Questions: Combined Power Cycles and Cogeneration Analysis

Question 1

A standalone gas turbine plant achieves 38% thermal efficiency and exhausts 550°C flue gas to the atmosphere. An engineer proposes adding a steam Rankine bottoming cycle using this exhaust as its heat source. What thermodynamic principle most directly explains the efficiency improvement?

• A. The additional turbine capacity allows more fuel to be burned at higher temperatures
• B. The HRSG recovers exhaust heat that would otherwise be wasted, extending the effective operating temperature range of the combined system
• C. The Rankine cycle is inherently more efficient than the Brayton cycle at all temperature ranges
• D. Steam cooling in the HRSG reduces gas turbine inlet temperature, lowering heat rejection losses

Answer: (B)

The Brayton cycle rejects heat at elevated temperatures — the 550°C exhaust represents significant thermodynamic work potential being discarded. The combined cycle treats this as a resource rather than waste: the HRSG uses it as the Rankine cycle's heat source. Carnot efficiency is (T_H - T_L)/T_H. The combined cycle's effective T_H is set by the high combustion temperatures of the gas cycle, while T_L is set by the steam condenser near ambient — achieving the full temperature span that neither cycle exploits alone. The improvement is second-law bookkeeping, not additional fuel.

Question 2

A hospital installs a cogeneration (CHP) system achieving 83% utilization factor, compared to 40% thermal efficiency for conventional grid power generation. The hospital previously bought grid electricity and burned gas separately for heating. What is the primary reason CHP achieves higher utilization?

• A. CHP uses a more advanced thermodynamic cycle that converts fuel to electricity more efficiently
• B. CHP captures heat that would otherwise be rejected in the condenser and uses it for building heating, eliminating the need to burn separate fuel
• C. CHP systems always operate at higher turbine inlet temperatures than grid-scale plants
• D. CHP eliminates electrical transmission and distribution losses from the grid

Answer: (B)

The utilization factor is total useful energy (electricity + process heat) divided by fuel input. Conventional power plants condense all steam back to liquid, rejecting the latent heat to the environment — this is the biggest thermodynamic loss in the Rankine cycle. CHP instead extracts some of that steam before or after the turbine and delivers it as useful process heat. The same fuel input that produced electricity also satisfies heating demand that would otherwise require a separate boiler. Utilization factors above 80% are achievable precisely because the 'waste' heat becomes a product.

Question 3

A smaller pinch point temperature difference in an HRSG allows more heat to be recovered from exhaust gas but requires a larger and more expensive heat exchanger.

• T. True
• F. False

Answer: True

The pinch point is the minimum temperature difference between the flue gas and the water-steam streams in the HRSG. Thermodynamics requires the flue gas to always be hotter than the fluid it is heating. A smaller pinch (5–10°C) means the heat exchanger extracts heat from the exhaust down to lower temperatures, recovering more energy — but the smaller driving temperature difference means slower heat transfer per unit area, requiring more heat exchanger surface and therefore higher capital cost. A larger pinch (20–30°C) is cheaper to build but leaves more recoverable heat in the stack exhaust.

Question 4

Combined-cycle plants achieve higher thermal efficiency than standalone gas turbines primarily because they burn fuel more mostly in the combined system.

• T. True
• F. False

Answer: False

Combustion completeness is not the mechanism. Combined-cycle efficiency gains come entirely from thermodynamic heat recovery — the Brayton cycle's exhaust heat is captured and converted to additional work by the Rankine bottoming cycle, rather than being discharged to the atmosphere. The fuel input may actually be similar or even less than running both cycles separately; the point is that the same heat input yields more total work output. The efficiency improvement is a second-law recovery story, not a combustion chemistry story.

Question 5

Explain why a combined-cycle plant achieves higher thermal efficiency than either a standalone Brayton or standalone Rankine cycle, using the concept of operating temperature range.

Model answer: Carnot efficiency scales with the temperature ratio (T_H - T_L)/T_H. A standalone Brayton cycle has a high T_H (combustion temperatures of 1000–1400°C) but rejects heat at elevated temperatures (400–600°C exhaust), narrowing the useful range. A standalone Rankine cycle is limited by its moderate heat source. The combined cycle uses the HRSG to transfer Brayton exhaust heat to the Rankine boiler: T_H is governed by the gas turbine's high combustion temperature while T_L is set by the steam condenser near ambient. This captures the full temperature span — from high combustion temperatures down to near-ambient rejection — that neither cycle achieves independently, yielding 55–62% efficiency versus 35–40% for either cycle alone.

The key insight is that the Brayton and Rankine cycles have complementary temperature ranges. Brayton excels at high temperatures but wastes high-temperature exhaust; Rankine excels at low-to-moderate temperatures but needs a heat source. Cascading them via the HRSG stitches their temperature ranges together into one thermodynamically superior system. The HRSG is not generating any additional heat — it is simply the conduit that prevents the Brayton cycle's exhaust from being wasted.