Institut für Technische Thermodynamik Dr.

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Modeling Direct-Methanol-Fuel Cells:

taking a look behind experimental current-voltage characteristics*

Anette Siebke, Birgit Thoben and Werner Schnurnberger

1. Modeling or numerical fitting

2. Modular DMFC Model

3. Model limits and boundary conditions

4. Results and sensitivity

5. Reality check

* Fuel Cell Research Symposium: Modelling and Experimental Validation ETH Zürich, March 18-19,

2004

Institut für Technische Thermodynamik Dr.

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V = E - Vact - Vohm - Vconc

V = E - [ V0 + Va(1-e-c1i)] - [iRohm] - [i (c2 i/imax)c3]

V (T; pi,; i;)

Air 95 0C 50 0C

Oxygen 95 0C 50 0C

Institut für Technische Thermodynamik Dr.

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0

200

400

600

800

1000

1200

0 500 1000 1500

i (mA/cm2)

U (

mV

)

U0,9 SLPM H2

0,9 SLPM O2

0,9 SLPM H2

1,5 SLPM Luft

900 °C

SOFC Variation of Oxygen partial pressure (single cell test)

Institut für Technische Thermodynamik Dr.

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Phaseo

Impedance /

Frequency / Hz

0

20

40

60

80

10m

30m

100m

300m

1

3

10m 100m 1 10 100 1K 10K 100K

PEFC in situ analytical tools: Electrochemical Impedance Spectra (EIS)

EIS: Bode diagramm PEFC ( E-TEK Electrodes, Nafion 117), at 80°C, pH2=pO2=1bar, at different current densities / cell voltages

O E=1024 mV; i= 0 mA/cm2

E= 841 mV; i= 45 mA/cm2

E= 597 mV; i= 392 mA/cm2

+ E= 317 mV; i= 761 mA/cm2

Institut für Technische Thermodynamik Dr.

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0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 800

Current density /mAcm-2

Ov

erv

olt

ag

e /m

V Diffusion

Membrane

Anode

Cathode

Impedance measurements at PEFC

Institut für Technische Thermodynamik

Contribution of the individual overvoltages to the cell overvoltage (equivalent circuit with the porous electrode model) atdifferent current densities

Institut für Technische Thermodynamik Dr.

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Air

Air H2

Local Current Density

[mA/cm²] 800.0 -- 850.0 700.0 -- 750.0 650.0 -- 700.0 600.0 -- 650.0 550.0 -- 600.0 500.0 -- 550.0 450.0 -- 500.0 400.0 -- 450.0 350.0 -- 400.0 300.0 -- 350.0 250.0 -- 300.0 200.0 -- 250.0 100.0 -- 150.0 0.0 -- 50.0

Porous Flow Field80°C iav = 380 mA/cm2

Pressure 2 barabs

H2, air: rel. humidity 80% Air Stoichiometry =1,8

Institut für Technische Thermodynamik Dr.

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Overview over Modeling Activities in PEM Fuel Cells

•kinetics of the electrochemical reactions (methanol oxidation; Kauranen, Divisek)

•membrane mass transport (mainly Nafion: Meier, Eikerling)

•transport processes in reaction layers (PEFC cathode: Broka, Springer DMFC anode: Baxter, Nordlund)

•flow field in gas distributor and GDL (mainly 1+2D models for the cathode: Van Nguyen, Kulikovski, Wieser)

•cell models focussing on different aspects

Institut für Technische Thermodynamik Dr.

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Modeling of Processes within the l-DMFC From cell performance, no clear

conclusions can be drawn concerning the processes within the cell, due to considerable voltage losses in both anode and cathode, and the strong coupling by membrane mass transport.

The main goal is to use modeling as a means to explain and quantify the influence of single effects on overall cell performance.

For this purpose, a detailed model is needed considering physical and electrochemical phenomena within the multi-layer structure.

Institut für Technische Thermodynamik Dr.

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Developed Model of the l-DMFC

•The cell model comprises submodels for species transport and electrochemical reaction within single elements of the multi-layer structure.

•The detailed one-dimensional discretized submodels are coupled both by flow variables and potentials.

•Cell potential results from the sum of the potential differences in the electric circuit

•Flooding of the cathode reaction layer may occur depending on the overall water balance.

Institut für Technische Thermodynamik Dr.

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Water Management of the Cathode

•The evaporating water flux is limited both by the available amount of water and the water saturation pressure.

•Excess water forms a liquid film and is removed by surface diffusion -> the thickness of the film is determined by the amount of liquid to be removed.

•oxygen transport is modeled 1+1dim: gas transport (dusty gas model) in z-direction and Fickian diffusion through water film in -direction.

Institut für Technische Thermodynamik Dr.

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DMFC: local effective reaction rate of ORRincluding reaction kinetics, O2 , H+ and H2O transport

Institut für Technische Thermodynamik Dr.

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Institut für Technische Thermodynamik Dr.

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DMFC Current density distribution depending on air flow

639 445 260 223

722 556 412 306

755 659 508 468

728 576 483 374

Stromdichte in mA/Segment

700-750

650-700

600-650

550-600

500-550

450-500

400-450

350-400

300-350

250-300

200-250

150-200

100-150

50-100

0-50

292 129 74 19

379 151 74 7

435 200 99 42

380 150 104 63

Stromdichte in mA/Segment

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000

900-950

850-900

800-850

750-800

700-750

650-700

600-650

550-600

500-550

450-500

400-450

350-400

300-350

250-300

200-250

150-200

100-150

50-100

0-50

R1

R2

R3

R4 1250-13001200-1250

1150-12001100-1150

1050-11001000-1050950-1000

900-950850-900

800-850750-800700-750

650-700600-650

550-600500-550450-500

400-450350-400

300-350250-300200-250

150-200100-150

50-1000-50

R1

R2

R3

R4 1250-13001200-1250

1150-12001100-1150

1050-11001000-1050950-1000

900-950850-900

800-850750-800700-750

650-700600-650

550-600500-550450-500

400-450350-400

300-350250-300200-250

150-200100-150

50-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-1250

1150-12001100-1150

1050-11001000-1050950-1000

900-950850-900

800-850750-800700-750

650-700600-650

550-600500-550450-500

400-450350-400

300-350250-300200-250

150-200100-150

50-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

R1

R2

R3

R4 1250-13001200-12501150-12001100-11501050-11001000-1050950-1000900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450350-400300-350250-300200-250150-200100-15050-1000-50

700-750

650-700

600-650

550-600

500-550

450-500

400-450

350-400

300-350

250-300

200-250

150-200

100-150

50-100

0-50

Cathode: Meander Anode: couterflow Cathode: 1,6 mg Pt/cm² Anode: 1,6 mg PtRu/cm²

Cell Voltage 200 mV

a) iav = 155 mA/cm2

b) iav = 475 mA/cm2

•Low Air Stoich: low current density at the air outlet

•High Air Stoich: incresaing overall current density - balancing of current desity distribution

Air Air

a) Airflow 600 sccm b) Airflow 3000 sccm

Institut für Technische Thermodynamik Dr.

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Modeling and Experimental Results

Institut für Technische Thermodynamik Dr.

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No change in:

-operating conditions

-membrane and backings

-structure of reaction layers

-overall catalyst loading

Institut für Technische Thermodynamik Dr.

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This explains the performance:

At 70°C humidification of the cathode does not impact cell performance since the current density is already limited by the anode.

Whereas the anode potential is strongly temperature dependent, the potential of the cathode does hardly change with temperature.

Institut für Technische Thermodynamik Dr.

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Conclusions and visions

•Sensitivity analysis vs „absolute“ U(i) Characteristics

•Modular structure of Models - improved transparency of results

•Boundary conditions and simplifications of the model influence significantly the numerical results!

•Help needed: physical input parameters and structural information - Diffusivity and transport coefficients (surface diffusion)

- Effective porosity and tortuosity data - wetting angle of contact = f(U)?- Structure of the reaction interface (ionomer) and three phase space (boundary)

- Kinetic data: rate constants, exchange current densities and activation enthalpies

•The two tier society of input parameters: set of constant parameters = independent of current density

which parameters are sensitive to the current density?