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

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.