Reference ID: MET-4964 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
A steam-jet ejector is a static device that uses high-pressure motive steam to create a low-pressure region (vacuum) and simultaneously compress the evacuated gas to a higher, still-sub-atmospheric pressure. The calculation below sizes the ejector by predicting the mass of motive steam required to entrain and compress a given suction load. It is a rapid screening tool for:
vacuum distillation, crystallisation and drying columns;
flash-cooling or solvent recovery systems;
barometric condensers and turbine condenser air-removal sections.
The result flags whether a single-stage ejector is thermodynamically feasible or whether a multi-stage (or booster) arrangement is required.
Methodology & Formulas
Unit consistency
Suction pressure is converted from mbar to bar to match the other pressures:
\[ P_{\text{s}} = \frac{P_{\text{s,mbar}}}{1000} \]
Compression ratio
The ratio of discharge to suction absolute pressures defines the duty:
\[ \text{CR} = \frac{P_{\text{d}}}{P_{\text{s}}} \]
Entrainment ratio
An empirical correlation (valid for 1.2 ≤ CR ≤ 12) gives the mass of gas entrained per mass of motive steam:
\[ \text{ER} = 0.75 - 0.25 \ln(\text{CR}) \]
The required motive steam flow is then:
\[ \dot{m}_{\text{m}} = \frac{\dot{m}_{\text{s}}}{\text{ER}} \]
Stage limit
The highest suction pressure at which a single-stage ejector can operate against the specified discharge pressure is estimated from:
\[ P_{\text{s}}^{*} = 0.18 \; P_{\text{m}}^{0.95} \]
If the actual suction pressure \( P_{\text{s}} \) is below this critical value, a single-stage device is adequate; otherwise a booster or multi-stage system is required.
Correlation limits
Parameter
Lower bound
Upper bound
Compression ratio CR
1.2
12
Motive steam pressure \( P_{\text{m}} \)
3 bar a
15 bar a
Close the vacuum breaker halfway; if suction pressure rises sharply the ejector is already steam-limited.
Install a temporary rotameter in the motive-steam line; if actual flow equals the curve value at design pressure, steam is not the bottleneck.
Measure condenser tail-pipe temperature; >10 °C above cooling-water inlet indicates condenser overload, not ejector limit.
Inject a known air bleed (e.g., 10 kg h⁻¹); if suction pressure climbs >5 mbar the ejector has excess capacity and the load is higher than expected.
Absolute suction pressure (mbar) stays the same, but vacuum gauge reading drops because it is referenced to barometric.
Motive-steam flow decreases ~1 % per 10 mbar above standard (1013 mbar) because the nozzle back-pressure is slightly higher; recheck the curve footnotes.
After-condenser vent pressure rises 17 mbar, so downstream ejector stages must handle a higher suction; increase their load rating by 2 % per 10 mbar.
No correction is needed for critical pressure ratio across the nozzle; the 1030 mbar change is negligible versus the 8–10:1 expansion ratio.
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Worked Example – Sizing a Single-Stage Steam-Jet Ejector for a De-aerator
A small boiler feed-water de-aerator is being designed to operate at 120 mbar absolute. Saturated motive steam at 6 bar(g) is available in the plant. The ejector must handle 80 kg h-1 of non-condensable gas plus associated water vapour and discharge against a back-pressure of 0.2 bar(g). Determine the required motive-steam flow.
Read the ejector performance chart (or correlation) for CR = 1.667 and Pm = 6 bar; the corresponding entrainment ratio is
\[ ER = 0.622 \]
Entrainment ratio relates suction mass flow to motive mass flow:
\[ ER = \frac{m_s}{m_m} \quad\Rightarrow\quad m_m = \frac{m_s}{ER} \]
Insert values (units cancel because ER is dimensionless):
\[ m_m = \frac{80}{0.622} = 128.6\ \text{kg h}^{-1} \]
Check critical pressure at nozzle throat (optional verification):
\[ P_s^* = 0.987\ \text{bar} \quad(\text{calculated from isentropic relations}) \]
Since Ps < Ps*, flow is choked and the above ER is valid.
Final Answer
Required motive-steam flow = 129 kg h-1 (rounded to nearest kilogram).
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
