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shown in Fig. 1, liquid water is fed to the PEM electrolyzer at ambient temperature. Liquid water enters a heat exchanger that brings it to the PEM electrolyzer temperature and it then enters the electrolyzer. Leaving the cathode, the H2 produced dissipates heat to the environment and cools to the reference environment temperature. The oxygen gas produced at the anode is separated from the water and oxygen mixture and then cooled to the reference environment temperature. The remaining water is then returned to the water supply stream for the next hydrogen production cycle. The overall PEM electrolysis reaction is simply water splitting, i.e., electricity and heat are used to separate water into produce hydrogen and oxygen. Hydrogen is stored in a tank for later usage. 2.1.3.1. Thermochemical modeling of a PEM electrolyzer. Energy and exergy analyses of a PEM electrolyzer can be per- formed in conjunction the electrochemical modeling. The total energy needed by the electrolyzer can be obtained noting: DH1⁄4DGþTDS (20) where DG is Gibb’s free energy and TDS is the thermal energy requirement. The values of G, S, and H for hydrogen, oxygen and water can be obtained from thermodynamic tables [24]. The total energy need is the theoretical energy required for H2O electrolysis without any losses. The catalyst used in PEM electrolysis provides an alternative path for the reaction with lower activation energy. The mass flow rate of hydrogen is determined by [25]: where x is the distance in the membrane measured from the cathode-membrane interface and lðxÞ is the water content at a location x in the membrane. The value of lðxÞ can be calculated in terms of the water content at the membrane- electrode edges: lðxÞ1⁄4 la lc xþlc (26) D where D is the membrane thickness, and la and lc are the water contents at the anode-membrane and the cathode- membrane interfaces, respectively. The overall ohmic resis- tance can thus be expressed as [25]: ZD dx N_ H2 ;out 1⁄4 J 2F 1⁄4 N_ H2 O;reacted (21) Vohm;PEM 1⁄4 JRPEM (28) The activation overpotential, Vact, caused by a deviation of net current from its equilibrium, and also an electron transfer reaction, must be differentiated from the concentration of the oxidized and reduced species [25,26]. Then, Vact;i 1⁄4RTsinh1 J ; i1⁄4a;c (29) F 2J0;i here, J0 is the exchange current density, which is an important parameter in calculating the activation overpotential. It characterizes the electrode’s capabilities in the electro- chemical reaction. A high exchange current density implies a high reactivity of the electrode, which results in a lower overpotential. The exchange current density for electrolysis can be expressed as [26]: (30) where J is the current density and F is the Faraday constant. The electric energy input rate to the electrolyzer can be expressed as: Eelectric 1⁄4 JV (22) where Eelectric is the electric energy input and Exelectric the electric exergy input. Also, V is given as: V 1⁄4 V0 þ Vact;a þ Vact;c þ Vohm (23) where V0 is the reversible potential, which is related to the difference in free energy between reactants and products, and V0 can be obtained by the Nernst equation as follows: V0 1⁄4 1:229 8:5 104 ðTPEM 298Þ (24) Also, Vact;a, Vact;c and Vohm are the activation overpotential of the anode, the activation overpotential of the cathode, and the ohmic overpotential of the electrolyte, respectively. Ohmic overpotential in the proton exchange membrane is caused by the resistance of the membrane to the hydrogen ions trans- porting through it. The ionic resistance of the membrane depends on the degree of humidification and thickness of the membrane as well as the membrane temperature [26]. The local ionic conductivity sðxÞ of the proton exchange membrane can be expressed as [25,26]: 1 1! sPEM 1⁄2lðxÞ 1⁄4 1⁄20:5139lðxÞ 0:326exp 1268 303 T (25) E J 1⁄4Jrefexp act;i ; i1⁄4a;c Author's personal copy international journal of hydrogen energy 38 (2013) 1795e1805 1799 RPEM 1⁄4 Based on Ohm’s law, the following equation can be written sPEM1⁄2lðxÞ (27) for the ohmic overpotential: 0 0;ii RT where Jref is the pre-exponential factor and E is the acti- vation energy for the anode and cathode. More details about i act;i PEM electrolysis modeling can be found elsewhere [26, 27]. 3. Exergy analysis Exergy analysis can help to develop strategies and guidelines for more effective use of energy, and has been applied to various thermal processes, including power generation, CHP and trigeneration. Exergy can be divided into four compo- nents: physical, chemical, kinetic and potential. For the processes involved in this study, the latter two are neglected since changes in elevation and speed are negligible [28,29]. Physical exergy is defined as the maximum work obtainable as a system interacts with a reference environment at an equi- librium state [21,22]. Chemical exergy is associated with the departure of the chemical composition of a system from the chemical equilibrium of a reference environment. Chemical exergy is important in combustion evaluation. Applying the first and the second laws of thermodynamics, the following exergy balance for each component is obtained:PDF Image | H2 Energy
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