Chloride retention model for concentrated solutions containing sodium chloride and sodium sulfate based on thermodynamic considerations

Modelling of nanofiltration processes focusses on dilute solutions, whereas industrial nanofiltration applications often feature the use of more concentrated solutions. Recently, nanofiltration models for dilute NaCl solutions were extended to higher concentrations of approximately 1.2 mol·L⁻¹. Furthermore, models for the prediction of the NaCl retention for saturated NaCl solutions containing impurities or anti-solvents based on thermodynamic considerations were proposed. However, proper models for intermittent NaCl concentrations were lacking. A new model, extending the earlier NaCl retention model for (near) saturated NaCl solutions, has been developed to fill the existing gap. The key assumption in the model is that the resistance for NaCl transport is a function of the sodium and chloride activities and is independent of the impurity concentration of the solution treated. Based on the experimental results generated in this study and obtained from open literature the validity of this model has been proven for NaCl solutions containing Na₂SO₄. Experimental NaCl retentions could be predicted by the developed model with sufficient accuracy (within 5 % absolute) over a wide range of NaCl and Na₂SO₄ concentrations up to saturation. The largest inaccuracies were obtained for nanofiltration of (near) saturated NaCl solutions at very low membrane flux.