Advanced exergoeconomic evaluation on supercritical carbon dioxide recompression Brayton cycle

Journal Pre-proof Advanced exergoeconomic evaluation on supercritical carbon dioxide recompression Brayton cycle

Zhan Liu, Zihui Liu, Xing Cao, Tao Luo, Xiaohu Yang PII:

S0959-6526(20)30584-9

DOI:

https://doi.org/10.1016/j.jclepro.2020.120537

Reference:

JCLP 120537

To appear in:

Journal of Cleaner Production

Received Date:

05 December 2019

Accepted Date:

10 February 2020

Please cite this article as: Zhan Liu, Zihui Liu, Xing Cao, Tao Luo, Xiaohu Yang, Advanced exergoeconomic evaluation on supercritical carbon dioxide recompression Brayton cycle, Journal of Cleaner Production (2020), https://doi.org/10.1016/j.jclepro.2020.120537

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Journal Pre-proof Advanced exergoeconomic evaluation on supercritical carbon dioxide recompression Brayton cycle Zhan Liua,b, Zihui Liua, Xing Caoa, Tao Luoc, Xiaohu Yangb,* a College b School c

of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P.R. China

of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

*Corresponding author. E-mail address: [email protected] (X. Yang)

Abstract: This study proposes a comprehensive understanding of the supercritical carbon dioxide recompression Brayton cycle by means of extending and applying the advanced exergoeconomic method as one of the first attempts. The advantages of this advanced exergy-based method are determining the real potential for improvement of each significant component and considering the interactions among system components, which cannot be achieved by using the conventional method. The unavoidable/avoidable and endogenous/exogenous concepts are introduced, and detailed modeling is performed to calculate exergy destruction and investment costs. The results demonstrate that the unavoidable value of each component is higher than the avoidable value for exergy destruction cost (except for high temperature recuperator). Even under the most optimistic scenario, the total exergy destruction cost can only be reduced by 2199.29 $/h (38.86%), and about half of this avoidable variable is exogenous. According to the results of traditional exergoeconomic analysis, the reactor is recommended as the governing component to improve the cost effectiveness of the cycle due mainly to its highest operating cost (5313.39 $/h). On the contrast, the turbine should have the highest improvement priority owing to the highest value of the avoidable operating cost (1390.88 $/ h). The findings provide a novel way to guide the design and evaluation of the carbon dioxide Brayton cycle through benefiting from the advanced exergoeconomic analysis.

Keywords: Performance evaluation; Supercritical CO2 recompression cycle; Thermoeconomic evaluation; Advanced exergoeconomic analysis; Costs splitting;

1

Journal Pre-proof

Nomenclature SCRBC Symbols A c C CRF E

f ir LMTD m

n N p q r U Z

Abbreviation s CO2 HTR LTR LCI MC PC R RC

area of heat exchange (m2)

T

specific cost ($/GJ) cost rate ($/h) capital recovery factor exergy flow rate (W) exergoeconomic factor interest rate logarithmic mean temperature difference (K) mass flow rate (kg·s−1) plant life time (y) annual operating hours pressure (Pa) heat transfer rate (W) relative cost difference heat transfer coefficient (W·m-2·K−1) investment cost rate ($/h)

Greeks η

Supercritical CO2 recompression Brayton cycle turbine

τ Δ

isentropic efficiency maintenance factor temperature (K) change quantity

Subscripts 1,2.3… D e F i k,r P

stream number destruction exit fuel inlet the k- or r-th component product



Superscripts carbon dioxide high temperature recuperator Low temperature recuperator Life cycle integrated main compressor pre-cooler reactor recompression compressor

AV CI EN EX UN OM Σ

2

avoidable capital investment endogenous exogenous unavoidable operation-maintenance summation

Journal Pre-proof 1. Introduction Energy resources should be utilized efficiently because of the growing energy demand and environmental pollution in the world. It is reported that NOx emissions in power plant contribute significantly to the environmental degradation (Han et al., 2019). For the time being, measures should be urgently taken to provide solutions to the energy shortage and environmental degradation. On the one hand, renewable energy resources should be paid sufficient attentions to. For instance, solar energy integrated with energy storage (Yang et al., 2018; Yang et al., 2019) in electricity generation process have demonstrated a strong vitality in both economical and environmentally friendly benefits. On the other hand, advanced technologies have to applied to the power generation cycles. Amongst these, the supercritical carbon dioxide (S-CO2) cycle has drawn increasing focus in numerous power production plants such as concentrated solar power plants and future nuclear power plants due to its compactness, better security, simplicity and economic aspects (Hay and Celik, 2019; Hu and Deng, 2016; Sharan et al., 2018). Thermophysical properties of the cycle working fluid CO2 undergo a sharp variation adjacent to the critical state, which is in favor of attaining a substantial reduction of the compression work (Dostal et al., 2006a). Other advantages of CO2 are no toxicity, no inflammability and high critical pressure (7.38 MPa) (Liu et al., 2019a). In comparison with the cycles of gas Brayton (~100 kPa) and steam Rankine (~10kPa), the S-CO2 cycle has much higher minimum pressure (~7380 kPa) that will bring about a large density of working fluid throughout the overall process. As an instance, the resulting low volume flow can make a 10 times smaller size of turbomachineries than that in steam Rankine cycle (Ahn et al., 2015). The pioneering studies reported in 1968 by Feher and Angelino (Angelino, 1968; Feher, 1968) concluded such characteristics in S-CO2 cycle as higher cycle efficiency, low ratio of volume to power and no turbine blade erosion. They demonstrated that the S-CO2 recompression Brayton cycle (SCRBC) was the most efficient configuration amongst the various cycles. Moreover, the economic superiority of the S-CO2 cycle has been revealed by comparison with other power generation configurations. Cost of the S-CO2 cycle was shown saving around 15% (Dostal et al., 2006b) and 30% (Iverson et al., 2013) compared to that of an equivalent helium cycle and steam indirect cycle, respectively. For the SCRBC, a number of works have been presented worldwide. Sarkar (Sarkar, 2009) studied exegetically a SCRBC through evaluating the effects of different operating and design parameters on system performance and component inefficiencies. Results demonstrated that heat exchangers were of more significance than turbomachineries in terms of irreversibility and compared to compressor isentropic efficiency, the turbine isentropic efficiency brought more predominant influence on exegetic efficiency. Later, Sarkar and Bhattacharyya (Sarkar and Bhattacharyya, 2009) compared the performance of an SCRBC with/without reheating and it was found a 3.5% increase of cycle efficiency by using reheating. Iverson et al. (Iverson et al., 2013) examined the dynamic actions of the SCRBC for solar-thermal power plants in the case of a pulsating thermal input. Results expressed that under the fluctuations the Baryton cycle was able to action normally for a short time with 3

Journal Pre-proof the effective assistance of system thermal mass. For improving the SCRBC thermal and economic performance, Akbari and Mahmoudi (Akbari and Mahmoudi, 2014) introduced an organic Rankine cycle (ORC) to take advantage of the waste heat rejected by the Baryton cycle and performed a comprehensive thermoeconomic investigation on this combined power generating cycle. It was increased 11.7% for exergy efficiency and was decreased 5.7% for total cost per unit product compared to the original stand-alone cycle. Jamali et al. (Jamali et al., 2014) carried out a parametric study exegetically and subsequently a multi-objective optimization work by using the evolutionary genetic algorithm for the proposed trigeneration system that comprises the SCRBC and an ejector refrigeration system. It was found that the energy saving was around 46% when the trigeneration cycle was used for simultaneously supplying heating, cooling and power instead of the separate configurations. Hu et al. (Hu et al., 2015) evaluated the effects on the SCRBC performance of CO2-based binary mixtures by taking place of the pure working fluid. It was stated that with the CO2-He and CO2-Kr mixtures, the cycle efficiency was improved and the heat exchange capacity in recuperators was reduced. Detailed energetic and exegetic analyses were implemented on four S-CO2 cycle configurations by Padilla et al. (Padilla et al., 2015) and the SCRBC with main compressor intercooling was demonstrated the best thermal cycle. Integrating the SCRBC to a biomass fuelled turbine along with a water heater, Gholamian et al. (Gholamian et al., 2016) developed a novel cogeneration system and the sensitivity analysis indicated that the system performance could be mostly impacted by the turbine pressure ratio. Nami et al. (Nami et al., 2017)] completed the synthetically energetic, economic and environmental evaluation on a cogeneration system by combining a gas turbine, an ORC and the SCRBC. It was revealed that the average unit cost of heating and power product was reduced by 0.56 $/GJ by comparison with that under the base condition. Akbari and Mahmoudi (Akbari and Mahmoudi, 2017) proposed and examined a cogeneration system through coupling internally the SCRBC with a transcritical CO2 refrigeration cycle, which was capable of providing cooling energy and power simultaneously or only cooling energy. In order to efficiently utilize solar heat, Wang et al. (Wang et al., 2018) combined the S-CO2 power cycle with high-temperature thermal storage using molten halide salt as the heat transfer fluid. Ma et al. (Ma et al., 2018) suggested to introduce an absorption chiller to utilize the low-grade thermal energy of CO2 from the SCRBC cold end. The assessment results illustrated that the energetic and exegetic efficiencies increased separately by 5.19% and 6.12% in comparison with the standalone power cycle. Zhao et al. (Zhao et al., 2018) coupled the S-CO2 power cycle with the process of coal gasification and the parametric study showed that both the turbine inlet temperature and turbine outlet pressure had considerable impact on cycle efficiency. Notice that all the afore-mentioned studies are carried out in terms of exergy and exergoeconomic aspects through conventional exergy-based analysis methods. Although the thermal system effectiveness, i.e., the location, magnitude and causes of inefficiencies and their monetary values can be assessed by the exergy-based analyses (Elbar et al., 2019), there exist some restrictions of giving very little information on both component interactions and real improvement potential when using 4

Journal Pre-proof conventional methods. In order to address the above shortages, the advanced techniques including advanced exergy and exergoeconomic analyses have been recently proposed as a new direction for assessment of the thermodynamic performance and cost effectiveness in thermal systems (Kelly et al., 2009; Tsatsaronis and Park, 2002). For any system component, the exergy destruction, investment cost can be considered as the consequence of the component itself and others by the definition of the endogenous and exogenous concepts. Besides, the introduction of the unavoidable and avoidable concepts offers engineers the limitation of improvement potential for components on account of the technical and economic constraints. Therefore, application of advanced exergy-based analyses provides a preferable comprehending of inefficiencies and rules to identify design changes for improving the component cost effectiveness (Hashemi et al., 2019; Mousavi and Mehrpooya, 2019; Sharshir et al., 2019). Recently, applications of the advanced techniques have been proposed in different energy conversion processes for cleaner productions. Liu et al. (Liu et al., 2019b) conducted a comprehensive analysis on a compressed carbon dioxide energy storage system based on conventional and advanced exergy analysis methods and found that the advanced method was more pragmatic in determining the improvement potentials of the system components. Yang et al. (Yang et al., 2016) presented a framework for examining and optimizing an oil shale retorting process based on advanced exergoeconomic analysis. Ansarinasab et al. (Ansarinasab et al., 2017) performed advanced exergy and exergoeconomic analyses on a hydrogen liquefaction process integrated with mixed refrigerant system. Results indicated that most of the irreversibility within the components was endogenous exergy destruction except turbo expanders. Three different strategies were thus suggested to improve the system based on advanced exergoeconomic results. Advanced life cycle integrated (LCI) exergoeconomic analysis method was applied to evaluate a building heating system and it was revealed that the maximum LCI endogenous exergy destruction cost ratio was due to the boiler (Açıkkalp et al., 2018). Mehdizadeh-Fard and Pourfayaz (Fard and Pourfayaz, 2019) examined in detail the avoidable and unavoidable exergy destructions for the heat exchanger networks in a complex natural gas refinery. It was found that about 59% of the overall irreversibility was avoidable by the optimization techniques. Shaygan et al. (Shaygan et al., 2019)carried out advanced energy and economic analysis of hybrid system consisting of photovoltaic cells, electrolyzer and polymer electrolyte membrane fuel cell to provide a clean power to run an electrolyzer for hydrogen production. Zhang et al. (Zhang et al., 2020) employed advanced exergy analysis to evaluate three modified ethane recovery processes with different refrigeration cycles. Results demonstrated that the most effective measures to reduce process exergy destruction were to improve compressor efficiency, to reduce the temperature approach of cold boxes and to improve the separating efficiency of the columns in sequence. As seen in the above literature review, it is expected that the advanced exergy-based method will be particularly beneficial to those who will comprehensively investigate thermal cycles for future studies.

5

Journal Pre-proof Up to time being, there are several studies on the S-CO2 cycle through advanced exergy analysis (Mohammadi et al., 2019; Petrakopoulou et al., 2013; Yang et al., 2013). However, to the best knowledge of the authors, studies on advanced exergoeconomic evaluation of the S-CO2 cycle have not appeared yet in the open literature. The advanced exergy-based analysis can determine the role of each component itself and the role of component interactions on one another, which cannot be provided by means of the conventional exergy-based method. Therefore, the primary purpose of this context is to carry out a complete investigation on modeling and analyzing the advanced exergoeconomic aspects for the S-CO2 cycle. To achieve this, both the exergy destruction and investment costs within system components are subdivided into unavoidable/avoidable and exogenous/endogenous parts, and the corresponding combinations of the two concepts are also addressed. The advanced examination in this work can be well conductive to explore and ameliorate the performance of the S-CO2 cycle. The issues examined in this paper have never been reported in current publications in the same way.

2. Cycle description The SCRBC considered in this study is configured with a main compressor (MC), a low-temperature recuperator (LTR), a recompression compressor (RC), a high-temperature recuperator (HTR), a reactor (R), a turbine (T) and a pre-cooler (PC), the schematic diagram of which is shown in Fig. 1. The supercritical carbon dioxide stream after receiving heat in a fast reactor (1-2) enters into the turbine for expanding and producing power (2-3). The exiting stream from turbine is directed into the HTR and then the LTR for heating stream 8 and 7, respectively. The LTR effectiveness is improved here by means of different mass flow rates between the two heat exchanging streams. The cooled S-CO2 at LTR exit (stream 5) is split into two streams with different mass flow rates. With a greater value of mass flow rate, stream 5a is chilled to a suitable temperature (5a-6) in the pre-cooler before entering the MC to advance the pressure of working fluid (6-7). Leaving the MC, the S-CO2 stream is heated in the LTR and afterwards is mixed with the exiting S-CO2 stream compressed in the RC. After receiving heat in the HTR, the S-CO2 stream flows to the reactor for closure of the SCRBC.

3. Conventional and advanced exergoeconomic analyses The cycle performance is simulated by solution of the equations of mass and energy conversions as well as the exergy balance for each cycle component, together with the property relations. The related equations considered for SCRBC components can be referred to Ref. (Moharamian et al., 2018). Special attention is focused on the exergy values at various streams and the calculated exergy destructions of different components. As a result, these values are the basis for analyzing and evaluating the energy conversion processes from the conventional and advanced exergoeconomic aspects. Several following

6

Journal Pre-proof presumptions are assigned to make the exergoeconomic analyses more traceable (Akbari and Mahmoudi, 2014; Sarkar and Bhattacharyya, 2009): (1) All the processes arise at the case of steady state in the overall cycle. (2) Changes for the potential and kinetic energies are negligible. (3) Pressure drops in the reactor and heat exchange units are considered. (4) Effectiveness is given for the LTR and HTR, and temperature difference is considered to the pre-cooler. (5) Isentropic efficiencies are considered for the compressors and turbine. (6) The cooling water used is at environmental condition. 3.1. Conventional exergoeconomic analysis Exergoeconomic analysis that couples economic principles to exergy analysis is capable of examining the unit exergy product cost at each system stream through well illustrating the cost formation processes, which is not available through conducting the individual exergy analysis or economic assessment. For the sake of obtaining the unit cost at each exergy stream, we must solve the exergoeconomic model of the SCRBC in which the cost balance equations are established for each system component along with auxiliary equations based on the exergy-based monetary costing. The equation of cost rate balance for the kth component is expressed as (Akbari and Mahmoudi, 2014):

 C

e, k

C w, k 

 C

i,k

C q , k  Z k

(1)

where

C  cE

(2)

The expression of Eq. (1) clears that the total cost rate in respect with the exiting exergy streams within a component is identical with the totality of cost rates associated with all the inlet exergy streams and the investment. The investment cost CI

associated with the kth component is expressed by the term Z k , which consists of the capital investment expense ( Zk ) and OM

the operating maintenance cost ( Zk

):

Zk  ZkCI  ZkOM

(3)

CI OM where the two term Zk and Zk are written below in the annual levelized form, respectively (Akbari and Mahmoudi,

2017):

 CRF  Z kCI    Zk  N 

(4)

ZkOM  ZkCI

(5)

7

Journal Pre-proof Here, N is the plant operating hours in a year,  denotes the weighting factor which is often assigned to be 1.06 (Akbari and Mahmoudi, 2017). CRF expresses a factor of capital recovery, which is given as:

CRF 

ir 1  ir 

n

(6)

1  ir n  1

The purchase expenses (Zk) for all the components in the SCRBC are provided at length in Table 1. Note herein that all the values of purchase expenses should be converted into the reference year (2018) from the original time by applying the cost index referred from the Chemical Engineering Plant Cost Index:

Cost at reference year  Original cost 

Cost index at the reference year Cost index at the original year

(7)

For the exeroeconomic modeling the Specific Exergy Costing (SPECO) method (Akbari and Mahmoudi, 2017) which is widely extended in various energy conversion systems is applied in the present study. The exergy streams must be first identified and then the fuel and product exergies are defined for each system component before we perform the application of the cost balance as well as auxiliary equations. In Table 2 it is defined clearly the fuel exergy and product exergy for all the components in the SCRBC. Table 3 shows the cost rate balance relations and corresponding auxiliary equations. The costs of each exergy stream are determined by solution of all the equations. The exergoeconomic factor ( fk ) and relative cost difference ( rk ) which are commonly applied in conventional exergoeconomic analysis to make key design changes in relation to the optimization of thermal systems are respectively given as: fk 

rk 

Z k Z k  C D , k

(8)

cP , k  cF , k

(9)

cF , k

where

C D,k  cF ,k E D,k cF , k 

(10)

C F , k E

(11)

C P , k E

(12)

F ,k

cP , k 

P,k

It is noted that the operating cost, C D , k  Z k , reveals the cost significance of the kth component on influencing the overall cycle based on the exergoeconomic evaluation guidelines (Keçebaş and Hepbasli, 2014). A component with larger 8

Journal Pre-proof operating cost will elaborate its more significance in promoting the system cost effectiveness. The first option for design changes should be given to the component that owns the largest operating cost in the processes of examining an energy conversion system. 3.2. Advanced exergoeconomic analysis It has been demonstrated that advanced exergoeconomic analysis possesses the benefits of determining the real cost savings of a system component as well as the cost impacts among system components, which will not be achieved via application of conventional exergoeconomic analysis. In analogy to dividing exergy destruction, for a component the costs in regard to exergy destruction and investment can be also split into the unavoidable and avoidable parts to assess the authentic potential for economically optimizing the component. The cost split is expressed by (Tsatsaronis and Park, 2002):

C D , k  C DUN, k  C DAV, k

(13)

Zk  ZkUN  ZkAV

(14)

where, UN  UN C D ,k  cF ,k ED,k

(15)

In Eq. (15) E UN D, k is the unavoidable exergy destruction that is incapable to be further lessened because of the technical constraints such as availability and cost of materials as well as manufacturing methods. In Eq. (14) the unavoidable investment UN cost, Zk , is the value that will always be surpassed when a similar component is applied. For calculating E UN D, k , the possible

best operating conditions are assumed for obtaining the minimum exergy destruction within each component that in the future UN just cannot be achieved. The value of Zk is determined under the most inefficient operating conditions for the component.

The unavoidable parts are given as follows, respectively:

E UN D,k

UN

 E D , k  E P , k   E  P,k

 Z Z kUN  E P , k  k  E  P,k

  

(16)

UN

  

(17)

By splitting the costs of each component into endogenous and exogenous parts we can examine the economic interdependences among system components (Petrakopoulou et al., 2013):

C D , k  C DEN, k  C DEX, k

(18)

Zk  ZkEN  ZkEX

(19)

9

Journal Pre-proof EN The endogenous costs ( C DEN,k , Zk ) are associated only with the internal operating conditions, which is determined when

the component considered functions with its realistic efficiency and all the other components work under the theoretical conditions. The exogenous costs are the values that can be reduced through upgrading system structure and improving other components. The endogenous cost rates can be calculated as:

C DEN,k  cF ,k E DEN,k

 Zk ZkEN  E PEN ,k   E  P, k

(20)

  

(21)

By combining the two concepts mentioned above, the costs caused by the kth component are further split into the following four parts in detail, respectively, favoring better understanding the economic interdependence among system components: UN , EN UN , EX C D , k  C D  C D  C DAV, k , EN  C DAV, k , EX ,k ,k

(22)

Z k  Z kUN , EN  Z kUN , EX  Z kAV , EN  Z kAV , EX

(23)

where the unavoidable costs for the kth component related to its operation itself can be calculated respectively by: UN , EN , EN C D  cF , k E UN ,k D,k

 Z k Z kUN , EN  E PEN ,k   E  P,k

(24) UN

  

(25)

with

 E D , k , EN E UN  E PEN ,k  D,k  E  P,k

UN

  

(26)

Afterwards, the other applicable cost rates are reached by: UN , EX UN  UN , EN C D  C D , k  CD , k ,k

(27)

Z kUN , EX  Z kUN  Z kUN , EN

(28)

UN , EN C DAV, k , EN  C DEN, k  C D ,k

(29)

Z kAV , EN  Z kEN  Z kUN , EN

(30)

C DAV, k , EX  C DAV, k  C DAV, k , EN

(31)

Z kAV , EX  Z kAV  Z kAV , EN

(32)

10

Journal Pre-proof To find out the real potential for improvement of components according to advanced exergoeconomic analysis, the new variables which are called the sums of avoidable cost due to exergy destruction and investment, respectively, are introduced below: C DAV, k ,  C DAV, k , EN +

n

 C

AV , EX , k D,r

(33)

r 1 r k

Z kAV ,  Z kAV , EN +

n

 Z

AV , EX , k r

(34)

r 1 r k

In Eqs. (33) and (34) the avoidable exogenous costs with regard to exergy destruction and investment for the rth component that are induced by the kth component can be respectively calculated by:

C DAV,r , EX ,k =cF ,k E DAV,r , EX ,k

(35)

Z rAV , EX , k = Z rEX , k  Z rUN , EX , k

(36)

with , EX , k E DAV, r , EX , k =E DEX, r , k  E UN D,r

(37)

with , EX , k  UN , EN , r  k , EN E UN =ED , r  E UN D,r D,r

(38)

Z rUN , EX , k = Z rUN , EN , r  k  Z rUN , EN

(39)

with UN

  , EN , r  k  EN , r  k ED , r E UN =EP , r   D,r  EP , r

  

 Z r ,r  k Z rUN , EN , r  k =E PEN   ,r  EP , r

  

(40)

UN

(41)

It is worth noticing that the sum of the operating cost, C DAV, k , +Z DAV, k , , is the best parameter for economically determining the significance of components, because it depends only on the avoidable cost values and simultaneously considers the economic interdependence among system components. In addition, a modified exergoeconomic factor ( f kAV , EN ) is applied in advanced exergoeconomic analysis through using the avoidable endogenous costs (Yang et al., 2016): f kAV , EN 

Z kAV , EN C AV , EN  Z AV , EN D,k

(42)

k

11

Journal Pre-proof In comparison with the variable fk , the variable f kAV , EN can contribute more valuable information in regard to the major cost source in the kth component, i.e., whether we should improve the second law efficiency or reduce the investment cost. The thermodynamic cycle based method (Liu et al., 2019b; Mohammadi et al., 2019) that is considered as one of the most reliable and convenient methods for energy systems is employed in this work. To facilitate the calculations, it is necessary to define the real thermodynamic cycle, unavoidable thermodynamic cycle and hybrid thermodynamic cycles (I and II). The real cycle indicates that all of the considered system components are operating under real conditions with irreversibility. The unavoidable cycle means a cycle that is created with all components working on the unavoidable conditions. The hybrid cycle I has the following assumptions: only the considered components work with the same performance as those in the real cycle, while the remaining components work on the ideal conditions. The hybrid cycle II assumes that two considered components work on the real condition and other components are under the ideal conditions. The general procedure for application of advanced exergoeconomic analysis that is described in detail in Refs. (Liu et al., 2019b; Yang et al., 2016) is extended and applied to the SCRBC here. A flow chart of the calculation procedure is illustrated in Fig. 2.

4. Results and discussion Both conventional and advanced exergoeconomic analyses are carried out in the present work to assess and compare the costs due to exergy destruction and investment for deciding about the design changes that will improve the design of the SCRBC. For modeling the SCRBC the parameter values given by Akbari and Mahmoudi (Akbari and Mahmoudi, 2014) under optimized conditions are considered as the input data, which is listed in Table 4. Also, the assumptions for simulation of the cycle performance under real, unavoidable and ideal conditions are shown in Table 5. In various cycles analyzed the net output power is kept always the same as the value at the real case. Using input data and by employing the mass and energy conservations and the exergy balance for each system component, coupled wtableith property relations from the database REFPROP 9.1, the SCRBC process is modeled and simulated with MATLAB code. The simulation results are the basis for performing the exergoeconomic analyses, as listed in Table 6. 4.1. Conventional exergoeconomic analysis results The exergoeconomic analysis based on the conventional technique is first conducted for the SCRBC prior to advancing the evaluation process by introducing the new calculation concepts. Conventional exergoeconomic analysis has a main feature of assigning the monetary price to exergy destruction. The cost associated with exergy destruction is estimated at the component level, and is compared with the relevant investment cost. The resulted exergoeconomic factor

fk can be

considered as an exergoeconomic indicator to determine the option for cost saving. A higher value of exergoeconomic factor

12

Journal Pre-proof implies the heavily investment cost of the kth component that should be reduced. In contrary, a lower data reveals that a reduction of the component exergy destruction is required to improve the exergy efficiency. In addition, the sum of above two cost terms, C D , k  Z k , indicates the cost importance of the evaluated component on influencing the overall system. A component with larger operation cost will elaborate its more significance in promoting the system cost effectiveness. The exergoeconomic parameters for the SCRBC components based on the conventional analysis are outlined in Table 7. We can observe that the highest operating cost is caused by the reactor, followed by the turbine and pre-cooler, respectively. It is also shown in Table 6 that the exergoeconomic factor of reactor is large among cycle components due to the high contribution of investment cost to the operating cost and the reactor has a high relative cost difference also. This indicates that efforts are not advocated to enhance the capital investment cost of reactor for improving the thermodynamic performance of the SCRBC. Besides, based on the low exergoeconomic factor value for pre-cooler along with the high relative cost difference, it is suggested that an increase of its investment cost is profit for improving the exergy efficiency of the cycle even if reducing its economic effectiveness. 4.2. Advanced exergoeconomic analysis results The advanced results of exergy destruction costs for the SCRBC components are outlined in Table 8, and for more clearly illustration, the combined parts of unavoidable/avoidable and endogenous/exogenous concepts are depicted in Fig. 3. We can notice from Table 8 that the unavoidable cost of exergy destruction is higher than the avoidable value for each cycle component apart from the HTR. This indicates that the true potential of advancing a system component should be determined based on its avoidable part rather than its total exergy destruction cost received from performing conventional exergoeconomic analysis. The highest unavoidability of the exergy destruction cost is concerned with the reactor (97.36% of C D , R ) since the high temperature difference between the reactor and the CO2 stream brings about very high inefficiencies in the process of heat exchanging. Furthermore, the highest absolute avoidable exergy destruction cost is due to the pre-cooler, HTR and LTR, respectively, which demonstrates the high potential of the heat exchange units in the SCRBC for improvement of the cycle thermodynamic performance. Another result obtained from Table 8 is the information about the exogenous/endogenous parts of exergy destruction cost. One can observe that all the endogenous values are great than the respect exogenous values for each system component apart from the LTR and pre-cooler. Thus, the main amount of the exergy destruction cost for most of the components originates from the internal inefficiencies by the component itself. The pre-cooler, LTR and HTR own the highest exogenous exergy destruction costs in sequence in the SCRBC, which reveals that the irreversibility within each of these components can be considerably influenced by a modification of the thermodynamic performance for the other components. 13

Journal Pre-proof When evaluate the costs associated with exergy destruction we should consider only the avoidable endogenous/exogenous parts since they are capable of being decreased by enhancing the efficiencies of the considered component itself and the other component efficiencies and cycle structure, respectively. By referring to Table 8 and Fig. 3, we can observe that except for the LTR and pre-cooler, all the cycle components have the higher values of C DAV, k , EN than that of C DAV, k , EX . It is mentioned that among cycle components the HTR owns the highest value of C DAV, k , EN , 30.30% of C DAV,tot, EN in the SCRBC cycle. In addition, the largest value of C DAV, k , EX in the cycle belongs to the pre-cooler, which occupies 52.80% of the C DAV,tot, EX . Therefore, a modification in other component performances brings a significant role on optimizing the pre-cooler. Fig. 4 illustrates the contributions on the overall exergy destruction cost in the SCRBC of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts. Concerning that only the avoidable parts can be reduced, a total amount of 2199.29 $/h can be cut from the overall exergy destruction cost. One can thus conclude that only 38.86% of the overall exergy destruction cost can be reduced even if under the most optimistic condition. Moreover, about half of the C DAV,tot is exogenous, which clears the strong interaction among system components in the considered S-CO2 cycle. The advanced results of investment cost for the SCRBC are shown in Table 9, and for more details and distinct, various parts of the unavoidable/avoidable and endogenous/exogenous combinations are exhibited in Fig. 5. It is found in Table 9 that UN there exists the highest unavoidable investment cost for the reactor, which makes up 92.69% of ZR and 92.24% of Ztot .

Therefore, the extent of improvement in the reactor from the economic view of point is very limited. In respect to the availability in the presented cycle, the turbine retains the largest absolute value among all the cycle components, running with AV 83.23% of ZT and 67.87% of Ztot . This demonstrates the high potential of the turbine for improvement of the cost

effectiveness in the SCRBC. Also, the information being associated with the endogenous and exogenous investment costs is illustrated in Table 9. One can observe that the endogenous investment cost expresses more contribution than the exogenous investment cost except in the the LTR and pre-cooler. Therefore, the main amount of the investment cost for most of the components originates from the internal inefficiencies by the component itself. Furthermore, the reactor has the highest endogenous and exogenous investment EN EX costs, with 68.84% of Ztot and 79.37% of Ztot , respectively.

By referring to Table 9 and Fig. 5, we can observe that apart from the LTR and pre-cooler, all the cycle components have the higher values of Z DAV, k , EN than that of Z DAV, k , EX . It is mentioned that among cycle components the turbine owns the highest

14

Journal Pre-proof value of Z DAV, k , EN , operating with 72.61% of Z DAV,tot, EN in the SCRBC cycle. In addition, the largest value of Z DAV, k , EX in the cycle belongs to the turbine also, which occupies 52.57% of the Z DAV,tot, EX . Fig. 6 shows the contributions on the overall investment costs in the SCRBC of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts. Concerning that only the avoidable parts can be reduced, a total amount of 1735.39 $/h can be cut from the overall investment cost. It can be thus concluded that only 27.65% of the overall investment cost can be reduced maximally. The exogenous costs especially the avoidable exogenous costs are further split in this study in order to preferably comprehend the interdependences among cycle components and to reflect additional potential for improvement of the entire cycle. Table 10 shows the results of splitting avoidable exogenous costs with regard to exergy destruction and investment for the system components in the SCRBC. As an instance, an improvement of the HTR can considerably reduce the exergy ,EX , HTR destruction cost in the pre-cooler by decreasing the value of C DAV, PC . The negative value of C DAV,T,EX , HTR indicates that a

reduction of the inefficiencies within the HTR will bring about an advance of the exergy destruction cost related to the turbine. Moreover, the mexogenous cost which is expressed as the difference between the exogenous cost and the sum of the split parts due to each of the other components is also outlined in Table 10. One can observe that the mexogenous exergy destruction cost of the pre-cooler and the mexogenous investment cost of the turbine are very high among the cycle components, which suggests the intense interaction of components and structure design for these components. The sum of avoidable operating cost within the kth component ( C DAV, k , + Z kAV , ) in the SCRBC is computed by the addition of the avoidable costs of exergy destruction and investment caused by its own inefficiencies and its operation on the other components. This variable is the best parameter for revealing the true potential for improving the kth component because it is determined based on the component availability and the interactions among cycle components. The calculated processes and results of C DAV, k , + Z kAV , are outlined in Table 11. From the table, while the HTR possesses the largest value of C DAV, k , due to the high exergy destruction, the turbine has the largest value of C DAV, k , + Z kAV , among the cycle components because of the high investment cost. By referring to Table 11 and Fig. 7, many different and interesting conclusions can be obtained on the component importance by comparing the operating costs on basis of conventional and advanced exergoeconomic analyses. The results of conventional technique suggest the reactor as the most important influential component for enhancing the economic effectiveness of the whole cycle due to the most amount of C D,k +Zk (5313.39 $/h), followed by the turbine and pre-cooler. With the different criteria used in advanced exeroecomomic analysis ( C DAV, k , + Z kAV , ), the turbine should be

15

Journal Pre-proof exposed the highest priority for modification due to the highest value of C DAV, k , + Z kAV , (1390.88 $/h), followed by HTR and MC. It is noted herein that conclusions gathered from advanced exergy analysis are more pragmatic since it is considered both the interactions among components as well as the technical limitations of each component. Fig. 8 shows the exergoeconomic factor results of each component through employment of conventional and advanced exergoeconomic analyses. On basis of the both methods, the investment costs of reactor and turbine should be decreased due to the higher amounts of exergoeconomic factor. The HTR, LTR and pre-cooler are suggested to reduce their exergy destructions because of the lower values of exergoeconomic factor. 4.3. System improvement for green energy development Recently, many countries put great efforts in the research and development of the S-CO2 cycle since it is one of the most promising cycles for future nuclear power plant. This hot research area is related to the green energy development. The analysis and improvement of this cycle are thus imperative. The conventional exergy-based analysis identifies the improvement potential from the real operating conditions to the best ideal conditions. The advanced exergy-based analysis enjoys the advantages of determining the real improving potential considering the technical and economic limitations. In order to illustrate the application of the research results in industrial aspects, the unit product costs of the cycle are quantitatively compared by using the parameter settings of real, unavoidable inefficiency and ideal processes in Table 5. Meanwhile, the isentropic efficiencies of the compressor and turbine remain the constant value of 0.90 on account of the cost relations considered in this work. It is found that the exergy efficiency of the real SCRBC is 0.48 and the unit product cost of the real cycle is 17.15 $/GJ. According to the conventional exergy-based analysis, the exergy efficiency of the ideal SCRBC is 0.64 and the unit product cost of the real cycle is 18.24 $/GJ. However, it is impossible to eliminate completely the pressure drops and temperature differences of heat exchangers even if using the best available technology. Therefore, in the real industrial application it may be more appropriate to employ the advanced exergy-based analysis to evaluate the system improvement characteristic. Under the unavoidable condition considered in this work, the system efficiency can be improved to 0.59 at a expense of increasing the investment cost, resulting in a higher unit product cost of 19.52 $/GJ. In other words, it is not always favorable to improve the cycle thermal performance, but should balance the trade-off between the cycle thermal and cost performances.

5. Conclusions The technique of advanced exergoeconomic analysis is extended and applied in the present work to the supercritical carbon dioxide recompression Brayton cycle for the first attempt. The base of this advanced technique is splitting into different

16

Journal Pre-proof parts of the exergy destruction cost and investment cost. The analysis results indicate that as a great reinforcement of conventional exergoeconomic analysis, the advanced exergoeconomic analysis proposed in this work can not only identify where and to what extend can the improvements in the cycle be achieved, but also can determine the sequence in optimizing an individual component or subsystem to accomplish its highest profits. In this regard, the main conclusions are summarized as following: (1) The unavoidable exergy destruction cost is larger than the avoidable value for each cycle components apart from the HTR. The largest exergy destruction cost is located at the pre-cooler (1540.32 $/h), LTR (948.58 $/h) and HTR (898.33 $/h), respectively, while based on the avoidable value the sequence is the pre-cooler (766.43 $/h), HTR (517.92 $/h) and LTR (282.56 $/h). At the whole cycle level only a total amount of 2199.29 $/h can be cut from the overall exergy destruction cost even if under the most optimistic conditions (38.86%). Therefore, more efficient and compact heat exchangers should be developed in the future, e.g. printed circuit heat exchangers for nuclear power plants. (2) In the cycle about half of the overall avoidable exergy destruction cost is exogenous (1100.94 $/h), indicating strong interactions among system components in the considered supercritical power cycle. The pre-cooler owns the highest avoidable-exogenous exergy destruction cost amongst all the components (581.33 $/h), occupying 52.80% for the overall avoidable-exogenous exergy destruction cost of the cycle. (3) The highest unavoidability concerning the component exergy destruction cost is owned by the reactor (97.36%, 773.54 $/h). Moreover, the highest absolute unavoidable investment cost exists at the reactor (4188.30 $/h), making up 92.69% of its total investment cost. Therefore, the extent of improvement in the reactor from the economic view of point is very limited. (4) An improvement of the HTR can considerably lessen the exergy destruction cost in the pre-cooler, while a reduction of the inefficiencies within the HTR will bring about an advance of the exergy destruction cost for the turbine. (5) The results of conventional exergoeconomic analysis suggest the reactor as the most important influential component for improving the cost effectiveness of the whole cycle due to the most amount of operating cost (5313.39 $/h), followed by the turbine and pre-cooler. Unlikely, the turbine should be exposed the highest priority for modification with the highest value for the sum of avoidable operating cost (1390.88 $/h), followed by HTR and MC. (6) As indicated above, the component interactions in the considered cycle is strong, and the exergy destruction cost and the investment cost is often contradictory to each other. To obtain more efficient clean energy conversion cycles, the trade-off between the above two parameters should be well balanced in the future work. It is worth noticing again that the supercritical carbon dioxide Brayton cycle has many advantages over the conventional steam Rankine cycle or Brayton cycle owing to its simple layout, higher efficiency, and compact equipment size. This cycle is considered suitable for different heat sources such as nuclear and solar thermal. This hot research area is related to the green 17

Journal Pre-proof energy development that can balance various power generations, creating a robust and smart grid. Due to the better efficiency and compact size, the supercritical carbon dioxide Brayton cycle also has the potential to be applied in distributed or portable energy systems. The advanced analysis proposed in this work is to provide cycle designers and operators with more useful information for improving the design and operation of such systems.

Acknowledgements This work was supported by the National Natural Science Foundation of China (51976155), the Research Funds for Young Stars in Science and Technology of Shaanxi Province (2019KJXX-098), China Post-Doctoral Science Foundation Funded Project (2018M640986), and the fundamental research funds for central universities (xtr042019019). The author (Xiaohu Yang) also gratefully acknowledged the support of K. C. Wong Education Foundation.

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Journal Pre-proof List of Table Captions Table 1 Cost relations for the capital investment costs in the SCRBC (Sarkar and Bhattacharyya, 2009). Table 2 Fuel and product exergies for the SCRBC components. Table 3 Cost balance equations and auxiliary relations for the SCRBC components. Table 4 Input data for simulating the SCRBC. Table 5 Values of assumption under various conditions (Moharamian et al., 2018). Table 6 Properties and mass flow rate at different streams under real, unavoidable and ideal processes. Table 7 Conventional exergoeconomic analysis results for each SCRBC component. Table 8 Advanced results of exergy destruction costs for the SCRBC components. Table 9 Advanced results of investment costs for the SCRBC components. Table 10 Results of splitting avoidable exogenous costs for the SCRBC components. Table 11 Results for the sum of avoidable operating cost within the SCRBC components.

22

Journal Pre-proof Table 1 Cost relations for the capital investment costs in the SCRBC (Sarkar and Bhattacharyya, 2009). Component

Capital investment cost equation

Reactor

Z R  0.283 q R

Turbine

   pi  1  0.036 i  54.4  Z T  479.34 m i   1 e  ln   0.93   T   p e 

LTR, HTR

Z k  2681Ak0.59， Ak 

Pre-cooler

0.514 Z PC  2143 APC , APC 

MC, RC

Z k  71.1m i





qk U k  LMTDk U PC

q PC  LMTDPC

pe  pe  1 ln   0.92   C pi  pi 

Table 2 Fuel and product exergies for the SCRBC components. Component

E F , k

E P,k

Reactor

E15

E 2  E1

Turbine

E 2  E 3

E 1 1

HTR

E 3  E 4

E1  E 8

LTR

E 4  E 5

E 8a  E 7

Pre-cooler

E 5a  E 6

E10  E 9

MC

E 1 3

E 7  E 6

RC

E12

E 8 b  E 5b

Table 3 Cost balance equations and auxiliary relations for the SCRBC components. Auxiliary relations

Component

Cost balance equations

Reactor

C2  C1 +Cfuel  Z R

Turbine

C3  C11  C2  ZT

C 2 E 2  C3 E3，C11 E11  C14 E14

HTR

C 4  C1  C3  C8 +Z HTR

C3 E3  C 4 E 4

LTR

C5  C8a  C 4  C 7  Z LTR

C 4 E 4  C5 E5

Pre-cooler

C 6  C10  C5a  C9  Z PC

C9  0

MC

C13 =C 6 +C13  Z MC

C11 E11  C13 E13

RC

C8b =C5b +C12  Z RC

C11 E11  C12 E12

23

Journal Pre-proof Table 4 Input data for simulating the SCRBC. Parameter

Unit

Value

Inlet pressure of MC

MPa

7.4

Inlet temperature of MC

K

308.15

Pressure ratio of MC

-

3

Outlet temperature of reactor

K

823.15

Reactor temperature

K

1073.15

Output power of reactor

MW

600

Ambient temperature

K

298.15

Ambient pressure

MPa

0.101

Annual working hours

h

8000

Interest rate

-

0.12

Expected life of the plant

y

20

Table 5 Values of assumption under various conditions (Moharamian et al., 2018). Component

Parameter, unit

Unavoidable

Real process

Unavoidable

investment cost

Ideal process

thermodynamic inefficiency

Reactor

Δp [˗]

0.1

0.02

0.01

0

Turbine

ηT [˗]

0.7

0.9

0.93

1

HTR

ε/Δp [˗/˗]

0.7/0.1

0.86/0.03

0.95/0.01

1/0

LTR

ε/Δp [˗/˗]

0.7/0.1

0.86/0.02

0.95/0.01

1/0

Pre-cooler

Δτ/Δp [K/˗]

20/0.1

10/0.01

3/0.005

0/0

MC

ηMC [˗]

0.7

0.85

0.92

1

RC

ηRC [˗]

0.7

0.85

0.92

1

Table 6 Properties and mass flow rate at different streams under real, unavoidable and ideal processes.

Unavoidable inefficiency

Real process

pStream (MPa) T (K) 1 m (kg/s) 2 3 4 5 6 7 8 9 10

p (MPa)

T (K)

m (kg/s)

p (MPa)

T (K)

m (kg/s)

21.10

669.16

3151.15

21.76

667.56

2444.41

20.68

823.15

3151.15

21.54

823.15

2444.41

7.86

708.04

3151.15

7.59

695.57

2444.41

7.63

555.16

3151.15

7.51

514.05

2444.41

7.47

411.74

3151.15

7.44

393.09

2444.41

7.40

308.15

2313.42

7.40

308.15

1781.36

22.20

388.39

2313.42

22.20

386.72

1781.36

21.76

530.27

3151.15

21.98

504.49

2444.41

0.10

298.15

4105.00

0.10

305.15

4105.00

0.10

320.91

4105.00

0.10

320.38

4105.00

24

Ideal process (%) pf k(MPa) T (K) rk (% ) 22.20 658.79 22.20 823.15 7.40 679.68 7.40 491.81 7.40 385.12 7.40 308.15 22.20 385.12 22.20 491.81 0.10 308.15 0.10 319.13

m (kg/s)

1954.84 1954.84 1954.84 1954.84 1954.84 1373.82 1373.82 1954.84 4105.00 4105.00

Journal Pre-proof Table 7 Conventional exergoeconomic analysis results for each SCRBC component. Component

c F , k ( $ GJ )

c P , k ( $ GJ )

C D , k ( $ h )

Zk ( $ h )

C D , k  Z k ( $ h )

Reactor

2.85

6.99

794.53

4518.86

5313.39

85.04

145.26

Turbine

10.02

11.48

678.45

1415.10

2093.55

67.59

14.57

HTR

10.02

10.96

898.33

17.41

915.74

1.90

9.38

LTR

10.02

11.60

948.58

17.77

966.35

1.83

15.77

Pre-cooler

10.02

40.29

1540.32

4.86

1545.18

0.31

302.10

MC

11.48

13.64

510.21

225.08

735.29

30.61

18.82

RC

11.48

12.83

289.78

76.90

366.68

20.97

11.76

f k (%)

rk (% )

Table 8 Advanced results of exergy destruction costs for the SCRBC components. Component

C DUN, k ($ h)

C DAV, k ($ h)

C DEN, k ($ h)

C DEX, k ($ h)

C DUN, k, EN ($ h )

C DUN, k, EX ($ h )

C DAV, k , EN ($ h )

C DAV, k , EX ($ h )

Reactor

773.54

20.99

531.41

263.12

517.37

256.17

14.04

6.95

Turbine

460.78

217.68

554.16

124.29

376.36

84.41

177.80

39.88

HTR

380.41

517.92

577.17

321.16

244.41

136.00

332.76

185.16

LTR

666.02

282.56

465.79

482.79

327.04

338.98

138.75

143.81

Pre-cooler

773.89

766.43

371.99

1168.33

186.90

587.00

185.10

581.33

MC

257.05

253.16

321.31

188.90

161.88

95.17

159.43

93.73

RC

149.23

140.55

186.52

103.26

96.05

53.18

90.47

50.08

Table 9 Advanced results of investment costs for the SCRBC components. Component

ZkUN ($ h)

ZkAV ($ h)

ZkEN ($ h)

ZkEX ($ h)

Z kUN , EN ($ h)

Z kUN , EX ($ h)

Z kAV , EN ($ h)

Z kAV , EX ($ h)

Reactor

4188.30

330.55

3022.36

1496.50

2801.28

1387.03

221.08

109.47

Turbine

237.31

1177.78

1155.85

259.24

193.84

43.48

962.01

215.77

HTR

12.23

5.18

11.19

6.22

7.86

4.37

3.33

1.85

LTR

10.89

6.87

8.72

9.04

5.35

5.54

3.37

3.50

Pre-cooler

2.17

2.70

1.17

3.69

0.52

1.64

0.65

2.05

MC

67.73

157.36

141.75

83.33

42.65

25.08

99.10

58.26

RC

21.94

54.96

49.50

27.40

14.12

7.82

35.37

19.58

25

Journal Pre-proof Table 10 Results of splitting avoidable exogenous costs for the SCRBC components. kth

C DAV,k,EX ($ h)

Z kAV , EX ($ h)

rth

C DAV, k ,EX , r Z kAV , EX , r kth ($ h) ($ h)

C DAV,k,EX ($ h)

Z kAV , EX ($ h)

rth

C DAV, k ,EX , r ($ h)

Z kAV , EX , r ($ h)

Reactor

6.95

109.47

Turbine

1.25

19.76

581.33

2.05

Reactor

28.58

0.10

HTR

1.66

26.09

Turbine

68.56

1.24

LTR

0.78

12.28

HTR

111.21

2.39

PC

0.05

0.8

LTR

39.69

3.14

MC

0.63

9.94

MC

35.38

4.12

RC

0.34

5.35

RC

17.80

5.06

mexo

2.24

35.25

mexo

280.11

-14.00

Reactor

1.70

9.18

Reactor

4.24

2.63

HTR

-8.93

-48.29

Turbine

29.09

19.08

LTR

15.23

82.41

HTR

43.40

28.98

PC

0.24

1.28

LTR

-7.06

-1.39

MC

10.14

54.84

PC

1.69

5.05

RC

7.31

39.57

RC

7.85

9.88

mexo

14.19

76.78

mexo

14.52

-5.97

Reactor

13.68

0.14

Reactor

2.37

0.93

Turbine

83.59

0.84

Turbine

16.26

7.36

LTR

24.09

0.24

HTR

-48.25

-16.87

PC

7.28

0.07

LTR

55.09

24.54

MC

15.04

0.15

PC

-0.39

3.85

RC

-5.49

-0.05

MC

3.23

6.26

mexo

46.97

0.46

mexo

21.77

-6.49

Reactor

3.94

0.10

Turbine

26.00

1.63

HTR

40.12

2.98

PC

-0.18

3.00

MC

9.45

4.23

RC

27.58

5.67

mexo

36.9

-14.11

Turbine

HTR

LTR

39.88

185.16

143.81

215.77

1.85

3.50

PC

MC

RC

93.73

50.08

58.26

19.58

Table 11 Results for the sum of avoidable operating cost within the SCRBC components. C DAV, k , ($ h)

Z kAV , ($ h)

C DAV, k , +Z kAV , ($ h)

13.08

68.55

234.16

302.71

202.69

48.38

380.49

1010.39

1390.88

3.33

139.21

-4.72

471.97

-1.39

470.58

138.75

3.37

127.82

121.22

266.57

124.59

391.16

Pre-cooler

185.10

0.65

8.69

14.05

193.79

14.7

208.49

MC

159.43

99.10

73.87

79.54

233.3

178.64

411.94

RC

90.47

35.37

55.39

65.48

145.86

100.85

246.71

C DAV, k , EN ($ h )

Z kAV , EN ($ h)



Reactor

14.04

221.08

54.51

Turbine

177.80

962.01

HTR

332.76

LTR

Component

n

C DAV, r , EX , k ($ h)

r 1 r k

n



Z rAV , EX , k ($ h )

r 1 r k

26

Journal Pre-proof List of Figure Captions Fig. 1. Schematic diagram for the SCRBC. Fig. 2. A flow chart of the calculation procedure. Fig. 3. Comparison of system component contributions on the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous exergy destruction costs. Fig. 4. Contributions on the overall exergy destruction costs of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts. Fig. 5. Comparison of system component contributions on the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous investment costs. Fig. 6. Contributions on the overall investment costs of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts. Fig. 7. Comparison of the operating costs between the conventional and advanced techniques. Fig. 8. Comparison of the exergoeconomic factors between the conventional and advanced techniques.

27

Journal Pre-proof

Fig. 1. Schematic diagram for the SCRBC.

28

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Fig. 2. A flow chart of the calculation procedure.

29

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Fig. 3. Comparison of system component contributions on the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous exergy destruction costs.

30

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Fig. 4. Contributions on the overall exergy destruction costs of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts.

31

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Fig. 5. Comparison of system component contributions on the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous investment costs.

32

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Fig. 6. Contributions on the overall investment costs of the unavoidable-endogenous, unavoidable-exogenous, avoidable-endogenous and avoidable-exogenous parts.

33

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Fig. 7. Comparison of the operating costs between the conventional and advanced techniques.

34

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Fig. 8. Comparison of the exergoeconomic factors between the conventional and advanced techniques.

35

Journal Pre-proof CRediT author statement Zhan Liu: Conceptualization, Methodology, Writing - Original Draft. Zihui Liu: Software, Formal analysis. Xing Cao: Validation, Formal analysis. Tao Luo: Data Curation, Visualization. Xiaohu Yang: Supervision, Writing - Review & Editing, Visualization.

Journal Pre-proof

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Highlights: 

Advanced exergoeconomic analysis is applied to supercritical CO2 Brayton cycle.



Only 38.86% of overall exergy destruction cost can be reduced at best conditions.



Strong interactions among components occur in the supercritical power cycle.



Precooler should be improved at the expense of increasing its investment cost.