a design focused dbfc
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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
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Naval Research LabUniversity of Maryland
Outline
Goals and Approach
Model Development
(Preliminary) Results with Reaction Rates
Transport Limited Results
Conclusions
2
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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
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Outline
Goals and Approach
Model Development
(Preliminary) Results with Reaction Rates
Transport Limited Results
Conclusions
4
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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
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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?
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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
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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.
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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
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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
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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.
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Outline
Goals and Approach
Model Development
(Preliminary) Results with Reaction Rates
Transport Limited Results
Conclusions
12
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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 ]
Distance From Anode [mm]
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 ]
Distance From Anode [mm]
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
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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
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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.
Distance from the inlet [m]
D i s t a n c e f r o m t h
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
(Preliminary) Results with Reaction Rates
Transport Limited Results
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
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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.
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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
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 ]
0.005 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
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 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
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 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
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
-1.5
-1
-0.5
0
0.5
1
1.5x 10
-11
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
-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.
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
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.
Distance from the inlet [m]
D i s t a n c e f r o m t h
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.