The break-even salinity for boiling brine

Boiling seawater directly into salt is technically straightforward and energetically ruinous. This paper computes the fuel cost of boiling brine as a function of its starting concentration, using a latent heat of vaporisation of 2257 kJ per kg of water, a brine specific heat of 3.9 kJ per kg per K, dry wood at 15.0 MJ per kg, and a stove efficiency of 0.15. Boiling seawater at a salt mass fraction of 0.035 requires 70.586 MJ of heat and 31.371 kg of wood for each kilogram of salt. At a mass fraction of 0.2 the cost falls to 10.491 MJ and 4.662 kg of wood, and at 0.26, near saturation, to 7.549 MJ and 3.355 kg of wood. Against a stated household affordability bound of 5.0 kg of wood per kilogram of salt, the break-even concentration is a mass fraction of 0.1888, or 188.8 g per kg. Below that concentration, boiling from scratch does not pay under the stated bound; above it, fuel finishing becomes a reasonable use of gathered wood. The arithmetic points to a hybrid schedule: concentrate seawater by solar evaporation to a mass fraction of 0.2, which removes 0.8549 of the original water at no fuel cost, and then finish by boiling. That schedule reduces wood use by 85.1 percent compared with boiling seawater directly.