The Electrodialysis–Reverse Osmosis Crossover for Brackish Groundwater: A First-Principles Energy Derivation and a Sized Village Electrodialysis Unit

Specific energies of electrodialysis (ED) and reverse osmosis (RO) are derived from stated first principles under one accounting rule for a 0.5 g/L product from feeds of 1-10 g/L NaCl-equivalent at 0.75 recovery. ED energy follows from Faraday's law at 0.85 current efficiency with the cell-pair voltage staged along the concentration path; RO energy follows from osmotic pressure with stated pump and energy-recovery efficiencies. The curves cross at 6.90 g/L, and the crossover vanishes up to 20 g/L if RO brine energy recovery is removed. A village ED unit for a 2.5 g/L borehole producing 5 m3/day is fully sized (26 cell pairs, 10.50 A, 7.49 V, 1.82 kWh/day, 0.41 kWp photovoltaic supply), and a gypsum solubility check limits recovery to 0.813. SIMULATED, NOT MEASURED: a reproducible computation, no unit built or tested.