A dimensionless approach to minimizing energy consumption in single-pass reverse osmosis desalination systems

This study presents a dimensionless approach to optimizing energy efficiency in single-pass multi-membrane reverse osmosis (RO) desalination. Two new dimensionless performance indices—the Recovery Ratio Index (RRI) and the Permeate Salinity Index (PSI)—were introduced to ensure feasible system recovery (0.5 ≤ RRI ≤ 1) and acceptable permeate salinity (PSI ≤ 1). A sensitivity analysis identified the dimensionless membrane parameter ($S_a^{*}$​) as the most influential factor affecting specific energy consumption, leading to its optimization under uniform and non-uniform distributions. For non-uniform cases, descending (higher $S_a^{*}$​ in early membranes) and ascending (higher $S_a^{*}$​ in later membranes) profiles were explored. The results showed that descending profiles maximize early-stage water recovery and improve efficiency for low-salinity feeds (≤ 10,000 ppm), while ascending profiles mitigate osmotic pressure buildup and enhance performance in high-salinity feeds (≥ 40,000 ppm). System size also influences the optimal strategy, with descending profiles being more effective in small systems and ascending or balanced distributions preferred in larger, multi-membrane setups. These findings provide practical design guidelines for tailoring single-pass RO configurations to feed salinity and system size.