Course Web Site:
http://courses.washington.edu/cheme445
Course Notes in
Instructors:
Fuel Cell Engineering
Prof. Eric M. Stuve
Dept. of Chem. Engr.
Univ. of Washington
Box 351750
Seattle, WA 98195-1750
Benson 105
stuve@u.washington.edu
Winter 2004
A course devoted to all aspects of fuel
cells: types, operation, design, and safety.
Laura Roen
roenlaur@u.washington.edu
Benson B7
Fuel Cell Engineering Course Notes
1
© 1998-2004 Eric M. Stuve
•Course Mechanics
- Lecture/homework/exams
- Grading percentages:
Homework (due Wed.)
Exam I (Feb. 4)
Exam II (March 3)
Design Project (March 15)
25
25
30
20
- Fuel Cell Technology Handbook (Gregory
Hoogers, Ed., CRC Press, 2002)
- Perry’s Chemical Engineers’ Handbook,
7th edition, Sections 2, 5, 6, and 27-55.
© 1998-2004 Eric M. Stuve
© 1998-2004 Eric M. Stuve
2
•Some history…
- Electrocatalysis research at UW
since ‘91
- Ugrad. research in PEM fuel cells
since ‘92
- Fuel Cell Locomotive project
started 9/96
- New courses in fuel cells
Intro. to Fuel Cells (2002)
Solid Oxide Fuel Cells (2003)
•Texts
- Course Notes in Fuel Cell Engineering
Fuel Cell Engineering Course Notes
Fuel Cell Engineering Course Notes
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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What is a Fuel Cell?
• Some similarity to a battery
except that energy must be
stored or built into a battery
• Batteries are closed systems.
• Device that converts the chemical
energy stored in a fuel directly to
electrical energy.
• Fuel cell is an open system.
–
–
H2
O2
Batt
ery
Fuel
Cell
+
+
H2O
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
5
Two Principles of the Course
6
• Replacement technology
- Replaces an existing product
electric vs. gas light
- New product must cost less
• Enabling technology
- Provides new capability
airplanes ––> flight
- Cost not so important
2. Match Energy Source to
Application
- Stationary / Vehicle / Portable
- Sometimes F/Cs won’t work
© 1998-2004 Eric M. Stuve
© 1998-2004 Eric M. Stuve
Design and Technology
1. Chemoelectricity
- Chemistry must occur before
energy flows
- F/C system like an entire
chemical plant
Fuel Cell Engineering Course Notes
Fuel Cell Engineering Course Notes
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Fuel Cell Reactions
• Fuel cells can fall into either
category
Let’s look at some possible
reactions (energies in kJ/mol)…
- Energy efficiency =>
- Environ. regulations =>
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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H2 + 1/2 O2 ––> H2O
–∆Ho –∆Go
286 237
CH4 + 2 O2 ––> CO2 + 2 H2O
890
Fuel Cell Engineering Course Notes
818
10
© 1998-2004 Eric M. Stuve
Select a Fuel
General oxyhydrocarbon reaction:
CxHyOz + (4x + y – 2z)/4 O2 ––>
x CO2 + y/2 H2O
Fuel \ HHV kJ/mol
MJ/kg
MJ/liter*
kJ/mol CO2
H2
286
142
1.73
CH4
890
55.5
0.04 / 24.0
890
CH3OH
638
19.9
15.8
638
C2H5OH
1235
26.8
21.2
618
Glucose
2814
15.6
24.3
469
Gasoline
46.8
34.1
≈ 600
Kerosene
45.9
37.6
≈ 600
Coal, bit.
27
21
< 600
∞
*H2: at 2200 psi; CH4: at STP and as LNG; Glucose: solid
HHV (LHV): Higher (lower) heating value [water as liquid
(vapor)]
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Energy Conversion
Oxidation and reduction at same
place & time
• Combustion: the time honored
way
CH4
CH4 + 2 O2 ––> CO2 + 2 H2O
O2
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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–
CH4
Oxidn
O2
Redn
Half reactions:
oxidn:
redn:
• Mnemonic
- Reduction occurs at the
cathode (redcats)
- Oxidation occurs at the anode
Oxidation and reduction separated
in space
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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• Definitions
- Cathode: electrode to which
cations migrate
- Anode: electrode to which
anions migrate
+
H2O
© 1998-2004 Eric M. Stuve
Cathode? / Anode?
• Direct energy conversion: fuel
cells
CO2
Fuel Cell Engineering Course Notes
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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What Makes a Fuel Cell?
Cell Potential
• Because oxidation and reduction
are physically separate, two
things must happen to complete
the reaction in a fuel cell:
• Cell potential E or Eo is the
difference between the cathode
potential Ec and the anode
potential Ea.
1. Ions travel through e-lyte:
- acidic f/c: cations to cathode
- alkaline f/c: anions to anode
Eo = Eco – Eao
• Fuel cells: Cathode (+); Anode
(–) ; E,Eo > 0
E = Ec – Ea
2. Electrons travel anode to cathode
Electrons fall through “potential
gradient” and thus do work.
Fuel Cell Engineering Course Notes
• Electrochem. cells: Cathode (–);
Anode (+); E,Eo < 0
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© 1998-2004 Eric M. Stuve
Reversible Cell Potential
Look at H2/O2 fuel cell:
Anode:
H2 ––> 2 H+ + 2 e–
© 1998-2004 Eric M. Stuve
© 1998-2004 Eric M. Stuve
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1.23
0
*she = standard hydrogen
electrode; hydrogen electrode (H2
<––> 2 H+ + 2 e–) in equilibrium at
standard conditions (unit activity of
protons in solution and 1 atm of H2)
(def.)
Reversible cell potential
Fuel Cell Engineering Course Notes
Fuel Cell Engineering Course Notes
Recall that the reversible cell
potential is defined consistently for
both fuel cells and electrochemical
cells.
Eoshe*/ V
Cathode:
O2 + 4 H+ + 4 e– ––> 2 H2O
or
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Gibbs Free Energy
Definitions
• Basic thermodynamic relation
between Gibbs free energy and
cell potential (memorize!)
ne = number of electrons
transferred per molecule of
reactant (fuel)
∆Go = –neFEo
F = Faraday’s constant
= 96,489 C/mol
• ∆Go is always negative for a
spontaneous process
Fuel cells:
Electrochem. cells:
Fuel Cell Engineering Course Notes
∆Go < 0
∆Go > 0
© 1998-2004 Eric M. Stuve
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
Equilibrium Potential
Nernst Equation
• An electrode is at its equilibrium
potential Eeq when it is in
equilibrium with all electrolyte
species. The equilibrium
potential can be calculated with
the Nernst equation.
where O is an oxidized species, R
a reduced species, and the
subscript M indicates that the
electron comes from the metal
electrode,
a
activity of R
K eq = R =
a O activity of O
•For a general reduction reaction
−
O + eM
↔R
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
E = Eo −
23
Fuel Cell Engineering Course Notes
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RT
RT ⎛ a R ⎞
ln K eq = E o −
ln⎜
⎟
ne F
ne F ⎝ a O ⎠
© 1998-2004 Eric M. Stuve
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Overpotentials
Overpotentials (cont.)
•In a real process the electrodes
cannot operate at their
equilibrium potentials.
Nonidealities in real processes
lead to efficiency losses or
resistances to the process.
•These shifted potentials are called
overpotentials.
•In a fuel cell the chemical energy
of the fuel drives the
overpotential, which in turn
drives the reaction.
•Electrodes must shift to potentials
more favorable for oxidation or
reduction to overcome efficiency
losses.
Fuel Cell Engineering Course Notes
H2/O2
Fuel Cell
Eao
ηa
0
Fuel Cell Engineering Course Notes
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© 1998-2004 Eric M. Stuve
Ec
0.5
© 1998-2004 Eric M. Stuve
E
RHE
Eao
Ec
ηc
1.0
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© 1998-2004 Eric M. Stuve
Water
Electrolysis o
Ec
Eco
Ea
Fuel Cell Engineering Course Notes
Ea
ηc
ηa
0
/V
0.5
E
RHE
27
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
/V
1.0
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Real Cell Potentials
Real Cell Potentials
•Overpotentials always reduce fuel
cell potentials, so that less
voltage is delivered per electron
transferred.
(
(
E = E eq − ηc + ηa
•Conversely, overpotentials always
increase electrochemical cell
potentials so that more voltage is
required per electron transferred.
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
) (
E = E c − E a = E eq,c − ηc − E eq,a + ηa
)
)
•Note that overpotentials are
always positive numbers.
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Ideal Thermodynamic Efficiency
Fuel Cell Engineering Course Notes
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© 1998-2004 Eric M. Stuve
Real Energy Conversion
(CO 2 )
• Thermal energy: ∆H (enthalpy)
• Elec. energy:
∆G (free energy)
(–)
Fuel
Anode
• Thermodynamic efficiency is
measure of electrical output vs.
possible heat output (if fuel were
simply burned)
o
ηt
=
Fuel Cell Engineering Course Notes
Electrolyte
Air
1. Reactant/product transport
2. Reaction at electrocatalyst
∆G o
Cathode
(+)
H2O
3. Ion transport through e-lyte
4. Electron transport
∆H o
© 1998-2004 Eric M. Stuve
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Polarization Curves
• Most common description of fuel
cell performance
Eo
• Measure cell voltage as a function
of current
o
E/V
E
E/V
0
0
Fuel Cell Engineering Course Notes
0
j / mA cm–2 = current density
j / mA cm–2
© 1998-2004 Eric M. Stuve
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• Regions of polarization curve
-
© 1998-2004 Eric M. Stuve
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Behave Ohm’s Law
(A = electrode area)
(3) Ion transport limitation …
“ohmic” resistance of
electrolyte (or membrane)
-
(1) External mass transfer
limitations
© 1998-2004 Eric M. Stuve
Fuel Cell Engineering Course Notes
• About ohmic losses
(2) Kinetic limitations … need to
achieve sufficient
overpotential for reaction
Fuel Cell Engineering Course Notes
0
35
Straight line on polarization
curve
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Put quantities on an area basis
(area of fuel cell)…
Fuel Cell Efficiency
.
N i = molar flux of species I
[=] mol cm–2 s–1
–
Fuel
Air
.
Fuel
Cell
W e = rate of elec. work (power)
done on F/C
Load
+
.
Water
[=] W/cm2
Q e = rate of heat supplied to F/C
[=] W/cm2
Fuel Cell Engineering Course Notes
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© 1998-2004 Eric M. Stuve
© 1998-2004 Eric M. Stuve
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• Thermodynamic efficiency
• Electrical efficiency
.
.
ηe =
Fuel Cell Engineering Course Notes
elec. work
We
− jE
ηt =
=
=
.
heat of rxn. .
o
o
N f ∆Hrxn N f ∆Hrxn
elec. work
We
− jE
=
=
.
max. elec. work
− jE o
W e,max
Note that
(for no excess fuel):
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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which becomes
⎞
⎛
−ne FE ⎜ E o ⎟ −ne FE o
=
•
ηt =
⎜ o⎟
o
o
E
∆Hrxn
∆Hrxn
⎝
⎠
⎛ E ⎞ ∆G o
rxn
•⎜
⎟=
o
o
⎝ E ⎠ ∆Hrxn
• Applies to both fuel cells and
heat engines
but
heat engine must absorb heat at
the flame temperature (2000+
K) and reject at 298 K
⎛ E ⎞
•⎜
⎟
⎝Eo ⎠
• Carnot efficiency
ηt =
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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T2 − T1 40 − 50% (power plants)
≈
T2
< 25% (automotive)
Fuel Cell Engineering Course Notes
Heat Dissipation
.
Q=
• Fuel cells not perfectly efficient, so
heat must be dissipated. Look at
energy balance…
42
© 1998-2004 Eric M. Stuve
.
o
N f ∆Hrxn
.
−We
By definition of thermo.
efficiency…
.
.
⎛ j ⎞
o
o
Q = (1 − ηt ) N f ∆Hrxn
= (1 − ηt )⎜
⎟∆Hrxn
⎝ ne F ⎠
Because the heat of combustion is
negative, heat must be removed
from the fuel cell.
Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Fuel Cell Engineering Course Notes
© 1998-2004 Eric M. Stuve
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Example
An H2/O2 fuel cell operates at 0.6 V
and supplying 1 A/cm2 at 298 K.
The area of the fuel cell is 1000
cm2. Determine the following:
(a)
electrical efficiency
(b)
thermodynamic efficiency
(c)
total electric power output
(d)
heat dissipation
(e)
flow rates of H2 and O2.
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© 1998-2004 Eric M. Stuve
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