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Sustainable Energy
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Mod.1: Fuel Cells & Distributed
Generation Systems
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Dr. Ing. Mario L. Ferrari
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Thermochemical Power Group (TPG) - DiMSET – University of Genoa, Italy
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A.A. 2011-2012
Lesson II
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Lesson II: fuel cells (electrochemistry)
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A.A. 2011-2012
Lesson II
Gibbs Free Energy and Nernst Potential (1/4)
• The maximum electrical work (ideal conditions)
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
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Lesson II
Gibbs Free Energy and Nernst Potential (2/4)
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• A general cell reaction
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• The standard state Gibbs free energy change
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G°i: partial molar Gibbs free energy for species i at temperature T
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• Enthalpy and entropy calculation (perfect gases)
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H°i, S°i, a,b,c: from tables
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Lesson II
Gibbs Free Energy and Nernst Potential (3/4)
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• The following equations
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• The Gibbs free energy change can be expressed
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∆G°: Gibbs free energy change of reaction at 1 atm and temperature T
fi: 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)
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• Combining with the initial equation
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Ε° is calculated from -∆G°/nF at the cell temperature (T)
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Lesson II
Gibbs Free Energy and Nernst Potential (4/4)
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• General form of Nernst equation
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Fuel cells generally operate at pressures low enough (perfect
gases): fugacity can be approximated by the partial pressure
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Lesson II
Ideal Performance (1/4)
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• Electrochemical reactions in fuel cells
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•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
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Lesson II
Ideal Performance (2/4)
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• Fuel cell reactions and Nernst voltage
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•E° at 298 K for H2+1/2*O2: 1.229 V (liquid water product) or 1.18 V (steam
product)
•The difference is Gibbs free energy change of vaporization
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Lesson II
Ideal Performance (3/4)
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• H2/O2 FC ideal potential function of temperature
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• H2/O2 ideal potential for different cells (and T)
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Lesson II
Ideal Performance (4/4)
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•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.
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A simple reaction pathway analysis explains why direct oxidation of CO and CH4 is
rarely the major reaction pathway under most fuel cell operating conditions (usually
internal reforming):
•The driving force for anodic oxidation of CO and CH4 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 CH4 oxidation.
•Mass-transfer of CO, CH4, 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
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A.A. 2011-2012
Lesson II
Energy balance
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•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.
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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
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•A typical energy balance determines the cell exit temperature knowing the reactant
composition, the feed stream temperatures, H2 and O2 utilization, the expected power
produced, and a percent heat loss.
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[n(H2 ) + 4 ⋅ n(CH4 ) + n(CO)]FC _ in − [n(H 2 ) + 4 ⋅ n(CH4 ) + n(CO)]FC _ out
[n(H2 ) + 4 ⋅ n(CH4 ) + n(CO)]FC _ in
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Fuel utilization factor: U f =
•Uf is related to current and fuel mass flow rate
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Lesson II
Cell efficiency (1/2)
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•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
∆G is the electric work
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•Example for a pure H2/O2 fuel cell:
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At 298 K: ∆H = 285.8 kJ/mol e ∆G = 237.1 kJ/mol
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Lesson II
Cell efficiency (2/2)
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•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:
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At 298 K and 1 atm: Εideal = 1.229 V
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•Since the fuel is typically not completely converted, the voltage efficiency must be
multiplied by the fuel utilization.
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Typical SOFC. Operating
conditions: 800°C, 50% initial
hydrogen concentration.
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Lesson II
Real performance (1/6)
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• Types of losses
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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)
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•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.
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A.A. 2011-2012
Lesson II
Real performance (2/6)
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•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.
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A.A. 2011-2012
Lesson II
Real performance (3/6)
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• Activation losses
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•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).
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Note: A voltage drop is expressed with η
•If
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Tafel equation
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and
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With:
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•The usual form of Tafel equation is:
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Processes contributing to activation losses: absorption of reactants, transfer of
electrons, desorption of products, and the nature of the electrode surface
A.A. 2011-2012
Lesson II
Real performance (4/6)
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• Ohmic losses
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•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.
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•The ohmic resistance normalized by the active cell area is the Area Specific
Resistance (ASR). ASR has the units Ωcm2.
•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).
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A.A. 2011-2012
Lesson II
Real performance (5/6)
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• Mass-transport-related (concentration) losses
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•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.
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Fick’s first law of diffusion
•D: diffusion coefficient
•CB, CS: bulk and surface concentration
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Limiting current (maximum rate at which a reactant can be supplied)
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Combining the equations:
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Nernst equation at zero and ≠0 current
So, concentration losses are:
A.A. 2011-2012
Lesson II
Real performance (6/6)
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• Cumulative effects of losses
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•Combined effect of losses (activation+concentration) is called polarization.
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•The effect of polarization is to shift the potential of the electrode (Eelectrode) to a
new value (Velectrode)
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•Real cell voltage.
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Losses can be minimised by modification on fuel
cell design (electrode, electrolyte, geometry)
A.A. 2011-2012