Electrodialysis cell a tutorial model
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Electrodialysis Cell A Tutorial Model. Introduction. Electrodialysis A separation process for electrolytes based on the use of electric fields and ion selective membranes Applications Desalination of process streams, effluents, and drinking water

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Electrodialysis Cell A Tutorial Model

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Electrodialysis CellA Tutorial Model


Introduction

  • Electrodialysis

    • A separation process for electrolytes based on the use of electric fields and ion selective membranes

  • Applications

    • Desalination of process streams, effluents, and drinking water

    • pH regulation in order to remove acids from, for examples fruit juices and wines (when you cannot add caustic)

    • Metal winning (precious metals)

Bench-scale electrodialysisstack with ~10 to100 unit cells

Electrodialysis cell. Image courtesy: Argonne National Laboratory


Model Definition, the Electrodialysis StackSchematic picture with 3 desalination units (in reality 10 - 20)

Concentrate

Anode reaction: H2O -> 1/2O2 + 2H+ + 2e-

Diluate

Electrode

Stream

Electrode

Stream

Cathode:

Negative

Electrode

Anode:

Positive

Electrode

Na +

Na +

Na +

Na +

Na +

Na +

Na +

Na +

SO4 2-

SO4 2-

SO4 2-

Cl -

Cl -

Cl -

Cl -

Cl -

Cl -

H +

OH -

Electrode

Stream

Electrode

Stream

Diluate

Concentrate

Cathode reaction: 2H2O +2e- -> H2 + 2OH-


Model Definition, the Model Geometry

The repetitive unit cell with one desalination unit

Na +

Na +

Na +

Cl -

Cl -

Cl -


Model Definition, a First Approximation

  • Parallel free channels with planar structure

    • In reality, cells are equipped with spacers for mechanical stability and increased mass transport in the direction perpendicular to the main flow

  • Variations in composition and potential along height and width are relatively large while they are small along the depth

    • 2D simplification of the 3D geometry

Na +

Na +

Na +

3D

2D

ModelGeometry

Cl -

Cl -

Cl -

Approximation

Na +

Na +

Na +

Depth

Cl -

Cl -

Cl -


Model Definition, Equations

Anion selective membrane

Cation selective membrane

½ concentrate channel

½ concentrate channel

Diluatechannel

0.2 m

1 mm

0.5 mm

0.5 mm

0.25 mm

  • Transport using the Nernst-Planck equations

    • Flux = diff. + conv. + migration

    • Conservation of species

    • Predefined flow field

  • Charge separation controlled throughPoisson’s equation

    • Membrane charge is included in the charge density

    • Other species can be included as supporting electrolyte in the channels


Model Definition, Boundary Conditions

Anion selective membrane

Cation selective membrane

½ concentrate channel

½ concentrate channel

Diluatechannel

0.2 m

1 mm

0.5 mm

0.5 mm

0.25 mm

  • Separate species balances for the channels and the membranes

    • Donnan equilibrium and flux continuity for species at channel/membrane boundaries

    • Given inlet fluxes and convective flux at outlets

    • Periodic boundary conditions at the boundaries running along the middle of the concentrate channels

  • Ionic potential set at the middle of the concentrate channels and continuity at the channel/membrane boundaries

  • All other conditions are insulating conditions


Model Results

Diluate concentration, Na+

Concentrate concentration, Na+

Diffusion

Diffusion

Migration

Migration

Net x-flux ≈ 0

Net x-flux ≈ 0


Model Results

Diluate concentration, Cl-

Concentrate concentration, Cl-

Diffusion

Diffusion

Migration

Migration

Net x-flux ≈ 0

Net x-flux ≈ 0


Model Results, Cross Section along the Middle of the Cell

Concentration profile, Na+

Concentration profile, Cl-

Donnan

Equilibria

Donnan

Equilibria

Cation

Selective

Membrane

Anion

Selective

Membrane

Cation

Selective

Membrane

Anion

Selective

Membrane


The Influence of Spacer in the Flow Channels


Model Definition

  • Spacers are introduced in the middle of the flow channels

    • This means that the flow field cannot be predefined as in the previous model, it has to be solved for.

  • Boundary conditions for the spacer walls are insulating conditions except for the flow field where slip conditions are applied

Anion selective membrane

Cation selective membrane

Schematic Spacer

Geometry

½ concentrate channel

Diluatechannel

0.2 m

1 mm

0.5 mm

0.5 mm

0.25 mm


Model Results, Flow Field

  • The presence of spacers enhances the convective transport in the x-direction in the channels

Low flow rate

High flow rate


Model Results, Cross Section along the Middle of the Cell

Concentration profile, Na+

Concentration profile, Cl-

Cation

Selective

Membrane

Anion

Selective

Membrane

Cation

Selective

Membrane

Anion

Selective

Membrane

Without spacer

With spacer


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