Online evaporator mass balance and steam economy calculator for dairy.

Calculate water evaporation rate, concentrate flow and steam consumption for single, multi-effect and MVR systems

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The Formula

Evaporator design uses a simple total mass and solids balance:

F × X_F = C × X_C (solids balance)
F = C + V (total mass balance)
⇒ C = F × X_F / X_C | V = F − C F = feed flow (kg/hr), C = concentrate flow, V = evaporation rate, X = solids fraction (F=feed, C=concentrate)

Steam consumption depends on the configuration. Steam Economy (SE) = kg water evaporated per kg steam:

Steam = V / SE Typical SE: 1-effect ≈ 0.9, 2-effect ≈ 1.8, 3-effect ≈ 2.5, 4-effect ≈ 3.2, 5-effect ≈ 3.8, MVR ≈ 15–30+

Multi-effect evaporators use the vapour from one effect to heat the next, with each effect operating at progressively lower temperature and vacuum. MVR (Mechanical Vapour Recompression) uses a compressor to raise vapour pressure for reuse as heating medium, giving the highest steam economy but requiring electrical power.

Worked Example

Problem: A skim milk concentrate (SMC) line at a dairy receives 25,000 kg/hr of raw skim milk at 12% TS and must produce concentrate at 48% TS for spray drying. The plant uses a triple-effect falling-film evaporator. Calculate the water evaporation rate, concentrate output and steam consumption.

Step 1. Solids balance: Solids in = Solids out. 25,000 × 12% = 3,000 kg solids/hr must end up in the concentrate at 48% TS.

Step 2. Concentrate flow: C = 3,000 / 48% = 6,250 kg/hr of concentrate at 48% TS

Step 3. Water evaporated: V = F − C = 25,000 − 6,250 = 18,750 kg/hr of water evaporated

Step 4. Steam consumption (triple-effect, SE ≈ 2.5): Steam = 18,750 / 2.5 = 7,500 kg/hr

Comparison: Same duty with MVR (SE ≈ 25) would use only 750 kg/hr steam plus electrical power for the compressor. A single-effect would need 18,750/0.9 = 20,833 kg/hr steam — nearly three times the feed rate, economically unworkable.

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Frequently Asked Questions

What's the typical steam economy for dairy evaporators?

Modern multi-effect falling-film evaporators in dairy give SE around 2.5 for triple-effect and 3.2 for quadruple-effect. MVR systems achieve 15–30+ but consume significant electrical power for the vapour compressor.

When does MVR make sense over multi-effect?

MVR makes sense when electricity is cheap relative to steam, when product is heat-sensitive (low temperatures throughout), or when steam supply is constrained. Multi-effect favours cheap steam and high throughput.

Why is the calculator's steam economy approximate?

Real steam economy varies with vacuum levels, feed temperature, concentrate viscosity, fouling, heat-transfer coefficient and condensate recovery. The published SE values are typical industrial averages; expect ±20% variation in practice.

What's the difference between feed solids and concentrate solids?

Feed solids (X_F) is the % total solids in the raw feed entering the first effect. Concentrate solids (X_C) is the % total solids in the final concentrate leaving the last effect. The concentration ratio is X_C/X_F.

Need expert support on evaporator mass & steam balance? Watson Dairy Consulting provides independent support including process design, plant audit, and troubleshooting. Contact Watson Dairy Consulting.

References & Further Reading

Bylund, G. (2015). Dairy Processing Handbook, 3rd ed. Tetra Pak Processing Systems AB.
Westergaard, V. (2010). Milk Powder Technology: Evaporation and Spray Drying, 5th ed. GEA Niro.
Tamime, A. Y. (Ed.) (2009). Dairy Powders and Concentrated Products. Wiley-Blackwell.
Schwartzberg, H. G. (2002). "Evaporation in food processing." In Handbook of Food Engineering Practice, CRC Press.

Further reading: John Watson publishes articles on dairy industry topics on LinkedIn. Browse all articles by John Watson on LinkedIn →

Disclaimer: This calculator and the calculations on this page are provided for educational and indicative purposes only. Real plant performance depends on many factors not captured by simple models. Always verify against your specific plant data, ingredient specifications, regulatory requirements and safety procedures. Watson Dairy Consulting accepts no liability for production, regulatory, safety or commercial decisions made on the basis of this calculator alone. For project-specific support, please contact Watson Dairy Consulting.

See related calculators: Evaporator Operator Training, Spray Drying, or browse all consultancy services.

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