electrodialysis cell a tutorial model. introduction electrodialysis –a separation process for...

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)

Electrodialysis cell. Image courtesy: Argonne National Laboratory

Bench-scale electrodialysis stack with ~10 to100 unit cells

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

Cathode:NegativeElectrode

Anode:PositiveElectrode

Diluate

Diluate

Concentrate

Concentrate

ElectrodeStream

ElectrodeStream

ElectrodeStream

ElectrodeStream

OH -

SO4 2-

Na +

Cl -Cl -

Na + Na +Na +

Cl -

Na +Na + Na +

Cl -Cl - Cl -SO4 2- SO4

2-

Na +

H +

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

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

Model Definition, the Model Geometry

Na +

Cl -

Na + Na +

Cl -Cl -

The repetitive unit cell with one desalination unit

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 +

Cl -

Na + Na +

Cl -Cl -

Na

+

Cl -

Na

+

Na

+

Cl -

Cl -

3D 2D

Approximation

Depth

ModelGeometry

Model Definition, Equations

• 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

Diluate channel

Cation selective membrane

Anion selective membrane

½ concentrate channel


1 mm 0.5 mm

0.5 mm

0.25 mm

0.2 m

Model Definition, Boundary Conditions

• 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

Diluate channel





1 mm 0.5 mm

0.5 mm

0.25 mm

0.2 m

Model Results

Diluate concentration, Na+ Concentrate concentration, Na+

Diffusion

Migration

Net x-flux ≈ 0 Net x-flux ≈ 0

Diffusion

Migration

Model Results

Diluate concentration, Cl- Concentrate concentration, Cl-

Diffusion

Migration

Net x-flux ≈ 0 Net x-flux ≈ 0

Diffusion

Migration

Model Results, Cross Section along the Middle of the Cell

Concentration profile, Na+ Concentration profile, Cl-

CationSelectiveMembrane

AnionSelectiveMembrane



DonnanEquilibria

DonnanEquilibria

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



0.2 m

0.5 mm

0.25 mm

1 mm 0.5 mm

Diluate channel


Schematic SpacerGeometry

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-





Without spacer

With spacer

electrodialysis cell a tutorial model. introduction electrodialysis –a separation process for...

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