Hong Life CalculatorsUnderstanding the evaporator water removal and steam economy calculator — concept and principle
Evaporators concentrate solutions such as milk, juice, sugar liquor and wastewater by boiling off water. Before heat-transfer design you need three numbers: water to remove, product leaving and heating steam required. This calculator gets all three from the feed rate, feed and product solids and the steam economy.
How it is calculated
- Product: P = F · x_F / x_P.
- Water evaporated: W = F − P = F · (1 − x_F / x_P).
- Steam needed: S = W / E, where E is the steam economy (kg water evaporated per kg steam).
F is the feed in kg/h, x_F and x_P are the solids percentages of feed and product. All flows come out in kg/h.
The principle
The dissolved solids do not boil off, so every kilogram of solids that enters must leave in the product: F·x_F = P·x_P. That single solids balance fixes the product flow, and the total mass balance F = P + W gives the water removed. Steam economy summarises the energy side. In a single-effect evaporator one kilogram of steam evaporates somewhat less than one kilogram of water, because the latent heat released by the steam is roughly the latent heat needed by the water. In multiple-effect units the vapour from one effect heats the next, so economy rises roughly with the number of effects.
Worked example
- Inputs: F = 10,000 kg/h, x_F = 10%, x_P = 40%, E = 2.5.
- Solids in feed: 10,000 × 0.10 = 1,000 kg/h.
- Product: 10,000 × 10 / 40 = 2,500 kg/h (it still carries the same 1,000 kg/h of solids, now at 40%).
- Water evaporated: 10,000 − 2,500 = 7,500 kg/h.
- Steam: 7,500 / 2.5 = 3,000 kg/h.
| Feed (kg/h) | Water evaporated (kg/h) |
|---|---|
| 2,500 | 1,875 |
| 5,000 | 3,750 |
| 7,500 | 5,625 |
| 10,000 | 7,500 |
| 12,500 | 9,375 |
| 15,000 | 11,250 |
| 20,000 | 15,000 |
How to read the result
Notice how much water is removed: going from 10% to 40% solids removes three quarters of the feed. Doubling the target concentration does not double the water removed, because W = F(1 − x_F/x_P) approaches F as x_P grows. Steam is usually the main operating cost, so the steam figure, multiplied by the steam price and operating hours, gives a quick cost estimate and shows the payoff of adding effects.
Common mistakes
- Mixing solids percent by mass with Brix or volume measures without conversion.
- Assuming the economy equals the number of effects exactly; heat losses and boiling-point elevation make it lower.
- Forgetting that the economy depends on feed temperature; a cold feed must first be heated.
Frequently asked questions
What is a typical steam economy?
Somewhat below 1 for a single effect, higher for multiple effects, and much higher with mechanical vapour recompression, which uses electricity instead of fresh steam.
Can I use this for continuous and batch operation?
Yes. For batch work, enter the batch mass instead of kg/h and read the results in kg.
Why does product solids percent matter more than feed rate?
The ratio x_F/x_P sets the fraction of feed that must be evaporated, while F only scales everything up or down.
Sources: W. L. McCabe, J. C. Smith and P. Harriott, Unit Operations of Chemical Engineering, McGraw-Hill · C. J. Geankoplis, Transport Processes and Separation Process Principles, Prentice Hall