MVR Compressor Power: Calculation With Worked Example

Last updated: 2026-11-08

MVR compressor power scales with the temperature lift you demand from the vapor: compressing 5 t/h of water vapor across a 15 K lift needs roughly 195 kW of electrical input, or about 39 kWh per tonne evaporated. This page walks through the full calculation — boiling point elevation, compression ratio, efficiency — inside our broader guide to evaporation and crystallization.

Key Takeaways

• Compressor power follows from the temperature lift: boiling point elevation plus heat-transfer ΔT set the pressure ratio.
• The worked example: 5 t/h of vapor, 15 K lift, 1.85 compression ratio, about 195 kW electrical draw.
• Compute with steam-table enthalpies and a declared 75% isentropic efficiency; cross-check with gas-law head.
• Single-stage centrifugal machines serve lifts to about 20–25 K; beyond that choose two-stage or hybrid TVR.
• Size the condenser for fouled, not clean, surfaces — fouling quietly inflates lift and power over the campaign.

What Is MVR Compressor Power? Working Definitions

Six definitions anchor the arithmetic on this page.

Mechanical vapor recompression (MVR) is a heat-pump arrangement that recompresses the water vapor evaporated from a liquor and returns it to the heating side of the same evaporator, so the latent heat is reused rather than dumped to cooling water; the compressor is the only place where external energy enters the loop, and the cycle logic is on our MVR working principle page.

MVR compressor power is the electrical power that the drive draws to raise the vapor from evaporator pressure to condensing pressure — the number on the motor feeder and on the electricity bill.

Temperature lift is the temperature span that the compressor must bridge between vapor leaving the boiling liquor and vapor condensing on the heating side, quoted on the pure-water saturation scale.

Boiling point elevation (BPE) is the temperature increment that dissolved solutes add to a solution’s boiling point above that of pure water at the same pressure — a property of the liquor, and the most commonly mishandled input in the calculation.

Compression ratio is the ratio of absolute discharge to absolute suction pressure that fixes the head and mechanical duty of the machine.

Isentropic efficiency is the ratio of ideal, frictionless compression work to the work a real machine consumes; MVR machines typically land at 70–80% (typical range, confirm with vendor test data).

This is easy to estimate in advance because the working fluid is pure water vapor, fully characterized by steam tables: the calculation closes within a few percent before any vendor quote arrives.

What Determines the Temperature Lift? BPE and Heat-Transfer ΔT

The lift is decided by the liquor and the heat exchanger, not by the compressor. Three contributions stack on the same axis:

1. Boiling point elevation. A liquor boiling with 8 K of BPE produces vapor whose saturation temperature sits 8 K below the solution temperature; the condensing side must stay hot enough to boil that liquor, so the BPE is paid inside the lift. Saturated sodium salts show 2–8 K; sulfate liquors and near-saturated brines can run 10–20 K (typical range, confirm with your liquor’s boiling-point curve).
2. Heat-transfer driving force. Vapor condenses on the heating side above the solution’s boiling point; that ΔT pushes heat through the tubes or plates. A clean design works at 4–8 K; a fouled end-of-campaign surface may need 8–15 K. The area arithmetic is on our evaporator heat transfer area page.
3. Superheat in and out. Vapor leaving a boiling solution is superheated by roughly its BPE, and the compressor adds 20–50 K of discharge superheat — neither changes the pressure lift, but both change the condenser area.

The first two contributions sum to the total lift: condensing temperature minus vapor-space saturation temperature. Table 1 collects the parameters and ranges we use at feasibility stage.

Read the table as an interaction: a low vapor temperature for a heat-sensitive liquor raises the compression ratio at the same lift, and so does a higher condensing temperature. Every degree of BPE and fouling allowance lands on the compressor shaft.

How Do You Calculate MVR Compressor Power? A Seven-Step Method

The seven steps below produce MVR compressor power from first principles, using only steam tables and two declared efficiencies.

1. Fix the suction state. Establish the vapor-space saturation temperature T_v and its pressure P_evap from the steam tables. BPE does not change the vapor’s saturation state; it tells you the suction arrives superheated by roughly BPE.
2. Fix the discharge pressure. Set the condensing temperature T_cond = T_v + ΔT_BPE + ΔT_HT and read P_cond from the steam tables. Compute the compression ratio r = P_cond / P_evap on absolute pressures.
3. Find the isentropic enthalpy rise. Take suction entropy s₁ and enthalpy h₁ from the saturated-vapor line. Follow s₁ at constant entropy to P_cond and read h₂ₛ; then Δhₛ = h₂ₛ − h₁. A gas-law cross-check, Δhₛ ≈ [κ/(κ−1)] × R × T₁ × [r^((κ−1)/κ) − 1] with κ ≈ 1.32 and R = 0.4615 kJ/(kg·K) for steam, should agree within 5–10%.
4. Compute the ideal power. P_ideal = ṁ × Δhₛ / 3,600, with ṁ in kg/h and Δhₛ in kJ/kg; the result is in kW.
5. Apply compressor efficiency. P_shaft = P_ideal / η_comp, with η_comp typically 0.70–0.80. Declare the value you use; it is the strongest lever in the estimate.
6. Apply drive losses. P_elec = P_shaft / η_motor (typically 0.94–0.96); subtract a further 3–5% for a VFD running continuously at part load. Compact form: P = ṁ × Δhₛ / (3,600 × η_comp × η_motor).
7. Cross-check and select. Verify the energy balance against the steam saved (heat-balance check below), then match the compression ratio and volume flow to a machine class.

Two habits make step 5 honest: quote isentropic efficiency consistently (polytropic, common in gas-compressor datasheets, reads 2–3 points higher at these ratios), and remember that a lightly loaded machine drifts below its best-point efficiency — a unit sized 50% oversize will not deliver the datasheet 75%.

Worked Example: 5 t/h Vapor From 70 °C Boiling to 85 °C Condensing

The example below is synthetic — representative, arithmetically clean figures, not drawn from any specific plant or quotation. The liquor is dilute, so BPE is negligible and 70 °C is treated as the vapor-space saturation temperature.

Step 1 — Suction state. Steam tables (values rounded): saturated vapor at 70 °C has P_evap = 31.2 kPa abs, h₁ = 2,627 kJ/kg, s₁ = 7.755 kJ/(kg·K), and latent heat h_fg ≈ 2,330 kJ/kg.

Step 2 — Discharge pressure. Condensing at 85 °C gives P_cond = 57.8 kPa abs. The compression ratio is r = 57.8 / 31.2 = 1.85.

Step 3 — Isentropic rise. At 57.8 kPa, saturated-vapor entropy is about 7.55 kJ/(kg·K), below s₁ = 7.755, so the discharge state isentropic is slightly superheated: solving s = 7.755 at 57.8 kPa gives ~40 K of superheat and h₂ₛ ≈ 2,727 kJ/kg. Therefore Δhₛ = 2,727 − 2,627 = 100 kJ/kg. Gas-law cross-check: ≈ 4.125 × 0.4615 × 343 × (1.85^0.242 − 1) ≈ 105 kJ/kg, within 5% — use 100 kJ/kg.

Step 4 — Ideal power. ṁ = 5,000 kg/h, so P_ideal = 5,000 × 100 / 3,600 = 138.9 kW.

Step 5 — Shaft power. With a declared isentropic efficiency η_comp = 0.75 (mid-range for a single-stage centrifugal at r ≈ 1.85): P_shaft = 138.9 / 0.75 = 185.2 kW.

Step 6 — Electrical power. With η_motor = 0.95: P_elec = 185.2 / 0.95 = 195.0 kW. The compact formula reproduces it: P = 5,000 × 100 / (3,600 × 0.75 × 0.95) = 195.0 kW. The MVR compressor power for this duty is therefore 195 kW, or 195 / 5 = 39.0 kW per tonne of water evaporated.

Step 7 — Heat-balance cross-check. The unit saves 5,000 kg/h of live steam worth 5,000 × 2,330 ≈ 11,650 MJ/h of latent heat; the electric input is 195 kW × 3.6 MJ/kWh = 702 MJ/h. Energy-equivalent steam at 2,330 kJ/kg is 702,000 / 2,330 ≈ 305 kg/h, so each kilowatt-hour returns 11,650 / 702 ≈ 16.6 kg of steam — consistent with published MVR practice at modest lifts (see our evaporator steam economy figures).

What the example excludes: the ~40 K discharge superheat must be desuperheated (vapor quench or extra condenser surface); the fouling margin is embedded in the 85 °C condensing choice; and VFD losses are not counted — add 3–5% for one, plus gland, bearing, and wear margins for a quotation-grade number.

How Sensitive Is Compressor Power to the Temperature Lift?

The lift enters through the compression ratio as a power law, so small temperature decisions have large power consequences. Table 2 holds the evaporator at 70 °C (31.2 kPa abs), applies the same enthalpy method and efficiencies, and rounds the steam-table inputs; all values are synthetic and indicative.

Power per tonne roughly triples between a 10 K and a 30 K lift, so area bought to narrow the ΔT is repaid in compressor capital and kilowatt-hours. The same lift costs slightly less power at higher absolute pressure, so a thermally sensitive liquor forced to run cold pays a premium. And the per-tonne figures are linear in flow: 5 t/h to 50 t/h scales 195 kW to about 1,950 kW.

Fan, Single-Stage, or Two-Stage: Matching the Machine to the Lift

The compression ratio from Table 2 maps directly onto machine classes; choosing the wrong class shows up as an oversized motor or a machine that cannot reach condensing pressure on fouled surfaces.

Fans and low-ratio machines serve lifts up to roughly 6–8 K, at ratios below about 1.25 — large-volume, low-head units for duties with near-zero BPE and generous heat-transfer design.

Single-stage centrifugal compressors cover lifts of roughly 10–25 K, ratios up to about 2.5–2.7 for water vapor. This is the workhorse class for brine and salt liquors at moderate concentration: one high-speed impeller (typically 8,000–20,000 rpm, vendor-specific) with a VFD for turndown. A well-behaved machine modulates to roughly 40–60% of design flow by speed alone before surge controls engage (indicative, confirm with the vendor’s surge map).

Two-stage centrifugal machines take over beyond roughly 20–25 K of lift, where ratios approach or exceed 2.7: splitting the compression halves the per-stage head, allows interstage desuperheating, and keeps each impeller inside its structural limits — at the price of capital, footprint, and another set of seals.

Hybrid TVR arrangements place a steam ejector beside or ahead of the compressor when live steam is cheap and the lift is high — see MVR vs TVR. For most salt and sulfate duties in the 10–20 K window, a single-stage machine in the worked example’s efficiency band is the default; unit-level integration options are on our MVR evaporator selection page.

Seven Calculation Mistakes That Distort the Power Estimate

These seven errors account for most of the failed compressor estimates we review.

1. Using BPE wrongly. The classic version: adding BPE to the vapor pressure, or reading suction pressure as the liquor’s saturation pressure instead of the vapor’s. BPE is a temperature effect — the vapor is pure water at the vapor-space pressure — so its cost appears as lift and suction superheat. Getting it backwards moves the estimate by tens of percent.
2. Using gauge pressures for the compression ratio. At evaporator conditions the absolute pressure is tens of kilopascals while gauge readings are strongly negative; a gauge-based ratio is meaningless. Every pressure in steps 1–3 must be absolute.
3. Forgetting superheat desuperheating. Discharge superheat of 20–50 K does not disappear: without vapor quench or oversized condenser surface, real condensing pressure climbs and the compressor rides toward its discharge-temperature trip — the estimate was right, the plant still disappoints.
4. Ignoring non-condensables. Air drawn through flanges and seals accumulates on the condensing side and, by Dalton’s law, forces total condenser pressure above the water-vapor partial pressure the design assumed. Lift silently grows while the compressor takes the blame — size the vents for realistic in-leakage and vent continuously.
5. Mixing isentropic and polytropic efficiency. Datasheets quoting polytropic efficiency read 2–3 points higher at MVR ratios; mixing them distorts power by roughly 3–5%, which compounds with optimistic fouling assumptions.
6. Double-counting or forgetting drive losses. Some estimates apply motor efficiency twice; others forget the VFD’s 3–5% continuous loss. Pick one consistent chain — ideal → shaft → electrical — and state it.
7. Sizing the heat-transfer area clean. A condenser designed at 4 K ΔT with no fouling margin will demand 8–10 K within months on scaling liquors; since lift enters power as a power law, that growth can raise power 40% or more over the campaign. Design for fouled surfaces from day one.

What Does MVR Compressor Power Cost per Tonne Evaporated?

Translating the calculation into money needs declared price assumptions; all prices below are synthetic-indicative. Basis: per tonne of water evaporated, electricity at $0.08/kWh, plant steam at $25/t, operating costs only — no capital, labor, or fixed charges.

The MVR path. The worked example delivers 39 kWh per tonne evaporated, so the power cost is 39 × 0.08 ≈ $3.12 per tonne of water; across the Table 2 window, the same basis runs from $2.20 at 10 K to $6.70 at 30 K. A wider framing is on our evaporator energy consumption page.

The steam path. A triple-effect evaporator evaporates roughly 2.5–3 kg of water per kilogram of live steam, so a tonne of water costs about 0.33–0.40 t of steam, or $8.25–10.00 — a $5–7 per-tonne spread in MVR’s favor, before boiler fuel handling, water treatment, and condensate-return losses worsen the steam path further.

The crossover logic. Cheap site steam narrows or reverses the gap; expensive grid power widens it. Screening rule: MVR wins when the site steam price exceeds roughly three times the power price per unit heat — the effect-count comparison is on our MVR vs multiple effect page. Either way, this page’s calculation fixes the kilowatt-hours per tonne before prices are applied, which is what makes the comparison defensible.

Synthetic Mini-Case: Concentrating a Lithium Sulfate Liquor

The case below is synthetic, built to show how BPE changes a real duty: concentrate a lithium sulfate liquor, evaporating 8 t/h of water in an MVR evaporation crystallization unit — a duty type common in the lithium industries we serve.

The liquor shows 8 K of BPE at operating concentration (assumed, to be confirmed by boiling-point curve measurement). To protect crystallization behavior, the evaporator runs with its vapor space at 62 °C saturation (P_evap ≈ 22 kPa abs, steam tables rounded); the solution itself boils at about 70 °C. Fouled-design heat-transfer economics set the condensing side at 82 °C (P_cond ≈ 50.5 kPa abs). Total lift is 20 K on the pure-water scale, with a compression ratio of 50.5 / 22 ≈ 2.3 — two-stage-or-rugged-single-stage territory.

From Table 2’s 20 K row, the electrical power is about 55 kW per t/h of vapor, giving 8 × 55 ≈ 443 kW of draw (≈ 55 kWh per tonne evaporated; synthetic estimate at η_comp = 0.75, η_motor = 0.95). The vapor arrives superheated by its 8 K BPE; the discharge carries another 35–40 K for the condenser or an interstage quench to remove. Motor selection: a 500 kW frame with VFD. The steam-equivalent check — 8 t/h of live steam replaced for 443 kW — puts specific economy at roughly 15 kg of steam per kWh at this deeper lift. The point is the bookkeeping: the 8 K of BPE moved both the lift and the superheat, and neither appears in a calculation that ignores the liquor.

Frequently Asked Questions

Is MVR compressor power the same as the motor nameplate rating?

MVR compressor power is the calculated electrical demand at the drive terminals — ideal compression work divided by compressor and motor efficiency. Nameplate rating is a standard frame size chosen above it. The worked example needs 195 kW, typically served by a 200–250 kW motor frame with VFD margin (indicative). Quote the calculated figure in energy comparisons and the frame size in procurement documents.

How much electrical power does MVR need per tonne of water evaporated?

For lifts of 10–30 K, the enthalpy method with 75% isentropic efficiency gives roughly 27–84 kWh per tonne evaporated, about 39 kWh per tonne at a 15 K lift (synthetic estimates, Table 2). The figure scales linearly with flow at fixed lift and rises steeply with boiling point elevation, since every kelvin of solute effect widens the compression ratio.

What compression ratio is typical for water vapor MVR?

Most duties fall between 1.3 and 3.0 on absolute pressures. A 70 °C evaporator condensing at 85 °C compresses from 31.2 to 57.8 kPa abs, a ratio of 1.85 — comfortably single-stage. Ratios beyond about 2.7 (lifts beyond roughly 25 K) generally require a two-stage machine with interstage desuperheating. Always compute the ratio from steam-table saturation pressures at your actual temperatures.

Why does a two-stage compressor become necessary above roughly 25 K of lift?

Above that lift the compression ratio for water vapor approaches 2.7 or more. A single impeller reaching that head needs high tip speed, which drives discharge temperature, mechanical stress, and efficiency loss toward limits. Splitting into two stages halves each stage’s head, permits interstage desuperheating, and restores margin — at the cost of capital, footprint, and additional seals. The lift calculation, not vendor preference, says when the single-stage machine has run out of headroom.

How does boiling point elevation change the calculation?

BPE widens the gap the compressor must bridge: the condensing side must stay hot enough to boil the liquor, so T_cond rises by roughly the BPE while the vapor-space saturation temperature does not. An 8 K BPE adds about 8 K of pure lift plus matching suction superheat. The vapor itself remains pure water at the vapor-space pressure — a common error is treating the vapor as if it carried the solute effects.

Does the compressor consume the evaporation energy, or add to it?

Both, in a useful way. The compressor’s 195 kW in the example enters the vapor as enthalpy, mostly as discharge superheat, and that energy is recovered in the condenser as part of the heating duty. Nothing is wasted to cooling water in normal operation — which is why the system returns roughly 16.6 kg of steam-equivalent per kilowatt-hour at modest lifts. The electricity is the pump that recirculates the latent heat.

When is TVR a better choice than MVR?

Thermovapor recompression wins when site steam is cheap and the lift is high enough to make a mechanical machine’s capital hard to justify. An ejector costs far less than a compressor train and has no rotating parts, but its economy is fixed by steam pressure and entrainment ratio, and it needs continuous live-steam supply. Choose MVR when power is the cheaper energy source and operation is steady; choose TVR when surplus steam exists and the duty is intermittent or lift-heavy.

Conclusion

MVR compressor power is not a vendor secret — it is a seven-step calculation any process engineer can close from steam tables and two declared efficiencies. The worked example shows the whole chain: a 5 t/h vapor duty compressed across a 15 K lift at a 1.85 compression ratio consumes about 195 kW of electricity, or 39 kWh per tonne evaporated, replacing roughly 16.6 kg of steam per kilowatt-hour. The sensitivities matter more than the point value: every kelvin of boiling point elevation and every kelvin of fouling allowance lands on the compressor shaft, and the machine class — fan, single-stage, or two-stage — follows from the compression ratio you compute, not from a datasheet’s best line. If you are sizing a mechanical vapor recompression duty or auditing a quotation, send us your evaporation rate, liquor analysis, and boiling-point curve through our request-a-quote form, and our process team will return a lift and power estimate you can check line by line.

References

1. Perry, R.H. and Green, D.W., Perry’s Chemical Engineers’ Handbook, 9th edition, McGraw-Hill — sections on evaporation equipment, vapor recompression, and compressor fundamentals.
2. Wagner, W. and Kretzschmar, H.-J., International Steam Tables Based on the Industrial Formulation IAPWS-IF97, Springer — thermodynamic properties of water and steam.
3. ASHRAE Handbook — Fundamentals, chapter on thermodynamics and refrigerant cycles, thermodynamic property tables for water.
4. Society for Mining, Metallurgy & Exploration (SME), SME Mineral Processing and Extractive Metallurgy Handbook — chapters on evaporation, crystallization, and brine concentration.
5. Bloch, H.P., A Practical Guide to Compressor Technology, 2nd edition, Wiley — centrifugal compressor selection, polytropic and isentropic head, surge behavior.
6. Peer-reviewed chemical engineering literature on mechanical vapor recompression performance in brine and liquor concentration — cited as general industry literature, no public URL.

Changelog

• 2026-11-08: First published.