**2. Methodology**

When a system is thermodynamically studied, based on the first principle of thermodynamics, the amount of energy is constant during the transfer or exchange and also, based on the second principle of thermodynamics, the degree of energy is reduced and the potential for producing work is lessened. But none of the mentioned principles are able to determine the exact magnitude of work potential reduction, or in other words, to analyse the energy quality. For an open system which deals with some heat resources, the first and second principles are written as follows (Bejan, 1988):

$$\frac{d\mathbf{E}}{dt} = \sum\_{i=0}^{n} \dot{\mathbf{Q}}\_{i} - \dot{\mathbf{V}} \dot{\mathbf{V}} + \sum\_{in} \dot{m}h^{0} - \sum\_{out} \dot{m}h^{0} \tag{1}$$

$$\dot{S}\_{gen} = \frac{dS}{dt} - \sum\_{i=0}^{n} \frac{\dot{Q}\_i}{T\_i} - \sum\_{in} \dot{m}s + \sum\_{out} \dot{m}s \ge 0 \tag{2}$$

In the above equations, enthalpy, *h* , is <sup>2</sup> <sup>0</sup> *h V gz T* ( /2) , is the surrounding temperature, *E* , internal energy, *S* ,entropy, and *W* and *Q* are the rates of work and heat transfer.

For increasing the work transfer rate ( ) *W* , consider the possibility of changes in design of system. Assumed that all the other interactions that are specified around the system 1 2 ( , ,..., , *QQ Qn* inflows and outflows of enthalpy and entropy) are fixed by design and only *Q*0 floats in order to balance the changes in *<sup>W</sup>* . If we eliminate *Q*<sup>0</sup> from equations (1) and (2), we will have (Bejan, 1988):

$$\dot{W} = -\frac{d}{dt}(E - T\_0 S) + \sum\_{i=0}^{n} \left(1 - \frac{T\_0}{T\_i}\right) \dot{Q}\_i + \sum\_{in} \dot{m} (h^0 - T\_0 s) - \sum\_{out} \dot{m} (h^0 - T\_0 s) - T\_0 \dot{S}\_{gen} \tag{3}$$

When the process is reversible ( 0) *Sgen* , the rate of work transfer will be maximum and therefore we will have:

$$
\dot{\mathcal{W}} = \dot{\mathcal{W}}\_{rev} - T\_0 \dot{\mathcal{S}}\_{gen} \tag{4}
$$

Combination of the two principles results in the conclusion that whenever a system functions irreversibly, the work will be eliminated at a rate relative to the one of the entropy. The eliminated work caused by thermodynamic irreversibility, ( ) *W W rev* is called "the exergy lost". The ratio of the exergy lost to the entropy production, or the ratio of their rates results in the principle of lost work:

$$
\dot{\mathcal{W}}\_{\text{lost}} = T\_0 \dot{\mathcal{S}}\_{\text{gen}} \tag{5}
$$

Since exergy is the useful work which derived from a material or energy flow, the exergy of work transfer, *Ew* , would be given as (Bejan, 1988):

In this paper, the cycle of a power plant and its details, with two kind fuels, natural gas and diesel, have been analysed at its maximum load and the two factors, losses and exergy

When a system is thermodynamically studied, based on the first principle of thermodynamics, the amount of energy is constant during the transfer or exchange and also, based on the second principle of thermodynamics, the degree of energy is reduced and the potential for producing work is lessened. But none of the mentioned principles are able to determine the exact magnitude of work potential reduction, or in other words, to analyse the energy quality. For an open system which deals with some heat resources, the first and

> *i in out dE Q W mh mh dt*

> > *i in out i*

0 0 0 0 0 0 0

(3)

( )1 ( )( )

*i i in out <sup>d</sup> <sup>T</sup> W E TS Q mh T s mh T s TS dt <sup>T</sup>*

When the process is reversible ( 0) *Sgen* , the rate of work transfer will be maximum and

Combination of the two principles results in the conclusion that whenever a system functions irreversibly, the work will be eliminated at a rate relative to the one of the entropy. The eliminated work caused by thermodynamic irreversibility, ( ) *W W rev* is called "the exergy lost". The ratio of the exergy lost to the entropy production, or the ratio of their rates

Since exergy is the useful work which derived from a material or energy flow, the exergy of

0 0

(1)

0

*i gen*

*W W TS rev* <sup>0</sup> *gen* (4)

*W TS lost* <sup>0</sup> *gen* (5)

<sup>0</sup> *h V gz T* ( /2) , is the surrounding temperature,

from equations (1) and

(2)

efficiency which are the basic factors of systems under study have been analysed.

0

0

*dt T*

*<sup>n</sup> <sup>i</sup>*

*dS <sup>Q</sup> <sup>S</sup> ms ms*

*E* , internal energy, *S* ,entropy, and *W* and *Q* are the rates of work and heat transfer. For increasing the work transfer rate ( ) *W* , consider the possibility of changes in design of system. Assumed that all the other interactions that are specified around the system 1 2 ( , ,..., , *QQ Qn* inflows and outflows of enthalpy and entropy) are fixed by design and only

*n i*

second principles are written as follows (Bejan, 1988):

In the above equations, enthalpy, *h* , is <sup>2</sup>

(2), we will have (Bejan, 1988):

results in the principle of lost work:

therefore we will have:

work transfer, *Ew*

*gen*

floats in order to balance the changes in *<sup>W</sup>* . If we eliminate *Q*<sup>0</sup>

0

, would be given as (Bejan, 1988):

*n*

**2. Methodology** 

*Q*0

$$\begin{aligned} \dot{E}\_w = \dot{V}\dot{V} - P\_0 \frac{dV}{dt} = -\frac{d}{dt}(E + P\_0 V - T\_0 S) + \sum\_{i=1}^n \left( \mathbf{1} - \frac{T\_0}{T\_i} \right) \dot{Q}\_{in} \\ + \sum\_{in} \dot{m} \left( h^0 - T\_0 s \right) - \sum\_{out} \dot{m} \left( h^0 - T\_0 s \right) - T\_o \dot{S}\_{gen} \end{aligned} \tag{6}$$

In most of the systems with incoming and outgoing flows which are considered of great importance, there is no atmospheric work, 0 ( ( / )) *P dV dt* and *W* is equal to *Ew* (Bejan, 1988):

$$\begin{aligned} \left(\dot{E}\_w\right)\_{rev} = \dot{W}\_{rev} - P\_0 \frac{dV}{dt} = -\frac{d}{dt}(E + P\_0 V - T\_0 S) + \sum\_{i=1}^n \left(1 - \frac{T\_0}{T\_i}\right) \dot{Q}\_{in} \\ + \sum\_{in} \dot{m} \left(h^0 - T\_0 s\right) - \sum\_{out} \dot{m} \left(h^0 - T\_0 s\right) \end{aligned} \tag{7}$$

The exergy lost, which was previously defined as the difference between the maximum rate of work transfer and rate of the real work transfer, can also be mentioned in another way, namely, the difference between the corresponding parameters and the available work (Figure 1):

$$
\dot{\mathcal{W}}\_{\rm lost} = \left(\dot{E}\_{w}\right)\_{rev} - \dot{E}\_{w} = \left(\dot{E}\_{w}\right)\_{\rm lost} \tag{8}
$$

Fig. 1. Exergy transfer via heat transfer

In equation (6), the exergy transfer caused by heat transfer or simply speaking, the heat transfer exergy will be:

$$
\dot{E}\_Q = \dot{Q} \left( 1 - \frac{T\_0}{T} \right) \tag{9}
$$

Using equation (1), the flow availability will be introduces as:

$$
\hbar \mathbf{b} = \hbar^0 - T\_0 \mathbf{s} \tag{10}
$$

In installation analysis which functions uniformly, the properties do not changes with time and the stagnation exergy term will be zero, in equation (6):

Exergy, the Potential Work 255

The second law emphasizes the fact that two features of the same concept of energy may have completely different exergies. Therefore, any feature of energy is defined by taking into account its own exergy. The efficiency of the second law will be used in calculating the

In order to analyse the above theories, the consequences have been analysed on the Shahid Rajaii power plant in Qazvin of Iran. This power plant has an installed capacity of 1000 MW electrical energy, which consists of four 250 MW steam-cycle units (Rankin cycle with reheating and recycling) and has been working since 1994. The major fuel for the plant is the

The Shahid Rajaii power plant consists of three turbines: high pressure, medium pressure, and low pressure. The 11-stage high pressure turbine has Curtis stage. The number of the stages in the medium pressure turbine is 11 reactionary stages and in the lower pressure, 2×5 reactionary stages. All of the turbines have a common shaft with a speed of 3000 rpm. The boiler is a natural circulation type in which there is a drum with no top. Other properties of the boiler are that the super-heater is three-staged and that the reheater and the economizer are both two-staged. Figure 2 illustrates the plant diagram overlooking the boiler furnace, cooling towers, attachment (circulation and discharge pumps, blowers, etc), turbine glands condenser and regulator lands, expansion valves and governors and feed

In Table 1, properties of water and vapour in the main parts of the cycle have been shown. Maximum losses of cycle water in this plant are 5 kg/hr, which is negligible due to the minute amount. In analyzing the cycle and drawing diagrams, it is assumed that the

With Figure 2, the conversion equation and energy balance of boiler will be written as

Description <sup>2</sup> *P kg cm abs T C*

Feed water incoming to boiler 150 247-202 Vapour incoming to HP turbine 140 838 Vapour incoming to reheater 17-40 358-287 Vapour incoming to IP turbine 15.2-37.3 538 Vapour incoming to LP turbine 8-3.5 320 Vapour incoming to condenser 0.241-0.960 64-45 Water outgoing from condenser pump 16-7 63-44

kinetic and potential energies are neglected because they are not so important

all elements of the cycle are considered to be adiabatic

Table 1. Properties of water and vapour in cycle

in this part, the combustion process of the boiler has been ignored.

, pressure is 90*kPa* and relative humidity is 30% as environmental

12 34 *mm mm* and (19)

reduction of ability in performing a certain amount of work.

natural gas and is augmented with diesel fuel.

**3. Case study** 

water tanks.

temperature is 30 *C*

(Jordan, 1997):

conditions. Other assumptions are:

$$\dot{E}\_{\rm av} = \sum\_{i=0}^{n} \left( \dot{E}\_{\rm Q} \right)\_{i} + \sum\_{in} \dot{m}b - \sum\_{out} \dot{m}b - T\_{0} \dot{S}\_{\rm gen} \tag{11}$$

The flow exergy of any fluid is defined as:

$$e\_x = b - b\_0 = h^0 - h\_0^0 - T\_0 \text{(s} - \text{s}\_0\text{)}\tag{12}$$

Substituting this definition into equation (11), we will have:

$$\dot{E}\_w = \sum\_{i=0}^n \left(\dot{E}\_Q\right)\_i + \sum\_{in} \dot{m} e\_x - \sum\_{out} \dot{m} e\_x - T\_0 \dot{S}\_{gen} \tag{13}$$

The flow exergy ( ) *xe* is the difference between the availabilities of a flow (b), in a specific condition and in the restricted dead state (in balance with the environment). Equation (13) is used to balance the exergy of uniform flow systems. The mechanisms which lead to the production of entropy and the elimination of exergy are listed as follows:

heat transfer caused by limited temperature difference (Bejan, 1988):

$$\dot{S}\_{\text{gen}} = \frac{\dot{Q}}{T\_H T\_L} (T\_H - T\_L) \tag{14}$$

frictional flow (Reistad, 1972):

$$\dot{S}\_{\text{gen}} = \dot{m} \int\_{out}^{in} \left( \frac{v}{T} \right)\_{l=\text{const.}} dp \tag{15}$$

combining (Stepanov, 1955):

$$\frac{1}{\dot{m}\_3} \dot{S}\_{\text{gen}} \equiv \text{x} \left[ \frac{1}{T} (h\_3 - h\_1) - \frac{v}{T} (P\_3 - P\_1) \right] + (1 - \text{x}) \left[ \frac{1}{T} (h\_3 - h\_2) - \frac{v}{T} (P\_3 - P\_2) \right] \tag{16}$$

The efficiency of the second law that determines used exergy is divided into two groups: Elements efficiency (Pump and Turbine) and Cycle efficiency (Thermal efficiency and coefficient of performance). The definition of the efficiency of the second law is (Wark, 1955):

$$\eta\_{ll} = \frac{\text{available} \text{of usefuloutgoing}}{\text{incoming available} \text{hily}} \tag{17}$$

The definition of the efficiency of the second law is more practical for the uniform flow systems, and is determined as follows (Bejan, 1988):

$$
\eta\_{ll} = \frac{\text{outgoing exergy}}{\text{incoming exergy}} \tag{18}
$$

<sup>0</sup>

(11)

0 00 0 ( ) *xe b b h h Ts s* (12)

(13)

(14)

*w Q gen <sup>i</sup> i in out E E mb mb T S*

0 0

<sup>0</sup>

*w Q x x gen <sup>i</sup> i in out E E me me T S*

The flow exergy ( ) *xe* is the difference between the availabilities of a flow (b), in a specific condition and in the restricted dead state (in balance with the environment). Equation (13) is used to balance the exergy of uniform flow systems. The mechanisms which lead to the

> *gen H L H L <sup>Q</sup> S TT T T*

*out h const <sup>v</sup> S m dp <sup>T</sup>* 

*v v S x hh PP x hh PP*

The efficiency of the second law that determines used exergy is divided into two groups: Elements efficiency (Pump and Turbine) and Cycle efficiency (Thermal efficiency and coefficient of performance). The definition of the efficiency of the second law is (Wark,

> availabilityof useful outgoing incoming availability

> > outgoingexergyrate incomingexergyrate

The definition of the efficiency of the second law is more practical for the uniform flow

*mT T T T*

*in*

.

31 31 32 32

(16)

(15)

*II* (17)

*II* (18)

0

0

production of entropy and the elimination of exergy are listed as follows: heat transfer caused by limited temperature difference (Bejan, 1988):

*gen*

1 1 <sup>1</sup> <sup>1</sup> *gen*

systems, and is determined as follows (Bejan, 1988):

*n*

Substituting this definition into equation (11), we will have:

The flow exergy of any fluid is defined as:

frictional flow (Reistad, 1972):

combining (Stepanov, 1955):

3

1955):

*n*

The second law emphasizes the fact that two features of the same concept of energy may have completely different exergies. Therefore, any feature of energy is defined by taking into account its own exergy. The efficiency of the second law will be used in calculating the reduction of ability in performing a certain amount of work.
