Thermodynamics of combined-cycle electric power plants

1 Thermodynamics of combined - cycle electric power )Department of Physics, Reed College, Portland, Oregon 97202(Received 7 October 2011; accepted 27 February 2012)Published data imply an average thermal efficiency of about for electricity generatingplants. With clever use of Thermodynamics and technology, modern gas and steam turbines can becoupled, to effect dramatic efficiency increases. These combined - cycle power plants now reachthermal efficiencies in excess of It is shown how the laws of Thermodynamics make this American Association of Physics Teachers.[ ]I. INTRODUCTIONIt is common in the study of Thermodynamics to examinereversibleheat engine models.

2 One learns that the maximumefficiency of a heat engine operating between colder (Tc) andhotter (Th) constant-temperature reservoirs isgcarnot 1 Tc=Th, that of areversibleCarnot cycle . Of course,there are no such reversible cycles in reality. Indeed, a re-versible cycle must be executed infinitely slowly and, there-fore, would have a power output of zero. This point is oftenoverlooked in modern books1,2take note of the fact that a rela-tively simple irreversible extension of the Carnot cycle ,entailing irreversible energy transfers from the hot and to thecold reservoir, yields an efficiency at maximum power out-put ofgnca 1 Tc=Th 1=2:(1)It is easy to see that3gcarnot=gnca 1 Tc=Th 1=2, fromwhich it follows that for 0<Tc<Th,12gcarnot<gnca<gcarnot:(2)Such irreversible models were investigated first in theengineering literature and then independently in the physicsliterature, and Eq.

3 (1)is sometimes referred to as the Novikov Curzon Ahlborn 7 These modelscan help students understand how one type of irreversibility,namely, energy transfer through finite temperature differen-ces, can lower the efficiencies of heat well-known article by Curzon and Ahlborn4hashelped spawn an entire field of study called finite-time ther-modynamics (FTT). In a recent review article on FTT,Andresen wrote,8 The immediate inspiration for finite-timethermodynamics was the seminal paper by Curzon andAhlborn in which they showed that a Carnot engine withheat resistance to its reservoirs has a maximal power produc-tion, and at that maximum its thermal efficiency can bedescribed by [Eq.]

4 (1)]..This expression has three remark-able features: It is simple and generic; it is amazingly similarto the Carnot efficiency; and it is independent of the magni-tude of the heat Among the many articleswritten about FTT and Eq.(1), a few authors have pointed 12 Interestingly, the efficiencygncaoccurs alsounder maximum work conditions for somereversibleheatengine models operating between fixed lowest and highesttemperaturesTcandTh, fortuitously,gncais a rough guide to the efficien-cies of many existing fossil fuel, nuclear, and geothermalelectric power plants . For example, a plant with combustiontemperature 838 K and ambient temperature 298 K has anactual plant efficiency of ,4which compares reasonablywell withgnca 0:40.

5 In contrast,gcarnot 0:64, consistentwith inequality (2).Electricity is ubiquitous in developed countries. In 2010,the United States used an estimated EJ (41:8 1018J)of primary energy to generate electricity, out of a total pri-mary energy use of 104 ,14 That is, electricity energygeneration accounts for about 40% of annual energyresource use. Electricity is so common that its availability isoften taken for many years, the average electric energy generated atfossil fuel combustion plants has been approximately onethird the concomitant energy released by the fuel. In 2010, Department of Energy data shows a net generation of3:97 1012kWh of electrical energy, with an input of11:6 1012kWh of fuel energy, which implies an efficiencyof by both environmental and economicconsiderations, considerable effort has gone into increasingthe efficiencies of electric generating plants .

6 As more effi-cient plants are added, the average efficiency will continueto recent years, the emergence of so-called combined - cycle plants has offered the opportunity to dramaticallyincrease the electricity-generating plant are now providing nearly 20% of all electric energyworldwide, up from less than 5% about a decade article is directed toward teachers who might like toshow students how straightforward Thermodynamics explainswhy combined - cycle plants can achieve such sharp effi-ciency combined - cycle THERMODYNAMICSA gas turbine cycle is depicted symbolically in , the efficiency of the gas turbine is given byggt _Wgt_Qh;(3)where_Qhis the energy inputratefrom the high-temperaturesource at temperatureTh, and_Wgtis the power output deliv-ered to an electric generator.

7 By energy conservation, therate of energy transfer to the lower-temperature reservoir atthe exhaust temperatureTexis515Am. J. (6), June 2012 American Association of Physics Teachers515_Qex _Qh _Wgt:(4)The gas- turbine cycle is based upon the reversible Joule Brayton cycle , illustrated in 1851, Joule conceivedan air engine using this cycle as a substitute for the George Brayton built a piston-driveninternal combustion engine based upon the same cycle , butits efficiency was too low to be Joule Brayton cycle models not only gas turbine power plants butalso the familiar gas turbines of jet they can burn relatively clean fuel, have relativelylow capital costs, and can be started and stopped quickly.

8 Gasturbines have become popular for electricity peaking andemergency power generation, as well as for base load opera-tions (providing minimum power requirements).16 Stationarygas turbines have the flexibility to burn not only methane butalso distillate oil, which though less clean than natural gas, isoften preferable to coal for power basic operation in compression of air(1 2), providing the high pressure needed to drive the tur-bine. Then combustion of a fuel, typically methane (2 3),increases the temperature and energy of the gas stream. Seg-ment 3 4 represents the combustion gases expanding as theydrive the rotating turbine , and 4 1 cools and exhausts the hotgases at constant atmospheric pressure, thereby dumping wasted energy to the environment.

9 Advances in metallurgyand cooling technology during recent years have enabledever higher combustion and exhaust gas turbines with ultra-high combustion tempera-tures have efficiencies of about , roughly the same as themost advanced coal-burning plants . However, they not onlyhave the advantage of much higher inlet temperatures thansteam turbines but also characteristically have the disadvant-age of much higher exhaust temperatures,T4 Texin , a gas turbine cycle can dump substantial amounts ofwasted energy to the environment, which limits its effi-ciency. For high-efficiency operation, one generally wants ahigh inlet (maximum)

10 Temperature, which gas turbines have,but also a low exhaust temperature, near that of the environ-ment, which gas turbines cites various sources of irreversibility that plague gasturbines and explains how clever engineering designs, entail-ing regenerative heat exchangers, reheaters, and intercoolers,can bring higher , even greater effi-ciency gains are possible for electricity generation by using thehigh-temperature exhaust of the gas turbine to power a steamcycle, which inherently has a much lower exhaust example, a gas turbine with inlet and exhaust temperatures1673 K and 873 K, respectively, might use the exhaust gases toheat a steam turbine that has exit temperature 350 K, achievingthe overall temperature range, 1673 K!