# Solution-Friction Analytical Approximation as a Robust Model Framework for Low-Salt-Rejection Reverse Osmosis

## TL;DR

This paper introduces a new model for low-salt-rejection reverse osmosis membranes that works well across a wide range of salt concentrations.

## Contribution

The SF-AA model is presented as a physically grounded and accurate alternative to empirical models for low-salt-rejection membranes.

## Key findings

- The SF-AA model accurately captures salt transport dependence on feed concentration and permeate flux.
- The model outperforms conventional models using only three intrinsic membrane parameters.
- The SF-AA is shown to be robust and generalizable for high salinity and leaky membranes.

## Abstract

Low-salt-rejection
reverse osmosis (LSRRO) is a promising approach
for concentrating hypersaline brines using moderate hydraulic pressures,
but predictive modeling of LSRRO membranes remains limited by empirical
frameworks that require salinity-dependent fitting parameters. Here,
we adapt and validate the solution-friction analytical approximation
(SF-AA) as a simple, closed-form, and physically grounded model for
low-salt-rejection membranes across a wide salinity range. Using three
low-salt-rejection membranes, including a highly “leaky”
membrane prepared by controlled chlorination, we conducted experiments
with NaCl solutions of up to 3.64 M to measure water flux, salt rejection,
and salinity-dependent salt permeability. With only three intrinsic
membrane parameters, the SF-AA accurately captures the dependence
of salt transport on both feed concentration and permeate flux, substantially
outperforming the conventional model. These results establish the
SF-AA as a robust and generalizable model for LSRRO and other membrane
processes with leaky membranes and high salinity.