Modeling of transport phenomena in a fuel cell anode. Frank A. Coutelieris

Transcription

1 Moeling o transport phenomena in a uel cell anoe Frank A. Coutelieris Department o Engineering an Management o Energy Resources, University o Western Maceonia, Bakola & Sialvera, Kozani, Greece, Tel: ; Fax: ; coutelieris@uom.gr an National Center or Scientiic Research Demokritos, Aghia Paraskevi Attikis, Greece, Tel: ; Fax: ; e- mail: rank@ipta.emokritos.gr Keyors: SOFC, anoe; catalyst layer; heat transer; mass transport. Abstract A mathematical moel or the simulation o the transport phenomena occurre in the anoe o a typical uel cell is presente here. The moel initially consiers a simple oneimensional geometry here the mass transport equation is combine ith a Tael-type escription or the current ensity. By assuming isothermal conitions, the numerical solution o the ierential equations as achieve ith the use o a non-linear shooting scheme in conjunction ith the multiimensional Neton algorithm. The space as iscretize through a constant-step mesh hile the resulting nonlinear system o orinary ierential equations as solve by using the 4th orer Runge-Kutta metho. The hole algorithm as implemente by eveloping a ne FORTRAN coe. In aition, a planar to-imensional geometry is also consiere, here the mass transport is escribe by the convection-iusion equation ithin the catalyst layer together ith the Navier- Stokes equation or laminar lo conitions an the electrochemical eects, hile the convective heat transer ithin the evelope iusion layer is also taken into account. This approach has been numerically implemente an solve by using the inite volume metho being applicable through the CFD-RC commercial package. For the sake o simplicity, the eestream o the uel cell as assume to be a hyrogen-rich mixture (H 2 >90%) or all cases. Both SOFC an PEM type uel cells ere consiere in this stuy, hile the results are presente in terms o uel concentration, prouce current ensity an overpotential. Introuction During the last years, uel cells have attracte consierable scientiic an engineering interest because they present high eiciency an very lo environmental impact. It is important that various uel options such as natural gas, methanol, ethanol an gasoline are consiere easible or uel cell operation, oering a very signiicant ecological imension in the problem o eective energy conversion [1]. Several types o uel cells have been investigate an applie till noaays, among hich Soli Oxie Fuel Cells (SOFCs) an Polymer Electrolyte Membrane Fuel Cells (PEMFCs) have attaine the ier acceptance in terms o applications [2]. The mass transport ithin a uel cell is a key actor to its perormance. Especially, PEM-type uel cell suers rom mass transport limitations preominantly at anoe, arising rom the iusion o uel in covering the active electrocatalyst layer an rom hyroynamics in the anoe lo channel. The geometrical characteristics o the electroes (thickness, volume porosity, tortuosity etc) are the crucial parameters aecting the mass transport o chemical species through the electroe/electrolyte 1

2 interace. This process inluences signiicantly the overpotential, thereore the eiciency o the cell in terms o poer prouction, mainly because o temperature singularities [2, 3]. Since there are serious iiculties in realizing prototypes, numerous multi-imensional simulation have been publishe because mathematical moeling is essential or the better unerstaning o the role o the main parameters that aect the perormance o a uel cell [4-6]. Most o these stuies have been ocuse on the anoe o the cell, because this is the place here the electrochemical reactions occur, thus it might play the most important role in the poer prouction process. Among these simulation activities, the most simple an interesting moel is that o Jeng an Chen [7] an Jeng et al. [8], ho manage to preict the behavior o a irect methanol PEM uel cell, hile the eect o the current ensity on uel crossover as also examine. Their oneimensional approach is very important because it is quite trouble-ree, accurate an easily applicable to other conigurations, although it suers rom some uncertainties (or example, they assume that methanol concentration in the iusion layer is insigniicant compare ith that o ater). In the present ork, the above mentione 1-D approach as use in orer to evelop a preictive mathematical moel or the transport phenomena occurring along the axis o a generic typical uel cell anoe. Obviously, a signiicant trial to overcome some o the above mentione eiciencies has been incorporate here. Further to this simple moeling approach, a more etaile 2-D simulation has also been implemente or the same processes in orer to overcome supericial assumptions an mathematical manipulations. A comparison beteen these to approaches, being applie to both SOFC an PEM uel cell conigurations, is also presente ith the purpose to urther investigate the value ae by the to-imensional approach. Moel escription The operation o a typical uel cell is base on the continuous supply o its anoe by a hyrogen-rich uel mixture hile cathoe is expose to atmospheric air. In any case, the prouce ions migrate trough electrolyte an heterogeneously react in orer to prouce ater, heat an poer. More precisely, the reactions that take place in a uel cell are as ollos Fuel cell type Place Reaction SOFC Cathoe 2 O2 4e 2O (1a) 2 SOFC Anoe H O H O e (2a) PEM Anoe 2H2 4H 4e (1b) PEM Cathoe O2 4H 4e 2H 2O (2b) A typical 2-D cut o a uel cell containing the anoe area is schematically presente in Fig. 1. In particular, anoe is ivie into three regions: an electrolyte region, an active catalyst region (catalyst layer) that provies a catalytic site or the oxiation o uel an a iusion region (iusion layer) compose o highly porous an electronically conuctive material. The electrolyte is assume to be ense in the case o SOFC an porous or the case o PEM uel cell. The iusion layer is locate ajacent to the lo channel an avoring the istribution o reactants to the catalyst layer. For the moeling point o vie, the area o interest is the catalyst layer. The uel e to the anoe compartment o the uel cell is assume to be a mixture o high hyrogen content (H 2 >90%). It is also assume that hyrogen reacts only partially in the catalyst/electrolyte interace; thereore a remaining portion ollos the stream to the outlet an/or crossovers to the cathoe compartment.

3 Figure 1: Schematic iagram o the simulate (anoe) area. One imensional moel By assuming that the pressure in both anoe an cathoe compartments is equal to 1 atm an that the major transport processes mainly occur at the irection parallel to the cell axis, the mass lux in the catalyst layer or steay-state isothermal conitions can be expresse as ollos C j D C j e (3) e here D is the eective iusivity o uel in the catalyst layer an j, j are the mass luxes o the uel an the ater, respectively. In the above equation, the convection term has been neglecte since the velocity is very lo ithin the catalyst layer [7, 8]. By taking into account the material balance or the ater, its mass lux is given as j j I i 4F (4) I i here is the lux o the prouce ater mass an j represents the ater lux entering the 4F catalyst through the iusion layer. By I an i the cell an ionic current ensity are enote, respectively, hile F represents the Faraay s constant. The ater lux rom iusion layer epens on uel cell type, being zero in the case o SOFC, i.e. j 0 (5a) For the case o PEM uel cell, the above mentione mass lux is approximate as [7] 3

4 j I F (5b) here is the electro-osmotic rag coeicient o ater. It is orth noticing that the oxiation o uel along the axis o the uel cell is linear ith the ionic current ensity, thus the variation o mass lux is analogous to the spatial evolution o current ensity, i.e. j 1 i 4F (6) By ierentiating eq. (3) an using eqs. (5b) an (6), the governing ierential equation or mass transer ithin the catalyst layer becomes as ollos D 2 C e C 2 1 C I i I I i 4F F 4F (7a) hich is vali or the case o PEM uel cell. When a SOFC is consiere, it becomes D e 2 C C 2 1 I i I i C 4F 4F (7b) Since the last equations combine the mass transport ith the local current ensity, it is necessary to evelop the relative expression or i. Starting rom the ell knon Butler-Volmer equation an ater same simpliications, a Tael-type equation can be obtaine i K C e 4a a F RT (8) here is the orer o the reaction, is the anoic overpotential an K is a coeicient incluing the geometrical an physical properties o the electrolyte. By involving the local potentials at catalyst layer an at ionomeric phase as ell as the Ohm s la, the variation o the overpotential ithin the catalyst layer is given as [7, 8] Rm Rs i RsI (9) here the soli phase. R m is the eective ionic resistance in the catalyst layer an R s is the eective resistance in

5 Again, by ierentiating eq. (8) an using eq. (9), it is easy to obtain the governing ierential equation or current ensity ithin the catalyst layer as ollos C 4a F 2 i a i 2 Rm Rs i Rs I C RT (10) In orer to numerically integrate the system o either eqs. (7a) & (10) or eqs. (7b) & (10), it is necessary to ecrease the orer by introucing ne unknons C an i (ongrae technique), thus a system o our equations is prouce or the case o PEM as ollos C C i i (11a) (11b) C 1 I i 4 I C I 1 C e i 4FD (11c) i C R R i R I i C RT 4a a F m s s (11) Note that eq. (11c) becomes or the case o SOFC C 1 I ic I 1 C e i 4FD (11e) Inepenently on the uel cell type, the bounary conitions accompanying the above system are as ollos C x 0 0 C x 0 C i x 0 0 i x 0 0 re (12a) (12b) (12c) (12) here re C is the uniorm reerence uel concentration at the inlet. Although it is rather obvious that i x cell length I (13) 5

6 the analysis here oes not use the relation above or the escription o the bounary conition as in [7], because it is better or the accurate convergence o a irst orer system o ierential equations to be accompanie by initial conitions at the same point o the omain [9]. Thereore, the above eq. (13) is consiere as one o the criteria against hich the solution o the system must be evaluate. The numerical solution o the systems o ierential equations (11a), (11b), (11c)/(11e) an (11) as achieve ith the use o a non-linear shooting scheme in conjunction ith the multiimensional Neton algorithm [10]. The space as iscretize through a constant-step mesh, hile the resulting nonlinear system o orinary ierential equations as solve by using the 4th orer Runge-Kutta metho. A ne FORTRAN coe as evelope to implement the above mentione numerical scheme, hile the values use are as in [7] an [8]. The computational time in a simple home PC is o orer o secons, epene on the initial guesses or the Neton metho. To imensional moel The coniguration o a typical planar uel cell is as in Fig. 2 here the simulate area has been ivie in seven separate regions: the anoe an the cathoe channel, the porous anoe an cathoe, the electrolyte layer an the to contacts. The uel an air mixtures enter the system through the anoe an cathoe channel respectively an have typical compositions. Figure 2: Simulate geometry a planar uel cell The steay state laminar lo is stuie by using the Navier-Stokes equation or incompressible luis 2 u u p u (14) here u is the local velocity vector, is the ensity, p is the pressure, an is the viscosity. All these quantities are reerre to the mixture o both the anoic an cathoic ee-stream. By neglecting the raiation term, the heat transer equation in the uel cell becomes as ollos u c T Q a c T c T u (15) p p p

7 here c p is the mixture s speciic heat, a is the iusion thermal coeicient an Q prouce or consume heat. is the Since only surace reactions are taken into account or the current simulations (no-bulk reactions), the mass transport equation is o the orm u C D C i i, mix i 0 (16) here C i is the concentration o i -species an D i, mix is the iusion coeicient o this component in the mixture. By assuming charge transer controlle process, the Butler-Volmer equation has been incorporate or the electrochemical reactions occurring in the cell an the calculation o current ensity, as aaf acf i i0 exp exp RT RT (17) here i 0 is the exchange current ensity, a a an a c are the anoic an cathoic charge transer coeicients, respectively, an R is the ieal gas constant. For the simulations presente here, constant values o mass inlo rates ere use or both the anoe an the cathoe channel mixtures an ixe pressure bounary conition o 1 atm as set to both outlets. A voltage o 0.73 V as applie to the cathoe contact an the bounary conition or the temperature as assume isothermal an ixe to 1073 K or the case o SOFC an 373K or the case o PEM. All the other bounary conitions ere set to all inication ith zero value o velocity, zero lux o temperature, species composition an current inication. In orer to achieve the numerical solution o the above equations, a 2-D mesh as evelope in accorance ith the speciic imensions as in Fig. 2. The inite volume metho as use through the commercially available sotare package CFD-RC or the solution o eqs. (14)-(17) here the simulate omain as iscretize by an unstructure gri. The values o the operational parameters are as in [7], [8], [11] an [12]. In orer to achieve resiual values loer than 10-4 or all the unknon quantities, a computational time o approximately hal an hour as on average necessary or runs on an Intel Pentium 3.2 GHz computer. Results an Discussion The hyrogen molar raction obtaine by the one-imensional moel as unction o imensionless normalize length is presente in Fig. 3 or various current ensities. As expecte [1], concentration ecreases ith the current ensity. It is also epicte that the concentration proiles are nearly linear or lo current ensities, because iusion ominates at this conitions, thereore only a small portion o hyrogen is consume in the catalyst layer. Finally, SOFC coniguration presents signiicantly higher hyrogen concentrations than those o PEM, because the membrane is permeable alloing a portion o hyrogen to escape toars the cathoe s sie. This is 7

8 not possible or the case o the ense electrolyte o a SOFC, presenting a zero aitional ater lux (see eqs. 5a & 5b). The comparison beteen the to ierent uel cell types is more clearly presente in Fig. 4, here the same results as those o Fig. 3 have been obtaine by the toimensional approach. Hyrogen is consume ith higher rates in the case o PEM, thus proucing higher heat amounts, as ell as more poer. H2 molar raction SOFC PEM I=0.1 I=0.2 I=0.3 I= imensionless istance Figure 3: Hyrogen concentration ithin the catalyst layer or various current ensities Figure 4: Hyrogen concentration or SOFC an PEM conigurations Fig. 5 presents the overpotential in the catalyst layer as estimate by the 1-D approach. As above, several values o current ensity an to uel cell types have also been consiere. A rather smooth increment rom the inlet to the outlet is observe (note the scale o y-axis), resulte by the consequent increment o the hyrogen consumption ith the istance, as it has been shon in Fig. 3. Furthermore, the overpotential increases ith current ensity, hich is in accorance ith previously presente experimental an theoretical results [7, 8, 11, 12]. It is important to note that overpotential values at the inlet area are not exactly zero since some consumption o hyrogen

9 alreay exists in the iusion layer or both SOFC an PEM cells. Finally, it is important to note that SOFC alays presents slightly higher overpotential values than those o PEM, mainly because o the higher operational temperature o the cell. Hoever, this ierence can be characterize as insigniicant since it is les than 0.05V or the same conitions. The same qualitative behavior is also observe in Fig. 6, here relative results rom 2-D moel are presente. In terms o quantitative analysis, the overpotential values are to some extent ierent (higher) than those o Fig. 5, because o the most etaile moel, being closer to elsehere obtaine overpotential [11, 12] than 1-D respective results o Fig SOFC, I=0.1 overpotential (V) SOFC, I=0.2 SOFC, I=0.3 SOFC, I=0.4 PEM, I=0.1 PEM, I=0.2 PEM, I=0.3 PEM, I= imensionless istance Figure 5: Overpotential ithin the catalyst layer or various current ensities Figure 6: Overpotential or SOFC an PEM conigurations Conclusions In the present ork, to approaches have been aopte to aequately simulate the transport phenomena occurre in the anoe o a uel cell. The irst one is a one imensional, relatively simple moel, hich is analogous to those presente in [7] an [8]. Such a moel shoul involve some assumptions (like isothermal operation, pre-eine current at outlet, etc.) to obtain the 1-D 9

10 solution. To overcome such theoretical issues, a more complicate to-imensional approach has also been evelope, incluing the couple solution or lo, heat transer, mass transport an electrochemistry. It is oun that both moels escribe ith suicient accuracy [11, 12] the operation o a uel cell in terms o eestock concentration an overpotential prouce. By using both the approaches, SOFC an PEM conigurations ere compare an a slight avantage o SOFC has been unerline, since it presents higher uel consumption as ell as higher overpotential values. Acknolegment Author oul like to thank Mrs. Eleni Vakoutsi or her technical assistantship in CFD-RC issues an Mr. Dimitrios Sarantaries or some ruitul iscussions on the topic. Reerences [1] Hirschenhoer JH, Stauer DB, Engleman RR, Klett MG, Fuel Cell Hanbook, 4th Eition e., Business/Technology Books: Orina, USA (1997). [2] R. Sousa, E.R. Gonzalez: J. Poer Sources Vol. 147 (2005), p. 32 [3] S.H. Chan, K.A. Khor, Z.T. Xia: J. Poer Sources Vol. 93 (2001), p. 130 [4] K. Scott, W. Taama, J. Cruickshank: J. Poer Sources Vol. 65 (1997), p. 159 [5] P.R. Pathapati, X. Xue, J. Tang: Reneable Energy Vol. 30 (2005), p. 1 [6] D. Cheie, N. Munroe: J. Poer Sources Vol. 147 (2005), p. 72 [7] K.T. Jeng, C.W. Chen: J. Poer Sources, Vol. 112 (2002), p. 367 [8] K.T. Jeng, C.P. Kuo, S.F. Lee: J. Poer Sources Vol. 128 (2004), p. 145 [9] Ames WF, Numerical methos or partial ierential equations, Acaemic Press: Ne York, USA (1977). [10] Keller HB, Numerical methos or to-point bounary-value problems, Blaisel: Waltham, USA (1968) [11] Bockris JOM, Rey AKN, Moern Electrochemistry, Plenum Press: Ne York, USA (1997). [12] P.A. Ramakrishna, S. Yang, C.H. Sohn: J. Poer Sources Vol. 158 (2006), p. 378