Exergy and exergoeconomic analyses of a supercritical CO2 cycle for a cogeneration application

Energy xxx (2016) 1e12

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Exergy and exergoeconomic analyses of a supercritical CO2 cycle for a cogeneration application Xurong Wang, Yi Yang, Ya Zheng, Yiping Dai* School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 November 2015 Received in revised form 7 September 2016 Accepted 8 November 2016 Available online xxx

Detailed exergy and exergoeconomic analyses are performed for a combined cogeneration cycle in which the waste heat from a recompression supercritical CO2 Brayton cycle (sCO2) is recovered by a transcritical CO2 cycle (tCO2) for generating electricity. Thermodynamic and exergoeconomic models are developed on the basis of mass and energy conservations, exergy balance and exergy cost equations. Parametric investigations are then conducted to evaluate the influence of key decision variables on the sCO2/tCO2 performance. Finally, the combined cycle is optimized from the viewpoint of exergoeconomics. It is found that, combining the sCO2 with a tCO2 cycle not only enhances the energy and exergy efficiencies of the sCO2, but also improves the cycle exergoeconomic performance. The results show that the most exergy destruction rate takes place in the reactor, and the components of the tCO2 bottoming cycle have less exergy destruction. When the optimization is conducted based on the exergoeconomics, the overall exergoeconomic factor, the total cost rate and the exergy destruction cost rate are 53.52%, 11243.15 $/h and 5225.17 $/h, respectively. The optimization study reveals that an increase in reactor outlet temperature leads to a decrease in total cost rate and total exergy destruction cost rate of the system. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Supercritical CO2 cycle Transcritical CO2 cycle Exergoeconomic Optimization

1. Introduction Many efforts have been devoted to the high efficiency and the cost reduction of electricity generated by nuclear power plant toward the successful future utilization of nuclear power. These advanced energy conversion technologies include the gas turbinemodular helium reactor (GT-MHR) [1e4] and the supercritical CO2 Brayton cycles (sCO2) [5e7]. Comparison to the GT-MHR, the main advantage of the sCO2 cycle is the comparable efficiency at considerable lower reactor outlet temperature. With a reactor outlet temperature of 550
C, the efficiency of sCO2 cycle can reach 45.3%, which is comparable with the helium Brayton cycle at a significantly higher temperature (850
C) [6]. This is because by utilizing the abrupt property changes near the critical point of CO2 the compressor work can be reduced, resulting in the significant efficiency improvement. Cooling the CO2 (to about 32
C) before compression process is beneficial. This leads to a considerable thermal energy (at a rate of about 300 MW) rejected to the heat

* Corresponding author. School of Energy and Power Engineering, Xi'an Jiaotong University, 28 Xianning West Road, Xi'an, Shaanxi, 710049, China. E-mail addresses: [email protected] (X. Wang), [email protected]. edu.cn (Y. Dai).

sink in the pre-cooler [8,9]. The performance of the sCO2 cycle can be improved after utilization of that thermal energy in low-grade waste heat recovery systems. Some investigations have been carried out on the recovery of waste heat from sCO2 cycles. Chacartegui et al. [10,11] studied the utilization of this waste heat for power production using Organic Rankine Cycles (ORCs). The results showed that the thermal efficiency of the sCO2 was improved by 7e12%, which depends on the turbine inlet temperature [11]. It should be noted that the simple
nchez et al. [12] sCO2 configuration is considered in that study. Sa investigated the utilization of sCO2 waste heat to drive ORCs using mixtures of hydrocarbons in the bottoming cycle, which was also on the basis of the simple sCO2 configuration. They observed that the performance of the combined cycle was directly affected by the mixture's composition. Besarati and Goswami [13] considered a thermodynamic comparison of three different sCO2/ORC combined cycles. They reported that the largest efficiency increase was achieved by using a simple sCO2 configuration as the topping cycle. The maximum overall efficiency, however, was obtained by the recompression sCO2/ORC cycle. Zhang et al. [14] studied a sCO2 part-flow cycle combined with an ORC with liquefied natural gas as the heat sink. They showed that the combined cycle achieved 52.12% of overall thermal efficiency. In another study, Akbari and

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Nomenclature

Greek symbols efficiency ε effectiveness Subscripts 0 environmental state c cooling water cnd condenser D destruction ex exergy HTR high temperature recuperator in inlet k kth component LTR low temperature recuperator MC main compressor p pump pc pre-cooler R reactor RC recompression compressor th thermal total total

h A C_ c E_ f h m_ P PRc Q_ r s T _ W x YD Z_

heat transfer area, m2 cost rate, $/h cost per exergy unit, $/GJ exergy rate, W exergoeconomic factor specific enthalpy, Jkg1 mass flow rate, kgs1 pressure, bar compressor pressure ratio heat addition, W relative cost difference specific entropy, Jkg1K1 temperature,
C, also K work flow rate-power, W recompressed flow ratio exergy destruction ratio, % capital cost rate, $/h

Mahmoudi [15] investigated a combined recompression sCO2/ORC cycle from the viewpoints of exergy and exergoeconomics. They found that the exergy efficiency of sCO2 cycle was enhanced by up to 11.7% and the total product unit cost was reduced by up to 5.7%. The results also indicated that the highest exergy efficiency and the lowest product unit cost for the sCO2/ORC cycle were obtained when isobutane and RC318 were used as the ORC working fluid, respectively. The ORC has low operating pressure and low cost because of simplicity. After finding appropriate working fluids, ORC can be well suited to any type of heat sources. However, an important limitation is the constant temperature evaporation which is the so called pinch problem. This leads to a significant mismatch of the two fluid states and generates a lot of irreversibility in the sCO2/ORC cogeneration system. Compared to the ORC, the transcritical CO2 cycle (tCO2) shows a better match. The evaporation temperature profile of the CO2 is gliding, generating a closer fit of the two curves, thereby having no pinch limitation. A comparison between the ORC and the tCO2 cycle shows that a power system with CO2 as the working fluid has a higher power output and is more compact than the one with organic fluids as the working media [16]. Recently, Yari and Sirousazar [17] proposed and analyzed the utilization of waste heat from the sCO2 cycle for electricity generation using a tCO2 cycle. They paid more attention to the combined cycle irreversibility. They showed that the second law efficiency of the recompression sCO2/tCO2 cycle was 5.5e26% higher than that of the single sCO2 cycle. Further, the exergy destruction of the new combined cycle was 6.7e28.8% lower than that of the stand-alone sCO2 cycle. Later, Wang et al. [18] investigated a combined recompression sCO2/tCO2 cycle from the viewpoint of thermodynamics and economics. The results showed that the capital cost per net power output of the combined cycle was 6.6 k$/kW, which was about 6% more expensive than that of the single sCO2 cycle. They reported the effects of key decision variables on the combined cycle performance, however, without a further parametric optimization. The cost of the reactor is also not considered in their study. In another work they conducted a thermodynamic comparison and optimization of two different configurations of sCO2/tCO2 cycle [19]. They showed that the thermal efficiencies of recompression and simple configurations of the sCO2 cycle were improved by

10.12% and 19.34%, respectively. Further, the simple and recompression sCO2/tCO2 cycles had a power ratio of 16.21% and 11.26%, respectively. The above mentioned background reveals that much research has been devoted to sCO2/ORC cycles concerning thermodynamics, performance comparison, exergy and exergoeconomic analyses, while little research has been done on the combination of sCO2 cycles and a tCO2 cycle. Besides, the available literature merely concerns a thermodynamic assessment of sCO2/tCO2 cycles. A comprehensive exergy and exergoeconomic study on this cogeneration system, to our knowledge, has not yet been performed. Making a right decision from the economic perspective needs a detailed exergoeconomic investigation as well as the thermoeconomic analysis. This paper focuses on the energy, exergy and exergoeconomic analyses of the sCO2/tCO2 cycle. Firstly, the combined cycle is analyzed from the viewpoints of energy and exergy. The theory of exergetic cost is then applied to the combined cogeneration cycle. Further, a parametric study is performed to reveal the effects of decision variables on the energy efficiency, exergy efficiency and total cost rate of the system. Finally, the sCO2/tCO2 cycle is optimized from the viewpoint of exergoeconomics using a genetic algorithm and the obtained results are compared. It is expected that the findings of present work may help to find an efficient and economical sCO2 cycle for nuclear power plants.

2. System description and assumptions Fig. 1 illustrates the configuration of combined sCO2/tCO2 cycle. The cogeneration system actually comprises a recompression sCO2 topping cycle and a simple tCO2 bottoming cycle. The CO2 from the pre-cooler 2 enters the main compressor where it is compressed to a pressure of around 200 bar. The stream is first preheated in the LTR (low temperature recuperator) and then merged with the stream exiting the recompression compressor (point 3). The mixture is heated in the HTR (high temperature recuperator), evaporates in the reactor and undergoes an expansion process in the turbine 1. After expansion, the CO2 flows across the HTR and then the LTR. The CO2 at LTR exit (point 8) is divided into two streams: stream 8a and stream 8b. The stream 8a enters the pre-

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Fig. 1. Diagram of combined sCO2/tCO2 cycle and the T-s diagram.

cooler 1, where it transfers partial of its waste heat to the bottoming tCO2 cycle, and then passes across the pre-cooler 2, where it is cooled to a temperature of around 32
C. The next process for this stream is compression in the main compressor. The stream 8b is compressed in the recompression compressor and then joined the CO2 from the LTR. In the tCO2 cycle, the heated CO2 from the precooler 1 further expands in the turbine 2 and is cooled in the condenser, then, pumped back to the pre-cooler 1. The T-s diagram of sCO2/tCO2 cycle is also shown in Fig. 1. The study is conducted with general assumptions below. The assumptions are essential and reasonable to develop the analysis model without strongly affecting the outcomes. This investigation concerns about a steady-state behavior, and dynamic and offdesign performance will be the objective in the future. In addition, pressure loss always occurs in the actual pipe network, which can have the efficiency and net power output calculated come down slightly. (1) The system reaches a steady state; the kinetic and potential energies and heat transfer with the ambient are neglected.

(2) Pressure losses in pipes and heat exchangers are neglected. (3) The cooling water enters the pre-cooler 2 and the condenser at environmental temperature and pressure. (4) Saturated liquid of the working fluid is supposed at the condenser outlet. (5) A temperature difference is considered at the pinch point in the pre-cooler 1 and the condenser.

3. Model design 3.1. Thermodynamic analysis The combined cogeneration cycle was developed based on the energy and exergy balances. This model is an extension of previous work presented by the authors [18,19]. Particular attention is paid to the second law of thermodynamics and the exergy values at each state point. Thermodynamic relations for HTR and LTR are given by

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h6  h7 ¼ h4  h3

(1)

ð1  xÞðh3  h2 Þ ¼ h7  h8

(2)

εHTR ¼ ðT6  T7 Þ=ðT6  T3 Þ

(3)

εLTR ¼ ðT7  T8 Þ=ðT7  T2 Þ

(4)

Entering the condenser, the CO2 can be either superheated vapor or two-phase flow. In the first situation, the CO2 is the superheated vapor, dividing the condenser into a single-phase region and a two-phase region as shown in Fig. 2. A pinch of 3
C at the saturated vapor point (point bb) is assumed. This assumption guarantees that the temperature profiles do not intersect. A temperature difference of 5
C is applied at the inlet of condenser between the working fluid and the cooling water. The water mass flow rate is then obtained with the energy balance applied to the two-phase region:

m_ CO2 ðhbb  h03 Þ ¼ m_ water ðhb  h05 Þ

(5)

where m_ CO2 is the mass flow rate of the tCO2 cycle. The exit temperature of the cooling water is calculated by

m_ CO2 ðh02  hbb Þ ¼ m_ water ðh06  hb Þ

(6)

In the second situation, the state of the CO2 at the exit of the turbine 2 falls in the two-phase region. Hence, the 3
C pinch is assumed at state 02. The global energy balance is then used to calculate the water mass flow rate. The net power output of the combined cycle can be expressed as

_ _ _ net ¼ W W
net;sCO2 þ W net;tCO2  _ _ _ ¼ W T1  W MC  W RC

sCO2


_p _ W þ W T2

(7) tCO2

Exergy analysis allows comparing power cycles of different types on the same thermodynamic basis, namely, how well the power cycle converts the available incoming thermodynamic power into actual usable power. Neglecting the changes in kinetic and potential exergies, the total exergy of a stream is the sum of physical and chemical exergies

E_ ¼ E_ ph þ E_ ch The physical exergy can be obtained by

(8)

_  h0 Þ  T0 ðs  s0 Þ E_ ph ¼ m½ðh

(9)

In the present work, the chemical exergy of the working fluid doesn't change from one point to another and therefore it has not been taken into account. The exergy balance equations are applied to each component of the system,

E_ Q þ

X

E_ i ¼ E_ W þ

X

E_ e þ E_ D

(10)

where subscripts i and e denote the control volume inlet and outlet, E_ D is the exergy destruction rate in the component. The energy efficiency of the combined cogeneration cycle can be defined as

_ W

hth ¼ _ net Q core

(11)

The exergy efficiency of the combined cycle is defined as

_ W

_ W

net hex ¼ _ net ¼ _ Ein Q core ð1  T0 =TR Þ

(12)

where E_ in is the exergy supplied to the reactor and TR is the temperature of reactor. The component exergy destruction ratio, YD,i, is employed to provide more information about the weak points of the cycle [20],

YD;i ¼

E_ D;i E_

(13)

in

To implement a validation exercise, the available data in literature are used. Table 1 presents the result of comparison. It is noted that the recompression mass fraction, xopt, is obtained using iteration technique. Table 1 indicates that results in the present work agree well with those in published literature for sCO2 and tCO2 cycles, respectively. 3.2. Exergoeconomic analysis In order to obtain a cost-effective energy conversion system, economic consideration should also be taken into account. Exergoeconomics is on the basis of the principles of exergy and economic analysis at the level of system components. Calculating total cost rate of the system with the cost formation process is the main purpose of an exergoeconomic analysis. Various approaches have been proposed for the exergoeconomics, such as the exergy cost theory [22], the average cost approach [23] and the specific exergy costing (SPECO) [24e26]. In this paper, the SPECO method is

Table 1 Performance comparison. sCO2 cyclea

Present work Ref. [9]

hth (%)

PRopt

xopt

41.18 41.18

2.641 2.64

0.333 0.334

tCO2 cycleb

Present work Ref. [21] a b

Fig. 2. Minimum temperature difference in the condenser.

hth (%)

WT (kW)

WP (kW)

8.484 8.48

12.109 12.099

3.651 3.648

hT ¼ 0.90, hC ¼ 0.85, εHTR ¼ 0.86, εLTR ¼ 0.86 hT ¼ 0.70, hP ¼ 0.80

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employed for its easy and straightforward scheme and efficient calculation by using a matrix formulation. To conduct this analysis, all energy and exergy values for streams must be quantified at first, which is done in section 3.1. The fuel and product should be defined then for each component. The fuel of a component is defined as all exergy additions to it and the product is all exergy removals from it. For the considered sCO2/tCO2 cycle, the fuel and product for each component are presented in Table 2. Finally, cost balance equations along with the auxiliary equations are applied to each component of the sCO2/tCO2 cycle. The cost balance equation for a system component receiving thermal energy and producing power has the form [20].

X

C_ out;k þ C_ w;k ¼

X

C_ in;k þ C_ q;k þ Z_ k

(14)

where the terms C_ w;k and C_ q;k are the cost rates associated with the output power from the component and the input thermal energy to the component, respectively. Eq. (14) states that the total cost rate of exiting exergy streams equals the total cost rate of entering exergy streams plus the total expenditure rate to accomplish the process. A cost per unit exergy is allocated to each flow such as the exergy flow of the entering or leaving material, work or heat flow entering or leaving the system, as shown below [27].

C_ k ¼ ck E_ k

(15)

_ C_ w ¼ cw W

(16)

C_ q ¼ cq E_ q

(17)

5

system component are provided in Table 3. The cost balance and required auxiliary equations for each system component are listed in Table 4. The auxiliary equations are formed on the basis of the F and P principles of the SPECO [20]. Note that the cooling water is considered as a free resource and then cost rate of cooling water is negligible. The linear system of equations in Table 4 includes 26 equations and 26 unknown variables. The solution to the linear equations reveals the cost rates for all exergy streams. In the solution, the Gauss-Seidel method is used. To assess the exergoeconomic behavior, several parameters are used, as given in Table 5. Note that the total cost rate is the sum of capital investment, operation and maintenance cost rates as well as the total exergy destruction cost rate. 3.3. Optimization method To have an efficient cogeneration system, it is necessary to perform an optimization. In the present study, the objective function is defined in order to minimize the total cost rate. The parameters chosen for optimizing the sCO2/tCO2 are pressure ratio of compressor, PRc, reactor outlet temperature, T5, turbine 2 inlet temperature, T01, and turbine 2 inlet pressure, P01. The constraints are given in Table 6. The genetic algorithm [29] is used to conduct the optimization. Fig. 3 is the flow chart of the optimization process. To perform efficiently, some input parameters of genetic algorithm were set up properly. 4. Results and discussion

where ck, cw, cq are the average costs per exergy unit, $/GJ. By inserting Eqs. (15)e(17) into Eq. (14), it then follows that

X


cout E_ out

 k

_ ¼ þ cw;k W k

X


cin E_ in

 k

þ cq;k E_ k þ Z_ k

(18)

The term Z_ k in Eq. (18) is the cost rate associated with the capital investment and operation and maintenance costs for the kth component: CI OM Z_ k ¼ Z_ k þ Z_ k CI where Z_ k ¼

(19)

 CRF

t

 Zk is the annual levelized capital investment,

and Z_ k ¼ gtk Zk is the annual levelized operating and maintenance cost. The details of factors CRF, t, gk and relations for Zk of each OM

Table 2 Fuel-product definition of the sCO2/tCO2 system. Component

Fuel (MW)

Product (MW)

Reactor

E_ 4 þ E_ fuel E_ 5  E_ 6 E_  E_ 7

E_ 5 _ T1 W

Turbine 1 HTR LTR Pre-cooler 1 Pre-cooler 2 Main compressor Recompression compressor Turbine 2 Condenser Pump

6

E_ 7  E_ 8 E_ 8a  E_ 9 E_  E_ 9

_ W MC _ W RC

1

E_ 01  E_ 02 E_ 02  E_ 03 _p W

E_ 4  E_ 3c E_ 3a  E_ 2 E_  E_ 01

04

E_ 06a  E_ 05a E_  E_ 2

1

E_ 3b  E_ 8b _ W T2

E_ 06  E_ 05 E_ 04  E_ 03

In this part, the results of energy, exergy and exergoeconomic performance and optimization are presented. The NIST REFPROP database [30] is used for thermodynamic properties of the working fluid. Input parameters are given in Table 7. Table 8 presents a base case operating condition of the sCO2/tCO2 cycle. 4.1. Energy, exergy and exergoeconomic performance Table 9 indicates the result of energy and exergy analysis for the sCO2/tCO2 system. Considering a typical sCO2 cycle, the net power output is 248.84 MW and the heat rejected to the pre-cooler is 351.16 MW. The energy efficiency of 41.47% is obtained for the sCO2 cycle and the exergy efficiency is 57.43%. By adding a tCO2 cycle, 9.45 MW of power is generated by the tCO2 cycle. Further, the heat transferred to the cooling water is reduced to 175.02 MW. Consequently, the energy efficiency of sCO2/tCO2 cycle increases to 43.05% with an improvement of 3.81%. In addition, the exergy efficiency increases up to 59.6%. Table 10 presents system cost rates associated with the exergy of each stream. Data in the table show a value of 10.048 $/GJ for the unit exergy cost of power produced by the turbine 1. For the power generated by the turbine 2, the unit exergy cost is 20.435 $/GJ. The result of exergy and exergoeconomic analysis is given in Table 11. Results show that the reactor has the highest value of Z_ þ C_ þ C_ , indicating that an attention should be paid to its k

D;k

L;k

exergoeconomic performance enhancement. Besides, the reactor obtains an exergoeconomic factor value of 66.15%, which suggests that the capital investment, operation and maintenance costs (Z_ ) k

dominate the exergy destruction cost. The second highest value of Z_ k þ C_ D;k þ C_ L;k is obtained by the turbine 1, i.e., 1752.13 $/h. Further, for the turbine 1, the exergoeconomic factor and exergy destruction ratio are 66.35% and 4.29%, respectively. It indicates that the exergy and exergoeconomic performance of this

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X. Wang et al. / Energy xxx (2016) 1e12 Table 3 Economic data and cost functions for economic modeling [15,28]. Factor Number of operation years (n) Annual plant operation hours (t) Interest rate (ir) Maintenance factor (gk) Capital recovery factor (CRF)

Economic data 20 8000 12% 0.06 ir ð1 þ ir Þn =½ð1 þ ir Þn  1

System component Reactor

Capital investment cost function c1 *Q_ r ; c1 ¼ 283 $=kWth 479:34*m_ in *½1=ð0:93  hT1 Þ*lnðPRcÞ*½1 þ expð0:036*T5  54:4Þ 71:1*m_ in *½1=ð0:92  hC ÞPRc  lnðPRcÞ

Turbine 1 Compressors HTR, LTR, and Pre-cooler1

2681*A0:59 k

Condenser and Pre-cooler 2

2143*A0:514 k

Turbine 2

_ 0:7 4405*W T2

Pump

_ 0:8 1120*W P

Table 4 Exergetic cost rate balance and auxiliary equations for system components. Component

Exergetic cost rate balance equation

Auxiliary equation

Reactor core

C_ 5 ¼ C_ fuel þ C_ 4 þ Z_ R C_ 6 þ C_ WT1 ¼ C_ 5 þ Z_ T1 C_ 7 þ C_ ¼ C_ þ C_ þ Z_ HTR

nil C_ 5 =E_ 5 ¼ C_ 6 =E_ 6 C_ 6 =E_ 6 ¼ C_ 7 =E_ 7 ; C_ 3c ¼ C_ 3a þ C_ 3b C_ 7 =E_ 7 ¼ C_ =E_

Turbine 1 HTR

4

6

3c

C_ 8 þ C_ 3a ¼ C_ 2 þ C_ 7 þ Z_ LTR C_ 9 þ C_ 01 ¼ C_ 8a þ C_ 04 þ Z_ pc1 C_ 06a þ C_ 1 ¼ C_ 9 þ C_ 05a þ Z_ pc2 C_ ¼ C_ þ C_ þ Z_

LTR Pre-cooler 1 Pre-cooler 2 Main compressor

2

1

WMC

MC

02

05

C_ 3b ¼ C_ 8b þ C_ WRC þ Z_ RC C_ 02 þ C_ WT2 ¼ C_ 01 þ Z_ T2 C_ þ C_ ¼ C_ þ C_ þ Z_

Recompression compressor Turbine 2 Condenser

03

06

C_ 04 ¼ C_ 03 þ C_ WP þ Z_ p

Pump

Table 5 Exergoeconomic evaluation parameters [20,26]. cF;k ¼ C_ F;k =E_ F;k c ¼ C_ =E_

Average cost per unit exergy of fuel Average cost per unit exergy of product

P;k

P;k

P;k

rk ¼ (cP,kcF,k)/cF,k C_ D;k ¼ cF;k E_ D;k fk ¼ Z_ k =ðZ_ k þ C_ D;k þ C_ L;k Þ P _ P _ Zk þ C D;k C_ total ¼

Relative cost difference Cost rate of exergy destruction Exergoeconomic factor Total cost rate

k

k

Table 6 Practical range of decision variable. Decision variable

Range

PRc T5 (
C) T01 (
C) P01 (bar)

2.2e4.2 550e700 70e130 100e180

component is satisfactory. The relative cost difference values in the condenser and the precooler 2 are higher than that in other components. For the condenser, examining the exergoeconomic factor reveals that only a 1.44% of total system cost is due to Z_ , meanwhile the majority k

portion of that is due to the exergy destruction cost. Considering the pre-cooler 2, 2.38% of total system cost is due to Z_ k . It indicates that reducing exergy destruction costs in condenser and pre-cooler 2 can improve system performance. Lower values of exergoeconomic factor in HTR and LTR show that both components

8

8

C_ 9 =E_ 9 ¼ C_ 8a =E_ 8a ; C_ 8a ¼ ð1  xÞC_ 8 C_ 1 =E_ 1 ¼ C_ 9 =E_ 9 ; C_ 05a ¼ 0 _ _ C_ W =W ¼ C_ W =W MC

MC

T1

T1

_ _ _ _ _ C_ WRC =W RC ¼ C WT1 =W T1 ; C 8b ¼ xC 8 _ _ _ _ C =E ¼ C =E 01

cnd

01

02

02

C_ 03 =E_ 03 ¼ C_ 02 =E_ 02 ; C_ 05 ¼ 0 _ p ¼ C_ _ C_ =W =W WP

WT2

T2

have higher exergy destruction costs. Special attention should be focused on these components. The overall value of f of the sCO2/tCO2 cycle is calculated to be 52.33%. It suggests that 47.67% of the total system cost is associated with the exergy destruction. 4.2. Sensitivity analysis Effects of design parameters are presented to study thermodynamic and exergoeconomic performance of the combined system. The considered parameters are PRc, turbine 2 inlet temperature T01, turbine 2 inlet pressure P01 and cooling water temperature Tc. Three indicators, energy efficiency, exergy efficiency and total cost rate, are adopted to evaluate the performance of the combined cogeneration cycle. When one specific parameter is evaluated, other parameters are constant. Fig. 4 presents effect of PRc on the energy and exergy efficiencies and total cost rate of the sCO2/tCO2 cycle. Because of a constant inlet pressure of the main compressor, work of both compressors and turbine 1 increases with an increase in PRc. Also, the reactor outlet temperature is kept constant when PRc increases, therefore making the net power of the topping cycle first increased and then decreased. Further, as the PRc increases the LTR outlet temperature (T8, which is equal to T8a) increases resulting from four facts, i.e., the reduction of mass flow rate in the topping cycle, the decrease in turbine 1 exit temperature and the increase in main compressor outlet temperature, and therefore the less heat transfer in the HTR and LTR. It should be noted that as the PRc increases, heat transferred to tCO2 cycle is increased which causes increases in mass flow rate and net work of tCO2 cycle. But the net power of sCO2

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Fig. 3. Optimization flow chart.

topping cycle is dominant. Consequently, the energy and exergy efficiencies increase first and then decrease with increasing PRc. Referring to Fig. 4, increasing PRc up to around 2.7 reduces total cost rate of the combined cycle from 11697 to 11419 $/h which is mainly due to the reduction of exergy destruction cost rate of the reactor. Further, with increasing PRc exergy destruction cost rates of recuperators are also reduced due to an increase in their heat transfer area. It should be noted that the capital investment, operation and maintenance costs (Z_ ) of turbine 1 and compressors k

increase with the increase in PRc. However, the reducing exergy destruction cost rate of the system is dominant when PRc is below about 2.7. The influence of these parameters finally causes the decrease of total cost rate. When PRc increases beyond 2.7, total cost rate of the cogeneration system increases. This is mostly because the rising capital investment, operation and maintenance

costs of the system become dominant. Fig. 5 shows the influence of turbine 2 inlet temperature (T01) on the energy and exergy efficiencies and total cost rate. By increasing the inlet temperature of turbine 2, the energy and exergy efficiencies of the system are increased. The increases in the sCO2/tCO2 energy and exergy efficiencies, as T01 changes, are related to the tCO2 cycle performance (see Fig. 6). This can be explained as follows: an increase in T01 generates a closer fit of temperature profiles of the heat source and working fluid in the bottoming cycle, leading to a better match of the two fluid states, thereby allowing for a higher energy efficiency and the exergy efficiency. On the other hand, exergy destruction cost rate of the pre-cooler 1 is reduced by increasing the inlet temperature of turbine 2. Meanwhile, an increase in heat transfer area is required in order to rise the inlet temperature of turbine 2 which results in an increase

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8

X. Wang et al. / Energy xxx (2016) 1e12 Table 7 Input parameter values used in the simulation.

Table 10 Cost flow rates and unit exergy costs for the sCO2/tCO2 system.

Parameters

Value

State

C_ ($/h)

c ($/GJ)

(
C) (bar) (bar) (
C) (
C)

25 1.01 74 32b 800c 600

1 2 3 4 5 6 7 8 9 05a 06a 01 02 03 04 05 06 _ W

14255.67 17211.06 31006.45 40402.41 48957.48 36003.62 26617.97 21683.83 14541.22 0 290.29 13562.03 12432.52 12046.35 12610.34 0 390.46 14116.42

8.8005 9.2703 9.4598 9.4461 8.8005 8.8005 8.8005 8.8005 8.8005 0 28.087 16.294 16.294 16.294 16.584 0 68.418 10.048

_ W MC _ W

2610.66

10.048

2504.71

10.048

_ W T2 _p W

1225.81

20.435

530.85

20.435

T0 P0 P1 T1 TR Q_

core (MW) Fuel cost ($/MW h)

ht1 ht2 hc hp

7.4a 0.90 0.85 0.89 0.80

εHTR and εLTR

0.86a

a b c

Ref. [15]. Ref. [7]. Ref. [8].

T1

Table 8 Thermodynamic properties and exergy flow rates of the sCO2/tCO2 cycle for a base design. State

Fluid

P (bar)

T (
C)

h (kJ/kg)

s (kJ/kg K)

m_ (kg/s)

E_ (MW)

1 2 3 4 5 6 7 8 9 05a 06a 01 02 03 04 05 06

CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 water water CO2 CO2 CO2 CO2 water water

74 207.2 207.2 207.2 207.2 74 74 74 74 1.01 1.01 110 72.14 72.14 110 1.01 1.01

32 96.19 225.47 383.09 550 428.01 253.83 118.26 57.9 25 35 100 65.98 30 42.26 25 30.74

378.60 413.26 630.29 828.86 1034.63 900.79 702.22 547.27 462.67 104.92 146.72 495.90 478.51 304.55 312.08 104.92 128.93

1.5857 1.5961 2.1076 2.4542 2.7335 2.7549 2.4297 2.0891 1.8532 0.3672 0.5051 1.8948 1.9039 1.3435 1.3482 0.3672 0.4470

2081.85 2081.85 2915.93 2915.93 2915.93 2915.93 2915.93 2915.93 2081.85 4187.19 4187.19 958.21 958.21 958.21 958.21 6941.51 6941.51

449.96 515.71 910.47 1188.10 1545.28 1136.41 840.16 684.42 458.98 0 2.87 231.20 211.95 205.36 211.21 0 1.59

Table 9 Comparison between a typical sCO2 cyclea and the sCO2/tCO2 systemb. Items

hth (%) hex (%)

_ net (MW) W _ W net; tCO2 (MW) Q_ (MW) pc

a b

sCO2 cycle

sCO2/tCO2 cycle

Value

Value

41.47 57.43 248.84

43.05 59.61 258.29

e

9.45

351.16

175.02

PRc ¼ 2.8, Tmax ¼ 550
C, T1 ¼ 32
C. PRc ¼ 2.8, T5 ¼ 550
C, T01 ¼ 100
C, P01 ¼ 110 bar.

in the Z_ k value of the pre-cooler 1. However, this increase in the cost rate of pre-cooler 1 is less than the decrease in the exergy destruction cost rate. As a result the total cost rate is reduced. Fig. 7 considers the effect of turbine 2 inlet pressure on the sCO2/ tCO2 performance. As can be seen, there is an optimum value of inlet pressure at which the efficiencies are maximized. These findings are understandable because for a fixed lower condensation temperature and a fixed upper turbine 2 inlet temperature, the size of the area enclosed by the path of the tCO2 cycle on the T-S diagram varies with the value of the pumped pressure P01. An increase in P01 leads to an increase and then a decrease in this area that represents

RC

the net work of the tCO2 cycle. Consequently, the efficiencies of the system are increased first and then decreased. Fig. 7 also indicates that, as P01 increases, the exergy destruction and the corresponding cost decrease for the pre-cooler 1 and condenser and increase for other tCO2 components. Thus, there is an optimum value of P01 with which the total cost rate is minimized. Fig. 8 shows the influence of cooling water temperature (Tc). Since the critical temperature of CO2 is low, it requires cooling water of very low temperature at all times. However, it is not available in all regions worldwide. A sea water heat sink with a temperature of 25
C was assumed here for the preliminary analysis. This is available in middle and high latitudes where the annual average sea water temperature is around or below 25
C, such as Russia, Japan, Iceland, Canada and northern China. In northern China like Dalian, in longer period of time the highest measured sea water temperature was 26
C and the lowest measured temperature was 3
C [31]. In the cold sea water temperature season, the cooling temperature can decrease below 25
C, resulting in an increase in energy efficiency and exergy efficiency of the combined cycle, as shown in Fig. 8. This is because as Tc decreases, the enthalpy drops of the working fluid across the turbine 2 increases. By reducing the cooling temperature, temperature difference between the water and CO2 decreases and surface requirements of the condenser are increased. However, the exergy destruction and its associated cost of condenser are decreased. As a result, the total cost rate of the system is decreased. 4.3. Exergoeconomic optimization The result of exergoeconomic optimization is shown in Table 12. The goal of exergoeconomic optimization is to minimize the total cost rate. The values of key operating parameters for the optimal condition are also given in Table 12. For the condenser, as can be seen, the related cost of exergy destruction rate is significantly higher than the investment, operation and maintenance costs, Z_ , k

for the optimized case, which is also true for the base case (see Table 11). This is because the exergy destruction in the cooling process is very high. Hence, this component exergetic efficiency

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X. Wang et al. / Energy xxx (2016) 1e12

9

Table 11 Exergy and exergoeconomic results of the sCO2/tCO2 cycle for the base design. Components

E_ F;k (MW)

E_ P;k (MW)

E_ D;k (MW)

YD,k (%)

cF,k ($/GJ)

cP,k ($/GJ)

C_ D;k ($/h)

Z_ k ($/h)

Z_ k þ C_ D;k þ C_ L;k ($/h)

rk (%)

fk (%)

Reactor Turbine 1 HTR LTR Pre-cooler 1 Pre-cooler 2 Main compressor Recompression compressor Turbine 2 Condenser Pump System

1621.41 408.87 296.25 155.74 29.67 9.01 72.17 69.25 19.26 6.58 7.22 2695.43

1545.28 390.26 277.63 134.32 19.99 2.87 65.75 64.66 16.66 1.59 5.85 2524.87

76.12 18.61 18.61 21.42 9.69 6.14 6.42 4.59 2.59 5.00 1.36 170.56

17.5684 4.2947 4.2960 4.9424 2.2355 1.4175 1.4823 1.0584 0.5983 1.1534 0.3150 39.36

7.6824 8.8005 8.8005 8.8005 8.8005 8.8005 10.0476 10.0476 16.2941 16.2941 20.4347 e

8.8005 10.0476 9.4009 9.4009 13.2260 28.0872 12.4854 11.3536 20.4347 68.4184 26.7749 e

2105.34 589.57 589.75 678.49 306.89 194.59 232.32 165.88 152.08 293.17 100.41 5408.50

4115.08 1162.56 10.30 15.96 11.55 4.74 344.73 138.11 96.30 4.30 33.14 5936.77

6220.42 1752.13 600.06 694.46 318.44 199.33 577.04 303.99 248.38 297.47 133.55 11345.27

14.5551 14.1709 6.8220 16.3185 50.2868 219.1534 24.2625 12.9976 25.4114 319.8965 31.0267 e

66.1544 66.3514 1.7171 2.2987 3.6274 2.3797 59.7398 45.4324 38.7702 1.4446 24.8117 52.33

Fig. 4. Effect of PRc on the energy efficiency, exergy efficiency and total cost rate.

Fig. 5. Effect of T01 on the energy efficiency, exergy efficiency and total cost rate.

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10

X. Wang et al. / Energy xxx (2016) 1e12

maintenance costs of the system components. Table 13 lists a detailed comparison between the base case and optimum case. It can be seen that the total cost rate as the objective function is decreased by 0.9%, which suggests that the operating parameters chosen for the base case are nearly equal to that for optimized case. The total exergy destruction rate is reduced by 2.46% and the related cost rate is decreased by 3.39%. Moreover, the exergy efficiency is increased from 59.61% to 60.58%. The net power output of the system is increased by about 1.63%. Table 14 presents exergoeconomic optimization result for higher reactor outlet temperatures. To conduct optimizations, cooling water temperature was conservatively selected to be 25
C. It can be seen that an increase in reactor outlet temperature leads to a decrease in C_ and C_ . Because of the constant fuel energy total

D; total

and exergy input to the reactor (Q_ core was set to be 600 MW), the Z_ k of the reactor is nearly unchanged and the exergy destruction cost decreases with an increase in reactor outlet temperature. Even though the exergy destruction costs of recuperators are increased Fig. 6. Effect of T01 on the heat transfer in pre-cooler 1.

Fig. 7. Effect of P01 on the energy efficiency, exergy efficiency and total cost rate.

should be improved by increasing its effectiveness. The next components are the HTR, LTR and pre-cooler 2. The lower values of exergoeconomic factor for these heat exchangers suggest that a decrease in exergy destruction cost rate can improve the system performance by increasing their exergetic efficiencies. A comparison between the base case and the optimum case reveals that the reactor has the highest investment, operation and maintenance costs Z_ , and the largest exergy destruction. This is k

because the reactor is the biggest and most complex component in the combined cycle. The material constraints for construction, capital investment and operation costs play an important role. Furthermore, its exergy destruction and exergy loss are very high due to the irreversibility during the heat transfer process. It can be also found from Table 12 that the optimization increases the overall exergoeconomic factor from 52.33% to 53.52% (2.27% relative improvement) indicating that the optimization process mostly reduced the associated cost of thermodynamic inefficiencies rather to increase the capital investment, operation and

due to the increase of heat transfer areas, the C_ D; total and then C_ total are decreased. Table 14 also shows that an increase in reactor outlet temperature improves energy and exergy efficiencies of the combined cycle. By increasing the reactor outlet temperature from 550
C to 700
C, an increase of about 12.83% in energy efficiency is obtained by the system. Moreover, the overall value of exergoeconomic factor accounts for more than a half and increases with an increase in reactor outlet temperature, suggesting that the total Z_ dominates the exergy destruction cost in this system. k

5. Conclusions The present paper developed an exergy and exergoeconomic analysis algorithm for a combined recompression sCO2/tCO2 energy conversion system. Detailed thermodynamic and exergoeconomic analyses and optimization have been successfully performed. Parametric investigation was carried out to study effects of key thermodynamic parameters on the energy and exergy efficiencies

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X. Wang et al. / Energy xxx (2016) 1e12

11

Fig. 8. Effect of Tc on the energy efficiency, exergy efficiency and total cost rate.

Table 12 Exergoeconomic result of the sCO2/tCO2 cycle for the optimum casea. Components

E_ F;k (MW)

E_ P;k (MW)

E_ D;k (MW)

YD,k (%)

cF,k ($/GJ)

cP,k ($/GJ)

C_ D;k ($/h)

Z_ k ($/h)

Z_ k þ C_ D;k þ C_ L;k ($/h)

rk (%)

fk (%)

Reactor Turbine 1 HTR LTR Pre-cooler 1 Pre-cooler 2 Main compressor Recompression compressor Turbine 2 Condenser Pump Overall system

1610.91 413.50 283.37 157.97 30.30 8.88 73.23 71.87 27.25 6.81 10.61 2694.71

1534.55 394.61 266.27 136.92 25.44 2.83 66.74 67.15 23.60 1.60 8.63 2528.35

76.36 18.89 17.10 21.05 4.86 6.05 6.49 4.72 3.65 5.21 1.97 166.36

17.6220 4.3599 3.9462 4.8582 1.1227 1.3970 1.4982 1.0885 0.8426 1.2027 0.4558 38.3938

7.6650 8.7913 8.7913 8.7913 8.7913 8.7913 10.0412 10.0412 13.7587 13.7587 17.3331 e

8.7913 10.0412 9.3665 9.3665 10.7074 28.0615 12.4970 11.3467 17.3331 59.2140 22.7494 e

2106.99 597.89 541.16 666.22 153.96 191.58 234.67 170.49 180.85 258.13 123.23 5225.17

4115.08 1177.72 10.23 16.11 21.50 4.71 355.39 145.10 122.88 4.18 45.10 6017.98

6222.06 1775.60 551.39 682.34 175.46 196.29 590.06 315.59 303.72 262.32 168.32 11243.15

14.6939 14.2174 6.5431 15.7466 21.7956 219.196 24.4579 13.0014 25.9795 330.376 31.2483 e

66.1369 66.3276 1.8551 2.3612 12.2525 2.3986 60.2294 45.9764 40.4563 1.5949 26.7917 53.5257

a

PRc ¼ 2.865, T01 ¼ 119.138
C, P01 ¼ 130.77 bar.

Table 13 Comparison between the optimum case and the base case. Properties

Base case

Optimum case

Variation (%)

Ctotal ($/h) E_ D; total (MW) ($/h) C_

11345.27 170.56

11243.15 166.36

0.9 2.46

5408.50

5225.17

3.39

hex (%) hth (%)

59.61 43.05 258.29

60.58 43.75 262.51

þ1.627 þ1.626 þ1.634

D; total

_ net (MW) W

and total cost rate of the system. For the proposed sCO2/tCO2 cycle, with the aim of evaluating the exergoeconomic performance, the following conclusions are drawn: C The most exergy destruction rate occurs in the reactor, and components in the tCO2 cycle have less exergy destruction. C The reactor, and turbine 1 have large amount of Z_ k þ C_ D;k þ C_ L;k , which can be reduced by increasing the

Table 14 Summary of optimization result. Optimum design parameters

T5 ¼ 550
C

T5 ¼ 600
C

T5 ¼ 650
C

T5 ¼ 700
C

PRc () T01 (
C) P01 (bar) C_ ($/h)

2.865 119.138 130.77 11243.15

3.048 127.494 135.57 10637.53

3.197 127.543 137.12 10126.69

3.249 128.429 138.47 9699.08

hth (%) hex (%)

43.75 60.58 262.51

45.96 63.65 275.79

47.86 66.27 287.15

49.36 68.35 296.18

5225.17

4650.73

4189.91

3845.79

53.5257

56.28

58.63

60.35

total

_ net (MW) W C_ D; total ($/h) foverall (%)

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X. Wang et al. / Energy xxx (2016) 1e12

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