Parametric Assessment on the Advanced Exergy Performance of a CO 2 Energy Storage Based Trigeneration System

: In this paper, conventional and advanced exergy analyses are comprehensively introduced on an innovative transcritical CO 2 energy storage based trigeneration system. Conventional exergy analysis can quantify in an independent way the component exergy destruction. However, the advanced technology is able to evaluate the interactions among components and identify the tangible promotion potential by allowing for the technical and economic limitations. In this method, the component exergy destruction is separated into avoidable and unavoidable parts, as well as the endogenous / exogenous parts. Calculation of the split parts is carried out by utilizing the thermodynamic cycle-based approach. Results coming from conventional exergy analysis indicate that the ﬁrst three largest exergy destructions are given by cold storage, compressor 1, and heat exchanger 3. However, advanced analysis results demonstrate that the cold storage, compressor 1, and compressor 2 should be given the ﬁrst improvement priority in sequence by depending on the avoidable exergy destruction. The turbine e ﬃ ciency produces a higher impact on overall exergy destruction than compressor e ﬃ ciency. The pinch temperature in cold storage causes the highest e ﬀ ect on exergy destruction amongst all the heat exchangers. There exists an optimum value in the compressor inlet pressure and ambient temperature.


Introduction
The energy requirement has been marked with a sharp increase worldwide in the last several decades by referring to the statistical data on the consumption of energy resources amongst 69 countries [1]. In particular, the scarcity of energy is directly intensified due to the significant augment of energy consumption in developing economies like China, India, South Africa, and Brazil, which are accelerating the urbanization process. For example, the energy use in China is inferred to be 15 times larger by 2050 in comparison with that in 1970 [2]. It is also reported that the oil demand will increase by 30% all around the world from 2007 to 2035 [2]. The increasing consumption of fossil fuels has brought serious energy shortages, environmental pollution, and global warming [3][4][5]. On one hand, measures can be made to promote the conversion efficiency of the existing energy systems. On the other hand, more efforts should be made to increase the utilization of renewable energies like wind, solar, and biomass energy to improve the currently unreasonable energy structure.
However, the remarkable randomness and intermittency make renewable energies the inordinate and discordant sources when integrated to an electricity grid, bringing the discard of some redundant energy during the dispatching stage [6]. The technology of compressed air energy storage (CAES) the conventional one. More importantly, the advanced exergy analysis tends to clear, potentially, the misleading deductions obtained from the conventional exergy analysis.
Based on the literature survey, several papers in the literature deal with the CAES-based CCHP system; only one is concerned on the CCHP system based on CCES, which is developed by authors [38]. Main investigation of the previous work is about the energy efficiency of the CCES-based CCHP system by using the first law of thermodynamics. As a further study, the focus of the present work is to pioneer the advanced exergy analysis of the CCES-based CCHP system. Splitting the component exergy destruction is clearly described. A particular focus is the sensitivity examination of the system to analyze the impacts of some key parameters on system performance. This advanced approach overcomes the most important limitations of a conventional exergetic analysis and, therefore, assists engineers in better understanding how thermodynamic inefficiencies are formed. Conventional exergy analyses only quantify the exergy destruction in different components, but cannot shed light on the interactions between components, while advanced exergy analyses overcome this weakness and uncover more of the accessible potential of the system.

Analysis Methods
The schematic diagram of CCES-based CCHP system is depicted in Figure 1, which is composed mainly by two compressors (C), two turbines (T), four heat exchangers (HE), two gas storage tanks (HST and LST), three thermal medium storage tanks (HFT and CFT) and two valves (TV). The pressured water is employed in this work as the thermal storage medium. The system running process is clearly given as follows. In the charging stage, the liquid CO 2 from LST is first cooled by the throttling action through TV1 to guarantee the CS (cold storage) function, and then is evaporated to gaseous state. The cold energy released is preserved in CS. Afterwards, the gaseous CO 2 is compressed to supercritical state powered by abundant electrical power, and is finally stored with supercritical state in HST. Meanwhile, the compression heat absorbed by water in HE1 can be offered to heat user, and the recovered heat by HE2 is stored in HFT1. In the discharging stage, the supercritical CO 2 in high pressure passes through TV2 which is used to maintain the inlet pressure of T1 constant, and then enters HE3 for preheating. The heat stored in HFT1 will be supplied for HE3. After that, the CO 2 expands through the turbine train to output electricity power. The outlet cryogenic CO 2 from T2 provides cooling ability in HE4, which is transferred to ambient air for satisfying the cooling users need. The gaseous CO 2 is then condensed in CS, and the liquid CO 2 is fed to the LST for application in the next cycle.

CCHP Model
For the compressor and turbine, isentropic efficiency is provided to represent their actual performance [24]: Enthalpy at the exit state is acquired through the property association f by using the REFPROP software [39]: where s is,e equals to the inlet entropy during isentropic compression/expansion processes. The power is calculated by: . .
For heat exchangers, the properties of supercritical CO 2 can largely change in a small temperature band. Therefore, the heat exchanger can be discretized many small sections that each of them can be considered with constant properties [26]. The discretization is completed by splitting the total enthalpy variation of hot fluid into several equal parts. The heat transfer and mass flow rate of water or air for each section n are respectively calculated by: .
m water or air (h water or air,n+1 − h water or air,n ) . m water or air = N n=1 . Q n (h water or air,N+1 − h water or air,1 ) The HST and LST are presumed to be completely insulated and the inlet and outlet conditions have no difference [36]: Isenthalpic process is assumed through the throttle valve: The heat transfer rate of CS is written as [24]:

Conventional Exergy Analysis
There is absence of chemical reactions in the developed CCHP system and the total exergy can be thus expressed as [32]: The specific exergy e j is separated deeply into its thermal and mechanical exergy [40]: where the node X is at the pressure p and ambient temperature τ 0 . Here, thermal exergy is mainly due to the temperature, and mechanical exergy mainly due to the pressure. The "fuel-product" definition is applied for exergy in the present analysis. At component level, the exergy balance can be expressed as [33]: and the exergy balance for overall system is: .
where . E P,k and . E F,k stands for product and fuel exergy, respectively.
. E L,tot is the exergy that will not be used further in the system. It is noteworthy that . E L,tot is considered merely for the overall system rather than for a specific component.
The following definitions are introduced to assess the exergy conversion rate in the conventional exergy analysis [31][32][33]: Exergy efficiency of a component: The system exergy efficiency: The ratio of exergy destruction: The relative exergy destruction: In Table 1, the fuel and product exergy is listed by referring to [35,40].

Advanced Exergy Analysis
Advanced exergy analysis [29][30][31][32] is introduced into the novel CCHP system based on TC-CCES to make the quality of the conclusions from conventional method better. Exergy destruction is separated into detailed parts, e.g., unavoidable/avoidable parts and endogenous/exogenous parts. Moreover, more valuable details can be received by combining the above two splitting measures for improving the system performance. It is noteworthy that exergy destruction is due to irreversibilities within the system, and exergy loss is the exergy transfer to the environment. Here, exergy loss is associated with the overall system but not with a component because each exergy stream exiting a component is considered either at the fuel or at the product side. Therefore, it is mainly concerned the exergy destruction in this section.
The component exergy destruction is not only dependent on the irreversibility occurring within the component itself, but also related to the interconnections among different components, which can therefore be written as: where . .

E
where . E UN D,k will always exists owning to the technological limitations, while . E AV D,k could be lessened by improvement measure. The splitting approach proposes the real potential to improve a specific component.
By coupling the above two concepts, four more detailed parts can be erected as follows: .
where . are the parts that can be and cannot be decreased, respectively, through promoting the characteristics of the other components and the system integration.

E
The thermodynamic cycle-based method [33] is adopted in the work to compute each part of exergy destruction. This approach for splitting the exergy destruction into different parts is based on the analysis of thermodynamic cycles. When the method is used, the real thermodynamic cycle, unavoidable thermodynamic cycle, and hybrid thermodynamic cycle should be defined. The real cycle means that the components in the system operate with real processes. Conventional exergy analysis is conducted just depending upon this cycle. The unavoidable cycle is formed by using the current best operating parameter of the components, which is limited by the technological limitations. The unavoidable part can be written as: is the unavoidability indicator. It is calculated through dividing product exergy by exergy destruction in the unavoidable cycle.
In the hybrid cycle, the component considered operates with real condition. The other components work at ideal conditions [40]: the component exergy destruction reaches zero if possible or otherwise the minimum value. In this case, the endogenous exergy destruction of the kth component can be obtained directly.
The unavoidable endogenous part of the exergy destruction . E EN,UN D,k is based on hybrid cycles and the cycle for the unavoidable exergy destruction mentioned above, and it is calculated by the following equation:

Result and Discussion
Detailed performance analyses are performed in this section through solving the real, unavoidable and hybrid thermodynamic cycles. The computing procedure is compiled in MATLAB and the fluid properties are resorted to the REFPROP database and subroutines. The flow chart of the calculation procedure is illustrated in Figure 2. Design parameters of the CCES-based CCHP system are shown in Table 2 and the three set of assumptions given for the real, unavoidable, and ideal cycles are summarized in Table 3. It is noted here that ambient temperature is chosen as the reference temperature for the exergy analysis in this work. The system exergy efficiency ε tot at the real cycle is 56.25% while at the unavoidable cycle it is 74.79%. This demonstrates that the system efficiency can be enhanced largely, attracting interest in the CCHP system based on TC-CCES concept. In addition, the exergy efficiency is almost equivalent with the CCHP system based on CAES (ε tot = 56.48 [18]). However, a large advantage of the system based on TC-CCES is its much higher exergy density (the ratio of total output exergy to the total volume of tanks [18]), 7.07 times of the value for CAES-based CCHP system. This authenticates the presented CCHP system as a promising option for satisfying the diversified need of users.    Table 4 lists the fundamental results calculated from the conventional exergy analysis on CCHP system. It is found that the CS possesses the biggest exergy destruction (y * CS = 23.20%) and the lowest exergy efficiency (ε CS = 80.15%) except for HE3 and HE4. The reason can be given that two phase-transition processes in CS results in high irreversible loss. The second biggest exergy destruction rate is located in C1 with y * C1 = 12.93%, followed by HE3, C2, T2, T1, and HE2 in sequence (y * HE3 = 12.79%, y * C2 = 11.27%, y * T2 = 10.34%, y * T1 = 9.84%, y * HE2 = 9.14%). The exergy destruction rates within TV2, HE1, TV1, HE4 are rather low, and together, they account for only 10.49% of the system exergy destruction. In addition, it is seen that HE2 and HE3 located in supercritical state have much more irreversible loss than HE1 and HE4 (y * HE1 = 2.69%, y * HE4 = 1.03%) within gaseous state. The logical explanation behind this phenomenon can be given in two aspects. The mass flow of cooling water is larger for supercritical CO 2 owning to its higher specific heat. Moreover, the properties of supercritical CO 2 are more sensitive to temperature, and thus a larger temperature difference will occur to guarantee the set pinch temperature. For instance, the upper terminal temperature difference of HE1 and HE2 are 5 K and 34.15 K, respectively. From the system point, the total fuel exergy . E F,tot originates from the power supplied to compressors, and . E P,tot is the summation of the power produced in turbines and the heating and cooling exergy. The overall system has an exergy efficiency of 56.25%, and therefore 43.20% of the system fuel exergy is destroyed. Using the approach aforesaid, all detailed exergy parts are shown in Table 5. One can notice that the endogenous part is much larger than the exogenous part, implying that the exergy destruction within each component is mainly induced by its own irreversibility. The exogenous part is zero for C2, HE2 and all throttle valves, indicating that for these components the exergy destructions are introduced only by their endogenous irreversibility. The negative exogenous exergy destructions within turbines and HE3 mean that enhancing the irreversible loss in other system components lessens the exergy destruction within these components. It is concluded that the communications of components in the CCHP system based on TC-CCES are not strong but rather complex. One can also see in Table 5 that only turbomachineries and CS possess higher avoidable part than unavoidable part and therefore 48.5% of the system exergy destruction cannot be eliminated in the studied condition. E D,HE4 can be lessened by raising the magnitude of its pinch temperature which results in a decline of the liquid carrying capacity at the outlet of T2. Table 6 lists the promotion priority of all the components in the presented CCHP system based on TC-CCES determined by different analysis methods. It can be observed that high diverse happens between conventional and advanced priorities because of different criteria. For an instance, the HE3 is considered the third priority in conventional exergy analysis. However, it is the eighth component for optimization in the advanced method. In short, the advanced exergy method offers much more trustworthy results since both technological limitations of each component and the interconnections among components are considered.  C1  3  HE3  C2  4  C2  T2  5  T2  T1  6  T1  HE2  7  HE2  TV1  8  TV2  HE3  9  HE1  HE1  10  TV1  HE4  11 HE4 TV2

Parametric Study
Conducting a parametric study is of significance by varying a parameter alone at the fixed remaining values in order to evaluate the characteristics of the exergy destruction. Therefore, the efficiencies of compressors and turbines (η), pinch temperatures of heat exchangers and CS (∆τ min ), pressure drop in TV2 (∆p TV2 ), storage pressure in HST (p 7 ), compressor inlet pressure (p 3 ) and ambient temperature (τ amb ) are examined individually. Figures 3-9 depict the impacts of the parameters on the results achieved from both conventional and advanced exergy analyses.

Effects of the Component Performance
In this section the dependency of the examined parameters is investigated on each turbomachinery efficiency as the remaining parameters are retained the identical values as in Table 2 and for the real condition in Table 3. Since the effects of turbomachinery efficiency shares similar behavior, only the results from the examination of C1 and T1 efficiencies are illustrated in Figure 3 for simplicity and clarity. As seen in Figure 3a E D,tot are separately 25.98 kW and 43.00 kW with the same change in η T1 . It is found that although the variation of the turbine exergy destruction is smaller than that in compressor, the turbine efficiency makes a higher influence on system exergy destruction.
This can be explained that the CCHP system based on TC-CCES is a closed loop thermodynamic cycle, and thus the outlet thermodynamic state from turbine will influence the power consumed in compressor. More detailed and fascinating features are identified in Figure 3b,d, which indicates that the increase in turbomachinery efficiency causes a relatively large decline in the endogenous part, avoidable part, and avoidable endogenous part of exergy destruction. Moreover, the avoidable exogenous part keeps almost the same constant versus efficiency. The results demonstrate that the exergy destructions in compressor and turbine can be decreased mainly by promoting the same component itself. In a word, larger turbomachinery efficiency favors reducing the exergy destruction.  E AV,EX D,CS , and the difference becomes larger with the increase of ∆τ min,CS since the increasing trend of the former part is sharper than the latter one. This make it clear that a reduction of . E D,CS is of more dependence on improving the performance of CS itself. In short, a smaller ∆τ min,CS favors the system performance for decreasing the exergy destruction and enhancing system exergy efficiency. Figure 5 shows the variation of exergy destructions and ε tot by changing the pinch temperature in HE2 and HE3. The results of exergy analyses for HE1 and HE4 are not given in this section since the values of their exergy destruction rate are rather small. It is pointed out that analyzing the component with high exergy destruction is more meaningful and advisable [35]. It is seen in Figure 5a,c that an increase in HE pinch temperature ∆τ min,HE shifts up . E D,HE and . E D,tot with a sensitivity of 13.40 kW and 7.60 kW for HE2 and 13.48 kW and 27.78 kW for HE3 respectively per Celsius degree. However, the avoidable part . E AV D,HE is so small, as shown in Figure 5b,d, that results in a rather low potential of improvement.

Effects of the Operating Parameters
The pressure drop in the TV2 (∆p TV2 ) has a large impact on the power production of the turbine. Figure 6 illustrates that a rise in ∆p TV2 introduces an increase of the exergy destruction for both TV2  The storage pressure in HST p 7 has a significance role in determining the power consumed in compressor and the power produced in turbine. Figure 7 illustrates the variation of system exergy destructions and exergy efficiency by varying the storage pressure. A rise in storage pressure produces a decline in overall system exergy destruction     Figure 9 presents the impact of ambient temperature (τ amb ) on system exergy destructions and exergy efficiency. It is observed that with an increase in ambient temperature, the system exergy destruction . E D,tot decreases firstly with sensitivity of 10.19 kW per Celsius degree and then increases monotonically with sensitivity of 13.78 kW per Celsius degree. The exergy destruction of heat exchangers is decreased with a higher ambient temperature, while the exergy destruction of CS shows a reverse trend. Moreover, with a larger ambient temperature, the change extent of exergy destruction within CS becomes larger than that within heat exchangers. Therefore, the refraction occurs in the figure. Simultaneously, the system exergy efficiency ε tot increases firstly and then decreases monotonically

Conclusions
In this paper, exergy analysis based on both the conventional and advanced technology is utilized to a novel CCHP system based on TC-CCES. Some important conclusions are drawn as follows.
(1) Based on the results obtained from conventional exergy analysis, the biggest exergy destruction exists in cold storage, followed by compressor 1 and heat exchanger 3. Heat exchanger with supercritical working fluid produces much more irreversible loss than that with gaseous working fluid. The system keeps an overall exergy efficiency of 56.25%.
(2) More interesting features can be obtained from advanced exergy analysis. Dividing exergy destruction into exogenous /endogenous parts clarifies that the component interactions in the system are not very sound but rather complex. Dividing exergy destruction into avoidable/unavoidable parts uncovers the real improvement potential and identifies heat exchanger 3 as the eighth component to be improved, amending the misleading conclusion deduced based on conventional exergy analysis results. The overall system exergy efficiency is 74.79% under the unavoidable condition, indicating a great improvement potential to the CCHP system based on TC-CCES.
(3) Sensitivity analysis demonstrates that an increase in turbomachinery efficiency and a reduction of pinch temperature in the heat exchanger and cold storage within technological permission benefits the system characteristics in terms of decreasing exergy destruction and increasing system exergy efficiency. Moreover, the efficiency in turbine keeps a higher influence on overall system exergy destruction than compressor efficiency. In addition, a smaller pressure drop in throttle valve 2 and a larger storage pressure are helpful for improving system exergy efficiency, and there exists optimum value through evaluating compressor inlet pressure and ambient temperature.
The application of advanced exergy analysis to the CCHP system based on TC-CCES provides more valuable and detailed information for the optimization of the system. The advanced exergy analysis can be considered as a meaningful supplement to the conventional exergy analysis.