Evaporators: single and multiple effect evaporation

Why it matters

Evaporators concentrate solutions by boiling off solvent, usually water: caustic soda, sugar juice, milk, fruit juices, black liquor in paper mills, and effluent before crystallisation or zero-liquid discharge. Evaporation is energy-hungry — roughly one kilogram of steam per kilogram of water in a single effect — so the choice of number of effects, feed arrangement and vacuum level is mainly an exercise in saving steam.

Key ideas

What an evaporator is. A heat exchanger (calandria, with steam condensing outside or inside tubes) plus a vapour space where the boiling liquor separates from the vapour, and a condenser (often with a vacuum system) for the last vapour. Common types: short-tube (Robert, calandria) for non-viscous liquors, long-tube vertical (rising or falling film) for heat-sensitive or foaming liquids, forced-circulation for viscous or scaling liquors, agitated thin-film for very viscous products.

Capacity and economy.

• Capacity = water evaporated per hour (kg/h).
• Economy = kg of water evaporated per kg of steam supplied. A single effect with feed near its boiling point has economy a little below 1, because the latent heat of the vapour formed is about the same as that of the steam condensed. Cold feed lowers it further; hot feed that flashes can raise it above 1.

Boiling-point elevation (BPR). Dissolved solids raise the boiling point of the solution above that of water at the same pressure (Dühring's rule: the solution boiling point is linear in the water boiling point at the same pressure). BPR reduces the useful temperature difference between steam and liquor. The vapour leaving is superheated by the BPR, but its useful condensing temperature in the next effect is the saturation temperature at its pressure.

Hydrostatic head. In tall tubes the liquor at the bottom is at higher pressure and boils at a higher temperature, further reducing ΔT; film evaporators minimise this.

Vacuum operation. Lowering the pressure lowers the boiling point: it protects heat-sensitive products, allows low-pressure or waste steam to be used, and increases the ΔT available for a given steam temperature, which reduces area. It does not reduce the latent heat needed (latent heat actually rises slightly at lower temperature).

Multiple-effect evaporation. The vapour from effect 1 is used as the heating medium of effect 2, which operates at a lower pressure (and so lower boiling point), and so on; only the first effect uses fresh steam and only the last vapour goes to the condenser. Roughly, N effects evaporate about N kg of water per kg of steam, so economy rises nearly in proportion to N (in practice less, about 0.8N, because of BPR, sensible-heat and losses). Capacity does not rise: the total available ΔT (steam temperature minus last-effect boiling point minus BPRs) is shared among the effects, so total area is roughly N times that of a single effect for the same capacity. The optimum N balances steam cost against capital cost.

Feed arrangements.

• Forward feed: liquor and vapour flow in the same direction (effect 1 → N); no pumps between effects (pressure falls), but the most concentrated, viscous liquor is in the coldest effect, lowering U there. Good for hot feed and heat-sensitive concentrated product.
• Backward feed: liquor enters the last (coldest) effect and moves to the first; pumps needed; the viscous concentrated liquor is in the hottest effect (better U). Good for cold feed and viscous products.
• Mixed and parallel feeds are used for special cases (e.g. salt crystallisation).

Vapour recompression. Mechanical (MVR) or thermal (steam-jet) compressors raise the vapour pressure so it can heat the same effect — very high equivalent economies, widely used for dairy and effluent duties.

Formulas

F·x_F = P·x_P, V = F − P Solute and total balances; F feed, P product (concentrate), V vapour (kg/h); x mass fraction of solids.

S·λ_S = F·c_pF·(T₁ − T_F) + V·λ_V Single-effect enthalpy balance (no BPR, negligible heat loss); S steam (kg/h), λ_S latent heat of steam at its saturation temperature (kJ/kg), c_pF feed specific heat (kJ/kg·K), T₁ boiling temperature (°C), λ_V latent heat of vapour (kJ/kg).

q = U·A·(T_S − T₁) Heat transfer in the calandria; T_S steam saturation temperature.

Economy = V/S Steam economy (kg water/kg steam).

ΔT_available = T_S − T_sat,last − Σ BPR Total useful temperature drop in a multiple-effect unit.

ΔT_i ∝ 1/U_i (equal areas, equal duties) Approximate distribution of ΔT among effects.

Worked examples

Example 1 (standard). A single-effect evaporator concentrates 10 000 kg/h of a 5 % (by mass) aqueous solution, fed at 30 °C, to 25 %. The vapour space is at 20 kPa (T_sat = 60.06 °C, λ_V = 2357.5 kJ/kg); BPR is negligible. Heating steam is saturated at 200 kPa (120.21 °C, λ_S = 2201.6 kJ/kg). Take c_pF = 4.0 kJ/kg·K and U = 2000 W/m²·K. Find the product rate, vapour rate, steam consumption, economy and area.

1. Solute balance: P = F·x_F/x_P = 10 000 × 0.05/0.25 = 2000 kg/h; V = 10 000 − 2000 = 8000 kg/h.
2. Heat required: F·c_pF·(T₁ − T_F) + V·λ_V = 10 000 × 4.0 × 30.06 + 8000 × 2357.5 = 1.2024 × 10⁶ + 18.860 × 10⁶ = 20.062 × 10⁶ kJ/h = 5573 kW.
3. Steam: S = 20.062 × 10⁶/2201.6 = 9113 kg/h.
4. Economy = 8000/9113 = 0.878.
5. Area: A = q/(U·(T_S − T₁)) = 5 573 000/(2000 × 60.15) = 46.3 m².

Answer: P = 2000 kg/h, V = 8000 kg/h, S ≈ 9110 kg/h, economy ≈ 0.88, A ≈ 46 m².

Example 2 (GATE level). A triple-effect forward-feed evaporator uses steam at 120 °C; the last effect boils at 50 °C. BPRs are negligible. The overall coefficients are U₁ = 3000, U₂ = 2000 and U₃ = 1200 W/m²·K, and the effects have equal areas and roughly equal duties. Find the temperature drop across each effect and the boiling temperature in effects 1 and 2.

1. Total available ΔT = 120 − 50 = 70 K.
2. Equal q and A give U₁ΔT₁ = U₂ΔT₂ = U₃ΔT₃, so ΔT_i ∝ 1/U_i.
3. Σ(1/U) = 1/3000 + 1/2000 + 1/1200 = 0.0003333 + 0.0005 + 0.0008333 = 0.0016667.
4. ΔT₁ = 70 × 0.0003333/0.0016667 = 14 K; ΔT₂ = 70 × 0.0005/0.0016667 = 21 K; ΔT₃ = 70 × 0.0008333/0.0016667 = 35 K.
5. Effect 1 boils at 120 − 14 = 106 °C; effect 2 at 106 − 21 = 85 °C; effect 3 at 85 − 35 = 50 °C ✓.

Answer: ΔT = 14, 21, 35 K; boiling at 106, 85 and 50 °C. The concentrated, viscous liquor in effect 3 has the lowest U and needs the largest ΔT — a reason to consider backward feed. In a full design these first estimates are refined with enthalpy balances until the areas come out equal.

Common mistakes

• Thinking multiple effects increase capacity; they increase economy, not capacity.
• Using the steam latent heat for the vapour (or vice versa); evaluate each at its own saturation temperature.
• Forgetting BPR and hydrostatic head when computing the available ΔT.
• Assuming economy is exactly N for N effects.
• Using the concentrated-product rate in place of vapour rate in the energy balance.
• Claiming vacuum reduces the energy needed per kg of water evaporated; it mainly increases ΔT and protects products.

For GATE CH

Expect material and enthalpy balances for single-effect units (steam rate, economy, area), the effect of feed temperature and pressure, multiple-effect concepts (economy vs capacity, forward vs backward feed), BPR and Dühring's rule, and ΔT distribution in multiple effects. Practise setting up the solute balance first and keeping track of which latent heat belongs to which stream.

Quick check

1. Feed 1000 kg/h at 10 % solids concentrated to 50 %. Water evaporated?
2. 3000 kg/h water evaporated with 1200 kg/h steam. Economy?
3. Which feed arrangement is better for a cold feed and viscous product?
4. Does a triple effect have about three times the capacity of a single effect with the same total ΔT and area per effect?
5. What does Dühring's rule relate?

Answers: 1. 800 kg/h. 2. 2.5. 3. Backward feed. 4. No — roughly the same capacity, about three times the economy. 5. The boiling point of a solution to that of water at the same pressure (linear relation).