Fuel Cell Technology
Sustainable Energy Science and Engineering Center Fuel Cell Technology
1. Technology overview 2. Fuel cell performance 3. Fuel cell systems 4. Sample calculations 5. Experiment using PEM cell
Goal: To provide a better understanding benefits and systems issues that influence its application.
of the fuel cell technology, its Reference: Fuel Cell Handbook, 5th Edition, US DOE, October 2000. Sustainable Energy Science and Engineering Center Fuel Cell Technology Overview
Fuel cell: A device for directly converting the chemical energy of a fuel into electrical energy in a constant temperature process. Besides offering high theoretical efficiency, especially at low temperatures, fuel cells emit low or zero levels of pollutants. They can run on wide variety of fuels ranging from gaseous fuels such as hydrogen and natural gas to liquid fuels such as methanol and gasoline. Main applications: Stationary power generation Transportation Battery replacement. Sustainable Energy Science and Engineering Center Ballard 250 kW PEMFC power system Sustainable Energy Science and Engineering Center
Vehicle Fuel Cell System Sustainable Energy Science and Engineering Center Solar Hydrogen System Sustainable Energy Science and Engineering Center
Operation of a Solid Polymer Fuel Cell (SPFC)
Under load a single cell produces about 0.7 volts. Sustainable Energy Science and Engineering Center Fuel Cell Stack In order to achieve a useful output power individual cells are connected together in a ‘stack’ using an interconnect called bipolar plate.
MEA: Membrane Electrode Assembly: A combination of electrolyte and electrodes Sustainable Energy Science and Engineering Center Fuel Cell Efficiency
Carnot efficiency: The maximum efficiency of a heat engine is subject to the Carnot efficiency limitation, which defines the maximum efficiency that any heat engine can have if its temperature extremes are known.
TL ηC =1− TH
Where TH and TL are the absolute high and low temperatures respectively. Fuel cell efficiency: The theoretical efficiency of a fuel cell is related to the ratio of two thermodynamic properties, namely the chemical energy, represented by Gibbs Free Energy (∆Go) and the total heat energy, represented by the Enthalpy (∆Ho) of the fuel. ΔGo η = FC ΔH o Sustainable Energy Science and Engineering Center Fuel Cell Efficiency
Efficiency vs Temperature
Fuel cell operating at low temperatures emit low levels of pollutants such as SOx and NOx when using methanol and natural gas.
Comparison of theoretical efficiency of a fuel cell running on hydrogen as a function of temperature with that of the Carnot efficiency at the same o temperature, assuming TL = 25 C Sustainable Energy Science and Engineering Center Fuel Cell Efficiency Under Load Sustainable Energy Science and Engineering Center Fuel Cell Types
Two classes: Low temperature High temperature Sustainable Energy Science and Engineering Center Fuel Cell Types
PEFC: Polymer electrolyte fuel cell; AFC: Alkaline fuel cell; PAFC: Phosphoric acid fuel cell; MCFC: molten carbonate fuel cell; ITSOFC: Intermediate temperature solid oxide fuel cell; TSOFC: Tubular solid oxide fuel cell Sustainable Energy Science and Engineering Center Fuel Cell Characteristics Low temperature fuel cell characteristics: Incorporation of precious metal electrocatalysts to improve performance Fast dynamic response and short start-up times Available commercially and near commercialization Pure supply of hydrogen as a fuel (e.g. catalysts are poisoned by CO) High temperature fuel cell characteristics: Fuel flexibility - use of hydrocarbon fuels Reduces the need for expensive electrocatalysts Generate useful ‘waste’ heat and well suited for cogeneration and combined cycle applications Long start-up times and are sensitive to thermal transients Expensive construction materials - reliability and durability is of concern At the demonstration stage Sustainable Energy Science and Engineering Center Fuel Cell Fuel
All fuel cell can run on hydrogen as a fuel. High temperature fuel cells can also run directly on other fuels, especially hydrogen rich gases such as methane. Low temperature systems can run on specific liquid fuels such as methanol. The application of the fuel cell system often determines on which fuel it will run, and whether that fuel first needs to be processed into hydrogen-rich ‘reformate’, possibly also containing carbon dioxide, nitrogen or other non- detrimental products. Sustainable Energy Science and Engineering Center Fuels for Stationary Power Generation
Common fuel: Natural gas - reformed by separate steam reformer before resulting hydrogen is fed into the fuel cell stack. High temperature fuel cells are able to operate directly to reform fuels such as methane directly on the anode of the fuel cell (DIRECT). This process causes severe temperature gradients across the stack. Use a separate catalyst bed within the system to split the hydrogen and carbon (INDIRECT). Typical fuel cell type: Phosphoric Acid Fuel Cell (PAFC) Sustainable Energy Science and Engineering Center Fuels for Transportation
Common fuel: Hydrogen - severe size, weight, cost and performance constraints Methanol is being suggested to be a good compromise fuel. It is easy to process into hydrogen using autothermal reforming. Reformer-based systems have longer response times and are less efficient and more polluting than direct hydrogen systems.
Typical fuel cell type: Direct Methanol Fuel Cell (PAFC) Sustainable Energy Science and Engineering Center Fuels for Battery Replacement
Common fuel: Propane or butane - severe size, weight, cost and performance constraints Fuel cell type: Solid Oxide Fuel cell (SPFC). The electrolyte is a solid, nonporous metal oxide, usually Y2O3-stabilized ZrO2. High power density for miniaturization. Also uses most easily handled electrolyte of the low temperature fuel cells. Sustainable Energy Science and Engineering Center Fuel Cell Stability
Suitability of different fuel cell types for applications Sustainable Energy Science and Engineering Center
Fuel Cell System Costs
The low temperature fuel cells can cost as little as $30/kW for transport and $300/kW for stationary power in mass production. Fuel cell system for large scale power generation < $1,500/kW Automobile fuel cell system < $50/kW (1 kW = 1.341 hp) Sustainable Energy Science and Engineering Center Fuel Cell State of the Art
1. Battery replacement for mobile phones/ laptops 2. Portable power systems of several hindered watts for replacement of small diesel generators. 3. Small power or cogeneration systems 4. Transport based fuel cell systems Sustainable Energy Science and Engineering Center TSOFC with a Gas Turbine Engine
Siemens Westinghouse Concept Sustainable Energy Science and Engineering Center Distributed Power Generating Systems
13.5 Sustainable Energy Science and Engineering Center System Performance Requirements Sustainable Energy Science and Engineering Center Subsystems and Components Sustainable Energy Science and Engineering Center Electrochemical reactions in fuel cells
See LECTURES 18 &19 of EML 4450, FALL 2006 Reference: Fuel Cell Handbook, 5th Edition, US DOE, October 2000. Sustainable Energy Science and Engineering Center Nernst Equation The Nernst equation and open circuit: The electrochemical work, which is done by the movement of electrons through a difference in a electrical potential, is denoted as We or Wcell. In electrical terms, the work done by electrons with the charge nF (n is the number of electrons transferred per mole of fuel and F is the charge carried by a mole of electrons, which is Faraday’s constant - 96,485C/mole-1) moving through a potential difference, E ( voltage difference across electrodes) is RT W = nFE E = E o − lnQ e nF ΔG =−nFE Eo is the standard electrode potential ΔGo =−nFE o o We also assume here that a complete ΔG =ΔG + RT lnQ reversible oxidation of a mole of fuel ΔGo RT E = − lnQ Electrical work done = charge x voltage nF nF Sustainable Energy Science and Engineering Center Hydrogen Fuel Cell
For a hydrogen-oxygen fuel cell, the overall reaction stoichiometry is 1 H + O → H O 2 2 2 2
The electrons transferred in this reaction, n = 2. Using the partial pressures of water, hydrogen and oxygen in the reaction coefficient, we then have
RT P E = E o − ln H 2O nF P P1/2 H 2 O2
Diluting the reactant gases will lower the maximum voltage that the cell can produce. Sustainable Energy Science and Engineering Center Fuel Cell Reactions Fuel cell reactions and the corresponding Nernst equation
a the cell reactions are obtained from the anode and cathode reactions shown in an earlier table. Sustainable Energy Science and Engineering Center Ideal Standard Potential Ideal Standard Potential, Eo : Standard conditions: one atmosphere and 25oC
The ideal cell voltage for H2/O2 fuel cell Eo = 1.229V with liquid water as product Eo = 1.18V with gaseous water as product Eo is a strong function of the cell temperature
Ideal voltage, E for the oxidation of hydrogen Sustainable Energy Science and Engineering Center Irreversible Losses
Fuel cell Voltage/Current plot
Activation Polarization: Related to the rates of electrochemical reactions at an electrode surface. Ohmic Polarization: Losses due to resistance to the flow of ions in the electrolyte and resistance to flow of electrons through the electrode materials Concentration Polarization: Due to inability of the surrounding reactant material to maintain the initial concentration.
Cell voltage, V = E- Losses Sustainable Energy Science and Engineering Center Activation Polarization
It is customary to express the voltage drop due to chemical polarization by strictly empirical equation, called the Tafel equation as
RT i ΔVchem = ln ~ 50 - 100 mV αnF io
Where α is the electron transfer coefficient of the
reaction at the electrode and io is the exchange current density Gas diffusion electrode reduces the chemical polarization by maximizing the three-phase interface of gas-electrode-electrolyte. The small pores create large reactive surface areas per unit geometrical area and allow free entrance to Tafel plot (η = ∆ ) reactants and exit to products. Increases in Vchem pressure and temperature will also generally decrease chemical polarization. Sustainable Energy Science and Engineering Center Ohmic Polarization
The ohmic losses can be expressed by the equation
ΔVohm = iR
Where i is the current flowing through the cell and R is the total cell resistance, which includes electronic, ionic and contact resistance. These losses can be reduced by decreasing the electrode separation and enhancing the ionic conductivity of the electrolyte. Hydrogen-oxygen fuel cells employing concentrated solutions of potassium or sodium hydroxide as electrolytes show that resistance polarization is negligibly low even at fairly high current densities. Sustainable Energy Science and Engineering Center Concentration Polarization The concentration polarization loss is given by the following equation: RT ⎛ i ⎞ ΔVconc = ln⎜ 1− ⎟ nF ⎝ iL ⎠
Where i is given by the Frick’s first law of diffusion (the rate of mass transport to an electrode surface) nFDC nFD() CB − CS B i = iL = δ δ
Where D is the diffusion coefficient of the reacting species, CB is its bulk concentration, CS is its surface concentration and δ is the thickness of the diffusion layer. The limiting current iL is a measure of the maximum rate at which a reactant can be supplied to an electrode and occurs when CS = 0. Sustainable Energy Science and Engineering Center Electrode Polarization
Activation and concentration polarizations can exist at both the positive (cathode) and negative (anode) electrodes in fuel cells. The total polarization at these electrodes is then the sum of ∆Vact and ∆Vconc .
∆Vanode = ∆Vact,a + ∆Vconc, a and
∆Vcathode = ∆Vact,c + ∆Vconc, c
Vanode = Eanode+ | ∆Vanode | ↑
Vcathode = Ecathode- | ∆Vcathode | ↓ PAFC fuel cell Sustainable Energy Science and Engineering Center
Cell Voltage
Vcell = Vcathode -Vanode - iR
Vcell = Ecathode- | ∆Vcathode | -(Eanode+ | ∆Vanode |) - iR
Vcell = ∆Ee - | ∆Vcathode | - | ∆Vanode | - iR
The goal is to minimize the polarization so that
Vcell → ∆Ee Sustainable Energy Science and Engineering Center Fuel Cell Performance Variables
Operating variables: Stationary power plant operation Temperature, pressure, gas composition, reactant utilizations Vehicle application and current density System requirements: Power level, voltage or system weight
Selection of a cell design point is dependant upon the system design. Sustainable Energy Science and Engineering Center Fuel Cell Performance Variables
Temperature and pressure: The changes in Gibbs free energy with temperature and pressure will effect the ideal potential, E. ⎛ ∂E ⎞ ΔS ⎜ ⎟ = ⎝ ∂T ⎠ P nF or ⎛ ∂E ⎞ −ΔV ⎜ ⎟ = ⎝ ∂P ⎠T nF
An increase in operating pressure has beneficial effects - reactant partial pressure, gas solubility, higher mass transfer rates and reduced electrolyte loss by evaporation. Adverse effects: parasite power costs and additional hardware costs Sustainable Energy Science and Engineering Center Fuel Cell Performance Variables
Reactant utilization and gas concentration: Utilization, U refers to the fraction of the total fuel or oxidant introduced into a fuel cell that reacts electrochemically. When H2 is the fuel, because it is only reactant involved in the electrochemical reaction (assuming no gas cross-over or leakage out of the cell), we have
H2,in − H2,out H2,consumed U f = = H2,in H2,in
Where H2,in and H2,out are the hydrogen mass flow rates at the inlet and outlet of the fuel cell respectively. Similar type of calculation is done to determine the oxidant utilization Sustainable Energy Science and Engineering Center High Temperature Fuel Cell Molten Carbonate Fuel Cell:
Water gas shift reaction
CO + H2O → H2 + CO2
The fuel utilization is defined by
H2,consumed U f = H2,in + COin
The Nernst equation in terms of the mole fraction of the gases (Xi) at the fuel cell outlet is MCFC
Where P is the cell gas pressure. Sustainable Energy Science and Engineering Center Fuel Cell Performance Variables
Gas Composition: Kinetic Overpotential H2/air fuel cell: o o ∆E ⏐T=25 C = 60 mV o o ∆E ⏐T=1200 C = 300 mV At high current densities, there is an inability to diffuse enough reactants to the reaction sites so the cell Ohmic Overpotential experiences a sharp performance decrease through reactant starvation. Concentration Overpotential iR also increase with current density. Sustainable Energy Science and Engineering Center Fuel Cell Performance Variables Heat Transfer:
In cells with high current densities, it is often important to calculate the heat transfer within a fuel cell. 1) The electrochemical reaction producing the current in the cell is not adiabatic which gives rise to a reversible heat transfer whose magnitude is TΔS. 2) Some of the fuel reacts chemically with the oxidizer rather than electrochemically to generate an irreversible heat transfer. 3) The cell operates at some voltage less than the theoretical open circuit 2 voltage with the difference manifesting itself as I R and I ΔV heat in the cell (I is the current drawn and R and ΔV represent irreversible resistances and voltage drops).
Ý Ý Ý Ý 1 Qt = Qrev + Qchem (irr) + QΔ V = []TΔS ++nF() Vac −V nF Generally small Sustainable Energy Science and Engineering Center Fuel Cell Efficiency
The ideal efficiency is simply the change in free energy, which is the maximum useful work we can obtain from any system, divided by the heat of reaction ΔG TΔS nFE ItE η = =1− = = i ΔH ΔH ΔH ΔH Where I is the current and t the time for which the current flows. In a fuel cell under load, the actual electromotive force that drives the electrons
through the external circuit will fall below E to some lower value, we will call Eac. The reasons for this drop are: a) An undesirable reaction may be taking place at the electrodes or else where in the cell; b) Something may be hindering the concentration gradient may be d) Joule heating associated with the IR The actual efficiency is come−nF Eestablished in the elec η = ac reaction at anode or cathode; c) a ac ΔH drop occurs in the electrolyte. trolyte or in the reactants; Sustainable Energy Science and Engineering Center Hydrogen Fuel Cell
Quantity H2 0.5O2 H2O Change
Enthalpy 0 0 -285.83 kJ ΔH = -285.83 kJ
Entropy 130.68 J/K 0.5 x 205.14 J/K 69.91 J/K TΔS = -48.7 kJ
Pressure: 1 atmosphere Temperature: 298K
W = PΔV = (101.3 kPa)(1.5 moles)(-22.4 x 10-3 m3/mol)(298K/273K) = -3715 J
ΔU = ΔH - PΔV = -285.83 kJ - 3.72 kJ = -282.1 kJ η = −237.1/−285.83 = 0.83 (83%) ΔG = ΔH - TΔS = -285.83 kJ + 48.7 kJ = -237.1 kJ Sustainable Energy Science and Engineering Center Actual Performance
Vactual ηac = Videal
Then the thermal efficiency of the fuel cell can then be written as
η = Useful Energy/∆H = Useful Power/(∆G/0.83) = 0.83 (Vactual/Videal) The cell voltage operating reversibly on pure hydrogen and oxygen at 1 atm pressure and 25oC is 1.229V. The thermal efficiency of an actual fuel cell operating at a voltage of Vcell, based on HHV of hydrogen is given by
ηideal = 0.83 (Vcell/Videal) = 0.83 (Vcell/1.229) = 0.675 Vcell
↓ Current density →↑Cell voltage →↑Fuel cell efficiency Then active cell area must be increased to obtain the requisite amount of power. Sustainable Energy Science and Engineering Center Polymer Electrolyte Fuel Cell
Characteristics: High power density, low weight, low cost and low volume. Operates at low temperature, allowing faster start ups and immediate response to changes in the demand for power. Water management has a significant impact on the cell performance.
Nafion membranes - DuPont electrolytes - fully fluorinated polymers Sustainable Energy Science and Engineering Center PEFC Performance
Low platinum loaded electrodes Sustainable Energy Science and Engineering Center PEFC Performance Dow Membrane Sustainable Energy Science and Engineering Center PEFC Performance Effect of CO Sustainable Energy Science and Engineering Center PEFC Performance
Effects of Pressure and Temperature Sustainable Energy Science and Engineering Center PEFC Performance
Effect of oxygen pressure Sustainable Energy Science and Engineering Center Direct Methanol Proton Exchange Fuel Cell
Single cell DMPEFC Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Sample calculations for the development of a fuel cell power system We will determine for a simple hydrogen-air fuel cell: Oxygen usage rate Air inlet flow rate Air exit flow rate Hydrogen usage and the energy content of hydrogen Rate of water production Heat production
References: Fuel Cell Handbook, 5th Edition, US DOE, October 2000. Fuel Cell systems explained by Larminie & Dicks, Wiley, 2003 Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Stoichiometry:
In the simple fuel cell reaction 2H2 + O2 → 2H2O exactly two moles of hydrogen would be provided for each mole of oxygen. Since two electrons are transferred for each mole of hydrogen, the reaction would produce exactly 4 F of charge. Where F is faraday constant, the charge on one mole of electrons, 96,485 Colulombs. One ampere of current is defined as 1 C/s. Hydrogen and oxygen are often supplied at greater than stoichiometric rate. The stoichiometry can be used as a variable and is denoted by the symbol λ. If the rate of ‘use’ of a chemical in a reaction is n Ý (moles/second) Rate of supply : λnÝ (moles/second) Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Electrical Power of the Whole Fuel Cell Stack, Pe:
Average voltage of each cell in the stack : Vc The electrical power of the fuel cell system is either given or known.
If Vc is not given, it can be assumed to be between 0.6 and 0.7 V
Polarization curve: The fuel cell stack is assumed to run under constant temperature (70oC) and pressure (3 bar). Sustainable Energy Science and Engineering Center Fuel Cell Calculations Efficiency: If the efficiency is given, then
Vc can be calculated using the equation:
V η = U c 100% f 1.48
Where Uf is fuel utilization coefficient (mass of fuel reacted in cell/mass of fuel input). E = 1.48 V if using the HHV E = 1.35 V if using the LHV For 100% efficient system Sustainable Energy Science and Engineering Center Fuel Cell Calculations Oxygen and Air Usage: At the cathode, oxygen reacts with electrons taken from the electrode and H+ ions from the electrolyte, to form water and four electrons are transferred for each mole of oxygen.
− + O2 + 4e + 4H → 2H2O
charge = 4F x amount of O2
O2 usage = (I/4F) moles/s I: current For a stack of n cells
O2 usage = (nI/4F) moles/s
If the voltage of each cell in the stack is VC then
Power, Pe = Vc I n
I = Pe/ (nVc)
O2 usage = Pe/ (4VcF) moles/s -3 -8 O2 usage = 32 x 10 Pe/ (4VcF) kg/s = 8.29 x 10 (Pe/Vc) kg/s Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Oxygen and Air Usage: continued The oxygen used will normally be derived from air, so we need to develop an expression for air usage. The molar proportion of air that is oxygen is 0.21 and the molar mass of air is 28.97 x 10-3 kg/mole.
-3 Air usage = (28.97 x 10 /0.21) (Pe/ (4VcF)) kg/s -7 = 3.57 x 10 (Pe/Vc) kg/s If the air was used at this rate, then as it left the cell it would be completely devoid of any oxygen. Therefore, in practice, the air flow is typically twice as much. If the stoichiometry is λ, then we have
-7 Air usage = 3.57 x 10 λ (Pe/Vc) kg/s
Note: 1 kg/s = 1795 SCFM 1 kg/s = 5.1 x 104 standard L/minute Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Air Exit Flow Rate: Exit air flow rate = Air inlet flow rate - oxygen usage
-7 -8 Exit air flow rate = 3.57 x 10 λ (Pe/Vc) - 8.29 x 10 (Pe/Vc) kg/s -7 -8 = (3.57 x 10 λ - 8.29 x 10 )(Pe/Vc) kg/s
e.g.: Given Pe = 5 kW operating for I h. Assume Vc = 0.7, λ = 2 -7 -3 air usage = 3.57 x 10 λ (Pe/Vc) = 5.1 x 10 kg/s = 9.154 SCFM ~ 10 SCFM Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Hydrogen Usage:
+ − Note that there are two electrons from each mole of hydrogen 2H2 → 4H + 4e
H2 usage = (nI/2F) moles/s
H2 usage = Pe/ (2VcF) moles/s The molar mass of hydrogen is 2.02 x 10-3 kg/mole, therefore
-3 H2 usage = 2.02 x 10 (Pe/ (2VcF)) kg/s -8 = 1.05 x 10 (Pe/ Vc) kg/s ~ 0.135 SCFM for 5 kW fuel cell Effective energy content of hydrogen fuel: Specific enthalpy (HHV)* = 1.43 x 108 k/kg = 39.7 kWh/kg
Specific electrical energy = 26.8 Vc kWh/kg Energy density at STP = 3.20 kWh/m3 = 3.2 Wh/SL * LHV = HHV x 0.846 Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Hydrogen Usage: continued The utilization of the fuel is defined as
H2,consumed U f = H2,in
Therefore the required fuel flow rate can be calculated
H2,consumed H2,in = U f
If Uf = 80% then for 5 kW fuel cell
H2 usage = 0.17 SCFM Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Water Production: Water is produced at the rate of one mole for every two electrons.
Water production = Pe /(2VcF) moles/s The molecular mass of water is 18.02 x 10-3 kg/mole, therefore
-8 Water production = 9.34 x 10 (Pe/Vc) kg/s = 0.6671 x 10-3 kg/s for 5kW fuel cell Since the density of water is 1.0 g/cm3 Water production = 0.6671 cm3/s In one hour : 2401 cm3 = 2.4 L Sustainable Energy Science and Engineering Center Fuel Cell Calculations
Heat Produced: If all the enthalpy of reaction of hydrogen fuel cell is converted into electrical energy, then the output voltage would be 1.48V if the water product is in liquid form or 1.35 V if the water product is in vapor form. The difference between the actual cell voltage and this voltage represents the energy that is not converted into electricity - it is converted into heat. For a stack of n cells the heat generated is then
Heating rate = n I (1.25-Vc) Watts
= Pe [(1.25/Vc) -1] Sustainable Energy Science and Engineering Center Fuel Cell System Sustainable Energy Science and Engineering Center Fuel Cell Calculations PAFC operating on reformed natural gas