Evaporator Heat Transfer Area: Calculation With Example

Last updated: 2026-10-31

Twenty tonnes per hour evaporated from a sodium sulfate brine at 80 °C carries 13.06 MW; at U = 1,000 W/(m² K) and an effective 33 K, the evaporator heat transfer area is 396 m², or 501 m² after a 15% fouling allowance and a 10% design margin — 700 tubes of 6 m by 38 mm. Each number is reproducible below.

Key Takeaways

• Area is Q divided by U and effective dT; the smallest credible dT sets the size.
• On 120 °C steam against 80 °C vapor, budget 33 K after BPE, hydrostatic head and non-condensables.
• A 20% error in U is a 20% error in area, so the coefficient needs test work.
• Fouling allowance and design margin are different things; counting both twice buys residence time.
• Doubling the effects halves the steam and doubles the surface — a trade, not a lunch.

What Governs Evaporator Heat Transfer Area?

Every evaporator is a heat exchanger with a process problem attached, and it obeys the standard rating equation:

Q = U × A × ΔT

Rearranged, the evaporator heat transfer area is:

A = Q / (U × ΔT)

with Q in W, U in W/(m² K), ΔT in K and A in m². Nothing in that rearrangement is specific to evaporation. What makes evaporation different is that ΔT is not a number you read off two thermometers; it is the residue left after the process takes its share of the temperature ladder. The equipment family is mapped in our evaporation and crystallization pillar.

Start from the gross difference: saturated steam at 120 °C against vapor at 80 °C is 40 K. That 40 K never reaches the surface, because four deductions come off first.

Boiling point elevation. Boiling point elevation is a thermodynamic penalty that raises the boiling temperature of the liquor above the saturation temperature of pure water at the same pressure, typically 3-6 K for a 25-35% sodium sulfate liquor at 80 °C (indicative, from a boiling point diagram or site measurement). Heat passes from 120 °C steam into a liquor boiling at 84 °C, so 4 K is gone before hydrostatics.

Hydrostatic head. Hydrostatic depression is a temperature penalty that arises because liquid at the bottom of a flooded bundle boils against a higher pressure than liquid at the free surface: typically 1-3 K in a falling film, 5-8 K in a deep submerged bundle.

Non-condensable partial pressure. Non-condensable blanketing is a mass transfer effect that lowers the condensing temperature the wall actually sees, typically 1-3 K with vents working and far more when they are not.

Subcooling and desuperheating take another 0.5-2 K, depending on how the condensate is drained.

What remains, 33 K in this case, is the number that sizes the plant. That is the first principle: duty is fixed by production, U is bounded by physics and fouling, and ΔT is the only term the flowsheet can spend. Every architectural choice — one effect or three, 120 °C steam or a compressor, deep vacuum or atmospheric — is a decision about spending ΔT. A three-effect train runs each effect on 8-12 K; an MVR unit on 8-10 K. Neither is better in area terms. Both trade steam for surface.

The Four Numbers You Need Before You Can Size Anything

Three of the four inputs are usually wrong on the first pass. The route from brine analysis to equipment selection is set out in brine concentrator sizing and selection; the numbers themselves are below.

Duty, Q. Duty is the heat crossing the surface per unit time, in kW, and it has three parts: latent heat at the vapor temperature, sensible heat to bring the feed to its boiling point, and, where the duty crystallizes, the heat of crystallization. Boiling point elevation is not a duty term. It belongs in ΔT, and putting it in both is the most common double count I see in client heat balances.

Overall coefficient, U. U is the conductance of the whole path from condensing steam to boiling liquor, in W/(m² K), and it is the one number you cannot calculate from first principles with acceptable accuracy. It carries the tube wall, both film coefficients and the fouling films, and it comes from test work, a vendor reference on the same liquor, or a pilot run in a lab-scale falling film evaporator.

Effective temperature difference, ΔT. ΔT is the gross steam-to-vapor difference minus every deduction above, in K. It separates a 400 m² machine from a 1,600 m² machine on identical duty.

Fouling resistance and margin. Fouling resistance is the reciprocal of the conductance lost to deposits, in m² K/W, and it belongs inside U. Design margin is a separate multiplier on the finished area. Both are treated below.

Those bands are indicative values from published practice and our own project records. Every one must be confirmed by test work or a written vendor guarantee before it enters a purchase specification.

Worked Example: 20 t/h of Water From a Sodium Sulfate Brine

The duty is 20 t/h of water evaporated from a sodium sulfate brine, vapor at 80 °C, saturated steam at 120 °C on the shell side. Feed is 60 t/h at 24% w/w solids, product 40 t/h at 36% w/w; the solids balance confirms it, 60 × 0.24 = 14.4 t/h and 40 × 0.36 = 14.4 t/h.

1. Fix the latent duty. At 80 °C the latent heat is about 2,310 kJ/kg (indicative; steam tables give 2,308 kJ/kg). Q_latent = 20,000 kg/h × 2,310 kJ/kg = 46,200,000 kJ/h. Divided by 3,600 s/h: 12,833 kW.

2. Add the sensible heat. The feed leaves the feed/product exchanger at 80 °C and the liquor boils at 84 °C, so 4 K of sensible rise remains inside the calandria. With cp = 3.4 kJ/(kg K), typical for a 24% sulfate liquor: Q_sensible = 60,000 × 3.4 × 4 = 816,000 kJ/h = 227 kW. Total Q = 12,833 + 227 = 13,060 kW.

3. Fix the gross temperature difference. Saturated steam at 120 °C (about 2.0 bar g) against vapor at 80 °C gives ΔT_gross = 120 − 80 = 40 K.

4. Deduct the losses. BPE 4 K, hydrostatic head 2 K in a falling film, non-condensables 1 K, subcooling 0 K with a proper drain. ΔT_eff = 40 − 4 − 2 − 1 = 33 K.

5. Sanity-check ΔT. If someone hands you 10 K for this duty, they are describing an MVR unit or a three-effect train, not a single effect on 120 °C steam. Hold that thought for the comparison below.

6. Divide by U. Take U = 1,000 W/(m² K), mid-range for a falling film on a moderately fouling sulfate liquor. A = 13,060,000 / (1,000 × 33) = 13,060,000 / 33,000 = 396 m².

7. Add the allowances. Fouling: 396 × 1.15 = 455 m². Design margin: 455 × 1.10 = 501 m², or 396 × 1.265 = 501 m² in one step. Two checks: evaporative flux is 20,000 / 501 = 40 kg/(m² h), inside the 25-45 kg/(m² h) band for a well-distributed film; heat flux is 13,060 / 396 = 33 kW/m², at the upper end for a liquor that can crystallize.

8. Convert area to tubes. A 38 mm OD tube, 6 m long, exposes π × 0.038 × 6 = 0.716 m². Tube count = 501 / 0.716 = 700, giving 700 × 0.716 = 501 m². On 48 mm triangular pitch the bundle footprint is 700 × 0.866 × 0.048² = 1.40 m², an equivalent diameter of √(4 × 1.40 / π) = 1.34 m. The shell is larger: 20,000 kg/h of vapor at 80 °C and 47 kPa has a density near 0.29 kg/m³, so 68,200 m³/h or 18.9 m³/s must be disengaged, and 5 m/s needs 3.8 m² — a 2.2 m shell.

The same duty as a two-effect arrangement changes the picture. Split it equally at 6.53 MW per effect, as in a multi-effect evaporation and crystallization unit run with one effect idle. Effect 1 takes 120 °C steam and boils at 105 °C: 15 K gross, less 3 K of BPE, 2 K of hydrostatic and 1 K of non-condensables, leaves 9 K, which is thin — hold the steam at about 123 °C and 12 K is available, so A1 = 6,530,000 / (1,000 × 12) = 544 m². Effect 2 is heated by 102 °C vapor from effect 1 and boils at 84 °C; 18 K gross less 3 K of losses leaves 15 K, so A2 = 6,530,000 / (1,000 × 15) = 435 m². Total 979 m² against 396 m², 2.5 times the surface. Steam falls from 47,016,000 / 2,202 = 21.4 t/h to 23,508,000 / 2,202 = 10.7 t/h. That is the argument between effects in one line: you buy coal with steel, or steel with coal.

Which U Value Should You Actually Use?

U is where most of the disagreement in a bid package lives, because it is the one input that cannot be defended with a drawing. The hierarchy is: measured data on your liquor, then a vendor reference unit, then published bands, then a guess. The bands are wide because they describe different machines, not different opinions.

What moves U inside a single machine matters more than the choice between types. Viscosity comes first: a falling film on 36% sulfate liquor carries a lower film Reynolds number than a dilute stream, and the film coefficient falls with it. A fouling film comes second: 0.0002 m² K/W on a clean conductance of 1,100 W/(m² K) gives 1 / (1/1,100 + 0.0002) = 901 W/(m² K), an 18% loss from a layer thinner than paint. Non-condensables come third, cheapest to fix and last to be checked. Liquid distribution and tube wetting come fourth: a film that does not wet the top third of the tube has lost that third of its area, whatever the datasheet says. The comparison between pumped and gravity-fed designs is set out in forced circulation versus falling film.

Because A = Q/(U × ΔT), the error propagates linearly. Take U as 800 instead of 1,000 and the duty needs 13,060,000 / (800 × 33) = 495 m² instead of 396 m², and 626 m² instead of 501 m² after margins. That is 125 m² of stainless steel bought or not bought on the strength of a coefficient nobody measured.

How Much Area Do Fouling and Margin Really Add?

Fouling resistance is a property of the duty, not of the equipment type, which is why tables quoting one number for “evaporators” are a starting point only.

The arithmetic is one line: U_dirty = 1 / (1/U_clean + R_f). At R_f = 0.00045, U falls to 1 / (1/1,100 + 0.00045) = 735 W/(m² K).

Design margin and fouling allowance are not the same thing, and adding both twice is a real and expensive error. A fouling allowance is a physical resistance that will certainly accumulate; it belongs inside U so the machine still makes rate on the day before cleaning. A design margin covers what you do not know — the heat balance, the U, the future debottleneck — and it is applied once, to the finished area. If the U you quote is already dirty, the 15% is contingency, not a second allowance. Say which one you are buying.

Over-sizing is not free. Extra surface at fixed duty means lower flux, which sounds kind and is not: in a crystallizer it means longer residence time at temperature, more thermal degradation of organics, more color pickup, and a larger liquor holdup to dump at shutdown. A 20% oversize on a 500 m² unit is 100 m² at USD 1,150/m², USD 115,000, plus about 15% more plot space and insulation. The right margin is the one you can defend in a review. Scale control practice is covered in evaporator scaling control, and the effluent case in zero liquid discharge.

Why Does Area Calculated on Paper Disappear in Operation?

Area does not vanish. It stops being effective, and the symptoms repeat across plants.

1. Falling U within weeks. Cause: a fouling film forms faster than the allowance assumed, usually because the feed carries fines or hardness outside the design basis. Action: pull a tube, measure the deposit, convert thickness and conductivity into R_f, then fix pretreatment or the antiscalant program.

2. Last effect losing dT. Cause: BPE rises with concentration through the train, and the last effect has the least ΔT to begin with. Action: re-run the boiling point diagram at the actual discharge concentration, not the design one, and reallocate duty.

3. Non-condensable blanketing. Cause: air in-leakage at gaskets and instrument connections, or a vent throttled to save energy. Action: compare vapor space temperature with saturation temperature at the measured pressure; the shortfall is the blanketing, and restoring venting recovers it.

4. Scaling on the steam side. Cause: boiler carryover or a fouled condensate system depositing on the condensing surface. Action: check steam quality and condensate conductivity; steam-side scale is invisible from the process side and is routinely misdiagnosed as process fouling.

5. Entrainment limiting vapor velocity. Cause: the unit is pushed above design rate, vapor velocity rises with throughput, and droplet separation becomes limiting rather than surface. Action: derate to the entrainment limit or fit a mesh pad; more area will not help.

6. Crystallizer area lost to solids inventory. Cause: a growing crystal bed blankets the lower tubes, so effective wetted area falls while the loop keeps circulating. Action: control bed height and seed inventory, and size the calandria for the blanked fraction rather than the geometric area.

What Does Area Cost?

Installed cost per square meter of heating surface for a 2 bar g calandria, on an indicative 2026 basis, runs about USD 900-1,400/m² in SS316L, USD 1,300-1,900/m² in duplex 2205 and USD 2,200-3,200/m² in titanium Gr2. These are budget figures to be confirmed by quotation; they exclude erection in difficult locations.

At 501 m² and USD 1,150/m², an SS316L bundle is about USD 576,000. The same surface in titanium is about USD 1,353,000. That gap is why chloride in the feed is worth measuring twice: 0.2 g/L can decide the material, and the material decides whether the project has a contingency left.

Area, material and pressure class do not interact as people expect. Pressure class moves the shell, tubesheet and flanges, not the surface, so 2 bar g to 6 bar g adds roughly 10-15% to the installed cost of a given area. Material is the multiplier that bites. The capital trade against energy decides the architecture. An MVR evaporation and crystallization unit on this duty needs about 1,500 m² because its effective ΔT is 8-10 K, plus 700 kW of compressor power; a two-effect unit needs 1,239 m² and 10.7 t/h of steam. At USD 0.10/kWh and 8,000 h/yr the MVR power bill is USD 560,000; at USD 12/t the two-effect steam bill is USD 1,027,000. The 261 m² of extra surface costs about USD 300,000 and earns about USD 467,000 a year — roughly USD 1,790 per extra square meter per year. That is the whole economic argument, and it is why MVR evaporator design is a question about electricity price first and thermodynamics second. The comparison across architectures is broken down in evaporator energy consumption.

Field Data: 45 t/h Three-Effect Unit, Area Reconciliation

A 45 t/h three-effect unit on a sulfate effluent was commissioned with 2,400 m² of surface, 800 m² per effect, and a design U of 900 W/(m² K) dirty, from a clean 1,100 W/(m² K) and R_f = 0.0002 m² K/W. Six months after start-up the measured U in effect 2 was 640 W/(m² K), 29% below design. Back-calculating, 1/640 − 1/900 = 0.00045 m² K/W of extra resistance had built up, more than three times the allowance.

The plant held 45 t/h by raising first-effect steam temperature about 2 K, which on an 11 K effect is 18% more driving force, and paid with steam consumption rising from 15.2 t/h to 17.6 t/h, a 16% increase. We then added 320 m² to effect 3, taking the unit to 2,720 m², and recovered most of the rate at the original steam pressure.

The reconciliation is uncomfortable. At U = 640, the duty needed 2,400 × 900/640 = 3,375 m² from day one. The 975 m² “saved” at the design stage has cost roughly USD 230,000 a year in steam ever since. The lesson was not that the vendor was optimistic about U; it was that the fouling allowance had been lifted from a clean-liquor table for a duty that crystallizes.

Frequently Asked Questions About Evaporator Heat Transfer Area

How is evaporator heat transfer area calculated?

Area is duty divided by the product of the overall coefficient and the effective temperature difference: A = Q/(U × ΔT). Convert Q to watts, keep U in W/(m² K), and use the effective ΔT after boiling point elevation, hydrostatic head and non-condensable deductions. For 13.06 MW at U = 1,000 W/(m² K) and 33 K, that is 396 m² before allowances.

What U value should I assume for a falling film evaporator?

For a sulfate liquor in a well-distributed falling film, 800-1,200 W/(m² K) is the indicative band, with 1,000 a reasonable first pass. Treat it as a placeholder until you have test work on your own liquor or a written vendor reference from a unit at the same concentration and fouling duty.

How much fouling allowance should I add?

Size it from the duty, not from habit: 0.00005-0.0001 m² K/W for clarified clean liquor, 0.00015-0.0003 for a crystallizing sulfate liquor, 0.0003-0.0006 for a scale-prone effluent with hardness. Convert it to a dirty U with U = 1/(1/U_clean + R_f) and quote the dirty value in the specification.

Does higher steam temperature always reduce the area?

It reduces area in proportion to the extra ΔT, but it raises the wall temperature, accelerates scaling and can push a crystallizing liquor into a different regime. Going from 120 °C to 140 °C steam adds about 20 K on this duty, cutting area by roughly a third, at the cost of faster fouling and a heavier shell.

Why is my calculated area smaller than the vendor’s?

Usually because the vendor used a dirtier U, a lower effective ΔT or a larger margin than you assumed, and sometimes because the quoted surface includes a spare or a preheater. Ask for the four inputs explicitly: duty, U, effective ΔT and the allowance stack. The difference is always in one of them.

How many tubes does 500 m² need?

At 38 mm OD and 6 m effective length, each tube exposes π × 0.038 × 6 = 0.716 m², so 500 m² needs about 700 tubes. Longer tubes cut the count and the shell diameter but raise pressure drop and the risk of poor distribution in a falling film; 6 m is the usual compromise.

Is an MVR unit smaller than a triple effect for the same duty?

No, it is larger. MVR runs on 8-10 K of effective ΔT against 12-30 K in a multi-effect train, so the same duty needs about 1,500 m² against 1,200 m² for two effects. MVR wins on energy and loses on surface; the decision is an electricity price calculation.

Conclusion

The evaporator heat transfer area for a 20 t/h duty on 120 °C steam closes at 396 m², becomes 501 m² once fouling and design margin are stated honestly, and lands on 700 tubes of 6 m by 38 mm. Every step is arithmetic you can reproduce, and every input is a number you should be able to defend in a design review. The discipline is not in the division; it is in the four inputs, and in refusing to let a fouling allowance and a design margin be the same number counted twice. If you want the arithmetic run against your own brine analysis and steam conditions, send the flowsheet through our quotation request and we will return the sizing with its assumptions exposed. More sizing notes sit in the resources library.

References

• Green, D. W. and Southard, M. Z. (eds.), Perry’s Chemical Engineers’ Handbook, 9th edition, McGraw-Hill. Evaporation and heat transfer sections.
• Smith, J. M., Van Ness, H. C. and Abbott, M. M., Introduction to Chemical Engineering Thermodynamics, McGraw-Hill. Vapor pressure and boiling point elevation of aqueous solutions.
• Kern, D. Q., Process Heat Transfer, McGraw-Hill. Overall coefficients, fouling resistances and temperature difference correction.
• Smith, R., Chemical Engineering Design (Coulson and Richardson’s Chemical Engineering, Volume 6), Butterworth-Heinemann. Evaporator design and multiple-effect calculations.
• McCabe, W. L., Smith, J. C. and Harriott, P., Unit Operations of Chemical Engineering, McGraw-Hill. Evaporation, boiling point elevation and steam economy.
• Weiss, N. L. (ed.), SME Mineral Processing Handbook, Society of Mining Engineers. Evaporation and crystallization in hydrometallurgical circuits.
• TAPPI Press, Pulp and Paper Manufacture series, evaporation and heat transfer volumes. Falling film practice and liquor scaling experience.

Changelog

• 2026-10-31: First publication.