integrated micropower generatorprogram review, october 18, 2002 single-chamber fuel cell models d....
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Integrated MicroPower Generator Program Review, October 18, 2002
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
• 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)
Seconds on a laptop PC
Minutes on a linux workstation
Minutes to hours
Computational expense
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
• No consideration of gas flow
• Approximate equilibrium treatment of hydrocarbon oxidation
• Includes diffusion through electrodes, activation polarizations, ohmic losses
• Can compute current-voltage curves
• Written in a simple scripting language (Python)
• Uses the Cantera software package to evaluate thermodynamic and transport properties, and compute chemical equilibrium (www.cantera.org)
• Good for semi-quantitative parametric studies
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
– Compositions can be set equal (single-chamber) or each independently specified (dual-chamber)
Uniform cathode-side gas
Uniform anode-side gas
Porous Cathode
Porous Anode
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
partially-oxidized gas mixture
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
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.2 0.4 0.6 0.8 1
Equilibrium Fraction Feq
Mo
le F
ract
ion
O2
H2CO2
C3H8
CO
H2O
CH4
600 C
Input: 1:3:12 C3H8/O2/He
Inlet gas
equilibrium gas
Feq1 - Feq
Integrated MicroPower Generator Program Review, October 18, 2002
Transport through electrodes
• Gas composition at electrode/electrolyte interface determined by diffusion through porous electrode
• Effective diffusion coefficients account for pore size, porosity, and tortuosity of electrode microstructure
• Concentrations at electrode/electrolyte interface used to calculate Nernst potential
reactant
product
electrode
Assumed uniform gas composition
concentration gradients in electrode drive diffusion
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
Range considered
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
1000/T (K-1)
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Lo
g( )
[-1cm
-1]
-4
-3
-2
-1
0
400°C500°C600°C700°C800°C975°C
Bi2O3
[B.C.H. Steele, Mat. Sci. and Eng., B13 (1992) 79-87][A.M. Azad, S.Larose and S.A. Akbar, J. Mat. Sci., 29 (1994) 4135-51]
Value for GDC used
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
Simulation of Test Results with Ni-SDCSDCSSC-Pt-SDC at 600 C
Integrated MicroPower Generator Program Review, October 18, 2002
Test results can be accounted for with physically-reasonable parameters
• Experimental Ni-SDCSDCSSC-Pt-SDC results at 600 C best fit by– I0,c = 70 mA/cm2
– 80% electrode selectivity– 50% conversion to equilibrium products
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200 250
Current Density (mA/cm2)
Vo
lta
ge
0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250
Current Density (mA/cm2)
Po
wer
Den
sity
(m
W/c
m2)
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
• For fuel-rich input mixtures, equilibrium composition contains significant CO and H2, in addition to CO2 and H2O
• Therefore, non-electrochemical oxidation of CO and H2 not likely to be a problem as long as a fuel-rich mixture is used 0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250
Current Density (mA/cm2)
Po
wer
Den
sity
(m
W/c
m2)
60%10%
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
0
20
40
60
80
100
120
140
160
0 50 100 150 200 250 300
Current Density (mA/cm2)
Po
wer
Den
sity
(m
W/c
m2)
Dual
Single
Integrated MicroPower Generator Program Review, October 18, 2002
Catalyst selectivity effects
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
Catalyst Selectivity Factor
OC
V
0
20
40
60
80
100
120
140
0 0.2 0.4 0.6 0.8 1
Catalyst Selectivity Factor
Max
Po
wer
Den
sity
(m
W/c
m2)
More selective Less selective
Catalysts must have reasonable selectivity for electrochemical reactions in order for SCFC to function
Integrated MicroPower Generator Program Review, October 18, 2002
SCFC Loss Mechanisms
• Dominated by losses due to– Low cathode activity– Incomplete cathode and anode selectivity
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100
Current Density {mA/cm 2}
Vo
ltag
e
Load Crossover Cathode Activation
Concentration Anode Activation Ohmic
Model 2: Microchannel SCFC Simulations
Integrated MicroPower Generator Program Review, October 18, 2002
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
CathodeAnode
Non-catalytic partitionPremixedFuel / air mixture
Cathode-side flow channel
Anode-side flow channel
Integrated MicroPower Generator Program Review, October 18, 2002
Mathematical Model
• Species equations finite-differenced 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 m, length = 10 mm• 200 m anode, 50 m cathode• Electrode porosity 0.4, pore size 0.1 m • 15 m 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
• Gas must diffuse through porous electrodes to reach electrochemically-active triple-phase boundary
• 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
reaction
reac
tan
ts
pro
du
cts
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 anode-side 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
X (mm)
Y(m
m)
2 4 6 8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Porous anode
Porous cathode
This velocity profile is imposed, based on known solution for viscous fully-developed flow
Integrated MicroPower Generator Program Review, October 18, 2002
Species Distributions at Max Power
flow
Anode on left
Cathode on right
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
Predicted Performance at 600 C
00.10.20.30.40.50.60.70.80.9
1
0 100 200 300 400
Current Density (mA/cm2)
Vo
lta
ge
• Predicted OCV = 0.9 V, peak power density = 85 mW/cm2
• Easily meets target SCFC performance of 50 – 100 mW/cm2.
0
10
20
30
40
50
60
70
80
90
0 100 200 300 400
Currrent Density (mA/cm2)
Po
we
r D
en
sit
y (
mW
/cm
2)
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 physically-reasonable 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.