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