fuel cell lectures
TRANSCRIPT
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Fuel Cell Thermodynamics
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Fuel Cells Basics
Fuel cells convert chemical energy directly into electrical energy.
Difference with batteries: fuel cells require a fuel to flow in order to produceelectricity.
Heat is produced from chemical reaction and not from combustion.
Types of fuel cells:Proton exchange membrane (PEMFC)Direct Methanol fuel cell (DMFC)Alkaline fuel cell (AFC)Phosphoric acid fuel cell (PAFC) (*)
Molten-carbonate fuel cell (MCFC) (*)Solid-oxide fuel cell (SOFC) (*)
(*) Suitable for microgrids.
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Fuel cells operation
Example: PEMFCThe hydrogen atoms electron and proton are separated at the anode.Only the protons can go through the membrane (thus, the nameproton exchange membrane fuel cell).
Hydrogen Oxygen
Water
2 2 2H H e
Heat
2 21/ 2 2 2 1O H e H O
Membrane(Nafion)
Catalyst (Pt)Anode (-)
Catalyst (Pt)Cathode (+)
dc current
2 2 22 2 ( 1.23 )
rO H H O E V
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Fuel cell thermodynamics
The first law of thermodynamics:
The energy of a system is conserved
In conservational fields, potential functions change depend only on initial andfinal values. Hence,
For a closed system (control masssystem), such as a piston
(The total energy change equals the sum of the change in internal energy, thechange in kinetic energy, and the change in potential energy)
Q W dE
Q W E
Change of heatprovided to the
system
Change ofwork provided
by the system
Change ofsystems total
energy
E U K P
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Fuel cell thermodynamics
For an open system with mass flow across its boundaries (control volume),such as a steam turbine
pV represents the work to keep the fluid flowing (p is pressure and V is
volume). Hence, if a magnitude called enthalpyHis defined as
Then,
If we use the 1stlaw of thermodynamics for a stationary control volume (i.e.
the kinetic and potential energies are constant in time, then
Thus, the enthalpy is the difference between the heat and the work involved
in a system such as the one defined immediately above.
( )E U K P pV
H U pV
H E K P
H Q W
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If the change in enthalpy is negative, heat is liberated and the reaction occursspontaneously (contrary to endothermic reactions that requires to apply heat in
order for the reaction to occur).
In the anode:In the cathode:
Hence, in a PEMFC, 285 kJ/mol are converted into heat (Q) and electricity(W).
Entropy: it is a property that indicates the disorder of a system or how
much reversible is a process. This last definition relates entropy to
energy quality.
In a reversible isothermal process involving a heat transfer Qrevat a
temperature T0, the entropy is defined as
Fuel cell thermodynamics
2 2 2 , 0H H e H kJ
2 21/ 2 2 2 1 , 285.8O H e H O H kJ
0
revQS
T
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In all processes involving energy conversion or interactions Sis non-
negative.
S
is zero only in reversible processes..
For any process then
The = in the above relationship will give us the minimum amount of heat
Qminrequired in a process.
From the enthalpy definition a fuel cell can be considered as a system like thefollowing one
Fuel cell thermodynamics
QS
T
H
QQ W
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Fuel cell thermodynamics
The maximum possible efficiency for a fuel cell is, then
An alternative derivation involves using Gibbs Free Energy
The definition of entropy is relates with the 2ndLaw of Thermodynamics. One
of its interpretations is that it is impossible to convert all the energy related withirreversible processes, such as heat or chemical energy, into work.
Hence, it is possible to define a magnitude with units of energy called GibbsFree Energy that represents the reversible part of the energy involved in the
process.
Hence, for fuel cells, the electrical work represents the Gibbs Free Energy andthe maximum possible energy conversion efficiency is
max
G
H
minmax
1 QWH H
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From tables:
In the anode:In the cathode:
And from slide #6 Hequals 285 kJ/mol. Thus,
The Gibbs Free Energy can also be used to calculate the output voltage of anideal fuel cell. Since the Gibbs Free Energy equals the electrical work, and the
electrical work equals the product of the charge and voltage, then
whereFis the Faraday constant (charge on one mole of electrons) the factor
of two represents the fact that two electrons per mole are involved in thechemical reaction.
2 2 2 , 0H H e G kJ
2 21/ 2 2 2 1 , 237.2 /O H e H O G kJ mol
Fuel cell thermodynamics
max 237.2 0.83285.8
GH
2o
W G FE
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Fuel cell thermodynamics
Thus,
and sinceF = 96,485 C/mole and G = -237.2 kJ/mole, then
E0is also denoted byEr, the reversible voltage.
This is the voltage that can be obtained in a single ideal PEMFC when thethermodynamic reaction limitations are taken into account. I.e., this is theoutput voltage of a single ideal PEMFC when it behaves as an ideal voltagesource. However, additional energy loosing mechanisms further reduce thisvoltage.
2o GE
F
( 237200)
1.229 1.23(2)(96,485)oE V
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The Tafel equation yields the cells output voltageEcconsidering additionalloosing mechanisms:
The first term is the reversible cell voltage (1.23V in PEMFCs)
The last term represents the ohmic losses, where iis the cells current density,and ris the area specific ohmic resistance.
The second term represent the losses associated with the chemical kineticperformance of the anode reaction (activation losses). This term is obtained
from the Butler-Volmer equation and its derivation is out of the scope of thiscourse.In the second term, i0is the exchange current density for oxygen reaction andbis the Tafel slope:
log( )
RTb
n e
PEMFC output: Tafel equation
0log( / )c rE E b i i ir
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In the last equationRis the universal gas constant (8.314 Jmol-1K-1), Fis the
Faraday constant, Tis the temperature in Kelvins, nis the number of electronsper mole (2 for PEMFC), and is the transfer coefficient (usually around 0.5).Hence, b is usually between 40 mV and 80 mV.
The Tafel equation assumes that the reversible voltage at the cathode is 0 V,which is only true when using pure hydrogen and no additional limitations, suchas poisoning, occur.
The Tafel equation do not include additional loosing mechanisms that aremore evident when the current density increases. These additional mechanismsare:
Fuel crossover: fuel passing through the electrolyte without reactingMass transport: hydrogen and oxygen molecules have troubles reachingthe electrodes.
Tafel equation also assumes that the reaction occurs at a continuous rate.
PEMFC output: Tafel equation
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PEMFC electrical characteristics
Maximum poweroperating point
Er= 1.23 V
Activation lossregion Ohmic loss region
(linear voltage to currentrelationship)
Mass transport loss region
Er =1.23V
b=60mV,
i0=10-6.7Acm-2
r=0.2cm2
Actual PEMFCs efficiency vary between 35% and 60%
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PEMFC electrical characteristics
This past curve represent the steady stateoutput of a fuel cell.
The steady stateoutput depends on the fuel flow:
Amrhein and Krein Dynamic Simulation for Analysis of Hybrid Electric Vehicle
System and Subsystem Interactions, Including Power Electronics
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Hydrogen production
Hydrogen needs to be produced, and sometimes it also needs to betransported and/or stored. Hydrogen is not a renewable source of energy.
Hence, FC are alternative sources of energy.
Methods for hydrogen production:
Methane Steam Reforming (MSR)It uses natural gas
Two-step process:1)
endothermic reaction (needs heat)2)
exothermic reaction (provides heat)
75 % to 80 % efficient.Partial oxidation (POX)
It also uses natural gas or other hydrocarbonand/or
POX is compact and has faster dynamic response than MSR, but MSRprovides higher hydrogen concentration.
4 2 23CH H O CO H
2 2 2CO H O CO H
4 2 21/ 2 2CH O CO H 4 2 2 22CH O CO H
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Hydrogen production
More methods for hydrogen production:
Electrolysis of waterWater molecules can be separated using electricity. But we use electricityto produce hydrogen to produce electricity again.Pure water is in many places an scarce resource.The electricity for the electrolysis needs to be produced and the waterneeds to be purified (soft de-ionized water is needed).
Reaction:
Electricity can be obtained at a large scale from nuclear reactors but thehydrogen needs to be stored and transported, and nuclear fuel is not a
renewable source of energy.At a VERY small scale wind or solar power can be used, but this energy isavailable only when there is wind or sunlight.
Gasification of Biomass, Coal or WastesThese methods are still a long way into the future.
2 2 22 2H O O H
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Hydrogen Storage
Hydrogen atoms are the lightest and smallest of all elements. For this reason,it is very difficult to keep hydrogen from escaping confined environments such
as tanks or pipes.
Since an effort (i.e. work) needs to be done to keep hydrogen stored, storinghydrogen implies loosing efficiency.
Some storage methods:Pressure Cylinders: Some efficiency is lost in the compressingprocessLiquid Hydrogen: it requires lowering the hydrogen temperature to20.39 K. This process already reduces 1/3 of the efficiency.
Metal Hydrides: These are compounds of hydrogen and Magnesium,titanium and other metals. Efficiency is low to medium and lot of heat isgenerated when the hydrogen is released, but these compounds arevery easy to store in the form of soils.Carbon nano-fibers: New technology.
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PEMFC Technology and issues
Expected life of PEMFC is very short (5,000 hours).
The most commonly used catalyst (Pt) is very expensive.
The most commonly used membrane (Nafiona sulfonated tetrafluorethylenecopolymer is also very expensive).
PEMFCs are very expensive.
CO poisoning diminishes the efficiency. Carbon monoxide (CO) tends to bindto Pt. Thus, if CO is mixed with hydrogen, then the CO will take out catalystspace for the hydrogen.
Hydrogen generation and storage is a significant problem.
Additional issues to be discussed when comparing other technologies:dynamic response and heat production.
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The main advantage is that they use a liquid fuel.Reactions:
AnodeCathode
Voltages: 0.046 V at anode, 1.23 V at cathode, 1.18 V overall.
Methanol has high energy density so DMFC are good for small portableapplications.
Issues:Cost
Excessive fuel crossover (methanol crossing the membrane)Low efficiency caused by methanol crossoverCO poisoningLow temperature productionConsiderable slow dynamic response
Direct Methanol Fuel Cells (DMFC)
3 2 26 6CH OH H O CO H e
2 21/ 2 2 2O H e H O
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One of their main advantages is their long life in the order of 40,000 hours.
The phosphoric acid serves as the electrolyte.
The reactions are the same than in a PEMFC. Hence, the reversible voltage is1.23 V
The most commercially successful FC: 200 kW units manufactured by UTC
They produce a reasonable amount of heat
They support CO poisoning better than PEMFC
They have a relatively slow dynamic response
Relative high cost is an important issue
Phosphoric Acid Fuel Cells (PAFCs)
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The main advantage is that their cost is relatively low (when considering the
fuel cell stack only without accessories.Reactions:
AnodeCathode
Developed for the Apollo program.
Very sensitive to CO2poisoning. So these FCs can use impure hydrogen butthey require purifying air to utilize the oxygen.
Issues:
Cost (with purifier)Short life (8000 hours)Relatively low heat production
Alkaline Fuel Cells (AFCs)
2 22 2 2H OH H O e
2 21/ 2 2 2 2O H O e OH
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One of the main advantages is the variety of fuels and catalyst than can beused.Reactions:
AnodeCathode
They operate at high temperature. On the plus side, this high temperature
implies a high quality heat production. On the minus side, the high temperaturecreates reliability issues.
They are not sensitive to CO poisoning.
They have a relatively low cost.
Issues:Extremely slow startupVery slow dynamic response
2
2 3 2 2 2H CO H O CO e
2
2 2 31/ 2 2O CO e CO
Molten Carbonate Fuel Cells (MCFCs)
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Solid Oxide Fuel Cells (SOFCs)
One of the main advantages is the variety of fuels and catalyst than can beused.
Reactions:AnodeCathode
They operate at high temperature with the same plus and minus than inMCFCs.
They are not sensitive to CO poisoning.
They have a relatively low cost.
They have a relatively high efficiency.
They have a fast startup
The electrolyte has a relatively high resistance.
2
2 2 2H O H O e
2
21/ 2 2O e O
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Comparison of the most common technologies
PEMFC DMFC AFC PAFC MCFC SOFC
Fuel H2 CH3OHH2 H2
H2, CO, CH4,hydrocarbons
H2, CO, CH4,hydrocarbons
ElectrolyteSolid polymer
(usually Nafion)Solid polymer
(usually Nafion)
Potasiumhydroxide
(KOH)
Phosporicacid (H3PO4
solution)
Lithium andpotassiumcarbonate
Solid oxide(yttria,
zirconia)
Charge carried inelectrolyte
H+ H+ OH- H+ O2-
Operationaltemperature (oC) 50100 50 - 90 60 - 120 175200 650 1000
Efficiency (%) 3560 < 50 3555 3545 4555 5060
Unit Size (KW) 0.1500 2.5
Installed Cost ($/kW) 4000 > 5000 < 1000* 30003500 8002000 1300 - 2000
Fuel cell technologies
2-
3CO
* Without purifier