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Yield calculations

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Parent
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Seawater Salt Production
Current
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Yield calculations

A ton of seawater holds at most about 55 lbs of sodium chloride, not the 70 lbs of the parent article, because the 3.5% salinity includes sulfates and magnesium, calcium and potassium salts, so 2,000 lbs of salt a year needs about 36.5 tons of seawater. Boiling it away burns roughly 20 to 41 lbs of dry wood per pound of salt at pan efficiencies of 30% to 15%, and a saturated spring brine needs 12.7 times less water evaporated. These sums use recalled standard figures for seawater composition, latent heat and wood energy, and the efficiencies are scenarios, not measurements.

Part of Salt Production & Sourcing

A salt yield calculation converts a source of seawater or brine into pounds of salt and into the fuel or land needed to make it.

Inputs, With Where They Came From

All of these are recalled, not measured here, and should be checked before anything is built on them:

  • Seawater salinity 35 g/kg; sodium 10.78 g/kg (standard seawater composition after Dittmar and Millero)
  • Molar masses: sodium chloride 58.44, sodium 22.99
  • Solubility of sodium chloride: 35.9 g per 100 g of water at room temperature (handbook value)
  • Latent heat of vaporisation of water at 100°C: 2.257 MJ/kg
  • Specific heat of seawater: about 3.99 kJ per kg per K
  • Seawater density: about 1.025 kg/L, 8.55 lbs per gallon
  • Air-dry wood: about 15 MJ/kg (14-15)
  • Pan efficiency: 15% and 30% as scenarios, not measurements (the parent’s 8-10 lbs of wood per gallon implies about 15-18.5%; see Boiling method for cloudy climates)

Step 1: Sodium Chloride In Seawater

Sodium chloride per kg = 10.78 × (58.44 ÷ 22.99) = 10.78 × 2.542 = 27.4 g, or 2.74% (see Seawater evaporation).

Per ton (2,000 lbs): 2,000 × 0.0274 = 54.8 lbs at most. The parent’s 70 lbs per ton is 2,000 × 0.035, the total of all dissolved salts, so it overstates sodium chloride by 70 ÷ 54.8 = 1.28, or 28%. The recovered figure is lower again: some sodium chloride stays in the bitterns and crystals, and the harvest includes gypsum and magnesium salts unless purified. I cannot source a recovery fraction, so 55 lbs is a ceiling, not a forecast.

Seawater for a year. To make 2,000 lbs of salt: 2,000 ÷ 0.0274 = 72,993 lbs of seawater, which is 36.5 tons. The parent’s 28.5 tons is 2,000 ÷ 0.035 ÷ 2,000.

Step 2: Energy To Boil Away The Water

For 100 lbs of sodium chloride, assuming all of it is recovered:

  1. Seawater needed: 100 ÷ 0.0274 = 3,650 lbs = 1,655 kg (427 gallons)
  2. Water in it: 1,655 × 0.965 = 1,597 kg
  3. Latent heat: 1,597 × 2.257 = 3,605 MJ
  4. Warming 1,655 kg from 15°C to 100°C: 1,655 × 3.99 × 85 ÷ 1,000 = 561 MJ
  5. Total: 3,605 + 561 = 4,166 MJ
  6. Wood at 15% efficiency: 4,166 ÷ (15 × 0.15) = 1,852 kg = 4,083 lbs
  7. Wood at 30% efficiency: 4,166 ÷ (15 × 0.30) = 926 kg = 2,041 lbs

So 100 lbs of salt costs 2,041 to 4,083 lbs of dry wood, about 20 to 41 lbs per pound of salt. The parent’s range of 3,000-4,000 lbs falls inside this, near the upper end. Its rule of 8-10 lbs of wood per gallon, applied to 427 gallons, gives 3,415-4,270 lbs; applied to the 334 gallons implied by the 3.5% figure (100 ÷ 0.035 ÷ 8.55), it gives 2,670-3,340. The parent’s range sits between those two cases, so I do not call it wrong, but the basis of the 3,000-4,000 is unstated.

Per gallon check. One gallon is 3.88 kg: latent 3.88 × 2.257 = 8.76 MJ, warming 3.88 × 3.99 × 85 ÷ 1,000 = 1.32 MJ, total 10.08 MJ. Wood at 15%: 10.08 ÷ 2.25 = 4.5 kg = 9.9 lbs, which matches the parent’s 8-10 lbs.

Step 3: A Year’s Wood

The salt article’s budget gives annual use as 1,040-1,870 lbs (the table total; the headline figure of 1,500-3,000 lbs in the same article does not match its own table). Wood for seawater boiling:

  • low: 1,040 lbs × 20.4 lbs of wood per lb of salt = 21,200 lbs, about 9.6 tonnes
  • high: 1,870 lbs × 40.8 = 76,300 lbs, about 34.6 tonnes

That is 10 to 35 tonnes of air-dry wood a year, which cannot also be burned for cooking and heating, and which a coppice must grow (Coppicing & Fuel Management). I have not converted this to hectares because that needs a coppice yield figure that this article does not source.

Step 4: A Saturated Brine

Saturated brine is 35.9 ÷ 135.9 = 26.4% salt. The water to evaporate per kg of salt is (100 − 26.4) ÷ 26.4 = 2.8, against 35.5 for seawater ((100 − 2.74) ÷ 2.74). The ratio is 35.5 ÷ 2.79 = 12.7. The sensible heat adds a few percent to each and changes the ratio little. This is why strong springs and brine wells are worth finding (Brine Boiling).

What You Need To Measure Yourself

  • The sodium chloride content of your own seawater or brine: evaporate a weighed sample to dryness
  • Your own pond evaporation rate: a marked stick over several weeks
  • Your own pan’s efficiency: weigh the water boiled away against the wood burned in a test run

Common Mistakes

  • Counting all dissolved salts as salt.
  • Taking the 3.5% as sodium chloride when sizing ponds or fuel.
  • Using one fuel number for every pan. Efficiency varies by a factor of two.

Safety

Do not size the fuel, or the stock, from these ceilings

The sodium chloride figure is a maximum and the wood figure is a range. Plan for the lower salt yield and the higher wood use, keep a reserve of salt through the winter, and do not cut the meat-curing salt below what the cure needs because the production sums looked tight (Salt Curing & Brining).

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