Incoprea hypothesis tests · volume II
The energy needed to separate salt from water is bounded below by the ratio of osmotic pressure to recovery, so higher recovery costs disproportionately more.
Minimum specific work should rise with recovery, and rise superlinearly; energy independent of recovery would remove the floor.
Falsified by: Energy independent of recovery would remove the thermodynamic floor.
Reversible free energy of mixing for feed osmotic pressure 27 bar (seawater, 35 g/L, 25 C): W_min(r) = pi0 * ln(1/(1-r)) / r. Computed on a grid from 2% to 82% recovery, checked for convexity, and compared with the reported 3-4 kWh/m3 of real seawater RO plants at about 50% recovery.
code/tests/desalination-minimum-work.py from the recorded run.| Minimum work at 50% (kWh/m3) | 1.04 |
| Penalty, 40% to 70% recovery | 35% |
| Saturation recovery | 83% |
| Second-law efficiency of real plants | 26% to 35% |
Minimum work is 1.04 kWh/m3 at 50% recovery and rises convexly: going from 40% to 70% recovery raises the floor by 35%. The brine reaching six times seawater at 83% recovery pushes the floor past 1.6 kWh/m3. Real plants at 3-4 kWh/m3 therefore sit at 26-35% of the thermodynamic minimum — the floor is real and the recovery penalty is real, but it is not what sets plant energy today.
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