Modeling & Simulation of Solid Oxide Fuel Cell Using COMSOL MULTIPHYSICS ®

Yi-Xiang SHI(史翊翔)Supervisor : Prof. Ning-Sheng CAI(蔡宁生)Department of Thermal EngineeringTsinghua University,Beijing, China

2006-12

Presented at the COMSOL Users Conferences 2006 Shanghai & Beijing

Why Solid Oxide Fuel Cell?

Extremely high efficiency ( Generation alone: 50-60%

SOFC/GT hybrid:60-75%Cogeneration : 80-90%)

High fuel flexibility (Hydrogen, coal syngas, biogas,various

hydrocarbon fuels, et al)

Low emissions without additional cleanupunit & secondary pollutants (near-zero SOx

,NOx, particle, be promising in CO2 capture )

Appropriate in both central & distributed power plant

From http://www.siemens.com

Why Modeling and Simulation?

• To understand the complex coupling transport and reaction processes

• To do parameter studies after comprehensive validation• Porous electrode microstructure• Operating conditions (Temperature, Pressure,Gas composition,…)

• To substitute some expensive, time-consuming, labor-intensive experiments• Detailed mechanistic model may lead to significant design

improvement

• To provide the fundamentals of SOFC-based hybrid system R&D

Mechanistic modeling methodology

Deb

ug&

Sen

sitiv

ity a

naly

sis

Mul

tidim

ensi

onal

th

eore

tical

moe

del

Anode-Supported SOFC button cell modeling

O2-

e-

H2 H2O

O2

O2-

e-

TPB

Anode active interlayer

Electrolyte layer

Cathode layer

Anode support layer

electronic conductor electronic conductor

Contact angle

ionic conductorionic conductor

Three phase boundary

• Button cells are widely used in SOFC experimental studies for its simple experiment setup and operation

• For detailed mechanistic model validation, button cell test data:• Easier to achieve, have better reliability& repeatability

Photograph and SEM micrograph of button cell

Assumptions:Steady state conditions; Iso-thermal; Ideal gasUniform active surface area Pressure driven flow neglectedTwo conducting phases: continuous and homogeneous

an-spΩ

elecΩcaΩca/ac∂Ω

ca/elec∂Ω

elec/an_act∂Ω

an-sp/fc∂Ω

symmetry∂Ωelec/ac∂Ω

an-actΩ

an-act/an-sp∂Ω

Calculation domain--Simplified to 2-D for

axis symmetry

Modeling Methodology

Ionic/electronicCharge balance

(Ohm’s law,B-V equation)

Open circuit voltage(Nernst equation, leak overpotential)

Mass balance(Dusty-gas model)

Operatingconditions

Cell VoltageCell Voltage

Parameters distributions;Polarization curves

Parameters distributions;Polarization curves

Electrochemical Reactions Kinetics

MechanisticMechanisticmodelmodel

Meshing in COMSOL MULTIPHISICS®

Conversional T-mesh

Structured Quad Mesh Generation Mesh Density Control Based on Mapping Approach X = (1+tanh(a*theta))/2

Model validation in the base case

H2 and H2O concentration distribution at anode in the base case

Un-uniformity at the anode due to the electrochemical reactions and asymmetric button-cell electrode

Reaction zone distribution

AnodeCathode

Modeling results by changing tortuosity

The model could not predict the experimental data well until the tortuosity was adjusted to 14

Model Calibration in the base case

Experimental tortuosity ：Usually 2~10For conventional SOFC thick anode :2~5 (Williford et al,2003)

(Anil V. Virkar, 2003 )(Anil V. Virkar, 2003 )

•Totuosity in the model have to be tuned to 17

Modifications to hydrogen concentration at the TPB

electronic conducterelectronic conducter

ionic conducterionic conducter

Ni YSZTPB

Inter Inter

H2O,CO2

Surface Diffusion

AdsorptionAdsorption

Fuel(H2,CO,etc)Products(H2O,CO2,etc)

O2-

TPB

H2,CO,etc

Surface

Diff

usion

TPBiC

TPB,ViC

• Figure out the source of large diffusion resistance near the TPB at high fuel utilization or large current density

2 1

Molecular diffusionKnudsen diffusion, etc

Competitive adsorptionSurface diffusion

Electric analogue circuit of H2 diffusion

Model Validation

Operating Conditions: 800℃ 101,325 pa; Oxidant:0.21 O2, 0.79 N2

0 20000 40000 60000 80000

0.2

0.4

0.6

0.8

1.0

H2,experimental85% H2+15% H2O,experimental50% H2+50% H2O,experimental35% H2+65% H2O,experimental20% H2+80% H2O,experimental Baseline for parameter estimation Calculated

Volta

ge/V

Current Density/(A/m2)

Model agreed well with published experimental data without any other calibrations after the parameter estimation according to the baseline (Anil V. Virkar, 2003 )

Some of the modeling results

0.0 0.1 0.2 0.3 0.4 1.2 1.3 1.4

0

4000

8000

12000

16000

Ionic,85% H2,15% H2O Electronic, fuel:85% H2,15% H2O Ionic,fuel:20% H2,80% H2O Electronic,fuel:20% H2,80% H2O

Cur

rent

den

sity

/(Am

-2)

x/mm

elec elec j( )eV J Qσ−∇⋅ ∇ − =r ( )i i ij u Rρω∇ ⋅ + =

rr r

( )k p Fρη

∇⋅ − ∇ =r

T( ( ) ) ( )u u u u p Fη ρ−∇⋅ ∇ + ∇ + ⋅∇ +∇ =rr r r r

p( )k T C Tu Qρ∇⋅ − ∇ + =r

Generalized Unit Cell Mechanistic Model

Coupling

Model Geometry

Air channel

Fuel channel

Anode

Cathode

Electrolyte

Interconnect

Interconnect

Tubular SOFC - Axial Tubular SOFC- Cross

Model Validation

1002003004005006000.4

0.5

0.6

0.7

0.8 Axial direction modeling results Experimental data(Siemens-Westinghouse)

Cel

l V

olta

ge/V

Current Density / (mA/cm2)Model validation in axial direction Model validation in cross direction

1002003004005006000.4

0.5

0.6

0.7

0.8 Cross direction modeling results Experimental data(Siemense-Westinghouse)

Cel

l Vol

tage

/V

Current density/(mA/cm2)

Operation Conditions: 1000℃ 101,325 pa; Fuel:97% H2, 3% H2O Oxidant:0.21 O2, 0.79 N2

Experimental data from：J.H. Hirschenhofer, D.B. Stauffer, R.R. Engleman, et al. Fuel Cell Hand Book (Seventh Edition), West Virginia: EG&G Technical Services, Inc. 2004. 7-31~7-44

Some of the Modeling Results

“Hot spot”area

3D planar SOFC modelingParametersAnode thickness 800um

Cathode thickness 60um

Electrolyte thickness 10um

Interconnect thickness 4 mm

Interconnect width 4 mm

Channel height 4 mm

Meshing

Extrude

EIS simulation using SOFC mechanistic transient model

Polarization is only a gross behavior of all the microcosmic processesEIS (Electrochemical Impedance Spectroscopy) is a kind of transient characterization technology, contain much more information about reaction and transport mechanism than polarization curves.

Most of the EIS are interpreted in Equivalent circuit analog

Physical& Chemicalprocesses

Physical& Chemicalprocesses

Equivalent Circuit Analog

Equivalent Circuit Analog

EIS plotEIS plot

Mechanistic model based on conservation equationsMechanistic model based on conservation equations

Much more uncertainties (form of equivalent circuit analog)

Basic ideas

Small sinusoidal perturbation in potential

Resultant current response

Magnitude Z0Phase shift φ

Real and Imaginary Component

Nyquist plotBode plot

SOFC transient Model

SOFC transient Model

Phase Shift(φ)

Normalized harmonic voltage signal imposed on button cell

Normalized observed current density signal Computer simulation is

almost the same with true experimental tests

Computer simulation is almost the same with true experimental tests

Summary

• Computer simulation in the SOFC R&D could provide insights for:• The detailed transport and reaction processes

• Improving cell design and electrode microstructure

• Commercial FEA software- Comsol Multiphysicscould be used for:• Single button cell modeling

• 2D or 3D Unit Cell modeling

• EIS modeling

Thank you ! Thank you !