Sizing a solar salt pan

A household that can reach the sea often asks a deceptively simple question: how large must a solar salt pan be? This paper derives a sizing rule from a water balance rather than from custom or anecdote. Salt can leave a pan no faster than water does, so the salt production rate is the net evaporation rate multiplied by the ratio of salt to water in the feed brine. Net evaporation is gross evaporation reduced by a factor of 0.85 for concentrated brine, minus rainfall. For seawater at a mass fraction of 0.035, the rule gives 5.059 m2 of pan per kilogram of salt per day in an arid coastal climate with net evaporation of 5.45 mm per day, and 19.694 m2 per kilogram per day in a humid coastal climate with net evaporation of 1.4 mm per day. Spread over a dry season, a stated household need of 30.0 kg per year requires only 0.63 m2 in the arid case and 4.92 m2 in the humid case, provided the pan is refilled as it dries. The binding constraint is therefore not area in most coastal settings. It is the seasonal total of net evaporation. A pan on 20.0 m2 fails that household need when the season total of net evaporation falls below 41.4 mm, and it produces nothing at all when average rainfall reaches 5.95 mm per day against arid gross evaporation, or 3.4 mm per day against humid gross evaporation. A single 10.0 mm rain event on nearly saturated brine dilutes it from a mass fraction of 0.26 to 0.1418 and costs 1.83 extra days of evaporation in the arid case and 7.14 days in the humid case.