Direct Energy Conversion: Fuel Cells -...

Sustainable Energy Science and Engineering Center

Section 4.7.1 in the Text Book

Direct Energy Conversion: Fuel Cells

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


Introduction:

Fuel Cells

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Hydrocarbon Fuels

Energy stored in chemical bonds

Combustion Useful power

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


PEM Fuel Cell Performance


Fuel Cells

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William Grove 1839

Grove noted with interest that this device, which used platinum electrodes in contact with dilute sulfuric acid would cause permanent deflection of a galvanometer connected to the cell. Healso noted the difficulty of producing high current densities in a fuel cell that uses gases.


Fuel Cells

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Mond & Langer (1889) - Gas battery


Daniell Cell

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We will use the term anode to mean the electrode at which oxidation takes place - losing of electrons

Cathode is the electrode at which reduction takes place - electrons are gained from the external circuit


Hydrogen Fuel Cell

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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.

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.


Historical Development

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Fuel Cell Types

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Hydrogen - Oxygen Fuel Cell

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2H2 → 4H + + 4e−

At the anode the hydrogen gas ionizes releasing electrons and creating H+ ions (or protons). This reaction releases energy.

O2 + 4e− + 4H + → 2H2O

At the cathode, oxygen reacts with electrons taken from the electrode, and H+ ions from the electrolyte, to form water

An acid with free H+ ions. Certain polymers can also be made to contain mobile H+ ions - proton exchange membranes (PEM)


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.


Fuel Cell Stack

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HydrogenHydrogen 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 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 AssemblyEach membrane electrode assembly consists of two electrodes (the anode and the cathode) with a very thin layer of catalyst, bonded to either side of a proton exchange membrane.AirAir 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 PlatesGases (hydrogen and air) are supplied to the electrodes of the membrane electrode assembly through channels formed in flow field plates.Fuel Cell StackTo 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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The fuel cells are 5 mm3 and generate up to 100 mWatts.

Micro Fuel Cell

CWRU (Case Western Reserve University) 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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PEM fuel cells use a solid polymer membrane (a thin plastic film) as the electrolyte. This polymer is permeable to protons when it is saturated with water, but it does not conduct electrons.

Proton Exchange Membrane Fuel Cells (PEMFC)

The reactions at the electrodes are as follows:

Anode Reactions: 2H2 => 4H+ + 4e-Cathode Reactions: O2 + 4H+ + 4e- => 2 H2OOverall 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 CellAlkaline 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 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 of KOH can be varied with the fuel cell operating temperature, which ranges from 65°C to 220°C. The charge carrier for an AFC is the 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 migrates back to the cathode to regenerate hydroxyl ions. The chemical 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 e-Cathode Reaction: O2 + 2 H2O + 4 e- => 4 OH-Overall Net Reaction: 2 H2 + O2 => 2 H2O

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 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.

Solid Oxide Fuel Cell


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Solid Oxide Fuel Cell


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The diaphragm between the anode and the cathode consists of a matrix filled with a carbonate electrolyte. Carbonate ions (CO3

2-) 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.

Molten-carbonate Fuel Cell


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Carbon (C) and oxygen (O2) can react in a high-temperature fuel 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 carbon combustion, but it allows greater efficiency for electricity production. The pure carbon dioxide (CO2) product can be sequestered in an underground reservoir or used to displace underground deposits of oil and gas.

Carbon Conversion Fuel Cell

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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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 external circuit to the cathode electrocatalyst where they are consumed together with oxygen in a reduction reaction. The circuit is maintained within the cell by the conduction of protons in the electrolyte. In modern cells, electrolytes based on proton conducting polymer electrolyte membranes (e.g., Nafion™) are often used, since these allow for convenient cell design and for 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

Direct Methanol Fuel Cell

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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Load

Condenser

Fuel cell stack



Fuel Cell Applications

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Stationary power generation ~ 5 - 250 kW

Portable applications ~ 1 kW or lower

Automotive applications ~ 5 - 100 kW

Airplane Applications ~ 10 - 250 kW

1kW = 1.3404826 horsepower


Stationary Power Generation

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Important factors:The hours of operation per year

The electric efficiency of the electricity generation process

The capital investment

Fuel cells are particularly suitable for on-site power generation. Utilizing the heat generated by the fuel cell improves the overall efficiency - Combined Heat and Power generation (CHP).


PEMPC Power Plant

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Process Flow Diagram for a Ballard 250 kW PEMFC Plant


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GM Electrovan

Alkaline fuel cell modules supplying 32 kW

Fuel Cell Powered Automobile - 1967


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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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Daimler-Chrysler NeCar:



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Ford Focus Hydrogen -powered fuel cell vehicle



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Honda fuel cell carFuel Cell Powered Automobile - Progress


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Toyota’s Methanol-powered Fuel cell Electric Vehicle

Methanol Fuel Cell Powered Automobile


Fuel Cell Powered Automobile

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An x-ray view of Mitsubishi's new fuel cell Grandis minivan.


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Typically well under 100W of power with significantly higher power densities or larger energy storage capacity than those of advanced batteries.

Power generation on a larger scale , say 1 kw continuous output to replace gasoline or diesel generators or supply quiet electric power on boats, caravans or trucks.

Portable Application


Solar Powered Airplane

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11Instead of jet fuel, Helios has about 62,000 solar cells across the wing. The solar cells collect 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

Helios


Electric Powered Airplane

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The new Electric Plane, or E-Plane, is a high-speed, all-carbon French DynAero Lafayette III, built and donated by American Ghiles Aircraft. The E-Plane is being converted from a combustion engine to electric propulsion in three stages. The first flights, planned for next year, will be on lithium ion batteries. The next flights will be powered by a combination of lithium ion batteries augmented by a fuel cell. Finally, the aircraft will be powered totally by a hydrogen fuel cell, with a range of more than 500 miles.

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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Fuel Cell Based Aircraft Propulsion

Source: NASA TM-2003-212393


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Fuel Cell Powered Aircraft


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 VehicleIntelligent Energy is currently developing devices called reformers that extracthydrogen from biodiesel fuels (typically made from vegetable oils or animal fats)and ethanol (generally made from grain or corn). The units would sell for aroundU.S. $1,500 and could produce enough hyd rogen to fill up the ENV for about 25cents per tank, Eggleston said.

National Geographic News, August 2, 2005.


Fuel Cell System


FC Implementation Requirements




References:






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2H2 → 4H + + 4e−

At the anode the hydrogen gas ionizes releasing electrons and creating H+ ions (or protons). This reaction releases energy.

O2 + 4e− + 4H + → 2H2O

At the cathode, oxygen reacts with electrons taken from the electrode, and H+ ions from the electrolyte, to form water

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

Fuel Cell

Oxygen Energy

Electricity Energy = VIt

Heat

Water

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 CellThe basic reaction:

2H2 + O2 → 2H2O

H2 +12

O2 → H2O

The product is one mole of H2O ( 18g = 1 gmole) and the reactants are one mole of H2 (2g = 1 gmole) and a half a mole of O2 (32g = 1 gmole). The molar specific Gibbs free energy, in ‘per mole’ form is commonly used.

g

∆g = g products − g reac tan ts

∆g = (g )H2O− (g )H2

−12

(g )O2

∆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 OutputIf 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 molecule of hydrogen used.

For one mole of hydrogen used, 2N electrons pass round the external circuit- where N is the Avogadro’s number. If -e is the charge of one electron, then the charge that flows is

-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

H2 → 2H + + 2e−

O2 + 2e− + 2H + → H2O

∆g = −2FE

E =−∆g 2F


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Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. The four thermodynamic potentials are related by offsets of the "energy from 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.

∆U = Q - W H = U + PVF = U - TS Helmoltz free energyG = U - TS + PV Gibbs free energy

Q: heat added to the systemW: work done by the systemU: internal energyT: absolute temperatureS: final entropyV: final volume

Thermodynamic Potentials


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Second Law of Thermodynamics

A fuel cell represented as a control volume. E stands for electrical potential, measured in volts.

For any isolated system, the 2nd law states that

∆Sisolated ≥ 0Sgen = ∆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

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 the difference between the entropy of products, SP and the reactants, SR with N representing the number of moles of each component in the reaction.

Any heat produced or consumed in the reaction is included in theexpression for the surroundings, where Qsurr is the heat transferred from the system to the surroundings and To is the temperature of the surroundings.

∆Ssys = Sp − SR = NP∑ s P − NR∑ s R

∆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 other measurable quantities.

The thermodynamic property relations are

du = Tds − Pdvdh = Tds − vdP

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 ThermodynamicsChemical 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 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

Wmax cell= −∆G

dG = dH − TdS − SdT = d(U + PV ) − Tds − SdTdG = dU + PdV + VdP − TdS − SdTdG = 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


For a reversible process:

If the system is restricted to doing expansion work then

n is the number of moles

For isothermal process

stands for standard reference state

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The effect of temperature and pressure on ∆G

δQ = TdS

δW = PdVdG = VdP − SdTPV = nRT

Ideal gas law

dG = nRT dPP

G2 − G1 = nRT ln P2

P1

G2 = Go + nRT ln P2

Po

Chemical Thermodynamics


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Equilibrium of a gas mixture:

For a chemical reaction occurring at constant pressure and temperature, the reactant gases A and B form products M and N.

Where a, b, m and n are stoichiometric coefficients.

The change in the Gibbs energy

Where g is in molar quantity (kJ/mol)

In terms of standard Gibbs energy. The reference pressure is usually taken as 1 atm.

aA + bB ⇔ mM + nN

∆G = mg M + ng N − ag A − bg B

∆G = m g Mo + RT ln PM

Po

+ n g No + RT ln PN

P o

− a g Ao + RT ln PA

P o

− b g Bo + RT ln PB

Po

∆Go = mg Mo + ng N

o − ag Ao − bg B

o



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Q: Reaction coefficient for the pressures

The change in Gibbs energy of a reaction involving gases is:

∆G = ∆Go + RT ln PMmPN

n

PAaPB

b

∆G = ∆Go + RT lnQ

Q =PM

mPNn

PAaPB

b

∆G = ∆Go + RTlnQ



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Maximum work:

The maximum work that a system can perform is related to the change in Gibbs energy. For a reversible process (δQ = TdS)

At constant pressure and temperature

Since there is only electrochemical work, We, in which electrical charge moves through a voltage, we have

The Gibbs energy change is negative of the electrochemical work, we can then write as

dG = −δW + PdV + VdP − SdT

dG = −δW + PdV = −(δW − PdV )

dG = −δWe

∆G = δWe



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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 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 constant - 96,485C/mole-1) moving through a potential difference, E ( voltage difference across electrodes) is

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

We = neFE∆G = −neFE∆Go = −neFE o


E =∆Go

neF−

RTneF

lnQ

E = E o −RTneF

lnQ



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For a hydrogen-oxygen fuel cell, the overall reaction stoichiometry is

The electrons transferred in this reaction, ne = 2. Using the partial pressures of water, hydrogen and oxygen in the reaction coefficient, we then have

Diluting the reactant gases will lower the maximum voltage that the cell can produce.

H2 +12

O2 → H2O

E = E o −RTneF

lnPH2O

PH2PO2

1/ 2



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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 0.1 MPa, the partial pressures of nitrogen and oxygen are 0.07809 MPa and 0.02095 MPa are respectively.

The product gas stream contains two parts of H2 and one part of O2 by moles and volume and the reaction takes place at 0.1 MPa, we will have

PH2=

23

× 0.1= 0.0667Mpa

PO2=

13

× 0.1 = 0.0333MPa


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Thermal efficiency of a reversible heat engine is determined by

Electrochemical cells such as storage batteries and fuel cells, operate at constant temperatures with the products of the reaction leaving at the same temperature as reactants (isothermal reaction). The chemical energy of the reactants is converted to 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

Thermal Efficiency

ηth =Wnet

Qin

=1−TL

TH

Wmax,cell = −∆G

Change in the Gibbs function between products and reactants


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Thermal Efficiency

Wcell = neFE

The work, which is done by the movement of electrons through a difference in electrical potential is

With the higher value of the fuel replaces Qin the maximum thermal efficiency at the open circuit voltage Eo , of an electrochemical cell is given by

For example, Eo = 1.23 V for a hydrogen-oxygen fuel cell

ηth,cell,max =neFE o

HHV

ηth,cell,max =neFE o

HHV=

2 × 96485 ×1.23285840

= 0.83

HHV of H2 = 285.84 kJ/mol; LHV = 241 kJ/mole


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Thermal Efficiency

The Gibbs energy of the formation of water vapor is -228.582 kJ/mol at 285.15K and 1 atm)

It decreases to -164.429 kJ/mol at 1500K.

The current efficiency, a measure of fuel utilization (or fuel consumed to produce an electrical current ) is given by

ηI =I

−neFN fuel

Fuel flow rate mol/s


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Maximum Efficiency

Pressure: 1 atm

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.


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Heating Values for Selected Fuels

Fuel HHV (MJ/kg) LHV (MJ/kg) HHV/LHV LHV/HHV

Coal 34.1 33.3 1.024 0.977

CO 10.9 10.9 1.000 1.000

Methane 55.5 50.1 1.108 0.903

Natural gas 42.5 38.1 1.115 0.896

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

For fuel cells, this can be written as

ηheatengine =Wact

WCarnot

ηR =ηact

ηrev

=neFEneFE o =

EE 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.


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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

Where I is the current and t the 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 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

ηi =∆G∆H

=1−T∆S∆H

=neFE∆H

=ItE∆H

ηac =−neFEac

∆H

Actual Efficiency


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Quantity H2 0.5O2 H2O Change

Enthalpy 0 0 -285.83 kJ ∆H = -285.83 kJ

Entropy 130.68 J/K 0.5 x 205.14 J/K 69.91 J/K T∆S = -48.7 kJ

W = P∆V = (101.3 kPa)(1.5 moles)(-22.4 x 10-3 m3/mol)(298K/273K) = -3715 J

Pressure: 1 atmosphere

Temperature: 298K

∆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

η= −237.1/−285.83 = 0.83 (83%)



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Due: November 3, 2005

Examine how the ideal efficiency of a simple hydrogen-oxygen fuel cell changes as its operating temperature is raised from 298K to 1000K. Also calculate the actual and ideal efficiencies for the cell operating in the standard conditions of 298K and 1 atm. The actual cell voltage is 0.75V while the cell delivers 1.5 amps. The hydrogen flow is 0.25 cm3/sec. Independent measurements reveal that 0.06 cm3/sec of hydrogen is escaping through electrolyte unreacted.

Homework Problem


Basic Fuel Cell Reactions

Reference: PEM fuel cells: theory and Practice, Frano Barber, Elsevier Academic Press, 2005

The overall reaction of a PEM fuel cell is:

This reaction is the same as the reaction of hydrogen combustion, which is an exothermic process (energy is released):

The heat, typically given in terms of enthalpy, of a chemical reaction is the difference between the heats of formation of products and reactants:

Heat of formation of liquid water: -286 kJ/mol at 25oC and at atmospheric pressure.

H2 +12

O2 ⇒ H2O

H2 +12

O2 ⇒ H2O + heat

∆H = hf( )H2O− h f( )H2

−12

h f( )O2= −286kJ /g − 0 − 0 = −286 kJ

mol

H2 +12

O2 ⇒ H2O l( )+ 286kJ /mol


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).

The difference between HHV and LHV is the heat of evaporation of water at 25oC:

H2 +12

O2 ⇒ H2O g( )+ 241kJ /mol

H fg = 286 − 241 = 45kJ /mol


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:

∆S is the difference between entropies of products and reactants:∆G = ∆H − T∆S

∆S = S f( )H2O− S f( )H2

−12

S f( )O2

0.18884-241.98Water (Vapor)0.06996-286.02Water (liquid)0.205170Oxygen0.130660Hydrogensf (kJ/mol)hf (kJ/mol)

At 25oC and at one atmosphere

∆G = −286.02 − 298 × 0.06996 − 0.13066 − 0.5 × 0.20517( )( )= −237.36kJ /mol

48.68 kJ/mol is converted into heat.


Theoretical Fuel Cell Potential

We = neFE = −∆GElectrical work:

ne = 2 (two electron per molecule); F =96,485 Coulombs/electron-mol.

The theoretical potential of fuel cell at 25oC and at one atmosphere:

Temperature Effect:

a, b and c are empirical

Coefficients, different

for each gas

E =−∆GneF

=237,340J /mol

2 × 96,485As /mol=1.23Volts



1.18E-060.00962130.62644H2O (g)

-3.9E-060.01298725.84512O2

2.01E-06-0.0008428.91404H2

cba

-228.74-0.0444-241.98

-237.34-0.1633-286.02

∆G (kJ/mol)∆S (kJ/mol)∆H (kJ/mol)

H2 +12

O2 ⇒ H2O l( )

H2 +12

O2 ⇒ H2O g( )

∆HT = ∆H298.15 + ∆a T − 298.15( )+ ∆bT − 298.15( )2

2+ ∆c

T − 298.15( )3

3

∆ST = ∆S298.15 + ∆a ln T298.15

+ ∆b T − 298.15( )+ ∆c

T − 298.15( )2

2

∆a = aH2O − aH2−

12

aO2

∆b = bH2O − bH2−

12

bO2

∆c = cH2O− c H2

−12

cO2

For T=298.15, E = 1.23 Volts

For T=373.15, E = 1.167 Volts


Theoretical Fuel Cell Efficiency

η =∆G∆H

=237.34286.02

= 0.83

η =∆G

∆HLHV

=228.74241.98

= 0.945

η =−∆G−∆H

=

−∆GneF−∆HneF

=1.23

1.482= 0.83

Potential corresponding to hydrogen’s higher heating

value


Theoretical Fuel Cell PotentialEffect of Pressure:

The change in Gibbs free energy may be shown to be:

Where Vm= molar volume, m3/mol and P = pressure, Pa

For an ideal gas:

Therefore:

Go : Gibbs free energy at standard temperature, 25oC and at one atmosphere

∆G = VmdP

PVm = RT

dG = RT dPP

G = Go + RT ln PPo


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For a chemical reaction occurring at constant pressure and temperature, the reactant gases A and B form products M and N.

Where a, b, m and n are stoichiometric coefficients.

The change in the Gibbs energy

Where g is in molar quantity (kJ/mol)

In terms of standard Gibbs energy. The reference pressure is usually taken as 1 atm.

aA + bB ⇔ mM + nN

∆G = mGM + nGN − aGA − bGB


∆G = ∆Go + RT ln

PM

Po

mPN

Po

n

PA

Po

aPB

Po

b


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Q: Reaction coefficient for the pressures

The change in Gibbs energy of a reaction involving gases is:

∆G = ∆Go + RT ln PMmPN

n

PAaPB

b


Q =PM

mPNn

PAaPB

b

∆G = ∆Go + RTlnQ



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For a hydrogen-oxygen fuel cell, the overall reaction stoichiometry is

The Nernst equation becomes:

H2 +12

O2 → H2O

∆G = ∆Go +RTneF

lnPH2O

PH2PO2

1/ 2


E = E o +RTneF

lnPH2

PO2

1/ 2

PH2O

When liquid water is produced in a fuel cell:

For higher reactant pressures the cell potential is higher

PH2O=1


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∆E = EO2− Eair =

RTneF

lnPO2

Pair

=RTneF

ln 10.21

0.5


Air vs oxygen:

At 80oC , the voltage loss becomes 0.012V. In practice, this is much higher.


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?


Electrochemical Kinetics

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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.

ElectrolyteBacking layer

Catalyst layer

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.


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The general half-reaction expression for the oxidation of a reactant is:

Where reactant R loses electrons and becomes Ox, the product of oxidation, and n is the number of electrons that are transferred in the reaction. For the opposite direction, Ox gains electrons, undergoing reduction to form R in the half-reaction.

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.



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Single-step Electrode reactions

Considering only one direction of the reaction, the current produced is

Where I is the current (in amperes), A is the active area of the electrode (cm2), Fis the Faraday’s constant (the charge per mole of electrons= 96,485 (coulombs/mole e-) and j is the flux of reactants reaching the surface (mole/sec). The current density (per unit area) is

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

i = nF . j

i = nF ⋅ j

j f = k f Ox[ ]o

Surface concentration of the reactantForward rate coefficient



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Single-step Electrode reactions

For the backward reaction (subscript b), the flux produced by the oxidation of Ris

The net flux is

The net current density that appears on the electrode when the current is produced is given by

jb = kb R[ ]o

Backward rate coefficient

j = j f − jb

i = n Fk f Ox[ ]o − Fkb R[ ]o( )



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Butler-Volmer Equation

From the Transition state theory (refer to any physical chemistry book), the heterogeneous rate coefficient, k. is a function of the Gibbs energy of activation and is given by

Because an electrochemical reaction occurs in the presence of an electrical field, the Gibbs energy of activation consists of both chemical and electrical terms

k =kBTh

exp −∆G ≠

RT

Gibbs energy of activation (kJ/mol)

Boltzmann’s constant

(1.38049x10-23 j/oK)Plank’s constant (6.621x10-34 Js)

∆G ≠ = ∆G c≠ + nF∆φ

∆G ≠ = ∆G c≠ − n 1− β( )F∆φ

Change in electrical potentialReduction

Oxidation

Transfer coefficient (0.5)



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k f =kBTh

exp−∆G c, f

≠

RT

exp −nβF∆φ

RT

kb =kBTh

exp−∆G c, f

≠

RT

exp

−n 1− β( )F∆φrev

RT

exp

−n 1− β( )FηRT

Reductionk f =kBTh

exp−∆G c, f

≠

RT

exp −nβF∆φrev

RT

exp −nβFη

RT

Oxidation


For a reduction reaction

Chemical Component Electrical Component

With the over potential is defined as η = ∆φ − ∆φrev

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.


when the electrode is in equilibrium and at its reversible potential, the overpotential and external current are both zero. In this case, the exchange current density, io is defined as

1

The current density is given by 34

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nF Ox[ ]o ko, f = nF R[ ]o ko,b ≡ io(A /cm2)

Butler-Volmer Equation

i = io exp −nβFηRT

− exp

−n 1− β( )FηRT

Reduction term Oxidation termIf 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.

η = ∆φ − ∆φrev



Fuel Cell Components

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Fuel Cell Components Impact on Performance

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.

The proton exchange membrane fuel cell (PEMFC)


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H2 → 2H + + 2e−

12

O2 + 2H + + 2e− →1H2O

Anode (Er = 0 V)

Cathode (Er = 1.23 V)

The Proton Exchange Membrane Fuel Cell (PEMFC)

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.


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The gas diffusion layer and backing layer (substrate) at the anode allows hydrogen to reach the reactive zone within the electrode. Upon reaching, protons migrate through the ion conducting membrane, and electrons are conducted through the gas diffusion layer and ultimately to the electric terminals of the fuel stack. The substrate therefore has to be porous to allow gas and electrically conducting. Not all of the chemical energy supplied to the MEA by reactants is converted into electric power. Heat will also be generated and the substrate also acts as a heat conductor to remove heat from the reactive zones of the MEA.

ElectrolyteBacking layer

Catalyst layer

Gas diffusion layer

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.

The PEM Fuel Cell


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Oxidant supply and distribution, electron conduction towards reaction zone, heat removal and water transport

Cathode substrate

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.

Cathode catalyst layer

Proton conduction, water transport, electronic insulation

Proton exchange membrane

Catalysis of anode reaction, proton conduction into membrane, electron conduction into substrate, water and heat transport

Anode catalyst layer

Fuel supply and distribution, Electron conduction, heat removal from reaction zone, water supply into electrocatalyst

Anode Substrate

Task/effectMEA Component

Source: Fuel cell technology handbook, Chapter 4

The PEM Fuel Cell


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Factors Limiting Fuel Cell Performance

Vac = V − ∆Vconc(c ) − ∆Vchem(c ) − ∆Vconc(a ) − ∆Vchem(a ) − IR∑

The losses that takes place at electrodes are generally attributed to some form of polarization - a term used to denote the difference between the theoretical voltage of a given electrode and the experimental voltage when the current is drawn from the cell. The losses are classified in three categories: Chemical polarization. Concentration polarization and resistance polarization. The theoretical value of the open circuit voltage of a hydrogen-oxygen fuel cell is given by

This gives a value of about 1.23 V for a cell operating at 298K.

V = E =−∆g f2F


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It is customary to express the voltage drop due to chemical polarization by strictly empirical equation, called the Tafel equation as

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.

∆Vchem = ′ a + ′ b lnJ

′ a =−RTαnF

ln( jo)

′ b =−RTαnF

Chemical or Activation Polarization


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The effect of current density and the exchange current density on chemical polarization loss

Chemical Polarization

Potential loss


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Concentration PolarizationAfter 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 voltage that a fuel cell would deliver under completely reversible conditions. The concentration of electrolyte in the vicinity of an electrode during reaction should be maintained at the desirable condition.

∆Vconc(c ) =RTnF

lncif

cb

cb : average concentration in bulk electrolyte

cif : concentration at the interface

∆Vconc(c ) =RTnF

ln JL

JL − J

∆Vconc(a ) =RTnF

ln JL + JJL

JL =nFD

′ δ cb

D: diffusion coefficient


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Concentration Polarization

An empirical equation better describes the concentration polarization losses:

Where c and d are empirical coefficients with values of c= 3 x10-5 V and d = 0.125 A/cm2.

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.

∆Vconc = c × ej

d


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Resistance Polarization

When an electrochemical reaction occurs at an electrode there is generally a significant change in the specific conductivity of electrolyte which involves an additional loss of potential.

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.

Ohmic Losses: V= IR

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.


Heat Transfer

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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 T∆S.

2) Some of the fuel reacts chemically with the oxidizer rather thanelectrochemically to generate an irreversible heat transfer.

3) 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).

Ý Q t = Ý Q rev + Ý Q chem( irr) + Ý Q ∆V =1

nFT∆S + +nF Vac −V( )[ ]

Generally small


0.5

0

0.3

0.2

0.1

0.4

Pote

ntia

l Lo s

s (V

)

0 15001000500

Current density (mA/cm2)

Activation polarization loss

Ohmic losses

Concentration polarization loss

Fuel Cell Voltage Losses


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Source: http://www.h2net.org.uk/PDFs/EndUse/H2NET-2.pdf

Polarization Curve




References and Sources:




Fuel Cell Hand Book, US DOE - available on the web.


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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 cell operates at a temperature of 298K and the fuel and air are supplied at one atmosphere.

The faradic efficiency (the fraction of the reaction which is occurring electrochemically to give a current is called faradic or current efficiency, ηF = 1/(nFNfu); where Nfu is the total number of moles of fuel reacted electrochemically per second) for the cell is estimated to be 95%

20% of the fuel supplied to the cell will escape through the electrolyte unreacted.

w =0.25cm

l =12cm

Separation between electrodes, w= 0.25cm

Height of the cell, l = 12 cm

Depth of the cell, d = 6cm

Average electrolyte velocity, u = 5cm/s(Supplied by an external pump)

Fuel Cell Design Calculation


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The physical properties of the electrolyte at 298K area as follows:

Concentration: 30% KOH (wt) or cb= 6.9 x 10-3 mole/cm3

Density: ρ = 1.294 gm/cm3

Dynamic Viscosity: µ = 2.43 x 10-2 poise

Kinematic Viscosity: ν = 1.887 x 10-2 cm2/s

Conductivity: σ = 0.625 (ohm-cm)-1

Diffusion Coefficient for OH- ions: D = 1.5 x 10-7 cm2/s

Electrolyte Properties


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We now calculate the open circuit voltage. We assume that each electrode reaction follows the half-cell reactions

Anode Eo = 0

Cathode Eo = 1.23v

Yielding a cell reaction of

We may now apply the Nernst equation to our cell potential

where Pt is the total pressure of the mixture and ni/nt is the mole fraction of the ith

constituent.

H2(g) → 2H + + 2e−

0.5O2(g) + 2H + + 2e− → H2O(l)

H2(g) + 0.5O2(g) → H2O(l)

E = E o −RTneF

lnPH2O

PH2PO2

1/ 2

Pi =ni

nt

Pt

Open Circuit Voltage


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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 from a solution. It is equal to partial pressure only when the vapor behaves like an ideal gas. We also define a quantity called the activity aA = fA/fA

o. We can then write the Nernst equation as

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 = E o −RTneF

lnaH2O

aH2aO2

1/ 2

E = V =1.23−1.99( ) 298( )2( ) 23060( )

ln1( )

1( ) 0.21( )0.5

E = V =1.23− 0.013ln(2.18) =1.22volts

Open Circuit Voltage


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We initially assume an operating current density for our fuel cell of 0.5 amp/cm2

Use Tafel equation to calculate losses due to chemical polarization.

Where the current density is expressed in milliamperes per square centimeter.

∆Vchem(a ) = 0.14 + 0.005ln J∆Vchem(c ) = 0.20 + 0.007ln J

∆Vchem(a ) = 0.14 + 0.005ln(500) = 0.17volt∆Vchem(c ) = 0.20 + 0.007ln(500) = 0.24volt

∆Vchem = ′ a + ′ b lnJ

′ a =−RTαnF

ln( jo)

′ b =−RTαnF

Chemical Polarization


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We now calculate the polarization due to concentration gradients in the electrolyte near the electrodes.

Calculation of the limiting current density:

Velocity of the electrolyte = 5 cm/s; For a fully established flow between the electrodes, we have

∆Vconc(c ) =RTnF

ln JL

JL − J

∆Vconc(a ) =RTnF

ln JL + JJL

JL =nFD

′ δ cb

JL,av =1.62nFcbu Rew( )−2 / 3 Sc( )−2 / 3 w / l( )−1/ 3

Rew = uwν

= 66.2

Sc =νD

=1.26x105

wl

= 0.0208

JL,av = 0.956amp /cm2



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11The gas side concentration polarization at the anode is ignored. We will calculate the gas side polarization at the air electrode using the partial pressure of oxygen in the air for pg.

Where Pr is the gas pressure in the pores of the electrode

∆Vconc(c ) =RTnF

ln JL

JL − J

≈ 0.01volt

∆Vconc(a ) =RTnF

ln JL + JJL

≈ 0.01volt

∆Vconc(g ) =RTnF

ln Pr

Pg

= 0.013ln 1

0.21

= 0.02volts



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We now compute the actual operating voltage of the fuel cell by subtracting from the open circuit voltage 1.22 volts, the various polarization losses and IR drop across the cell:

The power out put of the cell:

IR =Jwσ

=0.5 × 0.25

0.625= 0.2volts

Vac =1.22 − 0.17 − 0.24 − 0.01− 0.01− 0.02 − 0.02 = 0.57Volt

Po = VacI = VacJA = 0.57 × 0.5 × 72 = 20.5watts

Resistance Polarization


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The thermal efficiency is given by

F = 23.06 kcal/volt-mole

The efficiency based on the actual voltage is

Assuming that the product of the reaction is liquid water, the faradaic efficiency is given by.

ηac =−nFVac

∆H=

−2(mole − elec /mole) × 23.06(kcal /volt − mole) × 0.57Volt−68.32kcal /mole

= 38.5%

∆H = −68.32kcal /mole

ηF =JA

nFN fu

=0.5 × 72

2 × 96500 × N fu

= 0.95

N fu =1.96 ×10−4 moleH2 /s

F = 96,500 (amp-sec)/(mole-sec)

Efficiency

ηv =Vac

V=

0.571.22

= 46.7%


Heat Transfer

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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.

Ý Q rev = ηF N fu ∆H − ∆G( )= 0.95 × N fu × −68.32 − (−56.69)( )= −9.1watts∆H = −68.32kcal /mole∆G = −56.69kcal /mole

Ý Q chem(irr ) = 1−ηF( )N fu ∆H( )= −2.8wattsÝ Q ∆V = I Vac −V( )= −23.4watts


Home Work

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Design calculation for a fuel cell:

Home work: Using your own calculations reproduce the curve below for the fuel discussed in the class today.


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Heat GenerationArea = 100 cm2; Operating pressure = 1 atm; Operating Temperature = 80oC; E = 0.7 V; Current generation = 0.6 A/cm2.

Power due to heat = Total power generated - electrical power

Pheat = Ptotal - Pelectrical

= (Videalx Icell) - (Vcellx Icell)

= (1.2V -0.7V) x 60A

= 0.5 V x 60A = 30 J/s

= 108 KJ/hr = 30 W

While generating about 42 W of electrical energy.


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Operating Variables

Pressure, Temperature, Gas composition, Reactant utilization and Current density


Operating Pressure

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∆Vgain = C ln P2

P1

C ≈ 0.03− 0.06volts∆Vloss = 3.58 ×10−4 T1

ηmηc

P2

P1

0.286

−1

λ

Stoichiometry (~ 2.0)Compressor efficiency ~ 0.75

Motor and drive system efficiency~ 0.95


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Operating Pressure

Net voltage change resulting from operating at high pressure for two different PEM fuel cell models


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Temperature Effect


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Polarization Contribution


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Effect of Oxygen Pressure


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Source: http://www.h2net.org.uk/PDFs/EndUse/H2NET-2.pdf

Polarization Curve


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Polymer Electrolyte Membrane Fuel Cell

LoadFuel Cell stack


1

The Backing Layer

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.

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.

Porous carbon cloth or carbon paper, typically 100 - 300µm thick. About 4 - 12

sheets are used.

Equivalent concentration profile

δ Diffusion layer

True concentration

profile


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The Bipolar PlateMain tasks: Current conduction; Heat conduction; control of gas flow and product water removal

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.

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.


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Channels in bipolar plates

Use the water leaving the cell to do the humidification.

Water Management


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Some times referred to as Solid Polymer fuel cell (SPFC)

The electrolyte: Ion conduction polymer (works at low temperatures, hence start quickly)

Electrodes: Catalyzed porous electrodes

The anode-electrolyte-cathode assembly (membrane electrode assemblies (MEA)) is one item and is very thin.

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.

PEM Fuel Cells (PEMFC)


Polymer Electrolyte

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Most commonly used: sulphonated fluoropolymers - fluoroethylene

sulphonated fluoroethylene

(PTFE)

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.


Electrodes

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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.

The carbon-supported catalyst is fixed to a porous and conductive

material such as carbon cloth or carbon paper. The carbon paper

also diffuses the gas on to catalyst -the gas diffusion layer.

Alternatively, the platinum on carbon 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.


Platinum Loading Effect

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Water Management

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Proton conductivity is proportional to the water content.

The H+ ions moving from the anode to the cathode pull water

Molecules with them (up to five H2O molecules are dragged

for each proton - electro-osmotic drag). At high current

densities, the anode side of the electrolyte can be dried out.

At temperatures over 335K, the electrodes are typically dry.

Solution: Air and hydrogen humidification before

they enter the cell.


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Heat Production

12 W fuel cell2 kW fuel cell system


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PEM Fuel Cell Stack

Load


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Multi-cell Stack Performance

Source: Simulation study of a PEM Fuel cell system fed by Hydrogen produced by partial

oxidation by Ozdogan S., et al.

Simulation Results -PEMPC stack

Hydrogen produced from gasoline


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Multi-cell stack Performance


2 6 1

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Hydrogen tank

PEMFC System


Cooling Air Supply

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Ballard Nexa PEM Fuel cell.


Fuel Cell Systems and Hydrogen Production


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Fuel Cell Type

< 5kW

5 - 250kW

250kW

250kW - MW

2kW - MW

< 100W


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Electrochemical Reactions


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Efficiency


Efficiency

Source: Hazem Tawfik, Sept 2003


Hydrogen pressure

Oxygen pressure

Pressure Effects



Temperature Effect



Humidity effect at Room Temperature



Parametric Effects: Temperature has most effect



Air Vs O2



PEMFC Emissions

PC25 Fuel cell: 200 kW

Fuel: Natural gas



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Fuel Cell System

Fuel Cell Stack

Control System

Fuel Delivery

Air Delivery

Thermal Management

Water Management

Power Conditioning


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Critical Materials and Costs

Example: Polymer Electrolyte Fuel Cell Stack (1 kW)

- Polymer membrane

- Catalyst (precious metals)

- Bipolar plate

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


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



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Fuel Cell Types

Alkaline (AFC)

Solid Polymer (SPFC, PEM or PEFC)

Direct Methanol (DMFC)

Phosphoric Acid (PAFC)

Molten Carbonate (MCFC)

Solid Oxide (SOFC)


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Fuels

Type Application

Hydrogen Transport, stationary & Portable

Methanol Transport & Portable

Natural Gas Stationary

Gasoline Transport

Diesel Transport

Jet Fuels Military


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Hydrogen is produced from fuel reforming system such as methane and steam.

water gas shift reaction

Carbon monoxide has a tendency to occupy platinum catalyst sites, hence must be removed.

Other fuels:

CH4 + H2O→ 3H2 + COCO+ H2O→ H2 + CO2

C8H18 + 8H2O→17H2 + 8CO

Fuel Reforming


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Steam reforming: It is mature technology, practiced industrially on a large scale for hydrogen production. The basic reforming reactions for methane and a generic hydrocarbon CnHm are

CH4 + H2O→CO+ 3H2;∆H = 206kJ /mol

CnHm + nH2O→ nCO+m2

+ n

H2

CO+ H2O→CO2 + H2;∆H = −41kJ /mol

Fuel Reformer


DMFC System

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Liquid-Feed DMFC Reactions



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Operating at ambient conditions


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Micro-scale Methanol Fuel Processor


Hydrogen Production

Source:


Hydrogen From Water

There is enough water to sustain hydrogen!


Electrolysis


Photoelectrolysis


Hydrogen Production


Photoelectrochemical Conversion System


Electrolysis Efficiency

Systems that claim 85 %


Photoelectrolysis


Artificial Photosynthesis


Thermochemical Water Splitting


Thermochemical Production


Thermochemical Production

Thermal-to-hydrogen energy efficiency

Solar-thermal heat source is a logical choice


Thermochemical ProductionSolar-thermal heat source


Thermochemical Cycle Efficiency

Process Temperature (oC) Heat-to-Hydrogen Efficiency (%)

Electrolysis 20-25Sulfur-iodine

thermochemical cycle 850 45-49Calcium-bromine

thermochemical cycle 760 36-40Copper-chlorine thermochemical cycle 550 41*

* Energy efficiency calculated based on thermodynamics


Solar Thermochemical System


Thermochemical Process


Hydrogen Production


Fossil Fuel Use


Solar Heat Generation


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/

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