Download Direct Energy Conversion: Fuel Cells

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Direct Energy Conversion: Fuel Cells
Section 4.7.1 in the Text Book
References:
Direct Energy Conversion by Stanley W. Angrist, Allyn and Beacon,
1982.
Fuel Cell Systems, Explained by James Larminie and Andrew Dicks,
Wiley, 2003.
Fuel Cell Technology Hand Book, Edited by Gregor Hoogers, CRC
Press, 2002
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Fuel Cells
Introduction:
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Hydrocarbon Fuels
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3
Energy stored
in
chemical bonds 7
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Combustion
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Useful power
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Bypass the conversion-to-heat and mechanical-to-electrical processes
A fuel cell is an electrochemical device in which the chemical energy
of a conventional fuel is converted directly and efficiently into low
voltage, direct current electrical energy. Since the conversion can be
carried out isothermally (at least in theory), the Carnot limitation on
efficiency does not apply.
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Fuel Cell Efficiency
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PEM Fuel Cell Performance
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Fuel Cells
William Grove 1839
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Grove noted with interest that this device, which
electrodes in contact with dilute sulfuric acid
permanent deflection of a galvanometer connected
also noted the difficulty of producing high current
fuel cell that uses gases.
used platinum
would cause
to the cell. He
densities in a
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Fuel Cells
Mond & Langer (1889) - Gas battery
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Daniell Cell
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We
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mean the electrode at which
oxidation takes place - losing of
electrons
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Cathode is the electrode at which
reduction takes place - electrons
are gained from the external circuit
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Hydrogen Fuel Cell
The Fuel Cell is a device which converts hydrogen
and oxygen into electricity. It achieves this using a
process which is the reverse of electrolysis of
water first identified by William Grove in 1863.
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The common types of fuel cells are phosphoric acid (PAFC), molten carbonate
(MCFC), proton exchange membrane (PEMFC), and solid oxide (SOFC), all named
after their electrolytes. Because of their different materials and operating
temperatures, they have varying benefits, applications and challenges, but all share
the potential for high electrical efficiency and low emissions. Because they operate at
sufficiently low temperatures they produce essentially no NOx, and because they
cannot tolerate sulfur and use desulfurized fuel they produce no SOx.
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Historical Development
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Fuel Cell Types
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Hydrogen - Oxygen Fuel Cell
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At
the
anode
the
hydrogen
gas
ionizes
releasing electrons and
creating H+ ions (or
protons). This reaction
releases energy.
2H 2 → 4H + + 4e−
At the cathode, oxygen
reacts with electrons
taken from the electrode,
and H+ ions from the
electrolyte, to form water
O2 + 4e− + 4H + → 2H 2O
An acid with free H+ ions. Certain
polymers can also be made to
contain mobile H+ ions - proton
exchange membranes (PEM)
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Membrane Electrode Assembly
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The MEA consists of two electrodes, the anode and the cathode, which are each coated on one side with a thin
catalyst layer and separated by a proton exchange membrane (PEM). The flow-field plates direct hydrogen to the
anode and oxygen (from air) to the cathode.
When hydrogen reaches the catalyst layer, it separates into protons (hydrogen ions) and electrons.
The free electrons, produced at the anode, are conducted in the form of a usable electric current through the
external circuit. At the cathode, oxygen from the air, electrons from the external circuit and protons combine to
form water and heat.
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Fuel Cell Stack
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Hydrogen
Hydrogen flows through channels in flow field plates to the anode where the
platinum catalyst promotes its separation into protons and electrons.
Hydrogen can be supplied to a fuel cell directly or may be obtained from
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natural gas, methanol or petroleum using a fuel processor, which converts
the hydrocarbons into hydrogen and carbon dioxide through a catalytic
chemical reaction.
Membrane Electrode
Assembly
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Each membrane electrode assembly consists of two electrodes (the anode
and the
4 cathode) with a very thin layer of catalyst, bonded to either side of a
proton exchange membrane.
Air
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Air flows through the channels in flow field plates to the cathode. The
hydrogen protons that migrate through the proton exchange membrane
combine with oxygen in air and electrons returning from the external circuit
to form pure water and heat. The air stream also removes the water created
as a by-product of the electrochemical process.
Flow Field Plates
Gases (hydrogen and air) are supplied to the electrodes of the membrane
electrode assembly through channels formed in flow field plates.
Fuel Cell Stack
To obtain the desired amount of electrical power, individual fuel cells are
combined to form a fuel cell stack. Increasing the number of cells in a stack
increases the voltage, while increasing the surface area of the cells increases
the current.
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Micro Fuel Cell
The fuel cells are 5 mm3 and generate up to 100 mWatts.
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CWRU
(Case Western Reserve University)
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researchers have miniaturized this process
through the use of micro fabrication
technology, which is used to print multiple
layers of fuel cell components onto a
substrate. Inks were created to replicate
the components of the fuel cell, which
means that the anode, cathode, catalyst
and electrolyte are all made of ink, rather
than traditional fuel cell materials.
Researchers screen printed those inks
onto a ceramic or silicon structure to form
a functioning fuel cell.
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Proton Exchange Membrane Fuel Cells
(PEMFC)
PEM fuel cells use a solid polymer membrane (a
thin plastic
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is permeable to protons when it is saturated with
water, but it does not conduct electrons.
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The reactions at the electrodes are as follows:
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Anode Reactions:
2H2 => 4H+ + 4eCathode Reactions:
O2 + 4H+ + 4e- => 2 H2O
11 Overall Cell Reactions: 2H2 + O2 => 2 H2O
Compared to other types of fuel cells, PEMFCs
generate more power for a given volume or weight of
fuel cell. This high-power density characteristic
makes them compact and lightweight. In addition,
the operating temperature is less than 100ºC, which
allows rapid start-up. These traits and the ability to
rapidly change power output are some of the
characteristics that make the PEMFC the top
candidate for automotive power applications.
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Alkaline Fuel Cell
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Alkaline fuel cells (AFC) are one of the most developed technologies and have
been used since the mid-1960s by NASA in the Apollo and Space Shuttle
programs. The fuel cells on board these spacecraft provide electrical power for
on-board systems, as well as drinking water. AFCs are among the most
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efficient in generating electricity
at nearly 70%.
Alkaline fuel cells use an electrolyte that is an aqueous (water-based) solution
of potassium hydroxide (KOH) retained in a porous stabilized matrix. The
concentration
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which ranges from 65°C to 220°C. The charge carrier for an AFC is the
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hydroxyl
ion (OH-) that migrates from the cathode to the anode where they
react with hydrogen to produce water and electrons. Water formed at the anode
11 to the cathode to regenerate hydroxyl ions. The chemical
migrates back
reactions at the anode and cathode in an AFC are shown below. This set of
reactions in the fuel cell produces electricity and by-product heat.
Anode Reaction:
2 H2 + 4 OH- => 4 H2O + 4 eCathode Reaction:
O2 + 2 H2O + 4 e- => 4 OHOverall Net Reaction: 2 H2 + O2 => 2 H2O
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One characteristic of AFCs is that they are very sensitive to CO2 that may be present in the fuel or air.
The CO2 reacts with the electrolyte, poisoning it rapidly, and severely degrading the fuel cell
performance. Therefore, AFCs are limited to closed environments, such as space and undersea vehicles,
and must be run on pure hydrogen and oxygen. Furthermore, molecules such as CO, H2O and CH4,
which are harmless or even work as fuels to other fuel cells, are poisons to an AFC.
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Alkaline Fuel Cell System
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Solid Oxide Fuel Cell
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Solid oxide fuel cells (SOFC) can also utilize carbon monoxide (CO). This makes them more fuel flexible
and also generally more efficient with available fuels, such as natural gas or propane. Hydrogen and CO can
be produced from natural gas and other fuels by steam reforming, for example. Fuel cells like SOFCs that
can reform natural gas internally have significant advantages in efficiency and simplicity when using
natural gas because they do not need an external reformer. When the ions reach the fuel at the anode they
oxidize the hydrogen to H2O and the CO to CO2. In doing so they release electrons, and if the anode and
cathode are connected to an external circuit this flow of electrons is seen as a dc current. This process
continues as long as fuel and air are supplied to the cell.
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Solid Oxide Fuel Cell
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Molten-carbonate Fuel Cell
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The diaphragm between the anode and the
cathode consists of a matrix filled with a
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carbonate
electrolyte. Carbonate ions (CO32-) pass
through the diaphragm and reach the anode. Here
they discharge an oxygen atom, which combines
with the hydrogen flowing past to form water
(H2O). This sets carbon dioxide (CO2) and two
electrons free. The electrons flow over an
electronic conductor to the cathode: current
flows. Similarly, the remaining carbon dioxide
(CO2) is fed to the cathode side, where it absorbs
the electrons and an oxygen atom from the air
that is flowing past. It then re-enters the process
as a carbonate ion.
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Carbon Conversion Fuel Cell
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Carbon (C) and oxygen (O2) can react in a hightemperature10fuel cell with the carbon, delivering electrons
(e) to an external circuit that can power a motor. The net
electrochemical reaction— carbon and oxygen forming
carbon
dioxide—is the same as the chemical reaction for
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carbon combustion, but it allows greater efficiency for
electricity production. The pure carbon dioxide (CO2)
product
can be sequestered in an underground reservoir
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or used to displace underground deposits of oil and gas.
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Instead of using gaseous fuels, as is typically done, the new technology uses aggregates of
extremely fine (10- to 1,000-nanometer-diameter) carbon particles distributed in a mixture of
molten lithium, sodium, or potassium carbonate at a temperature of 750 to 850°C. The overall
cell reaction is carbon and oxygen (from ambient air) forming carbon dioxide and electricity.
The reaction yields 80 percent of the carbon–oxygen combustion energy as electricity. It
provides up to 1 kilowatt of power per square meter of cell surface area—a rate sufficiently
high for practical applications. Yet no burning of the carbon takes place.
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Direct Methanol Fuel Cell
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Fuel cell that utilizes methanol as fuel. When providing
current, methanol is electrochemically oxidized at the anode
electrocatalyst to produce electrons which travel through the
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external circuit
consumed together with oxygen in a reduction reaction. The
circuit is maintained within the cell by the conduction of
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protons
in the electrolyte.
In modern cells, electrolytes based on proton conducting
polymer electrolyte membranes (e.g., Nafion™) are often
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used,
high temperature and pressure operation. The overall reaction
occurring in the DMFC is the same as that for the direct
combustion of methanol,
CH3OH + 3/2O2
CO2 + 2H2O
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Since the fuel cell operates isothermally, all the free energy associated with this reaction
should in principle be converted to electrical energy. However, kinetic constraints within
both electrode reactions together with the net resistive components of the cell means that
this is never achieved. As a result, the working voltage of the cell falls with increasing
current drain. These losses are known as polarization and minimizing the factors that give
rise to them is a major aim in fuel cell research.
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Direct Methanol Fuel Cell
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Direct Methanol Fuel Cell
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Condenser
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Load
Fuel cell stack
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Fuel Cell Applications
Stationary power generation10~ 5 - 250 kW
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Portable applications
~ 1 kW or lower
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Automotive
applications
~ 5 - 100 kW
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Airplane Applications ~11 10 - 250 kW
1kW = 1.3404826 horsepower
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Stationary Power Generation
Important factors:
The hours of operation per year
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The electric efficiency of the electricity generation process
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capital
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Fuel cells are particularly
suitable for on-site power generation.
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Utilizing the heat generated 11by the fuel cell improves the overall
efficiency - Combined Heat and Power generation (CHP).
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PEMPC Power Plant
Process Flow Diagram for a Ballard 250 kW PEMFC Plant
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Fuel Cell Powered Automobile - 1967
GM Electrovan
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Alkaline fuel cell modules
supplying 32 kW
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Hydrogen Fuel Cell Car
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Automotive Applications
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Fuel Cell Performance
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Fuel Cell Powered Automobile - Progress
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Fuel Cell Powered Automobile - Progress
Daimler-Chrysler NeCar:
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Fuel Cell Powered Automobile - Progress
Ford Focus Hydrogen -powered fuel cell vehicle
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Fuel Cell Powered Automobile - Progress
Honda fuel cell car
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Methanol Fuel Cell Powered Automobile
Toyota’s Methanol-powered Fuel cell Electric Vehicle
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Fuel Cell Powered Automobile
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An x-ray view of Mitsubishi's new
fuel cell Grandis minivan.
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Portable Application
Typically well under 100W of power with significantly higher power densities or larger
energy storage capacity than those of advanced batteries.
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generation on a larger scale , say 1 kw 10
continuous output to replace gasoline or
diesel generators or supply quiet electric power on boats, caravans or trucks.
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Solar Powered Airplane
Helios
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Instead of jet fuel, Helios has about 62,000
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energy from the Sun and convert it to electricity, which runs the 14 small motors, which turn the
14 propellers. The propellers are specially designed to pull the aircraft aloft even in the very thin
air that's 18 miles high. The next project for the Helios is to use fuel cells to store enough of the
sun's energy during the day to continue flying through the night. When this happens, Helios will be
able to stay up for weeks and months at a time.
The Helios, developed by Paul McCready, CEO of Aerovironment Corp.,
March 11, 2002
DIGITAL PHOTOS FROM SOLAR AIRPLANE TO IMPROVE COFFEE HARVEST
Funded by NASA
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Electric Powered Airplane
Supported by Foundation for Advancing Science and
Technology Education (FASTec) showed off the plane it is
developing as the world’s first piloted fuel-cell-powered
aircraft.
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The new Electric Plane, or E-Plane, is a high-speed, allcarbon French
DynAero Lafayette III, built and donated by
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American Ghiles Aircraft. The E-Plane is being converted
from a combustion engine to electric propulsion in three
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stages. The first flights, planned
for next year, will be on
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lithium2 ion batteries.3 The next flights will be
combination of lithium ion batteries4 augmented by a fuel
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cell. Finally, the aircraft will be powered totally by a
hydrogen fuel cell, with a range of more than11500 miles.
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Fuel Cell Based Aircraft Propulsion
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Source: NASA TM-2003-212393
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Fuel Cell Powered Aircraft
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Fuel Cell Motorbike to Hit US Streets
Top Speed: 50 mph (80 kmh)
Range: 100 miles (160 km)
Hydrogen Storage tank capacity: 1 kg
Cost: $6,000 - 8000
Manufacturer: Intelligent Energy,
London, UK
ENY: Emission Neutral Vehicle
Intelligent Energy is currently developing d evices called reformers that extract
hydrogen from biodiesel fuels (typically made from vegetable oils or animal fats)
and ethanol (generally made from grain or corn). The units would sell for around
U.S. $1,500 and could produce enough hyd rogen to fill up the ENV for about 25
cents per tank,. Eggleston said.
National Geographic News, August 2, 2005
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Fuel Cell System
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FC Implementation Requirements
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Direct Energy Conversion: Fuel Cells
Section 4.7.1 in the Text Book
References:
Direct Energy Conversion by Stanley W. Angrist, Allyn and Beacon,
1982.
Fuel Cell Systems, Explained by James Larminie and Andrew Dicks,
Wiley, 2003.
Fuel Cell Technology Hand Book, Edited by Gregor Hoogers, CRC
Press, 2002
Sustainable Energy Science and Engineering Center
Hydrogen - Oxygen Fuel Cell
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At
the
anode
the
hydrogen
gas
ionizes
releasing electrons and
creating H+ ions (or
protons). This reaction
releases energy.
2H 2 → 4H + + 4e−
At the cathode, oxygen
reacts with electrons
taken from the electrode,
and H+ ions from the
electrolyte, to form water
O2 + 4e− + 4H + → 2H 2O
An acid with free H+ ions. Certain
polymers can also be made to
contain mobile H+ ions - proton
exchange membranes (PEM)
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Fuel Cell Input and Output
Hydrogen Energy
Electricity Energy = VIt
Fuel Cell
Heat
Water
Oxygen Energy
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Power = VI; Energy = VIt
Gibbs free energy: Energy available to do external work, neglecting any
work done by changes in pressure and/or volume. In a fuel cell, the external
work involves moving electrons round an external circuit.
It is the change in Gibbs free energy ∆G, difference between the Gibbs free
energy of the products and the Gibbs free energy of the reactants or inputs
is important.
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Hydrogen-oxygen Fuel Cell
The basic reaction:
2H 2 + O2 → 2H 2O
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The product
is one mole of H2O ( 18g = 1 gmole) and the reactants are
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one mole of H2 (2g
The molar specific Gibbs free11energy, g in ‘per mole’ form is commonly
used.
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H 2 + O2 → H 2O
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∆g = g products − greac tan ts
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∆g = (g ) H 2O − (g ) H 2 − (g )O2
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∆g = −237kJ /mole
∆g = −199.6kJ /mole
Liquid water product at 298K
Gaseous water product at 873K
Negative sign indicates that the energy is released
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Fuel Cell Input and Output
If there are no losses, then all the Gibbs free energy is converted into electrical
energy.
Two electrons pass round the external circuit for each water molecule produced and
each
1 molecule of hydrogen used.
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+
−
H 2 → 2H + 2e
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O2 + 2e− + 2H + → H 2O
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For one mole3 of hydrogen used,
2N electrons pass round the external circuit- where
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N is the Avogadro’s number. If -e is the charge of one electron, then the charge that
flows is
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-2Ne = -2F coulombs
F is the faraday constant, or the charge on one mole of electrons. The electrical
work done moving this charge round the circuit is (E is the voltage of the fuel cell)
Electrical work done = charge × voltage = -2FE joules
With no losses, we have
∆g = −2FE
E=
−∆g
2F
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Thermodynamic Potentials
∆U = Q - W
H =10U + PV
F = U - TS
Helmoltz free energy
G = U - TS + PV Gibbs free energy
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Four quantities called "thermodynamic
potentials" are useful in the chemical
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thermodynamics of reactions and noncyclic processes. They are internal
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energy, the 6enthalpy, the Helmholtz free
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energy and the Gibbs
3 free energy.
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The four thermodynamic 7potentials
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related by offsets of the "energy from11
the environment" term TS (energy you
can get from the system’s environment
by heating and the "expansion work"
term PV (work to give the system final
volume V at constant pressure.
Q: heat added to the system
W: work done by the system
U: internal energy
T: absolute temperature
S: final entropy
V: final volume
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Second Law of Thermodynamics
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A fuel cell represented
as a control volume. E stands for electrical
potential, measured in volts. 11
For any isolated system, the 2nd law states that
∆Sisolated ≥ 0
Sgen = ∆Stotal = ∆Ssys + ∆Ssurr ≥ 0
Total change in entropy of both
the system and surroundings
entropy change in the
components of the system
entropy change in the
surroundings
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Second Law of Thermodynamics
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Considering the chamber in which chemical reaction takes place, the
system is a control volume with mass flowing across its boundaries. The
entropy change for the system is the10difference between the entropy of
products, SP and the reactants, SR with N representing the number of moles
5 in the reaction.
of each component
4 sys = S p − SR = ∑ N P sP − ∑ N R sR
∆S
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Any heat produced or consumed in the reaction is included in the
expression for the surroundings, where Qsurr is the heat transferred from the
system to the surroundings and To is the temperature of the surroundings.
∆Ssurr =
Qsurr
To
Sgen = (SP − SR )sys +
Qsurr
To
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The Maxwell Relations
Consider a simple compressible control mass of fixed chemical composition. The
following relations are found to be useful in the calculation of entropy in terms of
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other
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The thermodynamic property relations are
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du = Tds −
Pdv
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dh = Tds − vdP
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Entropy can not
be measured
We eliminate entropy from these equation by introducing two new forms of the
thermodynamic property relation.
Helmholtz function: A = U - TS ; a = u - Ts
da = du - Tds - sdT = -sdT - Pdv
Gibbs function: G = H - TS; g = h - Ts
dg = -sdT + vdP
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Chemical Thermodynamics
Chemical reactions proceed in the direction that minimizes the Gibbs energy G. The
change in G is negative as the reaction approaches equilibrium and at chemical
equilibrium the change in G is zero. The maximum work that an electrochemical cell
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can perform is equal to the change in G as reactants
go to products. This work is done
by the movement of electrical charge through a voltage, and at equilibrium
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3W max cell
= −∆G
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dG = dH
− TdS − SdT = d(U + PV ) − Tds − SdT
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dG = dU + PdV + VdP − TdS − SdT
dG = δQ − δW + PdV + VdP − TdS − SdT
For a spontaneous reaction at constant temperature and pressure in a closed system
and doing only expansion-type work, we will get
dG = δQ − TdS ≤ 0
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Chemical Thermodynamics
The effect of temperature and pressure on ∆G
δQ = TdS
For a reversible process:
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If the system is restricted to doing expansion work then
δW = PdV
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n is the number of moles
dG = VdP − SdT
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PV = nRT
For isothermal process
dG = nRT
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Ideal gas law
dP
P
P 
G2 − G1 = nRT ln 2 
 P1 
P 
G2 = G o + nRT ln o2 
 P  stands for standard reference state
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Chemical Thermodynamics
Equilibrium of a gas mixture:
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aA + bB ⇔ mM + nN
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Where a,3b, m and n are stoichiometric coefficients.
1
1
For a chemical reaction occurring at constant pressure and temperature, the
reactant gases A and B form products M10and N.
4
The change in the7 Gibbs energy
11
∆G = mgM + ngN − agA − bgB
Where g is in molar quantity (kJ/mol)

 P  
 P  
 P  
 P 
∆G = mgMo + RT ln Mo  + ngNo + RT ln No  − agAo + RT ln Ao  − bgBo + RT ln Bo 
 P  
 P  
 P  
 P 

∆G o = mgMo + ngNo − agAo − bgBo
In terms of standard Gibbs energy. The reference pressure is usually taken
as 1 atm.
Sustainable Energy Science and Engineering Center
Chemical Thermodynamics
Equilibrium of a gas mixture:
PMm PNn
∆G = ∆G + RT ln a b
PA PB
10
o
5
2
o
6∆G = ∆G + RT lnQ
PMm3PNn
Q= a b
PA PB
7
9
Q: Reaction coefficient for the pressures
1
1
4
11
The change in Gibbs energy of a reaction involving gases is:
∆G = ∆Go + RTlnQ
Sustainable Energy Science and Engineering Center
Chemical Thermodynamics
Maximum work:
The maximum work that a system can perform is related to the change in Gibbs
energy. For a reversible process (δQ = TdS)
1
10
dG = −δW + PdV + VdP − SdT
5 and temperature
At constant pressure
6
9
3
7
1
2
dG =4−δW + PdV = −(δW − PdV )
Since there is only electrochemical
work, We, in which electrical charge moves
11
through a voltage, we have
dG = −δW e
The Gibbs energy change is negative of the electrochemical work, we can then
write as
∆G = δW e
Sustainable Energy Science and Engineering Center
Chemical Thermodynamics
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
1
10
work done by electrons with the charge neF (ne 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
5
-1) moving through a potential difference, E ( voltage
constant
96,485C/mole
6
9
2
3 electrodes) is
difference across
1
W e = n e FE
4
7
11
∆G = −n e FE
∆G = −n e FE
o
o
∆G = ∆G + RT lnQ
o
∆G o RT
E=
−
lnQ
ne F ne F
E = Eo −
RT
lnQ
ne F
Eo is the standard electrode potential
We also assume here that a complete reversible
oxidation of a mole of fuel
Electrical work done = charge × voltage
Sustainable Energy Science and Engineering Center
Hydrogen - Oxygen Fuel Cell
For a hydrogen-oxygen fuel cell, the overall reaction stoichiometry
is
2
5
6
3
10
1
H 2 + O2 → H 2O
2
9
1
1
The electrons7 transferred
in this reaction, ne = 2. Using the partial
4
pressures of water, hydrogen
and oxygen in the reaction coefficient,
11
we then have
PH 2O
RT
E = Eo −
ln
n e F PH 2 PO1/2 2
Diluting the reactant gases will lower the maximum voltage that the
cell can produce.
Sustainable Energy Science and Engineering Center
Partial Pressures
In a mixture of gases, the total pressure is the sum of all the “partial
pressures”
of the components of the mixture. For example, in air at
1
10
0.1 MPa, the partial pressures of nitrogen and oxygen are 0.07809
MPa and 0.02095 MPa
are respectively.
5
6
9
The2 product 3gas stream contains two parts of H2 and one part of O2 by
moles and volume 7and 4the reaction takes place at 0.1 MPa, we will
11
have
1
2
× 0.1 = 0.0667Mpa
3
1
PO2 = × 0.1 = 0.0333MPa
3
PH 2 =
Sustainable Energy Science and Engineering Center
Thermal Efficiency
Thermal efficiency of a reversible heat engine is determined by
2
ηth =
6
5
W net
T
= 1− 10L
Qin
TH
9
1
1
3
Electrochemical
cells such as storage batteries and fuel cells, operate at constant
4
7 products
temperatures with the
of the reaction leaving at the same temperature as
11 chemical energy of the reactants is converted to
reactants (isothermal reaction). The
electrical energy instead of being consumed to raise the temperature of the products,
like in heat engines. Therefore this conversion process is less irreversible than the
combustion reaction. The maximum work for electrochemical cell is given simply
by
W max,cell = −∆G
Change in the Gibbs function between
products and reactants
Sustainable Energy Science and Engineering Center
Thermal Efficiency
The work, which is done by the movement of electrons through a difference in
electrical potential is
10
W cell = n e FE
1
5
6
2 the
With
higher value of the fuel9replaces Qin the maximum thermal efficiency
3
at the open circuit voltage
E4 o , of an electrochemical cell is given by
7
1
11
ηth,cell,max
n e FE o
=
HHV
For example, Eo = 1.23 V for a hydrogen-oxygen fuel cell
ηth,cell,max
n e FE o 2 × 96485 ×1.23
=
=
= 0.83
HHV
285840
HHV of H2 = 285.84 kJ/mol; LHV = 241 kJ/mole
Sustainable Energy Science and Engineering Center
Thermal Efficiency
2
10
5
6
9
3
7
4
11
It decreases to -164.429 kJ/mol at
1500K.
1
1
The Gibbs energy of the formation
of water vapor is -228.582 kJ/mol at
285.15K and 1 atm)
The current efficiency, a measure of
fuel utilization (or fuel consumed to
produce an electrical current ) is
given by
ηI =
I
−n e FN fuel
Fuel flow rate mol/s
Sustainable Energy Science and Engineering Center
Maximum Efficiency
Pressure: 1 atm
1
10
5
9
3
7
1
2
4
11
Note: Voltage losses are nearly always less at higher temperatures, so in practice
fuel cell voltages are usually higher at higher temperatures.
The waste heat from higher temperature fuel cells is more useful
Fuel cells do not always have a higher efficiency limit than heat engine.
Sustainable Energy Science and Engineering Center
Heating Values for Selected Fuels
Coal
1
CO
2
Methane
Natural gas
HHV (MJ/kg)
LHV (MJ/kg)
HHV/LHV
LHV/HHV
34.1
33.3
1.024
0.977
10.9
1.000
1.000
9
10.9
6
3
5
55.5
42.5
7
4
10
50.1
1
Fuel
1.108
0.903
38.1
1.115
0.896
11
Propane
48.9
45.8
1.068
0.937
Gasoline
46.7
42.5
1.099
0.910
Diesel
45.9
43.0
1.067
0.937
Hydrogen
141.9
120.1
1.182
0.84
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Reversibility
Actual work against maximum work potential:
For a heat engine this is equivalent to
1
5
6
3
ηheatengine =
9
W act
WCarnot
1
2
10
For fuel cells, this
7 can4 be written as
11
ηR =
ηact n e FE
E
=
=
ηrev n e FE o E o
For a hydrogen-oxygen fuel cell, the value for Eo is 1.23V at 295K and 1 atm.
If the voltage were 0.7 V, the efficiency ηR would be 0.57, indicating that
43% of the available energy was not converted to work. This work potential
(exergy) is lost, dissipated as heat because of the inefficiencies or
polarizations within the fuel cell.
Sustainable Energy Science and Engineering Center
Actual 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
ηi =
1
∆G
T∆S n e FE ItE
= 1−
= 10 =
∆H
∆H
∆H
∆H
5
Where6I is the current and t the for9which the current flows.
1
2
3
In a fuel cell under load,
4 the actual electromotive force that drives the electrons
7
through the external circuit will fall below E to some lower value, we will call
11
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 reaction at anode or cathode; c)
a concentration gradient may become established in the electrolyte or in the
reactants; d) Joule heating associated with the IR drop occurs in the
electrolyte.
The actual efficiency is
ηac =
−n e FE ac
∆H
Sustainable Energy Science and Engineering Center
Hydrogen - Oxygen Fuel Cell
2
5
6
3
7
H2
0.5O2
Enthalpy
0
Entropy
9
130.68 J/K
10
H2O
∆H = -285.83 kJ
0.5 x 205.14 J/K 69.91 J/K
T∆S = -48.7 kJ
4 Pressure: 1 atmosphere
Temperature:
298K
11
W = P∆V = (101.3 kPa)(1.5 moles)(-22.4 x 10-3 m3/mol)(298K/273K) = -3715 J
∆U = ∆H - P∆V = -285.83 kJ - 3.72 kJ = -282.1 kJ
∆G = ∆H - T∆S = -285.83 kJ + 48.7 kJ = -237.1 kJ
Change
-285.83 kJ
0
1
1
Quantity
η= −237.1/−285.83 = 0.83 (83%)
Sustainable Energy Science and Engineering Center
Homework Problem
Due: November 3, 2005
Examine how the ideal efficiency of a simple hydrogen-oxygen fuel cell
1
changes
as its operating temperature is 10
raised from 298K to 1000K. Also
calculate the actual and ideal efficiencies for the cell operating in the standard
conditions of 298K 5and 1 atm. The actual cell voltage is 0.75V while the cell
6
9
2
delivers
1.53 amps. The hydrogen
flow is 0.25 cm3/sec. Independent
3
measurements reveal
7 that4 0.06 cm /sec of hydrogen is escaping through
electrolyte unreacted.
11
1
Sustainable Energy Science and Engineering Center
Basic Fuel Cell Reactions
The overall reaction of a PEM fuel cell is:
1
H 2 + O2 ⇒ H 2O
2
This reaction is the same as the reaction of hydrogen combustion, which is
an exothermic process (energy is released):
1
H 2 + O2 ⇒ H 2O + heat
2
The heat, typically given in terms of enthalpy, of a chemical reaction is the
difference between the heats of formation of products and reactants:
∆H = (h f )
H 2O
− (h f ) −
H2
1
kJ
h
=
−286kJ
/g
−
0
−
0
=
−286
( f )O2
mol
2
Heat of formation of liquid water: -286 kJ/mol at 25oC and at atmospheric
pressure.
1
H 2 + O2 ⇒ H 2O(l) + 286kJ /mol
2
Reference: PEM fuel cells: theory and Practice, Frano Barber, Elsevier Academic Press, 2005
Sustainable Energy Science and Engineering Center
Hydrogen HHV and LHV
Hydrogen heating value is used as a measure of energy input in a fuel cell.
Hydrogen heating value: the amount of heat that may be generated by a
complete combustion of 1 mol of hydrogen = the enthalpy of hydrogen
combustion reaction = 286 kJ/mol
The result of combustion is liquid water at 25oC and the value of 286 kJ/mol is
considered as Higher Heating Value (HHV).
If the combustion is done with excess oxygen and allowed to cool down to 25oC,
the product will be in the form of vapor mixed with unburned oxygen. The
resulting heat release is measured to be 241 kJ/mol, known as Lower Heating
Value (LHV).
1
H 2 + O2 ⇒ H 2O(g) + 241kJ /mol
2
The difference between HHV and LHV is the heat of evaporation of water at
25oC:
H fg = 286 − 241 = 45kJ /mol
Sustainable Energy Science and Engineering Center
Theoretical Electrical Work
Not all the hydrogen’s energy can be converted into electricity.
The portion of the reaction enthalpy that can be converted to electricity
corresponds to Gibbs free energy:
∆G = ∆H − T∆S
∆S is the difference between entropies of products and reactants:
At 25oC and at one atmosphere
∆S = (S f )
H 2O
− (S f ) −
hf (kJ/mol)
sf (kJ/mol)
Hydrogen
0
0.13066
Oxygen
0
0.20517
Water (liquid)
-286.02
0.06996
Water (Vapor)
-241.98
0.18884
H2
1
(S f )O2
2
48.68 kJ/mol is converted
into heat.
∆G = −286.02 − 298 × (0.06996 − 0.13066 − (0.5 × 0.20517)) = −237.36kJ /mol
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
Electrical work:
W e = n e FE = −∆G
ne = 2 (two electron per molecule); F =96,485 Coulombs/electronmol.
The theoretical potential of fuel cell at 25oC and at one
atmosphere:
E=
237,340J /mol
−∆G
=
= 1.23Volts
n e F 2 × 96,485As /mol
Temperature Effect:
a, b and c are empirical
Coefficients, different
for each gas
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
a
b
c
H2
28.91404
-0.00084
2.01E-06
O2
25.84512
0.012987
-3.9E-06
H2O (g)
30.62644
0.009621
1.18E-06
∆HT = ∆H 298.15 + ∆a(T − 298.15)
(T − 298.15)
+ ∆b
2
2
(T − 298.15)
+ ∆c
3
3
 T 
(T − 298.15)
∆ST = ∆S298.15 + ∆aln
 + ∆b(T − 298.15) + ∆c
 298.15 
2
∆H (kJ/mol)
∆S (kJ/mol)
∆G (kJ/mol)
1
H 2 + O2 ⇒ H 2O(l)
2
-286.02
-0.1633
-237.34
1
H 2 + O2 ⇒ H 2O(g)
2
-241.98
-0.0444
-228.74
2
1
∆a = a H 2O − a H 2 − aO2
2
1
∆b = bH 2O − bH 2 − bO2
2
1
∆c = c H 2O − c H 2 − cO2
2
For T=298.15, E = 1.23 Volts
For T=373.15, E = 1.167 Volts
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Efficiency
∆G 237.34
=
= 0.83
∆H 286.02
∆G
228.74
η=
=
= 0.945
∆H LHV 241.98
η=
−∆G
−∆G n e F
1.23
η=
=
=
= 0.83
−∆H
−∆H
1.482
ne F
Potential corresponding to
hydrogen’s higher heating
value
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
Effect of Pressure:
The change in Gibbs free energy may be shown to be: ∆G = Vm dP
Where Vm= molar volume, m3/mol and P = pressure, Pa
For an ideal gas:
Therefore:
PVm = RT
dG = RT
dP
P
P
G = G + RT ln
Po
o
Go : Gibbs free energy at
standard temperature, 25oC
and at one atmosphere
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
Equilibrium of a gas mixture:
For a chemical reaction occurring at constant pressure and temperature, the
and N.
1 reactant gases A and B form products M10
aA + bB ⇔ mM + nN
5
6
Where
a, b, m and n are stoichiometric
coefficients.
9
1
2
3
The change in the7 Gibbs4 energy
11 = mG + nG − aG − bG
∆G
M
N
A
B
Where g is in molar quantity (kJ/mol)
  m   n 
P
P
 M   N  
 P   P  
∆G = ∆G o + RT ln o a o b 
   
  PA   PB  
  Po   Po  
In terms of standard Gibbs energy. The reference pressure is usually taken
as 1 atm.
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
Equilibrium of a gas mixture:
PMm PNn
∆G = ∆G + RT ln a b
PA PB
10
o
5
2
o
6∆G = ∆G + RT lnQ
PMm3PNn
Q= a b
PA PB
7
9
Q: Reaction coefficient for the pressures
1
1
4
11
The change in Gibbs energy of a reaction involving gases is:
∆G = ∆Go + RTlnQ
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
For a hydrogen-oxygen fuel cell, the overall reaction stoichiometry
is
2
5
6
3
10
1
H 2 + O2 → H 2O
2
9
The Nernst equation
4 becomes:
7
11
∆G = ∆G o +
1
1
P
RT
ln H 2O1/ 2
n e F PH 2 PO2
1/ 2
P
P
RT
H
O
E = Eo +
ln 2 2
ne F
PH 2O
When liquid water is produced in a fuel cell: PH 2O = 1
For higher reactant pressures the cell potential is higher
Sustainable Energy Science and Engineering Center
Theoretical Fuel Cell Potential
Air vs oxygen:
10
2
5
6
3
9
∆E = E O2 − E air
7
4
0.5
RT PO2
RT  1 
=
ln
=
ln

n e F Pair n e F  0.21
1
1
11
At 80oC , the voltage loss becomes 0.012V. In
practice, this is much higher.
Sustainable Energy Science and Engineering Center
Home work
1. For a hydrogen/air fuel cell operating at 60oC with reactant
gases at atmospheric pressure and with liquid water as a
product, calculate the theoretical cell potential taking into
account the changes of reaction enthalpy and entropy with
temperature (equations for ∆HT and ∆ST).
2. Calculate the expected difference in theoretical cell potential
between a hydrogen/oxygen fuel cell operating 80oC and 5 bar
for reactant gases and the same fuel cell operating at
atmospheric pressure. What if the pressure is increased to 10
bar?
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
A chemical reaction involves both a transfer of electrical charge and a charge
in Gibbs energy. The electrochemical reaction occurs at the interface between
the electrode and electrolyte.
1
10
Electrolyte
Backing layer
6
9
3
Catalyst7layer
1
2
5
4
11
Gas diffusion layer
Typical Electrode Design
The charge must overcome an activation energy barrier in moving from
electrolyte to an electrode. The magnitude of the barrier determines the rate of
reaction. The Butler-Volmer equation gives the current density, that is derived
from transition state theory of electrochemistry.
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
The general half-reaction expression for the oxidation of a reactant is:
1
Where reactant R loses electrons and becomes Ox, the product of oxidation, and
6
9
2n is the
number
of
electrons
that
are transferred in the reaction. For the opposite
3
4
direction, Ox gains7 electrons,
undergoing reduction to form R in the halfreaction.
11
1
On an electrode at equilibrium conditions, both processes occur at equal rates
and the currents produced by two reactions balance each other, giving no net
current from the electrode
Source: Fuel cell technology Handbook - Chapter 3.
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
Single-step Electrode reactions
Considering only one direction of the reaction, the current produced is
1
10
5 (in amperes), A is the active area of the electrode (cm2), F
Where
I
is
the
current
6
9
is the Faraday’s
constant
(the
charge per mole of electrons= 96,485
3
i
= nF.j
(coulombs/mole e-) 7and j is4 the flux of reactants reaching the surface (mole/sec).
The current density (per unit area)11is
1
i = nF ⋅ j
The current is produced from the reactants that reach the surface of the electrode
and lose or gain electrons. The flux is determined by the rate of conversion of
the surface concentration of the reactant. For the forward reaction (subscript f),
the flux arising from the reduction of Ox is
j f = k f [Ox ]o
Forward rate coefficient
Surface concentration
of the reactant
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
Single-step Electrode reactions
For the backward reaction (subscript b), the flux produced by the oxidation of R
is 1
10
6
9
3
7
The net flux is
j b = k b [R]o
1
2
5
Backward
rate coefficient
4
11
j = j f − jb
The net current density that appears on the electrode when the current is
produced is given by
i = n(Fk f [Ox ]o − Fkb [R]o )
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
Butler-Volmer Equation
From the Transition state theory (refer to any physical chemistry book), the
1
heterogeneous
rate coefficient, k. is a 10
function of the Gibbs energy of
activation and is given by
2
6
5
3
Boltzmann’s constant
 −∆G ≠ 
kB9T
k=
exp

4
h
7
 RT

(1.38049x10-23 j/oK)
Plank’s constant (6.621x10-34 Js)
Gibbs energy of activation
(kJ/mol)
Because an electrochemical reaction occurs in the presence of an electrical
field, the Gibbs energy of activation consists of both chemical and electrical
terms
∆G ≠ = ∆Gc≠ + nF∆φ
Reduction
Change in electrical potential
≠
≠
Oxidation
∆G = ∆Gc − n (1− β )F∆φ
Transfer coefficient (0.5)
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
For a reduction reaction
 −∆Gc,≠ f   −nβF∆φ 
kB T
10
kf =
exp
 exp




h
RT
RT


1
6
3
9
Chemical Component
4
11 as
With the over potential is defined
1
2
5
Electrical Component
η = ∆φ − ∆φ rev
For a hydrogen-oxygen fuel cell, the reversible potential of the anode is 0 V; at the
cathode it is +1.23 V at 25oC.
 −∆Gc,≠ f   −nβF∆φ   −nβFη 
kB T
rev
kf =
exp
 exp
 exp





RT
RT
RT
h


Reduction
 −∆Gc,≠ f   −n (1− β )F∆φ   −n (1− β )Fη 
kB T
rev
kb =
exp
 exp
 exp

RT
RT
RT
h






Oxidation
Sustainable Energy Science and Engineering Center
Electrochemical Kinetics
Butler-Volmer Equation
when the electrode is in equilibrium and at its reversible potential, the
overpotential
and external current are
both zero. In this case, the
1
10
exchange current density, io is defined as
9
1
6
5
nF [Ox ]o k o, f = nF [R]o k o,b ≡ io (A /cm 2 )
The current3 density is given
by
4
7
  −nβFη 11
 −n (1− β )Fη 
i = io exp
 − exp



RT
RT



η = ∆φ − ∆φ rev
Reduction term
Oxidation term
If η > 0 then the oxidation component becomes large and the reduction reaction on the
on the electrode becomes small. The net current density is negative, which corresponds
to a net oxidation reaction where electrons leave the anode of the fuel cell. In operating
fuel cells, because of the cathode reaction of oxygen reduction requires a more
significant overpotential (η) than the anode reaction. For hydrogen-oxygen fuel cell, the
reversible potentials at the anode and cathode are 0V and 1.23 V respectively.
Sustainable Energy Science and Engineering Center
Fuel Cell Components
Fuel Cell Components Impact on Performance
The proton exchange membrane fuel cell (PEMFC)
1
5
6
9
3
7
1
2
10
4
11
Special plastic membrane used as the electrolyte + electrodes (anode & cathode)
is called the membrane electrode assembly (MEA). It is not thicker than a few
hundred microns. When supplied with fuel and air , generates electric power at
cell voltages around 0,7V and power densities up to about 1 W/cm2 electrode
area.
Sustainable Energy Science and Engineering Center
The Proton Exchange Membrane Fuel
Cell (PEMFC)
1
5
6
9
3
7
4
H 2 → 2H + + 2e−
Anode
1
O2 + 2H + + 2e− → 1H 2O
2
1
2
10
(Er = 0 V)
Cathode (Er = 1.23 V)
11
The electrochemical reactions take place at the anode and the cathode
catalyst layer respectively. The best catalyst is platinum. The catalyst is used
at the rate of about 0.2 mg/cm2. The basic raw material cost of platinum for a
1- kW PEMPC cell is about $10 - a small portion of the total cost.
Sustainable Energy Science and Engineering Center
The PEM Fuel Cell
The gas diffusion layer and backing layer (substrate) at
the anode allows hydrogen to reach the reactive zone
Backing layer
within the electrode. Upon reaching, protons migrate
through the
1 ion conducting membrane, and electrons 10
are conducted through the gas diffusion layer and
Catalyst layer
ultimately to the electric terminals of the fuel stack.
5
The substrate therefore
has
to
be porous to allow gas
6
9
2
and electrically conducting.
Not
all
of
the
chemical Gas diffusion layer
3
4 is converted
energy supplied to the MEA by7 reactants
into electric power. Heat will also be generated and the
11
substrate also acts as a heat conductor to remove
heat
from the reactive zones of the MEA.
Electrolyte
1
Membrane Electrode
Assembly (MEA)
Water is formed at the cathode. If the water is in liquid form, there is a risk of liquid blocking the pores
within the substrate and consequently gas access to the reactive zone. The oxidant used in most
applications is air, therefore, 80% of the gas present is inert. Fuel cell operation will result in depletion
of oxygen towards the active cathode catalyst.
The membrane acts as a proton conductor, thus requires it to be well humidified. Because
the proton conduction process relies on membrane water. As a consequence, an additional
water flux from anode to cathode is present and is associated with the migration of protons.
Humidity is often provided with the anode gas by pre-humidifying the reactant.
Sustainable Energy Science and Engineering Center
The PEM Fuel Cell
MEA Component
Task/effect
Anode Substrate
Fuel supply and distribution, Electron
conduction, heat removal from reaction zone,
water10
supply into electrocatalyst
Anode catalyst layer
2
6
5
3
7
Proton exchange membrane
Cathode catalyst layer
Cathode substrate
9
4
Catalysis of anode reaction, proton conduction
into membrane, electron conduction into
substrate, water and heat transport
1
1
Proton conduction, water transport, electronic
11 insulation
Catalysis of cathode reaction, oxygen transport to
reaction sites, proton conduction from membrane
to reaction sites, electron conduction from
substrate to reaction zone, water removal from
reaction zone into substrate and heat removal.
Oxidant supply and distribution, electron
conduction towards reaction zone, heat removal
and water transport
Source: Fuel cell technology handbook, Chapter 4
Sustainable Energy Science and Engineering Center
Factors Limiting Fuel Cell Performance
10
1
The losses that takes place at electrodes are
generally attributed to some form of
polarization - a term used to denote the
1 between the theoretical voltage of
difference
a given electrode and the experimental
voltage when the current is5 drawn from the
6
2
cell. The
losses 3are classified in 9three
4
categories:
Chemical 7
polarization.
Concentration polarization and resistance
11
polarization.
The theoretical value of the open circuit
voltage of a hydrogen-oxygen fuel cell is
given by
V=E=
−∆g f
2F
This gives a value of about 1.23 V for a cell
operating at 298K.
Vac = V − ∆Vconc(c ) − ∆Vchem(c ) − ∆Vconc(a ) − ∆Vchem(a ) − ∑ IR
Sustainable Energy Science and Engineering Center
Chemical or Activation Polarization
It is customary to express the voltage drop due to chemical polarization by strictly
empirical equation, called the Tafel equation as
2
5
6
3
7
∆Vchem = a′ + b′ ln10J
−RT
a′ =
ln( j o )
αnF
9
−RT
b4′ =
αnF
1
1
11
Where J is the apparent current density at the electrode, α and jo are kinetic parameters, the
former being a constant that represents the fraction of ∆Vchem that aids a reaction in proceeding
(For a hydrogen electrode, its value is about 0.5 for a great variety of electrode materials and
for the oxygen electrode it is between 0.1 and 0.5. The best possible value of b` will have little
impact), the later being the exchange current density, intimately related to the height of the
activation energy barrier. 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 reactants and exit to
products. Increases in pressure and temperature will also generally decrease chemical
polarization.
Sustainable Energy Science and Engineering Center
Chemical Polarization
The effect of current density and the exchange current density on
chemical polarization loss
1
5
6
9
3
7
4
11
Potential
loss
1
2
10
Sustainable Energy Science and Engineering Center
Concentration Polarization
After current begins to flow in an electrochemical cell, there is a loss of potential due
to inability of the surrounding material to maintain the initial concentration of the
bulk fluid. This uneven concentration produces a back EMF which opposes the
1
10 completely reversible conditions. The
voltage that a fuel cell would deliver under
concentration of electrolyte in the vicinity of an electrode during reaction should be
5
maintained
at
the
desirable
condition.
6
9
3
7
4
11
1
2
RT  c if 
∆Vconc( c ) =
ln 
nF  c b 
cb : average concentration in bulk electrolyte
cif : concentration at the interface
∆Vconc( c ) =
RT  J L 
ln

nF  J L − J 
∆Vconc( a ) =
RT  J L + J 
ln

nF  J L 
JL =
nFD
c
δ′ b
D: diffusion coefficient
Sustainable Energy Science and Engineering Center
Concentration Polarization
An empirical equation better describes the concentration polarization losses:
2
5
6
3
∆Vconc = c × e
9
j
d
1
10
1
Where c and d are empirical
4 coefficients with values of c= 3 x10-5 V and d =
7
0.125 A/cm2.
11
For less than 0.5 A/cm2, the potential loss due to concentration polarization is
quite small and increases rapidly to about 0.2 V at 1.5 A/cm2.
Sustainable Energy Science and Engineering Center
Resistance Polarization
When an electrochemical reaction occurs at an electrode there is generally
a significant change in the specific conductivity of electrolyte which involves
an1 additional loss of potential.
10
Hydrogen-oxygen fuel cells employing concentrated solutions of potassium
5
or sodium
hydroxide
as electrolytes
show that resistance polarization is
6
9
2
3 even at fairly high current densities.
negligibly low
1
7
4
Ohmic Losses: V= IR
11
In most fuel cells the resistance is mainly caused by the electrolyte, through
the cell interconnects or bipolar plates. Reducing these internal resistances
can be accomplished by the use of electrodes with the highest possible
conductivity, good design and use of appropriate materials for the bipolar
plates and cell interconnects and making electrolyte as thin as possible.
Typical values for R are between 0.1 and 0.2 Ωcm2.
Sustainable Energy Science and Engineering Center
Heat Transfer
In cells with high current densities, it is often important to calculate the
heat transfer within a fuel cell.
2
6
2)
3)
10
The electrochemical reaction producing
the current in the cell is not
adiabatic which gives rise to a reversible heat transfer whose
magnitude is 5T∆S.
1
9
1
1)
Some3 of the fuel reacts chemically with the oxidizer rather than
4
7
electrochemically
to generate an irreversible heat transfer.
11
The cell operates at some voltage less than the theoretical open circuit
voltage with the difference manifesting itself as I2R and I ∆V heat in
the cell (I is the current drawn and R and ∆V represent irreversible
resistances and voltage drops).
1
QÝt = QÝrev + QÝchem(irr) + QÝ∆V =
[T∆S + +nF (Vac − V )]
nF
Generally small
Sustainable Energy Science and Engineering Center
Fuel Cell Voltage Losses
0.5
Activation polarization loss
Potential Loss (V)
0.4
0.3
0.2
Ohmic losses
0.1
Concentration polarization loss
0
0
500
1000
Current density (mA/cm2)
1500
Sustainable Energy Science and Engineering Center
Polarization Curve
10
1
6
9
3
7
1
2
5
4
11
Source: http://www.h2net.org.uk/PDFs/EndUse/H2NET-2.pdf
Sustainable Energy Science and Engineering Center
Direct Energy Conversion: Fuel Cells
Section 4.7.1 in the Text Book
References and Sources:
Direct Energy Conversion by Stanley W. Angrist, Allyn and Beacon,
1982.
Fuel Cell Systems, Explained by James Larminie and Andrew Dicks,
Wiley, 2003.
Fuel Cell Technology Hand Book, Edited by Gregor Hoogers, CRC
Press, 2002
Fuel Cell Hand Book, US DOE - available on the web.
Sustainable Energy Science and Engineering Center
Fuel Cell Design Calculation
Performance of a single cell operating on hydrogen as the fuel and oxygen in air as the
oxidizer. The porous electrodes of either carbon or nickel employed are separated by a
30% solution
of KOH (potassium hydroxide). The
1
10 cell operates at a temperature of 298K
and the fuel and air are supplied at one atmosphere.
5 fraction of the reaction which is occurring electrochemically to
The faradic6 efficiency (the
9
give 2a current is 3called faradic or current efficiency, ηF = 1/(nFNfu); where Nfu is the total
4 electrochemically per second) for the cell is estimated to
number of moles of fuel reacted
7
be 95%
11
1
20% of the fuel supplied to the cell will escape through the electrolyte unreacted.
Separation between electrodes, w= 0.25cm
Height of the cell, l = 12 cm
w =0.25cm
Depth of the cell, d = 6cm
l =12cm
Average electrolyte velocity, u = 5cm/s
(Supplied by an external pump)
Sustainable Energy Science and Engineering Center
Electrolyte Properties
The physical properties of the electrolyte at 298K area as follows:
1
10
Concentration: 30% KOH (wt) or cb= 6.9 x 10-3 mole/cm3
2
9
3
Dynamic Viscosity:
µ = 2.434 x 10-2 poise
1
5
3
Density:
ρ
=
1.294
gm/cm
6
7
Kinematic Viscosity: ν = 1.887 x 1011-2 cm2/s
Conductivity: σ = 0.625 (ohm-cm)-1
Diffusion Coefficient for OH- ions: D = 1.5 x 10-7 cm2/s
Sustainable Energy Science and Engineering Center
Open Circuit Voltage
We now calculate the open circuit voltage. We assume that each electrode reaction
follows the half-cell reactions
2
10
H 2 (g) → 2H + + 2e−
6
+
−
0.5O
5 2 (g) + 2H + 2e → H 2O(l)
9
Yielding a cell
3 reaction of
Anode
Eo = 0
Cathode Eo = 1.23v
1
1
7 H (g)4+ 0.5O (g) → H O(l)
2
2
2
11
We may now apply the Nernst equation to our cell potential
E = Eo −
PH 2O
RT
ln
n e F PH 2 PO1/2 2
Pi =
ni
Pt
nt
where Pt is the total pressure of the mixture and ni/nt is the mole fraction of the ith
constituent.
Sustainable Energy Science and Engineering Center
Open Circuit Voltage
The partial pressures in the Nernst equation are often eliminated in favor of a
function that is derived from general equation of state, generally denoted by f,
the fugacity, which is a measure of the tendency of a component to escape
1
from
a solution. It is equal to partial pressure10only when the vapor behaves like
an ideal gas. We also define a quantity called the activity aA = fA/fAo. We can
5equation as
then write
the
Nernst
6
9
3
7
E 4= E o −
a H 2O
RT
ln
n e F a H 2 a1/O22
1
2
11
The activity of H2O to be used in this equation should be that of water in 30%
KOH solution. This value is somewhat less than one, but we may take it as one
to make our answer conservative. The hydrogen is supplied at one atm (has an
activity of one since the activity is equal to the partial pressure of an ideal gas),
the activity of oxygen is 0.21. Then we have
E = V = 1.23 −
(1.99)(298) ln (1)
(2)(23060) (1)(0.21)0.5
E = V = 1.23 − 0.013ln(2.18) = 1.22volts
Sustainable Energy Science and Engineering Center
Chemical Polarization
We initially assume an operating current density for our fuel cell of 0.5
amp/cm2
1
Use Tafel equation to calculate losses due to10chemical polarization.
2
6
5
∆Vchem = a′ + b′ ln J
7
−RT9
ln( j o )
4 αnF
−RT
b′ =
αnF 11
a′ =
3
∆Vchem(a ) = 0.14 + 0.005ln J
∆Vchem(c ) = 0.20 + 0.007ln J
Where the current density is expressed in milliamperes per square centimeter.
∆Vchem(a ) = 0.14 + 0.005ln(500) = 0.17volt
∆Vchem(c ) = 0.20 + 0.007ln(500) = 0.24volt
Sustainable Energy Science and Engineering Center
Concentration Polarization
We now calculate the polarization due to concentration gradients in the
electrolyte near the electrodes.
RT  J L 
∆Vconc(c ) =
ln

nF  J L − J 
1
JL =
 JL + J 
∆Vconc(a ) =
ln

nF  J L 9
5 RT
6
3
nFD
cb
δ′
1
2
10
4
Calculation of the limiting
current
density:
7
11 For a fully established flow between the
Velocity of the electrolyte = 5 cm/s;
electrodes, we have
J L,av = 1.62nFc b u(Re w )
−2 / 3
Re w =
Sc =
uw
ν
D
ν
= 66.2
= 1.26x10 5
w
= 0.0208
l
J L,av = 0.956amp /cm 2
(Sc ) (w /l)
−2 / 3
−1/ 3
Sustainable Energy Science and Engineering Center
Concentration Polarization
RT  J L 
∆Vconc(c ) =
ln
 ≈ 0.01volt
nF  J L − J  10
1
6
9
3
7
1
2
RT  J L + J 
ln
 ≈ 0.01volt
5∆Vconc(a ) =
nF  J L 
4
The gas side concentration polarization at the anode is ignored. We will
11 the air electrode using the partial pressure
calculate the gas side polarization at
of oxygen in the air for pg.
 1 
RT  Pr 
∆Vconc(g ) =
ln  = 0.013ln
 = 0.02volts
 0.21
nF  Pg 
Where Pr is the gas pressure in the pores of the electrode
Sustainable Energy Science and Engineering Center
Resistance Polarization
0.5 × 0.2510
IR =
=
= 0.2volts
0.625
σ
Jw
1
6
5
9
2 now compute the actual operating
We
voltage of the fuel cell by subtracting
3
from the open circuit7voltage
4 1.22 volts, the various polarization losses and IR
drop across the cell:
1
11
Vac = 1.22 − 0.17 − 0.24 − 0.01− 0.01− 0.02 − 0.02 = 0.57Volt
The power out put of the cell:
Po = Vac I = Vac JA = 0.57 × 0.5 × 72 = 20.5watts
Sustainable Energy Science and Engineering Center
Efficiency
The thermal efficiency is given by
−nFVac −2(mole − elec /mole) × 23.06(kcal /volt − mole) × 0.57Volt
=
= 38.5%
∆H
−68.32kcal
/mole
1
10
∆H = −68.32kcal /mole
ηac =
5
3
9
The efficiency based 7on the 4actual voltage is
ηv =
1
F2= 23.06
6 kcal/volt-mole
Vac 0.57 11
=
= 46.7%
V 1.22
Assuming that the product of the reaction is liquid water, the faradaic
efficiency is given by.
ηF =
JA
0.5 × 72
=
= 0.95
nFN fu 2 × 96500 × N fu
N fu = 1.96 ×10−4 moleH 2 /s
F = 96,500 (amp-sec)/(mole-sec)
Sustainable Energy Science and Engineering Center
Heat Transfer
QÝrev = ηF N fu (∆H − ∆G) = 0.95 × N fu × (−68.32 − (−56.69)) = −9.1watts
1 ∆H
= −68.32kcal /mole
10
∆G = −56.69kcal /mole
6
3
9
QÝchem(irr ) = (1− ηF )N fu (∆H ) = −2.8watts
1
2
5
4
7
QÝ∆V = I (Vac − V ) = −23.4watts
11
Total heat that must be removed from the cell for it to stay steady state is 35.3
watts, 50% larger than net power output of the cell.
Sustainable Energy Science and Engineering Center
Home Work
Design calculation for a fuel cell:
Home work: Using your own calculations reproduce the curve below for the
1
10
fuel discussed in the class today.
6
9
3
7
4
11
1
2
5
Sustainable Energy Science and Engineering Center
Heat Generation
Area = 100 cm2; Operating pressure = 1 atm; Operating Temperature = 80oC;
E = 0.7 V; Current generation = 0.6 A/cm2.
10 - electrical power
Power due to heat = Total power generated
1
6
3
= (Videalx Icell9) - (Vcellx Icell)
4
=7 (1.2V -0.7V) x 60A
11
= 0.5 V x 60A = 30 J/s
= 108 KJ/hr = 30 W
While generating about 42 W of electrical energy.
1
2
Pheat =5 Ptotal - Pelectrical
Sustainable Energy Science and Engineering Center
Operating Variables
Pressure, Temperature, Gas composition, Reactant utilization and Current density
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Operating Pressure
1
5
6
9
3
7
1
2
10
4
11
P2
P1
C ≈ 0.03 − 0.06volts
∆Vgain = C ln
0.286


T1  P2 
∆Vloss = 3.58 ×10
−1λ
 
ηmηc  P1 

−4
Motor and drive system
efficiency~ 0.95
Compressor
efficiency ~ 0.75
Stoichiometry (~ 2.0)
Sustainable Energy Science and Engineering Center
Operating Pressure
2
10
5
6
9
3
7
4
11
1
1
Net voltage change resulting
from
operating
at
high
pressure for two different PEM
fuel cell models
Sustainable Energy Science and Engineering Center
Temperature Effect
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Polarization Contribution
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Effect of Oxygen Pressure
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Polarization Curve
10
1
6
9
3
7
1
2
5
4
11
Source: http://www.h2net.org.uk/PDFs/EndUse/H2NET-2.pdf
Sustainable Energy Science and Engineering Center
Polymer Electrolyte Membrane Fuel Cell
Load
Fuel Cell stack
1
6
9
3
7
4
11
1
2
5
Sustainable Energy Science and Engineering Center
The Backing Layer
Equivalent concentration
profile
Effective diffusion of each reactant gas
to the catalyst on the Membrane
Electrode Assembly (MEA). The diffusion
takes place from a region of high
concentration, outer side of the backing
layer, to a region of low concentration,
the inner side of the backing layer next
to catalyst layer where the gas is
consumed by the reaction. The gas is in
contact with the entire surface area of
the catalyzed membrane.
1
True
concentration
profile
δ
Diffusion layer
Porous carbon cloth or carbon paper,
typically 100 - 300µm thick. About 4 - 12
sheets are used.
Assist in water management during the
cell operation. Allows the right amount
of water vapor to reach the MEA to keep
the membrane humidified. It also allows
the liquid water produced at the cathode
to leave the cell.
Sustainable Energy Science and Engineering Center
The Bipolar Plate
Main tasks: Current conduction; Heat
conduction; control of gas flow and product
water removal
10
2
5
6
9
3
7
4
11
The first main task is to provide reactant
gases evenly across the active area of the
MEA. Current designs have channels to
carry reactant gas from the point at which it
enters the cell to the point at which the gas
exits. The flow field in the channels has a
large impact on the distribution of gases.
The design also affects water supply to the
membrane and water removal from the
cathode.
1
1
The second main task is that of current
collector.
Usually made of graphite into which channels are
machined. These plates have high electronic and
good thermal conductivity and stable in the
chemical environment inside the cell.
Sustainable Energy Science and Engineering Center
Water Management
1
5
6
9
3
7
1
2
10
4
11
Use the water leaving the cell
humidification.
Channels in bipolar plates
to do the
Sustainable Energy Science and Engineering Center
PEM Fuel Cells (PEMFC)
Some times referred to as Solid Polymer fuel cell (SPFC)
The1 electrolyte: Ion conduction polymer10(works at low temperatures, hence
start quickly)
5
3
1
Electrodes:
Catalyzed porous electrodes
6
9
2
4
The anode-electrolyte-cathode
assembly (membrane electrode assemblies
7
(MEA)) is one item and is very thin.
11
The MEA’s are connected in series using bipolar plates.
No corrosive fluid hazards - suitable for use in portable applications and
widely used in cars and buses
The most commonly used polymer membrane: Nafion
Source: Fuel Cell systems Explained by James Larminie & Andrew Dicks, Wiley, 2003, Chapter 4.
Sustainable Energy Science and Engineering Center
Polymer Electrolyte
Most commonly used: sulphonated fluoropolymers - fluoroethylene
1
5
6
9
3
7
4
sulphonated fluoroethylene
1
2
10
(PTFE)
11
The strong bonds between the fluorine and the carbon make it durable and
resistant to chemical attack and can be made into very thin films (~50µm). It
is strongly hydrophobic, which helps to drive the product water out of the
electrode.
Sustainable Energy Science and Engineering Center
Electrodes
Platinum is used generally as the catalyst (0.2 mg/cm2)
Anode and cathode are essentially the same . The platinum is formed into very small particles
on the surface
of larger particles of finely divided carbon powders.
1
10
The carbon-supported catalyst is fixed to a porous and conductive
5
material2 such6 as carbon cloth or carbon paper.
The carbon paper
9
1
3
4-the gas diffusion layer.
also diffuses the gas on to catalyst
7
Alternatively, the platinum on carbon 11
catalyst is fixed directly to the electrolyte, thus
manufacturing the electrode directly on to the membrane. Then a gas diffusion layer - carbon
cloth or paper (200 to 500 µm thick) is added. It also forms an electrical connection between
the carbon-supported catalyst and the bipolar plate.
Sustainable Energy Science and Engineering Center
Platinum Loading Effect
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Water Management
Proton conductivity is proportional to the water content.
1 moving from the anode to the cathode 10
The H+ ions
pull water
Molecules with them (up to five
H2O molecules are dragged
5
4
7 electrolyte can be dried out.
densities, the anode side of the
11
At temperatures over 335K, the electrodes are typically dry.
Solution: Air and hydrogen humidification before
they enter the cell.
1
6
9
for each 2proton - electro-osmotic
drag).
At
high current
3
Sustainable Energy Science and Engineering Center
Heat Production
2 kW fuel cell system
12 W fuel cell
2
10
5
6
9
3
7
4
11
1
1
Sustainable Energy Science and Engineering Center
PEM Fuel Cell Stack
Load
1
6
9
3
7
4
11
1
2
5
Sustainable Energy Science and Engineering Center
Multi-cell Stack Performance
2
10
5
6
9
3
7
4
11
Source: Simulation study of a PEM Fuel cell
system fed by Hydrogen produced by partial
oxidation by Ozdogan S., et al.
Hydrogen produced from
gasoline
1
1
Simulation Results PEMPC stack
Sustainable Energy Science and Engineering Center
Multi-cell stack Performance
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
PEMFC System
Hydrogen
tank
10
1
5
9
3
7
4
11
1
2
6
Sustainable Energy Science and Engineering Center
Cooling Air Supply
1
5
6
9
3
7
1
2
10
4
11
Ballard Nexa PEM Fuel cell.
Sustainable Energy Science and Engineering Center
Fuel Cell Systems and
Hydrogen Production
Sustainable Energy Science and Engineering Center
Fuel Cell Type
10
1
6
< 5kW
9
3
7
1
2
5
4
5 - 250kW
11
< 100W
250kW
250kW - MW
2kW - MW
Sustainable Energy Science and Engineering Center
Electrochemical Reactions
10
1
6
9
3
7
4
11
1
2
5
Sustainable Energy Science and Engineering Center
Efficiency
10
1
6
9
3
7
4
11
1
2
5
Sustainable Energy Science and Engineering Center
Efficiency
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Pressure Effects
Hydrogen pressure
Oxygen pressure
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Temperature Effect
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Humidity effect at Room Temperature
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Parametric Effects: Temperature has most effect
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Air Vs O2
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
PEMFC Emissions
PC25 Fuel cell: 200 kW
Fuel: Natural gas
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Fuel Cell System
Fuel Cell Stack
1
Fuel Delivery
5
6
9
3
7
4
11
1
2
Control System
10
Air Delivery
Thermal Management
Water Management
Power Conditioning
Sustainable Energy Science and Engineering Center
Critical Materials and Costs
Example: Polymer Electrolyte Fuel Cell Stack (1 kW)
- Polymer membrane
1
10
- Catalyst (precious metals)
5
9
3
7
1
2
- Bipolar
plate
6
4
Source: Material development for cost reduction of PEFC by J. Garche, L. Jorissen & K.A. Friedrich, Center
for Solar energy and hydrogen research, Baden-Wuerttemberg (ZSW), Germany
Sustainable Energy Science and Engineering Center
PEMFC Challenges
• MEA tolerance for CO in reformed H2
• High temperature operation (~120oC)
• MEA Durability -
40,000 hrs with < 10% degradation, 1% cross over, area resistance <0.1 ohm.cm2
• Cost - $1500/kW, $10/kW for MEA
• Efficiency - 30 ~ 50%
• Fixed cost of Graphite bipolar plate: $130/kW
• Running cost of hydrogen per kWh : $0.405
Source: Hazem Tawfik, Sept 2003
Sustainable Energy Science and Engineering Center
Fuel Cell Types
Alkaline (AFC)
1
10
Solid Polymer (SPFC, PEM or PEFC)
6
9
Direct
Methanol
(DMFC)
3
7
4
Phosphoric Acid (PAFC)
11
Molten Carbonate (MCFC)
Solid Oxide (SOFC)
1
2
5
Sustainable Energy Science and Engineering Center
Fuels
Application
Hydrogen
10
Transport,
stationary & Portable
Methanol
2
6
Natural3Gas
Gasoline
Transport & Portable
5
9
7
4
Stationary
Transport
11
Diesel
Transport
Jet Fuels
Military
1
1
Type
Sustainable Energy Science and Engineering Center
Fuel Reforming
Hydrogen is produced from fuel reforming system such as
methane and steam.
1
6
3
CH 4 +
5 H 2O → 3H 2 + CO
CO + H 2O → H 2 +9 CO2
7
water gas shift reaction
1
2
10
4
11
Carbon monoxide has a tendency
to occupy platinum catalyst
sites, hence must be removed.
Other fuels:
C8 H18 + 8H 2O →17H 2 + 8CO
Sustainable Energy Science and Engineering Center
Fuel Reformer
Steam reforming: It is mature technology, practiced industrially on a
large scale for hydrogen production. The basic reforming reactions
CnHm are
1 for methane and a generic hydrocarbon
10
6
9
CH 4 + H 2O 3→ CO + 3H 2 ;∆H = 206kJ /mol
7 m 4 
Cn H m + nH 2O → nCO +  + n H 2
2

11
CO + H 2O → CO2 + H 2 ;∆H = −41kJ /mol
1
2
5
Sustainable Energy Science and Engineering Center
DMFC System
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Liquid-Feed DMFC Reactions
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Direct Methanol Fuel Cell
1
Operating at ambient
conditions
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Micro-scale Methanol Fuel Processor
1
5
6
9
3
7
4
11
1
2
10
Sustainable Energy Science and Engineering Center
Hydrogen Production
Source:
Sustainable Energy Science and Engineering Center
Hydrogen Production
Source:
Sustainable Energy Science and Engineering Center
Hydrogen From Water
There is enough water to sustain hydrogen!
Sustainable Energy Science and Engineering Center
Electrolysis
Sustainable Energy Science and Engineering Center
Electrolysis
Sustainable Energy Science and Engineering Center
Photoelectrolysis
Sustainable Energy Science and Engineering Center
Hydrogen Production
Sustainable Energy Science and Engineering Center
Photoelectrochemical Conversion System
Sustainable Energy Science and Engineering Center
Electrolysis Efficiency
Systems that claim
85 %
Sustainable Energy Science and Engineering Center
Photoelectrolysis
Sustainable Energy Science and Engineering Center
Photoelectrolysis
Sustainable Energy Science and Engineering Center
Photoelectrolysis
Sustainable Energy Science and Engineering Center
Artificial Photosynthesis
Sustainable Energy Science and Engineering Center
Thermochemical Water Splitting
Sustainable Energy Science and Engineering Center
Thermochemical Production
Sustainable Energy Science and Engineering Center
Thermochemical Production
Thermal-to-hydrogen energy efficiency
Solar-thermal heat source is a logical choice
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Thermochemical Production
Solar-thermal heat source
Sustainable Energy Science and Engineering Center
Thermochemical Cycle Efficiency
Process Temperature (oC)
Electrolysis
Sulfur-iodine
thermochemical cycle
Calcium-bromine
thermochemical cycle
Copper-chlorine
thermochemical cycle
Heat-to-Hydrogen
Efficiency (%)
20-25
850
45-49
760
36-40
550
41*
* Energy efficiency calculated based on thermodynamics
Sustainable Energy Science and Engineering Center
Solar Thermochemical System
Sustainable Energy Science and Engineering Center
Thermochemical Process
Sustainable Energy Science and Engineering Center
Hydrogen Production
Sustainable Energy Science and Engineering Center
Fossil Fuel Use
Sustainable Energy Science and Engineering Center
Solar Heat Generation
Sustainable Energy Science and Engineering Center
Solar Heat Generation
Sustainable Energy Science and Engineering Center
Solar Thermal Hydrogen Production
A concept for integrating solar thermal energy and
methane gas to produce a range of solar-enriched fuels
and synthesis gas (CO and H2) that can be used as a
power generation fuel gas, as a metallurgical reducing
gas or as chemical feed stock e.g. in methanol
production.
http://www.energy.csiro.au/