Single-Chamber Fuel Cell Models
D. G. Goodwin, Caltech
• Develop validated physics-based
models of SCFC operation
• Use models along with test results
to develop understanding of factors
determining performance
• Use to aid in design optimization
Integrated MicroPower Generator
Program Review, October 18, 2002
Multiple models
Computational
expense
Seconds on a
laptop PC
Minutes on a
linux
workstation
Minutes
to hours
• Model 1: a simple model for qualitative
parametric studies
– Allows rapid exploration of the effects of
various parameters on performance
• Model 2: Solves 2D channel flow assuming
fully developed flow. Computes
– Species concentration profiles
– Current density profiles
– Power output vs. load
• Model 3: Solves 2D reacting channel flow
accurately (in development, Yong Hao)
Integrated MicroPower Generator
Program Review, October 18, 2002
Model 1: a “zero-dimensional” fuel cell model
• Can be used to model
single- or dual-chamber
designs
• Written in a simple scripting
language (Python)
• Approximate equilibrium
treatment of hydrocarbon
oxidation
• Uses the Cantera software
package to evaluate
thermodynamic and
transport properties, and
compute chemical
equilibrium
(www.cantera.org)
• Includes diffusion through
electrodes, activation
polarizations, ohmic losses
• Good for semi-quantitative
parametric studies
• No consideration of gas flow
• Can compute currentvoltage curves
Integrated MicroPower Generator
Program Review, October 18, 2002
Idealized Geometry
• Each side exposed to uniform gas
with specified composition
– No depletion in gas
– Corresponds to limit of fast
transport
Uniform cathode-side gas
Porous Cathode
Porous Anode
Uniform anode-side gas
– Compositions can be set equal
(single-chamber) or each
independently specified (dualchamber)
Integrated MicroPower Generator
Program Review, October 18, 2002
Electrochemical Reactions
• Anode reactions
– H2 + O2- = H2O
– CO + ½ O2- = CO2
• Cathode reaction
– O2 = 2O2-
• Catalyst selectivity
– Reactions allowed to occur at opposite electrode with
relative rate 0 < Fc < 1
– Fc > 0 lowers OCV
– At Fc = 0, OCV = 0
Integrated MicroPower Generator
Program Review, October 18, 2002
Gas Composition
• Approximate treatment of partial oxidation
• Assume gas is a mixture of the input gas
composition + equilibrium composition
• No selectivity assumed – CO, CO2, H2, and H2O
all present
1 - Feq
equilibrium
gas
Feq
Input: 1:3:12 C3H8/O2/He
0.2
0.18
600 C
0.16
Mole Fraction
Inlet
gas
partially-oxidized
gas mixture
O2
0.14
0.12
H2
0.1
CO2
0.08
H2O
C3H8
0.06
CO
0.04
0.02
CH4
0
0
0.2
0.4
0.6
0.8
1
Equilibrium Fraction F eq
Integrated MicroPower Generator
Program Review, October 18, 2002
Transport through electrodes
• Gas composition at
electrode/electrolyte
interface determined
by diffusion through
porous electrode
concentration gradients
in electrode drive
diffusion
product
Assumed uniform
gas composition
reactant
electrode
• Effective diffusion
coefficients account for
pore size, porosity, and
tortuosity of electrode
microstructure
• Concentrations at
electrode/electrolyte
interface used to
calculate Nernst
potential
Integrated MicroPower Generator
Program Review, October 18, 2002
Electrode Kinetics
Integrated MicroPower Generator
Program Review, October 18, 2002
Cathode Activation Polarization
• Represents largest
loss
• Dependence on
oxygen partial
pressure assumed
first-order
Integrated MicroPower Generator
Program Review, October 18, 2002
Anode Activation Polarization
• Assumed not to be rate-limiting
• Anode exchange current density set to a large
multiple of cathode exchange current density
(100 – 1000)
Integrated MicroPower Generator
Program Review, October 18, 2002
Electrolyte Ohmic Loss
Value for GDC used
975°C
800°C 700°C
0
-1
-1
Log() [ cm ]
-2
(Zr
0.2 O
1. 9
O
(Zr
.9 (Y
2O
3 )0
.1
2)
0.8
2O
3 )0
.75 (
Y O
2
3 )0
(Zr
7 (C
-3
(Zr
aO
)
0. 1
3
2 Sm
O
2
7)
.25
O )
2 0
. 9 (S
c2 O
3 )0
.1
(Zr
2 Gd
2O )
7
-4
0.8
400°C
(Bi
2 )0
O
500°C
Bi2O3
Ce
0.8 Gd
-1
600°C
0.9
1.0
1.1
1.2
1.3
1.4
1.5
-1
1000/T (K )
[A.M. Azad, S.Larose and S.A. Akbar, J. Mat. Sci., 29 (1994) 4135-51]
[B.C.H. Steele, Mat. Sci. and Eng., B13 (1992) 79-87]
Integrated MicroPower Generator
Program Review, October 18, 2002
Current Density Computation
• Nernst potential calculated using concentrations
at electrode/electrolyte interfaces, and includes
effects of back reaction
• Given Eload, this equation is solved for the
current density
Integrated MicroPower Generator
Program Review, October 18, 2002
Simulation of Test Results with
Ni-SDCSDCSSC-Pt-SDC at 600 C
Test results can be accounted for with physicallyreasonable parameters
• Experimental Ni-SDCSDCSSC-Pt-SDC results at 600 C
best fit by
– I0,c = 70 mA/cm2
– 80% electrode selectivity
– 50% conversion to equilibrium products
0.9
90
0.8
80
Power Density (mW/cm2)
0.7
Voltage
0.6
0.5
0.4
0.3
0.2
70
60
50
40
30
20
10
0.1
0
0
0
50
100
150
Current Density (mA/cm2)
200
250
0
50
100
150
200
250
Current Density (mA/cm2)
Accurate modeling of transport limit requires more accurate
treatment of transport processes – see Model 2 results
Integrated MicroPower Generator
Program Review, October 18, 2002
Gas Composition Effects
• Increasing percent conversion to
equilibrium products moves the
transport limit to higher current
densities
90
80
• Therefore, non-electrochemical
oxidation of CO and H2 not likely to
be a problem as long as a fuel-rich
mixture is used
70
Power Density (mW/cm2)
• For fuel-rich input mixtures,
equilibrium composition contains
significant CO and H2, in addition to
CO2 and H2O
60
50
40
30
20
60%
10%
10
0
0
50
100
150
200
250
Current Density (m A/cm 2)
Integrated MicroPower Generator
Program Review, October 18, 2002
Single Chamber vs. Dual Chamber
• Dual chamber calculation sets cathode gas
composition to air, and eliminates the back reactions
at the electrodes
Power Density (mW/cm2)
160
140
120
Dual
100
80
60
40
Single
20
0
0
50
100
150
200
250
300
Current Density (mA/cm2)
Integrated MicroPower Generator
Program Review, October 18, 2002
Catalyst selectivity effects
Catalysts must have reasonable selectivity for electrochemical
reactions in order for SCFC to function
140
1
120
Max Power Density (mW/cm2)
1.2
OCV
0.8
0.6
0.4
0.2
100
80
60
40
20
0
0
0
0.2
0.4
0.8
0.6
1
Catalyst Selectivity Factor
More selective
0
0.2
0.4
0.6
0.8
1
Catalyst Selectivity Factor
Less selective
Integrated MicroPower Generator
Program Review, October 18, 2002
SCFC Loss Mechanisms
• Dominated by losses due to
– Low cathode activity
– Incomplete cathode and anode selectivity
Load
Crossover
Cathode Activation
Concentration
Anode Activation
Ohmic
0
40
80
1.2
1
Voltage
0.8
0.6
0.4
0.2
0
20
60
100
Current Density {m A/cm 2}
Integrated MicroPower Generator
Program Review, October 18, 2002
Model 2: Microchannel SCFC
Simulations
Model Overview
• Inputs
– Inlet gas composition, temperature, pressure
– Load potential
– Parameters characterizing kinetics, electrode transport,
geometry, etc.
• Outputs
– 2D spatial distributions of C3H8, CH4, CO, H2, CO2, and H2O
in channel
– Current density profile J(x)
• Assumes isothermal, isobaric conditions
• Includes an unsealed, non-catalytic plate (interconnect)
separating anode and cathode gas streams
Integrated MicroPower Generator
Program Review, October 18, 2002
Model Geometry
Electrolyte
Anode
Premixed
Fuel / air mixture
Cathode
Cathode-side flow channel
Non-catalytic partition
Anode-side flow channel
Integrated MicroPower Generator
Program Review, October 18, 2002
Mathematical Model
• Species equations finitedifferenced and
integrated in time to
steady state.
• Porous electrodes handled
by locally modifying
diffusion coefficients
• Species equations solved
simultaneously with
equation for current
density
Integrated MicroPower Generator
Program Review, October 18, 2002
Model Problem
•
•
•
•
•
•
•
Channel height = 700 mm, length = 10 mm
200 mm anode, 50 mm cathode
Electrode porosity 0.4, pore size 0.1 mm
15 mm GDC electrolyte
T = 600 C, P = 1 atm
Premixed 1:3 C3H8 / air
Partial oxidation rate at anode set to give
nearly complete consumption of propane
• Other parameters same as in zero-D model
Integrated MicroPower Generator
Program Review, October 18, 2002
Porous Electrode Transport
products
reactants
• Gas must diffuse through porous electrodes to
reach electrochemically-active triple-phase
boundary
reaction
• Process modeled with effective diffusion
coefficients for each species that interpolate
between Knudsen and ideal gas limits
• Effective diffusion coefficient close to the
Knudsen limit
Integrated MicroPower Generator
Program Review, October 18, 2002
Partial Oxidation
• Global partial oxidation reaction
C3H8 + 3/2 O2 => CO + 4H2
– Produces electrochemically-active
species
– assumed to occur throughout the
anode
– May occur on the cathode also
• Rate modeled as first-order in C3H8
and O2
• Magnitude set to lead to nearly
complete conversion in the anodeside exhaust
–
ample residence time for complete
conversion (50-100 ms vs. 1 ms)
– Degree of conversion can be tuned
experimentally by material choice,
and anode fabrication methods
Integrated MicroPower Generator
Program Review, October 18, 2002
Velocity Profile
1.4
1.3
This velocity profile is imposed, based on
known solution for viscous fully-developed
flow
1.2
1.1
1
Porous cathode
Y (mm)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Porous anode
0.1
2
4
6
8
10
X (mm)
Integrated MicroPower Generator
Program Review, October 18, 2002
Species Distributions at Max Power
Cathode on right
Anode on left
Integrated MicroPower Generator
Program Review, October 18, 2002
Current Density Distribution
• Movie shows steady-state J(x) for load
potentials ranging from zero to 0.9 V
Integrated MicroPower Generator
Program Review, October 18, 2002
Voltage
Predicted Performance at 600 C
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
• Predicted OCV = 0.9 V,
peak power density = 85
mW/cm2
0
100
200
300
400
Current Density (mA/cm2)
• Easily meets target SCFC
performance of 50 – 100
mW/cm2.
Power Density (mW/cm2)
90
80
70
60
50
40
30
20
10
0
0
100
200
300
400
Currrent Density (mA/cm2)
Integrated MicroPower Generator
Program Review, October 18, 2002
Conclusions
• Performance targets appear to be easily achievable
• Largest potential gains in performance:
– improved cathode catalytic activity
– improved electrode selectivity
• Separator plate may not be necessary
• As long as gas composition is fuel rich, non-electrochemical
oxidation of CO and H2 will not go to completion, and
therefore nonselective catalyst for partial oxidation is
acceptable.
Integrated MicroPower Generator
Program Review, October 18, 2002
Future Work
• Validation against all available test data –
single-chamber, dual-chamber, etc.
• Prediction of coking behavior
• Prediction of low-temperature performance
• Integration with Swiss Roll heat exchanger
model to predict operating temperature
Integrated MicroPower Generator
Program Review, October 18, 2002
Summary
• Two numerical models have been developed to predict
SCFC performance.
– A simple model useful for interpreting test data
– A channel flow model useful for predicting micropower
generator performance
•
Test results can be accounted for with physicallyreasonable kinetic parameters
• Using these parameters in the channel-flow model leads
to performance at 600 C that meets our targets
• Both models are suitable for use in design and
optimization studies, including system studies with the
Swiss Roll heat exchanger.
Integrated MicroPower Generator
Program Review, October 18, 2002