# Integrating Irreversible Thermodynamics and Response Surface Methodology to Elucidate Nitrate Transport in Nanofiltration and Reverse Osmosis Membranes

## TL;DR

This study combines thermodynamic models and statistical methods to understand how nitrate ions pass through nanofiltration and reverse osmosis membranes.

## Contribution

The novel integration of irreversible thermodynamics and response surface methodology provides new insights into nitrate transport mechanisms in membranes.

## Key findings

- NF membranes show significant sensitivity to initial nitrate concentration, unlike RO membranes.
- Response Surface Methodology effectively models the synergistic effects of operational parameters on NF performance.
- The integrated approach enhances understanding of nitrate rejection and permeate flux in membrane systems.

## Abstract

This study employs an integrated modeling approach to elucidate the mechanisms of nitrate ion transport through nanofiltration (NF) and reverse osmosis (RO) membranes. The investigation first applied models from irreversible thermodynamics, specifically the Kedem–Katchalsky and Spiegler–Kedem models, to describe convective/diffusive contributions and the impact of the initial nitrate concentration (50–150 mg/L) on phenomenological parameters (reflection coefficient σ, and solute permeability Ps). The results revealed a marked sensitivity of NF membranes to the initial nitrate concentration, in contrast to the stable performance of RO membranes. To deepen this analysis, Response Surface Methodology (RSM) was used as a robust statistical tool to systematically model and quantify the synergistic effects of the initial concentration and other key operational parameters, transmembrane pressure (TMP) and recovery rate (Y) on NF performance. The results highlight the complementarity between transport modelling and statistical approaches for analysing nitrate rejection and permeate flux. The proposed approach provides useful insight into NF membrane-specific behaviour and relative sensitivity to operating conditions, within the scope and limitations of the studied membrane and experimental configurations.