Questions: Regenerative Heat Recovery and Cycle Efficiency

Question 1

A simple Rankine cycle is modified to add a single open feedwater heater that extracts steam from the turbine at an intermediate pressure. Compared to the original cycle, what happens to the net turbine work, the heat added in the boiler, and the thermal efficiency?

• A. Net turbine work increases, heat input decreases, efficiency increases
• B. Net turbine work decreases, heat input decreases, but efficiency increases because heat input falls proportionally more
• C. Net turbine work decreases, heat input decreases, efficiency decreases because less work is produced
• D. Net turbine work and heat input are unchanged; only the distribution of heat changes

Answer: (B)

Extracting steam partway through the turbine reduces the mass flow through the lower-pressure stages, so those stages produce less work — net turbine work falls. The extracted steam preheats feedwater, so the boiler receives warmer water and needs less fuel to bring it to saturation — heat input falls. Thermal efficiency = W_net / Q_in increases because the fractional reduction in Q_in outweighs the fractional reduction in W_net, provided the extraction fraction is optimized. This is the fundamental trade-off of regeneration: sacrifice some turbine work to save more boiler heat.

Question 2

A power plant engineer claims that adding a 10th feedwater heater will improve efficiency as much as adding the 1st heater did. Is this correct, and why or why not?

• A. Correct — each heater extracts the same amount of heat regardless of how many heaters already exist
• B. Correct — efficiency improvements are additive and each heater contributes equally
• C. Incorrect — the marginal efficiency gain from each additional heater diminishes because successive heaters must operate over smaller and smaller temperature intervals with less heat to recover
• D. Incorrect — adding more than five heaters actually decreases efficiency due to increased entropy generation

Answer: (C)

Adding the first feedwater heater recovers heat over a large temperature interval (cold condensate to near saturation temperature), yielding a large efficiency gain. Each subsequent heater operates over a progressively narrower temperature interval, recovering less heat per unit of extracted steam and yielding a smaller marginal efficiency gain. This is why industrial plants plateau at 5–8 feedwater heaters: beyond that number, the diminishing marginal efficiency gain no longer justifies the capital cost, additional complexity, and reduced reliability. In the limit of infinitely many stages, the efficiency approaches the theoretical maximum for that temperature ratio.

Question 3

Regeneration improves Rankine cycle efficiency by increasing the net work output of the turbine.

• T. True
• F. False

Answer: False

Regeneration actually *reduces* net turbine work — steam extracted for feedwater heating bypasses the lower-pressure turbine stages that would otherwise have produced work. Efficiency improves despite this work reduction because the heat input to the boiler decreases by a proportionally larger amount: the boiler receives preheated water and needs less fuel to bring it to the working temperature. Thermal efficiency η = W_net / Q_in rises because Q_in falls more steeply than W_net. The improvement is about raising the average temperature at which heat is added, not about extracting more work per unit mass.

Question 4

The efficiency gain from regeneration comes from recovering heat internally within the cycle, which reduces the fuel energy that must be added externally to the boiler.

• T. True
• F. False

Answer: True

This is exactly the mechanism. Without regeneration, the boiler must raise cold feedwater all the way from near-condensate temperature to saturation temperature — a large heat addition at relatively low average temperature, which drags down cycle efficiency. Extracted steam from the turbine carries high-enthalpy heat that would otherwise be dumped to the condenser. By using this heat internally to warm the feedwater, the cycle avoids adding it from an external fuel source. Less fuel in for the same (slightly lower) net work out means higher thermal efficiency.

Question 5

Explain why preheating the feedwater before it enters the boiler improves thermal efficiency, even though the extracted steam that does the preheating could have done more work in the turbine if it hadn't been extracted.

Model answer: Thermal efficiency depends on the average temperature at which heat is added from the external source. In a simple Rankine cycle, the boiler must heat cold feedwater from near-condensate temperature to saturation — this low-temperature heat addition reduces the average heat-addition temperature and lowers efficiency. Regeneration replaces some of that low-temperature external heat addition with internal heat transfer from extracted steam: the boiler now receives warmer feedwater and adds heat over a shorter, higher-temperature range. The work lost by extracting steam early is smaller than the efficiency gain from raising the average heat-addition temperature. Equivalently, less fuel is burned for nearly the same output, so the ratio W_net/Q_in rises.

The thermodynamic argument is analogous to making the cycle approximate a Carnot cycle more closely: an ideal Carnot cycle adds all heat at the maximum temperature and rejects all heat at the minimum. Regeneration moves heat addition closer to the turbine inlet temperature by preheating feedwater internally, increasing the average temperature of heat addition without increasing the maximum cycle temperature. Real plants use 5–8 feedwater heaters to approximate this incrementally.