**3.6 The correction factor of the boiler efficiency**

All the measured data such as temperature, pressure, flow, etc and also the calculated magnitude of the exergy efficiency and losses were assumed under some specific environmental conditions. But the plant is not always under these specific conditions, and in fact there are some conditions under which the efficiency changes. These are divided into two parts: internal conditions such as excess air and moisture content and the external (environmental) conditions such as temperature and humidity.

An increase in the amount of air in the combustion process can easily decrease the adiabatic temperature of the flame so that the adiabatic exergy of the products is reduced and the exergy losses of the combustion increase. On the other hand, the combustion products have a lower temperature and greater mass flow as they flow inside the boiler, which leads to lower exergy losses in the heart transfer process.

The correction factor for the boiler exergy efficiency caused by the internal and external conditions is done using the equation (35). For instance, this factor due to the excess air is:

Exergy, the Potential Work 265

Fig. 7. The diagram of the exergy losses and exergetic efficiency of the different processes

processes of the boiler.

Figure 7 demonstrates the comparison of the exergy losses and efficiencies of the different

The important result is that the exergy losses in the heat transfer process are greater than that in the combustion process. In other words, the heat transfer process is more irreversible. Exergy efficiency, as an evaluating standard for exergy losses, shows that the heat transfer process is more inconvenient than the combustion process. This result is generally true for all the plant boilers. In order to optimize the boilers, engineers should focus on heat transfer processes, optimization of the heat exchangers and increasing their exergy efficiencies. One of the methods to achieve this aim is Pinch which helps us in the exergy analysis and in determining the arrangement of the pipes in order to reduce the irreversibility of the heat transfer. When using diesel fuel, exergy losses in the combustion process are greater than

$$
\Delta \eta\_{\Pi,B} = \frac{\sum\_{out} \dot{m}\_w e\_{x,w} - \sum\_{in} \dot{m}\_w e\_{x,w}}{\dot{m}\_f e\_{x,f} + \dot{m}\_a e\_{x,a} + \dot{V} \dot{V}\_{in,B}} \bigg|\_{EAR}^x \tag{42}
$$

Where EAR (Excess Air Ratio) is the ratio of the excess air to the time of the boiler test.

## **4. Results and discussions**

As is shown in Table 5, the lowest efficiency belongs to the gland condenser which is 28.9%. Its exergy loss at 46 kW is among the least. The highest exergy efficiency belongs to the high pressure and medium pressure turbines, and is 94.95%. In these turbines, 8617 kW of the 616505 kW of incoming exergy disappears and the rest is changed to work. The low pressure turbine has more exergy losses at 15303 kW and its efficiency is 87.47%, which is less than the high pressure turbine. The plant boiler, which is one of the most important elements of the cycle, has one of the lowest exergy efficiencies, 46.94%, which should be optimized.


Table 5. Exergy losses and exergy efficiency of the cycle elements of the plant

In Figure 4, exergy analysis shows that the major part of the exergy losses are because of the internal irreversibility of the boiler, while the chimney losses are less than one thirtieth of the boiler losses. Conversely, energy analysis shows that chimney losses are four times greater than boiler losses (heat transfer of the boiler to the surrounding area) and this is the major cause of efficiency reduction. Therefore, in order to reduce the energy losses, chimney losses are to be decreased, whereas the reduction of the internal exergy losses is more effective in the increase of exergy efficiency.

Figure 4 proves that energy efficiency is not dependent on the fuel type. The difference between the efficiencies of the two different fuels is 0.22% which is very minute. But the exergy efficiencies with two fuels are 3.02% different, based on Figure 4.

As is shown in Table 5, the lowest efficiency belongs to the gland condenser which is 28.9%. Its exergy loss at 46 kW is among the least. The highest exergy efficiency belongs to the high pressure and medium pressure turbines, and is 94.95%. In these turbines, 8617 kW of the 616505 kW of incoming exergy disappears and the rest is changed to work. The low pressure turbine has more exergy losses at 15303 kW and its efficiency is 87.47%, which is less than the high pressure turbine. The plant boiler, which is one of the most important elements of the cycle, has one of the lowest exergy efficiencies, 46.94%, which should be optimized.

Where EAR (Excess Air Ratio) is the ratio of the excess air to the time of the boiler test.

Boiler 371522 46.94 Low Pressure Turbine 15303 87.47 Condenser 12867 60.05 High Pressure Turbine 8617 94.95 Generator 5222 98.06 Feed water pump 2147 60.00 Heater 5 2026 86.04 Heater 6 1563 91.42 Heater 4 1555 85.38 Heater 3 456 88.71 Heater 2 730 81.72 Heater 1 449 81.29 Feed water motor pump 313 94.50 Main drain 120 31.94 Condenser pump 62 64.57 Gland condenser 46 28.90 Condenser motor pump 15 92.00 Total 423013 -

Table 5. Exergy losses and exergy efficiency of the cycle elements of the plant

exergy efficiencies with two fuels are 3.02% different, based on Figure 4.

effective in the increase of exergy efficiency.

In Figure 4, exergy analysis shows that the major part of the exergy losses are because of the internal irreversibility of the boiler, while the chimney losses are less than one thirtieth of the boiler losses. Conversely, energy analysis shows that chimney losses are four times greater than boiler losses (heat transfer of the boiler to the surrounding area) and this is the major cause of efficiency reduction. Therefore, in order to reduce the energy losses, chimney losses are to be decreased, whereas the reduction of the internal exergy losses is more

Figure 4 proves that energy efficiency is not dependent on the fuel type. The difference between the efficiencies of the two different fuels is 0.22% which is very minute. But the

,

*II B*

Cycle elements ( ) *<sup>w</sup> lost*

**4. Results and discussions** 

, ,

*f x f a x a in B EAR*

*x*

(42)

*E kW* (%)

*II*

, ,,

*out wxw wxw in*

*me me me me W*

Figure 7 demonstrates the comparison of the exergy losses and efficiencies of the different processes of the boiler.

The important result is that the exergy losses in the heat transfer process are greater than that in the combustion process. In other words, the heat transfer process is more irreversible. Exergy efficiency, as an evaluating standard for exergy losses, shows that the heat transfer process is more inconvenient than the combustion process. This result is generally true for all the plant boilers. In order to optimize the boilers, engineers should focus on heat transfer processes, optimization of the heat exchangers and increasing their exergy efficiencies. One of the methods to achieve this aim is Pinch which helps us in the exergy analysis and in determining the arrangement of the pipes in order to reduce the irreversibility of the heat transfer. When using diesel fuel, exergy losses in the combustion process are greater than

Exergy, the Potential Work 267

the evaporator. The secondary and the final super-heaters have the highest exergy efficiency (71.67%) when using diesel fuel, with the exergy losses of 27657 kW. The second one is the evaporator using the natural gas, with exergy efficiency of 67.1% and exergy losses of 58800 kW. The reheater has the lowest efficiency using the natural gas (40.99%), with exergy losses of 70933 kW. The evaporator using diesel fuel has the highest exergy loss of 114071 kW and

In Figure 8, as the excess air percentage becomes higher, the exergy losses of the natural gas increase at a lower rate. This reduction in the exergy losses of heat transfer based on the excess air percentage has a higher rate with natural gas than with diesel fuel. Generally, the gradients of exergy losses in the diagrams on combustion are more than in

In Figure 10, as the mass percentage of fuel humidity increases, the exergy efficiency of the

Fig. 10. The diagram of boiler efficiency changes based on the moisture content percentage In Figure 10, humidity in diesel fuel causes more reduction in the boiler efficiency than in the natural gas. According to this Figure, it can be said that moisture content does not have a

According to the Figure 11, we can say that as the relative air humidity percentage becomes higher, the boiler efficiency is reduced and the exergy efficiency reduction rate is more with

considerable effect upon the efficiency.

diesel fuel than the natural gas.

the economizer using diesel fuel has the lowest exergy losses of 7486 kW.

heat transfer.

boiler is reduced.

Fig. 8. The diagram of the internal exergy loss relative to the excess air percentage

In Figure 9, as the excess air percentage increases, the exergy efficiency of the boiler is reduced.

Fig. 9. The diagram of boiler efficiency based on the excess air percentage

when we use natural gas. But his is not the case for heat transfer. It is because the flow of combustion products is more when we use diesel fuel than when we use natural gas. On the other hand, the increase in the flow of combustion products is because of the great amount of incoming air to the furnace which leads to reduced exergy efficiency.In Figure 6, when we use natural gas, the exergy losses are greater in all elements than when we use diesel fuel, except the evaporator. The exergy efficiency, using diesel fuel, is less than when we use natural gas. The main reason behind the difference between the evaporator function and the other elements is that the combustion and heat transfer processes happen simultaneously in

Fig. 8. The diagram of the internal exergy loss relative to the excess air percentage

Fig. 9. The diagram of boiler efficiency based on the excess air percentage

when we use natural gas. But his is not the case for heat transfer. It is because the flow of combustion products is more when we use diesel fuel than when we use natural gas. On the other hand, the increase in the flow of combustion products is because of the great amount of incoming air to the furnace which leads to reduced exergy efficiency.In Figure 6, when we use natural gas, the exergy losses are greater in all elements than when we use diesel fuel, except the evaporator. The exergy efficiency, using diesel fuel, is less than when we use natural gas. The main reason behind the difference between the evaporator function and the other elements is that the combustion and heat transfer processes happen simultaneously in

reduced.

In Figure 9, as the excess air percentage increases, the exergy efficiency of the boiler is

the evaporator. The secondary and the final super-heaters have the highest exergy efficiency (71.67%) when using diesel fuel, with the exergy losses of 27657 kW. The second one is the evaporator using the natural gas, with exergy efficiency of 67.1% and exergy losses of 58800 kW. The reheater has the lowest efficiency using the natural gas (40.99%), with exergy losses of 70933 kW. The evaporator using diesel fuel has the highest exergy loss of 114071 kW and the economizer using diesel fuel has the lowest exergy losses of 7486 kW.

In Figure 8, as the excess air percentage becomes higher, the exergy losses of the natural gas increase at a lower rate. This reduction in the exergy losses of heat transfer based on the excess air percentage has a higher rate with natural gas than with diesel fuel. Generally, the gradients of exergy losses in the diagrams on combustion are more than in heat transfer.

In Figure 10, as the mass percentage of fuel humidity increases, the exergy efficiency of the boiler is reduced.

Fig. 10. The diagram of boiler efficiency changes based on the moisture content percentage

In Figure 10, humidity in diesel fuel causes more reduction in the boiler efficiency than in the natural gas. According to this Figure, it can be said that moisture content does not have a considerable effect upon the efficiency.

According to the Figure 11, we can say that as the relative air humidity percentage becomes higher, the boiler efficiency is reduced and the exergy efficiency reduction rate is more with diesel fuel than the natural gas.

Exergy, the Potential Work 269

The total exergy efficiency of the plant is 36.1% for natural gas and 35.5% for diesel

Among the main elements of the plant cycle, the greatest irreversibility (exergy losses or

 The internal losses of the boiler which includes the heat transfer losses, the combustion losses and the friction losses, are 362899 kW for natural gas and 411127 MW for diesel fuel, and the exergy losses of the chimney, which are caused because of the combustion hot gases exiting it, are 12453 kW for the natural gas and 12668 kW for diesel fuel. The natural gas and diesel fuel, respectively, have chemical exergies of 700182 kW and

 The comparison of the internal losses and the chimney losses shows that the outgoing exergy from the chimney is not considerable. Also, the exergy losses of the boiler are 46.68% for the natural gas and 43.66% for diesel fuel, under the assumed conditions

 Analysing the boiler processes shows that the exergy losses caused by heat transfer (255999 kW for the natural gas and 239302 kW for diesel fuel) are greater than the exergy losses of the combustion (106900 kW for the natural gas and 171835 kW for diesel fuel) and those against the heat transfer process in the combustion process of the

 After proving that the main cause of the exergy losses are the heat transfer has the boiler, the exergy analysis of the boiler elements shows that the reheater has the lowest exergy efficiency (40.99% for the natural gas and 46.6% for diesel fuel) and that the evaporator has the highest exergy losses (85800 kW for the natural gas and 114071 kW for diesel fuel). All these reports show that natural gas is better than diesel fuel in

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Brodianskii, V.M. (1973). Eksergeticheskii Method Termodinamicheskogo Analiza. *Energia,* 

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Gorji-Bandpy, M. and Ebrahimian, V. (2007). Exergy analysis of a steam power plant: a case

Gorji-Bandpy, M.; Goodarzian, H. and Biglari M. (2010). The Cost-effective Analysis of a Gas Power Plant. *Taylor&Francis Group, LLC*, Vol. 5, No. 4, pp. (348-358). Gorji-Bandpy, M.; Yahyazadeh-Jelodar, H. and Khalili, M.T. (2011). Optimization of Heat

Bejan, A. (1988). Advanced Engineering Thermodynamics. *Wiley,* New York.

study in Iran. *Int. J. Exergy*, Vol. 4, No. 1, pp. (54-71).

Exchanger Network. Vol. 31, Issue 5, pp. (770-784).

natural gas are less irreversible than in the diesel fuel combustion.

The exergy analysis of the power plant cycle has shown that

the least exergy efficiency) belongs to the boiler.

producing super heater vapour in the boiler.

*Exergy*, Vol. 2, No. 1, pp. (31-39).

**5. Conclusions** 

747995 kW.

**6. References** 

Moskow. pp. 32.

<sup>0</sup> ( 30 *T C* and 0*P kPa* 90 ).

fuel.

Figure 12 shows that an increase in the air temperature from the assumed temperature of the environment decreases the exergy efficiency, and under the other conditions, decrease or increase of the exergy efficiency is greater with the natural gas. (30 ) *C* 

Fig. 11. The diagram of boiler efficiency changes based on the air relative humidity percentage

Fig. 12. The diagram of boiler efficiency changes based on the air temperature
