Rankine cycle with regeneration
Regeneration bleeds some steam out of the turbine part-way through the expansion and uses it to preheat the feedwater. The bleed gives up its latent heat to the feedwater instead of to the condenser, so less heat is thrown away at the cold end — and the mean temperature of heat addition rises without raising the boiler pressure at all.
| Quantity | Value | Note |
|---|---|---|
| Boiler pressure | 10.0 bar | as entered |
| Extraction pressure | 1.00 bar | near the optimum |
| Condenser pressure | 0.10 bar | as entered |
| h₁ turbine inlet | 2777 kJ/kg | saturated vapour |
| h₂ at extraction | 2445 kJ/kg | after the first expansion |
| h₃ at condenser | 2011 kJ/kg | after the second |
| Condensate enthalpy | 340.5 kJ/kg | at the condenser pressure |
| Feedwater enthalpy | 418 kJ/kg | saturated liquid at the extraction pressure |
| Bleed fraction | 10.02% | from the heater balance |
| Turbine work | 722 kJ/kg | high pressure plus the remainder |
| Net work | 721 kJ/kg | less two pumps |
| Efficiency | 30.6% | simple cycle 27.7% |
Extracting 10.0% of the flow at 1.0 bar raises efficiency by 2.9 points. The optimum bleed pressure is near the geometric mean of the boiler and condenser pressures, about 1.0 bar — this one is close.
y = (h_fw − h_f)/(h₂ − h_f) · Heater energy balance.
w = (h₁ − h₂) + (1−y)(h₂ − h₃) · The bleed skips the low stages.
√(P_boiler × P_condenser) · Geometric mean.
(w − Σ pumps)/q_in · Two pumps, weighted by flow.
A clear path from inputs to results.
Regeneration bleeds some steam out of the turbine part-way through the expansion and uses it to preheat the feedwater. The bleed gives up its latent heat to the feedwater instead of to the condenser, so less heat is thrown away at the cold end.
How to use
- Set the boiler and condenser pressures.
- Choose the extraction pressure.
- Enter the turbine and pump efficiencies.
- Read the bleed fraction and the efficiency gain.
The formula
Reference: Energy balance on an open feedwater heater, with saturated properties from IAPWS-IF97.
Worked example
10 bar boiler, extraction at 1 bar
- Boiler 10 bar, extraction 1 bar, condenser 0.1 bar.
- Turbine 85%, pump 80%.
- 1
The expansion to 1 bar gives 2,592 kJ/kg at the extraction point.
- 2
The feedwater has to be heated from 192 to 417 kJ/kg.
- 3
The bleed fraction is (417 − 192)/(2,592 − 192) = 15.4%.
- 4
The remaining 84.6% continues to the condenser.
- 5
Efficiency rises from 27.7% to 29.6%, about two points, from a single heater.
15.4% bled · 29.6% · +2.0 points.
Interpreting the result
The optimum extraction pressure is the geometric mean of the boiler and condenser pressures, and the curve around it is fairly flat. A real plant uses five to seven heaters at different pressures and gains eight to twelve points — which is why regeneration, not reheat, is the larger of the two improvements.
Assumptions & limitations
- One open feedwater heater.
- Saturated vapour extracted, heater reaching saturation at the extraction pressure.
- Two pumps, weighted by the mass flow through each.
- No pressure loss in the heater or the extraction line.
Frequently asked questions
Why does bleeding steam help?
Because the bled steam condenses at the extraction pressure and gives its latent heat to the feedwater, raising the temperature at which heat enters the boiler — and the mean temperature of heat addition is what sets the efficiency.
Why is the optimum at the geometric mean?
Because the benefit falls as the extraction pressure drops and the work penalty rises; the two cross near the geometric mean of the boiler and condenser pressures.
Does regeneration work with reheat?
Yes, and the two are used together: the reheat raises the top temperature and the regeneration raises the average, which is why a modern plant reaches 45%.
What does it cost?
The bled fraction never reaches the low-pressure stages, so turbine work falls. The gain comes because the heat saved in the boiler is larger than the work lost.
How many heaters does a real plant use?
Five to seven, in a train of closed heaters plus a deaerator, each at a different pressure. The total gain is 8–12 points rather than the two a single heater gives.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.