Formula
An energy balance on the steam side of the user:
\(\dot m_s = \frac{\dot Q}{\Delta h} \qquad \Delta h = h_s - h_c \qquad h_c = h(p,\; T_{sat} - \Delta T_{sc})\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(\dot Q\) | heat duty delivered by the steam | W |
| \(p\) | absolute steam pressure at the user | Pa |
| \(\text{state}\) | dry saturated, or superheated at \(T_s\) | – |
| \(T_s\) | steam temperature when superheated | K |
| \(\Delta T_{sc}\) | condensate sub-cooling below saturation | K |
| \(\dot m_s\) | steam flow | kg/s |
| \(T_{sat}\) | saturation temperature at \(p\) | K |
| \(h_s\) | steam enthalpy | J/kg |
| \(h_c\) | condensate enthalpy | J/kg |
| \(\Delta h\) | heat given up per kg of steam | J/kg |
Method and standards
Steam and condensate enthalpies from FireCAD's IAPWS-IF97 implementation: region 2 for superheated steam, the saturation line for dry saturated steam, region 1 for the condensate at the steam pressure.
Assumptions and limits
- Steady state; no heat lost from the equipment to the surroundings.
- Condensate leaves at the steam pressure; the sub-cooling is relative to the saturation temperature at that pressure.
- Wet steam (dryness below 1) is not an input; it gives up less heat per kg.
References
- IAPWS R7-97(2012) IF97
Questions and answers
How much steam does 1 MW of heating need?
With dry saturated steam at 8 bar(a) and condensate leaving saturated, each kg gives up 2 047 kJ, so 1 MW needs 0.488 kg/s, about 1 760 kg/h.
Does superheat help?
A little. Superheat adds sensible heat per kg (12 bar(a) at 250 °C gives 2 181 kJ/kg to 10 K sub-cooled condensate), but most users want saturated steam because condensing gives a steady, high heat-transfer coefficient.
Should I add a margin?
The result is the theoretical steam for the stated duty. Add distribution losses, start-up loads and any heat losses from the equipment separately.