Comparison of exergy and advanced exergy analysis in three different organic rankine cycles

: Three types of organic Rankine cycles (ORCs): basic ORC (BORC), ORC with single regeneration (SRORC) and ORC with double regeneration (DRORC) under the same heat source have been simulated in this study. In the following, the energy and exergy analysis and the advanced exergy analysis of these three cycles have been performed and compared. With a conventional exergy analysis, researchers can just evaluate the performance of components separately to ﬁnd the one with the highest amount of exergy destruction. Advanced analysis divides the exergy destruction rate into unavoidable and avoidable, as well as endogenous and exogenous, parts. This helps designers ﬁnd more data about the e ﬀ ect of each component on other components and the real potential of each component to improve its e ﬃ ciency. The results of the advanced exergy analysis illustrate that regenerative ORCs have high potential for reducing irreversibilities compared with BORC. Total exergy destruction rates of 4.13 kW (47%) and 5.25 kW (45%) happen in avoidable / endogenous parts for SRORC and DRORC, respectively. Additionally, from an advanced exergy analysis viewpoint, the priority of improvement for system components is given to turbines, evaporators, condensers and feed-water heaters, respectively.


Introduction
Energy is known to be one of the most important elements in the development of any society. In recent years, many researchers have conducted many studies to discover ways to reduce energy consumption in different sections. Studies on industries have shown that a great amount of waste heat is generated during various processes that are placed in low-temperature ranges. This waste heat, which is released to the ambience directly, in many cases, causes a lot of problems for the environment, such as thermal pollution, ozone depletion, air pollution and so on [1]. There are some suggestions to use low-temperature waste heats, but recovering by organic Rankine cycles (ORCs) to produce power is offered as one of the best ways to increase process efficiency [2][3][4]. In the last two decades, different systems of ORCs have been studied widely by researchers, and their focus are more on working fluids of cycles and optimizing performance conditions [5][6][7][8][9]. Biomass, solar thermal energy and geothermal are some other heat sources for ORC applications to produce electricity [10]. The energy conservation law is not sufficient by itself, so the second low should be considered to have a wide view to design systems [11]. Huan et al. [12] selected a regenerative organic Rankine cycle (RORC) to analyze energy and exergy aspects of cycles with six different working fluids. In their study, they optimized the exergy efficiency of the cycles to find the best condition ranges for the inlet pressure and temperature of the   As it is seen in Figures 2 and 3, in regenerative cycles, the turbine outlet flow is split into two parts in single, and three parts in double, systems. These parts are in the vapor phase, which enters feed-water heaters to preheat the working fluid before going to the evaporator. By this method, more potential of the cycle energy is used, so a higher efficiency, compared with the basic type, is gained. In order to simulate the cycle performance in this study, the following assumptions are employed: • All processes in cycles are assumed to be at a steady state and steady flow.

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There are no pressure drops in the pipes [24].

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Heat and friction losses, as well as the variation of potential and kinetic energies, are neglected [25].
Exiting fluid from the condenser is a saturated liquid.

Energy and Conventional Exergy Analysis
The purpose of the energy analysis is to design thermal systems. However, the aim of the exergy analysis is to determine the thermodynamic efficiency of the cycles and compare them to find out the best system performance. There are two important basic laws in thermodynamics: the first and the second law. The first law analyzes the conservation of energy in processes, while the second law is used to discuss the quality of energy and materials. The main equations for energy and mass balance used in the first law analysis for a controlled volume of each component are written below: Mass balance:

Energy and Conventional Exergy Analysis
The purpose of the energy analysis is to design thermal systems. However, the aim of the exergy analysis is to determine the thermodynamic efficiency of the cycles and compare them to find out the best system performance. There are two important basic laws in thermodynamics: the first and the second law. The first law analyzes the conservation of energy in processes, while the second law is used to discuss the quality of energy and materials. The main equations for energy and mass balance used in the first law analysis for a controlled volume of each component are written below: Mass balance: . Energy balance: Exergy analysis has two advantages compared with the conventional energy analysis method. It provides a more precise measurement of the real inefficiencies in a system, as well as their exact places. The main goal of the second law is to recognize the place, type and quantity of energy loss resources in system processes and the factors affecting them. The exergy balance equation for a control volume of each component can be written as [24]: where .
I is the total exergy rate of a destroyed system, and . E Q and . E w are the exergy transfer rates for heat and work, respectively. The equivalent work of any form of energy is defined as its exergy, so work is equivalent to exergy in every respect.
For a heat transfer rate ( . Q r ) and system temperature where heat transfer happens (T r ), the maximum rate of conversion from thermal energy to work is: τ is called the dimensionless exergetic temperature and is equal to the Carnot efficiency for special cases when the environment is at temperature T 0 . Exergy of each stream in a system, . E, is divided into four different parts: where . E 0 with low-grade energies. In this research, kinetic and potential exergy is neglected.
Physical exergy of each stream can be calculated from the following Equation (0 refers to environmental state): and the chemical exergy of the mixture for ideal gas can be expressed as below: Here, x i is the mole fraction of the ith component in the mixture, and ex chi in this relation is the chemical exergy of each component. As it is seen, exergy loss depends on the amount of heat that is transferred to ambient. So, convectional exergy analysis is only influenced by the entire condition of a system and does not deal with the effect of system components on other components' exergy destructions.
The basic equations used for the kth component in the conventional exergy analysis are shown in Equations (9)- (12). E P.k represent the exergy destruction rate, exergy of fuel and exergy of product, respectively. Additionally, ε k , y k and y * k are the exergy efficiency, the exergy loss ratio and the exergy of fuel with the total exergy destruction in the kth component, respectively. The exergy equations for components of the three cycles are expressed in Table 1.
In order to observe the system performance for the research, the first and the second law efficiencies are calculated from the equations below [12]: where T 0 is environmental temperature, and T m is source of heat; mean temperature can be calculated by the following equation: By the uses of Equations (13) and (14), the energy efficiency and exergy efficiency for the basic cycle can be obtained: For SRORC, the first and the second law efficiencies are presented as: For DRORC, efficiencies are calculated from the equations below:

Advanced Exergy Analysis
By a conventional exergy analysis, the only thing the researchers can discuss is the quantity of destruction rates in systems, and this method does not give any information about the type of these losses. Advanced exergy analysis is a new method that speaks about the details of the destructions to help researchers recognize different factors that affect component losses. Generally, advanced exergy analysis divides the loss rate of each component into two parts: endogenous/exogenous and avoidable/unavoidable.

Exogenous/Endogenous Exergy Destruction
To observe the effect of the parts on each other in a system, the kth component destruction rate is split into exogenous and endogenous parts: The endogenous exergy destruction ( . E EN D.k ) is the destruction rate associated with irreversibility due to inefficiency in the kth component, while all the residual components work preferably. The exogenous exergy destruction ( . E EX D.k ) is related to the destruction rate that happens in the remaining components. This dividing shows the real location of destructions in the systems, so that researchers can focus on the exact parts to improve system performance. There are two ways to compute the endogenous exergy destruction rate: engineering method and thermodynamic or hybrid cycle [26]. In this study, hybrid cycles of the systems are selected for the analysis. In this method, to calculate the rate of endogenous exergy destruction in the kth component, it is set on its real condition, and the other components work on their ideal conditions (with no irreversibilities). The components' ideal conditions selected for this study are shown in Table 2.

Avoidable/Unavoidable Exergy Destruction
Some values of exergy loss rates in each part, which are called unavoidable exergy destruction ( . E UN D.k ), cannot be reduced owing to technical limitations such as accessibility, cost of materials and making.
In order to calculate the unavoidable exergy destruction, some assumptions for the unavoidable conditions of the components are needed, which are usually obtained by researchers' experiences with component operations. In this study, these assumptions are selected from references [12,16,[27][28][29], and these conditions for each component are written in Table 2. To calculate the unavoidable exergy destruction of the kth component, all components are set on their best possible conditions (unavoidable conditions), and the unavoidable loss rates for the kth component are obtained from the equation below [29]: Avoidable exergy loss in the kth part is obtained by the subtraction of the unavoidable portion from the exergy loss rate of that part (Equation (23)). The avoidable exergy loss rate is recoverable and can be decreased, so designers should localize this sector to improve system performance.

Cycle Component Real Conditions Unavoidable Conditions Ideal Conditions
Evaporator

Combination of Splitting
To have more information about the share of each component of a system in total exergy destruction, the two main parts discussed above can be combined. Researchers can use a combination of endogenous or exogenous parts with avoidable or unavoidable parts for a more detailed designing of the systems [30]. By combining the two main splitting parts, the exogenous/unavoidable and the endogenous/unavoidable, the exogenous/avoidable and the endogenous/avoidable rates are obtained. To reach the unavoidable endogenous rate of the kth component, the equation below is used [31,32]: In this equation, the ratio of exergy loss to exergy of product in this kth component is obtained in unavoidable conditions of the cycle, and the endogenous product exergy is obtained for the kth component when it is in hybrid cycle conditions. The unavoidable exogenous rate for the kth component is obtained from the following equation: Then, the avoidable endogenous and exogenous parts of the exergy destruction for the kth component can be gained by reducing the unavoidable endogenous and exogenous exergy losses from the endogenous and exogenous exergy losses of that component, respectively.
The real potential of components in a system to improve their performances and to have the best efficiencies in a general system may be determined and analyzed by a mixture of the exergy loss sections mentioned above. There is no way to decrease the unavoidable/endogenous section of exergy loss because of technological limitations of the kth part, while avoidable/endogenous parts of the exergy destruction can be decreased by improving the efficiency of related components. The exogenous/unavoidable part of exergy loss for each component cannot be reduced because of technological constraints associated with other system components. However, the exogenous/avoidable parts may be decreased by the betterment of the total system performance, the efficiency of related components and, also, by improving the performance of other components in a system.

Simulation, Results and Discussion
The EES (engineering equation solver) is one of the most commonly used softwares to simulate power cycle operations. In this research, the EES was used to simulate cycle processes and to calculate properties of parameters in a system to reach cycle efficiencies. The input data and parameters for system components' working conditions of waste heat conditions used in this study are obtained from previous studies [12]. The conditions are shown in Table 3. These conditions are used for both conventional and advanced exergy analysis in this research. Table 3. Heat source parameters and assumptions [12].

Parameter Value
Temperature of heat source (K) 420 Mass flow of heat source (kg s −1 ) 14 Heat capacity of hot gases in constant pressure (kj kg −1 K −1 ) 1.

Model Validation
For validation, the comparison between the present models and Reference [8] is considered in this section (Table 4). There might be some errors due to the basic equations that EES uses to derive the characteristics of fluids. As results show, the deviation is low, and the models can be used for this analysis. As shown in Table 4, DRORC has a maximum exergy efficiency with 65.2% among the present systems. BORC produced more power compared with two other cycles, but as it is seen, this system has the lowest exergy efficiency because of its high exergy destruction rate in its components.

Conventional and Advanced Exergy Analysis
Considering conventional exergy analysis and by using the equations for each component of the cycles presented in Table 1, the exergy destruction rates are obtained. In the three cycles, the total exergy fuel rate is obtained from subtracting the exergy rate of the working fluid that leaves the evaporator from exhaust gases that enter the evaporator, and the total product exergy is the turbine power output. The main results of the conventional exergy analysis for BORC, SRORC and DRORC are presented in Tables 5-7, respectively. E F , E P , E P , E D , Y K ,Y * K in this tables are exergy of fuel, exergy of product, exergy destruction, exergy loss ratio and exergy of fuel with the total exergy destruction. It can be said that the components with higher exergy destruction rates have more effects on the efficiency of systems from an exergy point of view compared with other components. Referring to Table 5, in BORC, the maximum exergy destruction rate happens in the evaporator, followed by the turbine, the condenser and the pump. Table 6 shows the exergy destruction rates for the SRORC components. As it is seen, in single-regenerative systems, turbines show the highest exergy destruction rates among cycles components due to their design, and evaporators, condensers, feed-water heaters and pumps are in the next ranks, respectively. For DRORC, the exergy destructive rates are shown in Table 7. In these systems, as in single-regenerative cycles, turbines have the maximum exergy destructive rate, and they are followed by evaporators. However, unlike SRORC, pump1 and feed-water heater 2 are placed in the next ranks because of the second flow that extracts from the turbine. As a summary, it can be concluded that evaporators, turbines and feed-waters have more potential to reduce their destructive rates and to increase system efficiency. As it is seen, a conventional exergy analysis just focuses on components with high rates of exergy destruction, and it is not possible to specify whether these destructions occur in other components or in the component itself. These irreversibilities may only be specified by advanced exergy tools. As discussed above, an advanced exergy analysis evaluates the effects of component interactions and the real possibility of components to improve system efficiency.  By advanced exergy analysis, the exergy destructions of each component calculated in the previous section can be discussed in detail to find the sources of these destructions and real potentials of each component to amend the efficiency of the whole system. As mentioned above, these irreversibilities can be divided into exogenous, endogenous, unavoidable and avoidable parts to help researchers observe the effects of technological limitations and component interactions on the exergetic efficiency of a system for improvements [33]. In the advanced exergy analysis, the endogenous part of exergy loss for the kth component is calculated by defining real and ideal conditions for the cycles first. Then, the exogenous destruction rate is obtained by the difference of the total exergy and endogenous part (Equation (22)). To calculate the unavoidable exergy rate of loss in the kth part, instead of real conditions in cycles, unavoidable conditions are considered, and avoidable exergy is obtained from Equation (23). Furthermore, the values of exogenous/avoidable, endogenous/avoidable, exogenous/unavoidable and endogenous/unavoidable are determined using Equations (25) to (28). Advanced exergy analysis results for each part in three different cycles (BORC, SRORC and DRORC) are presented in Tables 8-10. As indicated in Table 9, for BORC, the exogenous exergy rate is greater than the endogenous exergy rate in system components, except the evaporator. So, system performance and modification of other components are necessary for turbines and condensers to decrease their exogenous destruction rates. The greater share of exergy destruction in the evaporator is caused by irreversibility of the component itself because of its high exergy loss rate in the endogenous part. As it was discussed before, the avoidable destruction rate in exergy can be controlled and reduced in practice. Table 8 shows that a turbine consists of a high value of avoidable destruction rates (7.4 kW) among the components of a system. Thus, the efficiency of this component can be improved using some technical modifications and new technologies or by replacing the component with the ones with higher efficiencies. It is important to note that, unlike the conventional analysis, a turbine is the most effective component due to its avoidable destruction rate to reduce irreversibilities. So, the main focus will be on the avoidable/endogenous parts of the exergy destruction, which can be decreased by improving the efficiency of the kth component. It follows by an investigation on the exogenous/avoidable exergy rates of loss, which can be reduced by improving the efficiency of other parts [34]. As it is stated in [17], Table 8 shows that the avoidable/endogenous exergy destruction rates in the turbine are greater than the unavoidable/endogenous destruction rates for BORC. This shows that the efficiency can be improved by technical modifications of this component. Table 8 also indicates that, except the condenser, the exogenous/avoidable exergy destruction rates are higher than the exogenous/unavoidable exergy rates of loss for the components. Results of the advanced exergy analysis for the division of the exergy rate of loss in the main parts in BORC are shown in Figure 4. As Figure 4 indicates, for the turbine, 79% of the total exergy rate of loss is avoidable, and from this rate, 53% can be reduced by amending other components efficiencies, and 26% of this rate depends on the performance of the component itself.    In Table 9, for SRORC, except the condenser, the endogenous exergy destruction rate is higher than the exogenous exergy destruction rate in the system's components, which shows that, unlike BORC, the greater share of the destruction rate is because of the internal irreversibilities in the component itself. So, among all components in SRORC, the turbine consists of the highest destruction rate in the exogenous part (1.77 kW), and the evaporator has the maximum endogenous destruction rate (2.56 kW) among the system's components due to its irreversibilities. As it is seen in Table 9, the avoidable part of the exergy destruction rate is higher than the unavoidable part in all components of SRORC. This indicates that there is a great potential in a system to reduce its irreversibilities by using some efficient and new components. Splitting the exergy destruction rates into endogenous/avoidable and exogenous/avoidable parts provides some important information that helps researchers to optimize systems. As it is seen in Table 9, the avoidable/endogenous exergy destruction rates in all equipment are higher than the exogenous/avoidable rates, except for the condenser. Priority in the improvement process of a component should be given to the turbine and the evaporator because of their higher values in the endogenous/avoidable destruction rates. For a better analysis, results for splitting the exergy destruction rate for the components in SRORC are shown in Figure 5. The highest unavoidable/endogenous exergy destruction rates belong to the evaporator in the system, with about a 54% of the total exergy destruction rate, which shows low potential in reducing the irreversibility for this component.      By referring to Table 10, it can be seen that, for DRORC, the endogenous exergy rate of loss is higher than the exogenous part for the evaporator and the turbine. This means that, in order to reduce the destruction rate, designers should focus on improving the efficiency of these components. Additionally, from these results, it is observed that there is a considerable contribution of the exergy rate of loss in pumps, feed-water heaters and condensers because of other components' performances in the systems. As it is mentioned above, the avoidable exergy destruction rate is an important part in reducing destruction. Table 10 shows that the avoidable exergy destruction rate is higher than the unavoidable part for all components in DRORC, which indicates that a system has a great potential for reducing its total exergy destruction by using modern technologies or replacing components with new, efficient ones. Among components, turbines with 6.587 kW consist of the highest avoidable exergy destruction rate, which should be paid more attention to in designing. As it is shown in Table 10, the endogenous/avoidable exergy destruction rates for the evaporator, turbine and pump1 is higher than the endogenous/unavoidable destruction rates in DRORC. Modifications in these components and improving working conditions should be noticed by designers to reduce this part of the exergy destruction. Priority in improving the performance of components in DRORC should be given to the turbine, the evaporator, pump 1 and feed-water heater 2. As for the previous cycles, the results of the advanced exergy analysis for DRORC components are shown in Figure 6.  In addition, the total exergy destruction rate for different parts obtained from an advanced exergy analysis for the three cycles are shown in Figures 7-9. As indicated, the total avoidable exergy rate of loss in these three systems is higher than unavoidable part, which shows a good potential to reduce irreversibilities. Avoidable exergy rate of loss with about 78% of the total rate of loss in DRORC is the first to be noticed by designers. SRORC and BORC with 74% and 55%, respectively, are given the next priorities. Additionally, in SRORC and DRORC, the total endogenous/avoidable exergy destruction rates are about 47% and 45% of the total exergy destruction rate, respectively, which are higher than other three combination parts.   In addition, the total exergy destruction rate for different parts obtained from an advanced exergy analysis for the three cycles are shown in Figures 7-9. As indicated, the total avoidable exergy rate of loss in these three systems is higher than unavoidable part, which shows a good potential to reduce irreversibilities. Avoidable exergy rate of loss with about 78% of the total rate of loss in DRORC is the first to be noticed by designers. SRORC and BORC with 74% and 55%, respectively, are given the next priorities. Additionally, in SRORC and DRORC, the total endogenous/avoidable exergy destruction rates are about 47% and 45% of the total exergy destruction rate, respectively, which are higher than other three combination parts. In addition, the total exergy destruction rate for different parts obtained from an advanced exergy analysis for the three cycles are shown in Figures 7-9. As indicated, the total avoidable exergy rate of loss in these three systems is higher than unavoidable part, which shows a good potential to reduce irreversibilities. Avoidable exergy rate of loss with about 78% of the total rate of loss in DRORC is the first to be noticed by designers. SRORC and BORC with 74% and 55%, respectively, are given the next priorities. Additionally, in SRORC and DRORC, the total endogenous/avoidable exergy destruction rates are about 47% and 45% of the total exergy destruction rate, respectively, which are higher than other three combination parts.

Conclusions
In this research, conventional and advanced exergy analysis are performed for three different models of organic Rankine cycles (BORC, SRORC and DRORC) at specified operating conditions by the use of a low-temperature heat source. The main results obtained from the present study are listed as below:

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According to the conventional exergy analysis, the highest exergy destruction was obtained in the evaporator for BORC, and for SRORC and DRORC, the maximum exergy destruction belongs to the turbine. Additionally, results of the conventional exergy analysis show that the condenser in three cycles is the third important component that should be noticed in designing.
The exergy destruction rate for pumps may be neglected.

Conclusions
In this research, conventional and advanced exergy analysis are performed for three different models of organic Rankine cycles (BORC, SRORC and DRORC) at specified operating conditions by the use of a low-temperature heat source. The main results obtained from the present study are listed as below:

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According to the conventional exergy analysis, the highest exergy destruction was obtained in the evaporator for BORC, and for SRORC and DRORC, the maximum exergy destruction belongs to the turbine. Additionally, results of the conventional exergy analysis show that the condenser in three cycles is the third important component that should be noticed in designing.
The exergy destruction rate for pumps may be neglected.

Conclusions
In this research, conventional and advanced exergy analysis are performed for three different models of organic Rankine cycles (BORC, SRORC and DRORC) at specified operating conditions by the use of a low-temperature heat source. The main results obtained from the present study are listed as below: • According to the conventional exergy analysis, the highest exergy destruction was obtained in the evaporator for BORC, and for SRORC and DRORC, the maximum exergy destruction belongs to the turbine. Additionally, results of the conventional exergy analysis show that the condenser in three cycles is the third important component that should be noticed in designing. The exergy destruction rate for pumps may be neglected.

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The advanced exergy analysis showed that the exogenous exergy destruction rate is greater than the endogenous exergy destruction rate, except the evaporator, for BORC. However, in SRORC, the endogenous exergy rate of loss is higher than the exogenous part, except for the condenser. This indicates the greater share of the exergy destruction rate because of the internal irreversibilities in the component itself compared with BORC. Avoidable rate of exergy destruction in BORC, SRORC and DRORC are about 78%, 74% and 55% of the total destruction rate, respectively. Among the existing components, the condenser has the maximum value of exogenous exergy destruction rate, which can be reduced by the modification of other components.

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The endogenous/avoidable exergy destruction was identified as an important part of the destruction. Thirty-one percent, forty-seven percent and forty-five percent of the total exergy destruction rate in BORC, SRORC and DRORC placed in this part, respectively, can be reduced by improving the efficiency of the components.

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By the advanced exergy analysis, unlike the conventional exergy analysis, the preference of improvement should be given to turbines, evaporators, condensers and feed-water heaters, respectively. Additionally, regenerative cycles have high potentials to reduce their irreversibilities compared with basic systems. Chemical exergy η energy efficiency ε exergy efficiency E F exergy of fuel E P exergy of product E D exergy destruction Y K exergy loss ratio with the total exergy destruction Y *