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depends on the degree of humidification and thickness of the membrane as well as the membrane temperature. The local ionic conductivity ( ) of the proton exchange membrane is expressed as [100]: () () [ ( )] (5.69) where is the distance into the membrane measured from the cathode-membrane interface and ( ) is the water content at a location in the membrane. The value of ( ) can be calculated in terms of the water content at the membrane-electrode edges: ( ) (5.70) Here, is the membrane thickness, and and are the water contents at the anode-membrane and the cathode-membrane interfaces, respectively. The overall ohmic resistance can thus be expressed as [100]: ∫ () (5.71) Based on the Ohm’s law, the following equation can be written for the ohmic overpotential: (5.72) The activation overpotential, , caused by a deviation of net current from its equilibrium and an electron transfer reaction, must be differentiated from the concentration of the oxidized and reduced species. Then, sinh-1 ( ) (5.73) Here, is the exchange current density, which is an important parameter in calculating the activation overpotential. It characterizes the electrode’s capabilities in the electrochemical 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 [99] ( ) (5.74) where is the pre-exponential factor and is the activation energy for the anode and cathode. Further details about PEM electrolysis modeling can be found elsewhere [99, 100]. 5.5.2 Exergy analysis In this section, exergy balance equation for system I is presented using the formula provided in section 5.4. 79PDF Image | Energy Systems for Multigeneration Purposes
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