Steam economy of a double-effect evaporator with two feed preheaters: 22-Agric-B8 Food Process Engineering (Part 1), May 2017, Q9

Question 9: Steam economy of a double-effect evaporator with two feed preheaters (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The source figure (reproduced below, from the page immediately following the question in the source paper) shows a forward-feed double effect with two feed preheaters recovering heat from the vapour and condensate streams.

Double-effect evaporator with two feed preheaters: Heater 1 uses Effect II's vapour V2 (100°C); Heater 2 uses the condensate from Effect I's vapour V1 after it gives up its latent heat in Effect II's coil (125°C).

Stream data read from the figure
Stream	Value
Feed	0.25 kg/s at 16°C
Steam to Effect I	140°C, saturated
Effect I boiling temperature	125°C (vapour V1 leaves at 125°C)
Effect II boiling temperature	100°C (vapour V2 leaves at 100°C)
Feed path	16°C → Heater 1 → 75°C → Heater 2 → 110°C → Effect I
Product	0.125 kg/s at 100°C

Find. The steam economy V₁+V₂)/mṊ.

Approach. Mass balance fixes total vapour (V1+V2) directly from feed and product flow — independent of the V1/V2 split. To get the steam rate, however, effect I's own energy balance still needs V1 individually, which follows from effect II's own energy balance (coil duty from V1 condensing, plus flash heat from the liquid entering at 125°C and boiling at 100°C, supplies V2's evaporation).

Check: the liquid stream leaving Effect I is taken as the mass-balance quantity (0.25−V1) rather than literally as printed, and Heater 2 is taken as using the condensate of V1 (still at 125°C, cooling by sensible heat as it gives up the last of its usefulness) to raise the feed from 75°C to 110°C, consistent with the figure's overall heat-integration layout.

Overall mass balance (independent of the V1/V2 split). $$V_1+V_2 = F-P = 0.25-0.125 = \boxed{0.125\ \text{kg/s}}$$
Effect II energy balance fixes the split. V1 (at 125°C) condenses in Effect II's coil; the liquid arriving from Effect I (at 125°C, quantity F−V1) also flashes down to Effect II's 100°C boiling point, releasing further sensible heat: $$V_1 h_{fg,125}+(F-V_1)C_{p}(125-100)=V_2 h_{fg,100}=(0.125-V_1)h_{fg,100}$$ Using steam-table values h᷇ᵤ(125°C)=2188.5 kJ/kg, h᷇ᵤ(100°C)=2257.0 kJ/kg and Cᶲ=4.186 kJ/(kg·K) for the dilute feed, and solving for V1: $$V_1 = \boxed{0.0590\ \text{kg/s}}, \qquad V_2 = 0.125-0.0590 = \boxed{0.0660\ \text{kg/s}}$$
Effect I energy balance gives the steam rate. The feed enters Effect I already preheated to 110°C, so steam only needs to supply the last 15°C of sensible heating plus V1's latent heat: $$\dot m_s h_{fg,140} = F C_p(125-110)+V_1 h_{fg,125}$$ $$\dot m_s(2\,144\,700) = (0.25)(4186)(15)+(0.0590)(2\,188\,500) = 15\,700+129\,100=144\,800$$ $$\dot m_s = \boxed{0.0675\ \text{kg/s}}$$
Steam economy. $$\text{Economy}=\frac{V_1+V_2}{\dot m_s}=\frac{0.125}{0.0675}=\boxed{1.85\ \text{kg vapour/kg steam}}$$ An economy above 1.0 (rather than the ≈1.0 of a single effect) is exactly the payoff expected from a double effect with heat-integrated preheating — each kg of live steam ultimately drives nearly two kg of evaporation once the vapour and condensate are re-used through the two preheaters.

Final results
Quantity	Value
V₁, V₂	0.0590, 0.0660 kg/s
Steam rate, mṊᵣ	0.0675 kg/s
Steam economy	1.85 kg vapour/kg steam

Topic: Steam economy of a multiple-effect evaporator with vapour/condensate heat recovery via feed preheaters.

Key relations: economy=(ΣVᵢ)/mṊᵣ; each effect's energy balance = coil duty (+ flash sensible heat where the feed enters above the local boiling point) = vapour generated × latent heat.

Why this works: the OVERALL mass balance is always solvable first and is independent of internal splits or preheater arrangement, because it depends only on the feed/product endpoints; the preheaters raise economy above a single effect's ≈1.0 by recovering vapour/condensate heat that would otherwise be thrown away, without changing the fundamental evaporation duty the effects themselves must perform.

Common pitfall: crediting the preheater duty as EXTRA evaporation — the preheaters do not evaporate anything themselves; they only reduce the sensible-heating burden that would otherwise fall on the live steam in Effect I, which is exactly how they raise economy.

Source: Geankoplis, Transport Processes and Separation Process Principles, steam economy and feed preheating in multiple-effect evaporators.

Question 9 of 10: Steam economy of a double-effect evaporator with two feed preheaters

Question 9: Steam economy of a double-effect evaporator with two feed preheaters (20 marks)