Concentration distribution along the electrodialyzer

• A simple model describing countercurrent single-pass electrodialysis is established. • Concentration distribution along the membrane is calculated. • Influence of concentration distribution on scaling risk is discussed.

A simple model based on division of electrodialyzer into the elementary units and measuring the current density distribution along the membrane was established. The model was used to describe a single-pass electrodialytic desalination performed in a counter-current mode. The results indicate that the concentration distribution along the electrodialyzer is not linear, as we previously assumed [15]. The calculated linear velocity does not change monotonically along the concentration compartment — a behavior which was predicted by our previous study on electrodialyzer hydrodynamics [22]. Concentration polarization at high current density and feed concentration was calculated to be small; however the neglect of concentration polarization can strongly influence the scaling risk calculated in a previously described manner [15]. The results are based on the experiments performed in a counter-current mode of operation. In a co-current mode, although the same approach can be used, the results would be probably different, as the diffusion and osmosis driving forces show completely Table 6 Gypsum nucleation induction time of simulated electrodialysis for experiments at highest current density. l [cm] Nucleation induction time [s] Experiment no. 3 Experiment no. 6 Case 1 Case 2 Case 3 Case 1 Case 2 Case 3 47.5 21.7 10.8 6.9 53.2 23.5 11.9 7.8 57.6 28.1 14.6 7.8 22.9 11.0 6.3 0.5 25.4 11.9 6.9 4.7 36.7 17.4 8.8 4.7 different distribution along the membrane. The concentration difference along the membrane surface strongly depends on the operation mode [34]. The results may be important for scaling-up the ED solution we proposed in the previous papers — a single-pass, counter-current electrodialysis with supersaturated concentrate, because the maximum water recovery strongly depends on properly assessing the scaling risk. Nomenclature Δl elementary unit length [cm] a empirical parameter of velocity distribution model C concentration [g·L−1] CP degree of concentration polarization [%] D diffusion coefficient [cm2·s−1] dh hydraulic diameter [cm] Ji flux of i-th ion across the membrane [g·cm−2·s−1] Jw flux of water across the membrane [cm·s−1] k empirical parameters of a mass transfer model L effective membrane length [cm] l position along the electrodialyzer [cm] n number of elementary unit Re Reynolds number S gypsum saturation s intermembrane distance [cm] Sc Schmidt number Sh Sherwood number tind gypsum nucleation induction time [s] Subscripts Cl− chloride anion d diluate k concentrate Na+ sodium cation CAL calculated value EXP experimental value Superscripts A anion-exchange membrane K cation-exchange membrane m value at the membrane surface Acknowledgment This work was partially financed by the Polish National Science Center upon Decision No. DEC-2012/05/N/ST8/02951.