*3.2. Exergetic E*ffi*ciencies*

Exergy-based performance analysis is the performance study of a system based on the second law of thermodynamics, which overcomes the limitations of studying the system based on the first law of thermodynamics. Exergy is a measure of the maximum useful work of a system as it proceeds to a specified final state in equilibrium with its surroundings (dead state). Exergy is destroyed in the system, not conserved as energy is.

Two different approaches are generally used to calculate the exergy efficiency of a system, one is called "brute force", while the other is called "functional" [16].

The brute force form of exergy efficiency is used in this paper. The brute force form requires accuracy and an explicit definition of each input and output exergy term before calculating the exergy efficiency as shown in Table 2. The input exergy terms of the ISCC represent the chemical exergy of the fuel and the exergy associated with the solar thermal energy input.

**Table 2.** Definitions of the exergy destruction and second law efficiency.


So, the second law efficiency (η*II*) (exergetic efficiency) is given by

.

$$
\eta \mu \mathbf{u} = \frac{\text{Exergy output}}{\text{Exergy input}} \tag{8}
$$

The net exergy transfer by heat ( *Xheat*) at the source temperature (*Ts*) and dead state temperature (*T*0) is given by

$$
\dot{X}\_{\text{heat}} = \sum (1 - \frac{T\_0}{T\_s}) \dot{Q}\_s \tag{9}
$$

and the specific exergy (Ψ) is given by

$$\Psi = (h - h\_0) - T\_0(s - s\_0) \tag{10}$$

where *h*, *h*0, *s*, and *s*0 are the specific enthalpy, the specific enthalpy under the dead state condition, the specific entropy, and the specific entropy under the dead state condition, respectively.

Then, the total exergy rate associated with a fluid stream ( *X*) at the mass flow rate ( .*m*) becomes

$$
\dot{X} = \dot{m} \ast \Psi = \dot{m} [(h - h\_0) - T\_0(s - s\_0)].\tag{11}
$$

.

The exergy destruction rate in the ISCC as a whole ( *IISCC*) was obtained from

.

$$\dot{I}\_{\rm ISCC} = \dot{I}\_{\rm compressor} + \dot{I}\_{\rm CC} + \dot{I}\_{\rm GT} + \dot{I}\_{\rm SF} + \dot{I}\_{\rm SFHere} + \dot{I}\_{\rm condenser} + \dot{I}\_{\rm CP} + \dot{I}\_{\rm FWP} + \dot{I}\_{\rm ST} + \dot{I}\_{\rm HRSG}.\tag{12}$$

.

#### 3.2.1. The Exergetic Efficiency of the Solar Field

The solar heat input from the HTF ( *QHTF*) to the water in the solar field heat exchanger is given by

.

$$
\dot{Q}\_{\rm HTF} = \dot{m}\_{23} (h\_{23} - h\_{24}),
\tag{13}
$$

$$
\dot{Q}\_{\text{water}} = \dot{m}\_{17} (h\_{18} - h\_{17}).\tag{14}
$$

The exergy destruction rate in the solar field ( *ISF*) is calculated from

$$
\dot{I}\_{\rm SF} = \dot{X}\_{\rm SF,in} - \dot{X}\_{\rm SF,gain} \tag{15}
$$

$$
\dot{X}\_{SF\_{\text{Qmin}}} = \dot{X}\_{23} - \dot{X}\_{24} \tag{16}
$$

$$
\dot{X}\_{\text{SF,in}} = \dot{Q}\_{\text{inc}} [1 - \left(\frac{T\_0}{T\_{\text{sum}}}\right)] \tag{17}
$$

where *Tsun* is the sun temperature, which equals 5777 K. The exergetic efficiency of the solar field (η*II*,*SF*) is given by .

$$
\eta\_{II,SF} = \frac{\dot{X}\_{SF,\text{gain}}}{\dot{X}\_{SF,\text{in}}}.\tag{18}
$$

#### 3.2.2. The Exergetic Efficiency of the ISCC

The fuel chemical exergy per unit time ( *Xf uel*) equals

$$
\dot{X}\_{fuel} = \zeta \ast \dot{Q}\_{fuel} \tag{19}
$$

where ζ is the ratio of the chemical exergy to the net calorific value, which equals 1.04 for natural gas [23].

.

The exergetic efficiency of the ISCC (η*II*,*Cycle*) is given as

$$
\eta\_{II, \text{Cycle}} = \frac{\dot{W}\_{\text{clcc,ISCC}}}{\dot{X}\_{I \text{SCC,in}}},
\tag{20}
$$

$$
\dot{X}\_{I\text{SCC},in} = \dot{X}\_{\text{SF},in} + \dot{X}\_{f\text{ref}}.\tag{21}
$$

#### **4. Results and Discussion**

The performance of the ISCC power plant was analyzed under different design conditions. The analyses were performed for different solar field thermal outputs (0 MW, 50 MW, and 75 MW) and different ambient temperatures (5, 20, and 35 ◦C). All calculations were made based on design condition data.

The energy efficiency (first law efficiency) and the exergetic efficiency (second law efficiency) were calculated based on the heat input to the plant by the fuel and the sun.

#### *4.1. The Overall Thermal E*ffi*ciency of the ISCC Power Plant*

The overall thermal efficiency of the ISCC power plant in Kureimat at different ambient temperatures for solar heat inputs of 0 MW, 50 MW, and 75 MW is shown in Figure 2.

**Figure 2.** The overall thermal efficiency of the power plant at different ambient temperatures for different solar heat inputs.

The overall thermal efficiency of the power plant at different ambient temperatures for solar heat input equal to 0 MW, which represents the combined cycle regime, is shown in Figure 2. At no solar heat input (combined cycle regime), the thermal efficiency of the plant was reduced from 51.14% at ambient temperature 5 ◦C to 48.67% at 35 ◦C.

Figure 2 shows that the overall thermal efficiency of the ISCC decreases with increasing ambient temperature at different solar heat inputs (0, 50, 75 MW), and that appears most distinctly at ambient temperature 35 ◦C. This may be due to the direct effect of the ambient temperature increase on the efficiency of the condenser and the gas turbine: the condenser and gas turbine efficiency decreases with increasing ambient temperature.

The overall thermal efficiency of the ISCC is lower than the overall thermal efficiency of the plant in the combined cycle regime in all cases (different solar heat inputs and ambient temperatures). Figure 2 shows that the integration of the solar field with the combined cycle (i.e., ISCC) reduced the thermal efficiency of the power plant at all ambient temperatures. This may be because the target of the ISCC is not to increase the overall thermal efficiency of the Brayton cycle, like the combined cycle, but to increase the economic feasibility of the solar power plants. Elimination of the thermal storage system reduces the cost of the power plant [24–26].

#### *4.2. Exergy Destruction in Each Component of the ISCC as a Percentage of the Total Exergy Destruction in the Whole ISCC*

The exergy destruction in each component of the ISCC and the exergy destruction in the whole ISCC were calculated for different solar heat inputs and ambient temperatures 5 ◦C, 20 ◦C, and 35 ◦C.

The percentages of exergy destruction in each component of the ISCC out of the total exergy destruction of the power plant at different ambient temperatures for solar heat inputs 0 MW, 50 MW, and 75 MW are shown in Figures 3–5, respectively.

**Figure 3.** Percentage of exergy destruction in each component of the ISCC out of the total exergy destruction of the plant at different ambient temperatures for solar heat input equal to 0 MW.

**Figure 4.** Percentage of exergy destruction in each component of the ISCC out of the total exergy destruction of the plant at different ambient temperatures for solar heat input equal to 50 MW.

**Figure 5.** Percentage of exergy destruction in each component of the ISCC out of the total exergy destruction of the plant at different ambient temperatures for solar heat input equal to 75 MW.

It is revealed in Figure 3 that the combustion chamber (CC) has the highest percentage of exergy destruction, and this value is higher in the combined cycle regime than in the ISCC regime. This may ensure that the solar field has high irreversibility weight, which affects the percentage of exergy destruction in the combustion chamber compared to its value in the combined cycle regime.

However, Figure 3 shows that the exergy destruction in the combustion chamber decreases slightly with the increase of the ambient temperature under the combined cycle regime (0 MW solar heat input).

It can be observed from Figures 4 and 5 that the exergy destruction in the combustion chamber decreases significantly with the increase of the ambient temperature in the case of ISCC. This may account for the weight of exergy destruction in the solar field. Also, the exergy destruction in the solar field increases with increasing ambient temperature, in contrast to the exergy destruction in the combustion chamber.

Figures 3–5 show that the combustion chamber and the solar field have the highest exergy destruction among all the subsystems. This is valid for all cases of solar heat input. It was also revealed from the values at different ambient temperatures that the exergy destruction of the solar field decreases with increasing solar thermal input.

#### *4.3. The Exergetic E*ffi*ciency of the Main Components of the ISCC*

The exergetic efficiency of different components of the ISCC at different ambient temperatures for solar heat inputs 0 MW, 75 MW, and 50 MW is shown in Figures 6–8, respectively.

Figure 6 depicts the exergetic efficiency of different components of the ISCC at different ambient temperatures in the absence of the solar field (solar heat input equal to 0 MW), i.e., under the combined cycle regime. Under the combined cycle regime, the condenser has the lowest exergetic efficiency except at ambient temperature 5 ◦C. That may be due to the decrease in the low-temperature reservoir which increases the heat dissipated to the condenser cooling water.

**Figure 6.** Exergetic efficiency of different components of the ISCC at different ambient temperatures for solar heat input equal to 0 MW.

The exergetic efficiency of the solar field decreased from 31.3% to 14.5% when the ambient temperature increased from 5 ◦C to 35 ◦C, as shown in Figure 7. The condenser exergetic efficiency also decreased from 75.5% to 19.3% when the ambient temperature increased from 5 ◦C to 35 ◦C for solar heat input equal to 50 MW. This may be due to the decrease in the temperature difference between the exhausted steam from the low-pressure turbine and the cooling water from the cooling tower.

**Figure 7.** Exergetic efficiency of different components of the ISCC at different ambient temperatures for solar heat input equal to 50 MW.

Figure 8 shows that the exergetic efficiency of the solar field decreased from 47% to 21.7% when the ambient temperature increased from 5 ◦C to 35 ◦C. The condenser exergetic efficiency also decreased from 65.8% to 19.3% when the ambient temperature increased from 5 ◦C to 35 ◦C for solar heat input equal to 75 MW.

**Figure 8.** Exergetic efficiency of different components of the ISCC at different ambient temperatures for solar heat input equal to 75 MW.

As shown in Figures 6–8, the exergetic efficiency of the HRSG decreased with increasing ambient temperature, and this may be due to the existence of the attemperators in the HRSG which limit the steam temperature to the setpoint value. In the HRSG installed in the Kureimat power plant, attemperators were installed at the surface of the superheaters to control the temperature at the inlet of the high-pressure steam turbine. These attemperators use water directly from the main feedwater pump of the power plant. An increase in the ambient temperature may lead to an increase in the flue gas temperature of exhaust from the gas turbine into the HRSG, and the attemperators limit the effect of this temperature increase on the temperature of the superheated steam going into the steam turbine using water directly from the main feedwater pump. This may be a reason for the decreasing exergetic efficiency of the HRSG with increasing ambient temperature as shown in Figures 6–8.

Unlike the thermal efficiency [27], the exergetic efficiency of the solar field explicitly decreased with increasing ambient temperature, as shown in Figures 7 and 8. This may be due to the increase of the exergy destruction in the solar field with increasing ambient temperature, as shown in Figures 4 and 5.

#### *4.4. The Exergetic E*ffi*ciency of the ISCC Power Plant*

The exergetic efficiency of the ISCC power plant was calculated for different solar heat power inputs. The comparison was implemented at three different ambient temperatures: 5, 20, and 35 ◦C.

The ISCC power plant exergetic efficiency for solar heat inputs 0 MW, 50 MW, and 75 MW at different ambient temperatures is depicted in Figure 9. The exergetic efficiency of the ISCC power plant was calculated based on the design condition data for the different solar heat power inputs.

Figure 9 reveals that the exergetic efficiency of the ISCC power plant is inversely proportional to the ambient temperature, where it decreased from 47.2% to 46% with increasing ambient temperature from 5 ◦C to 35 ◦C for solar heat input equal to 75 MW. In addition, it decreased from 48.2% to 46.58% when the ambient temperature increased from 5 ◦C to 35 ◦C for solar heat input equal to 50 MW.

Figure 9 also illustrates the exergetic efficiency of the combined cycle regime (solar heat input equal to 0 MW) at different ambient temperatures. In the absence of the solar field, the exergetic efficiency of the plant reached 49.18% and 47.21% at ambient temperatures 5 ◦C and 35 ◦C, respectively. This demonstrates that the exergetic efficiency of the ISCC power plant in Kureimat has higher efficiency under the combined cycle regime than under the ISCC regime, as shown in Figure 9. This may be due to the existence of the solar field, which needs precise design optimization of solar energy integration in a CCPP.

Like the overall thermal efficiency, the exergetic efficiency of the ISCC power plant decreased with increasing ambient temperature, mainly at ambient temperature 35 ◦C. This may be due to the sharp decrease in the exergetic efficiency of the condenser and the solar field with increasing ambient temperature, as shown in Figures 6–8. These figures also show that the exergetic efficiency of the gas turbine and the HRSG decreased with increasing ambient temperature, and that also affected the exergetic efficiency of the ISCC power plant, as shown in Figure 9.

**Figure 9.** ISCC power plant exergetic efficiency at different ambient temperatures for different solar heat inputs.

#### *4.5. Investigating the Sources of Exergy Destruction*

From the attained results, it is clear that the amount of exergy destruction in the various components of the ISCC is altered. This variation is assumed to be due to different reasons such as the type of device, the process, etc.

Moreover, the results showed that the combustion chamber and the solar field represent the sites of highest exergy destruction in the ISCC. In this section, an attempt is made to explore and clarify the sources of exergy destruction in the solar field and the combustion chamber to identify the possibility of enhancing the performance of these components.

#### 4.5.1. Irreversibility in the Solar Field

The exergy destruction in the solar field is due to heat transfer between the sun and the absorber, heat transfer between the absorber and the HTF, and the friction of the viscous HTF. The exergy loss is due to the optical efficiency (the ratio of sunlight capture to incident sunlight) and the heat transfer to the surroundings.

The solar collector is considered to be the main source of exergy destruction in the solar field due to the high temperature difference in the collector. The major contribution to the exergy destruction in the solar collector is due to the heat transfer between the sun and the absorber, while the major exergy loss occurs due to optical errors [28].

It was reported that exergy destruction due to heat transfer between the sun and the absorber accounts for 35% to 40% of the total exergy destroyed. Exergy losses to the surroundings account for 5% to 10% of the total exergy destroyed [28].

It is thought that to decrease the exergy losses from the solar collector (i.e., increase the collector energetic efficiency), attention should be pointed toward improving the optical parameters of the collector (such as mirror reflectivity, transmissivity of the glass envelope, absorptivity of the heat collection element selective coating, focal length of the collectors etc.).

Regarding the exergy destruction due to heat transfer, improving that part may involve grea<sup>t</sup> challenges because of the existence of the finite temperature di fferences which are essential for the heat transfer process and cannot be avoided.

#### 4.5.2. Irreversibility in the Combustion Chamber

The combustion process is complex. Thus, the entropy generation during the combustion process is rather high due to the complexity of that process. It was reported that oxidation of fuel during the combustion process utilizes around 1/3 of the usable fuel energy [29]. This feature of the combustion process causes it to have the highest exergy destruction. The combustion process includes di ffusion, chemical reaction, heat transfer, friction, and mixing. To implement all of these subprocesses, a considerable amount of the available energy is consumed. Most of this energy is unreachable (combustion activation energy, mixing, and di ffusion).

There are three major physicochemical subprocesses responsible for entropy production during the combustion process [29]:


These processes cause exergy consumption (destruction) and thus result in a reduction in the system exergy. On one hand, all these processes destroy up to 40% of the useful exergy of the fuel. On the other hand, it was found that the dominant process of exergy destruction is the internal thermal energy exchange process. It was found that more than 2/3 of the exergy destruction in the combustion process occurs at the internal thermal exergy exchange process, while fuel oxidation is responsible for up to 30% of the exergy destruction, and the exergy destruction due to the mixing process is about 3% of the total exergy destruction of the combustion process [29].

The thermodynamically irreversible combustion process is path-dependent. To ge<sup>t</sup> a quantitative solution for the total entropy production during the combustion process, correct information of the sequence of the combustion process and reactions must be o ffered.

Many factors a ffect the exergy destruction in the combustion chamber. For example, the exergy destruction decreases with decreasing excess air and increasing preheating temperature. Mixing at a large temperature di fference leads to high exergy destruction [30]. Also, the exergy destruction of the combustion chamber is a ffected by the molecular structure of the fuel, where the exergy destruction of the combustion chamber increases with the increase of the hydrocarbon chain length [31].

An attempt was made to avoid this heat transfer by introducing the concept of reversible combustion, where it was proposed theoretically to preheat the reactants to the equilibrium temperature and partial pressures without a reaction, but it could not be achieved in practice [29].

The major exergy destruction in the combustion chamber occurs during the phase of the internal thermal energy exchange between the system particles [29]. The unavoidability of the internal thermal energy exchange makes reducing the exergy destruction during the combustion process very di fficult.
