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Crossover in a Vanadium Redox Flow Battery using COMSOL ...Vanadium Redox Flow Battery •...

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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
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  • 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

    http://www.mem.drexel.edu/energy

  • 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 mo

    Momentum

    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


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