Electrochemical Energy Systems Laboratory Department of Mechanical Engineering
Drexel University, Philadelphia PA
www.mem.drexel.edu/energy
Simulating Performance and Species
Crossover in a Vanadium Redox Flow Battery
using COMSOL Multiphysics
Ertan Agar, K.W. Knehr, C. R. Dennison
and E.C. Kumbur
Presented at the 2011
COMSOL Conference
Boston, MA, October 13, 2011
Vanadium Redox Flow Battery
Positive Storage
Tank
V5+
V4+ + H2O
Spent Electrolytes and water
Charged Electrolytes dissolved in
H2SO4
Negative Storage
Tank
V2+
V3+
Spent Electrolytes
Charged Electrolytesdissolved in
H2SO4
Pump Pump
Ion
Exc
han
ge M
em
bra
ne
H+
H+
e-
e- V2+ →
V3+ + e-
V3+
V2+ V5+
e-+ V5+ + 2H+
→ V4+ + H2O
Cell Stack
V4+ + H2O
External Circuit + -
Load
2
Vanadium Redox Flow Battery
• Advantages:
– Decoupled power and energy ratings • Power rating (kW) ~ Size of Cell • Energy rating (kWh) ~ Volume of Electrolyte
– Large cycle life: 12,000+ cycles – Limited self-discharge – Low Maintenance
• Disadvantages:
– Low energy and power density • Energy density: 20 – 35 Wh/L • Power density: 25 – 100 W/L
3
Motivation
Less than 15 published models in the last 4 years
VRFB i (A/cm2)
Q (mL/s)
ϕ (V)
ci (M)
Majority modeling efforts: Macroscopic, 2-D, and transient models
• Poor experimental agreement
• Ideal membrane assumption (no crossover)
Restricted to single
charge/discharge cycle
Simplified membrane performance
Current:
Flow Rate:
Potential
Concentration
Crossover is one of the key issues limiting the
performance of vanadium redox flow batteries (VRFB)
4
Current Modeling: Membrane
5
Cu
rren
t C
ollecto
r
Neg
ati
ve E
lec
tro
de
Po
sit
ive E
lec
tro
de
Mem
bra
ne
Cu
rren
t C
ollecto
r
-
-
-
-
-
-
- -
-
-
Positive Electrolyte Negative Electrolyte
1. Only H+ and H2O exist in membrane
4HSO
Membrane
5V3V
2V
H
OH2
4HSO
H
4V
OH2
Flo
w R
ate
Flo
w R
ate
2. Two transport mechanisms: Migration and Convection only
Convection
Migration:
In the membrane, current modeling efforts assume single ion (hydrogen) transport
Real Scenario: Membrane
6
Proper models should account for all these physics
-
-
-
-
-
-
- -
-
-
Positive Electrolyte Negative Electrolyte
1. All species in electrolytes exist in membrane
4HSO
Membrane
5V3V
2V
H
OH2
4HSO
H
4V
OH2
Flo
w R
ate
Flo
w R
ate
2. All transport mechanisms: Migration, Diffusion, Convection
3. Interfacial physics and side reactions
Migration:
Convection
Diffusion: c
Objective
7
1) Membrane
2) Membrane/Electrode Interface
3) Open Circuit Voltage
Develop a comprehensive, 2-D, transient model which incorporates the proper membrane physics to accurately capture the crossover effect on charge/discharge cycling
using COMSOL
Main Components of Present Model
Formulation: Membrane Convection
8
lexternal FF
difflexternal FF
Effective diffusion potential
Membrane Pore
2. Viscous Forces
+ +
externalF
Fluid convection
1. Osmotic Pressure
Convection
Membrane
tyConductiviLiquid
FluxDiffusiondiff
_
_
i
iii
i
iii
cDz
cDz
F
RT2
Simplified Membrane: Migration Only
Real Scenario: Migration & Diffusion
Neg
ati
ve E
lec
tro
lyte
Po
sit
ive E
lec
tro
lyte
Membrane|Electrolyte Interface
9
Migration Diffusion Zero Net
Charge Transfer
Diffusion will violate electro-neutrality
Proton gradient facilitates diffusion into membrane
Membrane Negative
Electrolyte m
l
e
lMigration
x
Volt
Membrane Negative
Electrolyte
e
Hc
f
m
Hcc
Diffusion
x
mol m-3
Membrane|electrolyte interface is key for proper coupling
of electrode and membrane physics
Interfacial Regions
10
• At interfacial region, concentration and potential change linearly
− Junction Concentration
• Two Regions • Additional Variables
− Junction Potential
1. Electrolyte Region
2. Membrane Region
Interfacial Thickness
11
• Electrode:
einterfacial thickness = diffuse boundary layer thickness
Membrane Electrolyte Interface
Bu
lk V
elo
city
Velocity
profile next
to interface moMomentum
boundary layer
thickness
• Membrane: me
interfacial thickness = electrode interfacial thickness
31
eff
avg
mo
eD
Electrode Interfacial Thickness
Verification: Interfacial Case Study
12
0dt
dEcell
m
H
e
HD
Theoryc
c
F
RTlnemD
sim
• Does simulated potential jump equal the Donnan Potential?
D
theory
D
sim
Simplifications
• Static cell • Zero current • Sulfuric acid only
• Approach: Develop a simplified case study & solve for equilibrium
Equilibrium
condition in cell
?
• Verification at Equilibrium Conditions
Verification: Interfacial Case Study
e
m
Hc
e
Hc
memD
sim
Error of Comparison
0.35% to 0.61%
m
e
Directly from
simulated potentials
e
Hc
Computed from simulated
concentrations
m
H
e
HD
Theoryc
c
F
RTln
13
Formulation: Crossover
14
• Instantaneous side reactions in the electrolyte interfacial region
Crossed over species
Electrolyte reactant
Electrolyte product
• Vanadium species (V+2, V+3, V+4, V+5) crossing over through the membrane initiate side reactions.
Membrane Electrolyte
Reactant
Products Crossover Species
Interface
V +3
5V
4V4V
Formulation
15
Open Circuit Voltage
&
Electrode Structure
Open Circuit Voltage
Common Issue:
– Observed discrepancy between theoretical and experimental voltage
32
22ln0
VVO
VVO
cc
cc
nF
RTEE
Reason for Deviation:
– Originates from inaccuracy of calculated OCV in models Standard Nernst Equation:
• e.g., 130 to 140 mV difference between predicted and measured VRB performance
- Typical implementation of the Nernst equation does not account for all electrochemical phenomena
16 Knehr, K. W. and Kumbur, E. C., Electrochemistry Communications, 13 (2011) 342
Extended Nernst Equation
Initial concentrations: Negative - 2M V3+ and 6M H+
Positive - 2M VO2+ and 4M H+
HVVO
HHVVO
ccc
cccc
F
RTEE
32
22
2
0 ln
32
22ln0
VVO
VVO
cc
cc
nF
RTEE
Donnan Potential Proton Contribution
17 Knehr, K. W. and Kumbur, E. C., Electrochemistry Communications, 13 (2011) 342
Validation
18 P. Qian et. Al.., J. Power Sources, 175 (2008) 613
Operating Conditions
Half-cell volume: 30 mL
Vanadium concentration: 1.5 M
Current: 0.4 A
Cell size: 5 cm2
Results: Reaction Current Density
19
Reaction is concentrated near current collector
Current (A m-2): Charging at 50% state of charge
Results: Current Density
20
Able to track variations in current
density throughout the cell
Ave
rag
e C
urr
en
t D
en
sit
y (
Am
-2)
Slope is equivalent
to reaction current
Results: Hydrogen Proton Distribution
21
H+ transport across the membrane is higher than the
production in the electrode caused by the reaction
Concentration (mol m-3): Charging at 50% state of charge
Maximum concentration due to
reaction near current collector
Inlet Conc: 5064.6 mol m-3
Outlet Conc: 5063.5 mol m-3
Inc
reasin
g
Results: Distributions in Membrane
H+ Concentration (mol m-3) HSO4- Concentration (mol m-3)
y(c
m)
100
100
100
120
120
120
140
140
140
160
160
160
180
180
180
200
200
200
220
1 1.005 1.01 1.015 1.020
0.5
1
1.5
2
2.5
3
3.5
x(cm)
y(c
m)
V4+ Concentration (mol m-3)
y(c
m)
3260
3270
3270
3270
3280
3280
3280
3290
3290
3290
3300
3300
3300
3310
3310
3310
3320
3320
3320
1 1.005 1.01 1.015 1.020
0.5
1
1.5
2
2.5
3
3.5
3000
3010
3010
3010
3020
3020
3020
3030
3030
3030
3040
3040
3040
3050
3050
3050
3060
3060
3060
1 1.005 1.01 1.015 1.020
0.5
1
1.5
2
2.5
3
3.5
0.2
20.2
20.2
2
0.2
21
0.2
21
0.2
21
0.2
22
0.2
22
0.2
22
0.2
23
0.2
23
0.2
23
0.2
24
0.2
24
0.2
24
0.2
25
0.2
25
0.2
25
0.2
26
0.2
26
0.2
26
0.2
27
0.2
27
0.2
27
1 1.005 1.01 1.015 1.020
0.5
1
1.5
2
2.5
3
3.5
Liquid Potential (V)
x(cm)
y(c
m)
22
Results: Membrane Concentration
Net Flux % convection % diffusion % migration
Charging -6.72 x 10-3 26.0% 8.0% 66.0%
Discharging 6.65 x 10-3 25.4% -5.2% 79.8%
H+ Flux in membrane (mol m-2 s-1)
Net Flux % convection % diffusion % migration
Charging -8.28 x 10-5 94.8% 2.7% 2.5%
Discharging 7.42 x 10-5 101.1% -4.3% 3.2%
V4+ Flux in membrane (mol m-2 s-1)
Migration of protons generates electro-osmotic convection
which governs direction of vanadium flux in the membrane
102 greater than vanadium flux
23
Conclusions
24
• A new model is developed to account for multi-ionic transport through the membrane
• A framework for the membrane|electrolyte interface was defined to couple the species transport in the membrane with the electrode
• Simulated results agreed well with experimental data without the need for a fitting voltage (via use of extended Nernst equation)
• The model can predict transient performance and spatial distributions of species concentration, potentials, reactions in the membrane and electrode
Acknowledgements
• Extensive experimental validation • Parametric study of extended charge/discharge cycles • Performance simulations for multiple membrane
materials and electrode microstructures
Ongoing Work
• Dr. Michael Hickner (Materials Science and Engineering, Pennsylvania State University)
• Henrik Ekström, PhD (Product Specialist, COMSOL AB) 25
