Formula
Mass and energy balances on the deaerator, outlet saturated liquid and vent saturated vapour at \(p_d\):
\(\dot m_w + \dot m_s = \dot m_{out} + \dot m_v\)
\(\dot m_w h_w + \dot m_s h_s = \dot m_{out} h_{f,d} + \dot m_v h_{g,d}\)
\(\dot m_s = \frac{\dot m_{out}\,(h_{f,d} - h_w) + \dot m_v\,(h_{g,d} - h_w)}{h_s - h_w}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(\dot m_{out}\) | deaerated feedwater outlet flow | kg/s |
| \(p_d\) | deaerator absolute pressure | Pa |
| \(\dot m_v\) | vent steam flow | kg/s |
| \(T_w\) | mixed inlet water temperature | K |
| \(p_s\) | heating steam absolute pressure | Pa |
| \(\text{state}\) | dry saturated, or superheated at \(T_s\) | – |
| \(T_s\) | heating steam temperature when superheated | K |
| \(\dot m_s\) | heating steam flow | kg/s |
| \(\dot m_w\) | inlet water flow | kg/s |
| \(\dot m_s / \dot m_{out}\) | steam per kg of feedwater | – |
| \(T_d\) | deaerator saturation temperature | K |
| \(h_w\) | inlet water enthalpy | J/kg |
| \(h_s\) | heating steam enthalpy | J/kg |
| \(h_{f,d}\) | saturated liquid enthalpy at \(p_d\) | J/kg |
| \(h_{g,d}\) | saturated vapour enthalpy at \(p_d\) | J/kg |
Method and standards
First-law balance on a direct-contact heater, enthalpies from FireCAD's IAPWS-IF97 implementation. Steam throttled from \(p_s\) to \(p_d\) keeps its enthalpy.
Assumptions and limits
- No heat loss from the deaerator shell.
- Inlet streams (condensate, make-up, flash steam returns) are entered as one mixed water stream; add other steam inputs to the heating steam or work them out separately.
- Outlet water leaves saturated at deaerator pressure.
References
- IAPWS R7-97(2012) IF97
Questions and answers
How much steam does a deaerator use?
For 50 t/h of feedwater at 0.2 bar g (105.1 °C) from water at 80 °C, with dry saturated steam at 3 bar(a), about 0.614 kg/s (2.2 t/h), or 4.4 % of the outlet flow.
Why include the vent?
The vent releases non-condensable gases with a little steam. That steam leaves as saturated vapour at deaerator pressure and must be supplied too; it is often 0.05–0.1 % of the outlet flow.
What if the inlet water is already hot?
If the mixed inlet is at or above the deaerator saturation temperature, no heating steam is needed and the water flashes instead; the calculator stops with a message.