 V (2)

can be combined to produce the following overall fuel cellreaction

C3H8 + 5O2 = 3CO2 + 4H2O 120601CELL = 1093 (3)

The electrode potentials at 25∘C for the anode 120601A andcathode 120601C together with the fuel cell potential difference120601CELL [30] are also shown above with their respectivestoichiometric reactions

An undesirable reaction carbon formation is thermody-namically possible via an overall fuel cell reaction in which Crather than CO2 is the product of the reactants in (3) (120601CELL= 0071 V [30]) However carbon formation has not beengenerally reported in the fuel cell literature for propane [13ndash18] Specifically Grubb andMichalske reported 993 carbondioxide formation in 44 experiments using a phosphoric acidaqueous electrolyte [13] Cairns reported 100 carbon diox-ide using a hydrofluoride aqueous electrolyte [14] Savadogoand Rodriguez [15] reported 100 CO2 using Nafion and

polybenzimidazole polymer electrolytes Cheng et al [16]reported that CO and CO2 were the only products formedusing a polybenzimidazole polymer electrolyte Neverthelesscarbon formation has been reported in fuel cell experimentswith longer chain hydrocarbon molecules n-octane [7] anddiesel fuel [9] In contrast carbon formation has neverbeen reported in any low temperature direct hydrocarbonfuel cell when methane was the fuel These experimentalresults suggest that the hydrocarbon chain length of the fuelmolecule determines whether or not carbon is formed ina direct hydrocarbon fuel cell Since carbon formation wasnot reported in the fuel cell experiments with propane itsformation was not included in this model

Themodeling domain of the DPFC consisted of an anodecatalyst layer (ACL) an electrolyte (membrane) layer (ML)and a cathode catalyst layer (CCL) Zirconium phosphate(Zr(HPO4)2∙H2O or ZrP) was the proton conducting mate-rial or the electrolyte used in the model The membranelayer consisted of solid ZrP that filled the pores of porouspolytetrafluoroethylene (PTFE) [31] The catalyst layer wascomposed of carbon supported platinum (Pt) catalyst andZrP electrolyte Interdigitated flow fields (IDFF) were usedboth for the anode and cathode One of the flow channels inthe flow field was used for the reactants and the other for theproducts The catalyst layer was composed of three phasesie the gas phase the solid electrolyte phase and the solidcatalyst phase

Khakdamanrsquos mathematical description [28] of a fuel cellformed the starting point for the model used here Fourconservation equations were used in the model the conser-vation of momentum total mass total charge and individualcomponent species including a reaction term The governingequations of the model included (a) the conservation of massin the gas phase (b) the Ergun equation (c) the Butler-Volmerequation (used to calculate the reaction rate at the anode andcathode) and (d) conservation equations for water and forprotons in the electrolyte phase and in the two catalyst layers

The governing equations are shown below(a) Conservation of mass in the gas phase

nabla ∙ (120576G 120588G u) + nsumi

]i119872119882119894119895119911119865 = 0 (4)

Mass conservation in the gas phase is described by (4)Electrochemical reactions in the gas phase can be either asource or sink They are described by the second term in theequation

(b) Conservation of momentum in the gas phase

ndashnabla119875 = 150[120583119866 (1 minus 120576G)211986321198661205762119866 ] u (5)

The Ergun equation in linear form is shown in (5) Since thecatalyst layers are packed beds the Ergun equation can beused to calculate the pressure profiles in the gas phase Themagnitude of the quadratic term in the Ergun equation ismuch smaller than that of the linear term at the conditionsused in this studyThe velocity and pressure profiles in the gas


phase of the catalyst layers were obtained by simultaneouslysolving (4) and (5)

(c) Conservation of noncharged species in the gas phase

nabla ∙ (120576119866 119888119866 u yi) minus nabla ∙ (120576119866 119888119866 119863119894 nabla yi) + ]119894119895119911119865 = 0 (6)

i = C3H8 and CO2 for the anode and O2 and H2O for thecathode

Equation (6) was used to obtain mass balances foreach of the individual gas phase species Separate terms forconvection diffusion and reaction are included in (6)

(d) Conservation of species in the electrolyte phases of themembrane and catalyst layers

(d1) For water

ndashnabla ∙ (119888119864119871119884 (11986110158401198672119874ndash1198672119874 ndash11986110158401198672119874ndash119867+) nabla119909119867+) + nabla∙ (11988811986411987111988411986110158401198672119874ndash119867+119865 119909119867+119877119879 nabla120601119864119871119884) minus 119895119911119865 = 0

(7)

(d2) For protons

nabla ∙ (119888119864119871119884 (1198611015840119867+ ndash119867+ndash1198611015840119867+ndash1198672119874)nabla119909119867+) + nabla∙ (1198881198641198711198841198611015840119867+ndash119867+119865119909119867+119877119879 nabla120601119864119871119884) + 119895119911119865 = 0

(8)

Mass balances for water and protons in the electrolytephases of the catalyst and membrane layers were obtainedusing (7) and (8) Concentrated solution theory through thegeneralized Maxwell Stefan equations was used to describediffusion The 1198611015840 terms are composition-dependent param-eters obtained using the methodology given by Khakdamanet al [31] that include the diffusivities for the various mobilespecies

(e) Butler-Volmer equation at the anode

119895119860 = 1198950119860119860119875119905 (exp (120572119860119865120578119860119877119879 ) ndash exp (ndash120572119860119865120578119860119877119879 )) (9)

where 1198950119860 = (1198951198623 119874119909)0119903119890119891( 1199011198623(1199011198623)119903119890119891)

sdot exp((1198661198623119874119909)plusmn119877 ( 1119879119903119890119891 minus 1119879))(10)

The rate of production of protons at the anode jA is describedby the Butler-Volmer equation in (9) and has a positivevalue The exchange current density used in (9) is givenin (10) It is a function of both the operating temperatureand the partial pressure of the propane reactant The anodereference exchange current density (jC3-Ox)0-ref term includesthe reaction rate constant for the anode reaction

(f) Butler-Volmer equation at the cathode


where 1198950119862 = (1198951198742 119877119889)0119903119890119891 ( 1199011198742(1199011198742)119903119890119891)


The rate of consumption of protons at the cathode isdescribed by the Butler-Volmer equation in (11) and has anegative value The exchange current density used in (11) isgiven in (12) It is a function of the operating temperatureand the partial pressure of the oxygen The cathode referenceexchange current density (j1198742minus119877119889)

0minus119903119890119891 term includes thereaction rate constant for the cathode reaction

(g) The overpotentials at the anode 120578A and cathode 120578Care given by (13) and (14) respectively

120578119860 =120601119860 minus 120601119864119876119860= (120601119875119905-119860 minus 120601119864119871119884-119860) minus ([120601119875119905-119860]119864119876 minus [120601119864119871119884]119864119876) (13)


In the work described here Khakdamanrsquos model [28]was improved by adding a progressive time-stepping methodwithin the iteration loop that contained all the governingequations Themodified iteration loop is shown on the right-hand side of the modeling flow chart shown in Figure 1 Thisprogressive time-stepping method speeds up the computa-tion of the polarization curve by doing a fixed number Nof time-steps (N=19 for ΦAg - ΦNi ge 0793 and N=39 forΦAg - ΦNi lt 0793) After the N time-steps ΦAg - ΦNi isdecremented by a small value to proceed further along thepolarization curve instead of completing the time loop beforechanging ΦAg - ΦNi Φ is the equilibrium potential of thecathode Ag and anode Ni electrodes respectively The pro-gressive time-stepping method included a local overpotentialcut-off value at the anode and cathode of 0432 V Any gridpoint having an overpotential larger than 0432 V was forcedto take the value 0432 V This occurred at very few points inthe anode and cathode The value of 0432 V was set by trialand error to limit the impact of this cut-off

Figure 2 shows the fuel cell performance predicted bythe DPFC model with and without the progressive time-stepping method in the iteration loop The figure representsthe polarization curve for a DPFC at 150∘C and 1 atm It isa plot of cell potential difference ΔΦcell (V) versus currentdensity (mAcm2) The progressive time-stepping methodimproved convergence and thereby is seen to extend thepolarization curve to larger current densities Specificallyconvergence occurred up to a current density of 106mAcm2for the model with the progressive time-stepping method incomparison to 51 mAcm2 for the nonprogressive method


Define problem discretize equations

Define geometry generate mesh

Balance proton productionconsumption

Momentummass atanodecathode

Proton and water at anode

Proton and water atcathode

Proton and water atmembrane (electrolyte)

Iteration

Iteration

Iteration

Iteration with progressivetime-stepping loop

Output result for post-processing

Updatingtransfer

conditionsproperties anodecathode

Gaseous species at

Figure 1 The computational procedure with the time-stepping progressive iteration loop [2]

The DPFC polarization curve shown in Figure 2 resultingfrom the progressive time-stepping method was used as thereference case The reference case polarization curve wascompared to the other polarization curves that were obtainedat the variety of conditions investigated in this study Themaximum current density at which convergence occurredwas different for each variable investigated Values for thevarious variables used in the DPFC model are shown inTable 1 Design and operational variables other than thosein Table 1 were the same as the ones reported by Khakdamanet al [28]

Several assumptions were made during the developmentof the model As explained already one of the assumptionswas that no solid carbon was formed from the propane feed-stock and that all of the carbon atoms in the feedstock left thefuel cell in the form of carbon dioxide Also it was assumedthat no degradation in fuel cell performance occurred by anyother phenomena (eg CO poisoning of Pt anode catalyst)Several properties diffusivities proton conductivity in the

electrolyte electrical resistivity in the membrane and chargetransfer coefficients were assumed to have the values shownin Table 1 It was assumed that concentrated solution theorycould be used to describe the behavior of species in theelectrolyte It was assumed that the mole fraction in theelectrolyte could be calculated by assuming that each protonwas associated with one water molecule rather than multiplewater molecules It was assumed that there was no cross-over of propane from the anode catalyst layer to the cathodecatalyst layer

3 Results and Discussion

Polarization curves are plots of potential difference betweenthe anode and cathode ΔΦcell (V) versus current density(mAcm2) The operating conditions were 150∘C and 1 atmFor hydrogen PEMFCs polarization curves can be dividedinto different regions In each region a different mechanism


MODEL WITHOUT PROGRESSIVE TIME-STEPPING LOOP

REFERENCE CASE MODEL WITH PROGRESSIVE TIME-STEPPING LOOP

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CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)

10 20 30 40 50 60 70 80 90 100 110 1200CURRENT DENSITY (mAcm2)

Figure 2 The effect of progressive and nonprogressive time-stepping loops on the polarization curve for a direct propane fuel cell model(DPFC) at 150∘C and 1 atm The above two cases were represented by the following symbols (i) open circles model without a progressivetime-stepping loop and (ii) solid diamonds model with a progressive time-stepping loop

controls the performance of the fuel cell At small currentdensities the reaction rate is controlled by the electrodeoverpotential 120578 At intermediate current densities Ohmiclosses (proton transport across the electrolyte) control thereaction rate Finally at high current densities mass transferlimitations (eg oxygen transport through liquid water at thecathode of a PEM fuel cell) may control the reaction rateWhen the value of a variable was changed in this study itseffect on the polarization curvewas used to indicate its impacton the performance of the fuel cell In the investigationreported here all the variableswere held constant (at the samevalues as in the reference case) except for the variable beingstudied

The first variable investigated was the anode referenceexchange current density (jC3-Ox)0-refThe reference exchangecurrent density represents the electrocatalytic propertiesof the catalyst used in the membrane electrode assembly

(MEA) of the fuel cell It includes the rate constant for theelectrocatalytic reaction Changes in the reference exchangecurrent density reflect changes in the rate constant The effectof the anode reference exchange current density on the overallperformance of a direct propane fuel cell (DPFC) is shownin Figure 3 A current density of 40 mAcm2 was chosento compare the results obtained in Figure 3 As the anodereference exchange current density (jC3-Ox)0-ref increased byfour orders of magnitude (ie from 007 to 7 to 700mAm2)the potential difference between the fuel cell electrodes alsoincreased (ie from 038 to 072 to 104 V respectively)These data indicate that the anode reference exchange currentdensity (and therefore the anode catalyst composition) has alarge impact on fuel cell performance

The Butler-Volmer equation for the anode is shown in (9)The anode exchange current density j0A like the anode refer-ence exchange current density is related to the rate constant


Table 1 Operational electrochemical and design parameters of the reference case of the DPFC model (see [28])

Parameter ValueTemperature T 423 KPressure P 1 atmPropane inlet molar flow rate mP 8x10minus6 gmol sminus1

Propane inlet mole fraction yPinput 01Reference exchange current density at the anode j0AN-ref 7x10minus5 Amminus2Pt-catalystReference exchange current density at the cathode j0CA-ref 3x10minus8 A mminus2Pt-catalystProton diffusivity coefficient in the electrolyte (ZrP) phase DH+-ZrP 3x10minus9 m2 sminus1

Water diffusivity coefficient in the electrolyte (ZrP) phase DH2O-ZrP 2x10minus8 m2 sminus1

Proton-water diffusivity coefficient DH2O-H+ 132x10minus8 m2 sminus1

Proton conductivity in the electrolyte (membrane) layer 120590ELY 5 S mminus1

Specific surface area of anode and cathode carbon catalyst support ACAT 200 m2catalyst gndash1catalystLand width Lw 44 mmAnode and cathode thickness ThA ThC 300 120583mMembrane thickness ThM 100 120583mFluid channels width in bi-polar plates 02 mmElectrical resistivity in membrane RPTFE 1x1016ΩmCharge transfer coefficients 120572A and 120572C 1

0 10 20 30 40 50 60 70 80 90 100 110 120

(jC3-Ox)0-ref=7x10-1 Am2

Ref (jC3-Ox)0-ref=7x10-5 Am2

CURRENT DENSITY (mAcm2)

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CELL

PO

TEN

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IFFE

REN

CE Δ

C

ell

(V)




Figure 3 The effect of the anode reference exchange current density (jC3-Ox)0-ref (Am2) on the polarization curve for a direct propane fuelcell model (DPFC) at 150∘C and 1 atmThe values of (jC3-Ox)0-ref (Am2) for the above five cases were represented by the following symbols (i)open circles 7x10minus1 Am2 (ii) solid squares 7x10minus3 Am2 (iii) solid diamonds 7x10minus5 Am2 (reference case) (iv) solid circles 7x10minus8 Am2and (v) open triangles 7x10minus10 Am2 All the other parameters were the same as the reference case mentioned in Table 1


(k) for the electrochemical reaction Therefore changing thecatalyst composition can change the rate constant and therebychange both the reaction rate and the current density

For hydrogen-oxygen fuel cells with acidic membranesand platinum electrodes the anode exchange current densitycan be five to seven orders of magnitude greater than thecathode exchange current density [32] Nevertheless anodecomposition does have an effect For example with hydrogenfuel cells changing the composition of the anode from Ptto Ir can cause a change in the anode exchange currentdensity of almost two orders of magnitude [33] Thereforeanode composition (and therefore anode exchange currentdensity) does cause a difference in performance as indicatedin Figure 3

Direct hydrocarbon fuel cells are different than hydro-gen fuel cells For example with platinum electrodes theanode exchange current density for ethylene and the cathodeexchange current density for oxygen are virtually the same[33] Similarly our previous work with propane-air fuel cells[27] indicated that the exchange current density at the anodewas somewhat less than that at the cathode These examplesindicate that the difference between the anode and cathodeexchange current densities is much larger in hydrogen fuelcells than in direct hydrocarbon fuel cells

The review by Davydoda et al [34] shows that thebeginning of life performance with anion exchange mem-branes approaches that of proton exchange membranes Itis now known that the performance of platinum anodecatalystswith anion exchangemembranes ismuchworse thanwith proton exchange membranes Experiments in anionexchange membrane fuel cells with several non-platinumanode catalysts indicated that the results varied with anodecatalyst composition A Ni-Mo anode catalyst was one of thebest non-platinum catalysts [34] It is apparent that the familyof fuel cells having anion exchange membranes is similarto direct hydrocarbon fuel cells in that the anode catalystcomposition has a large effect on fuel cell performance in bothof them

There are some indications that it may be possible toimprove the performance of the anode catalysts and thereforeimprove the performance of the anode exchange currentdensity in direct hydrocarbon fuel cells We have performeddensity functional theory computations for anode electrodeshaving different compositions [32 35] The base calculationwas made with an anode electrode composition of purenickel which is used in the anodes of alkaline fuel cells Sub-sequently calculations were performed with copper-nickelalloys The activation energy of some alloy catalyst was foundto be one-third of the value of a pure nickel electrode [35]

The effect of the cathode reference exchange current den-sity j(O2-Rd)0-ref on the performance of the DPFC is shown inFigure 4 At a current density of 40 mAcm2 as the cathodereference exchange current density j(O2-Rd)0-ref increasedby two orders of magnitude (ie from 3 to 300 nAm2)the potential difference between the fuel cell electrodes alsoincreased (ie from 038 to 054 V respectively) Fromthese observations it was clear that the cathode referenceexchange current density (and therefore the cathode catalyst

composition) also had a large effect on fuel cell performancebut not as much as the anode reference exchange currentdensity

Like the anode composition mentioned above changingthe cathode composition can affect the cathode exchangecurrent density Numerous studies have been performed inwhich the cathode catalyst composition has been changedin order to improve the oxygen reduction reaction at thecathodeWang et al [36] incorporated polyhedron nanocrys-tals into the cathode catalyst layer and reported improvedperformance Liang et al reported superior performancewith intermetallic metal-platinum (metal = Fe Co Cu Ni)nanocrystals [37] as the cathode catalyst Chandran et al [38]used Pd alloys Liu et al [39] reported that a Pt-Co alloy wassuperior to pure Pt Pt-Ni and Pt-Fe alloys Kiani et al[40]reviewed a variety of non-platinum cathode catalysts Thereview by Higgins and Chen [41] indicated that the mostpromising catalyst materials are prepared by the pyrolysisof transition metalndashnitrogenndashcarbon complexes In each ofthese cases a change in the cathode catalyst composition(which affects cathode exchange current density) caused achange in performance

The catalyst layer thickness in both the anode (ThA)and cathode (ThC) are other variables that could also affectthe fuel cell performance because they affect the volumeof the catalyst per unit face area available for the reactionBoth layers had the same thickness (ThA = ThC) in thepolarization curves shown in Figure 5 At a current density of40 mAcm2 as the thickness of the catalyst layers (ThA andThC) was increased by a factor of two (ie from 02 to 04mm) the potential difference between the fuel cell electrodesalso increased (ie from 0335 to 041 V corresponding to23) From these observations it was evident that catalystlayer thickness did have an impact on the overall performanceof the DPFC It should be noted that the catalyst layerthickness only increased by a factor of two and not by theorders of magnitude increases made for the exchange currentdensities

Darab et al [42] performed hydrogen fuel cell experi-ments in which the thickness of the cathode catalyst wasvaried In their work they kept the total Pt loading constantThey found that the initial electrochemical performancewas independent of catalyst layer thickness The results inFigure 5 were obtained with the Pt catalyst content increasingwith increasing thickness of the catalyst layer The resultsof constant performance with constant total Pt that wereobtained by Darab et al would appear to be consistent withthe results in Figure 5 where the performance improved asthe total Pt content increased (total Pt content increased withincreasing catalyst layer thickness)

The variable investigated in Figure 6 was the membranelayer thickness (ThM) of the fuel cell Its effect can beseen when the Ohmic loss is rate controlling normally themiddle part of a hydrogen polarization curve At a currentdensity of 40 mAcm2 as the thickness of the electrolyte(membrane) layer was increased by a factor of five from100 to 532 120583m the potential difference between the fuelcell electrodes decreased from 038 to 035 V Furthermore


(jO2-Rd)0-ref =3x10-7 Am2

Ref (jO2-Rd )0-ref =3x10-9 Am2

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L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2

Figure 4The effect of the cathode reference exchange current density j(O2-Rd)0-ref (Am2) on the polarization curve for a direct propane fuelcell (DPFC)model at 150∘C and 1 atmThe values of j(O2-Rd)0-ref (Am2) for the above three caseswere representedby the following symbols (i)open circles 3x10minus7 Am2 (ii) solid diamonds 3x10minus9 Am2 (reference case) and (iii) open triangles 3x10minus12 Am2 All the other parameterswere the same as the reference case mentioned in Table 1

when the membrane layer thickness (ThM) was increasedfrom 25 to 100 120583m there were no significant changes inpotential difference From these observations it was evidentthat the resistance caused by the membrane layer thicknessdid not have a significant effect on the fuel cell performancein comparison to other variables De Caluwe et al [43]measured the properties of Nafion membranes of varyingthicknessThey found that the relationship between the watercontent and the proton conductivity was nonlinear They didnot report any measurements of fuel cell performance

The proton conductivity (120590ELY) of the membrane (elec-trolyte) layer was also investigated The term proton conduc-tivity refers to themigration of protons caused by an electricalpotential gradient It is different than proton diffusivity thatwill be discussed next The effect of the membrane layerproton conductivity (120590ELY) on the fuel cell performance canbe seen in Figure 7 At a current density of 40 mAcm2 whenthe proton conductivity of the electrolyte (membrane) layer(120590ELY) was increased from 5 Sm to 1x1020 Sm there wasno significant change in fuel cell performance Therefore the

membrane layer proton conductivity was not rate limitingand had almost no effect on the performance of the DPFC

Zaidi [44] used hydrogen fuel cell performance to com-pare two membranes having different proton conductivitiesTheHyflonmembrane had a greater proton conductivity thanthe Nafion membrane It had superior fuel cell performanceat current densities greater than 500 Am2 However at smallcurrent densities such as the values in Figure 7 the fuelcell performance with the two different membranes wasessentially the same Thus Zadirsquos experimental results wereconsistent with the computational results shown in Figure 7indicating that proton conductivity had no effect at smallcurrent densities

Proton diffusivity in the electrolyte phase was also inves-tigated The term proton diffusivity refers to the diffusion ofprotons caused by a proton concentration gradientThe effectof proton diffusivity on the fuel cell performance is shownin Figure 8 When the proton diffusion coefficient (DH+-ZrP)increased by more than an order of magnitude (from 3x10minus10

to 7x10minus9 m2s) there was minimal change over the range


A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


Figure 5 The effect of the anode and cathode catalyst layer thickness ThA = ThC (120583m) on the polarization curve for a direct propane fuelcell (DPFC)model at 150∘C and 1 atmThe values of ThA = ThC (120583m) for the above three cases were represented by the following symbols (i)open circles 400 120583m (ii) solid diamonds 300 120583m (reference case) and (iii) open triangles 200 120583m All the other parameters were the sameas the reference case mentioned in Table 1

of variables investigated From these observations it wasconcluded that the proton diffusion coefficient did not affectfuel cell performance when compared to the other variables

Water diffusivity in the electrolyte phase was also inves-tigated Its effect on the fuel cell performance is shown inFigure 9 When the water diffusion coefficient (DH2O-ZrP)changed from 2x10minus10 to 2x10minus2m2s there was no noticeablechange at any position in the polarization curve Therefore itwas evident that changes to thewater diffusion coefficient hadvirtually no effect on the overall performance of the DPFC

The propane inlet mole fraction in the feed (yPinput)(which is related to the reactantsrsquo ratio of propane to water)to the fuel cell was also investigated Its influence on theoverall performance of the fuel cell is shown in Figure 10At a current density of 20 mAcm2 as the propane inletmole fraction increased (from 008 to 08) the potentialdifference between the fuel cell electrodes also increased (iefrom 045 to 065 V) Increasing the propane inlet molefraction increases the propane partial pressure and therebyincreases the propane adsorption rate That would be oneexplanation for its comparatively large impact on the fuel cellperformance

Thepropane inletmolar flow ratewas also investigated Itseffect on the overall performance of the fuel cell is shown in

Figure 11 At a current density of 40 mAcm2 as the propaneinlet molar flow rate (mP) increased by a factor of eight from2x10minus6 to 16x10minus6 gmols the potential difference betweenthe fuel cell electrodes also increased from 036 to 040 VTherefore the propane inlet molar flow rate had little impacton the propane partial pressure as shown in Figure 11 Thepropane inlet molar flow rate will only have an effect if itchanges the propane mole fraction It is known that changingthe propane inlet mole fraction shown in Figure 10 hada significant impact on the propane partial pressure Sincethe current densities with all the DPFC polarization curvesdiscussed in this report are small compared to those withhydrogen PEMFCs the conversion of propane will also besmall As a result the gas phase concentration of propanewill not change muchThat is consistent with the observationin Figure 11 that at an inlet propane mole fraction of 01variations in the inlet propane flow rate only caused smallchanges to the performance of the DPFC

The effect of the fuel cell operating temperature on itsoverall performance is shown in Figure 12 At a current den-sity of 40 mAcm2 as the fuel cell operating temperature (T)increased from 373 K (100∘C) to 523 K (250∘C) an increase inabsolute temperature of 29 the potential difference betweenthe fuel cell electrodes increased from 035 to 043 V It was


Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)

10 20 30 40 50 60 70 80 90 100 110 120 1300CURRENT DENSITY (mAcm2)

Figure 6The effect of the electrolyte (membrane) layer thickness ThM (120583m) on the polarization curve for a direct propane fuel cell (DPFC)model at 150∘C and 1 atmThe values of ThM (120583m) for the above three cases were represented by the following symbols (i) open triangles 25120583m (ii) solid diamonds 100 120583m (reference case) and (iii) open circles 531 120583m All the other parameters were the same as the reference casementioned in Table 1

evident that temperature caused an appreciable improvementin the fuel cell performanceThe potential difference betweenthe electrodes of a fuel cell normally increases when the fuelcell operating temperature increases

The report by Chandran et al [38] examined fuel cellperformance when the temperature increased from 40 to60∘C In addition Ferrell et al [45] demonstrated that fuelcell performance increased when the temperature increasedfrom 60 to 80∘C Both those results are consistent withthe increase in fuel cell performance that occurred withincreasing temperature shown in Figure 12 However Ferrellet al also performed experiments at 100∘C The fuel cellperformance at 100∘Cwas inferior to that at 80∘CThe dimin-ished performance was caused by the decrease in electrolytemembrane water content as the temperature approached theboiling point of water

The final variables investigated were the anode andcathode total operating pressures in a DPFC Their effecton the overall performance of the fuel cell is shown inFigure 13 At a current density of 40 mAcm2 as the fuelcell operating pressure (P) increased from 1 to 11 atm the

potential difference between the fuel cell electrodes increasedfrom 038 to 071 V From these observations it was clearthat the fuel cell total operating pressure increased thepropane partial pressure and therefore caused amajor role inenhancing the overall performance of the DPFC This resultis consistent with the work of Ferrell et al [45] who alsoreported that fuel cell performance improved with increasingpressure

The variables described above were divided into twogroups The ones related to mass transport were the mem-brane thickness (Figure 6) the proton conductivity (Fig-ure 7) the proton diffusivity in the electrolyte (Figure 8) thewater diffusivity in the electrolyte (Figure 9) and the propaneinlet molar flow rate (Figure 11) The previous discussionindicated that all of these mass transport variables had littleinfluence on the polarization curves

The variables related to reaction rate were the anodeexchange current density (Figure 3) the cathode exchangecurrent density (Figure 4) the electrode layer thickness(Figure 5) the propane inlet mole fraction (Figure 10) thetemperature (Figure 12) and the pressure (Figure 13) The


Ref ELY=5 SmELY =1x10-4 Sm

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm

Figure 7 The effect of the membrane layer proton conductivity 120590ELY (Sm) on the polarization curve for a direct propane fuel cell (DPFC)model at 150∘C and 1 atm The values of 120590ELY (Sm) for the above three cases were represented by the following symbols (i) open triangles1x1020 Sm (ii) solid diamonds 5 Sm (reference case) and (iii) open circles 1x10minus4 Sm All the other parameters were the same as thereference case mentioned in Table 1

previous discussion indicated that all of these reaction ratevariables had a significant influence on the polarizationcurves Therefore mass transport appears to have little effectwhile reaction rate appears to have a significant effect on thepolarization curves

These results indicate that direct propane fuel cells arequite different than hydrogen PEMFCs For hydrogen PEM-FCs transport processes such as proton transport across theelectrolyte and transport of oxygen through the liquid phasewater at the cathode are important phenomena For any typeof fuel cell (including a DPFC) for which reaction rate is thedominant process throughout the entire polarization curvethe ΔΦcell ordinate of the polarization curve should decreaseand approach the limiting current density j (abscissa of thepolarization curve) asymptotically That asymptotic approachhas been reported in all the experimental work on directpropane fuel cells that were reviewed in the introductionof this report In contrast it is common for experimentalpolarization curves for hydrogen PEMFCs to contain aldquokneerdquo at larger current densities where an almost horizontalslope changes to an almost vertical slope as the limiting

current density is approachedThe ldquokneerdquo is normally causedby a change in the oxygen transport mechanism through thecathode diffusion layer

Reaction rate phenomena are dominant up to approxi-mately 100 mAcm2 in both DPFCs and hydrogen PEMFCsThe difference is that DPFCs are near their limiting currentdensity at 100 mAcm2 In contrast hydrogen PEMFCs oftenhave limiting current densities in excess of 2000mAcm2 Forhydrogen PEMFCs phenomena other than the reaction rateare dominant in the region of current density between 100and 2000 mAcm2

The results of this investigation indicate that adjustingthe reaction rate variables appropriately should improveDPFC performance However there are some limitationsAn inlet propane mole fraction of 10 cannot be exceededSpecies transport could become limiting if the thickness ofcatalyst layers is increased too much A large increase intemperature would eliminate the advantage of rapid start-upthat comes with low temperature fuel cells Large pressuresare also undesirable In contrast anode catalyst compositionor anode exchange current density there are variables that


DH+-ZrP =3x10-10 m2s

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s

Ref DH+-ZrP =3x10-9 m2s

Figure 8The effect of the proton diffusivity coefficient in the electrolyte phase DH+-ZrP (m2s) on the polarization curve for a direct propane

fuel cell (DPFC) model at 150∘C and 1 atmThe values of DH+-ZrP (m2s) for the above three cases were represented by the following symbols

(i) open triangles 3x10minus10 m2s (ii) solid diamonds 3x10minus9 m2s (reference case) and (iii) open circles 7x10minus9 m2s All the other parameterswere the same as the reference case mentioned in Table 1

could have a greater impact without negative side effectsAs noted earlier in this report the performance of SOFCsfed with methane improved substantially when the methanewas converted to hydrogen in a catalyst layer that precededthe layer where the electrochemical reaction of hydrogenmolecules to protons occurred In DPFCs there are severalchemical reactions that precede the electrochemical reac-tion [9] They include water dissociation dehydrogenationcarbonndashcarbon bond cleavage and hydroxylation In prin-ciple catalysts for those reactions could be added near thecatalyst layer used for the hydrogen to proton electrochemicalreaction

4 Conclusions

Mass transport appeared to have little effect while reactionrate appeared to have a significant effect on DPFC polariza-tion curves In at least one way DPFCs were found to bedifferent than hydrogen PEMFCs For DPFCs the surfacereaction rate is the dominant process for the entire polariza-tion curve In contrast for hydrogen PEMFCs the dominantphenomenon changes from reaction rate to migration of

protons through the electrolyte to oxygen transport throughthe cathode diffusion layer as the current density increasesHowever hydrogen PEMFCs are able to operate at muchlarger current densities than direct hydrocarbon PEMFCs Atthe same small absolute values of current densities surfacereaction rate phenomena are dominant in both types offuel cells Finally there is some indication in the literaturethat alternate catalyst compositions that have more favorableexchange current densities in direct hydrocarbon fuel cellsmay be found

Nomenclature

APt Platinum surface area per catalyst volume(m2Pt m

ndash3catalyst)

B1015840 Composition-dependent transportparameter described by Khakdaman et al[31]

c Molar concentration of mixture (kmolmndash3)

ci Molar concentration of species 119894 (kmolmndash3)


DH2O-ZrP =2x10-10 m2s

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref D H2O-ZrP =2x10-8 m2s

Figure 9The effect of the water diffusivity coefficient in the electrolyte phase DH2O-ZrP (m2s) on the polarization curve for a direct propanefuel cell (DPFC)model at 150∘C and 1 atmThe values of DH2O-ZrP (m

2s) for the above three cases were represented by the following symbols(i) open triangles 2x10minus10 m2s (ii) solid diamonds 2x10minus8 m2s (reference case) and (iii) open circles 2x10minus2 m2s All the other parameterswere the same as the reference case mentioned in Table 1

Di Diffusion coefficient of species 119894 in the gasmixture (m2 sndash1)

Di Diffusion coefficient of ion 119894 in a solution(m2 sndash1)

Dp Effective particle diameter (120583m)F Faradayrsquos constant 96485 (C molndash1charge)(G)plusmn Activation energy for the exchange current

density (kJ kmolndash1)j Volumetric current density rate of produc-

tion of proton in electrodes (A mndash3catalyst)

j0 Exchange current density at operating con-ditions (A mndash2

Pt )(j)0119903119890119891 Reference exchange current density at the

reference conditions (A mndash2Pt )

m Molar flow rate (mol sndash1)MWi Molecular weight of species 119894 (kg molndash1)n Number of speciespi Partial pressure of species 119894 (kPa)P Total pressure (kPa)PTFE Polytetrafluoroethylene

R Universal gas constant 8314 (kJkmolndash1 Kndash1)

T TemperatureTh Thickness of catalyst layers and

membrane (120583m)u Superficial velocity of gas mixture

(ms)ui Mobility of ion 119894 in a solution

(cm2molJs)yi Mole fraction of species 119894 in the gas

phasexi Mole fraction of species 119894 in the

electrolyte phasez Moles of transferred electrons in

anode and cathode reactions(kmolelectrons kmolndash1propane)

ZrP Zirconium phosphate

Greek Letters

120572A and 120572C Anodic and cathodic charge transfercoefficients120576 Volume fraction


Ref yPinput=01

yPinput=10

yPinput=005yPinput=008

yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


Figure 10The effect of the propane inlet mole fraction yPinput on the polarization curve for a direct propane fuel cell (DPFC)model at 150∘Cand 1 atmThe values of yPinput for the above five cases were represented by the following symbols (i) solid circles 1 (ii) open circles 08 (iii)solid diamonds 01 (reference case) (iv) open diamonds 008 and (v) open triangles 005 All the other parameters were the same as thereference case mentioned in Table 1

120578 Overpotential (V)120583 Dynamic viscosity (kg mndash1 sndash1)]i Stoichiometric coefficient of species 119894

positive for reactants and negative forproducts120588 Mass density (kg mndash3)120601 Electrical potential (V)[120601119875119905]119864119876 Equilibrium potential of catalystphase (V)[120601119864119884119871]119864119876 Equilibrium potential of electrolytephase (V)

120601 Potential difference (Volt)120590 Proton conductivity (Sm)

Subscripts and Superscripts

A AnodeC CathodeC3 PropaneELY Electrolyte

EQ Equilibrium stateG Gas mixtureH+ Protoni Species in gas or solid phase propane

water CO2 O2 H+ and ZrP

M Membrane electrolytePt Platinum catalystref Reference conditionsZrP Zirconium phosphate in the electrolyte

phase

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article


Ref mP=8x10 -6 gmols

mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


Figure 11 The effect of the propane inlet molar flow rate mP (gmols) on the polarization curve for a direct propane fuel cell (DPFC)modelat 150∘C and 1 atm The values of mP (gmols) for the above three cases were represented by the following symbols (i) open circles 16x10minus6gmols (ii) solid diamonds 8x10minus6 gmols (reference case) and (iii) open triangles 2x10minus6 gmols All the other parameters were the same asthe reference case mentioned in Table 1

Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


Figure 12 The effect of the fuel cell operating temperature T (∘C) on the polarization curve for a direct propane fuel cell (DPFC) model at1 atm The values of T (∘C) for the above three cases were represented by the following symbols (i) open circles 250∘C (ii) solid diamonds150∘C (reference case) and (iii) open triangles 100∘C All the other parameters were the same as the reference case mentioned in Table 1

Acknowledgments

Financial assistance is gratefully acknowledged A Discoverygrant was awarded by the Canadian Federal Governmentrsquos

Natural Sciences and Engineering Research Council (grantRGPIN-2015-05300) A Clean Rail grant was awarded byTransport Canada a department within the Canadian Fed-eral Government


Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


Figure 13 The effect of the fuel cell operating pressure P (atm) on the polarization curve for a direct propane fuel cell (DPFC) model at150∘CThe values of P (atm) for the above three cases (ywaterypropane = 0901) were represented by the following symbols (i) open circles 11atm (ii) open triangles 3 atm and (iii) solid diamonds 1 atm (reference case) All the other parameters were the same as the reference casementioned in Table 1

References

[1] W R Grove ldquoOn voltaic series and the combination of gases byplatinum Philosophical MagazinerdquoLondon vol 4 pp 127ndash1291845

[2] M L Perry and T F Fuller ldquoA historical perspective of fuel celltechnology in the 20th centuryrdquo Journal of e ElectrochemicalSociety vol 149 no 7 pp S59ndashS67 2002

[3] M Eisler ldquoGetting power to the people Technological dra-maturgy and the quest for the electrochemical enginerdquo Historyand Technology vol 25 no 1 pp 49ndash68 2009

[4] J O M Bockris and S Srinivasan Fuel cells eir electrochem-istry McGraw-Hill New York NY USA 1969

[5] W R Grove ldquoOn the Gas Voltaic Battery Voltaic Action ofPhosphorus Sulphur and Hydrocarbonsrdquo Philosophical Trans-actions of the Royal Society A Mathematical Physical amp Engi-neering Sciences vol 135 no 0 pp 351ndash361 1845

[6] J A A Katelaar ldquoHistoryrdquo in Fuel Cell Systems L JM J Blomenand M N Mugerwa Eds Plenum Press New York NY USA1993

[7] H A Liebhafsky and E J Cairns ldquoDirect hydrocarbon fuel cellwith aqueous electrolytesrdquo in in Fuel Cells and Fuel Batteries pp458ndash523 John Wiley and Sons New York NY USA 1968

[8] E J Cairns ldquoAnodic oxidation of hydrocarbons and thehydrocarbon fuel cellrdquoAdvances in Electrochemical Sciences andEngineering vol 8 pp 337ndash391 1972

[9] Y Zhu A Y Tremblay G A Facey andM Ternan ldquoPetroleumDiesel and Biodiesel Fuels Used in a Direct HydrocarbonPhosphoric Acid Fuel Cellrdquo Journal of Fuels vol 2015 pp 1ndash92015

[10] J G Lee O S Jeon H J Hwang et al ldquoDurable and High-Performance Direct-Methane Fuel Cells with Coke-Tolerant

Ceria-Coated Ni Catalysts at Reduced Temperaturesrdquo Elec-trochimica Acta vol 191 pp 677ndash686 2016

[11] M Liu Y Choi L Yang et al ldquoDirect octane fuel cells Apromising power for transportationrdquo Nano Energy vol 1 no3 pp 448ndash455 2012

[12] Y Zhang F Yu XWang Q Zhou and J Liu ldquoDirect operationof Ag based solid oxide fuel cells on propanerdquo Journal of PowerSources vol 366 no 1 pp 56ndash64 2017

[13] W T Grubb and C J Michalske ldquoAHigh Performance PropaneFuel Cell Operating in the Temperature Range of 150∘ndash200∘CrdquoJournal of e Electrochemical Society vol 111 no 9 pp 1015ndash1019 1964

[14] E J Cairns ldquoHydrocarbon Fuel Cells with Fluoride Elec-trolytesrdquo Journal of e Electrochemical Society vol 113 no 11pp 1200ndash1204 1966

[15] O Savadogo and F J Rodriguez Varela ldquoLow-temperaturedirect propane polymer electrolyte membranes fuel cell(DPFC)rdquo Journal of New Materials for Electrochemical Systemsvol 4 no 2 pp 93ndash97 2001

[16] C K Cheng J L Luo K T Chuang and A R SangerldquoPropane fuel cells using phosphoric-acid-doped polybenzim-idazole membranesrdquo e Journal of Physical Chemistry B vol109 no 26 pp 13036ndash13042 2005

[17] M W Verbrugge and R F Hill ldquoExperimental and theoreticalinvestigation of perfluorosulfonic acid membranes equilibratedwith aqueous sulfuric acid solutionsrdquo e Journal of PhysicalChemistry C vol 92 no 23 pp 6778ndash6783 1988

[18] T E Springer T A Zawodzinski and S Gottesfeld ldquoPolymerelectrolyte fuel cell modelrdquo Journal of e ElectrochemicalSociety vol 138 no 8 pp 2334ndash2342 1991


[19] D M Bernardi and M W Verbrugge ldquoA Mathematical Modelof the Solid-Polymer-Electrolyte Fuel Cellrdquo Journal of eElectrochemical Society vol 139 no 9 pp 2477ndash2491 1992

[20] J Kim S-M Lee S Srinivasan and C E Chamberlin ldquoMod-eling of proton exchange membrane fuel cell performance withan empirical equationrdquo Journal of e Electrochemical Societyvol 142 no 8 pp 2670ndash2674 1995

[21] J C Amphlett R M Baumert R F Mann B A Peppleyand P R Roberge ldquoPerformance modeling of the Ballard MarkIV solid polymer electrolyte fuel cell I Mechanistic modeldevelopmentrdquo Journal of the Electrochemical Society vol 142 no1 pp 1ndash8 1995

[22] A Z Weber and J Newman ldquoTransport in polymer-electrolytemembranes II Mathematical modelrdquo Journal of e Electro-chemical Society vol 151 no 2 pp A311ndashA325 2004

[23] A Jarauta and P Ryzhakov ldquoCHAllenges in ComputationalModeling of Two-Phase TRAnsport in POLymer ElectrolyteFuel CELls FLOw CHAnnels A Reviewrdquo Archives of Computa-tional Methods in Engineerin State-of-the-Art Reviews vol 25no 4 pp 1027ndash1057 2018

[24] U R Salomov E Chiavazzo M Fasano and P AsinarildquoPore- andmacro-scale simulations of high temperature protonexchange fuel cells ndash HTPEMFC ndash and possible strategies forenhancing durabilityrdquo International Journal ofHydrogen Energyvol 42 no 43 pp 26730ndash26743 2017

[25] G Zhang and K Jiao ldquoMulti-phase models for water andthermal management of proton exchange membrane fuel cellA reviewrdquo Journal of Power Sources vol 391 pp 120ndash133 2018

[26] G Psofogiannakis Y Bourgault B E Conway and M TernanldquoMathematical model for a direct propane phosphoric acid fuelcellrdquo Journal of Applied Electrochemistry vol 36 no 1 pp 115ndash130 2006

[27] HKhakdamanA two dimensionalmodel of a direct propane fuelcell with an interdigitated flow field [PhD thesis] University ofOttawa 2012

[28] H Khakdaman Y Bourgault and M Ternan ldquoA MathematicalModel of a Direct Propane Fuel Cellrdquo Journal of Chemistry vol2015 2015

[29] V Danilov P De Schepper and J Denayer ldquoA TSR modelfor direct propane fuel cell with equilibrium adsorption anddesorption processesrdquo Journal of Renewable Energy vol 83 pp1084ndash1096 2015

[30] J OM Bockris and S Srinivasan ldquoThermodynamic Aspects ofElectrochemical Conversionrdquo in Fuel cells eir Electrochem-istry pp 144ndash175 McGraw-Hill New York NY USA 1969

[31] A Al-Othman A Y Tremblay W Pell et al ldquoA modified silicicacid (Si) and sulphuric acid (S)-ZrPPTFEglycerol compositemembrane for high temperature direct hydrocarbon fuel cellsrdquoJournal of Power Sources vol 224 pp 158ndash167 2013

[32] G Psofogiannakis A St-Amant and M Ternan ldquoMethaneoxidation mechanism on Pt(111) a cluster model DFT studyrdquoe Journal of Physical Chemistry B vol 110 no 48 pp 24593ndash24605 2006

[33] J O M Bockris and S Srinivasan ldquoElectrocatalysisrdquo in FuelCells eir Electrochemistry p 290 McGraw-Hill New YorkNY USA 1969

[34] E S Davydova S Mukerjee F Jaouen and D R DekelldquoElectrocatalysts for Hydrogen Oxidation Reaction in AlkalineElectrolytesrdquo ACS Catalysis vol 8 no 7 pp 6665ndash6690 2018

[35] S Vafaeyan A St-Amant andM Ternan ldquoNickel alloy catalystsfor the anode of a high temperature pem direct propane fuelcellrdquo Journal of Chemistry vol 2014 Article ID 151638 8 pages2014

[36] Y-J Wang W Long L Wang et al ldquoUnlocking the doorto highly active ORR catalysts for PEMFC applicationsPolyhedron-engineered Pt-based nanocrystalsrdquo Energy amp Envi-ronmental Science vol 11 no 2 pp 258ndash275 2018

[37] J Liang Z Miao F Ma et al ldquoEnhancing oxygen reductionelectrocatalysis through tuning crystal structure Influence ofintermetallic MPt nanocrystalsrdquo Chinese Journal of Catalysisvol 39 no 4 pp 583ndash589 2018

[38] P Chandran A Ghosh and S Ramaprabhu ldquoHigh-per-formance Platinum-free oxygen reduction reaction and hydro-gen oxidation reaction catalyst in polymer electrolyte mem-brane fuel cellrdquo Scientific Reports vol 8 no 1 2018

[39] Z Liu L Ma J Zhang K Hongsirikarn and J G Goodwin ldquoPtalloy electrocatalysts for proton exchange membrane fuel cellsa reviewrdquo Catalysis Reviews - Science and Engineering vol 55no 3 pp 255ndash288 2013

[40] M Kiani J Zhang Y Luo et al ldquoRecent developments inelectrocatalysts and future prospects for oxygen reductionreaction in polymer electrolyte membrane fuel cellsrdquo Journal ofEnergy Chemistry 2018

[41] D C Higgins and Z Chen ldquoRecent progress in non-preciousmetal catalysts for PEM fuel cell applicationsrdquo e CanadianJournal of Chemical Engineering vol 91 no 12 pp 1881ndash18952013

[42] M Darab A O Barnett G Lindbergh M S Thomassen andS Sunde ldquoThe Influence of Catalyst Layer Thickness on thePerformance and Degradation of PEM Fuel Cell Cathodes withConstant Catalyst Loadingrdquo Electrochimica Acta vol 232 pp505ndash516 2017

[43] S C DeCaluwe A M Baker P Bhargava J E Fischer and JA Dura ldquoStructure-property relationships at Nafion thin-filminterfaces Thickness effects on hydration and anisotropic iontransportrdquo Nano Energy vol 46 pp 91ndash100 2018

[44] S M J Zaidi ldquoResearch trends in polymer electrolyte mem-branes for PEMFCrdquo in Polymer Membranes for Fuel Cells TMatsuura and SM J Zaidi Eds pp 7ndash25 Springer WeinheimFederal Republic of Gemany 2009

[45] S J R Ferrell III T A Strobel G Gopalakrishan et al ldquoExplor-ing the fuel cell Limits of direct oxidation proton exchangemembrane fuel cells with platinum based electrocatalystsrdquoJournal of the Electrochemistry Society vol 159 no 4 pp B371ndashB377 2012

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Journal ofNanomaterials

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( ndash 252∘C) or a metal hydride All of the hydrogen storageoptions are more expensive than liquid storage (c) Theenergy density of hydrocarbons is much greater than that ofhydrogen (d)The electrochemical reactions of hydrocarbonshave fractional theoretical energy efficiencies of 092ndash096[4] In contrast that for hydrogen is 063 (a combination of083 [4] for the electrochemical energy efficiency and 075 forthe energy efficiency of the endothermic hydrocarbon steamreforming reaction) Every carbon atom used in a DHFCor in a combination of a process to make hydrogen fromhydrocarbons and a H2FC will produce one carbon dioxidemolecule The above difference in their theoretical energyefficiencies indicates that the amounts of carbon dioxideemitted to the atmosphere per unit of energy generated couldbe smaller for DHFCs than for H2FCs

Grove performed the first DHFC experiment [5] in 1845Early research on DHFCs by Becquerel Jablochkof JacquesBorchers Liebenow and Stresser Haber and Hofmann hasbeen documented by Ketelaar [6] who concluded that ldquofuelcell development had reached a relatively low level duringthe first 100 years of researchrdquo In the 1960s a concentratedresearch effort on DHFCs was funded in the USA Resultsfrom that program have been reported in three reviews [47 8] Sporadic DHFC research has been performed sincethat time In our laboratory a phosphoric acid fuel cell wasused for experiments that included a commercial low-sulphurdiesel fuel at 200∘C [9] Although the current densities wereextremely small the results were encouraging in that steady-state operation was demonstrated for 15 hours with each offour different diesel fuels

Recently there have been several more encouragingDHFC studies using high temperature direct hydrocarbonsolid oxide electrolyte fuel cells (SOFCs) In those studies aninternal reforming catalyst layer had been added to the anodecatalyst layer Its purpose was to convert the hydrocarbon tohydrogen before it reached the adjacent anode catalyst layerLee and coworkers [10] added aNi-Fe reforming catalyst layerto an anode layer consisting of NiOndashYSZ (yttria stabilizedzirconia) in experiments with methane at 750∘C Later [10]they reported a 1000 h continuous fuel cell operation usinga ceria coated Ni reforming catalyst in experiments withmethane at 610∘C Liu and coworkers [11] added a reformingcatalyst layer containing Ni YSZ and BaZr(1minus119883) Y119883O(3minus120575)in experiments with iso-octane at 750∘C Zhang et al [12]showed that direct propane solid oxide fuel cells havingelectrodes composed of a blend of silver and gadoliniumdoped ceria maintained a stable performance for 160 h time-on-stream However experiments with a nickel-gadoliniumdoped ceria experienced serious deactivation after 40 h oftime-on-stream In all of the above reports on SOFCs thecurrent densities were slightly smaller but of the same orderof magnitude as those in H2FCs

Propanewas the fuel chosen for this work for two reasonsPropane is used to provide space heating in rural areasTherefore the infrastructure for direct propane fuel cells(DPFCs) in rural areas is already in place Second the cost foran electrical utility to deliver electrical power in rural areas ismuch greater than in urban areas even though the price of

electrical power in rural and urban areas is similar Thereforeelectrical power from a fuel cell system in a rural locationmaybe cost competitive with rural electrical power costs even if itis too expensive for urban areas

Results with low temperature proton exchange mem-brane fuel cells (PEMFCs) operating on propane have beenless encouraging Some of the most promising results withpropane from the 1960s were obtained with a phosphoricacid electrolyte Grubb and Michalske [13] and with ahydrofluoric acid electrolyte Cairns [14] However in recentyears only a limited amount of work has been reported onDPFCs Examples are the propane work using Nafion andpolybenzimidazole electrolyte membranes by Savadogo andVarela [15] and using a polybenzimidazole membrane byCheng et al [16]

Our long-term objective is to seek DPFC characteristics(processing conditions materials and equipment config-urations) for which the performance of low temperatureDPFCswould become competitivewithH2FCs Two steps arenecessary to achieve this objective (a) identifying the limitingphenomena that are responsible for small current densitiesin DPFCs and (b) identifying the DPFC characteristics thatwould remove those limitations

To contribute to the first step in this work we haveused mathematical modeling to examine the effect of severalvariables that influence DPFC performance Experimentsare always more definitive than models However thereare some variables that are extremely difficult to measureexperimentally An example would be the pressure gradientacross the electrolyte layer In contrast they can sometimes becomputed precisely using models By studying large changesin each of the variables it should be possible to identify thosevariables having the greatest potential to improve fuel cellperformance

Mathematical models of fuel cells have been used todescribe a wide range of physical chemical electrochemicaland mass transfer phenomena There were several earlymodels Verbrugge and Hill [17] used dilute solution theoryto describe the migration of protons in a fuel cell having aperfluorosulfonate ionomer membrane Springer et al [18]developed one of the first models for a hydrogen fuel cellIt predicted a ratio of water flux to proton flux in a Nafion117 membrane that was consistent with the experimentalvalue Bernardi and Verbrugge [19] modeled the transportmechanisms of several species within a PEMFC and foundthat the diffusion of dissolved gases to the catalyst limited fuelcell performance Since then models of various complexitieshave been developed from simple (analytical models) Kim etal [20] to more complex (mechanistic models) Amphlett etal [21] and numerical models Weber and Newman [22] Anextremely large body of literature describing fuel cell modelsnow exists Some recent reviews are those by Jarauta andRyzhakov [23] Salomov et al [24] and Zhang and Jiao [25]

The first mathematical model of a direct propane fuelcell (DPFC) was developed by Psofogiannakis et al 2006[26] It was a one-dimensional computational fluid dynamics(CFD) model It used a phosphoric acid electrolyte andPt anode catalyst Overpotential was found to control fuelcell performance Subsequently Khakdaman et al [27 28]





2 Model Description




5O2 + 20H+ + 20endash = 10H2O 120601C = 1229 V (2)


C3H8 + 5O2 = 3CO2 + 4H2O 120601CELL = 1093 (3)







nabla ∙ (120576G 120588G u) + nsumi

]i119872119882119894119895119911119865 = 0 (4)












(d1) For water


(7)

(d2) For protons


(8)




where 1198950119860 = (1198951198623 119874119909)0119903119890119891( 1199011198623(1199011198623)119903119890119891)





where 1198950119862 = (1198951198742 119877119889)0119903119890119891 ( 1199011198742(1199011198742)119903119890119891)

















Iteration

Iteration

Iteration



Updatingtransfer


Gaseous species at










00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)















0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls








2 Model Description




5O2 + 20H+ + 20endash = 10H2O 120601C = 1229 V (2)


C3H8 + 5O2 = 3CO2 + 4H2O 120601CELL = 1093 (3)







nabla ∙ (120576G 120588G u) + nsumi

]i119872119882119894119895119911119865 = 0 (4)












(d1) For water


(7)

(d2) For protons


(8)




where 1198950119860 = (1198951198623 119874119909)0119903119890119891( 1199011198623(1199011198623)119903119890119891)





where 1198950119862 = (1198951198742 119877119889)0119903119890119891 ( 1199011198742(1199011198742)119903119890119891)

















Iteration

Iteration

Iteration



Updatingtransfer


Gaseous species at










00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)















0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls











(d1) For water


(7)

(d2) For protons


(8)




where 1198950119860 = (1198951198623 119874119909)0119903119890119891( 1199011198623(1199011198623)119903119890119891)





where 1198950119862 = (1198951198742 119877119889)0119903119890119891 ( 1199011198742(1199011198742)119903119890119891)

















Iteration

Iteration

Iteration



Updatingtransfer


Gaseous species at










00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)















0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls












Iteration

Iteration

Iteration



Updatingtransfer


Gaseous species at










00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)















0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls







00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)















0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls












0 10 20 30 40 50 60 70 80 90 100 110 120




00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)




















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls



















00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


(jO2-Rd)0-ref =3x10-12 Am2









A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





A =C =400 m

Ref A =C =300 m

A =C =200 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)










Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





Ref M =100 m

M=531m

M =25 m

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


ELY =1x1020 Sm









00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)


DH+-ZrP =7x10-9 m2s






4 Conclusions



Nomenclature


ndash3catalyst)






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls






00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)
























Greek Letters



Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





Ref yPinput=01

yPinput=10


yPinput=08

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)











phase

Data Availability






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls






mP =16x10-6 gmols

mP =2x10-6 gmols

00

01

02

03

04

05

06

07

08

09

10

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Ref T=150degC

T=250degC

T=100degC

00

01

02

03

04

05

06

07

08

09

10

11

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



Acknowledgments




Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





Ref P=1 atm

P=3 atm

P=11 atm

00

01

02

03

04

05

06

07

08

09

10

11

12

CELL

PO

TEN

TIA

L D

IFFE

REN

CE Δ

C

ell

(V)



References





















































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls





































Journal of

Chemistry





Journal of

Volume 2018






Volume 2018




Journal of






Enzyme Research


Journal of



MaterialsJournal of






Na

nom

ate

ria

ls




an investigation of direct hydrocarbon (propane) fuel cell...

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