MATHEMATICAL MODELING OF A MOLTEN-CARBONATE FUEL CELL

USING MATHCAD

David Blekhman

Associate Professor

California State University, Los Angeles, CA, USA

Stephen T. McClain

Assistant Professor

Baylor UniversityWaco, TX, USA

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 2

Molten-Carbonate Fuel Cell Operation

H2

CO2

CO

N2

CO2

O2

CO2

Cat

hode

and

gas

dif

fusi

on la

yer

Ano

de a

nd g

as d

iffu

sion

laye

r

Mem

bran

e

Cat

hode

bip

olar

pla

te

Ano

de b

ipol

ar p

late

Single fuel cell assembly Fuel passage Oxidizer passage

Current from previous cell

Current to next cell CO3

=

2e-

H2O

2eCOOHCOH 2232

2eCO2COCO 23

32221 CO2eCOO

MCFC Operation

Reactions provide specific mole count

Very slow

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 3

Code Execution Block Diagram

ProjectEquilibrium Calculation

at Operating Temperature

Hydrogen is

Consumed in the Stack

No, n=n+1All Fuel is Consumed

Simple Calculation of

Oxidizer Composition

n times

YesNernst OCV Potential as Function of Utilization

Plots, Curves, etc.

H2 , C

H4 , C

O2 ,

CO

, N2 –

dry

+H

2 O

Ca

tho

de

Mix:

O2 , C

O2 , N

2

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 4

Project Description

anodecathode ,222,221

2 COOHCOOH

Project

Determine open cell voltage potential as reactants flow in a high-temperature fuel cell.

In a molten-carbonate fuel cell

5.1,

,

5.0

0

,22

,222lntotalo

totalf

COOH

COOHu

N

N

NN

NNN

nF

TREE

anode

cathode

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 5

Fuel Reforming/Equilibrium

COOH

COH

NN

NNK

2

22

1

222 COHCOOH1

K

CO3HCHOH 242

2

K

Steam-reforming reaction Water-gas shift reaction

Equilibrium constants, can be given or calculated

Three element conservation equations for H, O and C

Fuel Reforming

at inlet and through the fuel cell anode

23

2

2224242

21

NCOCOOHCHHCHOH

COH

NNNNNNNN

NNK

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 6

Fuel Reforming/Equilibrium

Fuel Reforming

at inlet and through the fuel cell anode

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 7

Fuel Reforming/Equilibrium

Fuel Reforming

at inlet and through the fuel cell anode

Conjugate Gradient

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 8

Fuel Choices

Fuel /Gas H2 H2O CO CO2 CH4 N2

Low-Btu 1, dry 71°C 0.213 0 0.193 0.104 0.011 0.479

Low-Btu 2, dry 60°C 0.402 0 0 0.399 0 0.199

Low-Btu 2, wet 60°C

0.336 0.164 0 0.333 0 0.166

Low-Btu 2, 650°C 0.2319 0.2673 0.0988 0.2344 0.0017 0.1668

Fuels and Oxidizers

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 9

Oxidizer Choices

1. 30% O2-60% CO2-10%N2

2. 30% O2-70% CO2

3. 13% O2-26% CO2-61%N2 --from air

Stoichiometry =0.5 (twice oxidizer)

Carbon dioxide =twice that of Oxygen

21.0

2

0,,0,,

0,,0,,

0,_0,,

22

22

22

OoxNox

OoxCOox

availHOox

NN

NN

NN

Fuels and Oxidizers

0,0,0,0, 4222 CHCOHavailableH NNNN

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 10

Fuel Flow Results

Utilization

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 11

Fuel / Oxidizer Utilization

0,_

,_0,_,

2

22

availH

iavailHavailHif N

NNu

0,,

,,0,,,

2

22

Oox

iOoxOoxiox N

NNu

Oxidizer

Fuel

Utilization

Fuel mixture composition as it flows through the fuel cell

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 12

Nernst Potential

Nernst Potential

Open circuit potential as a function of fuel utilization in the fuel cell

5.1,

,

5.0

0

,22

,222lntotalo

totalf

COOH

COOHu

N

N

NN

NNN

nF

TREE

anode

cathode

• Introduction

• Authors

• Project

• MCFC Operation

• Fuel Reforming

• Fuels and Oxidizers

• Utilization

• Nernst Potential

• Conclusions

David Blekhman, PhD 6th International Fuel Cell Science, Engineering and Technology Conference Page 13

Topics Reviewed by the Project

• Psychrometrics

• Ideal Gas Mixtures

• Reacting Systems

• Chemical Equilibrium

• Fuel CellsConclusions