Techno-economic optimization of large-scale two-stage brackish water reverse osmosis systems using dimensionless modeling

Large-scale brackish-water reverse osmosis (RO) systems require simultaneous co-design of array layout and operating conditions under discrete sizing constraints. This study extends a validated dimensionless two-stage RO framework to plant-array sizing and solves a multi-objective optimization that minimizes specific energy consumption (SEC) and specific cost of water (SCW) over feed pressures of 20–40 bar and feed salinities of 3000–15,000 ppm at 30 °C, subject to feasibility constraints that enforce conservative operating limits. For each condition, Pareto fronts are generated, knee points are selected, and global maps are synthesized for performance, decision variables, and feasibility metrics capturing recovery, product quality, and pressure-rating safety margins. Optimal arrays consistently favor a large first stage with a smaller polishing stage (vessel ratio ≈0.40–0.43) and near-standard element loading (6–7 elements per vessel). The optimizer primarily adapts to increasing osmotic loading by increasing the second-stage pressure ratio and the dimensionless active-area parameter (S_a^*), thereby maintaining recovery and product quality. Across the grid, knee-point SEC and SCW span ∼0.96–2.03 kWh/m³ and 0.67–0.87 $/m³, respectively. A dimensional case study at 22 bar and 5000 ppm yields an overall system recovery of about 77%, with independent DuPont WAVE verification giving 80.3% recovery. The results provide scale-independent design guidance and a tabulated lookup for rapid sizing and benchmarking.