Modeling and Simulation of Nanofiltration for Separating Calcium, Magnesium, and Sulfate from Rejected Brine to Produce High-Purity Salt
Keywords:
DSPM-DE, Industrial salt, Ion transport modeling, Nanofiltration, Rejected brineAbstract
Rejected brine from seawater desalination is a concentrated stream rich in NaCl but containing elevated levels of Ca²⁺, Mg²⁺, and SO₄²⁻ that limit its use as a feed for high-purity industrial salt. This study aims to evaluate whether nanofiltration can selectively remove these divalent ions and to provide a mechanistic description of ion transport and process performance. A steady-state, isothermal model of a commercial spiral-wound KeenSen NF1-4040F element is developed using the Donnan-Steric Pore Model with Dielectric Exclusion coupled to the Extended Nernst–Planck equations. Radial transport inside the pores is coupled with axial mass balances for the feed and permeate streams, and solved numerically over feed pressures of 2.5 - 12.5 bar and inlet flow rates of 1.08 - 3.60 m³·h⁻¹. The simulations predict that permeate-water flux increases linearly with pressure, while along the module the retentate flow rate decreases and the permeate flow rate increases linearly with axial position. Stage recovery rises with pressure but decreases with increasing inlet flow rate. Mechanistic flux decomposition indicates that convection dominates cation transport, particularly for Na⁺, whereas diffusion and electromigration contribute more strongly to the transport of anions. Under the investigated conditions, sulfate and magnesium achieve rejections above 97%, calcium about 96%, while chloride and sodium show lower but still significant rejections. Overall, the model suggests that operating at moderate-to-high pressure and moderate inlet flow can maximise recovery while maintaining high divalent-ion rejection, supporting the use of nanofiltration as a pre-purification step to upgrade rejected brine to a higher-purity salt feedstock.
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