What is Evaporation?

Evaporation is a unit operation that concentrates a solution by boiling off the volatile solvent — almost always water — while the dissolved solids remain in the liquid phase. Unlike distillation, the goal is not to separate two volatile components but simply to remove solvent, so the vapor leaving the unit is treated as essentially pure.

Evaporation is energy-intensive: vaporizing one kilogram of water requires roughly 2257 kJ. Because of this, the central design problem is not whether the separation is possible, but how much steam it costs. Nearly every design decision described below exists to reduce that steam bill.

Material Balance

The starting point is a balance on the dissolved solids, which leave only in the product stream. If F is the feed rate with solids fraction x_F, and P is the product rate at x_P:

Note that W depends only on the feed and the target concentration — it is fixed by the process requirement. The number of effects does not change how much water must be evaporated; it changes how much steam that evaporation costs.

Steam Economy

Steam economy is the ratio of water evaporated to live steam consumed:

In a single effect, each kilogram of steam evaporates roughly one kilogram of water, so the economy is near 1.0. The insight behind multiple effect evaporation is that the vapor produced in the first effect is itself a heating medium: if the second effect is held at a lower pressure, that vapor will condense and boil more solution. Repeating this reuses the same latent heat several times.

An N-effect system therefore approaches an economy of N, but never reaches it — sensible heating of the feed, boiling point elevation, and heat losses all take a share. A practical rule of thumb is:

This 0.8 factor is the approximation used by the calculator. A rigorous design solves the effect-by-effect energy balances iteratively, since the latent heat, the boiling point elevation, and the temperature split all vary between effects.

Boiling Point Elevation (BPE)

A solution boils at a higher temperature than pure water at the same pressure, because dissolved solids lower the solvent's vapor pressure. This difference is the boiling point elevation, and it is the main reason multiple effect systems hit diminishing returns.

BPE is costly because it consumes temperature driving force without producing any additional evaporation. The vapor leaving an effect is at the pure-water saturation temperature, not the elevated boiling temperature of the solution, so the elevation is simply lost from the temperature budget of every effect:

Each added effect subtracts another BPE from the available driving force while also dividing what remains. Add enough effects and ΔT per effect approaches zero, at which point the required heat transfer area becomes unbounded. This is the physical limit on how many effects a system can use, independent of cost.

BPE rises with concentration, so it is largest in the effect producing the final product. For a given solution it is commonly estimated from Dühring's rule, which states that the boiling point of a solution is a linear function of the boiling point of pure water at the same pressure.

Heat Transfer Area

Each effect is a heat exchanger, sized by the standard rate equation. The duty comes from condensing steam, and the driving force is the per-effect temperature difference established above:

The latent heat of steam falls slightly as pressure rises; the calculator uses the linear approximation λ ≈ 2257 − 2.3·(T_steam − 100) kJ/kg. Typical overall coefficients U range from about 1000 W/m²·K for viscous or fouling liquors up to 3000 W/m²·K for thin, clean solutions.

Effects are usually built with equal areas so that units are interchangeable, which is why area is reported per effect. Achieving equal areas in a rigorous design requires adjusting the temperature split between effects rather than dividing ΔT evenly, so the equal-split assumption used here is a first approximation.

Choosing the Number of Effects

The number of effects is an economic trade-off, and the two sides move in opposite directions:

• Operating cost falls with more effects, since steam consumption is roughly inversely proportional to N.
• Capital cost rises with more effects — each one is an additional vessel, and shrinking ΔT means every vessel also needs more area.

Savings diminish sharply: going from one effect to two halves the steam bill, but going from four to five improves it by only about five percent. Most industrial systems land at 3 to 5 effects. Expensive steam or a high-value product pushes the optimum higher; cheap waste steam, a fouling liquor, or a heat-sensitive material pushes it lower.

Feed Arrangements

The order in which liquor passes through the effects is a separate decision from their number, and it affects viscosity, pumping, and product quality:

• Forward feed — liquor and vapor flow in the same direction, from hot to cold. Pressure differences move the liquor, so no inter-effect pumps are needed. The drawback is that the most concentrated, most viscous liquor sits in the coldest effect, where U is lowest.
• Backward feed — liquor enters the coldest effect and moves toward the hottest, against the vapor. The concentrated product is then handled at high temperature where it is least viscous, improving heat transfer, but pumps are required to move liquor against the pressure gradient.
• Parallel feed — fresh feed enters every effect and product is withdrawn from each. Common in crystallizing evaporators, where transferring a slurry between effects is impractical.
• Mixed feed — a combination chosen to balance viscosity handling against pumping cost.

Backward feed is generally favored for cold feeds and viscous products; forward feed suits hot feeds and heat-sensitive materials, since the product spends its time in the coolest effect.

Assumptions and Limitations

The calculator is intended for screening and feasibility work. Its main simplifications are:

• Steam economy uses the approximation 0.8·N rather than solving the effect-by-effect energy balances.
• Evaporation is split equally among effects; in practice it varies with the local latent heat and temperature.
• BPE is entered as a single value per effect, though it actually rises with concentration and so differs between effects.
• Sensible heating of subcooled feed is neglected, which understates steam demand when the feed enters well below its boiling point.
• The final condenser is fixed at 40 °C, and vapor is treated as pure water.

For detailed design — particularly with fouling, crystallizing, or heat-sensitive liquors — use rigorous effect-by-effect calculations with measured physical property data.

References

1. McCabe, W.L., Smith, J.C., Harriott, P., "Unit Operations of Chemical Engineering", 7th Edition, McGraw-Hill (2005)
2. Geankoplis, C.J., "Transport Processes and Separation Process Principles", 4th Edition, Prentice Hall (2003)
3. Perry, R.H., Green, D.W., "Perry's Chemical Engineers' Handbook", 8th Edition, Section 11: Heat-Transfer Equipment, McGraw-Hill (2008)
4. Billet, R., "Evaporation Technology: Principles, Applications, Economics", VCH (1989)
5. Minton, P.E., "Handbook of Evaporation Technology", Noyes Publications (1986)