Download Fuel cells class notes - The University of Texas at Austin

EE 394V New Topics in Energy Systems
Distributed Generation Technologies
Fall 2012
Clarifications from Course Introduction
Course Description:
• Graduate level course. You are already engineers or hold some other
baccalaureate degree. So you are expected to show a proactive and independent
attitude towards your work. You are expected to also be inquisitive about
everything the instructor says. So please, do ask questions in class.
• The course’s 2nd goal supports this approach.
• The 10 % of the grade for “participation” also supports this course concept.
• The use of a recommended text supported by papers and references in class are
also in line with the course’s concept.
• Goal #1: To discuss topics related with distributed generation technologies.
• Goal #2: To prepare the students to conduct research or help them to improve
their existing research skills.
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Microsources
• Most common microsources:
Small wind turbine (<10
kW/turbine)
Microturbine (<100 kW/unit)
Reciprocating Engine – e.g.
diesel generator (<100
kVA/unit)
Fuel Cell (<400 kW/unit)
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PV Module (<250 W/module)
© Alexis Kwasinski, 2012
Real microsources
Wind turbines +
PV modules
PAFC
Microturbines
MCFC
http://static.flickr.com/39/101004887_6525c88bfc.jpg
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Ideal sources
Characteristics:
• For a voltage (current) source, the internal impedance is zero (infinity):
• No internal losses.
• Instantaneous dynamic response.
• For an ideal voltage source, current has no effect on the voltage output:
• The output voltage value and waveform are always the same regardless
of the load.
• For current sources replace current by voltage in the last statement.
• An ideal capacitor with an infinite capacitance behaves as a dc voltage
source.
dv
q
C
v
i C
dt
• An ideal inductor with an infinite inductance behaves as a dc current source.
L
5

i
di
vL
dt
© Alexis Kwasinski, 2012
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 produce
electricity.
• 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: PEMFC
• The hydrogen atom’s electron and proton are separated at the anode.
• Only the protons can go through the membrane (thus, the name
proton exchange membrane fuel cell).
dc current
Heat
Oxygen
Hydrogen
Water
Catalyst (Pt)
Anode (-)
Membrane
(Nafion)
Catalyst (Pt)
Cathode (+)
H 2  2 H   2e 
1/ 2O2  2 H   2e   1H 2O
O2  2H 2  2H 2O
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(Er  1.23 V )
Fuel cell thermodynamics
The first law of thermodynamics:
• The energy of a system is conserved
 Q   W  dE
Change of heat
provided to the
system
Change of
work provided
by the system
Change of
system’s total
energy
•In conservational fields, potential functions change depend only on initial and
final values. Hence, Q  W  E
• For a closed system (control mass system), such as a piston
E  U  K  P
(The total energy change equals the sum of the change in internal energy, the
change in kinetic energy, and the change in potential energy)
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Fuel cell thermodynamics
• For an open system with mass flow across its boundaries (control volume),
such as a steam turbine
E  U  K  P  ( pV )
pV represents the work to keep the fluid flowing (p is pressure and V is
volume). Hence, if a magnitude called enthalpy H is defined as
H  U  pV
• Then,
H  E  K  P
• If we use the 1st law of thermodynamics for a stationary control volume (i.e.
the kinetic and potential energies are constant in time, then
H  Q  W
• Thus, the enthalpy is the difference between the heat and the work involved
in a system such as the one defined immediately above.
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Fuel cell thermodynamics
• If the change in enthalpy is negative, heat is liberated and the reaction occurs
spontaneously (contrary to endothermic reactions that requires to apply heat in
order for the reaction to occur).


• In the anode: H 2  2 H  2e ,


• In the cathode: 1/ 2O2  2 H  2e  1H 2O,
H  0 kJ
H  285.8 kJ
• Hence, in a PEMFC, 285 kJ/mol are converted into heat (Q) and electricity
(W). How much electricity W can we ideally obtain?
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 Qrev at a
temperature T0, the entropy is defined as
Q
S  rev
T0
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Fuel cell thermodynamics
In all processes involving energy conversion or interactions ΔS is nonnegative. ΔS is zero only in reversible processes..
Q
• For any process then S 
T
• The “=“ in the above relationship will give us the minimum amount of heat
Qmin required in a process.
• From the enthalpy definition a fuel cell can be considered as a system like the
following one
Q
W
Q
ΔH
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Fuel cell thermodynamics
• The maximum possible efficiency for a fuel cell is, then
max 
Q
W
 1  min
H
H
• An alternative derivation involves using “Gibbs Free Energy”
• The definition of entropy is relates with the 2nd Law of Thermodynamics. One
of its interpretations is that it is impossible to convert all the energy related with
irreversible processes, such as heat or chemical energy, into work.
• Hence, it is possible to define a magnitude with units of energy called Gibbs
Free 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 and
the maximum possible energy conversion efficiency is
G
max 
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H
Fuel cell thermodynamics
• From tables:
H 2  2 H   2e  ,
In the anode:


In the cathode: 1/ 2O2  2 H  2e  1H 2O,
G  0 kJ
G  237.2 kJ / mol
• And from slide #10 ΔH equals 285 kJ/mol. Thus,
max
G 237.2


 0.83
H 285.8
• The Gibbs Free Energy can also be used to calculate the output voltage of an
ideal fuel cell. Since the Gibbs Free Energy equals the electrical work, and the
electrical work equals the product of the charge and voltage, then
W  G  2FEo
• where F is the Faraday constant (charge on one mole of electrons) the factor
of two represents the fact that two electrons per mole are involved in the
chemical reaction.
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Fuel cell thermodynamics
• Thus,
G
Eo  
2F
and since F = 96,485 C/mole and ΔG = -237.2 kJ/mole, then
(237200)
Eo  
 1.229  1.23V
(2)(96, 485)
•E0 is also denoted by Er, the reversible voltage.
• This is the voltage that can be obtained in a single ideal PEMFC when the
thermodynamic reaction limitations are taken into account. I.e., this is the
output voltage of a single ideal PEMFC when it behaves as an ideal voltage
source. However, additional energy loosing mechanisms further reduce this
voltage.
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PEMFC output: Tafel equation
• The Tafel equation yields the cell’s output voltage Ec considering additional
loosing mechanisms:
Ec  Er  b log(i / i0 )  ir
• The first term is the reversible cell voltage (1.23V in PEMFCs)
• The last term represents the ohmic losses, where i is the cell’s current density,
and r is the area specific ohmic resistance.
• The second term represent the losses associated with the chemical kinetic
performance of the anode reaction (activation losses). This term is obtained
from the Butler-Volmer equation and its derivation is out of the scope of this
course.
• In the second term, i0 is the exchange current density for oxygen reaction and
b is the Tafel slope:
RT
b
n log(e)
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PEMFC output: Tafel equation
• In the last equation R is the universal gas constant (8.314 Jmol-1K-1), F is the
Faraday constant, T is the temperature in Kelvins, n is the number of electrons
per mole (2 for PEMFC), and β 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, such
as poisoning, occur.
• The Tafel equation do not include additional loosing mechanisms that are
more evident when the current density increases. These additional mechanisms
are:
• Fuel crossover: fuel passing through the electrolyte without reacting
• Mass transport: hydrogen and oxygen molecules have troubles reaching
the electrodes.
• Tafel equation also assumes that the reaction occurs at a continuous rate.
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PEMFC electrical characteristics
Er = 1.23 V
Maximum power
operating point
Er =1.23V
b=60mV,
i0=10-6.7Acm-2
r=0.2Ωcm2
Activation loss
region
Ohmic loss region
(linear voltage to current
relationship)
Actual PEMFCs efficiency vary between 35% and 60%
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Mass transport loss region
PEMFC electrical characteristics
• This past curve represent the steady state output of a fuel cell.
• The steady state output 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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PEMFC electrical characteristics
• A very good dynamic model of a PEMFC is discussed in: Wang, Nehrir, and
Shaw, “Dynamic Models and Model Validation for PEM Fuel Cells Using
Electrical Circuits.” IEEE Transactions on Energy Conversion, vol 20, no. 2,
June 2005.
• Some highlight for this model:
Basic circuit
• Rohm: represents ohmic losses
• Ract: represents the activation losses (related with 2nd term in Tafel equation)
• Rconc: losses related with mass transport.
• C: capacitance related with the fact that there are opposing charges buildup
between the cathode and the membrane.
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PEMFC electrical characteristics
• Model for the internal fuel cell voltage E
Equal to Er


N cell RT
where, f1 ( I , T )  
ln pH* 2 pO* 2  N cell k E (T  298)
2F
f 2 ( I )  N cell Ed ,cell
• Comments:
• The voltage drop related with fuel and oxidant delay is represented by
Ed,cell.
•The fuel cell output voltage depends on hydrogen’s and oxygen’s pressure
• The fuel cell output voltage also depends on the temperature.
• The time constants for these chemical, mechanical, and thermodynamic
effects are much larger than electrical time constants.
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PEMFC electrical characteristics
• Ed,cell can be calculated from the following dynamic equation:
E d ,cell ( s)  e I( s)
 es
 es  1


dEd ,cell (t )
dt

1
e
Ed ,cell (t )  e
di(t )
dt
where τe is the overall flow delay.
• In steady state, both derivatives are zero, so Ed,cell = 0. But when the load
changes, di(t)/dt is not zero, so Ed,cell will be a non-trivial function of time that will
affect the fuel cell internal output voltage.
•When considering fuel cells dynamic behavior, they all tend to have a slow
response caused by the capacitance effect in slide 19, the flow delays, the
mechanical characteristics of the pumps, and the thermodynamic
characteristics.
• Thermodynamic characteristics were introduced in the model through an
analogous electric circuit, as shown in the next slide.
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PEMFC electrical characteristics
• Simulation model and equivalent electric circuit for the thermodynamic block:
• Fuel cells have a slow dynamic response, as shown in the next figure that
evaluates the response of a fuel cell to multiple fast step load changes:
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Hydrogen production
• Hydrogen needs to be produced, and sometimes it also needs to be
transported 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) CH 4  H 2O  CO  3H 2
endothermic reaction (needs heat)
2) CO  H 2O  CO2  H 2
exothermic reaction (provides heat)
• 75 % to 80 % efficient.
• Partial oxidation (POX)
• It also uses natural gas or other hydrocarbon
CH 4  1/ 2O2  CO  2H 2 and/or CH 4  O2  CO2  2H 2
• POX is compact and has faster dynamic response than MSR, but MSR
provides higher hydrogen concentration.
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Hydrogen production
More methods for hydrogen production:
• Electrolysis of water
• Water molecules can be separated using electricity. But we use electricity
to 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 water
needs to be purified (soft de-ionized water is needed).
• Reaction:
2H 2O  O2  2H 2
• Electricity can be obtained at a large scale from nuclear reactors but the
hydrogen 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 is
available only when there is wind or sunlight.
• Gasification of Biomass, Coal or Wastes
• These methods are still a long way into the future.
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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, storing
hydrogen implies loosing efficiency.
• Some storage methods:
• Pressure Cylinders: Some efficiency is lost in the compressing
process
• Liquid Hydrogen: it requires lowering the hydrogen temperature to
20.39 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 is
generated when the hydrogen is released, but these compounds are
very 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) and not suitable for DG.
• The most commonly used catalyst (Pt) is very expensive.
• The most commonly used membrane (Nafion – a sulfonated tetrafluorethylene
copolymer is also very expensive).
• PEMFCs are very expensive.
• CO poisoning diminishes the efficiency. Carbon monoxide (CO) tends to bind
to Pt. Thus, if CO is mixed with hydrogen, then the CO will take out catalyst
space 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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Direct Methanol Fuel Cells (DMFC)
• The main advantage is that they use a liquid fuel.
• Reactions:
• Anode CH 3OH  H 2O  CO2  6 H   6e 
• Cathode 1/ 2O2  2 H   2e   H 2O
• 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 portable
applications.
• Issues:
• Cost
• Excessive fuel crossover (methanol crossing the membrane)
• Low efficiency caused by methanol crossover
• CO poisoning
• Low temperature production
• Considerable slow dynamic response
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Phosphoric Acid Fuel Cells (PAFCs)
• 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 is
1.23 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
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Alkaline Fuel Cells (AFCs)
• The main advantage is that their cost is relatively low (when considering the
fuel cell stack only without “accessories”.
• Reactions:
H 2  2OH   2 H 2O  2e 
• Anode
1/ 2O2  2 H 2O  2e   2OH 
• Cathode
• Developed for the Apollo program.
• Very sensitive to CO2 poisoning. So these FCs can use impure hydrogen but
they require purifying air to utilize the oxygen.
• Issues:
• Cost (with purifier)
• Short life (8000 hours)
• Relatively low heat production
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Molten Carbonate Fuel Cells (MCFCs)
• One of the main advantages is the variety of fuels and catalyst than can be
used.
• Reactions:
2

• Anode H 2  CO3  H 2O  CO2  2e

2
• Cathode 1/ 2O2  CO2  2e  CO3
• They operate at high temperature. On the plus side, this high temperature
implies a high quality heat production. On the minus side, the high temperature
creates reliability issues.
• They are not sensitive to CO poisoning.
• They have a relatively low cost.
• Issues:
• Extremely slow startup
• Very slow dynamic response
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Solid Oxide Fuel Cells (SOFCs)
• One of the main advantages is the variety of fuels and catalyst than can be
used.
• Reactions:
H 2  O 2  H 2O  2e 
• Anode

2
• Cathode 1/ 2O2  2e  O
• They operate at high temperature with the same plus and minus than in
MCFCs.
• 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.
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Fuel cell technologies
• Comparison of the most common technologies
PEMFC
DMFC
AFC
PAFC
MCFC
SOFC
H2
CH3OH
H2
H2
H2, CO, CH4,
hydrocarbons
H2, CO, CH4,
hydrocarbons
Solid polymer
(usually Nafion)
Solid polymer
(usually Nafion)
Potasium
hydroxide
(KOH)
Phosporic
acid (H3PO4
solution)
Lithium and
potassium
carbonate
Solid oxide
(yttria,
zirconia)
H+
H+
OH-
H+
CO32-
O2-
Operational
temperature (oC)
50 – 100
50 - 90
60 - 120
175 – 200
650
1000
Efficiency (%)
35 – 60
< 50
35 – 55
35 – 45
45 – 55
50 – 60
Unit Size (KW)
0.1 – 500
<< 1
<5
5 – 2000
800 – 2000
> 2.5
4000
> 5000
800 – 2000
1300 - 2000
Fuel
Electrolyte
Charge carried in
electrolyte
Installed Cost ($/kW)
< 1000*
3000 – 3500
* Without purifier
• All fuel cells occupy a lot of space. Much more than any of the other types of
microsources
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