An optimization of reverse osmosis (RO) networks for seawater desalination with spiral-wound modules (SWM) was presented in this work. The membrane transport model, which was based on the mass and momentum transport equations, took into consideration the longitudinal variation of the velocity, the pressure, and the salt concentration in the membrane modules. The pressure exchanger (PX) was included in the RO superstructure, and salinity increase caused by volumetric mixing in the PX was considered. The results obtained from the presented model were compared with the actual plant operational data from literature and found to be in good agreement with relative errors of 0.81%∼2.15% and 0.01%∼0.09%, in terms of water recovery and salt rejection, respectively. The optimum design problem was formulated as a mixed integer nonlinear programming (MINLP) problem. The variation of feed salinity was studied using the RO networks model. For the feed concentration higher than 32 kg/m3, one-stage RO system is favored. When the feed concentration is below 28 kg/m3, two-stage RO system is the better choice. The unit product cost increases with the decreases of permeate concentration requirement. For the looser permeate concentration requirement (0.30 kg/m3), one-pass configuration can meet the required quality of desalted water. When the lower permeate quality requirement of concentration is from 0.050–0.20 kg/m3, a two-pass system is more suitable. The influence of system recovery rate on the plant performance was discussed. Finally, sensitivity analysis showed that the total annualized cost is highly sensitive to the feed flow rate, the operating pressure, and electricity cost, while the energy consumption is highly sensitive to the operating pressure, the feed salinity, and the feed temperature.

•Variation of velocity, pressure, and concentration in membrane module is considered.•Salinity increase caused by volumetric mixing in pressure exchanger is considered.•Lexicographic optimization is proposed to calculate a more effective payoff table.•Augmented ε-constraint method is proposed to avoid inefficient Pareto solutions.•The solution with the highest membership is selected by a fuzzy decision maker.This study proposes a multi-objective optimization (MOO) of reverse osmosis (RO) networks for seawater desalination. The membrane transport model takes into consideration of the longitudinal variation of the velocity, the pressure, and the concentration in the membrane modules. The RO network with three type energy recovery device options (pressure exchanger (PX), Hydraulic Turbocharger, and turbine) is introduced. Lexicographic optimization (for calculation of a more effective payoff table) and augmented ε-constraint method (to avoid inefficient Pareto solutions) are proposed to solve the MOO problem. A fuzzy decision maker is introduced to derive the most efficient solution among Pareto-optimal solutions. Firstly, different energy recovery option studies show that using PX is seen to be the most profitable option. Exergy analysis is used to evaluate the contribution of the equipments in energy degradation. Secondly, the proposed multi-objective framework simultaneously optimizes the total annualized cost (TAC) and energy consumption. With the increases of weighting for the main objective function: TAC, the most efficient solution moves to lower TAC direction. Finally, system recovery rate is added as the third objective function. It is reasonable to stay at the appropriate system recovery rather than to increase up to its limit and generating high energetic losses.