Lumped Model for Proton Exchange Membrane Fuel Cell (PEMFC)

Transcription

1 Int. J. Electroche. Sci., 5 ( International Journal of ELECTROCHEMICAL SCIENCE Luped Model for Proton Exchange Mebrane Fuel Cell (PEMFC M. ELSayed Youssef 1,*, Khairia E.AL-NAdi, Moataz H.Khalil 1 1 Coputer Based Engineering Applications Departent, IRI, Mubarak city, Egypt Matheatical Departent, Faculty of Science, Alexandria University, Egypt. * E-ail: elsayed168@gail.co Received: 10 August 009 / Accepted: 5 February 010 / Published: 1 February 010 This work aied to develop luped odel for proton exchange ebrane fuel cells (PEMFCs. The developed luped odel has been validated with published experiental results. The odel has been developed depend on linear algebra equations. This odel is used to study the effects of several operating and design paraeters on fuel cell perforance. The paraeters have been studied their effects on cell. These paraeters are input teperature, pressure, stoichioetric ratio, ebrane thickness and gas diffusion layer thickness. The luped odel has been prograed using software MATLAB. Keywords: PEM fuel cell, PEM odeling, luped odel, paraetric study. 1. INTRODUCTION A fuel cell is a device that can directly transfer cheical energy to electric and theral energy. There are different types of fuel cells. Aong this different fuel cell types a proton exchange ebrane fuel cell (PEMFC [1-4] has been selected. Proton exchange ebrane fuel cell can be operated at low teperature (about 80 K with high power density product and at sae tie without ipact environent. Proton exchange ebrane has high startup syste and shadow syste perforance [5]. These advantages have been attended aount of research in last years, especially in stationary and obile power generators and electric vehicles [5]. Two factors have been controlled on Proliferation of trade of fuel cell technology. They are high perforance and low cost []. Low cost covered econoy fuel cell research. Fuel cell perforance has been anaged by ore eleents such as operating conditions, aterial properties and cell design. It is necessary understand paraeters effect on fuel cell perforance []. The physical and

2 Int. J. Electroche. Sci., Vol. 5, atheatical is principle device in this work. Where, the atheatical odel is iportant tool in siulation and odeling [1]. The developent of physical odels allows dependable siulation process under practical conditions paraeters, where it is necessary in fuel cell developent and optiization []. This study presents luped odel for proton exchange eber fuel cell. Proton exchange ebrane fuel cell (PEMFC systes consist fro therodynaics, electrocheistry, hydrodynaics and ass transfer theory. So, it is very difficult to deign copleted atheatical odel. The luped odel allow to study fuel cell odel by know the input and output of fuel cell. The linear algebraic equations have been used on luped odel. Paraetric study for this luped odel has been developed. The paraetric study on fuel cell perforance has been discussed.. MODEL DESCRIPTION Luped odel has been developed in this study. Luped odel is odel with zero diensions. The odel was developed with soe assuptions such as, the transport process is steadystate which resolves coupled transport in ebrane, all gases obey the ideal gas low, the gas flow channels is lainar,the catalysts is very thin,the change phase of water was neglected,the heat transport cross solid ediu as gas ediu, the output teperature is cell teperature. The developed odel has five ajor sections. Theses included ass transport, heat transport, electrical characterization, water anageent and losses product..1. Coputational doain A coputational odel of an entire cell would needed very huge coputing eory and very long siulation tie. The coplete coputational doain contains cathode, anode, gas diffusion layer channels and ebrane electrode. A scheatic diagra of a PEM fuel cell with the reactant and product gases and ion conduction flow is shown in Fig. 1. Figure 1. Coputational doain of proton exchange ebrane fuel cell odel.

3 Int. J. Electroche. Sci., Vol. 5, Model equations The developed odel has been controlled by set of equations. They are ass conversation equation, energy balance equation, power cell and cell potential..3. Mass conversation equation First, the ass balance of cell should be estiated. Because the flow calculations are iportant for deterining the correct fuel rate of cell [6]. The ass conservation calculations are all depended on current flow [7]. Fig. depicts the ass flow rate of input and output of fuel cell. Figure. Conservation of ass diagra illustrating two bi-polar plates, MEA, and the product flows between the. Mass flow rate of hydrogen at anode can be calculated as following: H = S H I M H F Where H is the ass flow of hydrogen fro anode, SH (1 is the stoichioetric flow ratio of hydrogen, Coulob I is the current flow, M H is the olecular weight and F is the faraday s constant ( ol While the ass flow rate of oxygen fro cathode can calculate as following: I M O O = SO ( 4 F By using conservation ass low, the aount of water generation can be calculated by I M H I M O H gen = +, F 4 F (3 The water leaves the cell as liquid and vapor. The vapor water was coing fro vapor water entering with air at cathode. So, the total aount of water goes out fro cell can be calculated as following:

4 Int. J. Electroche. Sci., Vol. 5, ( HO l ( HO v = ( HO out + (4 Where ( HO l is the ass flow rate of water at liquid state ( HO v vapor state. The ass flow rate of vapor water can be calculated as following: is the ass flow rate of water at H O( v = M H O PH P O( V ( o out cathode M O ( N sys + M N (5 Where M, M, M are the olecular weight of water, oxygen,nitrogen, P ( is the partial H O O N pressure of water, P cathode is the pressure of cathode, ( O out fro cell and ( N sys is the ass flow rate of nitrogen. HO V is the ass flow rate of oxygen output.4. Energy balance equation The energy balance on fuel cell is the total aount of energy input to cell equals the total aount of energy product fro cell [6]. The general energy balance equation can be forulated as following: i in hi in Wel + ( hi out + Where ( h is the total input enthalpy to cell, ( ( = Q (6 i out h is the total output enthalpy fro cell, Wel is electrical power and Q is the heat leaving cell by convection, radiation or coolant. The electrical power can be expressed as following: W el = I V (7.5. Cell power following: The fuel is providing cell by power as fuel power, which can be forulated as Where P = H LHV (8 fuel P fuel is the fuel power and LHV is the low heating value. The power provided by fuel in reacted hydrogen is converted into two types; electricity and heat. Therefore, P = W heat (9 fuel el +

5 Int. J. Electroche. Sci., Vol. 5, Cell potential The Nernst equation allows one to deterine the voltage of an electrocheical Cell ( E. It is derivation fro therodynaic principles. Nernst equation is shown as general foral as following [8]. E = E o R T lin N F 1 [ P ] [ ] [ ] H P O PH O Where R is the universal gas constant, T is the absolute teperature, n is the charge nuber of the electrode reaction and, P P are the partial pressure of hydrogen, oxygen and water PH O, HO o respectively. While E is standard electrode Potential, The standard electrode potential is actual cell potentials different under standard condition, the standard condition which ean here, there teperature at 98 K and pressure about 1.0 bar. It calculated as shown by Maher []. (11 o 3 5 E = ( T T ( lin( P lin( H P O (11 Once of iportant output a source is the electrical energy. The actual cell potentialv act is lower o than the stranded cell potential E because cell losses. Fuel cell has three types of losses are activation loss, concentration loss and ohic loss, which can be calculated as following: V act = E o V V V (1 activation con ohic The activation losses can estiate fro the following: V activation R T i R T = ln + ln F α a ia 4 F α c i i c (13 Where i current density and α is transfer coefficient. The ohic losses can be forulated as following: V ohic = I r (14 Where r is the resistance. It can be coputed fro the following equation: l lc r = + λ A λ A e c (15 Where l c, l are the gas diffusion layer thickness, is the wet ebrane thick-ness, λ, λ e is the ebrane ionic conductivity,the electrode ionic conductivity, A, A are the cross sections of ebrane and cross section of electrode. The concentration loss can be calculated fro the following equation: c

6 Int. J. Electroche. Sci., Vol. 5, R T PH 1 (ln ln + P h O V = cocn F Pa Pc (16 By solving equations (11, (13, (14, (16 in equation (1 can get the actual volt of cell. 3. SOLUTION ALGORITHM The previous equations have been solved by using MATLAB software. The values of olecular weight and range of current density and stoichioetric are used as input paraeters. The ass conversation has been solved. The ass flow rate of input/output was produced. By Copensation on heat balance equation and with erged the fuel power and electrical power the input/output heat was produced and the output teperature of gas can be calculated. Then losses of cell can be calculated with standard electrode potentials calculations. The actual cell voltage can be estiated and cell power too. Figure 3. Coparison between experiental data and odel data 4. RESULTS AND DISCUSSION The values of geoetric details of cell are listed in Table 1. Table shows the electrocheical transport paraeters values for base case operating condition as given by Maher A.R []. The results for base case operating conditions were verified with experiental results provided by Wang et al. [9]. The coputed polarization curve of validation luped odel for proton exchange ebrane fuel cell (PEMFC was achieved good agreeent with published experiental polarization curve as shown in Fig.3. The results for base case operating conditions were verified with experiental results provided by Maher A.R.[].

7 Int. J. Electroche. Sci., Vol. 5, However, the luped odel has been deviated for experiental result when current densities in the ass transport liited region (>1.5 A/c or higher. This divergence is a coon characteristic of single-phase odels where the effect of reduced oxygen transports due to water flooding at the cathode at high current density cannot be accounted for [10]. In addition to this flooding effect, anode drying can also be a contributing factor to the reduced perforance at high current density [11]. On another hand, for siplification local current density has been used instead of a liiting current density.the luped odel has been ore validated for region (current density = 1000 A. - to A. -. Fig. 4 shows the power curve of odel with current density. It was noted that with increasing current density the power was increasing.so, the high power value would be in high current density value. Table 1. Geoetrical and operational paraeters for base case conditions Paraeters Unit Value Channel length 0.05 Channel weight 1e-3 Channel height 1e-3 Gas diffusion layer thickness 0.6e-3 Mebrane thickness 0.3e-3 Hydrogen reference ole fraction oxygen reference ole fraction Intel pressure at 3 Intel teperature K Huidity % 100 Air stoichioetric flow ratio - Fuel stoichioetric flow ratio - Table. Electrode and ebrane paraeters for base case operating conditions Paraeters Unit Value Electrode electronic conductivity Mebrane ionic conductivity S 100 S 17.1 Anode transfer coefficient Cathode transfer coefficient Anode reference current density A 1.8e-3 Cathode reference current density A 465.5

8 Int. J. Electroche. Sci., Vol. 5, Teperature effect on PEMFC Perforance The teperature has basic effect in the different transport phenoena inside the fuel cell, and open circuit voltage. The coposition of the incoing gas streas depends strongly on the teperature. Fig 6 shows I-V curve at different teperature values K, K, K, K and K. Figure 4. Power density of PEMFC Versus cell current density It was found that at teperature increasing the cell voltage increasing due to losses voltage decreasing. The activation loss decreases with increasing teperature. This is due to the exchange current density of the oxygen reduction reaction increases rapidly with teperature due to the enhanced reaction kinetics, which reduces activation losses. At the sae tie, the open circuit voltage ( E is function on teperature and pressure.so, when teperature increasing the open circuit voltage increasing. It was observed that at teperature increasing by 0 K the voltage increasing by about 0.V. Figure 5. PEMFC perforance at different fuel cell teperature

9 Int. J. Electroche. Sci., Vol. 5, Pressure effect on PEMFC Perforance Pressure is one of effective basic operating paraeter siilar to the teperature. The operating pressure has an effect on any transport paraeters that are iportant for the fuel cell operation. The saturation pressure of water vapor depends only on the teperature and it reains constant for a variation of the inlet pressure. The open circuit volt is function on input teperature and input pressure. Fro equation described in previous section, it was found that the change in pressure effects in open circuit volt,but the variation would be have sall effect because the pressure factor ultiple in very sall nuber. The pressure has ajor effect on aount of water vapor water product fro cathode and aount of vapor water enter with hydrogen at anode side. Pressure would be increasing leads to ass flow rate increasing in due to increasing in output heat. Fig.6 shows I-V curve for different pressure values, 3, 5 bar variation at cell polarization curve. It was noted that the activation losses decreases when pressure increasing, due to increasing the cell voltage with pressure increasing. On another hand, unliited pressure increasing could not achieve higher voltage. Because, with increasing pressure the cell voltage increasing very sall value. Furtherore, the cost used for increasing pressure doesn t produce higher voltage as expected. And, the cell could be daaged in case pressure ore than 1 bars Effect of ebrane thickness on PEMFC Perforance The effect of ebrane thickness has been studied on the fuel cell Perforance. Fro relation between the ebrane thickness and cell resistance, it was observed that the ajor effect of thickness variation would be appeared at ohic losses. The ohic loss is function on ebrane thickness, current density, cross section area, electronic conductivity and ionic conductivity. Figure 6. PEMFC perforance at different fuel cell pressure Fig.6 shows the effect of ebrane thickness on cell voltage. It was observed that with increasing of ebrane thickness of PEMFC leads to increasing of ohic cell losses.consequently

10 Int. J. Electroche. Sci., Vol. 5, decreasing the cell output voltage. It was found that the effect of ebrane thickness on polarization curve has been cleared starting fro the ohic losses region to end of polarization curve. Figure 7. PEMFC perforance at different fuel cell ebrane thickness Figure 8. PEMFC Perforance at different GDL 4.4. Effect of gas diffusion thickness (GDL on PEMFC Perforance Gas diffusion layer is iportant key affected in fuel cell perforance. The ajor effect of gas diffusion layer has been appeared in cell losses particularly at ohic losses. Because, ohic losses is function depend on gas diffusion layer, ebrane thickness and theral conductivity, current density and cross section area. Fig. 8 despites the result of variation of gas diffusion layer thickness on cell voltage. It was noted that with increasing gas diffusion layer thickness leads to cell losses increasing

11 Int. J. Electroche. Sci., Vol. 5, lead to cell voltage drop. And, it was found that the divergence has been cleared at ohic losses region on polarization as is shown in the figure. There another loss has been affected by variation gas diffusion layer. It is concentration losses, because concentration losses are losses of proton transport which depends on gas diffusion layer. 5. CONCLUSIONS Luped odel for proton exchange ebrane fuel cell has been developed. The luped odel has been validated by published experiental results. Good agreeent has been obtained between luped odel and experiental data. It has been observed that there is sall deviation at higher current density.this deviation is coon in all polarization curve at 1.5 A/c or higher.because the oxygen transport reduced due to the water flooding at cathode at high current density cannot be accounted-for. Beside that, anode drying can also be a contributed factor to the reduce perforance at higher current density. Paraetric and optiization study using this odel has been perfored. The study quantifies the ipact of operating and design paraeters on fuel cell perforance. It was observed that, (1 the voltage of fuel cell has been increased with increasing the input teperature of fuel cell. ( Increasing pressure of gases leads to increase of the voltage and power of cell. (3 At increasing ebrane thickness or gas diffusion layer, the voltage of cell and its power were decreasing. References 1. Shaoduan Ou, Luke E.K. Achenie, Journal of Power Sources, 140 ( Maher A.R.Sadiq Al-Baghdadi,Haroun A.K. Shahad Al-Janabi, Renewable energy, 3 ( J. Arun kuar, P. Kalyani and R. Saravanan, Int. J. Electroche. Sci., 3 ( Balaji Krishnaurthy and S. Deepalochani, Int. J. Electroche. Sci., 4 ( Laurencelle F, Chahine R, Haelin J, Agbossou K, Fournier M, Bose TK, et al. Fuel Cells J, 1 ( Collen Spiegel, PEM Fuel Cell Modeling and Siulation Using Matlab ElSEVIER, Bryan W.Shevock, Sytste level odeling of thereal transients in PEMFC systes, EG&G Services Parsons, Fuel Cell Handbook, 000, fifth edition. 9. Wang L, Husar A, Zhou T, Liu H.,Int J Hydrogen Energy,8(11 ( WANG Rui-in, CAO Guang-yi, ZHU Xin-jian, Journal of Zhejiang University SCIENCE A,006, 5, Phong Thanh Nguyen, Torsten Berning, Ned Djilali, Journal of Power Sources, 130( by ESG (