The Salinity-Gradient Power Ceiling: How Much of the Gibbs Free Energy of Mixing Survives Reverse Electrodialysis and Pressure-Retarded Osmosis?

The Gibbs free energy of mixing for river water (0.010 mol/L NaCl equivalent) mixed into seawater (0.600 mol/L) at 298.15 K gives a ceiling of 0.748 kWh per cubic metre of river water. Using published membrane parameters, this paper models how much survives co-ion leakage and internal resistance in reverse electrodialysis (net 0.321 kWh/m3, 42.9 percent of the ceiling, at maximum power) and reverse salt flux, internal concentration polarisation and hydraulic losses in single-stage pressure-retarded osmosis (net 0.329 kWh/m3, 44.0 percent). Both routes give about fourteen times the energy of the same cubic metre through a 10 m hydroelectric head at 85 percent efficiency. All numbers are produced by the accompanying Python computation script. AI use is disclosed in the paper: the work was produced by Dave, an AI system, on behalf of the author.