A Design Focused DBFC

7/27/2019 A Design Focused DBFC

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A Design Focused Direct BorohydrideFuel Cell Model

2012 Fuel Cell Seminar Uncasville, CT

Richard Stroman

Naval Research Laboratory,

Washington, DC

Gregory Jackson

University of Maryland

College Park, MD



Naval Research LabUniversity of Maryland

Outline

Goals and Approach

Model Development

(Preliminary) Results with Reaction Rates

Transport Limited Results

Conclusions

2




Goals and Approach

Goals: Answer these questions…

• What DBFC design(s) is(are) “best”?

• What roles do transport processes and reaction kinetics play indetermining DBFC performance?

Approach: Our efforts to answer them…

• Build a model which relates cell parameters to performance.• Use the model to identify and quantify trends.

3




Outline

Goals and Approach

Model Development



Conclusions

4




Model Development: Overview

5

• Assumptions: 2D, steady state, isothermal, ideal solutions

• Solution Approach: Finite volume; conserving mass, momentum and charge

• Top-level Model Function: Specify inlet flows; then Icell V cell or V cell Icell




Model Development: Challenges

6

Transport Challenges

• Diffusion, migration, advection are all

important in the channels

• Boundary conditions and interfaces

• Estimating fluxes through membrane

• Solubility limits for solids and gases

Reaction Rate Challenges

• Mixed potentials at electrodes

• Complex (and poorly understood) reactionmechanism

• Side reactions producing H2 and O2

BH4- , OH-

BO2-

BH3 OH-

H2

H2O

others?




Model Development: Transport in Solution

Net Mass Flux of k

Diffusion – Fick’s Law

Migration

Advection

7

An equation of state

relates mass density

to composition.

• State variables: velocity, pressure, mass fraction, electric potential

• Water diffusion flux adjusted to ensure mass fractions sum to 1

•

Solve conservation equations and electroneutrality for state variables




Model Development: Transport through Membrane

8

• Membrane: fully hydrated Nafion 115 in Na+ form

• Transport phenomena: Migration, diffusion, electro-osmotic drag

•

Non-discretized phase with gradients assumed linear

Bulk Oxidizer

Interfaces

ϕ f

ϕo

Δϕ

Bulk Fuel Membrane

X Na+

X H2O

• Membrane surfaces in equilibrium with

electrolyte solutions

• Empirical data1 used to estimatediffusivities, mobilities, electro-osmotic

drag coefficient.

•

Equal fluxes on each side – no storage.

• Only Na+ and H 2O pass through

1Okada, T., et al., Ion and water transport characteristics of perfluorosulfonated ionomer membranes

with H+ and alkali metal cations. Journal of Physical Chemistry B, 2002. 106(6): p. 1267-1273.




Model Development: Reactions

Anode Reactions

• BOR:

• BHR:

• HOR:

Cathode Reactions

• PRR:

• PDR:

• ORR:

9

E 0 = -1.24 V

E 0 = -0.828 V

E 0 = 1.763 V

E 0 = 0.695 V

* all potentials vs. RHE




Model Development: Reaction Rates

• Reaction rate expression for reaction j

• Specify one rate constant, the standard reduction potential and cell OCV, then

solve for remaining rate constants to ensure thermodynamic consistency:

Standard reduction potentials:

Electrode open circuit potential:

10

• Total species fluxes are the sums over all reactions.

• This approach can handle mixed potentials.

Electrode Bulk Solution

Interface

ϕe

ϕint

Δϕ

ݎ

= ℓ ൭ , ෑܥ , ߚ , Δ߶

− , ෑܥ − , ߚ , Δ߶

൱

0 = ,,jߚ , ܧ 0

− ,− , ߚ , ܧ 0

0 = ℓ ቀ , , ߚ , ܧ 0 − , − , ߚ , ݂ܧ 0ቁ




Model Development: Reaction Rates

• Attempting to calibrate rates by fitting rate parameters to RDE data from the

literature:

11

Electrode Bulk Solution

Interface

ϕe

ϕint

Δϕ

• So far, unreasonable error in the fits – perhaps the mechanism is lacking detail?

Use the present mechanism to explore relationships

Look at a transport limited cell where reaction rates are unimportant

Concha, B. M. and M. Chatenet (2009). "Direct oxidation of sodium borohydride on Pt, Ag and alloyed Pt-

Ag electrodes in basic media. Part I: Bulk electrodes." Electrochimica Acta 54(26): 6119-6129.




Outline

Goals and Approach

Model Development



Conclusions

12




0.90

0.92

0.94

0.96

0.98

1.00

0.0 0.2 0.4 0.6 0.8

N o r m a l i z e d C o n c e n t r a t i o n [ C k / C k , f u

e l ]

Distance From Anode [mm]

0 mA/cm^2100 mA/cm^2

200 mA/cm^2

Preliminary Results: Concentrations (1D)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.0 0.2 0.4 0.6 0.8

N o r m a l i z e d C o n c e n t r a t i o n [ C k / C k , f u e l ]


0 mA/cm^2

100 mA/cm^2

200 mA/cm^2

0

50

100

150

200

250

300

350

400

450

0.0 0.2 0.4 0.6 0.8

N o r m a l i z e d C o n c e n

t r a t i o n [ C k / C k , f u

e l ]


0 mA/cm^2

100 mA/cm^2

200 mA/cm^2

[BH4-]

[H2]

[Na+]

13

Shows how transport, electroneutrality

and reaction rates interact to determine

cell performance.

Fuel depletion at anode leads

to concentration overpotential

Migration and

electroneutrality suppress

[Na+] near the membrane.

Rising anode voltage shifts reaction

rates away from H2 production




0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5

E l e c t r i c P o t e n t i a

l [ V ]

Distance from Anode [mm]

i = 0 mA/cm^2

i = 100 mA/cm^2

i = 200 mA/cm^2

Preliminary Results: Electric Potential (1D)

Anode

Channel

Cathode

Channel

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5

E l e c t r i c P o t e n t i a l [ V ]

Distance from Anode [mm]

i = 0 mA/cm^2

i = 100 mA/cm^2

i = 200 mA/cm^2

Anode

Channel

Cathode

Channel

Zoom in on channel

Migration contribution to charge fluxes

14

Fuel: [BH4-] = 0.1 M, [OH-] = 2 M

Oxidizer: [H2O2] = 0.1 M, [H+] = 2 M

Relative importance of loss mechanisms




Preliminary Results: Polarization Curve (2D)

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

0 5 10 15 20 25 30 35

C e l l V o l t a g e [ V ]

Average Channel Current Density [mA/cm2]

Activation Overpotential

Ohmic Overpotential

Concentration OverpotentialPolarization Curve

15

Shows the model captures the activation,

ohmic and concentration overpotentials

(losses) in a fuel cell Polarization Curve

Useful tool forcomparisons

between designs

Indicates dominant

loss mechanisms



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Concentration ofH2 in the anode channel.

Distance from the inlet [m]

D i s t a n c e f r o m t h

e a n

o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10

-4

1

2

3

4

5

6

7

8

9

10

11x 10

-6

Preliminary Results: Losses to H2 and O2 (2D)

Concentration ofO2 in the cathode channel.



e c a t h

o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10

-4

0

2

4

6

8

10

12x 10-3

16

• Rate of reactant loss varies with conditions down the channel.

• Loss rates effected by both concentration and electric potential.

H2 mass flux in anode channel O2

mass flux in cathode channel

Bulk Flow

Membrane

Anode

Bulk Flow

Cathode

Membrane



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Outline

Goals and Approach

Model Development



Conclusions

17



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Distance from the inlet [mm]

D i s t a n c e f r o m t h e

a n o d e [ m m ]

5 10 15 20 25 30 35 40 45

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Transport Limited BH4- Concentration

18

Bulk Flow

Membrane

Anode

• 2D model captures down-the-channel effects related to concentration

• Useful info, and hard to obtain from a simpler model or experiments.

Fuel: [BH4-] = 0.2 M, [OH-] = 4 M

Cell Voltage: 2.0 V

Inlet

Outlet



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0 5 10 15 20 25 30 35 40 45 50200

400

600

800

1000

1200

1400

1600

Distance from Inlets [mm]

C u r r e n t D e n s i t y

[ m A / c m

2 ]

Anode

Cathode

Transport Limited Current Density

19

Membrane

Anode

• Once the concentration boundary layer develops, current density (for this

configuration) is limited to 400 mA/cm2 , even for fast reaction kinetics

Fuel: [BH4-] = 0.2 M, [OH-] = 4 M

Cell Voltage: 2.0 V



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Transport Limited Electric Potential

20

• Voltage losses vary down the channel as the fluid composition changes.

• Most loss is in the membrane; limits transport to/from the anode

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Position [mm]

E l e c t r i c P o t e n t i a l [ V ]

Anode Channel

Membrane

Cathode Channel

Near InletNear Outlet

Fuel: [BH4-] = 0.2 M, [OH-] = 4 M

Cell Voltage: 2.0 V



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Conclusions

21

• Over most of the DBFC operating envelope, reaction kinetics are only

relevant to the reaction path, not the overall rate.

– How much reactant is lost to H2, O2 or intermediates?

• Transport to/from the electrodes and through the membrane dictate power

density… at high current density, mostly the membrane.

– Narrow channels with high bulk flow rates are preferred

– Thinner or higher conductivity membranes would improve performance

• A model that captures cell behavior and quantifies these points enables us

to make informed design decisions.

– Transport phenomena: Cell geometry and flow conditions

– Reaction rates: Losses to side reactions and intermediates



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Next Steps

22

• Move to a more realistic cell configuration

– Porous catalyst layer on the membrane, or throughout channel

• Accurate reaction kinetics

– Phenomenological fit to experimental RDE data

–

In progress: have an RDE model and fitting code

• Study the DBFC operating envelope given the new cell

configuration and including losses to side reactions



Naval Research Lab

University of Maryland 23

This work was funded by generous support from

The NRL Edison Memorial Training Program and

the NRL Chemistry Division

The authors thank Karen Swider-Lyons and other members of the NRL Code6113 Alternative Energy Section for their advice and suggestions.



Backup Slides



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Concentration ofBO2 in the anode channel.

Distance from the inlet [mm]

D i s t a n c e f

r o m t h

e a n o d e [ m m ]

5 10 15 20 25 30 35 40 45

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2



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Electric potential in the anode channel



e a n o d e [ m ]

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

1

2

3

4

5

6

7

8

9

x 10-4

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2



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Model Development: Domain

27

Model Domain and Geometry



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Model Development: Assumptions

Overall model:

• The system is isothermal.

• Wall (‘edge”) effects can be ignored in the z-direction.

Channel and Membrane Models

• Fluid flow in the channels is laminar and incompressible.

• The viscosities of the fuel and oxidizer solutions are the same as pure water atthe same temperature.

• Electrolyte solutions are electrically neutral (electrochemical double layers arethin and part of interfaces).

• The solutions are ideal, i.e. activity coefficients are equal to 1.

• Only Na+ and H2O cross the membrane.

• The membrane is Nafion in the Na+ form and fully hydrated.• Fluids enter the channels with a fully developed momentum boundary layer.

• All membrane fluxes are in the y -direction.

28



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Model Development: Assumptions

29

Reaction Rates

• Catalyst layers are “flat”, i.e. 2D, but have a roughness that increases

the surface area.

• Only two electrochemical reactions take place at each the anode andcathode.

• Both catalyst layers remain in their reduced states (no oxide

formation or oxidation related hysteresis).



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Direct Borohydride Fuel Cells and Systems

Example DBFC system:

Design parameters: Channel length and height, membrane thickness

Operating parameters: Inlet concentrations, fluid flow rates, timing and rates

of injection and waste removal

30



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Prior Modeling Efforts

Sprague LFFC model

Modeled Cell Model Domain

31



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Model Development: Inlet Boundary conditions

32



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Model Development: Outlet Boundary conditions

33



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Model Development: Interface Boundary Conditions

34



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Verification: Transport Model



e a n o d e [ m ]

0 0.01 0.02 0.03 0.04

0

1

2

3

4

5

6

7x 10

-4

-9

-8

-7

-6

-5

-4

-3

-2

-1x 10

-6



e a n o d e [ m ]

0 0.01 0.02 0.03 0.04

0

1

2

3

4

5

6

7 x 10

-4

0

0.5

1

1.5

2

2.5x 10

-5


D i s t a n c e f r o m

t h e a n o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10

-4

-1.5

-1

-0.5

0

0.5

1

1.5x 10

-11


D i s t a n c e f r o m

t h e a n o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10

-4

-10

-8

-6

-4

-2

0

2

4

6

8x 10

-8

35

BH4

-

fluxes in anode channelBO

2

- fluxes in anode channel

Mass conservation error Electroneutrality error



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Preliminary Results (2D): Counter Ion Distributions

Concentration ofNa in the anode channel.


D i s t a n c e f r o m t h e

a n o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10

-4

2.055

2.06

2.065

2.07

2.075

2.08

2.085

2.09

2.095

2.1 Concentration ofNa in the cathode channel.



e c a t h o d e [ m ]

0.01 0.02 0.03 0.04 0.05

1

2

3

4

5

6

7x 10-4

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

36

[Na+] in anode channel[Na

+

] in cathode channel

Cation distribution is more complex than expected...

Depletion of Na+ on anode side of membrane may limit power density



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Verification: Reaction Rate Model

-1.2E+4

-8.0E+3

-4.0E+3

0.0E+0

4.0E+3

8.0E+3

1.2E+4

-2.0 -1.5 -1.0 -0.5 0.0

C u r r e n t D e

n s i t y [ A / m 2 ]

φa - φint

i_R1 (standard)

i_R2 (standard)

i_a (standard)

i_a (realistic)

-100

-80

-60

-40

-20

0

20

40

60

80

100

-1.02 -0.98 -0.94 -0.90 -0.86 -0.82 -0.78

C

u r r e n t D e n s i t y [ A / m 2 ]

φa - φint

i_R1 (standard)

i_R2 (standard)

i_a (standard)

i_a (realistic)

37



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References

38

1. Sanli, A. E., M. L. Aksu, et al. (2011). "Advanced mathematical model for the passive direct borohydride/peroxide fuel cell."

International Journal of Hydrogen Energy 36(14): 8542-8549.

2. Rostamikia, G. and M. J. Janik (2010). "First principles mechanistic study of borohydride oxidation over the Pt(111) surface."

Electrochimica Acta 55(3): 1175-1183.

3. Zhang, J. S., Y. Zheng, et al. (2007). "1 kW(e) sodium borohydride hydrogen generation system Part II: Reactor modeling."

Journal of Power Sources 170(1): 150-159.

4. Vera, M. (2007). "A single-phase model for liquid-feed DMFCs with non-Tafel kinetics." Journal of Power Sources 171(2): 763-

777.

5. Sprague, I. B. and P. Dutta (2011). "Modeling of Diffuse Charge Effects in a Microfluidic Based Laminar Flow Fuel Cell."

Numerical Heat Transfer Part a-Applications 59(1): 1-27.

6. Okada, T., S. Moller-Holst, et al. (1998). "Transport and equilibrium properties of Nafion (R) membranes with H+ and Na+

ions." Journal of Electroanalytical Chemistry 442(1-2): 137-145.

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A Design Focused DBFC