Theory Based Process Modeling for Evaluation of Fuel Cells in Advanced Energy Systems

Theory Based Process Modeling for Evaluation of Fuel Cells in Advanced Energy Systems

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Author: Rodney A. Geisbrecht (Fellow) | Visits: 1909 | Page Views: 1965
Domain:  Green Tech Category: Battery & Fuel Cell Subcategory: Process Modeling 
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Contents:
Theory Based Process Modeling for Evaluation of Fuel Cells in Advanced Energy Systems

Rodney A. Geisbrecht National Energy Technology Laboratory

AIChE 2002 Spring National Meeting New Orleans, LA. March 11 - 15, 2002

Fuel Cell/Heat Engine Cycles in Hybrid Systems
Fuel Cell Cycle (fuel side) Topping Hybrids/V21 Programs SW MTI HW MCP FCE Other Concepts SOFC-PEMFC POXHE-SOFC SOFC p-coflow-iir PEMFC p-coflow SOFC p-crossflow GT/ICE SOFC t-coflow-iir SOFC p-crossflow SOFC p-coflow MCFC p-coflow MCFC p-crossflow-dir GT GT GT GT GT Bottoming Heat Engine Firing Direct Indirect

SOFC-PEMFC Hybrid Sequestering Version

Natural Gas Steam H2

FPR

SOFC

LTS

SCO

PEFC

BC

HRU

Air

Water

O2

Air

FPR - fuel prep reactors (pre-reform/sulfur sorbent) SOFC - solid oxide fuel cell LTS - low temperature shifter SCO - selective catalytic oxidizer PEFC - polymeric electrolyte fuel cell BC - booster compressor Non-sequestering Version Exhibit 3 HRU - hydrogen recovery unit

Compressed Carbon Dioxide
5

Direct Fired Reforming Heat Engine-Bottoming Fuel Cell Hybrid

Fuel

POX
Rich Mode

Air

anode

Lean Mode

HE

HX COX

FC cathode

Motivation for Engine Based POX Reforming
0.5 0.4 Yield 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Oxygenation (Fuel Conversion) Equivalent
carbon net energy

Direct POX Reforming of CH4 with Dry Air to Equilibrium at 1400 F and 10 ATM.

Basic Aspects of Fuel Cell Process Modeling

� Heat and Material Balances � System Integration � Current Density Distribution � Fuel Cell Sizing

Current Density Distribution for Coflow with Constant Resistivity

im/ir = {(



Xr

((E (( r � Ec) / (E - Ec)) dX ) / Xr} )

-1

where: im average current density ir reference current density = (Er � Ec) /

Typical Nernst Potential Curve for SOFC
1.2 1 En 0.8 0.6 0 0.2 0.4 X
1000C, 1 ATM, 1.5 Air:Fuel Equivalence Ratio, 50% Dry H2

0.6

0.8

1

Typical Current Density Distribution Index
10 8 6 i m /i r 4 2 0 0.00

0.05

0.10 Er - Ec, volts

0.15

0.20

Fuel Cell Process Model Rating Stage Sequence � splitters, mixers, heaters, restricted equilibrium reactors � executed repeatedly during flowsheet convergence � uses cell voltage or voltage efficiency as an input Design Stage Sequence � same models and physical properties packages � executed once - after flowsheet convergence � uses a Fortran Tear Variable for discretized calculations

Important Features � Reactant Manifolding � coflow, crossflow, counterflow � Reaction Thermodynamics and Kinetics � reforming, shifting, carbon formation � Temperature Effects � ohmic resistances, electrode activation � Gas Diffusion Resistances � anode, cathode

Rating Stage Sequence SOFC

F W
O2

Reactor Q-split QL

Reactor Q-Split Design Spec

Fs

A

Split

Heater

Heater

Av

Design Spec

- isentropic - isothermal

Design Stage Sequence

Initialize Stream Arrays Element Index I

Select Feed Streams for Index I
F, A

Design Spec dA X

Set Current dA*(En-Ec)/ for Index I Tear Variable Index I Update Stream Arrays

split

Rating Model
Fs, Av

Index Control I+1 or I Compute X

Predicted V-I Curve with High Nernst Potential Losses
0.9 0.8 Ec 0.7 0.6 0.5 0.00

0.10 Im *R

0.20

0.30

Co-flow SOFC @ 1000C/1ATM/Dry H2/2.5 AFR/95% Fuel Conversion.

Model vs SOFC Benchmark
0.9 0.8 E c (V) 0.7 0.6 0.5 0.4 0 100 200 300 im (mA/cm )
Model FCHB 2

400

500

600

SOFC Performance per FCHB, Fig. 5-11 at 1000C, 85% Fuel Utilization and 25% Air Utilization. Fuel (67% H2/22% CO/11% H2O).

Model vs PEMFC Benchmark

1.5 E c (V) 1 0.5 0 0 200 400 600 800 1000 im (mA/cm2)
Model Correlation Mark IV

PEMFC Performance per Mark IV (Amphlett et al., 1995) for H2/ and Air at 70 C and 3 Atm.

SOFC Model Parameters
PST (Kinoshita, 1988)
cathode thickness, cm anode thickness, cm electrolyte thickness, cm interconnect thickness, cm tube diameter, cm interconnect chord length, cm 0.07 0.01 0.04 0.04 1.27 0.60

AES (Singhal, 1998)
0.22 0.01 0.004 0.0085 2.2 0.6 (estimated)

Derived from Kinoshita, 1988
cathode, ohm-cm interconnect, ohm-cm anode, ohm-cm electrolyte, ohm-cm Exp(-5.48+1210/(T+273.)) Exp(-4.51+4770/(T+273.)) Exp(-6.03-1100/(T+273.)) Exp(-6.01+10510/(T+273.))

Reference @ 1000C (FCHB)
0.013 0.5 0.001 10

Computed Network Equivalent Cell Resistance @ 1000C
ohm-cm^2 0.92 0.6

PEMFC Model Parameters

Resistivities
apparent cell resistivity, ohm-cm^2 ionic resistivity, ohm-cm^2 0.35 0.19 --------apparent electronic resistivity, ohm-cm^2 0.16 derived from Fig. 6-3, FCHB for 7 mil Nafion 117 7 mil Nafion at .09 S/cm (Jacoby, 1999)

Activation
Tafel slope, volts/decade apparent exchange current density, mA/cm^2 0.07 0.04 Amphlett et al.,1995 (.0037 @ .15 mg/cm^2 Pt/C, Fischer and Wendt, 1996)

Diffusion
limiting current density, mA/cm^2 1100 estimated/arbitrary cutoff point

Hypothetical Crossflow MCFC with DIR to Equilibrium

2
1600

1.5
1400

i/im

1
F

1200

0.5 0 1 2 3 4 1 5 3

5 Fuel Out

1000 800 600 1 2 Air In 3 4 1 5 3 Fue l O ut 5

Air In

5 4 3 Fuel Out

5

4

3 Fue l O ut

2
2

1 1 2 3 Air In 4 5
1 2 3 Air In 4 5 1

current density

temperature

Hypothetical Crossflow SOFC without DIR

2 1.5 i/im 1 0.5 0 1 2 3 4 5 Air In 1 5 Fuel Out

1.5 1 i/i m 0.5 0 1 2 3 4 5 Air In 1 5 Fuel O ut

5 4 3 Fuel Out 2 1 1 2 3 Air In 4 5 1 2 3 Air In 4 5

5 4 3 Fuel Out 2 1

high AFR

low AFR

Assuming AFR is Independently Variable

mA/cm 2

150 100 50 1 2 3 AFR 4 5 6

Acknowledgements

U.S. Department of Energy National Energy Technology Laboratory Office of Systems and Policy Support

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