Advanced modeling and optimization of nitrate removal in nanofiltration and reverse osmosis using RSM and Nernst–Planck theory

ABSTRACT These models are essential tools for simplifying and elucidating the behavior of intricate chemical processes. In this study, the statistical tool response surface methodology (RSM) was coupled with the mathematical model of the Nernst–Planck equation, combined with film theory (NP–FT), to investigate groundwater denitrification using nanofiltration (NE90) and reverse osmosis (RE-BN). Quadratic equations derived from RSM were used to model nitrate permeate concentration (Cp), permeate flux (Jp), and nitrate retention (RR) as functions of the initial nitrate concentration (Ci), transmembrane pressure (TMP), and volume concentration factor (VCF), covering nitrate concentrations up to 500 ppm. For both membranes, nitrate permeability (Ps) and reflection coefficient (σ), along with the thickness of the concentration polarization layer (δ), were determined by fitting the NP–FT model to the results generated by the RSM models. The pore radius (rp) of both membranes was calculated using the steric hindrance pore (SHP) model. RSM demonstrated excellent predictive power, with coefficients of determination (R2) surpassing 93.7%. The NP–FT model showed an almost perfect fit with the RSM-predicted data, achieving R2 values exceeding 99%. For RO, within the study's range, nitrate concentrations in the permeate and all parameters calculated using the NP–FT model varied according to the initial nitrate concentration.