5 - Fuel Cell Thermodynamics - von Unwerth.pdf

Shows the change of standard OCV when differing from
standard conditions
EN : Nernst voltage [V]
E0 : standard open cell voltage OCV [V]
R : universal gas constant (8,314 J/mol K)
T : thermodynamic temperature
z : number of electrons as per reaction equation
F : Faraday constant (F = e NA = 96485 C/mol)
ai : activity (ai = i ci ; i = 1 for diluted gases
ai = ci = pi/p0 for ideal gases)
b f l ti t i hi t f t ) 
i : number of moles as per reaction ( stoichiometry factor)

1. Fuel Cell Thermodynamics
Prof. Dr.-Ing. Thomas von Unwerth Thomas

von

Unwerth
Department
Advanced Powertrains
Prof. Dr.-Ing. Thomas von Unwerth
11.07.2011 International Summer School - Izmir
1
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

2. Content
Fuel cell thermodynamics • Calculation of fuel cell potentials • Efficiency calculations • Mass flow (hydrogen, air, water) • Comparision to ICE Carnot efficiency •
Polarization curve and voltage losses
•
Polarization

curve

and

voltage

losses
2
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

3. Fuel Cell thermodynamics PEM reaction H
2
+ ½ 0
2
= H
2
O(H<0, exothermal)
Enthalpy H (germ. Enthalpie)
overall
fuel energy content
H = Heating value
lower heatin
g
value LHV
(g
erm. H
u
)
:
g
aseous reaction
p
roducts
,
LHV = 241
,
82 kJ/mol
g(g
u
)
gp,
,
higher heating value HHV (germ. H
O
): incl. Enthalpy of wa ter condensation, HHV = 285,83 kJ/mol
Gibbs free ener
gy
G
(g
erm. Freie Enthal
p
ie
)
gy (g p )
usable
fuel energy content
G = H – TS
G
0
(gaseous reaction products) = 228,57 kJ/mol
G
0
(incl. enthalpy of water condensation) = 237,13 kJ/mol
X
0
= standard conditions:
T=298K, p=1,013*10
5
Pa
3
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
(Wertequelle: Kurzweil)

4. Schematic fuel cell polarization curve
E
H
Thermoneutral voltage
Entropy term
ics
Fz
H
E
H



0
0
ST
E
0
Standard OCV
Entropy

term
Difference to standard conditions
hermodynam
y
es for high
eat
Fz
G
E



0
0
Fz

E [V]
E
N
Nernst voltage
Activation overvoltage
th
heat
Anergy
eam processe
ture waste he

  
i
i N
i
a
zF
RT
E E

ln
0
A

voltage
E
Z
Cell voltage
Ohmic losses
Concentration overvoltage
cinetics
Downstre
temperat
C

i
RI


O
p
eration ran
g
e
energy
rgy
pg
electrical
Exer
4
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
current I [A]

5. Thermodynamic efficiency
0
0
Reaction n
-

H
0
[kJ mol
-1
]
E
0
H
[V]
-

G
0
[kJ mol
-1
]
E
0
[V]
th
H
2
+1/2O
2
-
>H
2
O
li
2
286 0
1482
237 13
1 229
0829
H
2

+

1/2

O
2
>

H
2
O

li
q
2
286
,
0
1
,
482
237
,
13
1
,
229
0
,
829
H
2
+ 1/2 O
2
-> H
2
O
gas
2 241,8 1,253 228,6 1,185 0,946
CO + 1/2 O
2
-> CO
2
2 283,1 1,467 257,2 1,333 0,909
CH
3
OH + 1 1/2 O
2
->
6
726 6
1255
702 5
1 214
0967
CO
2
+ 2 H
2
O
liq
6
726
,
6
1
,
255
702
,
5
1
,
214
0
,
967
CH
4
+ 2 O
2
->
CO
2
+2H
2
O
8 802,4 1,039 800,9 1,038 0,999
CO
2
+

2

H
2
O

gas
5
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

6. Chemical potential 
The chemical potential describes the Gibbs free enthalpy change of a
s
y
stem under variation of its com
p
osition.
G





yp
For > 0 the Gibbs free enthalpy increases with growing n.
The chemical
p
otential can be ex
p
ressed b
y
the activit
y
. Therein

0
means
Tp
n
,




0
ppyy

the standard potential at T=298K and p=1,013bar.
The activity a
i
of a substance i is link ed with the concentration c
i
of this
i i i
a
RT
ln
0




substance by the activity coefficient 
i. For ideal behaviour it is =1.
A
ctivity a
is dimensionless, for solid substances it is a=1.
for ideal gases:
i i i
c a



For ideal gases the activity a
i
is the ratio of partial pressure p
i
and standard
pressure p
0
=1,013bar.
Th h i l t ti l f id l i d ib bl f ti f it
0
p
p
a
i
i



Th
e c
h
em
ica
l po
t
en
ti
a
l o
f
an
id
ea
l gas
is
d
escr
ib
a
bl
e as a
f
unc
ti
on o
f

it
s
partial pressure.








 
0
0
ln
p
p
RT
i
i i
 
6
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

7. Nernst equation

  
i
i N
i
a
zF
RT
E E

ln
0
i
Shows the change of standard OCV when differing from
standard conditions
E
N
: Nernst voltage [V]
E
0
: standard open cell voltage OCV [V] R
:
universal gas constant (
8
314
J/mol K)
R
:
universal

gas

constant

(
8
,
314

J/mol

K)
T : thermodynamic temperature z : number of electrons as per reaction equation F
:
Faraday constant (F = e N
=
96485
C/mol)
F
:
Faraday

constant

(F

=

e

N
A
=

96485

C/mol)
a
i
: activity (a
i
=

i
c
i
;

i
= 1 for diluted gases
a
i
= c
i
= p
i/p
0
for ideal gases)
bfl ti(tihi tft)

i
: num
b
er o
f
mo
les as per reac
ti
on
(
s
t
o
ic
hi
ome
t
ry
f
ac
t
or
)
thermodynamic sign rule:
products – educts (reactants)
7
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
exponential: products / educts (n is negative for educts)

8. Nernst equation for various cell reactions
Reaction Nernst equation Fuel cell
AFC, PEFC, PAFC,
SOFC
OH O H
2 2 2
2
1 


1
0
2
ln
2
OH
N
p
F
RT
E E 
SOFC
2
2 2
2
1CO O CO 


2
2 2
2
O H
p p
F



2
1
0
2
ln
2
CO
N
p
p
p
F
RT
E E 
DMFC
2
O
H
CO
O OH CH
2 3
2
2
3

 


2
2
2
O CO
p
p
F



2
3
0
2
ln
6
CO
N
p
a
p
F
RT
E E 
(w/ a
H20
=1)
MCFC
O
H
CO
2 2
2

) (2 2 2
2
1
Kathode
CO
O
H
CO O H

  


) (2 2
2
1
0
ln
2
Anode
CO
O
H
CO OH
N
p
p
p
p p
F
RT
E E



 


2
2 3
6
O OH CH
p
a
F

) (2 2
A
node
CO
O
H



) (2 2 2Kathode
CO
O
H
p
p
p
8
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

9. Thermoneutral voltage and standard potential (OCV) as a function of temperature at
p
i
=
1
,
013
bar
1.31.4
as

a

function

of

temperature

at

p
i

1
,
013
bar
1
1.1
1.2
1.3
E
0
E
H
0.8
0.9
1
enzial [V]
0.5 0.6
0.7
tandardpote
Standardpotenzial Heizwertspannung
020.3
0.4
S
t
0
0.1
0
.
2
0
100
200
300
400
500
600
700
800
900
1000
9
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth 0
100
200
300
400
500
600
700
800
900
1000
Temperatur [°C]

10. Nernst voltage E
N
= f(T) for various pressures p
i
1.31.4
1
1.1
1.2
1.3 070.8
0.9
1
nnung [V]
0.5
0.6
0
.
7
Nernstspan
pH2=1bar; pO2=1bar; pH2O=1bar pH2=0,5bar; pO2=0,2bar; pH2O=0,5bar pH2
=
0 8bar; pO2
=
0 2bar; pH2O
=
02bar
0.2
0.3
0.4
N
pH2 0
,
8bar;

pO2 0
,
2bar;

pH2O 0
,
2bar
0
0.1
0 100 200 300 400 500 600 700 800 900 1000
10
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
Temperatur [°C]

11. Fuel cell cinetics (voltage losses)
type of
overvoltage
cause Influencing variables technical scopes
of influence
regime
activation - Limited velocit
y
of -
p
artici
p
atin
g
-hi
g
her workin
g
- low current
overvoltage
(activation
polarization)
y
charge transfer at phase boundary bw. electr./ionic conductor
-
occurs at each
ppg reactands
- elektrolyte
- elektrodes
- temperature
gg
temperature
- elektrode material
- elektrode texture
densitiy
- non-linear to
current density
-
occurs

at

each

electrochem.
reaction
concentration
-
Too slow mass
-
underconcentrated
-
porous or thinner
-
high current
concentration

overvoltage
(concentration
polarization)
Too

slow

mass

transport to or from
the electrodes
underconcentrated reactands
- porosity of elektrodes
- current density
porous

or

thinner

elektrodes
- Lower current density
for prevention of local
shortage with
reaktants lower
high

current

density
- non-linear to
current density
reaktants
,
lower

depletion
Ohmic losses
(ohmic polarization)
- Conductivity
process inside
material
- Ohmic resistance:
elektrolyte,
elektrodes
- use of materials with
high conductivity
-
temperature
increase
- medium current
density
-
linear
to current
material
elektrodes
,
interconnector,
(assembly layers)
temperature
increase

(ceramic, ionic
conductor, molten salts)
linear

to

current

density
r
eac
ti
o
n
o
v
e
rv
o
lt
age

–
n
o
n
su
ffi
c
ie
nt r
eac
ti
o
n r
a
t
e

o
f
o
n
e
r
eac
ti
o
n
s
t
ep
in
s
ide

coup
led
r
ea
kti
o
n
s;

p
r
ese
nt
a
t
a
ll
a
r
eas

o
f
11
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
eac o o e o age
o su c e eac o a e o o e eac o s ep s de coup ed ea o s; p ese a a a eas o
polarization curve; increases with curr ent density; difficult to differentia te from concentration overvoltage
reference: W.Vielstich – Electrochemistry)

12. Fuel Cell efficiencies
0
0
H
th
EE


thermodynamic efficiency
Hydrogen:

=
94
%
H
E
Hydrogen:

th
=

94
%
Methane :
th
= 99%
CO :
th
= 91%
0
EE
Z
E


voltage (potential) efficiency
E
E
0
H
Z
E th Z
EE
  
  
cell efficiency / charge efficiency
12
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

13. Relevance of cell efficiency
0Z
E
th
Z
E
 




cell efficienc
y

/
char
g
e efficienc
y
Target values for PEFC-development (as PNGV*):
– power density 600mW/cm²
hd /i
ti
0H
E
th
Z
E



y
gy
–
h
y
d
rogen
/
a
ir
-opera
ti
on
– power variant: 600 mV @ 1000mA 

= 48%
– efficiency variant: 800 mV @ 750mA 

= 64%
NG2000: 292 cm² cell area
G
²
13
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
(*PNGV: Partnership for new generation vehicles, U.S.)
N
G
3000: 596 cm
²
cell area

14. Wirkungsgrad –von der Zelle zum Stapel
Utilizationof fuel within fuel cell (dt : Gasnutzung)
M
(dt
.
:

Gasnutzung)
M: molar mass [g/mol]
m: mass flow [g/s]
F:
Faraday
-
constant
[C/mol=As/mol]
ein
ges
ein
B
G
umgesetzt BG
t
m
I
zF
M
m
m
u
 


 
,
,
F:

Faraday
-
constant

[C/mol=As/mol]
ein
ein
G
,
Stack efficiency (incl. utilization)
overall cell efficiency relative to gas input
(
cell efficienc
y
*utilization
)
t Z St
u




(y) Faraday efficiency alternative to cell efficiency includes
I
I


alternative

to

cell

efficiency
,
includes

utilization, easier to measure
n
I: mole flow [mol/s]
I
I
n zF


14
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth

15. Thermoneutral voltage, standard potential and thermodynamic efficiency
(p
i=
1
,
013
bar)
efficiency

(p
i
1
,
013

bar)
1.3
1.4
1
1.1 1.2
E
0
E
H
0.8
0.9
1
tenzial [V]
0.5
0.6
0.7
tandardpo
t
Standardpotenzial Heizwertspannung thermodynamischer Wirkungsgrad

th
0.20.3
0.4
S 0
0.1
0.2
0
100
200
300
400
500
600
700
800
900
1000
15
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth 0
100
200
300
400
500
600
700
800
900
1000
Temperatur [°C]

16. Comparison with Carnot efficiency
09
1
070.80
.
9
V]

th
0.60
.
7
tenzial [V

C
0.4
0.5
andardpo
0.2 0.3
Sta
thermodynamischer Wirkungsgrad Carnotwirkun
g
s
g
rad
(
25°C
)
0
0.1
0
100
200
300
400
500
600
700
800
900
1000
gg ( )
16
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth 0
100
200
300
400
500
600
700
800
900
1000
Temperatur [°C]

17. Characteristic curve and heat production
Better characteristic curve:
Rd f l t
17
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
-
R
e
d
uces
f
ue
l cos
t
s
- Reduces heat production simplified cooling

18. Comparison of energy flows
+
Wasserstoff-Energie-
Hydrogen energy
35%
Einsatz
Hydrogen energy
in
p
ut
input Diesel energy
input
p
50%
33%
Waste heat exhaust
Waste heat
5%50%
33%
Waste heat cooler
Friction, intercooler
Mech
Mech
Waste heat exhaust
cooler
Mech
.
work
Mech
.
work
18
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
45% 33%

19. Typical polarization curves of different fuel cells different

fuel

cells
e ell voltage Ce
Current density
19
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
(Quelle: K.Krischer, TU München)

20. Some selected substancial correlations Faraday‘s law
Transported charge by Ions = z
.e
Transported charge pro Mole = N
A
.
z
.ez: valency [-]
e: elementar
y
char
g
e
e
.
N
A
= F [C/mol]
Electric charge:
yg
N
A
: Avogadro constant
F: Faraday constant e=
1
6022
10
-
19
C
Electric

charge:
Q = n
.
Z
.
E
.
N
A
= n
.
Z
.
F = I
.
T
e

=

1
,
6022
.
10
-
19
C
N
A
= 6,023*10^23 mol
-1
F = 96485 C/mol
Elektrochemical converted mass of
substances m:
I: elektric current [A]
t: time [s]
Q: electr. charge [C]
M:
m
olar mass
[g/mol]
Faradaygesetz
M
F
tI M
FQ
m





M:

m
olar

mass

[g/mol]
N: amount of substance [mol]
m: mass of substance [g]
20
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth
z
F
z
F

21. Fuel Cell thermodynamics
Thank you for your attention!
21
Advanced Powertrains – Prof. Dr.-Ing. T. von Unwerth