Department of Chemical and Environmental Engineering
Illinois Institute of Technology
Design and Analysis of Distributed
Feed Solid Oxide Fuel Cell Stacks
Donald Chmielewski
Ayman M. Al-Qattan
Presented at Argonne National Laboratory
January 21st, 2004
Department of Chemical and Environmental Engineering
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Outline
Motivation
Hydrogen Fed Case
Internal Reforming
Multi-Dimensional Analysis
Conclusions
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Tubular Design SOFC
Fuel
Anode
Electrolyte
Cathode
Interconnect
Air
Air
Cathode
2 O=
V
-
+
Solid
Electrolyte
Anode
2H2
2H2O
O2+ 4 e- 2 O=
2H2+ 2 O= 2 H
2O +4 e-
O2
4 e-
4 e-
Heat
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Flat-Plate Hydrogen Fed SOFC
Fuel Cell Stack
Anode
Flow
Cathode
Flow
Cathode
2 O=
V
-
+
Solid
Electrolyte
Anode
2H2
2H2O
O2+ 4 e- 2 O=
2H2+ 2 O= 2 H
2O +4 e-
O2
4 e-
4 e-
HEATRELEASED
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Planar Design Characteristics
Advantages:
• Shorter current path => Lower ohmic loss
• Lower fabrication cost
Disadvantages
• Expensive seals
• Susceptible to thermal stresses
=> Shorter life-span
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Review of SOFC Electrochemistry
OHOH 2221
2
OH
HH
C
CTTr
2
2
2ln)()(
Electrochemical Reaction:
Heat Generation:
FF
nhrjljGHn
jQ Hii 2
)()( 2
Reaction Rate:
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Flow Configurations
Air Channel
Fuel Channel
InterconnectCathode
Anode
Electrolyte
Fuel
Flow
Air Flow
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Plug Flow Reactor Analogy
Feed Exhaust
Reaction
Rate
Conventional Design
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Figure taken from Selimovic Dissertation, Lund University, (2002).
Thermal Stresses in the Literature
Peters et al., state that
“ Large temperature gradients in either direction can cause damage to one or of the components or interfaces due to thermal stresses”
Yakabe et al., state that
“ … the internal stress would cause cracks or destruction of the electrolytes”
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Fuel Cell Stack
Air Channel
Fuel Channel
InterconnectCathode
Anode
Electrolyte
Internal Reforming SOFC
CH4
Air Flow
H2O
CO2
H2 H
2O
O=
Fuel Flow
O2
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Internal Reforming
44224 3 CHrefCH
kCkrHCOOHCH ref
eq
COH
COOHfshiftCO
k
K
CCCCkrHCOOHCO fshift 22
22
,
,222
is very large Endothermic
is also large Exothermic fshiftk ,
refk
2
1222
2 OHOH Hr Exothermic
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Clarke et al, (1997) claim: “Internal reforming
offers:
• Reduced System Cost (reforming unit eliminated).
• Less Steam Required (anode reaction makes steam).
• More Uniform Temperature Distribution.
• Higher Conversions (equilibrium limiting products
consumed by the other reaction).”
The Promise of Internal Reforming
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Figure taken from Selimovic Dissertation, Lund University, (2002).
Impact of Internal Reforming
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Plug Flow Reactor Analogy (Internal Reforming)
ReformingReaction Rate
Reforming HeatGeneration
ElectrochemicalReaction Rate
ElectrochemicalHeat Generation
Combined HeatGeneration
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Effective Structure of IR SOFC
• Heat and steam produced not used by reforming.
• Pre-heating steam is expensive.
• Steam in the feed lowers hydrogen utilization (reaction rate is a function of hydrogen to steam ratio).
ElectrochemicalSection
ReformingSection
Pre-Heater
222
224 3
COHOHCO
COHOHCH
OHOH 22
Methane
Steam
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Additional Impacts of Non-Uniformity
• Electrolyte under-utilized at
low temperatures
• Hot-spots force the use of
more expensive high
temperature tolerant materials
• Large temperature range
restrict operational window
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Exhaust
Feed
Feed
Distributed Feed Plug Flow Reactors
Distributed Feed Design
• Makes PFR act like a CSTR.
• Improves Yield and Selectivity.
• Improves Thermal Management.
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Material Balance
Fz+ d z
, Tz+ d z
, vz+ d z
CH( ), C
H O( )z+d z
2z+d z
2
h
d z
Anode Channel
w
Fz , T
z , v
z, C
H (z),C
H O
(z)2 2
,F̂OHH CC
22
ˆ,ˆ,T̂
Control Volume
Side Feed Variables
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Isothermal Model
22
2
22
2
ˆ)(
ˆ)(
HOHs
OH
HHs
H
s
rCfdV
FCd
rCfdV
FCd
fdV
dF
General Model:
channel. cell fuel the in rate flow Volumetric
feed.d distribute the in species of ionConcentrat
volumereactor per flowfeed d Distribute
:
:ˆ
).sec(: 313
F
iC
mmf
i
s
)()(
ln)()(
2
2
2
2
2
ii
H
OH
H
H
ljGHn
jQ
nhrj
C
CTTr
F
F
Rate Equations:
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Achieving Uniform Heat Generation
OH
H
H
H
ii
C
CTTr
nhrj
ljGHn
jQ
2
2
2
2
ln)()(
)()( 2
F
F
QC
C
OH
H Constant Constant : HSR
2
2
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Isothermal Design of
Distributed Feed Flow Rates
Define:
Set
This is achieved if
sp )(
)()(
2
2
zC
zCz
OH
H
Constant )ln( 02
spHrdz
d
)ˆˆ(
)]ln()[1(
22
*
spOHH
spsp
ssCC
ff
sp )0(
and = the desired HSR
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Energy Model
)(
)ˆ(ˆˆ)(
)()(0
cschc
ccc
aaaasaha
aa
asahcsch
TTwhddz
dTCpCF
TTCpCFTTwhddz
dTCpFC
TThdTThdQw
Interconnect
Ta(z)
Tc(z)
ha
Q(z), Ts(z)
hc
d z
Anode
Cathode
Electrolyte
Adiabatic Wall
Fuel
z
Air
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Hydrogen to Steam Ratio
Conventional vs. Side Feed
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Electrolyte Temperature
Conventional vs. Side Feed
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Continuous vs. Discrete
Fuel Injection
Exhaust
Feed L1
L2
L3
L4
F1
F2
F3
F4
F5
A
Exhaust
Feed
Feed
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Hydrogen Fed Simulations
Hydrogen to Steam Ratio
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Hydrogen Fed Simulations
Solid Temperature Profile
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Hydrogen Fed Simulations
Fuel Temperature Profile
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Hydrogen Fed Simulations
Air Temperature Profile
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Variations in Air Side Flow Rate
Case 1:
Fuel to Air Flow Rate Ratio = 1:5000
Case 2:
Fuel to Air Flow Rate Ratio = 1:50
Case 3:
Fuel to Air Flow Rate Ratio = 1:10
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Impact of Reducing Air Flow Rate
Fuel to Air Ratio 1:5000 Fuel to Air Ratio 1:50
Solid Temperature
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Further Reduction in Air Flow Rate
Fuel to Air Ratio 1:50 Fuel to Air Ratio 1:10
Solid Temperature
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Impact of Reducing Air Flow Rate
Air Gas Temperature
Fuel to Air Ratio 1:5000 Fuel to Air Ratio 1:50
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Impact of Injection Point Location
Exhaust
Feed L1
L2
L3
L4
F1
F2
F3
F4
F5
A
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Impact of Injection Point Location
Solid Temperature at Fuel to Air Ratio of 1:5000
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Impact of Injection Point Location
Solid Temperature at Fuel to Air Ratio of 1:10
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Full Energy Model
)(
)ˆ(ˆˆ)(
)()(2
2
cschc
ccc
aaaasaha
aa
asahcschs
s
TTwhddz
dTCpCF
TTCpCFTTwhddz
dTCpFC
TThdTThdQwdz
Tdak
Interconnect
Ta(z)
Tc(z)
ha
Q(z), Ts(z)
hc
d z
Anode
Cathode
Electrolyte
Adiabatic Wall
Fuel
z
Air
Solid Temperature
Boundary Conditions:
Zero Heat Flux at z = o and z = L
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Impact of Heat Conduction Term
Solid Temperature at Fuel to Air Ratio of 1:5000
Without Conduction With Conduction
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Impact of Heat Conduction Term
Solid Temperature at Fuel to Air Ratio of 1:10
Without Conduction With Conduction
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Fuel Utilization in the
Hydrogen Fed Case
inH
outHinH
C
CCU
,
,,
2
22
Changes in utilization achieved by variations in fuel feed flow rate
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Summary of the Hydrogen Fed Case
• Continuous distributed feed will mitigated
temperature non-uniformity.
• Discrete injection and air side convection
will reduce uniformity.
• Utilization also impacted.
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Internal Reforming SOFC
• Heat and steam produced not used by reforming.
• Pre-heating steam is expensive.
• Steam in the feed lowers hydrogen utilization (reaction rate is a function of hydrogen to steam ratio).
ElectrochemicalSection
ReformingSection
Pre-Heater
222
224 3
COHOHCO
COHOHCH
OHOH 22
Methane
Steam
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Methane Fed Design Equations
22
2
24
2242
2
2242
2
44
4
4
ˆ)(
ˆ)(
ˆ)(
3ˆ)(
ˆ)(
2
COCOs
CO
COCHCOsCO
HCOCHOHs
OH
HCOCHHs
H
CHCHs
CH
CHs
rCfdV
FCd
rrCfdV
FCd
rrrCfdV
FCd
rrrCfdV
FCd
rCfdV
FCd
rC
fdV
dF
General Model:
)(
)(
ln )()(
2
,
2
2
22
22
44
2
2
2
iiHii
H
eq
COH
COOHfshiftCO
CHrefCH
OH
H
H
ljrSTrHQ
nhrj
K
CCCCkr
Ckr
C
CTTr
F
Rate Equations:
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Carbon Deposition
OH
CHCO
C
CCCMMSR
OHCHCO
OHCHCO
COCCO
HCCH
2
4
222
22
2
24
22
2
2
CMMSR is a suggested measure for the risk of carbon deposition under SOFC operating conditions.
If CMMSR > 1: Carbon deposition risk
CMMSR < 1: No risk of carbon deposition
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Methane Fed Design Scheme
Again define:
And set
This is achieved if
Constant )ln(02
spHrdz
d
)ˆˆ)(1()ˆˆ)((
)432()]ln()[1)((
222
*
4
2
*
spCOCOeqspspOHHeqsp
CHeqspeqspspspspeqsp
sCCKCCK
rKKKf
sp )0(
sp )(
)()(
2
2
zC
zCz
OH
H and = the desired HSR
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Internal Reforming
Simulation Scenarios
Fuel to air flow rate ratio = 1:100
Inlet steam to carbon ratio (SCR)
Case 1: Conventional stack, inlet SCR = 2:1
Case 2: Conventional stack, inlet SCR = 1:1
Case 3: Distributed feed design, inlet SCR = 1:2
Case 4: Discrete injection, inlet SCR = 1:2
inCHinOH CC ,, 42:
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Non-Isothermal Simulation of the
Internal Reforming Case
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Non-Isothermal Simulation of the
Internal Reforming Case
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Impact of Fuel Flow Rate
Fuel LHV Rate 3.28 J/sec Fuel LHV Rate 4.1 J/sec
Solid Temperature at Fuel to Air Ratio of 1:100
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Impact of Fuel Flow Rate
Fuel LHV Rate 3.28 J/sec Fuel LHV Rate 4.1 J/sec
CMMSR at Fuel to Air Ratio of 1:100
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Impact of Air Flow Rate
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Utilization in the
Internal Reforming Case
inHout
inCHout
outHout
outCHout
CFCF
CFCFU
24
24
4
41
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Measures of Efficiency
StackFuel Feed
Power
Ko1195
(a)
Stack
Fuel FeedPower
Steam Feed
preH
Ko298
Ko1195
(b)
Stack
Power
Fuel
Exhaust
Burner
Fuel Feed
Steam Feed
Ko298
Ko1195
Ko373netH
(c)
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Conventional Efficiency
LHV
Pe1inHout
inCHout
outHout
outCHout
CFCF
CFCFU
24
24
4
41
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Modified Stack Efficiency
pre
e
HLHV
P
2
LHV
Pe1
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System Efficiency
pre
e
HLHV
P
2
LHV
HHP preposte )(45.03
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Summary of Internal Reforming Case
• Greater uniformity in temperature is
achieved.
• Less steam is required for CO protection.
• Utilization and efficiency improved.
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Two Dimensional Analysis
Air Channel
Fuel Channel
Interconnect Rib
y
xz
Cathode
Anode
Electrolyte
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2-D Distributed Feed Design
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2-D Distributed Feed Design
Side FeedChannels
z1 z
2z
3z
4z
5
Active Area WallInactive Area
zx
Section of a stack layer
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Sizing of the By-Pass Streams
3,
2,,
,
*
8
ˆ
ni
niniini
isi
A
pFzP
LAfF
Exhaust
Feed L1
L2
L3
L4
F1
F2
F3
F4
F5
A
Hagen-Poiseuille Equation:
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Isothermal Velocity Profile for
Hydrogen Fed DFSOFC Stack
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Isothermal Concentration Profile
Hydrogen Fed DFSOFC
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Mixing Issues
0.08 0.09 0.1
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Length (m)
Wid
th (
m)
Surface: Concentraion Arrow: [x velocity (u),y velocity (v)]
5
5.5
6
6.5
7
7.5
8
8.5
9Max: 9
Min: 5
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Alternative Design
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Isothermal Velocity Profile for
Hydrogen Fed DFSOFC Stack
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Isothermal Concentration Profile for
Hydrogen Fed DFSOFC Stack
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Mixing Issues
Concentration peaks at injection points could
cause high stress or carbon deposition regions.
Side FeedChannels
Hot Active Area
Wall
Cold Inactive Area
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Summary
• Distributed feed design successfully mitigated
temperature non-uniformity.
• Utilization and efficiency was greatly improved
in the internal reforming case.
• 2-D simulations indicate that static mixers are
required to distribute fuel radially.
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Acknowledgement
• Kuwait Institute for Scientific Research.
• Armour College of Engineering, IIT.
• Dr. Said Al-Hallaj and Dr. J. Robert Selman.
• Ali Zenfour, Nawwaf Al-Oraior
• Process System Engineering Laboratory
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Power Load Transition Dynamics
How does the stack get from one operating point to
another?
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Sensitivity Analysis
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
3.50E-06
4.00E-06
800 900 1000 1100 1200
Temperature (K)
Reacti
on
Rate
(m
ol/
cm
2)
HSR = 0.1
HSR = 1
HSR = 10
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