Steam Jet Ejector Design — HEI Standards, Air Leakage & SSC

💨 How a Steam Jet Ejector Works

A steam jet ejector uses high-pressure motive steam to entrain and compress a suction gas (air, non-condensables, or vapour) from a low-pressure vacuum space to a higher discharge pressure. It has no moving parts — making it extremely reliable for continuous industrial vacuum service.

// STEAM JET EJECTOR — CROSS SECTION

The Four Zones

Zone	What Happens	Pressure	Velocity
Nozzle	Motive steam expands — converts pressure energy to kinetic energy	Drops from P_motive to P_suction	Supersonic (Mach >1)
Suction Chamber	High-velocity steam jet entrains suction gas by momentum transfer	P_suction (lowest)	Mixed stream accelerating
Throat	Mixing complete — combined stream at throat velocity	Intermediate	Approximately sonic
Diffuser	Velocity energy converted back to pressure (pressure recovery)	Rises to P_discharge	Decreasing to subsonic

💡

Why steam ejectors for vacuum? No moving parts means no seal leakage, no lubrication, no vibration, and maintenance-free operation for years. They handle wet gas, condensable vapours, and entrained liquid droplets that would destroy mechanical vacuum pumps. Standard choice for surface condenser vacuum systems and evaporator vacuum service.

🔧 Single vs Multi-Stage Ejector Configurations

A single ejector stage can only achieve a limited compression ratio (typically 5–7:1). To reach deep vacuum, multiple stages are used in series, with inter-condensers between stages to remove condensable vapour and reduce the load on downstream stages.

1-Stage

100 – 200 mmHg abs

Simple, lowest cost. Suitable for mild vacuum — evaporator final effects, flash tanks.

2-Stage

25 – 100 mmHg abs

With inter-condenser. Most common for process evaporators and surface condensers.

3-Stage

5 – 25 mmHg abs

Deep vacuum. Sugar, pharmaceutical, petroleum refinery vacuum distillation.

4–5 Stage

0.5 – 5 mmHg abs

Ultra-high vacuum. Vacuum distillation, molecular distillation, freeze drying.

With and Without Inter-Condensers

Configuration	Steam Consumption	Cooling Water	Best Use
Non-condensing (no inter-cond.)	Highest	Not required	Where CW is unavailable or very small systems
With contact inter-condenser	Moderate	Required	Standard design — reduces downstream stage load
With surface inter-condenser	Moderate	Required	Where condensate must be kept clean/separate
Full condensing (after-cond.)	Lowest overall	More CW	Most energy-efficient, preferred when CW is cheap

✅

Design choice: Always use inter-condensers between stages wherever cooling water is available. An inter-condenser after Stage 1 can remove 80–90% of the vapour load before it reaches Stage 2 — dramatically reducing Stage 2 steam consumption and size.

🌬️ Air Leakage Estimation — HEI Standards

The most critical — and most commonly mishandled — step in ejector design is estimating the air leakage into the vacuum system. This is the quantity of non-condensable gas (predominantly air) that leaks into the system through flanges, valve stems, instrument connections, and equipment joints at vacuum conditions.

🚨

Critical warning — Cunningham correlation: The Cunningham correlation (W_air = C × V^0.5, where V is system volume) is widely cited in textbooks but gives air leakage values that are far too low compared to real plant measurements. It was developed for very small, well-sealed laboratory systems. Always use HEI Standards tables for industrial equipment. Using Cunningham on a real plant design leads to an undersized ejector system that cannot maintain the required vacuum.

HEI Air Leakage — Industrial Equipment

The Heat Exchange Institute (HEI) Standards for Steam Jet Vacuum Systems tabulate air leakage based on the type, number, and size of equipment in the vacuum system. Key leakage sources are:

// TYPICAL AIR LEAKAGE CONTRIBUTION BY SOURCE

Flanged joints

Flanges

Small

Valve stems/glands

Valves

Moderate

Pump/agitator seals

Seals

Significant

Large equipment bodies

Equipment

Major

HEI Air Leakage Table (Indicative Values)

Equipment / Source	Leakage (kg/h air)	Remarks
Each flanged joint (well-maintained)	0.01 – 0.05	Good gaskets, proper bolt torque
Each flanged joint (average)	0.05 – 0.15	Typical plant condition
Each valve stem (gate/globe)	0.05 – 0.20	Per valve, both sides
Each pump mechanical seal	0.10 – 0.50	Major leakage source
Surface condenser (per unit)	0.5 – 5.0	Depends on size and tube count
Each agitator seal (double)	0.20 – 1.0	Reactor agitators under vacuum
Evaporator body (per effect)	1.0 – 5.0	Large vessels — major contributor
Inter-condenser / after-condenser	0.5 – 2.0	Shell-side at vacuum

// Total System Air Leakage

W_air(total) = Σ(leakage from each source) × Safety factor

Safety factor = 1.5 to 2.0 for design purposes. Add all equipment leakages from HEI table. Never use a single formula — each piece of equipment contributes differently based on size, number of joints, and seal type.

📊 Steam Specific Consumption (SSC) from Charts

The Steam Specific Consumption (SSC) is the mass of motive steam required per unit mass of gas handled by the ejector. It is read from HEI performance charts as a function of three pressures:

// SSC Definition

SSC = S_motive / W_gas [kg steam / kg gas]

S_motive = motive steam flowrate (kg/h) | W_gas = gas (air + vapour) handled by ejector (kg/h)

Three Pressures That Determine SSC

Pressure Parameter	Symbol	Typical Range	Effect on SSC
Suction pressure	P_s	5 – 300 mmHg abs	Lower P_s → much higher SSC (harder job)
Discharge pressure	P_d	76 – 760 mmHg abs	Higher P_d → higher SSC (more compression)
Motive steam pressure	P_m	3 – 14 bar g	Higher P_m → lower SSC (more energy available)

Compression Ratio — The Key Sizing Parameter

// Compression Ratio per Stage

CR = P_discharge / P_suction

Typical maximum CR per stage = 5 to 7 (for steam ejectors). If required CR exceeds 7, add another stage. Example: P_s = 20 mmHg, P_d = 760 mmHg → CR = 38 → requires 3 stages (7 × 7 = 49 > 38).

Indicative SSC Values (from HEI charts)

Suction Pressure (mmHg abs)	Discharge (mmHg abs)	Motive Steam (bar g)	SSC (kg/kg)
100	760	7	3 – 5
50	760	7	5 – 8
25	760	7	8 – 14
10	760	10	15 – 25
5	760	10	25 – 45

⚠️

Important: The values in the table above are indicative only. For actual design, always use the HEI Standards charts (or vendor performance curves) at your specific suction, discharge, and motive steam pressures. SSC is highly sensitive to all three pressures — small changes in suction pressure at deep vacuum cause large changes in SSC.

♨️ Motive Steam Calculation

Once air leakage (W_air) and SSC are known, the motive steam requirement is calculated directly:

// Total Gas Load on Ejector

W_gas = W_air + W_vapour

W_air = air leakage (kg/h) | W_vapour = condensable vapour in suction gas (kg/h) — calculate from partial pressure of vapour at suction temperature using Dalton's law

// Vapour Load — Dalton's Law

W_vapour / W_air = (p_v × M_v) / (p_air × M_air)

p_v = partial pressure of vapour (mmHg) = P_suction − p_air | M_v = molecular weight of vapour | M_air = 29 g/mol | p_air = partial pressure of air

// Motive Steam to Ejector

S_motive = W_gas × SSC

S_motive = motive steam flowrate to the ejector stage (kg/h) | For multi-stage systems, calculate separately for each stage

Motive Steam Quality Requirements

Parameter	Requirement	Reason
Steam quality	Dry saturated or superheated	Wet steam erodes the nozzle and causes slug flow at throat
Superheat (preferred)	10 – 20°C superheat	Ensures dry steam even with pipe heat losses before nozzle
Steam pressure stability	±5% of design	SSC is sensitive to motive pressure — instability affects vacuum level
Steam cleanliness	No scale or oil carryover	Nozzle throat is very small — any deposits cause rapid performance degradation

❄️ Inter-Condenser Design

An inter-condenser is placed between ejector stages to condense the steam discharged from the first stage before it enters the second stage. This dramatically reduces the gas load on the downstream stage.

Contact vs Surface Inter-Condensers

Type	How It Works	Advantage	Disadvantage
Barometric (contact)	Direct contact between steam and cooling water — water sprayed into steam	Simple, low cost, very effective condensation	Condensate is contaminated with process vapour — cannot recover
Surface (shell-tube)	Steam condenses on tube surfaces cooled by CW — no direct contact	Clean condensate recovery, handles toxic vapours	Higher cost, larger, requires more cooling water

Inter-Condenser Duty Calculation

// Heat Duty of Inter-Condenser

Q_ic = S_stage1 × λ_steam + W_air × Cp_air × ΔT

S_stage1 = motive steam from Stage 1 (kg/h) | λ_steam = latent heat of steam at inter-condenser pressure (kJ/kg) | W_air × Cp × ΔT = sensible cooling of non-condensables (usually small)

// Cooling Water Required

m_cw = Q_ic / (Cp_water × ΔT_cw)

ΔT_cw = cooling water temperature rise (typically 5–10°C) | Cp_water = 4.18 kJ/kg·K

✅

Barometric leg: If a barometric (contact) inter-condenser is used, a barometric leg (sealed water column) of at least 10.3 m height must be provided below the condenser to maintain the pressure differential and prevent back-flooding. This is a common design error — always include the barometric leg in layout planning.

📋 Complete Ejector Design Procedure

1

Define vacuum level required

From process requirements — what absolute pressure must be maintained at the suction equipment? This is your P_suction for Stage 1.
2

Determine number of stages

Calculate required compression ratio (CR = P_atm / P_suction). If CR > 7, use multi-stage. Each stage handles a CR of 5–7. Design stages from discharge end backwards.
3

Estimate air leakage using HEI Standards

List all vacuum equipment — vessels, condensers, pumps, valves. Look up HEI leakage for each. Sum all contributions. Apply safety factor 1.5–2.0.
4

Calculate vapour load (Dalton's Law)

At suction temperature and pressure, find the partial pressure of vapour. Calculate vapour-to-air ratio from molecular weights and partial pressures.
5

Read SSC from HEI charts

At suction pressure, discharge pressure (to inter-condenser or atmosphere), and motive steam pressure — read SSC from HEI/Ludwig charts for each stage.
6

Calculate motive steam for each stage

S_motive = W_gas × SSC for each stage. For downstream stages, W_gas includes only non-condensables (if inter-condensers are fitted) plus motive steam from upstream stage.
7

Design inter-condensers

Calculate heat duty and cooling water required for each inter-condenser. Specify contact or surface type. Ensure barometric leg height if contact type.
8

Sum total motive steam and utilities

Total steam = Σ(S_motive for all stages). Total CW = Σ(cooling water for all inter-condensers + after-condenser). Issue to vendor for detailed nozzle design.

🧮 Worked Example — 2-Stage Ejector for Evaporator

Problem: Design a 2-stage steam jet ejector for a triple effect evaporator. Required vacuum in Effect 3 = 65 mmHg abs (≈ 65°C boiling point for water). Motive steam available at 7 bar g. Cooling water at 30°C available for inter-condenser.

System: One evaporator body (Effect 3), one surface condenser, 8 flanged joints in vacuum system, 2 valve stems, 1 pump seal.

Step 1 — Number of Stages

// CR Required

CR_total = 760 / 65 = 11.7

CR per stage = √11.7 = 3.4 (both stages equal)

2 stages easily handles CR = 11.7 (well within 7 per stage limit). Stage 1: 65 → 222 mmHg. Stage 2: 222 → 760 mmHg (atmosphere).

Step 2 — Air Leakage (HEI)

Source	Count	Leakage/unit (kg/h)	Total (kg/h)
Evaporator body	1	2.5	2.50
Surface condenser	1	1.5	1.50
Flanged joints	8	0.08	0.64
Valve stems	2	0.10	0.20
Pump seal	1	0.25	0.25
Sub-total	—	—	5.09 kg/h
Design value (×1.5 safety factor)	—	—	7.64 kg/h

Step 3 — Vapour Load (Dalton's Law)

// Vapour at 65 mmHg, 65°C (water vapour)

P_vapour(water at 65°C) ≈ 187 mmHg → but P_suction = 65 mmHg

∴ system is below water vapour pressure → mostly water vapour with some air

p_air = 65 − 55 = 10 mmHg (assuming partial pressure of air)

W_vapour/W_air = (55 × 18) / (10 × 29) = 990/290 = 3.41

W_vapour = 3.41 × 7.64 = 26.1 kg/h

W_gas(Stage 1) = 7.64 + 26.1 = 33.7 kg/h

Step 4 — SSC and Motive Steam

Parameter	Stage 1	Stage 2	Unit
Suction pressure	65	222	mmHg abs
Discharge pressure	222	760	mmHg abs
Motive steam pressure	7	7	bar g
SSC (from HEI charts)	6.5	3.5	kg/kg
Gas load (W_gas)	33.7	7.64*	kg/h
Motive steam (S = W_gas × SSC)	219 kg/h	26.7 kg/h	kg/h

*Stage 2 handles only non-condensables (air) after inter-condenser removes water vapour

Step 5 — Total Summary

Parameter	Result	Unit
Vacuum maintained	65 mmHg abs	(≈ 65°C boiling point)
Design air leakage	7.64	kg/h
Stage 1 motive steam	219	kg/h
Stage 2 motive steam	26.7	kg/h
Total motive steam	246 kg/h	kg/h
Inter-condenser duty (approx.)	219 × 2100 kJ/kg ≈ 128 kW	—