A Batch Reverse-Osmosis Cycle Whose Pressure Follows the Osmotic Curve: First-Principles Energy Accounting and a Sized Village Unit

SIMULATED, NOT MEASURED. Seawater reverse osmosis is usually run as a continuous process at a roughly constant feed pressure, set high enough to desalinate the most concentrated brine in the system. The plant therefore pays peak-pressure energy for water produced while the feed is still dilute. This paper specifies a different cycle: a fixed charge of seawater is held in a closed circuit and desalinated as a batch, while the feed pressure is ramped so that it follows the instantaneous osmotic pressure of the concentrating charge, holding a constant net driving pressure throughout. The full energy accounting is done from first principles for seawater at 35 g/L and 50% recovery. The osmotic pressure rises from 27.61 bar in the feed to 55.23 bar in the final brine. The thermodynamic minimum specific energy, obtained by integrating the osmotic pressure over the recovered volume, is 1.063 kWh per cubic metre of permeate, and an ideal batch cycle that follows the osmotic curve attains exactly that minimum. With stated practical losses — pump efficiency 0.85, a net driving pressure of 5.0 bar, circulation work, and pretreatment and flush allowances — the batch cycle uses 1.814 kWh/m3. A conventional continuous plant with isobaric energy recovery at 0.96 efficiency, computed from the same inputs at the same recovery and inside the same accounting boundary, uses 2.318 kWh/m3. The batch cycle therefore saves 0.504 kWh/m3, a reduction of 21.7%, while reaching the same peak pressure of 61.23 bar; its mean set pressure is 44.28 bar against the continuous plant's constant 61.23 bar. A village unit producing 10 m3/day is sized in full: 33.3 m2 of membrane at an average flux of 15 litres per square metre per hour, five cycles per day of 4.5 hours each, a batch tank of 4.4 m3 nominal volume, and a high-pressure pump peaking at 1.00 kW. Nothing in this paper was built or tested; all results are calculations, reproducible from the accompanying script.