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Electrodialysis Cell A Tutorial Model

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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  1. Electrodialysis CellA Tutorial Model

  2. 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

  3. 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-

  4. Model Definition, the Model Geometry The repetitive unit cell with one desalination unit Na + Na + Na + Cl - Cl - Cl -

  5. 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 -

  6. 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

  7. 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

  8. Model Results Diluate concentration, Na+ Concentrate concentration, Na+ Diffusion Diffusion Migration Migration Net x-flux ≈ 0 Net x-flux ≈ 0

  9. Model Results Diluate concentration, Cl- Concentrate concentration, Cl- Diffusion Diffusion Migration Migration Net x-flux ≈ 0 Net x-flux ≈ 0

  10. 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

  11. The Influence of Spacer in the Flow Channels

  12. 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

  13. 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

  14. 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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