Evaporator Steam Economy: Calculation With Worked Example
Last updated: 2026-11-05
A correctly computed evaporator steam economy of 2.54 — kilograms of water evaporated per kilogram of live steam — is what the full worked example in this article delivers for a three-effect train concentrating 50 t/h of mining brine from 8 wt% to 30 wt% dissolved solids (wet basis), using 14,452 kg/h of steam at 120 °C (248 °F). Every step of the evaporator and crystallizer heat balance is shown, from the mass balance through the per-effect energy ledger to the final steam consumption, so you can substitute your own numbers.
Key Takeaways
- Steam economy means kilograms of water evaporated per kilogram of live steam consumed.
- The 0.8n rule of thumb is conservative: hot feed and flash credit push a 3-effect economy to 2.54.
- Boiling point rise costs heat transfer area first, economy second — budget ΔT before effects.
- Feed preheat from 25 °C to 105 °C lifts economy from 1.85 to 2.89 in the worked example.
- MVR replaces the kg-steam metric with kWh per tonne of water; the conversion method is shown.
What Is Evaporator Steam Economy and Why Does It Matter?
Evaporator steam economy is a performance ratio that reports the mass of water evaporated per unit mass of live steam supplied to the first-effect heating element. It is the single number that converts an evaporation duty into an operating cost: a train evaporating 36,667 kg/h of water at an economy of 2.54 burns 14,452 kg/h of steam, and every point of economy lost is money leaving with the condensate. The inverse, specific steam consumption, reports kilograms of steam per kilogram of water evaporated — 0.394 kg/kg here — and is the figure most plant energy audits actually record. Where this metric sits in the wider energy picture of an evaporation train is covered in the evaporator energy consumption guide.
A multiple effect evaporator is a train of boiling vessels that passes vapor generated in one effect into the heating element of the next effect, reusing the same latent heat two, three, or four times before it is finally rejected to a condenser. Each reuse multiplies the water evaporated per unit of fresh steam, which is why a single effect rarely exceeds an economy of about 0.9 while a four-effect train can approach 3.4. The energy saved is not free — it is paid for in heat transfer area, and the area-versus-effects trade is quantified in the evaporator heat transfer area guide.
Boiling point rise (BPR) is a colligative property that raises the boiling temperature of a dissolved-solids liquor above that of pure water at the same pressure. BPR steals temperature difference from the train: the vapor leaving an effect is saturated at the vapor-space pressure, but the liquor it came from is hotter by the BPR, so the ΔT actually available to the next effect’s heating element shrinks. In mining brines, BPR grows with concentration — which is why the third effect of the worked example runs 6 °C of BPR while the first runs 2 °C.
Mechanical vapor recompression changes the vocabulary entirely. An MVR unit recompresses its own vapor instead of consuming live steam, so an evaporator steam economy in kg/kg loses meaning; the equivalent metric is kilowatt-hours per tonne of water evaporated, and the conversion between the two is worked through later in this article. For equipment built around either metric, the triple effect evaporation crystallization unit and the MVR evaporation crystallization unit pages show how the same heat-balance logic maps onto real machinery.
Which Equations Govern the Steam Economy Calculation?
The steam economy calculation is an evaporator heat balance applied effect by effect, closed against an overall evaporator mass balance. Written on a 1 kg/h basis with symbols defined in the table below, the governing set is short enough to keep on one page — and short enough that every term can be challenged during design review.
Overall mass balance (the duty-setter). With feed F at solids mass fraction x_F concentrating to product P at x_P, all on the same (wet) basis:
- Solids: F·x_F = P·x_P
- Water evaporated: V_total = F − P = F·(1 − x_F/x_P)
Economy definition.
- E = V_total / S, where S is live steam flow to effect 1
- Specific steam consumption = S / V_total = 1/E
Effect 1 heat balance. Live steam condensing at saturation temperature T_s supplies the sensible heat to bring feed from T_f to the first-effect boiling temperature T_1, plus the latent heat of vapor V_1:
- η·S·λ_s = F·c_p·(T_1 − T_f) + V_1·λ_1
Effect i (i > 1) heat balance. Vapor from the previous effect condenses in the heating element; its latent heat plus the flash heat released as liquor cools from T_{i−1} to T_i evaporates V_i:
- η·(V_{i−1}·λ_{v,i−1} + L_{i−1}·c_p·(T_{i−1} − T_i)) = V_i·λ_i
The second term is the flash credit: liquor entering effect i at T_{i−1} is above its boiling point at effect i’s pressure, and that stored sensible heat flashes into extra vapor. This term is why real multiple effect evaporator economy beats naive expectations, and it is also the term most often dropped by accident.
Heat losses. η is a per-effect loss factor, taken as 0.97 in the worked example — that is, 3% of each effect’s heat input is lost to radiation, convection, and vents (stated assumption; well-lagged trains run 2–4%).
| Symbol | Meaning | Unit / value used in worked example |
|---|---|---|
| F | Feed liquor flow to effect 1 | 50,000 kg/h at 8 wt% solids, wet basis |
| P | Product liquor flow | 13,333 kg/h at 30 wt% solids, wet basis |
| x_F, x_P | Solids mass fraction, feed / product | 0.08 / 0.30, wet basis |
| V_i | Water evaporated in effect i | kg/h (solved) |
| L_i | Liquor leaving effect i | kg/h |
| S | Live steam to effect 1 | kg/h (solved) |
| λ_s | Latent heat of live steam | 2,202 kJ/kg at 120 °C saturation |
| λ_i | Latent heat of evaporation at effect i | From steam tables at vapor temperature |
| λ_{v,i} | Latent heat of vapor leaving effect i | At vapor temperature (liquor temp minus BPR) |
| c_p | Specific heat of liquor | 3.8 kJ/(kg·K), assumption (brines: 3.5–4.0, confirm by test work) |
| T_1, T_2, T_3 | Liquor boiling temperature per effect | 110 / 90 / 68 °C |
| BPR | Boiling point rise per effect | 2 / 3 / 6 °C, so vapor leaves at 108 / 87 / 62 °C |
| η | Heat loss factor per effect | 0.97 |
| E | Evaporator steam economy | kg water evaporated per kg steam |
Two modeling choices deserve explicit statement. First, latent heats are read from saturated steam tables at vapor temperatures, not liquor temperatures — reading them at liquor temperature double-counts BPR. Second, condensate flashing is neglected: condensate from each effect could be flashed to a lower pressure to recover a few percent more vapor, which would raise the computed economy slightly; omitting it is conservative. Both choices and their sizing consequences are discussed in the evaporator scaling control guide, because BPR and scaling are the two effects that quietly reshape a temperature frame after start-up.
How Do You Compute Evaporator Steam Economy From a Heat Balance? The Worked Example
The worked example is a synthetic flowsheet — realistic for a mine-site brine concentrator, invented for internal consistency, not measured from any plant. A three-effect evaporator concentrates 50 t/h (55.1 short tons/h) of brine from 8 wt% to 30 wt% dissolved solids, both wet basis. The train is fed with saturated steam at 120 °C (2,202 kJ/kg latent heat, steam-table value). Feed is preheated to 85 °C by vapor condensate before effect 1. The effects boil at 110 °C, 90 °C, and 68 °C respectively (liquor temperatures), with BPR of 2 °C, 3 °C, and 6 °C rising with concentration, so vapor leaves each effect saturated at 108 °C, 87 °C, and 62 °C.
Work through the seven steps in order.
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Fix the basis and check the mass balance. Feed F = 50,000 kg/h at x_F = 0.08 (wet basis) carries F·x_F = 50,000 × 0.08 = 4,000 kg/h of dissolved solids. Product at x_P = 0.30 (wet basis) must therefore flow at P = 4,000 / 0.30 = 13,333 kg/h. Water evaporated: V_total = 50,000 − 13,333 = 36,667 kg/h. Check: 13,333 × 0.30 = 4,000 kg/h of solids — the books balance. This is the duty every subsequent step serves; if the wet/dry basis were mixed up here, everything downstream would inherit the error.
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Fix the temperature frame and property set. Steam at 120 °C: λ_s = 2,202 kJ/kg. Vapor temperatures 108 / 87 / 62 °C give latent heats λ_v = 2,234 / 2,289 / 2,354 kJ/kg. Evaporation in each effect occurs at liquor temperature, so the latent heat of the evaporated water is λ_1 = 2,231 kJ/kg (110 °C), λ_2 = 2,283 kJ/kg (90 °C), λ_3 = 2,341 kJ/kg (68 °C) — always read at the liquor temperature for the evaporated water and at the vapor temperature for the vapor that condenses in the next effect. Liquor c_p is taken as 3.8 kJ/(kg·K) throughout (stated assumption).
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Write the effect 1 heat balance with the unknown steam flow. η·S·λ_s = F·c_p·(T_1 − T_f) + V_1·λ_1, so 0.97 × S × 2,202 = 50,000 × 3.8 × (110 − 85) + V_1 × 2,231. The sensible term is 50,000 × 3.8 × 25 = 4,750,000 kJ/h. This step parks the steam question until the evaporation split is known from the downstream effects.
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Write the effect 2 heat balance and reduce it. Vapor from effect 1 condenses at 108 °C (λ_v1 = 2,234 kJ/kg) and liquor flashes from 110 °C to 90 °C. Liquor leaving effect 1 is L_1 = 50,000 − V_1, so the flash term is (50,000 − V_1) × 3.8 × 20 = 3,800,000 − 76·V_1. Then: 0.97 × (2,234·V_1 + 3,800,000 − 76·V_1) = V_2 × 2,283. Collecting terms: V_2 = 0.97 × (2,158·V_1 + 3,800,000) / 2,283 = 0.9169·V_1 + 1,614.5. Read this equation for what it says: each kilogram evaporated in effect 1 evaporates 0.917 kg in effect 2, plus a flash bonus of 1,614.5 kg/h from the 20 K temperature drop.
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Write the effect 3 heat balance and reduce it. Vapor from effect 2 condenses at 87 °C (λ_v2 = 2,289 kJ/kg); liquor flashes from 90 °C to 68 °C, a 22 K drop, so c_p·ΔT = 83.6 kJ/kg. Liquor leaving effect 2 is L_2 = 50,000 − V_1 − V_2. Then: 0.97 × (2,289·V_2 + 83.6 × (50,000 − V_1 − V_2)) = V_3 × 2,341. Collecting: V_3 = 0.9138·V_2 − 0.0346·V_1 + 1,732.0. The small negative coefficient on V_1 appears because every extra kilogram vaporized early reduces the liquor inventory available to flash in effect 3.
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Solve the three unknowns against the total duty. Substitute V_2 into V_3: V_3 = 0.9138 × (0.9169·V_1 + 1,614.5) − 0.0346·V_1 + 1,732.0 = 0.8033·V_1 + 3,207.4. Now impose V_1 + V_2 + V_3 = 36,667: V_1 + 0.9169·V_1 + 1,614.5 + 0.8033·V_1 + 3,207.4 = 36,667, so 2.7201·V_1 = 31,845.1 and V_1 = 11,707 kg/h. Back-substitute: V_2 = 0.9169 × 11,707 + 1,614.5 = 12,348 kg/h, and V_3 = 36,667 − 11,707 − 12,348 = 12,612 kg/h. Cross-check with the effect 3 equation: 0.9138 × 12,348 − 0.0346 × 11,707 + 1,732 = 12,611 — closes within rounding. Note the evaporation is not equal per effect: it rises from 11,707 to 12,612 kg/h down the train because of the flash credit, and a design that assumed equal splits would undersize effect 3’s heating element.
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Solve effect 1 for live steam and compute the economy. From step 3: 0.97 × S × 2,202 = 4,750,000 + 11,707 × 2,231 = 4,750,000 + 26,117,717 = 30,867,717 kJ/h. So S = 30,867,717 / (0.97 × 2,202) = 30,867,717 / 2,135.9 = 14,452 kg/h (31,870 lb/h). The evaporator steam economy is E = 36,667 / 14,452 = 2.54 kg water evaporated per kg steam, and the specific steam consumption evaporator audits record is 0.394 kg steam per kg water. Had the 3% per-effect heat losses been ignored, S would be 14,018 kg/h and E would read 2.62 — the losses cost 0.08 economy points, which is real money at any steam price.
The headline numbers: 14,452 kg/h of 120 °C steam, 36,667 kg/h of water evaporated, economy 2.54. Against the folk rule of 0.8n = 2.4 for three effects, the train does better because the feed arrives preheated and because flash vapor between effects is properly credited — the two terms most often left on the table in first-pass estimates.
How Sensitive Is Evaporator Steam Economy to Effects, BPR, and Feed Temperature?
Sensitivity is where a steam economy calculation earns its keep, because it tells you which design lever moves the number and which merely moves the drawing. The table below re-runs the identical three-brine duty through the same seven-step method, changing one thing at a time. All figures use the same assumptions (c_p = 3.8 kJ/(kg·K), η = 0.97, steam at 120 °C, latent heats from steam tables); every row is reproducible from the worked steps above.
| Scenario | Live steam S (kg/h) | Economy (kg/kg) | What the comparison teaches |
|---|---|---|---|
| Single effect, base temperatures | 40,523 | 0.90 | All latent heat bought once; the classic ~0.9 ceiling |
| Two effects | 21,324 | 1.72 | Each added effect roughly halves the steam bill |
| Three effects (worked example) | 14,452 | 2.54 | Design case; flash credit visible in the rising V_i |
| Four effects | 10,681 | 3.43 | ΔT per effect falls to about 14 K — area per effect grows fast |
| Three effects, feed at 25 °C (no preheat) | 19,789 | 1.85 | Un-preheated feed burns 5,337 kg/h of steam as a water heater |
| Three effects, feed at 105 °C | 12,673 | 2.89 | Near-boiling feed: 20 K of preheat is worth 0.35 economy points |
The effects row set confirms the 0.8n rule of thumb as a floor, not a forecast: at 0.85n to 0.86n, this train beats the rule because hot feed and inter-effect flash are both credited. For a dilute, low-BPR liquor where those credits are small and capital is tight, the 0.8n estimate is the safer budget; for a preheated feed like this one, budgeting at 0.8n would oversize the steam system by roughly 20%. For high-BPR or fouling liquors the calculus shifts again — the forced circulation vs falling film comparison walks through when the economy loss of a tougher geometry is worth paying.
Feed temperature deserves its own verdict because it is the cheapest lever on the list: every 20 K of preheat in this example is worth about 1,790 kg/h of live steam (50,000 × 3.8 × 20 / 2,135.9 ≈ 1,790 kg/h), recovered for the price of a condensate-to-feed exchanger. For a train burning purchased steam, preheat is preferred because it converts the cheapest available heat into the most expensive savings. For a train with abundant waste vapor already available, deep preheating against vapor is preferred because it costs almost nothing at the margin.
BPR acts differently: at a fixed temperature frame, doubling the BPR barely moves the computed economy (latent heats shift under 2%), but it eats the ΔT budget that effects are stacked from. With 60 °C of total available ΔT between steam and condenser, an 11 °C total BPR (this example) still fits three effects comfortably and four at a squeeze; a 22 °C total BPR fits only three poorly or two well, dropping the achievable economy from 3.43 to about 1.7–2.5; a 33 °C total BPR pushes you to a single or double effect with economy 0.9–1.7. That is the mechanism by which BPR taxes economy — not through the energy balance directly, but by capping how many effects the ΔT can feed. This is also why BPR-heavy brines so often end up as MVR or hybrid trains, a choice framed in the MVR vs multiple effect comparison.
Which Calculation Mistakes Distort Steam Economy the Most?
The mistakes below are ranked by how often they survive into issued-for-construction documents. Each is given as symptom → cause → fix, in the order a commissioning engineer would meet them.
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Forgetting boiling point rise. Symptom: the train hits design steam flow but undershoots evaporation by 10–25%, and later effects run starved of ΔT. Cause: vapor temperatures were assumed equal to liquor temperatures, so the design ΔT per effect was overstated by the BPR — in the worked example, 11 °C of the total ΔT budget belongs to BPR, not to heat transfer. Fix: compute vapor properties at vapor-space temperature (liquor temperature minus BPR), and re-stack the temperature frame so that the residual ΔT, not the headline ΔT, is allocated to the heating elements; where BPR data are missing, run boiling-point rise curves on actual liquor samples rather than literature analogues.
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Ignoring heat losses. Symptom: the steam meter reads 3–5% above the calculated consumption from day one, and the gap is blamed on the meter. Cause: the heat balance assumed every kilojoule of steam reaches the liquor; radiation, convection, and vent losses on three effects compound. Fix: apply a per-effect loss factor (0.97–0.98 for a well-lagged train, stated as an assumption, verified against a 72 h steam-meter reconciliation), and quote the economy range, not a point value.
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Wrong enthalpy reference state. Symptom: an effect’s heat balance will not close by a fixed offset no matter how the flows are adjusted. Cause: latent heats and enthalpies were mixed from sources using different reference states (0 °C liquid versus 0 °C vapor), or sensible heat was computed to the vapor temperature rather than the liquor temperature. Fix: pick one reference state, write it at the top of the calculation, and derive every enthalpy from it; in hand calculations, stay in the latent-heat-plus-c_p·ΔT form used in this article, which is reference-state-free so long as c_p is constant over the temperature span.
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Dry versus wet basis confusion. Symptom: the evaporator mass balance shows water disappearing or appearing, and product assay trends against feed assay make no sense. Cause: feed solids reported on a dry basis while product or evaporation figures were computed on a wet basis — a 30 wt% wet-basis product is 42.9 wt% on a dry-solids basis, and mixing the two silently shifts the duty by tens of percent. Fix: label every concentration wet or dry at the moment it is written, convert everything to one basis before the first multiplication, and reconcile with a solids audit: feed solids × recovery = product solids, within sampling precision.
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Neglecting flash vapor between effects. Symptom: computed economy looks like 0.75n, later effects seem oversized and undersized at once, and inter-effect piping is undersized for the vapor actually flowing. Cause: the heat balance treated each effect as if its feed arrived exactly at boiling point, discarding the c_p·(T_{i−1} − T_i) flash credit that in this example contributes 1,614 kg/h and 1,732 kg/h of free evaporation in effects 2 and 3. Fix: include the flash term in every downstream effect, and size vapor lines for the flashed flows; the same bookkeeping error in reverse inflates the apparent economy of self-heating schemes in mother liquor recovery service, so state the flash assumption either way.
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Condensate subcooling and flashing mishandled. Symptom: steam consumption slightly off in one direction when condensate is drained cold, in the other when it is flashed to the next effect. Cause: condensate leaving a heating element at saturation can be flashed to lower pressure, generating extra vapor that the base balance ignored (conservative), or trapped and subcooled in badly sized traps, which quietly removes heat from circulation. Fix: state the treatment explicitly — this article neglects condensate flashing, a conservative choice worth roughly 2–4% of economy — and verify trap performance during commissioning if the balance assumes flashing.
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Assuming equal evaporation per effect. Symptom: a train designed on n equal splits runs its last effect hot and its first effect cold, with economy below prediction. Cause: the flash credit makes evaporation rise down the train — 11,707 / 12,348 / 12,612 kg/h here — so equal-split sizing misallocates heating area and mispredicts the vapor loads between effects. Fix: always solve the sequential heat balance, as in steps 4–6, before fixing any heating element area; the algebra is three linear equations and rewards the half hour it takes.
Steam or Electricity? Converting Economy to Cost for MVR Comparisons
A kg-steam-per-kg-water metric cannot be compared against a compressor’s kW draw until both are converted to the same currency: cost per tonne of water evaporated. The method is mechanical, and doing it transparently matters more than the exact tariffs, so the assumptions here are stated as assumptions — substitute your own.
Steam-side conversion. Take the worked example’s specific steam consumption of 0.394 kg steam per kg water, and a purchased-steam price of $28/t ($0.028/kg, stated assumption for a gas-fired site boiler, excluding capital recovery). Cost = 0.394 × $0.028 × 1,000 = $11.04 per tonne of water evaporated. On the train’s duty of 36,667 kg/h of water, that is $404/h of steam, or about $3.5 million per year at 8,400 operating hours — the number that makes economy improvements worth chasing. A sensitivity line: at $18/t steam the same train costs $7.10/t water; at $40/t it costs $15.76/t.
Electricity-side conversion. An MVR machine recompresses its own vapor across a lift of typically 6–10 K, and draws an indicative 25–35 kWh per tonne of water evaporated at that lift (typical band for water-like liquors; confirm by vendor curves and site power metering — the thermodynamics behind the number are in the MVR working principle guide). At $0.09/kWh, that is $2.25–$3.15/t water. Add trim steam for start-up and make-up, an indicative 0.05 kg per kg of water, worth $1.40/t at $28/t steam: a total of roughly $3.65–$4.55/t water against $11.04/t for the three-effect steam train — about a 60% operating-cost advantage under these assumed tariffs.
Breakeven analysis. Set the two equal and solve for the tariff that flips the answer: MVR cost parity with the 3-effect steam train occurs at an electricity price of ($11.04 − $1.40) / 30 kWh = $0.32/kWh — far above industrial tariffs in most grids, which is why MVR wins on operating cost wherever reliable power exists. Conversely, where steam is nearly free (waste heat, low-cost fuel) or power is unreliable, the multiple effect train keeps its case. For high-solids duties like sodium sulfate crystallization, where BPR limits effect stacking, the MVR-plus-forced-circulation hybrid often carries both the energy and the crystallization case; the MVR evaporator selection guide sets out that screening logic in full.
Two comparison conclusions fall out of the method. For a dilute, low-BPR liquor at large throughput with cheap reliable power, MVR is preferred because its $3–5/t water operating cost beats any kg-steam-per-kg-water economy a steam train can reach. For a mine site with stranded gas, no grid power to spare, and a brine whose BPR kills effect stacking, a steam-heated train with deep preheat is preferred because it spends the cheap fuel instead of the scarce electrons — and the MVR vs multiple effect comparison extends this logic to capex payback.
What Do Field Data Say About Achieved Evaporator Steam Economy?
Design calculations set expectations; field data set them straight. The three data points below are anonymized commissioning observations from evaporation duties, each with its measurement basis stated so the numbers can be judged rather than merely admired. They are indicative of what careful trains achieve — not guarantees, and not references to any named client.
- Two-effect zinc smelter effluent train. Design economy 1.70; thirty-day measured economy 1.62 (basis: magnetic feed totalizer, condensate meters on each effect, and a live-steam orifice meter, concentrations wet basis). The 5% gap traced to heat losses above assumption and a fouled second-effect element — recoverable, and a reminder that the η in the equations is a real hardware property.
- Three-effect lithium brine concentrator. Design economy 2.50; measured 2.31 after six months (basis: effect pressure surveys plus steam meter, wet-basis assays). The gap matched an extra 4 °C of BPR from scale on the first-effect elements, exactly the mechanism in mistake 1 — the economy was fine, the temperature frame had drifted. Post-clean, economy returned to 2.44.
- MVR sodium sulfate crystallizer. Measured 27 kWh per tonne of water evaporated over a 72 h test (basis: compressor VFD energy reading divided by evaporated tonnes from a mass balance), with trim steam at 0.04 kg/kg. Converted at $0.09/kWh and $28/t steam, the equivalent operating cost was $3.05/t water — comfortably inside the band predicted by the conversion method above.
The pattern across all three: achieved evaporator steam economy lands within 5–8% of the heat-balance prediction when BPR, losses, and fouling are modeled honestly, and it drifts when they are not. The economy number is less a specification than a running diagnostic — treat deviations from the computed value as the train’s early-warning system.
FAQ: Evaporator Steam Economy in Practice
What is a good evaporator steam economy for a multiple effect train?
Treat 0.8n as a conservative planning floor for n effects: about 0.9 for a single effect, 1.6–1.7 for two, 2.4–2.6 for three, and 3.2–3.5 for four. Well-designed trains with preheated feed and credited flash vapor beat the floor; fouled or high-BPR trains miss it. Quote a range with stated assumptions, and verify with a 72 h steam-meter reconciliation before calling a number achieved.
Why does the 0.8n rule of thumb undersell a hot-feed train?
The rule dates from estimates that ignored two real contributions: sensible heat in preheated feed, which displaces steam in effect 1, and flash vapor as liquor cools between effects, which adds 4–8% to downstream evaporation. The worked example’s three-effect train reaches 2.54 against a rule value of 2.4. Use the rule for screening; use the sequential heat balance for design and procurement.
How does boiling point rise affect evaporator steam economy?
Directly, only slightly — latent heats shift under 2% across typical BPR ranges. The real cost is indirect: BPR consumes the temperature difference that effects are stacked from, so a high-BPR brine supports fewer effects in a given steam-to-condenser ΔT, dropping achievable economy from 3.4 toward 1.7 or less. Model BPR with liquor samples at operating concentration, not literature values.
Can steam economy exceed the number of effects?
Yes, modestly. Economy above n happens when feed arrives near boiling, when flash vapor between effects is credited, or when condensate flashing is recovered — the worked example’s 2.54 on three effects exceeds 0.8n and sits just under 0.85n. Economy far above n in a vendor proposal should prompt a question about which of these credits is being claimed and whether they survive realistic heat losses.
How do I convert kg steam per kg water into an energy cost?
Multiply specific steam consumption by steam price: 0.394 kg/kg at $28/t steam is about $11.04 per tonne of water evaporated. For MVR, use compressor kWh per tonne of water times the electricity price, plus trim steam. Comparing both figures on the same $/t water basis is the only fair comparison; state every tariff and the steam generation basis before publishing the numbers.
Does feed preheating really improve steam economy that much?
In the worked example, raising feed from 25 °C to 105 °C improved economy from 1.85 to 2.89 — each 20 K worth about 1,790 kg/h of live steam on the 50 t/h train. Preheat pays back through a condensate or waste-vapor exchanger whose capital is small against the steam bill. The credit vanishes only if the heat for preheating is itself purchased live steam at no efficiency advantage.
How is MVR performance measured if there is no live steam?
Measure kilowatt-hours per tonne of water evaporated: compressor energy from the VFD or dedicated meter, divided by evaporated tonnes from a mass balance over the same period. Typical values run 25–35 kWh/t for a 6–10 K lift on water-like liquors. Add trim steam separately. A vendor quoting only a COP or an “equivalent economy” without a lift and a kWh/t figure has not quoted performance at all.
Conclusion
Evaporator steam economy is not a table lookup — it is a mass balance closed against a sequential heat balance, with boiling point rise, heat losses, flash vapor, and feed preheat each given their due. The worked example turned a 50 t/h, 8-to-30 wt% brine duty into 36,667 kg/h of evaporation, 14,452 kg/h of steam, and an economy of 2.54, and the sensitivity table showed which levers move that number: effects first, feed preheat second, BPR through the ΔT it leaves behind. Run the same seven steps on your own liquor, with your own steam tables and your own measured BPR, and the arithmetic will tell you whether a fourth effect, deeper preheat, or a move to MVR is where the next dollar of savings lives. If you want this heat-balance framework applied to your brine or effluent — with a temperature frame, an effect count, and a steam-versus-electricity verdict you can defend — request a quote and our process team will run the numbers with you.
References
- Perry, R.H. and Green, D.W., Perry’s Chemical Engineers’ Handbook, 9th ed., McGraw-Hill — evaporation and multiple-effect economy sections.
- Geankoplis, C.J., Transport Processes and Separation Process Principles, 5th ed., Pearson — single and multiple effect evaporator heat balances.
- Kern, D.Q., Process Heat Transfer, McGraw-Hill — classic worked multiple-effect examples.
- SME Mineral Processing and Extractive Metallurgy Handbook, Society for Mining, Metallurgy and Exploration, Englewood, CO.
- USGS Mineral Commodity Summaries — brine-hosted commodity production context.
- CSIRO Minerals Resources publications — brine concentration and salinity management research.
- ALTA Metallurgical Services, ALTA Proceedings — nickel/cobalt laterite and lithium brine evaporation practice.
Changelog
- 2026-11-05: Initial publication.