Prof. Mario L. Ferrari
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1 Sustainable Energy Mod.1: Fuel Cells & Distributed Generation Systems Dr. Ing. Mario L. Ferrari Thermochemical Power Group (TPG) - DiMSET University of Genoa, Italy
2 Lesson II Lesson II: fuel cells (electrochemistry)
3 Gibbs Free Energy and Nernst Potential (1/4) The maximum electrical work (ideal conditions) Lesson II n: number of electrons participating in the reaction F: Faraday s constant (96,487 coulomb/mole electron) E: ideal potential of the cell The Gibbs free energy change is also given by: H: enthalpy change S: entropy change
4 Lesson II Gibbs Free Energy and Nernst Potential (2/4) A general cell reaction The standard state Gibbs free energy change G i : partial molar Gibbs free energy for species i at temperature T Enthalpy and entropy calculation (perfect gases) H i, S i, a,b,c: from tables
5 Gibbs Free Energy and Nernst Potential (3/4) The following equations Lesson II The Gibbs free energy change can be expressed G : Gibbs free energy change of reaction at 1 atm and temperature T f i : fugacity of species i (fugacity is an effective pressure which replaces the true mechanical pressure in accurate chemical equilibrium calculations it is related to the tendency of a fluid to expand at isothermal condition) Combining with the initial equation Ε is calculated from - G /nf at the cell temperature (T)
6 Gibbs Free Energy and Nernst Potential (4/4) General form of Nernst equation Lesson II Fuel cells generally operate at pressures low enough (perfect gases): fugacity can be approximated by the partial pressure
7 Lesson II Ideal Performance (1/4) Electrochemical reactions in fuel cells The cell potential increases with an increase in the partial pressure (concentration) of reactants and a decrease in the partial pressure of products For example, for the hydrogen reaction, the ideal cell potential at a given temperature can be increased by operating at higher reactant pressures
8 Lesson II Ideal Performance (2/4) Fuel cell reactions and Nernst voltage E at 298 K for H 2 +1/2*O 2 : V (liquid water product) or 1.18 V (steam product) The difference is Gibbs free energy change of vaporization
9 Ideal Performance (3/4) H 2 /O 2 FC ideal potential function of temperature Lesson II H 2 /O 2 ideal potential for different cells (and T)
10 Ideal Performance (4/4) Lesson II The open circuit voltage of a fuel cell is also strongly influenced by the reactant concentrations. The maximum ideal potential occurs when the reactants at the anode and cathode are pure. In an air-fed system or if the feed to the anode is other than pure dry hydrogen, the cell potential will be reduced. Reduced open circuit voltage affects the operation of the entire cell. A simple reaction pathway analysis explains why direct oxidation of CO and CH 4 is rarely the major reaction pathway under most fuel cell operating conditions (usually internal reforming): The driving force for anodic oxidation of CO and CH 4 is lower than that for the oxidation of hydrogen. The kinetics of hydrogen oxidation on the anode are significantly faster than that of CO or CH 4 oxidation. Mass-transfer of CO, CH 4, and even more so of higher hydrocarbons, to the threephase boundary and through the porous anode is more than ten times slower than that of hydrogen. Nevertheless, direct oxidation can be important under certain conditions, such as at the entrance of a cell
11 Lesson II Energy balance The energy balance around the fuel cell is based on the energy absorbing/releasing processes (e.g., power produced, reactions, heat loss) that occur in the cell. Enthalpy flow of the reactants entering the cell = Enthalpy flow of the products leaving the cell + Heat from physical and chemical processes within the cell + DC energy output from the cell + Heat loss from the cell to its surroundings A typical energy balance determines the cell exit temperature knowing the reactant composition, the feed stream temperatures, H 2 and O 2 utilization, the expected power produced, and a percent heat loss. Fuel utilization factor: U f = [ n( H2 ) + 4 n( CH4 ) + n( CO) ] [ n( H ) ( CH ) ( CO) ] FC in n 4 + n _ [ n( H2 ) + 4 n( CH4 ) + n( CO) ] FC _ in FC _ out U f is related to current and fuel mass flow rate
12 Lesson II Cell efficiency (1/2) Fuel cells convert chemical energy directly into electrical energy. In the ideal case of a fuel cell the change in Gibbs free energy ( G) of the reaction is available as useful electric energy at the temperature of the conversion. H is the change in enthalpy between the product and feed streams Example for a pure H 2 /O 2 fuel cell: G is the electric work At 298 K: H = kj/mol e G = kj/mol
13 Cell efficiency (2/2) Lesson II The efficiency of an actual fuel cell is often expressed in terms of the ratio of the operating cell voltage to the ideal cell voltage. For a hydrogen/oxygen fuel cell: m& At 298 K and 1 atm: Ε ideal = V Since the fuel is typically not completely converted, the voltage efficiency must be multiplied by the fuel utilization. Typical SOFC. Operating conditions: 800 C, 50% initial hydrogen concentration.
14 Real performance (1/6) Lesson II The actual cell potential is decreased from its ideal potential because of several types of irreversible losses (often they ate referred to as polarization, overpotential or overvoltage) Types of losses Activation-related losses. These come from the activation energy of the electrochemical reactions at the electrodes. These losses depend on the reactions, the electro-catalyst material and microstructure, reactant activities, and weakly on current density. Ohmic losses. Ohmic losses are caused by ionic resistance in the electrolyte and electrodes, electronic resistance in the electrodes, current collectors and interconnects, and contact resistances. These losses are proportional to the current density, depend on materials selection, stack geometry and temperature. Mass-transport-related losses (or concentration-related losses). These come from finite mass transport limitation rates of the reactants and depend strongly on the current density, reactant activity, and electrode structure.
15 Lesson II Real performance (2/6) Activation and concentration polarization data presented are generally only valid for that particular cell and operating geometry. A mathematical model will generally be required to interpret activation and concentration polarization data and translate it into data useful for stack engineers. Detailed reactant concentration information (including utilization) is essential for interpretation of activation and concentration polarization data. Several cell data presented and published are taken at finite utilization.
16 Lesson II Real performance (3/6) Activation losses Activation losses are caused by sluggish electrode kinetics. There is a close similarity between electrochemical and chemical reactions in that both involve an activation energy that must be overcome by the reacting species (a sort of energetic barrier). If Note: A voltage drop is expressed with η Tafel equation The usual form of Tafel equation is: With: and Processes contributing to activation losses: absorption of reactants, transfer of electrons, desorption of products, and the nature of the electrode surface
17 Lesson II Real performance (4/6) Ohmic losses Ohmic losses occur for resistance to the flow of ions in the electrolyte and resistance to flow of electrons through the electrodes. The dominant ohmic losses through the electrolyte are reduced by decreasing the electrode separation and enhancing the ionic conductivity of the electrolyte. The ohmic resistance normalized by the active cell area is the Area Specific Resistance (ASR). ASR has the units Ωcm 2. The ASR is a function of the cell design, material choice, manufacturing technique, and, because material properties change with temperature, operating conditions. Ohmic resistance may be determined through impedance spectroscopy. Based on the detailed cell geometry, the length of both the ionic and electronic current paths and cross-sectional area for current conduction can be measured. Contact resistance is calculated from R (the difference).
18 Real performance (5/6) Mass-transport-related (concentration) losses Nernst equation at zero and 0 current Lesson II Reactant is consumed at the electrode and finite mass transport rates limit the supply of fresh reactant and the evacuation of products. A concentration gradient is formed which drives the mass transport process. While at low current densities and high bulk reactant concentrations mass-transport losses are not significant, under practical conditions (high current densities, low fuel and air concentrations), they often contribute significantly to loss of cell potential. Fick s first law of diffusion D: diffusion coefficient C B, C S : bulk and surface concentration Limiting current (maximum rate at which a reactant can be supplied) Combining the equations: So, concentration losses are:
19 Real performance (6/6) Cumulative effects of losses Combined effect of losses (activation+concentration) is called polarization. Lesson II The effect of polarization is to shift the potential of the electrode (E electrode ) to a new value (V electrode ) Real cell voltage. Losses can be minimised by modification on fuel cell design (electrode, electrolyte, geometry)
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