Advanced exergy and exergoeconomic analysis of a novel liquid carbon dioxide energy storage system

Energy Conversion and Management 205 (2020) 112391

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Advanced exergy and exergoeconomic analysis of a novel liquid carbon dioxide energy storage system

T

⁎

Zhan Liua,b, , Zihui Liua, Xuqing Yanga, Hongyan Zhaia, Xiaohu Yangc a

College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, PR China School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China c School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Compressed gas energy storage Liquid carbon dioxide Exergy analysis Exergoeconomic analysis Advanced exergy-based method

In the present study a liquid carbon dioxide energy storage system with 10 MW output power production is analyzed thermo-economically by utilizing conventional and advanced exergy-based analysis. New exergy-based concepts such as unavoidable/avoidable and endogenous/exogenous exergy destruction, exergy destruction costs and investment costs as well as the combination of the two concepts are introduced to provide valuable knowledge about the interchanges among system components and the true latent capacity for improvement of each significant system component. It is demonstrated from the overall system analysis that the avoidable endogenous value is only 42.1% for total exergy destruction, 43.42% for total exergy destruction costs and 55.43% for total investment costs in the proposed system. Results from conventional exergy analysis suggest that the compressor contributes the utmost influence to the overall exergy destruction, while results from both the advanced exergy and exergoeconomic evaluation introduce the expander as the most significant component that has the highest improvement priority. In brief, the advanced exergy-based analyses can enhance engineers perception on the processes of energy conversion in the proposed system and also can improve the quality of the conclusions.

1. Introduction Compressed air energy storage (CAES) holds a proven track record for supporting the flexible and scalable integration of wind power generation into electricity grid, which is in favor of increasing the penetration growth in power market [1,2]. In differentiation with air, carbon dioxide (CO2) is liable to liquefaction by using current measures since its critical state is easier to access (30.98 °C, 7.38 MPa) [3]. When a CO2 energy conversion system runs above the critical condition, the working fluid holds a high density overall the system in advantage of reaching a low volume to power ratio [4]. Thereby it can be expected the compactness of system components such as turbo-machineries and heat exchange units. In addition, nearby the critical point the compression work in supercritical CO2 cycle is much reduced due to the large variation of CO2 thermo-physical properties resulting in a 0.2–0.5 compressibility factor of CO2 [5]. Moreover, utilizing CO2 instead of air in compressed gas energy storage will also offer a probability for utilization of CO2 on a large scale, favoring reducing carbon emissions. All the above merits make the compressed CO2 energy storage (CCES) cycle a more preference system. Increasing attentions have been therefore

⁎

attracted on developing new CCES systems, such as transcritical and supercritical CCES systems [6–9], hybrid thermal CCES system [10], trigeneration concept-based CCES system [11], and liquid CO2 energy storage (LCES) system [12]. Today the rapid increase in energy need is also driving researchers to develop the energy conversion system that is more efficient and cost effective with the exception of seeking for renewable clean energy sources. The exergy-based methods are recognized the most powerful tool in appraisement of the function of an energy conversion cycle. For example, in contrast to a first-law energy analysis which remains the energy quantity, conventional exergy analysis can assist designers to discover the location and magnitude of irreversibilities. With special regard to CO2 energy storage, all of the abovementioned systems [6–12] have been evaluated and improved by means of conventional exergy analysis. One should be emphasized here that implementation of the exergy analysis for a thermal system is only from the viewpoint of thermodynamics, which pursues the maximization of thermodynamic efficiencies. As a result, a thermodynamically optimal system is usually economically infeasible because of the unacceptable capital investment and product cost. Both thermodynamic and economic performances

Corresponding author at: College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, PR China. E-mail address: [email protected] (Z. Liu).

https://doi.org/10.1016/j.enconman.2019.112391 Received 10 September 2019; Received in revised form 6 December 2019; Accepted 7 December 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

TV

Symbols

Greeks

A c Ċ CRF D e Ė f h ir LMTD ṁ n p Q̇ s U Ẇ y* Ż

η ϕ τ ε Δ

area of heat exchange (m2) specific cost ($/GJ) cost rate ($/d) capital recovery factor day (d) specific exergy flow rate (J·kg−1) exergy flow rate (W) exergoeconomic factor specific enthalpy (J·kg−1) interest rate logarithmic mean temperature difference (K) mass flow rate (kg·s−1) plant life time (y) pressure (Pa) heat transfer rate (W) specific entropy (J·kg−1·K−1) heat transfer coefficient (W·m−2·K−1) power (W) exergy destruction ratio investment cost rate ($/d)

throttle valve

isentropic efficiency maintenance factor temperature (K) exergy efficiency change quantity

Subscripts 0 D j e F i is k L P r tot

reference state destruction stream number exit fuel inlet isentropic the k-th component loss product reference total

Abbreviations

Superscripts

C CAES CCES CO2 CON E EV G HPT HT LPT M LCES

PH PT KN CH τ M CI OM AV UN EN EX

compressor compressed air energy storage compressed CO2 energy storage carbon dioxide condenser expander evaporator generator high-pressure tank hot tank low-pressure tank motor liquid CO2 energy storage

physical potential kinetic chemical thermal mechanical capital investment operation-maintenance avoidable unavoidable endogenous exogenous

drying process [18], a supercritical power plant by firing the coal [19], natural gas liquefaction [20] and a geothermal-based Kalina cycle [21]. It can be deduced that this new exergy analysis method is a promisingly influential tool for scrutinizing the thermodynamic nature of compressed gas energy storage systems. That said, advanced exergy analysis of gas energy storage systems remains very limited amount of researches. Based on this new exergy analysis method, Wang et al. [22] analyzed a 2 MW underwater CAES system and the results demonstrated a significant potential of system improvement by comparing an 84.3% system exergy efficiency under unavoidable conditions with a value of 53.6% under the real conditions. It was also found that the system components interacted complexly but not very severely. He et al. [23] examined a supercritical CCES system and a CAES system through application of advanced exergy principles. The results was reported that a higher efficiency of compressor, combustor and turbine could make for better system performance. Liu et al. [24] implemented both conventional and advanced exergy analysis on a two-stage transcritical CCES system. Results from conventional exergy analysis recognized that optimization of the system should be started with the cold storage because of the largest exergy destruction, whereas the advanced method identified the first compressor as the most important component due to the largest avoidable exergy destruction. Meanwhile, there have occurred several advanced exergoeconomic analyses to different

should be synthesized to balance their trade-off in a rational use of energy conversion processes. Conventional exergoeconomic analysis as another elegy-based approach has been therefore extensively devoted to assessing the thermo-economic performance of many energy systems. Throughout exergoeconomic analysis we can determine also the costs of irreversibilities in an energy system besides the location, magnitude and causes. To be conclusive from the aforementioned studies, although provides useful information about the exergy destruction and related costs, the conventional exergy-based analysis neither provides the efficiency of interactions among the interlinking components, nor gives the real potential that can be improved by overcoming the technical and economic limitations. To better address the limitations of conventional exergy analysis, the novel ideal was first reported and further developed of subdividing exergy destruction within each component into unavoidable/avoidable as well as exogenous/endogenous parts by Tsatsaronis and co-workers [13–15], which is called advanced exergy analysis. With this advanced method, engineers can obtain additional details for further comprehending how thermodynamic inefficiencies are formed, favoring improving the energy conversion processes. In recent years, applications of this advanced technique have been proposed in different energy conversion systems, such as absorption refrigeration machines [16], a cogeneration system based on liquefied natural gas (LNG) [17], a food 2

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concepts. As a result, one can detect that whether the irreversibilities in one component is because of other components or is imposed on the components by its own inefficiencies, and determine major sources of irreversibilities and better design of this system. The suggestions derived from this work can not only be conductive to improve the performance of the advised LCES system but also guide the design and optimization of other new gas energy storage systems. The issues examined in this paper have never been reported in current publications in the same way.

thermal systems, in which we can gain knowledge of cost interactions and improvement potential by splitting costs associated with exergy destruction as well as investment costs into unavoidable/avoidable and exogenous/endogenous parts. Application of advanced exergoeconomic analysis has been carried out in a gas turbine system [25], a LNG plantbased cogeneration system [26], a power plant with CO2 capture [27], geothermal district heating-systems [28,29], tri-generation cycles [30,31], an electricity facility works with natural gas [32], a complex industrial plant [33], a heat pump based on gas engine [34], a desalination system [35], an oil shale retorting processes [36], the combined cycles of firing biomass and natural gas [37], a solar energy system [38], and an air refrigeration system [39]. However, there is no report on use of advanced exergoeconomic analysis for examination of a gas energy storage system. The fundamental innovation of this investigation is to perform synthetically the thermodynamic and economic analysis of a novel LCES system by means of both conventional and advanced exergy-based approaches in a first attempt. Exergy destruction, costs related to exergy destruction as well as the investment costs within system components are split into unavoidable/avoidable and exogenous/endogenous parts, and also the corresponding combinations of the two

2. Analysis methods 2.1. System description An innovative LCES system is developed in this research on account of supercritical Brayton cycle and liquid storage, the schematic and the T-s diagram of which is well given in Fig. 1. This LCES cycle is configured with a low-pressure tank (LPT), a throttle valve (TV), two evaporator (EV1 and EV2), a compressor (C), a motor (M), a cooler, two condensers (CON1 and CON2), a high-pressure tank (HPT), a heater, a expander (E), three hot tanks (HT1, HT2 and HT3). For the sake of

Fig. 1. (a) Schematic diagram of the LCES system; (b) T-s diagram for LCES system. 3

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charging stage and the discharging stage. (3) Pressure drops in pipes, tanks and heat exchange units are neglected. (4) LPT and HPT are not insulated, thus the outlet temperature equals to ambient temperature. (5) The HT2 and HT3 are insulated completely and the flow processes are isothermal.

Table 1 Equations of energy balance for modeling LCES system. Component

Energy balance equations

Compressor

WĊ = ṁ (h4 − h3) ẆE = ṁ (h9 − h10) ̇ 1 = ṁ (h3 − h2) = ṁ 12 (h12 − h13) QEV ̇ QCooler = ṁ (h4 − h5) = ṁ 14 (h15 − h14 )

Expander EV1 Cooler CON1

̇ QCON1 = ṁ (h5 − h6) = ṁ 18 (h19 − h18)

EV2

Q̇EV 2 = ṁ (h8 − h7) = ṁ 18 (h20 − h21) Q̇Heater = ṁ (h9 − h8) = ṁ 14 (h16 − h17)

Heater CON2 TV

Modeling of the presented system thermodynamically is in view of the control volume method. Application of mass and energy conservations over a control volume of system, the common governing equations are written respectively as:

̇ QCON 2 = ṁ (h10 − h11) = ṁ 22 (h23 − h22) h2 = h1

significantly reducing the limitations of current CO2 energy storage systems [6–12], the main superiorities and differences of the presented LCES system can be summarized as: (a) no extra heat sources is needed, eliminating the use of fossil fuels; (b) liquid CO2 is stored in artificial storage tanks, removing the dependence on huge cravens; (c) no extra cold sources and enormous packed-bed cold storage units are required, and the ambient water is applied to liquefy the gaseous CO2 after expansion in the discharging stage and to evaporate the liquid CO2 in the charging stage. Therefore, the main difference between the proposed system and the previous LCES systems [7,11,12] is that liquefaction of the gaseous CO2 after expansion in the discharging stage is carried out by utilizing a huge cold storage device. During off-peak time, the LCES system is situated at charging stage. Surplus electricity from the external grid is applied to drive compressor. Liquid CO2 (stream 1) rejected from LPT passes through TV to lower its pressure and temperature, and subsequently become gaseous phase after evaporation in EV1 which is fed with ambient water. The CO2 is then pulled into compressor for pressure boost. A great deal of heat is simultaneously produced over the process of compression. Heat exchange units are therefore required to retrieve the heating energy and in the meantime to cool down the high-temperature supercritical CO2 fluid (stream 4). It has been mentioned before that supercritical CO2 experiences commonly a large variation of thermo-physical properties, thus two heat exchanger units (cooler and CON1) are arranged to reduce the thermodynamic irreversibilities. The HTC and LTC are fed with water discharged from HT1 and ambience, respectively. After the two heat exchangers, the high-temperature supercritical fluid is cooled to liquid fluid, and this high-pressure liquid CO2 is transferred to HPT (stream 6). The hot water carried compression heat is separately stored in HT2 and HT3. During peak time, the LCES system is situated at discharging stage. The high-pressure liquid CO2 delivered from HPT (stream 7) is heated twice by passing it through two consecutive heat exchanger units (EV2 and heater). The reverse direction fluid is also water that is offered by HT3 and HT2, respectively. The high-temperature supercritical CO2 (stream 9) then enters into expander for generating power. Subsequently, the released CO2 gas (stream 10) is chilled down and subsequently condensed to liquid state (stream 11) in CON2 by taking advantage of the ambient cold water. After leaving CON2, this lowpressure liquid is stored in LPT.

∑ ṁ i − ∑ ṁ e = 0

(1)

Q̇ − Ẇ =

(2)

∑ (mḣ )e − ∑ (mḣ )i

where ṁ , Q̇ , Ẇ and h denote mass flow rate, heat transfer rate, power and enthalpy, respectively. Subscripts i and e stand for in and exit, respectively. Isentropic efficiency of compressor and expander is calculated as, respectively:

ηC =

(his,4 − h3 ) (h4 − h3 )

(3)

ηE =

(h9 − h10 ) (h9 − his,10 )

(4)

where η is isentropic efficiency of turbomachinery and the subscript is denotes the isentropic compression and expansion. Applying the above equations and assumptions, the equations of energy balance for each system component are indexed in Table 1. 2.3. Conventional exergy and exergoeconomic analyses According to the second thermodynamic law, exergy is defined as the maximum work potential when an energy system converses from a given condition to an ambience condition. The overal exergy of each material stream in the system is given as follows [24]: PH

Ej̇ = E j̇

CH

+ E j̇

PT

+ E j̇

KN

+ E j̇

(5)

where E ̇ is the exergy and j is the stream number; superscripts PH, CH, PT and KN denotes physical, chemical, potential and kinetic exergy, respctively. As chemical reaction does not occur in each component of LCES system and the system is recognized as rest relative to environment, the overall exergy is thus calculated only involving the physical exergy as: PH ̇ jPH = ṁ [(hj − h 0 ) − τ0 (sj − s0 )] Ej̇ = E j̇ = me

(6)

In some LCES components analyzed, the temperature during component operation may be always lower than reference temperature (TV), or the temperature is crossed (compressor and EV1). In either case, it is suggested to subdivide the physical exergy into its thermal and mechanical parts [13]:

ejPH = ejτ + ejM

2.2. Thermodynamic modeling

= For the sake of directing exergy-based analysis, the initial step is performing thermodynamic modeling to simulate the whole LCES system. Several presumptions are assigned in the following section to make the exergy-based analysis more traceable:

[(hj − hj, X ) − τ0 (sj − sj, X )]p = const + [(hj, X − hj,0 ) − τ0 (sj, X − sj,0 )]τ0= const

(7)

in which the former part is mainly due to temperature and the latter one is mainly due to pressure; the point X is defined at the reference temperature τ0 under a given pressure p. The exergy balance equation is given in Eq. (8) for each component, and the subsequent equation is for the overall system:

(1) All the processes arise at the case of steady state in the overall system. (2) The working fluid runs with the same mass flow rate between the

EḞ , k = EṖ , k + EḊ , k 4

(8)

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EḞ , tot = EṖ , tot + EḊ , tot + EL̇ , tot

a system component in advanced exergy analysis is determined via performing the division of the exergy destruction in the component with avoidable and unavoidable parts [25]:

(9)

where EṖ , k is described as the anticipated result acquired by the component, and EḞ , k stands for the exergy sources expended in the component to produce EṖ , k . EL̇ , tot is the exergy that will not be used further in the system. One should note herein that the boundaries of a thermal system are identified to be the reference environment in the determination of exergy balance equations. In consequence, the exergy loss is only attributed to the overall system. In Table 2 it is defined clearly the fuel exergy and product exergy for each analyzed component and likewise for the overall LCES system. Exergoeconomics combines the economic concepts with exergy principles to represent a powerful tool in ameliorating the cost effectiveness of an energy system. Based on exergoeconomic analysis we can obtain the products unit cost as a major economic criterion for evaluating the system. The economic model should be additionally introduced to compute the cost of each exergy stream by considering the amortization of both capital investment costs and the operation-maintenance costs. Therefore, the equation of cost rate balance for each system component is given below in the interest of developing an exergoeconomic model [31]:

∑ Cė ,k+CẆ ,k = ∑ Ci̇ ,k+CQ̇ ,k + Zk̇

UN

UN EḊ , k ⎞ UN EḊ , k = EṖ , k ⎜⎛ ⎟ ̇ ⎝ EP, k ⎠

EN

refers to the endogenous exergy destruction belong In Eq. (18) to the kth component when the specific component under consideration functions with its actual efficiency and the other ones works in ideal EX processes. The exogenous part EḊ , k is the thermal inefficiencies that can be cut down through upgrading the overall system structure and promoting the performance of other components. This division favors in determining where the attention should be paid for, the kth or the other component. For working out the percentage of endogenous inefficiencies the means based on thermodynamic cycles [24] is employed in this study because of the much uniform rules and few requirement of engineering intuition. In thermodynamic cycles based method, the hybrid cycles should be created with the kth component working at authentic conditions and the other ones operating at complete condiEN EX tions. After EḊ , k is determined, EḊ , k is calculated based Eq. (18). By incorporating above-mentioned new concepts, the following four categories of the exergy destruction occurring in the kth component are further obtained in favor of providing a deeper comprehending of the interdependencies among system components [16]:

in which the annual levelized

(12) CI Zk̇

and

OM Zk̇

can be respectively given as:

CRF CI ⎞ Zk Zk̇ = ⎛ ⎝ D ⎠

(13)

OM Zk̇

(14)

=

CI ϕZk̇

Here, ϕ denotes the maintenance factor and is often assigned to be 1.06 [29] and D is the annual operation days for the unit. It is noted that the gas energy storage system is not operating continuously, but includes the charge stage, the spare stage and the discharge stage in one day. Therefore, it may be more appropriate to express the investment cost of the LCES system in $ per day. CRF stands for the capital recovery factor that can be expressed by:

CRF =

ir (1 + ir )n (1 + ir )n − 1

(18)

EN EḊ , k

where c is the average cost per unit of exergy. The investment cost Zk̇ in Eq. (10) associates with the kth component, and the term includes the CI capital investment cost (Zk̇ ) and the operation-maintenance cost OM ̇ (Zk ): OM

EX

EḊ , k = EḊ , k + EḊ , k

(11)

CI

(17)

Dividing exergy destruction of the component into exogenous and endogenous parts we can evaluate the reciprocal interconnections among system components [16]:

(10)

Zk̇ = Zk̇ + Zk̇

(16)

UN In Eq. (16) EḊ , k is defined as the unavoidable part that will not be further lessened as a consequence of the technical constraints such as availability and cost of materials as well as manufacturing methods. AV The avoidable part EḊ , k is a useful element which expresses the potential of optimization in the component. For the purpose of calculating UN the value of EḊ , k , the possible best operation conditions should be assumed to each component. Under these conditions we can obtain the minimum exergy destruction within each component that in the future just cannot be achieved. The unavoidable exergy destruction is thus estimated by taking advantage of the unavoidable thermodynamic cycle:

The expression of Eq. (10) clears that total cost rates regarding to the exiting exergy streams within a component is identical with the totality of cost rates related to the entering exergy streams along with the investment cost rate. In this equation, the cost rate of an exergy stream can be expressed as:

Ċ = cE ̇

AV

EḊ , k = EḊ , k + EḊ , k

UN , EN

EḊ , k = EḊ , k

UN , EX

+ EḊ , k

AV , EN

+ EḊ , k

AV , EX

+ EḊ , k

(19)

UN , EN EḊ , k

needs to be calculated based on One can notice that only hybrid cycles, which is given using the following equation: UN , EN

EḊ , k

̇ , k UN EN ED ⎞⎟ = EṖ , k ⎛⎜ ̇ ⎝ EP, k ⎠

(20)

(15) Table 2 Definition of the fuel exergy as well as the product exergy.

In Eq. (13) Zk is the capital investment expense for the kth component. Table 3 shows the cost functions for each component of the LCES system. Note herein that all the values of investment cost should be converted from the original time into the reference year (2017) by using the cost index referred from the Chemical Engineering Plant Cost Index [41]. Based on the aforementioned equations, the cost balance equation and likewise the auxiliary relations for each component are clearly outlined in Table 4. The costs of each exergy stream are determined by solution of these sets of equations.

Component

EḞ , k

EṖ , k

Compressor

WĊ + ṁ 3 e3τ ̇ E9̇ − E10

ṁ 3 (e4M − e3M ) + ṁ 4 e4τ ẆE ̇ − E12 ̇ E13 ̇ − E14 ̇ E15

Expander EV1 Cooler CON1 EV2 Heater

The true potential for enhancing the thermodynamic performance of 5

̇ − E21 ̇ E20 ̇ − E17 ̇ E16

̇ − E18 ̇ E19 E8̇ − E7̇

TV

̇ − E11 ̇ E10 E1̇

E9̇ − E8̇ ̇ − E22 ̇ E23 E2̇

Overall system

WĊ

ẆE

CON2

2.4. Advanced exergy and exergoeconomic analyses

E2̇ − E3̇ E4̇ − E5̇ E5̇ − E6̇

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Z. Liu, et al. UN

UN

Component

Zk̇ = Zk̇

Function of capital investment cost

Compressor

Zk = 71.1ṁ i

Expander

pe 1 0.92 − ηC pi

p

Zk = Zr

Tank

Ak 0.6 , Ar

( )

Ak =

Qk Uk × LMTDk

(21)

AV

+ Zk̇

(22)

UN UN CḊ , k = cF , k EḊ , k

(23)

where

p

ln ⎛ e ⎞ [40] ⎝ pi ⎠

1 ⎞ ln ⎛ i ⎞ (1 + e (0.036τi − 54.4) ) [40] Zk = 479.34ṁ i ⎛ ⎝ 0.93 − ηE ⎠ ⎝ pe ⎠

Heat exchanger

AV

CḊ , k = CḊ , k + CḊ , k

Table 3 Cost functions to all components of the LCES system.

AV CḊ , k

[40]

AV = cF , k EḊ , k

(24) UN Zk̇

is the unavoidable part of investment cost which In Eq. (22) will always be surpassed when a similar component is made use of in a system. Unavoidable part of investment cost is determined under the most inefficient operation conditions assumed, which is expressed by:

Zk = 4042V k0.506 [38]

Table 4 Cost balance equations and auxiliary relations used in the LCES system.

UN

Zk̇

UN Ż = EṖ , k ⎜⎛ k ⎟⎞ ̇ ⎝ EP, k ⎠

Component

Cost balance equations

Auxiliary relations

TV

C2̇ = C1̇ ̇ = C2̇ + C12 ̇ + ZEV ̇ 1 C3̇ + C13 ̇ + ZĊ C4̇ = C3̇ + C24

̇ = 0, C2̇ E2̇ = C3̇ E3̇ C12

̇ = C4̇ + C14 ̇ + ZCooler ̇ C5̇ + C15 ̇ = C5̇ + C18 ̇ + ZCON ̇ C6̇ + C19 1 ̇ C7̇ = C6̇ + ZHPT

̇ = 0, C5̇ E5̇ = C6̇ E6̇ C18

EN EX CḊ , k = CḊ , k + CḊ , k

(26)

̇ E20 ̇ E21 ̇ = C21 ̇ C20 ̇ E16 ̇ E17 ̇ = C17 ̇ C16 ̇ E10 ̇ C9̇ E9̇ = C10

EN EX Zk̇ = Zk̇ + Zk̇

(27)

EV1 Compressor Cooler CON1 HPT EV2 Expander

̇ + C25 ̇ = C9̇ + ZĖ C10 ̇ + C23 ̇ = C10 ̇ + C22 ̇ + ZCON ̇ C11 2 ̇ + ZLPT ̇ C1̇ = C11

CON2 LPT HT1

The cost interactions among system components can be evaluated by taking advantage of dividing the exergy destruction costs as well as the capital investment costs into exogenous/endogenous parts:

̇ = 0, C4̇ E4̇ = C5̇ E5̇ C14

̇ = C7̇ + C20 ̇ + ZEV ̇ 2 C8̇ + C21 ̇ = C8̇ + C16 ̇ + ZHeater ̇ C9̇ + C17

Heater

where

̇ E10 ̇ E11 ̇ = C11 ̇ C10

HT3

EN

EN

EX

EX

CḊ , k = cF , k EḊ , k

̇ = C17 ̇ + ZHT ̇ 1 C14 ̇ = C15 ̇ + ZHT ̇ 2 C16 ̇ = C19 ̇ + ZHT ̇ 3 C20

HT2

EN

Table 5 Comparison of the present results with those from Ref. [42].

Compressor Cooler Expander Heat exchanger Recuperative heat exchanger

EḊ , k (kW) 620 1048 685 336 3087

EḊ , k (kW) [42] 574 966 688 316 3145

(29)

Ż EN = EṖ , k ⎜⎛ k ⎞⎟ ̇ E ⎝ P, k ⎠

(30)

In advanced exergoeconomic analysis we can draw the experience of all discussions about the incorporations and extensions of the exergy concepts, i.e., the costs can be respectively subdivided into four parts:

Relative error [%]

UN , EN

CḊ , k = CḊ , k

8.01 8.49 −0.4 6.3 −1.8

UN , EN

Zk̇ = Zk̇

UN , EX

+ CḊ , k

UN , EX

+ Zk̇

AV , EN

+ CḊ , k

AV , EN

+ Zk̇

AV , EX

+ CḊ , k

AV , EX

+ Zk̇

(31) (32)

where UN , EN

CḊ , k

Table 6 Input information assumed for simulation of the LCES system.

UN , EN

= cF , k EḊ , k

(33) UN

UN , EN

Parameter

Unit

Value

Ambient pressure Ambient temperature Compressor inlet temperature Compressor outlet pressure Expander outlet pressure Outlet temperature of cooler System rated output power Charge time Discharge time Annual working days Maintenance factor Interest rate Expected life of the system

MPa K K MPa MPa K MW h h d – – y

0.1013 293.15 281.31 22 6.44 353.15 10 6 6 300 1.06 0.12 20

Zk̇

Ż EN = EṖ , k ⎜⎛ k ⎟⎞ ̇ E ⎝ P, k ⎠

(34)

Then, the other parts of relevant costs can be calculated by: UN , EX CḊ , k

= CḊ , k − CḊ , k

AV , EN

= CḊ , k − CḊ , k

AV , EX

= CḊ , k − CḊ , k

CḊ , k CḊ , k

UN , EX Zk̇

=

UN

UN , EN

EN

UN , EN

AV

AV , EN

UN Zk̇

UN , EN Zk̇

AV , EN

= Zk̇

AV , EX

= Zk̇

Zk̇ Zk̇

EN EṖ , k

(28)

CḊ , k = cF , k EḊ , k

Zk̇

Component

(25)

−

UN , EN

EN

− Zk̇

AV

− Zk̇

AV , EN

(35) (36) (37) (38) (39) (40)

EN EḊ , k .

in which is achieved simultaneously with Advanced exergoeconomic analysis possesses the benefit of evaluating the cost savings of a system component and cost impacts among system components, which will not be reached via application of advanced exergy analysis. In analogy, splitting the capital investment costs and the exergy destruction costs into unavoidable/avoidable parts has the advantages of showing the authentic potential of cost savings within the system components:

2.5. Performance criteria In conventional exergy-based analysis, the exergy efficiency (εk ), exergy destruction ratio ( yD∗, k ), cost per unit of exery associated with fuel and product (cF , k , cP, k ), exergy destruction cost (CḊ , k ) and exergoeconomic factor ( fk ) are often applied to make key decisions in concerning improving thermal systems [31,39]: 6

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Table 7 Values of assumption under different operation conditions. Component

Parameter, unit

The assumed worst conditions

Real conditions

The unavoidable conditions

Ideal conditions

Compressor Expander EV1 Cooler CON1 EV2 Heater CON2 TV

ηC [−] ηE [−] Δτ [K] Δτ [K] Δτ [K] Δτ [K] Δτ [K] Δτ [K] –

0.7 0.7 20 20 20 20 20 20 –

0.86 0.86 5 5 5 5 5 4 Isenthalpic

0.92 0.93 1.5 1.5 1.5 1.5 1.5 1.5 Isenthalpic

1 1 0 0 0 0 0 0 Isentropic

AV , EN

Table 8 Data at material streams of the LCES system for the real cycle. Stream

P (MPa)

τ (K)

ṁ (kg·s−1)

1 2 3 4 5 6 7 8 9 10 11

6.44 4.30 4.30 22.00 22.00 22.00 22.00 22.00 22.00 6.44 6.44

293.15 281.31 281.31 417.79 353.15 303.15 293.15 340.31 394.07 303.87 298.19

246.10 246.10 246.10 246.10 246.10 246.10 246.10 246.10 246.10 246.10 246.10

εk =

EṖ , k EḞ , k EḊ , k EḊ , tot

(42)

cF , k =

CḞ , k EḞ , k

(43)

cP, k =

CṖ , k EṖ , k

(44)

CḊ , k = cF , k EḊ , k

(45)

Zk̇ Zk̇ + CḊ , k

(46)

fk =

AV , EX

AV , EN Zk̇ AV , EN AV , EN + CḊ , k Zk̇

(49)

Table 9 presents the results acquired from a detailed conventional exergy analysis of the LCES cycle. From the exergy destruction ratio ( yD∗, k ) it is shown that of the nine components evaluated in the considered system, the compressor and expander occur the largest amounts of exergy destruction and accounts for about 22.67% and 18.18% of the total exergy destruction in the system, respectively. The reason of these results is most that the turbo-machineries in the real cycle run with low assumed isentropic efficiency. The EV1 also has rather large exergy destruction with a 14.84 percentage of system overall exergy destruction. This occurrence is mostly illustrated by the much large

̇

EP, k UN

fkAV , EN =

3.1. Conventional exergy-based analysis results

The advanced exergy efficiency (εkAV , EN ), exergy destruction ratio and exergoeconomic factor ( fkAV , EN ) are used in advanced exergy-based analysis to identify causes of inefficiencies, reveal betterment potential and offer enhancement strategies [31,39]:

EḞ , k − EḊ , k − EḊ , k

(48)

In order to verify the validity of the LCES model, some component (e.g. expander, compressor heat exchanger) models are validated by compared the present results with the data of conventional exergy analysis in the literature, showing a good agreement, as shown in Table 5. The input data for the comparison can be found in Ref. [42]. In order to illustrate the application on the LCES system of advanced exergy-based analysis, an appropriate simulation code has been compiled with MATLAB code and the material properties are computed based on the database REFPROP 9.1 [43]. The basic input specifications for this developed LCES system are recorded in Table 6. The system output electric power is 10 MW, which is obtained by referring the first 10 MW adiabatic CAES demonstration project in China [44]. The assumed operation conditions for real, unavoidable and ideal cycles are well listed in the respective columns of Table 7. In addition, thermodynamic data of the real cycle at different streams are listed in Table 8 to better understand the system.

, EN ) ( yD∗AV ,k

εkAV , EN =

EḊ , k EḊ , tot

3. Results and discussion

(41)

yD∗, k =

, EN yD∗AV = ,k

(47)

Table 9 Conventional exergy-based analysis results for each evaluated component. Component

Compressor Expander EV1 Cooler CON1 EV2 Heater CON2 TV

EḞ , k (MW)

EṖ , k (MW)

EḊ , k (MW)

ε (\%)

20.00 11.58 1.79 7.90 3.01 2.33 6.86 0.66 50.47

18.03 10.00 0.50 7.32 2.35 1.91 6.06 0.08 49.66

1.97 1.58 1.29 0.58 0.66 0.42 0.80 0.58 0.81

90.15 86.36 27.93 92.66 78.07 81.97 88.34 12.12 98.40

(\%)

cF ($ GJ)

cP ($ GJ)

CḊ ($ d)

Ż ($ d)

CḊ + Z ̇ ($ d)

f (%)

22.67 18.18 14.84 6.67 7.59 4.83 9.21 6.67 9.32

11.20 24.36 24.95 22.76 22.76 32.27 28.02 24.36 24.55

16.98 35.19 100.19 24.98 30.16 40.85 32.04 248.52 24.95

475.86 828.97 692.16 287.22 323.47 293.49 480.83 304.56 429.95

1776.30 1509.85 126.47 62.54 52.68 60.43 45.22 69.23 0.00

2252.16 2338.82 818.63 349.76 376.15 353.92 526.05 373.79 429.95

78.86 64.56 15.40 18.00 14.10 17.00 8.57 18.45 0.00

yD∗

7

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Fig. 2. Effect of interest rate on (a) capital investment cost and (b) exergy destruction cost for system components. Table 10 Advanced exergy analysis results for the LCES system. Component

Compressor Expander EV1 Cooler CON1 EV2 Heater CON2 TV

UN

AV

EN

EX

EḊ , k

EḊ , k

EḊ , k

EḊ , k

(MW)

(MW)

(MW)

(MW)

1.08 0.72 0.37 0.34 0.34 0.16 0.50 0.06 0.81

0.89 0.85 0.91 0.24 0.32 0.26 0.30 0.52 0.00

1.51 1.58 1.06 0.44 0.54 0.41 0.61 0.49 0.66

0.45 0.00 0.22 0.14 0.12 0.01 0.19 0.09 0.15

UN , EN

UN , EX

AV , EN

AV , EX

EḊ , k

EḊ , k

EḊ , k

EḊ , k

(MW)

(MW)

(MW)

(MW)

0.83 0.72 0.31 0.26 0.28 0.15 0.38 0.05 0.66

0.25 0.00 0.06 0.08 0.06 0.00 0.12 0.01 0.15

0.68 0.85 0.75 0.18 0.26 0.26 0.23 0.44 0.00

0.21 0.00 0.16 0.06 0.06 0.01 0.07 0.08 0.00

εkAV , EN

yk∗AV , EN

(\%)

(\%)

96.34 92.15 40.05 97.54 89.94 88.08 96.39 15.05 100.00

7.89 9.82 8.69 2.13 3.03 2.98 2.62 5.02 0.00

operation cost will elaborate its more significance in promoting the system cost effectiveness. The most amounts of the operation cost outlined in Table 9 are respectively occurred in compressor, expander and EV1, from which we can consider them as important components in accordance of the exergoeconomic viewpoint. Exergoeconomic factor, fk , is another exergoeconomic indicator to determine the option of cost savings. A higher value of fk implies a heavily investment costs of the kth component that should be reduced. In contrary, a lower data of fk reveals that a reduction of exergy destruction within the kth component is required to improve the exergy efficiency. The highest values of fk are associated to compressor and expander, respectively. It is deduced that the costs originated from compressor and expander are much respected to the investment costs. Therefore, economic analysis does not advocate focusing efforts on increasing the capital investment costs of compressor and expander to improve their thermodynamic performance. The lower amounts of exergoeconomic factor for the other components verifies that the high expenses of these components are mainly related to exergy destruction. This result means that increasing their capital investment costs is beneficial for optimization of themselves rather than an economical restriction. In addition, the effect of interest rate on capital investment cost and exergy destruction cost for system components is shown in Fig. 2 in order to give better understanding on how sensitive the system in responding the change.

Fig. 3. Unavoidable/avoidable exergy destruction through advanced exergy analysis.

temperature difference of heat exchange between the vapor–liquid cool CO2 and the incoming ambient water. In consequence, the exergy efficiency of EV1 is located at the lowest level (εEV 1 = 27.93%) in the LCES system excluding the CON2 (εCON 2 = 12.12%). To be conclusive from Table 9, the priority for betterment of the system components based on the conventional exergy analysis is arranged as: compressor, expander, evaporator 1, throttle valve, heater, condenser 1, condenser 2, cooler and evaporator 2. The results calculated from conventional exergoeconomic analysis are also shown in Table 9. As a exergoeconomic indicator, the operation cost, CḊ , k + Zk̇ , indicates the cost importance of the evaluated component on the influence of overall system. A component with larger

3.2. Advanced exergy-based analysis results The results of advanced exergy analysis are represented in Table 10. For clearly illustrating the results, Fig. 3 represents the unavoidable/ avoidable parts of exergy destruction within each component in the LCES system. We can note that the unavoidable exergy destruction of each component is always larger than zero, which means that the true 8

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and friction losses of fluid flowing and mechanism. The condenser 2 has AV the second largest EḊ , k value (89.66%). Note that the throttle valve gives no room for improvement although rather significant inefficiencies occur in it. Fig. 4 shows the exogenous and endogenous parts of exergy destruction regarding to each component in the LCES system. One can observe from the figure that the endogenous part occupies a most portion of total exergy destruction within each system component (> 75%). It is indicated that the interactions among components of the proposed LCES system is weak and the component exergy destruction originates generally from the inefficiencies of components themselves. The expander owns the highest endogenous exergy destruction and percentage (100%), demonstrating that the exergy destruction occurring in expander is only resulted from its own inefficiencies. In addition, all the positive exogenous exergy destruction clears that the improving thermodynamic performance of any component can be attained through decreasing the exergy destruction associated with other components. It is depicted in Fig. 5 the overall exergy destruction ratio of the proposed system through combining the definitions of unavoidable/ avoidable and exogenous/endogenous. One can note that in the system 84.08% of the overall exergy destruction is endogenous, revealing again that the interactions of system components have a not significant role. Besides, in evaluation of energy conversion systems the avoidable exergy destruction is mostly the focus because of its a measure for improvement potential. Therefore, the attention in this work is highly AV , EN centered on the avoidable-endogenous exergy destruction, EḊ , k . In AV , EN accordance with the value of EḊ , k , we can formulate the rules of

Fig. 4. Exogenous/endogenous exergy destruction through advanced exergy analysis.

deciding the preference of component for enhancing the overall system performance through improving the single components. It is compared in Fig. 6 the yD∗, k of each component based on conventional and advanced exergy analysis and much interesting results can be revealed. From this figure it is convenient generally that a significant difference is found out between the priorities based on conventional and advanced exergy analysis due to the different criteria used. The analysis of conventional exergy method suggested the compressor as the most important influential component, but the expander is introduced with owning the first improvement priority in enhancing the overall system performance based on advanced exergy analysis due to the highest avoidable endogenous exergy destruction. In addition, the throttle valve has the fourth largest exergy destruction according to the conventional exergy analysis, while the advanced analysis gives that all of the exergy destruction in throttle valve is completely unavoidable and thus this component cannot be further improved. It is noted herein that conclusions gathered from advanced exergy analysis are more pragmatic since it is considered both the interactions among system components as well as the technical limitations of each component. In Tables 11 and 12 there lists the results of exergy destruction costs for each system component according to advanced exergoeconomic analysis, along with the investment costs also. Fig. 7 displays the unavoidable/avoidable exergy destruction costs and also the costs related to the exogenous/endogenous exergy destruction of every component in LCES cycle. By referring to the definition of advanced exergy destruction cost in Section 2.4, it is believed that the percentages of the costs in linkage to each exergy destruction through advanced exergy analysis will be similar to Figs. 3 and 4 due to these split costs being calculated based on exergy destruction. The unavoidable/avoidable and exogenous/endogenous parts of investment costs within each system component are depicted as follows in Fig. 8. It is clear based on Fig. 8(a) that the avoidable investment costs contribute more influence than the unavoidable investment costs for all components except the CON1 and heater. Compressor, with 74.69% of avoidable expenses, exists the most avoidable investment costs, followed by the expander (51.73%) and evaporator 1 (86.37%).

Fig. 5. System exergy destruction ratio through combining the definitions of unavoidable/avoidable and exogenous/endogenous exergy destruction.

Fig. 6. Comparison on the exergy destruction ratio of each component between conventional and advanced exergy analysis.

potential of advancing a system component should be determined based on its avoidable part rather than its total exergy destruction received from performing conventional exergy analysis. In addition, the largest avoidable exergy destruction is located in evaporator 1 (71.09% of EḊ , EV 1), compressor (45.18% of EḊ , C ) and expander (54.14% of EḊ , E ), respectively, indicating that the three components have the highest potential of improvement. It is believed that the irreversibilities in evaporator can be mostly decreased by means of lessening the temperature differences between the two heat exchanging fluids. The inefficiencies of compressor and expander can be largely influenced by their isentropic efficiency based on the heat losses of thermal processes 9

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Table 11 Exergy destruction cost results for the system components through advanced exergy analysis. Component

Compressor Expander EV1 Cooler CON1 EV2 Heater CON2 TV

UN

UN , EX

UN , EN

CḊ , k

CḊ , k

AV

CḊ , k

EN

CḊ , k

($ d)

($ d)

($ d)

($ d)

EX

260.64 380.56 200.09 167.03 165.84 109.53 301.53 31.88 429.95

215.22 448.41 492.07 120.19 157.63 183.97 179.30 272.68 0.00

366.02 828.97 571.56 217.22 265.53 287.48 368.69 255.97 348.64

109.84 0.00 120.60 70.00 57.93 6.02 112.14 48.59 81.30

CḊ , k

CḊ , k

($ d)

($ d)

200.48 380.56 165.23 126.32 136.14 107.28 231.21 26.79 348.64

60.16 0.00 34.87 40.71 29.70 2.25 70.32 5.09 81.30

AV , EN

CḊ , k

AV , EX

CḊ , k

($ d)

($ d)

165.54 448.41 406.33 90.90 129.40 180.20 137.48 229.17 0.00

49.68 0.00 85.74 29.291 28.231 3.771 41.82 43.51 0.00

Table 12 Investment cost results for the system components through advanced exergy analysis. Component

Compressor Expander EV1 Cooler CON1 EV2 Heater CON2 TV

UN

EN

UN , EN

EX

UN , EX

AV , EN

AV , EX

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

Zk̇ ($ d)

fkAV , EN

449.64 728.85 17.24 27.65 42.18 0.65 29.56 3.37 0.00

1326.66 781.00 109.23 34.90 10.50 59.78 15.66 65.86 0.00

1366.30 1509.85 104.43 47.30 43.25 59.20 34.68 58.18 0.00

410.00 0.00 22.04 15.24 9.44 1.24 10.55 11.05 0.00

345.85 728.85 14.23 20.91 34.63 0.64 22.66 2.84 0.00

103.78 0.00 3.00 6.74 7.55 0.01 6.89 0.54 0.00

1020.44 781.00 90.20 26.39 8.62 58.56 12.01 55.35 0.00

306.21 0.00 19.03 8.51 1.88 1.23 3.65 10.51 0.00

86.04 63.53 18.17 22.50 6.25 24.53 8.03 19.45 –

AV

(%)

As observed in Fig. 8(b), the endogenous investment costs of each component in the LCES system occupy much higher contribution over exogenous investment costs. The expander owns the highest endogenous investment prices with 100% endogenous expenses, followed by compressor (76.92%) and evaporator 1 (82.58%). Fig. 9 illustrates the cost ratio of overall system associated with exergy destructions and investment through combining the new definitions of unavoidable/avoidable and exogenous/endogenous costs. This figure states that the endogenous part of the exergy destruction costs constitutes the most of total exergy destruction costs in LCES system (85.27%). While the avoidable exergy destruction cost forms 50.27% of the total value, only a small part is exogenous (6.85%). The results indicate that the LCES system has considerable potential for improvement by optimizing the single components. It can be also seen in this figure that 55.43% of total investment costs in the LCES cycle is avoidable-endogenous, which demonstrates a significant potential for reducing the investment costs. The comparison of operation costs for each system component according to conventional and advanced exergoeconomic analysis is shown in Fig. 10. As mentioned before, a component with a higher operation costs which consist of exergy destruction costs and investment costs will bring a higher influence on improving the price effectiveness of LCES system. We can observe that from both conventional and advanced exergoeconomic means, the expander has the most amount of operation costs, then the compressor and subsequently the evaporator 1. The difference become occurring from the fourth priority in determining the significant component because of the different criteria used between the conventional and advanced methods. Based on the total operation costs of a component the heater is the fourth vital component in the LCES system, while the fourth priority is assigned to condenser 2 by reference to the avoidable-endogenous operation cost values. Therefore, it is deduced that advanced exergoeconomic analysis can give further pragmatic conclusions by taking into account of technical limitations of each component as well as the interactions among system components. Fig. 11 shows the exergoeconomic factor results of each component

Fig. 7. Splitting of exergy destruction costs: (a) unavoidable and avoidable parts; (b) exogenous and endogenous parts.

10

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according to conventional exergy-based analysis are significantly reinforced by the results of advanced exergy-based analysis. Consequently, we can identify the source of thermodynamic inefficiencies and options for energy and cost savings. Some interesting conclusions are summarized in the following section. (1) Results prove that only 49.6% of overall exergy destruction and 50.27% of overall exergy destruction costs in the proposed system can be avoidable. One can also obtain that a large part of the overall investment cost (64.91%) is avoidable. In addition, a most of exergy destruction (84.08%), its costs (85.27%) and investment costs (87.04%) is endogenous, which reveals weak interactions among the system components. (2) In conventional exergy analysis compressor with a largest exergy destruction ratio of 22.67% is suggested as the principal influential component in optimizing the overall system performance, while based on advanced exergy analysis the expander is introduced with the initial improvement priority by reference to the supreme avoidable endogenous exergy destruction ratio (9.82%). (3) In terms of both conventional and advanced exergoeconomic analysis, the expander has the most amounts of operation costs, followed by the compressor and the evaporator 1. While the conventional exergoeconomic analysis recommends that the heater has the fourth largest operation costs, the advanced analysis suggests the condenser 2 as the fourth priority to ameliorate the cost effectiveness of system based on the criterion of avoidable-endogenous operation cost values. This paper is mainly aimed to show the importance of splitting exergy destruction and costs in analyzing the thermal systems. A detailed parametric study and multi-objective optimization based on the advanced-exergy based methods for the proposed system will be presented in a future work.

Fig. 8. Splitting of investment costs: (a) unavoidable and avoidable parts; (b) exogenous and endogenous parts.

through employment of conventional and advanced exergoeconomic analysis. Based on the both methods, the investment costs of compressor and expander should be decreased due to the higher amounts of exergoeconomic factor. The other components is suggested to reduce their exergy destructions because of the lower values of exergoeconomic factor.

CRediT authorship contribution statement Zhan Liu: Conceptualization, Methodology, Writing - original draft, Supervision. Zihui Liu: Software, Formal analysis. Xuqing Yang: Validation, Formal analysis. Hongyan Zhai: Data curation, Visualization. Xiaohu Yang: Writing - review & editing, Visualization.

4. Conclusions Declaration of Competing Interest

A thermo-economic analysis of the liquid carbon dioxide energy storage system is performed in this paper by employing the conventional/advanced exergy-based means in a first attempt. The base of advanced exergy-based approach is splitting into different parts of the exergy destruction, its costs and investment costs. Results calculated

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.

Fig. 9. Ratio of system (a) exergy destructions costs and (b) investment costs through combining the definitions of unavoidable/avoidable and exogenous/endogenous costs. 11

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Fig. 10. Comparison on the operation costs of each component between conventional/advanced exergoeconomic analysis.

Fig. 11. Comparison of the exergoeconomic factor between the two methods.

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