- Email: [email protected]
Exergy analysis of a PEM fuel cell at variable operating conditions
Energy Conversion and Management 45 (2004) 1949–1961 www.elsevier.com/locate/enconman
Exergy analysis of a PEM fuel cell at variable operating conditions Ayoub Kazim
*
Department of Mechanical Engineering, Faculty of Engineering, United Arab Emirates University, P.O. Box 17555, Al-Ain, United Arab Emirates Received 18 September 2002; received in revised form 24 June 2003; accepted 27 September 2003
Abstract This paper presents a comprehensive exergy analysis of a 10 kW PEM fuel cell at variable operating temperatures, pressures, cell voltages and air stoichiometrics. The calculations of the physical and chemical exergies, mass flow rates and exergetic efficiency are performed at temperature ratios ðT =T0 Þ and pressure ratios ðP =P0 Þ ranging from 1 to 1.25 and 1 to 3, respectively. In addition, the analysis is conducted on fuel cell operating voltages of 0.5 and 0.6 V and at air stoichiometrics of 2, 3 and 4 in order to determine their effects on the efficiency of the fuel cell. The calculated results illustrate the significance of the operating temperature, pressure, cell voltage and air stoichiometry on the exergetic efficiency of the fuel cell. However, it is recommended that the fuel cell should operate at stoichiometric ratios less than 4 in order to maintain the relative humidity level in the product air and to avoid the membrane drying out at high operating temperatures. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: PEM fuel cell; Exergetic efficiency; Chemical exergy; Physical exergy
1. Introduction Determination of an effective utilization of a proton exchange membrane (PEM) fuel cell and measuring its true performance based on thermodynamic laws are considered to be extremely essential. Theoretically, the efficiency of a PEM fuel cell based on the first law of thermodynamics makes no reference to the best possible performance of the fuel cell, and thus, it could be
*
Tel.: +971-3-705-1435; fax: +971-3-762-3158. E-mail address: [email protected] (A. Kazim).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.09.030
1950
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
Nomenclature e E_ m_ W_ h h0 s s0 Cp T T0 P P0 k V R x
total exergy per unit mass, kJ/kg total exergy rate, kW mass flow rate, kg/s electrical energy output rate, kW enthalpy, kJ/kg specific enthalpy at standard conditions, kJ/kg entropy, kJ/kg K specific entropy at standard conditions, kJ/kg K average specific heat, kJ/kg K temperature, K standard temperature, 298.15 K pressure, atm standard pressure, 1 atm specific heat ratio cell voltage, V universal gas constant, 8.314 kJ/kmol K mole fraction
Greek letters e exergetic efficiency k stoichiometry of air Subscript air air hydrogen H2 H2 O water R reactant P product Superscript CH chemical PH physical
misleading. On the other hand, the second law efficiency or exergetic efficiency of a PEM fuel cell, which is the ratio of the electrical output over the maximum possible work output, could give a true measure of the PEM fuel cellÕs performance. Energy analysis performed on a system based on the second law of thermodynamics is known as exergy analysis (availability analysis). Unlike energy, which deals merely with the quantity of energy, exergy deals with both the quantity as well as the quality of energy [1]. The total exergy consists of physical exergy, which is associated with the temperature and pressure of the matter, and chemical exergy, which is associated with the departure of the chemical composition of a system from that of the environment [2].
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1951
Extensive and detailed studies have been conducted on energy and exergy analysis on various types of fuel cells and have demonstrated the significance of the second law efficiency to hydrogen and the fuel cell system processes [3–6]. Other studies analyzed the efficiency of a PEM fuel cell, its economics at various loads [7–9] and its potential applications, especially in transportation [10,11]. Others performed energy and exergy analyses of PEM fuel cell systems with varying degrees of cogeneration in order to seek and develop fuel cell systems with better economic and energy saving characteristics than the conventional systems of power generating plants [12–14]. It should be noted that the above studies were performed without conducting a complete exergy analysis of the fuel cell efficiency taking into consideration all the variations of the fuel cellÕs operational conditions, such as operating pressure and temperature, cell voltages and stoichiometric ratio of air in the electrochemical process. Furthermore, these analyses did not discuss the details of the physical and chemical exergies of the reactants, which are air and hydrogen, and the products, which are water and air, except the works of Oosterkamp et al. [3] and Dincer [5], even though they did not demonstrate the trends of the physical exergies of the reactants and the products against the variable operating temperature and pressure of the fuel cell. Therefore, there is a strong need for conducting an exergy analysis that takes into account all the operational aspects of a fuel cell as well as the trends of the physical exergy of each reacting and producing element in the electrochemical process. The objective of the current study is to perform a comprehensive exergy analysis on a 10 kW PEM fuel developed by Energy Partners Inc. [15]. The analysis will consider both the physical and chemical exergies of all the reactants and the products of the electrochemical process in the fuel cell at variable operating conditions, which are the fuel cell operating temperature and pressure, cell voltage and fuel cell inlet air stoichiometry. Moreover, the overall exergetic efficiency of the electrochemical process of the fuel cell will be determined at variable operating conditions.
2. Mathematical model Exergetic efficiency, which is defined as the second law efficiency, gives the true value of the performance of an energy system from the thermodynamic viewpoint [1–3]. The exergetic efficiency of a fuel cell system, shown in Fig. 1, is the ratio of the power output W_ , over the differences between the exergy of the reactants (air + hydrogen) and the exergy of the products (air + water), which can be determined by the following formula:
Fig. 1. Schematic diagram of fuel cell system.
1952
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
ElectricalOutput ðExergyÞR ðExergyÞP W_ e¼ ðE_ air;R þ E_ H2 ;R Þ ðE_ air;P þ E_ H2 O;P Þ e¼
ð1Þ
where E_ air;R , E_ H2 ;R , E_ air;P and E_ H2 O;P are the total exergies of the reactants, air and fuel (hydrogen), and the products air and water, respectively. Assuming negligible potential and kinetic energy effects on the fuel cell electrochemical process, the total exergy transfer per unit mass of each reactant and product consists of the combination of both physical and chemical exergies [2]: e ¼ eCH þ ePH
ð2Þ
2.1. Physical exergy Physical exergy is associated with the temperature and pressure of the reactants and the products in the fuel cell system. The physical exergy is expressed in terms of the differences of enthalpy from those and entropy from those at standard conditions of temperature and pressure of T0 ¼ 298 K and P0 ¼ 1 atm, respectively. The general expression of the physical exergy can be described as: ePH ¼ ðh h0 Þ T0 ðs s0 Þ
ð3Þ
where h0 and s0 denote the specific enthalpy and entropy evaluated at standard conditions, respectively. The physical exergy of an ideal gas with constant specific heat Cp and specific heat ratio k can be written as: " # k1 k T T P ePH ¼ Cp T0 1 ln ð4Þ þ ln T0 T0 P0 2.2. Chemical exergy The chemical exergy is associated with the departure of the chemical composition of a system from that of the environment. For the sake of simplicity, the chemical exergy considered in the analysis is rather a standard chemical exergy that is based on the standard values of the environmental temperature of T0 ¼ 298 K and pressure of P0 ¼ 1 atm. Generally, these values are in good agreement with the calculated chemical exergy relative to alternative specifications of the environment [2]. Values of the chemical exergies for both the reactants and products are taken from published literature and presented in Table 2. However, the chemical exergy of air produced from the electrochemical reaction should be calculated in terms of the mole fraction of each component in the mixture x using the following equation: X X xn eCH þ RT ð5Þ xn ln xn eCH ¼ 0 n The main reason for using the above chemical exergy equation for the product air is that the mole fractions of mixtures in air would be different than those at the standard condition, especially the
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1953
mole fraction of oxygen that will be reduced as a result of the combination with hydrogen to form water. 2.3. Mass flow rates of the products and the reactants in the fuel cell Depending on the power output W_ and a fuel cell voltage V , and the stoichiometry of air k, the mass flow rates of the reactants and the products in the fuel cell can be easily evaluated from the equations used by Larminie and Dicks [16]. The mass flow rates of the inlet air and fuel, hydrogen, can be evaluated through the following equations: ! kW_ 7 ð6Þ m_ air;R ¼ 3:57 10 V m_ H2 ;R ¼ 1:05 108
W_ V
! ð7Þ
The mass flow rate of the product, air, can be defined as the difference between the amount of oxygen in the electrochemical reaction and the amount of oxygen consumed by reacting with hydrogen to produce water: ! ! _ _ W k W ð8Þ 8:29 108 m_ air;P ¼ 3:57 107 V V The amount of water produced by the fuel cell can be calculated by the following equation: ! _ W ð9Þ m_ H2 O;P ¼ 9:34 108 V Subsequently, the total exergy of the reactants and the products can be determined through the following equations: E_ H2 ;R ¼ m_ H2 ;R eH2 ;R ¼ m_ H2 ;R ðeCH þ ePH ÞH2 ;R
ð10Þ
E_ air;R ¼ m_ air;R eair;R ¼ m_ air;R ðeCH þ ePH Þair;R
ð11Þ
E_ H2 O;P ¼ m_ H2 O;P eH2 O;P ¼ m_ H2 O;P ðeCH þ ePH ÞH2 O;P
ð12Þ
E_ air;P ¼ m_ air;P eair;P ¼ m_ air;P ðeCH þ ePH Þair;P
ð13Þ
At standard atmospheric conditions, the air molal analysis (%) would be: 77.48 N2 , 20.59 O2 , 0.03 CO2 and 1.9 H2 O (g). The calculations of the physical and chemical exergies, mass flow rates and efficiency will be performed at temperature ratios ðT =T0 Þ and pressure ratios ðP =P0 Þ ranging from 1 to 1.25 and 1 to 3, respectively. These ranges of the operating temperature and pressure are specifically to be typical for PEM fuel cells. In addition, the analysis will be conducted on 2 cases, namely at cell voltages of 0.5 and 0.6 V. Moreover, exergetic efficiency calculations will be peformed at air stoichiometries of 2, 3 and 4 and at a cell voltage of 0.5V. The properties of the PEM
1954
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
Table 1 Properties at the standard condition [1,2,15] Property
Value
Standard temperature, T0 Standard pressure, P0 Average specific heat of air, Cp Average specific heat of hydrogen, Cp Specific heat ratio for air and hydrogen, k Enthalpy of water at standard condition, h0 Entropy of water at standard condition, s0 Enthalpy of product air at standard condition, h0 Entropy of product air at standard condition, s0 Electrical energy output, W_ Stoichiometry of air, k
298 K 1 atm 1.005 kJ/kg K 14.3 kJ/kg K 1.4 104.88 kJ/kg 0.3674 kJ/kg K )21,120.0 kJ/kmol 129.17 kJ/kmol K 10 KW 3
Table 2 Chemical exergy and the calculated mass flow rates of the reactants and the products of a PEM fuel cell at cell voltages of 0.5 and 0.6 V [2,16] Reactant/product
Chemical exergy, eCH (kJ/kg)
Mass flow rate at V ¼ 0:5 V, m_ (kg/s)
Mass flow rate at V ¼ 0:6 V, m_ (kg/s)
Reactant––Air Reactant–– Hydrogen Product––Water Product––Air
0 159,138
0.02142 0.00021
0.01785 0.000175
2.5 8.58
0.001868 0.019762
0.001557 0.01647
fuel cell with the specified operating conditions are presented in Table 1. The analysis will be performed on an experimentally tested 10 kW PEM fuel stack developed by Energy Partners Inc. [15]. The fuel cell consists of 40 cells with an active cell area of 780 cm2 , capable of generating 10 kW DC power output at 40% efficiency at 300 kPa and 65 °C [7].
3. Results and discussions The physical exergy of air entering the fuel cell, shown in Fig. 2, ranges from zero at the respective temperature and pressure of 298 K ðT =T0 ¼ 1Þ and 1 atm ðP =P0 ¼ 1Þ to 95 kJ/kg at the respective temperature and pressure of 298 K ðT =T0 ¼ 1Þ and 3 atm ðP =P0 ¼ 3Þ. Furthermore, a 15% increase in the physical exergy of the air can be achieved if the operating temperature is increased from 298 K ðT =T0 ¼ 1Þ to 373 K ðT =T0 ¼ 1:25Þ. In the analysis, air was treated as an ideal gas and Eq. (4) was used to determine its physical exergy. The first two dimensionless terms of the equation represent the thermal and mechanical components of the exergy associated with air, but generally, the physical exergy cannot be represented by these two components. By the same token, the physical exergy of the fuel, hydrogen, entering the fuel cell, shown in Fig. 3, ranges from zero at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 1.350 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3. Again, hydrogen was treated as an ideal gas and Eq. (4)
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1955
Fig. 2. Physical exergy of inlet air.
Fig. 3. Physical exergy of inlet hydrogen.
was used to determine its physical exergy. The trends of both reactant gases are similar with the exception of their magnitude, which is higher in the case of hydrogen than in the case of air due to the higher average specific heat of hydrogen Cp than that of air. In the current analysis, the chemical exergy of reactant air is taken to be zero, since the composition of air at the reference environment is considered as being negligibly different from the actual environment. However, the value of the chemical exergy of hydrogen was estimated to be 159,138 kJ/kg, which is considered the highest of all the reactants and products. These values are consistent with those of Model I, which was illustrated by Bejan [2]. This model represents the standard chemical exergy based on the environmental temperature T0 and pressure P0 , namely at
1956
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
298.15 K and 1 atm. The model attempts to satisfy the equilibrium requirement of thermodynamic theory, and the chemical composition of the gas phase is acceptably approximated to the composition of the natural atmosphere. The physical exergy of the product water leaving the fuel cell ranges from zero at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 160 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3, as depicted in Fig. 4. Depending on the pressure ratio, an increase in the physical exergy of water of at least 3 fold can be achieved if the operating temperature is increased from the standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). Eq. (3) was used to determine the physical exergy of water, with values of enthalpy and entropy taken from available steam and
Fig. 4. Physical exergy of product water.
Fig. 5. Physical exergy of product air.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1957
saturated water tables [1]. With the exception of air, the chemical exergy of the product water is the least among the reactants and products according to Model I (eCH ¼ 2:5 kJ/kg), and it could be neglected in the analysis with a minor percentage of error. The physical exergy of product air leaving the fuel cell, presented in Fig. 5, ranges from 320 kJ/ kg at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 420 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3. In addition, a slight increase in the physical exergy of air, of approximately 2%, could take place if the operating temperature is increased from the standard operating temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). Similar to the product water, Eq. (3) was used to determine the physical exergy of the air. However, the physical exergy of each element contained in the product air mixture (N2 , O2 , CO2 and H2 O (V)) was calculated individually and added later according to their mole fractions in the air mixture. The values of enthalpy and entropy were taken from available properties of ideal gas tables [1]. Similarly, the chemical exergy of air was calculated to be 8.58 kJ/kg, which was determined through summation of the chemical exergies of all the elements in the product air mixture and represented in terms of standard chemical exergy and mole fraction of each element as illustrated in Eq. (5). The differences in exergetic efficiency of a PEM fuel cell tend to be prominent at variable operating pressures and temperatures, as depicted in Fig. 6. This is mainly attributed to the increase in the cell voltage, which is a strong function of the system pressure, in an equation commonly called the ÔNernstÕ equation, which is a function of the Gibbs free energy, the partial pressures of hydrogen and oxygen and the operating temperature, leading to an increase in the system efficiency. For instance, a 2% increase in the exergetic efficiency can be obtained if the operating pressure of the system is increased from P =P0 ¼ 1 to P =P0 ¼ 3. Similarly, a maximum increase in the exergetic efficiency of 2.5% can be achieved if the fuel cell operating temperature is increased from the standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). However, it should be emphasized that it is always recommended to operate PEM fuel cells at lower inlet
Fig. 6. Exergetic efficiency of a PEM cell at variable operating pressure and temperature and at cell voltage of V ¼ 0:5 V.
1958
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
hydrogen pressure in the anode than the inlet air pressure in the cathode in order to enhance the electro-osmotic drag that occurs between the cathode and the anode, resulting in a better fuel cell efficiency. This observation was verified theoretically and experimentally [17]. Variable PEM fuel cell voltages plays a significant role in the exergetic efficiency of the cell operation as depicted in Fig. 7. The lower the cell voltage, the greater is the mass flow rates required for the reactants and the products to operate the fuel cell in order to produce a power output of 10 kW. This will result in a higher magnitude of the difference between the total exergies of the reactants and the products, leading to lower exergetic efficiency. For example, a 7% increase in the efficiency could be acquired if the fuel cell operates at a cell voltage of 0.6 V rather than 0.5 V. Furthermore, the efficiency of a PEM fuel cell can be increased through increasing its operating temperature in spite of its small and low operating temperature range, as opposed to other types of fuel cells that operate at high temperatures, such as solid oxide fuel cells and molten carbonate fuel cells [18]. For instance, a maximum increase in the exergetic efficiency of 2.5% can be achieved if the fuel cell operating temperature is increased from a standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). The calculations of the mass flow rates of the reactants and the products in the electrochemical reaction are performed based on Eqs. (6)–(9) and are presented in Table 2. The difference between the flow rates of the inlet and outlet air represents the amount of oxygen being consumed by combining with hydrogen. The oxygen usage of a PEM fuel cell operating at voltages of V ¼ 0:5 and V ¼ 0:6 V are calculated to be 0.00166 kg/s and 0.00138 kg/s, respectively. Depending on the stoichiometry of air k the efficiency of the fuel cell can be greatly improved if the air stoichiometry is increased because the reactant mass flow rate of air is a strong function of its stoichiometry. In order to demonstrate the relation between the air stoichiometry and the fuel cell exergetic efficiency, an exergy analysis is performed at air stoichiometries of 2 and 4 and at an operating fuel cell voltage of V ¼ 0:5 V and compared against the calculated results at an air stoichiometry of 3 as shown in Fig. 8. Without any doubt, a fuel cell with higher air stoichiometry
Fig. 7. Exergetic efficiency at operating fuel cell voltage V ¼ 0:5 and 0.6 V and ðP =P0 Þ ¼ 1.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1959
Fig. 8. Exergetic efficiency at variable air stoichiometry and at operating fuel cell voltage of V ¼ 0:5 V and ðP =P0 Þ ¼ 1.
has better exergetic efficiency as opposed to lower air stoichiometry. For instance, a 7% improvement in the fuel cell efficiency could be achieved if the air stoichiometry in the fuel cell is switched from 2 to 4. However, one should be extremely careful in setting up the air stoichiometry greater than the recommended range, which is between 2 and 4. This is because, at high fuel cell operating temperature and air stoichiometry, the relative humidity of the exit air will be lowered, leading to a higher risk for the cells to dry out and a sharp decrease in the efficiency of the fuel cell could take place [16,19]. A general remark can be made regarding the limited and small range of variation in the exergetic efficiency of the fuel cell with respect to variations in the fuel cell operating conditions. This limited range of variation is mainly attributed to the consistency of the physical exergies of the products and reactants that follow similar trends with increasing or decreasing the fuel cell operating conditions, even though they differ in magnitudes. Hence, a minor difference of the total exergy between the reactants and the products occurs, resulting in a minor variation in the exergetic efficiency. Nevertheless, it should be emphasized that the general calculated results at various fuel cell operating conditions are consistent with the theoretical and experimental results demonstrated in published works. For instance, a higher cell voltage can be attained as a result of a higher operating temperature or pressure as demonstrated by Bernardi and Verbrugge [17] and Kazim et al. [20], leading to a higher power output. Consequently, a greater fuel cell exergetic efficiency is achieved, since the cell efficiency is directly proportional to the cell power output as illustrated in Eq. (1). Furthermore, greater cell voltage and exergetic efficiency are achieved through a higher stoichiometric ratio, which is also demonstrated by Buchi and Srinivasan [19].
4. Conclusion Exergy analysis of a proton exchange membrane fuel cell (PEM) is conducted at variable operating temperatures, pressures, cell voltages and air stoichiometry. In the analysis, the exergetic
1960
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
efficiency of a fuel cell system is determined in terms of the ratio of the power output of the fuel cell over the differences between the total exergies of the reactants and products of the fuel cell electrochemical process. The total exergy of the reactants and the products consist of both physical and chemical exergies, which are calculated for each element in the electrochemical process. From the current results, a general conclusion could be drawn concerning the fuel cell exergetic efficiency, which can be improved significantly by adopting any or a combination of the four operational measures. Firstly, the exergetic efficiency of a PEM fuel cell can be improved by having a higher operating pressure. However, a high pressure difference between the cathode and the anode is recommended in order to enhance the electro-osmotic drag phenomena between the two electrodes. Secondly, the efficiency of the fuel cell can be increased through increasing the fuel cell operating temperature in spite of the small and low temperature range of a PEM fuel cell as opposed to other types of fuel cells that operate at high temperatures. Thirdly, higher exergetic efficiency could be attained if the fuel cell operates at relatively higher cell voltages that would require less mass flow rates for the reactants and the products to achieve a high electrical output. Fourthly, by having a high air stoichiometry, a significant increase in the efficiency of the fuel cell can be achieved, although it would be recommended to have an air stoichiometry in the range between 2 and 4 in order to maintain the relative humidity level in the product air and avoid the fuel cell membrane drying out at high operating temperatures. References [1] Cengel Y, Boles M. Thermodynamics––an engineering approach. 2nd ed. Mc Graw-Hill, Inc.; 1994. [2] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. John Wiley & Sons, LTD; 1996. [3] Oosterkamp PF, Goorse AA, Blomen LJ. Review of an energy and exergy analysis of a fuel cell system. J Power Sources 1993;41:239–52. [4] Rosen MA, Scott DS. An energy-exergy analysis of the Koppers–Totzek process for producing hydrogen from coal. Int J Hydrogen Energy 1987;12:837–45. [5] Dincer I. Technical, environmental and exergetic aspects of hydrogen energy systems. Int J Hydrogen Energy 2002;27(3):265–85. [6] Dunbar W, Lior N, Gaggioli R. Combining fuel cells with fuel-fired power plants. Energy Int J 1991;16:1259–74. [7] Barbir F, Gomez T. Efficiency and economics of proton exchange membrane (PEM) fuel cells. Int J Hydrogen Energy 1996;21(10):891–901. [8] Kazim A. A novel approach on the determination of the minimal operating efficiency of a PEM fuel cell. Renew Energy 2002;26(3):479–88. [9] Johnson R, Morgan C, Witmer D, Johnson T. Performance of a proton exchange membrane fuel cell stack. Int J Hydrogen Energy 2001;26(8):879–87. [10] Cowanden R, Nahon M, Rosen M. Modeling and analysis of a solid polymer fuel cell system for transportation applications. Int J Hydrogen Energy 2001;26(6):615–23. [11] Cowanden R, Nahon M, Rosen M. Exergy analysis of a fuel cell power system for transportation applications. Exergy Int J 2001;1(2):112–21. [12] Rosen MA, Scott DS. A thermodynamic investigation of the potential for cogeneration for fuel cells. Int J Hydrogen Energy 1988;13(12):775–82. [13] Rosen MA. Comparison based on energy and exergy analyses of the potential cogeneration efficiencies for fuel cells and other electricity generation devices. Int J Hydrogen Energy 1990;15(4):267–74. [14] Matsumoto Y, Yokoyama R, Ito K. Engineering-economic optimization of a fuel cell cogeneration plant. J Eng Gas Turbines Power––Trans ASME 1994;116:8–14.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1961
[15] Barbir F. Progress in PEM fuel cell system development. In: Yurum Y, editor. Hydrogen energy system. NATO ASI Series E, vol. 295, 1995. p. 203–13. [16] Larminie J, Dicks A. Fuel cell systems explained. John Wiley & Sons, LTD; 2001. [17] Bernardi DM, Verbrugge MW. A mathematical model of the solid-polymer-electrolyte fuel cell. J Electrochem Soc 1992;140:2767–72. [18] Hirschenhofer JH, Stauffer DB, Engelman RR, Kilett MG. Fuel cell handbook. 4th ed. Parsons Corporation, US Dept. of Energy report no. 1998; DOE/FETC-99/1076. [19] Buchi FN, Srinivasan S. Operating proton exchange membrane fuel cells without external humidification of the reactant gases. Fundamental aspects. J Electrochem Soc 1997;144(8):2767–72. [20] Kazim A, Liu HT, Forges P. Effects of the variable cathode operating conditions on the performance of PEM fuel cell with interdigitated flow fields. Int J Energy Res 2003;27(4):401–14.
Exergy analysis of a PEM fuel cell at variable operating conditions Ayoub Kazim
*
Department of Mechanical Engineering, Faculty of Engineering, United Arab Emirates University, P.O. Box 17555, Al-Ain, United Arab Emirates Received 18 September 2002; received in revised form 24 June 2003; accepted 27 September 2003
Abstract This paper presents a comprehensive exergy analysis of a 10 kW PEM fuel cell at variable operating temperatures, pressures, cell voltages and air stoichiometrics. The calculations of the physical and chemical exergies, mass flow rates and exergetic efficiency are performed at temperature ratios ðT =T0 Þ and pressure ratios ðP =P0 Þ ranging from 1 to 1.25 and 1 to 3, respectively. In addition, the analysis is conducted on fuel cell operating voltages of 0.5 and 0.6 V and at air stoichiometrics of 2, 3 and 4 in order to determine their effects on the efficiency of the fuel cell. The calculated results illustrate the significance of the operating temperature, pressure, cell voltage and air stoichiometry on the exergetic efficiency of the fuel cell. However, it is recommended that the fuel cell should operate at stoichiometric ratios less than 4 in order to maintain the relative humidity level in the product air and to avoid the membrane drying out at high operating temperatures. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: PEM fuel cell; Exergetic efficiency; Chemical exergy; Physical exergy
1. Introduction Determination of an effective utilization of a proton exchange membrane (PEM) fuel cell and measuring its true performance based on thermodynamic laws are considered to be extremely essential. Theoretically, the efficiency of a PEM fuel cell based on the first law of thermodynamics makes no reference to the best possible performance of the fuel cell, and thus, it could be
*
Tel.: +971-3-705-1435; fax: +971-3-762-3158. E-mail address: [email protected] (A. Kazim).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.09.030
1950
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
Nomenclature e E_ m_ W_ h h0 s s0 Cp T T0 P P0 k V R x
total exergy per unit mass, kJ/kg total exergy rate, kW mass flow rate, kg/s electrical energy output rate, kW enthalpy, kJ/kg specific enthalpy at standard conditions, kJ/kg entropy, kJ/kg K specific entropy at standard conditions, kJ/kg K average specific heat, kJ/kg K temperature, K standard temperature, 298.15 K pressure, atm standard pressure, 1 atm specific heat ratio cell voltage, V universal gas constant, 8.314 kJ/kmol K mole fraction
Greek letters e exergetic efficiency k stoichiometry of air Subscript air air hydrogen H2 H2 O water R reactant P product Superscript CH chemical PH physical
misleading. On the other hand, the second law efficiency or exergetic efficiency of a PEM fuel cell, which is the ratio of the electrical output over the maximum possible work output, could give a true measure of the PEM fuel cellÕs performance. Energy analysis performed on a system based on the second law of thermodynamics is known as exergy analysis (availability analysis). Unlike energy, which deals merely with the quantity of energy, exergy deals with both the quantity as well as the quality of energy [1]. The total exergy consists of physical exergy, which is associated with the temperature and pressure of the matter, and chemical exergy, which is associated with the departure of the chemical composition of a system from that of the environment [2].
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1951
Extensive and detailed studies have been conducted on energy and exergy analysis on various types of fuel cells and have demonstrated the significance of the second law efficiency to hydrogen and the fuel cell system processes [3–6]. Other studies analyzed the efficiency of a PEM fuel cell, its economics at various loads [7–9] and its potential applications, especially in transportation [10,11]. Others performed energy and exergy analyses of PEM fuel cell systems with varying degrees of cogeneration in order to seek and develop fuel cell systems with better economic and energy saving characteristics than the conventional systems of power generating plants [12–14]. It should be noted that the above studies were performed without conducting a complete exergy analysis of the fuel cell efficiency taking into consideration all the variations of the fuel cellÕs operational conditions, such as operating pressure and temperature, cell voltages and stoichiometric ratio of air in the electrochemical process. Furthermore, these analyses did not discuss the details of the physical and chemical exergies of the reactants, which are air and hydrogen, and the products, which are water and air, except the works of Oosterkamp et al. [3] and Dincer [5], even though they did not demonstrate the trends of the physical exergies of the reactants and the products against the variable operating temperature and pressure of the fuel cell. Therefore, there is a strong need for conducting an exergy analysis that takes into account all the operational aspects of a fuel cell as well as the trends of the physical exergy of each reacting and producing element in the electrochemical process. The objective of the current study is to perform a comprehensive exergy analysis on a 10 kW PEM fuel developed by Energy Partners Inc. [15]. The analysis will consider both the physical and chemical exergies of all the reactants and the products of the electrochemical process in the fuel cell at variable operating conditions, which are the fuel cell operating temperature and pressure, cell voltage and fuel cell inlet air stoichiometry. Moreover, the overall exergetic efficiency of the electrochemical process of the fuel cell will be determined at variable operating conditions.
2. Mathematical model Exergetic efficiency, which is defined as the second law efficiency, gives the true value of the performance of an energy system from the thermodynamic viewpoint [1–3]. The exergetic efficiency of a fuel cell system, shown in Fig. 1, is the ratio of the power output W_ , over the differences between the exergy of the reactants (air + hydrogen) and the exergy of the products (air + water), which can be determined by the following formula:
Fig. 1. Schematic diagram of fuel cell system.
1952
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
ElectricalOutput ðExergyÞR ðExergyÞP W_ e¼ ðE_ air;R þ E_ H2 ;R Þ ðE_ air;P þ E_ H2 O;P Þ e¼
ð1Þ
where E_ air;R , E_ H2 ;R , E_ air;P and E_ H2 O;P are the total exergies of the reactants, air and fuel (hydrogen), and the products air and water, respectively. Assuming negligible potential and kinetic energy effects on the fuel cell electrochemical process, the total exergy transfer per unit mass of each reactant and product consists of the combination of both physical and chemical exergies [2]: e ¼ eCH þ ePH
ð2Þ
2.1. Physical exergy Physical exergy is associated with the temperature and pressure of the reactants and the products in the fuel cell system. The physical exergy is expressed in terms of the differences of enthalpy from those and entropy from those at standard conditions of temperature and pressure of T0 ¼ 298 K and P0 ¼ 1 atm, respectively. The general expression of the physical exergy can be described as: ePH ¼ ðh h0 Þ T0 ðs s0 Þ
ð3Þ
where h0 and s0 denote the specific enthalpy and entropy evaluated at standard conditions, respectively. The physical exergy of an ideal gas with constant specific heat Cp and specific heat ratio k can be written as: " # k1 k T T P ePH ¼ Cp T0 1 ln ð4Þ þ ln T0 T0 P0 2.2. Chemical exergy The chemical exergy is associated with the departure of the chemical composition of a system from that of the environment. For the sake of simplicity, the chemical exergy considered in the analysis is rather a standard chemical exergy that is based on the standard values of the environmental temperature of T0 ¼ 298 K and pressure of P0 ¼ 1 atm. Generally, these values are in good agreement with the calculated chemical exergy relative to alternative specifications of the environment [2]. Values of the chemical exergies for both the reactants and products are taken from published literature and presented in Table 2. However, the chemical exergy of air produced from the electrochemical reaction should be calculated in terms of the mole fraction of each component in the mixture x using the following equation: X X xn eCH þ RT ð5Þ xn ln xn eCH ¼ 0 n The main reason for using the above chemical exergy equation for the product air is that the mole fractions of mixtures in air would be different than those at the standard condition, especially the
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1953
mole fraction of oxygen that will be reduced as a result of the combination with hydrogen to form water. 2.3. Mass flow rates of the products and the reactants in the fuel cell Depending on the power output W_ and a fuel cell voltage V , and the stoichiometry of air k, the mass flow rates of the reactants and the products in the fuel cell can be easily evaluated from the equations used by Larminie and Dicks [16]. The mass flow rates of the inlet air and fuel, hydrogen, can be evaluated through the following equations: ! kW_ 7 ð6Þ m_ air;R ¼ 3:57 10 V m_ H2 ;R ¼ 1:05 108
W_ V
! ð7Þ
The mass flow rate of the product, air, can be defined as the difference between the amount of oxygen in the electrochemical reaction and the amount of oxygen consumed by reacting with hydrogen to produce water: ! ! _ _ W k W ð8Þ 8:29 108 m_ air;P ¼ 3:57 107 V V The amount of water produced by the fuel cell can be calculated by the following equation: ! _ W ð9Þ m_ H2 O;P ¼ 9:34 108 V Subsequently, the total exergy of the reactants and the products can be determined through the following equations: E_ H2 ;R ¼ m_ H2 ;R eH2 ;R ¼ m_ H2 ;R ðeCH þ ePH ÞH2 ;R
ð10Þ
E_ air;R ¼ m_ air;R eair;R ¼ m_ air;R ðeCH þ ePH Þair;R
ð11Þ
E_ H2 O;P ¼ m_ H2 O;P eH2 O;P ¼ m_ H2 O;P ðeCH þ ePH ÞH2 O;P
ð12Þ
E_ air;P ¼ m_ air;P eair;P ¼ m_ air;P ðeCH þ ePH Þair;P
ð13Þ
At standard atmospheric conditions, the air molal analysis (%) would be: 77.48 N2 , 20.59 O2 , 0.03 CO2 and 1.9 H2 O (g). The calculations of the physical and chemical exergies, mass flow rates and efficiency will be performed at temperature ratios ðT =T0 Þ and pressure ratios ðP =P0 Þ ranging from 1 to 1.25 and 1 to 3, respectively. These ranges of the operating temperature and pressure are specifically to be typical for PEM fuel cells. In addition, the analysis will be conducted on 2 cases, namely at cell voltages of 0.5 and 0.6 V. Moreover, exergetic efficiency calculations will be peformed at air stoichiometries of 2, 3 and 4 and at a cell voltage of 0.5V. The properties of the PEM
1954
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
Table 1 Properties at the standard condition [1,2,15] Property
Value
Standard temperature, T0 Standard pressure, P0 Average specific heat of air, Cp Average specific heat of hydrogen, Cp Specific heat ratio for air and hydrogen, k Enthalpy of water at standard condition, h0 Entropy of water at standard condition, s0 Enthalpy of product air at standard condition, h0 Entropy of product air at standard condition, s0 Electrical energy output, W_ Stoichiometry of air, k
298 K 1 atm 1.005 kJ/kg K 14.3 kJ/kg K 1.4 104.88 kJ/kg 0.3674 kJ/kg K )21,120.0 kJ/kmol 129.17 kJ/kmol K 10 KW 3
Table 2 Chemical exergy and the calculated mass flow rates of the reactants and the products of a PEM fuel cell at cell voltages of 0.5 and 0.6 V [2,16] Reactant/product
Chemical exergy, eCH (kJ/kg)
Mass flow rate at V ¼ 0:5 V, m_ (kg/s)
Mass flow rate at V ¼ 0:6 V, m_ (kg/s)
Reactant––Air Reactant–– Hydrogen Product––Water Product––Air
0 159,138
0.02142 0.00021
0.01785 0.000175
2.5 8.58
0.001868 0.019762
0.001557 0.01647
fuel cell with the specified operating conditions are presented in Table 1. The analysis will be performed on an experimentally tested 10 kW PEM fuel stack developed by Energy Partners Inc. [15]. The fuel cell consists of 40 cells with an active cell area of 780 cm2 , capable of generating 10 kW DC power output at 40% efficiency at 300 kPa and 65 °C [7].
3. Results and discussions The physical exergy of air entering the fuel cell, shown in Fig. 2, ranges from zero at the respective temperature and pressure of 298 K ðT =T0 ¼ 1Þ and 1 atm ðP =P0 ¼ 1Þ to 95 kJ/kg at the respective temperature and pressure of 298 K ðT =T0 ¼ 1Þ and 3 atm ðP =P0 ¼ 3Þ. Furthermore, a 15% increase in the physical exergy of the air can be achieved if the operating temperature is increased from 298 K ðT =T0 ¼ 1Þ to 373 K ðT =T0 ¼ 1:25Þ. In the analysis, air was treated as an ideal gas and Eq. (4) was used to determine its physical exergy. The first two dimensionless terms of the equation represent the thermal and mechanical components of the exergy associated with air, but generally, the physical exergy cannot be represented by these two components. By the same token, the physical exergy of the fuel, hydrogen, entering the fuel cell, shown in Fig. 3, ranges from zero at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 1.350 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3. Again, hydrogen was treated as an ideal gas and Eq. (4)
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1955
Fig. 2. Physical exergy of inlet air.
Fig. 3. Physical exergy of inlet hydrogen.
was used to determine its physical exergy. The trends of both reactant gases are similar with the exception of their magnitude, which is higher in the case of hydrogen than in the case of air due to the higher average specific heat of hydrogen Cp than that of air. In the current analysis, the chemical exergy of reactant air is taken to be zero, since the composition of air at the reference environment is considered as being negligibly different from the actual environment. However, the value of the chemical exergy of hydrogen was estimated to be 159,138 kJ/kg, which is considered the highest of all the reactants and products. These values are consistent with those of Model I, which was illustrated by Bejan [2]. This model represents the standard chemical exergy based on the environmental temperature T0 and pressure P0 , namely at
1956
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
298.15 K and 1 atm. The model attempts to satisfy the equilibrium requirement of thermodynamic theory, and the chemical composition of the gas phase is acceptably approximated to the composition of the natural atmosphere. The physical exergy of the product water leaving the fuel cell ranges from zero at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 160 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3, as depicted in Fig. 4. Depending on the pressure ratio, an increase in the physical exergy of water of at least 3 fold can be achieved if the operating temperature is increased from the standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). Eq. (3) was used to determine the physical exergy of water, with values of enthalpy and entropy taken from available steam and
Fig. 4. Physical exergy of product water.
Fig. 5. Physical exergy of product air.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1957
saturated water tables [1]. With the exception of air, the chemical exergy of the product water is the least among the reactants and products according to Model I (eCH ¼ 2:5 kJ/kg), and it could be neglected in the analysis with a minor percentage of error. The physical exergy of product air leaving the fuel cell, presented in Fig. 5, ranges from 320 kJ/ kg at the respective temperature and pressure ratios of T =T0 ¼ 1 and P =P0 ¼ 1 to 420 kJ/kg at T =T0 ¼ 1 and P =P0 ¼ 3. In addition, a slight increase in the physical exergy of air, of approximately 2%, could take place if the operating temperature is increased from the standard operating temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). Similar to the product water, Eq. (3) was used to determine the physical exergy of the air. However, the physical exergy of each element contained in the product air mixture (N2 , O2 , CO2 and H2 O (V)) was calculated individually and added later according to their mole fractions in the air mixture. The values of enthalpy and entropy were taken from available properties of ideal gas tables [1]. Similarly, the chemical exergy of air was calculated to be 8.58 kJ/kg, which was determined through summation of the chemical exergies of all the elements in the product air mixture and represented in terms of standard chemical exergy and mole fraction of each element as illustrated in Eq. (5). The differences in exergetic efficiency of a PEM fuel cell tend to be prominent at variable operating pressures and temperatures, as depicted in Fig. 6. This is mainly attributed to the increase in the cell voltage, which is a strong function of the system pressure, in an equation commonly called the ÔNernstÕ equation, which is a function of the Gibbs free energy, the partial pressures of hydrogen and oxygen and the operating temperature, leading to an increase in the system efficiency. For instance, a 2% increase in the exergetic efficiency can be obtained if the operating pressure of the system is increased from P =P0 ¼ 1 to P =P0 ¼ 3. Similarly, a maximum increase in the exergetic efficiency of 2.5% can be achieved if the fuel cell operating temperature is increased from the standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). However, it should be emphasized that it is always recommended to operate PEM fuel cells at lower inlet
Fig. 6. Exergetic efficiency of a PEM cell at variable operating pressure and temperature and at cell voltage of V ¼ 0:5 V.
1958
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
hydrogen pressure in the anode than the inlet air pressure in the cathode in order to enhance the electro-osmotic drag that occurs between the cathode and the anode, resulting in a better fuel cell efficiency. This observation was verified theoretically and experimentally [17]. Variable PEM fuel cell voltages plays a significant role in the exergetic efficiency of the cell operation as depicted in Fig. 7. The lower the cell voltage, the greater is the mass flow rates required for the reactants and the products to operate the fuel cell in order to produce a power output of 10 kW. This will result in a higher magnitude of the difference between the total exergies of the reactants and the products, leading to lower exergetic efficiency. For example, a 7% increase in the efficiency could be acquired if the fuel cell operates at a cell voltage of 0.6 V rather than 0.5 V. Furthermore, the efficiency of a PEM fuel cell can be increased through increasing its operating temperature in spite of its small and low operating temperature range, as opposed to other types of fuel cells that operate at high temperatures, such as solid oxide fuel cells and molten carbonate fuel cells [18]. For instance, a maximum increase in the exergetic efficiency of 2.5% can be achieved if the fuel cell operating temperature is increased from a standard temperature of 298 K (T =T0 ¼ 1) to 373 K (T =T0 ¼ 1:25). The calculations of the mass flow rates of the reactants and the products in the electrochemical reaction are performed based on Eqs. (6)–(9) and are presented in Table 2. The difference between the flow rates of the inlet and outlet air represents the amount of oxygen being consumed by combining with hydrogen. The oxygen usage of a PEM fuel cell operating at voltages of V ¼ 0:5 and V ¼ 0:6 V are calculated to be 0.00166 kg/s and 0.00138 kg/s, respectively. Depending on the stoichiometry of air k the efficiency of the fuel cell can be greatly improved if the air stoichiometry is increased because the reactant mass flow rate of air is a strong function of its stoichiometry. In order to demonstrate the relation between the air stoichiometry and the fuel cell exergetic efficiency, an exergy analysis is performed at air stoichiometries of 2 and 4 and at an operating fuel cell voltage of V ¼ 0:5 V and compared against the calculated results at an air stoichiometry of 3 as shown in Fig. 8. Without any doubt, a fuel cell with higher air stoichiometry
Fig. 7. Exergetic efficiency at operating fuel cell voltage V ¼ 0:5 and 0.6 V and ðP =P0 Þ ¼ 1.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1959
Fig. 8. Exergetic efficiency at variable air stoichiometry and at operating fuel cell voltage of V ¼ 0:5 V and ðP =P0 Þ ¼ 1.
has better exergetic efficiency as opposed to lower air stoichiometry. For instance, a 7% improvement in the fuel cell efficiency could be achieved if the air stoichiometry in the fuel cell is switched from 2 to 4. However, one should be extremely careful in setting up the air stoichiometry greater than the recommended range, which is between 2 and 4. This is because, at high fuel cell operating temperature and air stoichiometry, the relative humidity of the exit air will be lowered, leading to a higher risk for the cells to dry out and a sharp decrease in the efficiency of the fuel cell could take place [16,19]. A general remark can be made regarding the limited and small range of variation in the exergetic efficiency of the fuel cell with respect to variations in the fuel cell operating conditions. This limited range of variation is mainly attributed to the consistency of the physical exergies of the products and reactants that follow similar trends with increasing or decreasing the fuel cell operating conditions, even though they differ in magnitudes. Hence, a minor difference of the total exergy between the reactants and the products occurs, resulting in a minor variation in the exergetic efficiency. Nevertheless, it should be emphasized that the general calculated results at various fuel cell operating conditions are consistent with the theoretical and experimental results demonstrated in published works. For instance, a higher cell voltage can be attained as a result of a higher operating temperature or pressure as demonstrated by Bernardi and Verbrugge [17] and Kazim et al. [20], leading to a higher power output. Consequently, a greater fuel cell exergetic efficiency is achieved, since the cell efficiency is directly proportional to the cell power output as illustrated in Eq. (1). Furthermore, greater cell voltage and exergetic efficiency are achieved through a higher stoichiometric ratio, which is also demonstrated by Buchi and Srinivasan [19].
4. Conclusion Exergy analysis of a proton exchange membrane fuel cell (PEM) is conducted at variable operating temperatures, pressures, cell voltages and air stoichiometry. In the analysis, the exergetic
1960
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
efficiency of a fuel cell system is determined in terms of the ratio of the power output of the fuel cell over the differences between the total exergies of the reactants and products of the fuel cell electrochemical process. The total exergy of the reactants and the products consist of both physical and chemical exergies, which are calculated for each element in the electrochemical process. From the current results, a general conclusion could be drawn concerning the fuel cell exergetic efficiency, which can be improved significantly by adopting any or a combination of the four operational measures. Firstly, the exergetic efficiency of a PEM fuel cell can be improved by having a higher operating pressure. However, a high pressure difference between the cathode and the anode is recommended in order to enhance the electro-osmotic drag phenomena between the two electrodes. Secondly, the efficiency of the fuel cell can be increased through increasing the fuel cell operating temperature in spite of the small and low temperature range of a PEM fuel cell as opposed to other types of fuel cells that operate at high temperatures. Thirdly, higher exergetic efficiency could be attained if the fuel cell operates at relatively higher cell voltages that would require less mass flow rates for the reactants and the products to achieve a high electrical output. Fourthly, by having a high air stoichiometry, a significant increase in the efficiency of the fuel cell can be achieved, although it would be recommended to have an air stoichiometry in the range between 2 and 4 in order to maintain the relative humidity level in the product air and avoid the fuel cell membrane drying out at high operating temperatures. References [1] Cengel Y, Boles M. Thermodynamics––an engineering approach. 2nd ed. Mc Graw-Hill, Inc.; 1994. [2] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. John Wiley & Sons, LTD; 1996. [3] Oosterkamp PF, Goorse AA, Blomen LJ. Review of an energy and exergy analysis of a fuel cell system. J Power Sources 1993;41:239–52. [4] Rosen MA, Scott DS. An energy-exergy analysis of the Koppers–Totzek process for producing hydrogen from coal. Int J Hydrogen Energy 1987;12:837–45. [5] Dincer I. Technical, environmental and exergetic aspects of hydrogen energy systems. Int J Hydrogen Energy 2002;27(3):265–85. [6] Dunbar W, Lior N, Gaggioli R. Combining fuel cells with fuel-fired power plants. Energy Int J 1991;16:1259–74. [7] Barbir F, Gomez T. Efficiency and economics of proton exchange membrane (PEM) fuel cells. Int J Hydrogen Energy 1996;21(10):891–901. [8] Kazim A. A novel approach on the determination of the minimal operating efficiency of a PEM fuel cell. Renew Energy 2002;26(3):479–88. [9] Johnson R, Morgan C, Witmer D, Johnson T. Performance of a proton exchange membrane fuel cell stack. Int J Hydrogen Energy 2001;26(8):879–87. [10] Cowanden R, Nahon M, Rosen M. Modeling and analysis of a solid polymer fuel cell system for transportation applications. Int J Hydrogen Energy 2001;26(6):615–23. [11] Cowanden R, Nahon M, Rosen M. Exergy analysis of a fuel cell power system for transportation applications. Exergy Int J 2001;1(2):112–21. [12] Rosen MA, Scott DS. A thermodynamic investigation of the potential for cogeneration for fuel cells. Int J Hydrogen Energy 1988;13(12):775–82. [13] Rosen MA. Comparison based on energy and exergy analyses of the potential cogeneration efficiencies for fuel cells and other electricity generation devices. Int J Hydrogen Energy 1990;15(4):267–74. [14] Matsumoto Y, Yokoyama R, Ito K. Engineering-economic optimization of a fuel cell cogeneration plant. J Eng Gas Turbines Power––Trans ASME 1994;116:8–14.
A. Kazim / Energy Conversion and Management 45 (2004) 1949–1961
1961
[15] Barbir F. Progress in PEM fuel cell system development. In: Yurum Y, editor. Hydrogen energy system. NATO ASI Series E, vol. 295, 1995. p. 203–13. [16] Larminie J, Dicks A. Fuel cell systems explained. John Wiley & Sons, LTD; 2001. [17] Bernardi DM, Verbrugge MW. A mathematical model of the solid-polymer-electrolyte fuel cell. J Electrochem Soc 1992;140:2767–72. [18] Hirschenhofer JH, Stauffer DB, Engelman RR, Kilett MG. Fuel cell handbook. 4th ed. Parsons Corporation, US Dept. of Energy report no. 1998; DOE/FETC-99/1076. [19] Buchi FN, Srinivasan S. Operating proton exchange membrane fuel cells without external humidification of the reactant gases. Fundamental aspects. J Electrochem Soc 1997;144(8):2767–72. [20] Kazim A, Liu HT, Forges P. Effects of the variable cathode operating conditions on the performance of PEM fuel cell with interdigitated flow fields. Int J Energy Res 2003;27(4):401–14.