Comparison with Combustion
The maximum theoretical efficiency of a machine for the conversion of chemical combustion energy into power is given by the formula for a reversible Camot process:
p is the fraction of the power w produced by the cycle over the heat of combustion q added to the cycle. TL and TH are the lowest and the highest absolute temperatures of the cycle. The lowest temperature is almost always the ambient (or cooling water) temperature, and hence the formula immediately shows how important the maximum temperature is for the cycle efficiency. A graphical representation of the above formula is given in Figure 7-10.
Figure 7-10. Carnot Efficiency as a Function of Temperature |
Table 7-Ю Theoretical and Practical Efficiencies of Various Power Plant Cycles |
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Temperatures, |
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°С |
Efficiencies, % LHV |
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Actual as |
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Cycle |
Fuel |
T Low |
THigh |
Carnot Actual |
% Carnot |
|
Conventional steam |
||||||
power plant |
Coal |
27 |
540 |
63 |
40 |
63 |
Ditto Ultra supercritical |
Coal |
27 |
650 |
67 |
45 |
67 |
IGCC |
Coal |
27 |
1350 |
82 |
46 |
56 |
Open-gas turbine cycle |
Gas |
27 |
1210 |
80 |
43 |
54 |
Combined cycle |
Gas |
27 |
1350 |
82 |
58 |
71 |
Tophat cycle |
Gas |
27 |
1350 |
82 |
60 |
73 |
Low-speed marine |
Heavy |
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diesel |
fuel oil |
27 |
2000 |
87 |
48 |
55 |
Low-speed marine |
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diesel with |
Heavy |
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supercharger |
fuel oil |
27 |
2000 |
87 |
53 |
61 |
The Carnot efficiency for various cycles are given in Table 7-10, together with some real values.
As can be seen, the potential for any particular cycle as represented by its Carnot efficiency is by no means the only consideration when looking at the merits and limitations of different cycles. The efficiencies offered by gas turbines, which operate with an upper temperature of between 1200 and 1400°C (compared with 500-650°C for steam turbines), are restricted by the fact that the gas turbine itself requires a clean gaseous or liquid fuel, whereas the conventional combustion processes can handle dirty fuels including solids. The diesel engine cycles benefit from the high temperatures (2000°C), but precisely this property contributes to the extremely high NOx emissions connected with this technology.
In summary, the conclusion can be drawn that in the actual processes only 54-73% of the Carnot efficiency is realized. The best results can be obtained in a so-called Tophat cycle that is a single cycle based on a gas turbine, as discussed in Section 7.3.3. The Carnot efficiencies as given in Figure 7-10 for cryogenic cycles have been calculated for a TH of 27°C and a TL of -100 and -200°C. These data are solely given here as they illustrate how energy-intensive cryogenic cycles, as applied in ASUs, are. The negative efficiency of -80% of a cryogenic cycle in an ASU that has a minimum temperature of about -200°C is in absolute terms about equal to a cycle with a maximum temperature of 1200°C. A negative efficiency for cryogenic cycles is caused by the fact that the energy for such cycles constitutes a loss. Before dealing with the pro’s and con’s of various more complex cycles, the basic principles of the steam and gas turbine cycles will be discussed.