Formula
Flash vessel (isenthalpic flash of saturated boiler water) and drain cooler:
\(x = \frac{h_{f,b} - h_{f,f}}{h_{g,f} - h_{f,f}} \qquad \dot m_{fs} = x\,B \qquad \dot m_l = (1-x)\,B\)
\(\dot Q_{fs} = \dot m_{fs}\,(h_{g,f} - h_{mu}) \qquad \dot Q_{hx} = \dot m_l\,(h_{f,f} - h_d) \qquad \dot Q_{rec} = \dot Q_{fs} + \dot Q_{hx}\)
\(\dot Q_{bd} = B\,(h_{f,b} - h_{mu}) \qquad \eta_{rec} = \frac{\dot Q_{rec}}{\dot Q_{bd}} \qquad h_{mu,2} = h_{mu} + \frac{\dot Q_{hx}}{\dot m_{mu}}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(B\) | blowdown flow | kg/s |
| \(p_b\) | boiler drum absolute pressure | Pa |
| \(p_f\) | flash vessel absolute pressure | Pa |
| \(T_d\) | drain temperature leaving the cooler | K |
| \(\dot m_{mu}\) | make-up water flow through the cooler | kg/s |
| \(T_{mu}\) | make-up water inlet temperature | K |
| \(p_{mu}\) | make-up water absolute pressure | Pa |
| \(x\) | flash steam fraction | – |
| \(\dot m_{fs}\) | flash steam flow | kg/s |
| \(\dot m_l\) | residual blowdown to the cooler | kg/s |
| \(\dot Q_{fs}\) | heat in the flash steam above make-up temperature | W |
| \(\dot Q_{hx}\) | heat transferred in the drain cooler | W |
| \(\dot Q_{rec}\) | heat recovered | W |
| \(\dot Q_{bd}\) | heat in the blowdown above make-up temperature | W |
| \(\eta_{rec}\) | share of blowdown heat recovered | – |
| \(T_{mu,2}\) | make-up water outlet temperature (from \(h_{mu,2}\)) | K |
| \(T_f\) | flash vessel saturation temperature | K |
| \(h_{f,b}\) | saturated liquid enthalpy at drum pressure | J/kg |
| \(h_{f,f}\) | saturated liquid enthalpy at flash pressure | J/kg |
| \(h_{g,f}\) | saturated vapour enthalpy at flash pressure | J/kg |
| \(h_d\) | drain enthalpy | J/kg |
| \(h_{mu}\) | make-up water inlet enthalpy | J/kg |
Method and standards
Energy balances on the flash vessel and the drain cooler with enthalpies from FireCAD's IAPWS-IF97 implementation. The make-up outlet temperature is found from its pressure and enthalpy (IF97 backward equation, refined on the forward equation).
Assumptions and limits
- Saturated blowdown at drum pressure; equilibrium flash; no carry-over of liquid with the flash steam.
- No heat loss from the vessel or cooler; the cooler is counter-flow when the make-up leaves hotter than the drain.
- The flash steam is used where it condenses at the flash pressure (usually the deaerator).
References
- IAPWS R7-97(2012) IF97
Questions and answers
How much heat can be recovered from blowdown?
With a flash vessel feeding the deaerator and a drain cooler, typically over 90 %. For 2 t/h at 45 bar(a), flashing at 2 bar(a) and cooling the drain to 35 °C against make-up at 30 °C, 545 kW of the 553 kW above make-up temperature is recovered.
Where does the flash steam go?
Usually into the deaerator at the flash vessel pressure, where it condenses and heats the feedwater. Its heat is counted above the make-up water temperature.
Why is the make-up temperature rise small?
The residual blowdown is a small flow cooled across a wide range, while the make-up flow is many times larger, so its temperature rises only a few kelvin.