<![CDATA[Rejected brine is a concentrated NaCl stream whose elevated Ca²⁺, Mg²⁺, and SO₄²⁻ depress the quality of industrial salt. We built a mechanistic model of a spiral-wound KeenSen NF1-4040F nanofiltration (NF) element using the Donnan–Steric Pore Model with Dielectric Exclusion coupled to the Extended Nernst–Planck equations. Radial transport is coupled to axial mass balances and solved at steady, isothermal conditions over bar and . Water flux increases almost linearly with ; along the module falls and rises nearly linearly. Recovery increases with but decreases with . Flux decomposition shows cations are convection-dominated, whereas anions carry larger shares of diffusion and electromigration. Predicted end-of-module rejections are ≈ 99.0-99.3%, ≈ 97.6-98.1%, ≈ 96.0-96.6%, ≈ 88-89%, and ≈ 74-75%, confirming divalent ≫ monovalent selectivity. Linking to product quality, the simulated permeate at bar and yields a conservative dry-salt purity of ~96.9 wt% NaCl when all non-halite salts co-precipitate. Under halite-first crystallization with a gypsum pre-step and bittern purge, only a minor fraction co-crystallizes, giving ≥98.5 wt% (≈99.5 wt% for a 20% co-crystallization assumption). Thus, operating at moderate-to-high with moderate cross-flow not only maximizes recovery and divalent rejection but also supplies a permeate that can be crystallized to SNI-compliant high-purity salt.]]>
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