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 cell a tutorial model

Electrodialysis CellA Tutorial Model


Introduction

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


Electrodialysis cell a tutorial model

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

Model Definition, the Model Geometry

The repetitive unit cell with one desalination unit

Na +

Na +

Na +

Cl -

Cl -

Cl -


Model definition a first approximation

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

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

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

Model Results

Diluate concentration, Na+

Concentrate concentration, Na+

Diffusion

Diffusion

Migration

Migration

Net x-flux ≈ 0

Net x-flux ≈ 0


Model results1

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

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

The Influence of Spacer in the Flow Channels


Model definition

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

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 cell1

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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