Integrated MicroPower GeneratorProgram Review, October 18, 2002 Single-Chamber Fuel Cell Models D....

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


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


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

http://www.cantera.org/


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


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


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


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


Electrode Kinetics


Cathode Activation Polarization

• Represents largest loss

• Dependence on oxygen partial pressure assumed first-order

Range considered


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)


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


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


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


Po

wer

Den

sity

(m

W/c

m2)

Accurate modeling of transport limit requires more accurate treatment of transport processes – see Model 2 results


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


Po

wer

Den

sity

(m

W/c

m2)

60%10%


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


Po

wer

Den

sity

(m

W/c

m2)

Dual

Single


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


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


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


Model Geometry

Electrolyte

CathodeAnode

Non-catalytic partitionPremixedFuel / air mixture

Cathode-side flow channel

Anode-side flow channel


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


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


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


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


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


Species Distributions at Max Power

flow

Anode on left

Cathode on right


Current Density Distribution

• Movie shows steady-state J(x) for load potentials ranging from zero to 0.9 V


Predicted Performance at 600 C

00.10.20.30.40.50.60.70.80.9

1

0 100 200 300 400


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)


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.


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


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.

Integrated MicroPower GeneratorProgram Review, October 18, 2002 Single-Chamber Fuel Cell Models D....

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