Generalized optimal energy-cost design and operation of electrodialysis system for brackish water desalination across feed salinity and recovery

Brackish groundwater is an increasingly important freshwater source, yet inland desalination is constrained by energy cost and concentrate management. Electrodialysis (ED) is well suited to low-to-moderate salinity duties, but many optimization studies remain tied to a single salinity, recovery, or configuration, limiting transferable design guidance. This study develops a generalized energy-cost optimization framework for brackish-water ED across feed salinity and recovery using a one-dimensional axial stack model with concentration polarization and a two-step optimization. Step 1 identifies the minimum-energy operating point at various fixed membrane areas under a segmentwise limiting-current constraint, and Step 2 selects the cost-optimal membrane area using a normalized cost ratio, r, that captures local electricity tariffs and membrane costs. A practical feasibility screen based on the concentration factor, CF<5, is further introduced to exclude unrealistically severe high-recovery duties from the admissible design space. Over 1000–9000 ppm and recoveries of 0.50–0.90 (product quality fixed at 500 ppm), the cost-optimal per-cell voltage increases from ∼0.83 to ∼1.11 V/cell at R=0.90, while increasing cost ratio r from 25 to 150 W/m² reduces the cost-optimal membrane area by ∼55%. The resulting optimization maps provide duty- and location-transferable guidance through r and identify membrane resistance and electrochemical-potential losses as primary targets for further performance improvement.