Formula
Energy balance on a closed heater with no cascaded drains entering:
\(\dot Q = \dot m_{fw}\,(h_{fw,2} - h_{fw,1}) \qquad \dot m_e = \frac{\dot Q}{h_e - h_d}\)
\(TTD = T_{sat,e} - T_{fw,2} \qquad T_d = T_{fw,1} + DCA \;\;(\text{drain cooler}) \quad\text{or}\quad T_d = T_{sat,e}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(\dot m_{fw}\) | feedwater flow | kg/s |
| \(p_{fw}\) | feedwater absolute pressure | Pa |
| \(T_{fw,1}\) | feedwater inlet temperature | K |
| \(T_{fw,2}\) | feedwater outlet temperature | K |
| \(p_e\) | extraction steam absolute pressure at the heater | Pa |
| \(\text{state}\) | dry saturated, or superheated at \(T_e\) | – |
| \(T_e\) | extraction steam temperature when superheated | K |
| \(\text{drain}\) | saturated drain, or drain cooler with \(DCA\) | – |
| \(DCA\) | drain cooler approach | K |
| \(\dot m_e\) | extraction steam flow | kg/s |
| \(\dot m_e / \dot m_{fw}\) | extraction per kg of feedwater | – |
| \(\dot Q\) | heat duty | W |
| \(T_{sat,e}\) | shell saturation temperature at \(p_e\) | K |
| \(TTD\) | terminal temperature difference | K |
| \(T_d\) | drain temperature | K |
| \(h_{fw,1}\) | feedwater inlet enthalpy | J/kg |
| \(h_{fw,2}\) | feedwater outlet enthalpy | J/kg |
| \(h_e\) | extraction steam enthalpy | J/kg |
| \(h_d\) | drain enthalpy | J/kg |
Method and standards
First-law balance with enthalpies from FireCAD's IAPWS-IF97 implementation; TTD and DCA as defined in the HEI Standards for Closed Feedwater Heaters.
Assumptions and limits
- No drains cascaded in from a higher-pressure heater; for a heater that receives drains, subtract their heat from the duty first.
- No shell heat loss; the drain leaves at the extraction pressure.
- Pressure drop in the extraction line is included by entering the pressure at the heater.
References
- IAPWS R7-97(2012) IF97
- HEI Standards for Closed Feedwater Heaters (terms)
Questions and answers
What are TTD and DCA?
The terminal temperature difference is the shell saturation temperature minus the feedwater outlet temperature. The drain cooler approach is the drain temperature minus the feedwater inlet temperature. Both are design figures of the heater.
How much extraction steam does an HP heater take?
For 60 kg/s of feedwater heated from 200 to 240 °C by steam at 40 bar(a) and 350 °C with a 5.6 K drain cooler approach, about 4.88 kg/s, or 8.1 % of the feedwater.
Can the TTD be negative?
Yes, with a desuperheating zone the feedwater can leave above the shell saturation temperature. The calculator allows it and warns, because it needs enough superheat in the extraction steam.