Exergoeconomic analysis of utilizing the transcritical CO2 cycle and the ORC for a recompression supercritical CO2 cycle waste heat recovery: A comparative study

Applied Energy 170 (2016) 193–207

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Exergoeconomic analysis of utilizing the transcritical CO2 cycle and the ORC for a recompression supercritical CO2 cycle waste heat recovery: A comparative study Xurong Wang, Yiping Dai ⇑ School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, China

h i g h l i g h t s
An exergoeconomic analysis is performed for sCO2/tCO2 cycle.
Performance of the sCO2/tCO2 cycle and sCO2/ORC cycle are presented and compared.
The sCO2/tCO2 cycle performs better than the sCO2/ORC cycle at lower PRc.
The sCO2/tCO2 cycle has comparable total product unit cost with the sCO2/ORC cycle.

a r t i c l e

i n f o

Article history: Received 26 August 2015 Received in revised form 16 February 2016 Accepted 20 February 2016 Available online 4 March 2016 Keywords: Supercritical carbon dioxide cycle Transcritical carbon dioxide cycle Organic Rankine cycle Exergoeconomic Comparison Optimization

a b s t r a c t Two combined cogeneration cycles are examined in which the waste heat from a recompression supercritical CO2 Brayton cycle (sCO2) is recovered by either a transcritical CO2 cycle (tCO2) or an Organic Rankine Cycle (ORC) for generating electricity. An exergoeconomic analysis is performed for sCO2/tCO2 cycle performance and its comparison to the sCO2/ORC cycle. The following organic fluids are considered as the working fluids in the ORC: R123, R245fa, toluene, isobutane, isopentane and cyclohexane. Thermodynamic and exergoeconomic models are developed for the cycles on the basis of mass and energy conservations, exergy balance and exergy cost equations. Parametric investigations are conducted to evaluate the influence of decision variables on the performance of sCO2/tCO2 and sCO2/ORC cycles. The performance of these cycles is optimized and then compared. The results show that the sCO2/tCO2 cycle is preferable and performs better than the sCO2/ORC cycle at lower PRc. When the sCO2 cycle operates at a cycle maximum pressure of around 20 MPa (2.8 of PRc), the tCO2 cycle is preferable to be integrated with the recompression sCO2 cycle considering the off-design conditions. Moreover, contrary to the sCO2/ORC system, a higher tCO2 turbine inlet temperature improves exergoeconomic performance of the sCO2/tCO2 cycle. The thermodynamic optimization study reveals that the sCO2/tCO2 cycle has comparable second law efficiency with the sCO2/ORC cycle. When the optimization is conducted based on the exergoeconomics, the total product unit cost of the sCO2/ORC is slightly lower than that of the sCO2/tCO2 cycle. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Because of their higher efficiency and lower costs associated with nuclear power plants, they are becoming more popular for future electricity generation. In recent years, the supercritical CO2 Brayton cycle (sCO2) has received more attention because it ⇑ Corresponding author at: School of Energy and Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, Shaanxi 710049, China. Tel./fax: +86 029 82668704. E-mail addresses: [email protected] (X. Wang), [email protected]. edu.cn (Y. Dai). http://dx.doi.org/10.1016/j.apenergy.2016.02.112 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

is simple, compact and less expensive, and offers high efficiency. With a reactor outlet temperature of 550 °C, the efficiency of sCO2 cycle can reach 45.3% [1] which is comparable with the helium Brayton cycle at a significantly higher temperature (850 °C). Convergence on sCO2 cycle is occurring from the nuclear [1–4] and solar-thermal [5–8]. By utilizing the abrupt property changes near the critical point of CO2 the compressor work can be reduced, resulting in the significant efficiency improvement. Meanwhile, a considerable low grade thermal energy (about 50 percent input energy) is rejected to the heat sink in the precooler [9,10]. Utilization of this thermal energy in different systems

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Nomenclature A C_ c cp;tot E_ h _ m NK NP P PRc Q_ s T Te _ W x Z_

heat transfer area (m2) cost rate ($/h) cost per exergy unit ($/GJ) total product unit cost ($/GJ) exergy rate (W) specific enthalpy (Jk g1) mass flow rate (kg s1) number of system components number of system products pressure (bar) compressor pressure ratio heat addition (W) specific entropy (Jk g1 K1) temperature (K/°C) evaporation temperature of the ORC (°C) work flow rate-power (W) recompressed flow ratio capital cost rate ($/h)

e DT E DT sup

effectiveness pinch point temperature difference (°C) degree of superheat (°C)

Subscripts 0 environmental state c critical point cnd condenser E evaporator ex exergy HTR high temperature recuperator in inlet LTR low temperature recuperator p pump pc pre-cooler R reactor th thermal tot total

Greek symbols g efficiency

can improve the overall efficiency of the sCO2 cycle. In this regard, recently, some efforts have been made by researchers. Chacartegui et al. [11,12] 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 7–12%, which depended on the turbine inlet temperature [12]. It should be noted that the simple sCO2 configuration was considered for that study. Sánchez et al. [13] 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 composition. Besarati and Goswami [14] considered a thermodynamic comparison of three different sCO2/ORC combined cycles. They reported that the highest 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. [15] studied a sCO2 part-flow cycle combined with an ORC with liquefied natural gas as the heat sink. They showed that the combined cycle achieve 52.12% overall thermal efficiency. In another study, Akbari and Mahmoudi [16] 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. Recently, Yari and Sirousazar [17] proposed and analyzed the utilization of waste heat from the sCO2 cycle for electricity generation using a transcritical CO2 cycle (tCO2). They showed that the second law efficiency of the recompression sCO2/tCO2 cycle was 5.5–26% higher than that of the single sCO2 cycle. Further, the exergy destruction of the new combined cycle was 6.7–28.8% lower than that of the stand-alone sCO2 cycle. Later, Wang et al. [18] offered a technoeconomic analyses of a combined recompression sCO2/tCO2 cycle to show 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 without a further parametric optimization. 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

Fig. 1. Temperature variation in the heat recovery heat exchanger for ORC and transcritical cycles.

X. Wang, Y. Dai / Applied Energy 170 (2016) 193–207

195

Fig. 2. Schematic diagram of the sCO2 cogeneration cycle and the T–s diagram. Table 1 Working fluids used in the ORC and their properties. Working fluid

Tc (°C)

Pc (bar)

Tmax (°C)

R123 R245fa Toluene Isobutane Isopentane Cyclohexane

183.68 154.05 318.6 134.66 187.2 280.45

36.6 36.4 41.3 36.29 33.78 40.75

175 140 300 130 175 270

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. Both the ORC and the tCO2 cycles are attractive technologies for the conversion of low-grade thermal energy into electricity

[20–30]. The ORC has low operating pressure and low cost because of its 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 point problem, as shown in Fig. 1. This leads to a significant mismatch of the two fluid states and generates a lot of irreversibility in the sCO2/ORC cogeneration system. A better match is shown in (the right plot of) Fig. 1. The temperature profile of the working fluid 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 [23]. Compared to the ORC, a drawback of the transcritical cycle is the high absolute pressure

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performed. In addition, many investigators concerned mostly about the thermodynamic analysis of the combination of sCO2 cycle with a bottoming cycle. An assessment and optimization of the sCO2/tCO2 cycle from the viewpoints of exergy and exergoeconomics, to our knowledge, is also not yet reported. Thus, a detailed and comprehensive exergoeconomic analysis is called for. Hence, the present paper conducts an exergoeconomic analysis and comparison of utilizing the tCO2 cycle and the ORC for a recompression sCO2 cycle waste heat recovery unit aiming at more efficient use of energy from nuclear power plant systems. This paper extends the recently published works [18,19] by focusing on the exergoeconomic analysis of the sCO2/tCO2 cycle and the comparison between the sCO2/tCO2 and sCO2/ORC cycles. The theory of exergetic cost is applied to the combined cogeneration cycles in order to obtain the optimum design conditions. Firstly, a parametric study is performed to reveal the effects of decision variables on the first law efficiency, the second law efficiency and the total product unit cost. The exergoeconomic comparison of the sCO2/tCO2 cycle to the sCO2/ORC cycle is also presented under the same operating condition. The sCO2/tCO2 cycle and the sCO2/ORC cycle are then optimized from the viewpoints of thermodynamics and 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 bottoming cycle to utilize the waste heat from the sCO2 cycle for power generation and contribute to the knowledge of the sCO2 cycle for next generation nuclear reactors. 2. System description and assumptions

Fig. 3. Position of minimum temperature difference in the condenser.

of the supercritical CO2. This may be one of the reasons why the tCO2 cycle has not received as much attention as the ORC. However, in most applications the compactness of the CO2 machines, because of the higher density of CO2 near the critical region, offsets the weight and cost increase due to the high pressure of the CO2. As mentioned above, each of waste heat recovery technologies has its own merits and demerits when integrated with the sCO2 cycle. A performance comparison of both cogeneration systems under identical operating conditions, however, has not yet been

A schematic diagram of the combined sCO2/tCO2 cycle and the T–s diagram associated with this cycle are shown in Fig. 2. The cycle is actually a combination of the sCO2 cycle and the tCO2 cycle so that the heat rejected in the pre-cooler of the sCO2 cycle is utilized to run the tCO2. The CO2 exiting the pre-cooler is pressurized by running through compressor 1. The stream is first preheated in the LTR (low temperature recuperator) and then joins the stream exiting the compressor 2 (point 3 on T–s diagram). The mixture is heated in the HTR (high temperature recuperator), evaporates in the reactor and undergoes an expansion in the turbine 1. The expanded stream then flows to the HTR to heat the stream 3, and afterward to the LTR to heat the stream 2. The CO2 at LTR exit (point 8) is divided into two streams: stream 8a and stream 8b. The former enters the evaporator where it transfers part of the heat to the bottoming tCO2 cycle, and then passes to the pre-cooler before being compressed in the compressor 1. The latter stream

Table 2 Comparison of sCO2a, tCO2b and ORCc cycles between the present work and those published in literature. Parameters Tmin (°C)

Present work Tmax (°C)

Recompression sCO2 cycle 32 32 50 50

550 550 550 550

200 300 200 300

tCO2 cycle 10

65

100

ORC cycle 29 a b c

110.4

Reference

Pmax (bar)

8.98

gT ¼ 0:90, gC ¼ 0:85, eHTR ¼ 0:86, eLTR ¼ 0:86. gT ¼ 0:70, gP ¼ 0:80. Isopentane, gT ¼ 0:85, gP ¼ 0:80,DT sup ¼ 0.

PRopt

xopt

gth (%)

PRopt

xopt

gth (%) [10]

2.641 3.862 2.39 2.79

0.3332 0.3550 0.1838 0.2528

41.18 43.31 36.70 38.93

2.64 3.86 2.40 2.80

0.334 0.355 0.184 0.254

41.18 43.32 36.71 38.93

W P (kW)

W T (kW)

gth (%)

W P (kW)

W T (kW)

gth (%) [30]

3.6507

12.109

8.484

3.648

12.099

8.48

_ (kg/s) m

W net (kW)

gth (%)

_ (kg/s) m

W net (kW)

gth (%) [32]

80.64

5303

14.07

80.13

5270

14.1

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X. Wang, Y. Dai / Applied Energy 170 (2016) 193–207 Table 3 Economic data and cost functions for economic modeling. Factor

Economic data

Number of useful operation years (n) Annual plant operation hours (s) Interest rate (ir ) Maintenance factor (ck ) Capital recovery factor (CRF)

20 8000 12% 0.06

System component Reactor

Capital investment cost function c1  Q_ r ; c1 ¼ 283$=kWth
 1 _ in  0:93 479:34  m gT 1  lnðPRcÞ  ð1 þ expð0:036  T5  54:4ÞÞ h i 1 _ in  0:92 71:1  m g  PRc  lnðPRcÞ

ir ð1þir Þn ð1þir Þn 1

Turbine 1 Compressors

C

HTR, LTR, and Evaporator

2681  A0:59 k

Condenser and Pre-cooler Turbine 2

2143  A0:514 k _ 0:7 4405  W

Pump

_ 0:8 1120  W P

T2

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

None

Turbine 1 Compressor 1 Compressor 2 LTR

C_ 2 ¼ C_ 1 þ C_ WC1 þ Z_ C1

HTR

C_ 7 þ C_ 4 ¼ C_ 6 þ C_ 3 þ Z_ HTR

Evaporator

Pre-cooler Turbine 2 Condenser Pump

_ C_ 5 ¼ CE_ 6 E_ 5 6 C_ WC1 C_ WT1 _ C1 ¼ W _ T1 W

C_ 3b ¼ C_ 8b þ C_ WC2 þ Z_ C2

C_ WC2 _ C2 W

¼

C_ 8 þ C_ 3a ¼ C_ 2 þ C_ 7 þ Z_ LTR

C_ 7 E_ 7

C_ 8 E_ 8

C_ 9 þ C_ 01 ¼ C_ 8a þ C_ 04 þ Z_ E C_ 06a þ C_ 1 ¼ C_ 9 þ C_ 05a þ Z_ pc C_ 02 þ C_ WT2 ¼ C_ 01 þ Z_ T2 C_ 03 þ C_ 06 ¼ C_ 02 þ C_ 05 þ Z_ cnd C_ 04 ¼ C_ 03 þ C_ WP þ Z_ P

C_ 6 E_ 6 C_ 9 E_ 9

¼

C_ WT1 _ T1 , W

C_ 8b ¼ xC_ 8

_ ¼ CE_ 7 , C_ 3 ¼ C_ 3a þ C_ 3b 7

_

¼ CE_ 8a , 8a

C_ 8a ¼ ð1  xÞC_ 8 C_ 05a ¼ C_ 06a ¼ 0 C_ 01 E_ 01

_

¼ CE_ 02

3. Thermodynamic analysis The combined cogeneration cycles have been modeled based on the energy and exergy balance of individual components [9,10,18,19,28,31]. Particular attention is paid to the second law of thermodynamics and the exergy values at different state points are determined. Thermodynamic relations for HTR and LTR are given by

02

C_ 05 ¼ C_ 06 ¼ 0 C_ WP _ P W

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

¼

C_ WT2 _ T2 W

is compressed in the compressor 2 and then merged with the CO2 from the LTR. When the tCO2 cycle serves as the bottoming cycle, the heated CO2 from the evaporator further expands in the turbine 2 and is cooled in the condenser, then, pumped back to the evaporator. Adopting an ORC to utilize the waste heat from the evaporator yields the combined sCO2/ORC cycle (also see Fig.2). In the bottoming ORC, the working fluid exits the condenser as saturated liquid before being pumped to the evaporator where it is heated by the hot CO2. The ORC working fluid enters the turbine 2 and after expansion it passes to the condenser to reject heat to the cooling water. The selection of the working fluid substantially affects the performance of the ORC. In this work the following organic fluids are considered: R123, R245fa, toluene, isobutane, isopentane and cyclohexane. Table 1 presents values for critical properties of these organic fluids and their maximum operating temperatures that preserve organic fluids from degradation. The working fluid at the ORC turbine inlet can be either saturated or superheated. The effect of degree of superheat on the combined sCO2/ORC cycle performance will be discussed later on. The general assumptions in this study are as follows: (1) The system reaches a steady state; the kinetic and potential energies and heat transfer to the ambient are neglected.

h6  h7 ¼ h4  h3

ð1Þ

ð1  xÞðh3  h2 Þ ¼ h7  h8

ð2Þ

eHTR ¼ ðT 6  T 7 Þ=ðT 6  T 3 Þ

ð3Þ

eLTR ¼ ðT 7  T 8 Þ=ðT 7  T 2 Þ

ð4Þ

Eq. (4) is valid when the heat capacity of high pressure fluid is more than that of low pressure fluid; otherwise Eq. (5) is applicable.

eLTR ¼ ðT 3  T 2 Þ=ðT 7  T 2 Þ

ð5Þ

The mass flow rate for the bottoming cycle is calculated based on energy balance in the evaporator. For the ORC, the mass flow rate can be obtained using the pinch point temperature difference. Since the organic fluid undertakes constant temperature evaporation, for a given evaporator temperature, the mass flow rate can be easily calculated. Once the mass flow rate is obtained, state 9 can be available from energy balance in the evaporator. For the tCO2 cycle, the mass flow rate is computed based on the minimum temperature difference, which is not less than 3 °C. For a given inlet temperature of CO2 turbine (T 01 ), an iteration is employed to find the position of minimum temperature difference. The iteration starts with state 9 aligning state 8 (no bottoming cycle). The evaporator outlet temperature (T 9 ) is then decreased gradually until the position is found. When the iteration ends, state 9 is determined and the mass flow rate can be then obtained. Both CO2 and organic fluid can be superheated vapor at the turbine 2 outlet, dividing the condenser into a single-phase region and a two-phase region as shown in Fig. 3. A pinch of 3 °C at the satu-

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Fig. 4. Logic structure of the simulation procedure.

rated 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

b c d

_ water ðh06  hb Þ _ bottoming ðh02  hbb Þ ¼ m m

Parameters

Value

T0 (°C) P0 (bar) P1 (bar) PRc T1 (°C) Tmax (°C) Te or T01 (°C) DTE (°C) DTsup (°C) P01 (bar) TR (°C) Q_ core (MW)

25 1.01 74 2.2–4.2a 32b 550 80–140 3–15 0–5 100–180 800c 600

Fuel cost ($/MW h)

7.4a 0.90 0.85 0.89d 0.80 0.86a

eHTR and eLTR a

Ref. Ref. Ref. Ref.

[16]. [3]. [9]. [18].

_ water ðhb  h05 Þ _ bottoming ðhbb  h03 Þ ¼ m m

ð6Þ

_ bottoming is the mass flow rate of CO2 or organic fluid. where m The exit temperature of the cooling water is calculated by

Table 5 The input parameter values used in the simulation.

gt1 gt2 gc gp

then obtained with the energy balance applied to the two-phase region:

ð7Þ

In the tCO2 cycle, the state of the CO2 at the exit of the turbine 2 may fall in the two-phase region. In this situation, 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 cogeneration cycle can be expressed as

_ net W

_ net;a þ W _ net;b ¼W _ t1  W _ c1  W _ c2 Þ ¼ ðW

sCO2

_ t2  W _ pÞ þ ðW bottoming cycle

ð8Þ

The first law efficiency of the combined cogeneration cycle can be defined as

_ W

gth ¼ _ net Q core

ð9Þ

Exergy analysis allows comparing power cycles of different types on the same thermodynamic basis, namely, how well the power cycle converts the available resource into actual usable power.

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Table 6 Thermodynamic properties and costs of exergy streams for a typical sCO2/tCO2 cycle.a State

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

Fluid

P (bar)

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

74 207.2 207.2 207.2 207.2 74 74 74 74 120 72.14 72.14 120 1.01 1.01

T (°C)

32 96.19 225.47 383.09 550 428.01 253.83 118.26 50 110 68.61 30 44.85 25 30.88

_ (kg/s) m

h (kJ/kg)

2081.85 2081.85 2915.93 2915.93 2915.93 2915.93 2915.93 2915.93 2081.85 1093.31 1093.31 1093.31 1093.31 7920.17 7920.17

378.60 413.26 630.29 828.86 1034.63 900.79 702.22 547.27 447.38 504.18 482.58 304.55 313.98 104.92 129.50

E_ (MW)

s (kJ/kg K)

1.5857 1.5961 2.1076 2.4542 2.7335 2.7549 2.4297 2.0891 1.8064 1.9046 1.9158 1.3435 1.3494 0.3672 0.4488

449.96 515.71 910.47 1188.10 1545.28 1136.41 840.16 684.42 456.17 269.64 242.38 234.32 242.68 0 1.89

Costs C_ ($/h)

c ($/GJ)

12,851 15,541 27,843 36,197 43,518 32,003 23,661 19,275 12,847 18234.44 16391.03 16395.58 17297.54 0 0

7.934 8.371 8.495 8.463 7.823 7.823 7.823 7.823 7.823 18.78 18.78 19 19.8 0 0

PRc = 2.8, T 01 = 110 °C, P 01 = 120 bar.

Table 7 Thermodynamic properties and costs of exergy streams for a typical sCO2/ORC cycle with R123 as the ORC working fluid a.

a

State

Fluid

P (bar)

T (°C)

_ (kg/s) m

h (kJ/kg)

s (kJ/kg K)

E_ (MW)

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

CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 R123 R123 R123 R123 water water

74 207.2 207.2 207.2 207.2 74 74 74 74 6.24 1.10 1.10 6.24 1.01 1.01

32 96.19 225.47 383.09 550 428.01 253.83 118.26 85.06 90 44.32 30 30.27 25 27.12

2081.85 2081.85 2915.93 2915.93 2915.93 2915.93 2915.93 2915.93 2081.85 436.61 436.61 436.61 436.61 8838.35 8838.35

378.60 413.26 630.29 828.86 1034.63 900.79 702.22 547.27 504.55 434.43 409.70 230.26 230.70 104.92 113.78

1.5857 1.5961 2.1076 2.4542 2.7335 2.7549 2.4297 2.0891 1.9749 1.6822 1.6961 1.1049 1.1052 0.3672 0.3968

449.96 515.71 910.47 1188.10 1545.28 1136.41 840.16 684.42 470.57 14.015 1.414 0.021 0.177 0 0.277

Costs C_ ($/h)

c ($/GJ)

13,940 16,739 29,658 38,442 45,764 33,655 24,881 20,269 13,936 619.41 62.48 66.15 79.24 0 0

8.606 9.016 9.049 8.988 8.226 8.226 8.226 8.226 8.226 12.28 12.28 871 124.7 0 0

PRc = 2.8, T 01 = 90 °C, DT E = 5 °C, DT sup = 0.

Neglecting the changes in kinetic and potential exergies, the total exergy of a stream is the sum of physical and chemical exergies

in the present work and those published previously for sCO2, tCO2 and ORC cycles, respectively.

E_ ¼ E_ ph þ E_ ch

4. Exergoeconomic analysis

ð10Þ

The physical exergy can be obtained by

_ E_ ph ¼ m½ðh  h0 Þ  T 0 ðs  s0 Þ

ð11Þ

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 second law efficiency of the combined cogeneration cycle is defined as

_ W

_ W

net gex ¼ _ net ¼ _ Ein Q core ð1  T 0 =T R Þ

ð12Þ

where E_ in is the exergy supplied to the reactor and T R is the temperature of reactor. In order to implement a validation exercise, the available data in literature is used [10,30,32]. The comparison of simulation results with those reported in the literature is shown in Table 2. It can be noted that the recompression mass fraction is calculated using an effective iteration technique. Table 2 indicates a good agreement between values of performance parameters calculated

Exergoeconomic analysis is on the basis of the principles of exergy and economic analyses at the level of system components [16,33–38]. Calculating the cost per unit exergy of product streams by revealing the cost formation process is the main purpose of an exergoeconomic analysis. To conduct this analysis, a cost balance equation along with the auxiliary equations is applied to each component of the sCO2/tCO2 and sCO2/ORC cycles. 4.1. Cost balance The cost balance equation for a system component receiving thermal energy and producing power has the form [33]

X

C_ out;k þ C_ w;k ¼

X

C_ in;k þ C_ q;k þ Z_ k

ð13Þ

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. (13) states that the total cost rate of exiting exergy streams equals the total cost rate of entering

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Fig. 5. Effects of PRc on the first law efficiency and net power output (a), the second law efficiency (b) and cp;tot (c) of the sCO2/tCO2 and sCO2/ORC cycles. (sCO2/tCO2: T max = 550 °C, T 01 = 90 °C, P 01 = 120 bar; sCO2/ORC: T max =550 °C, T e = 90 °C, DT E = 3, DT sup = 0).

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 [34]

C_ k ¼ ck E_ k

ð14Þ

_ C_ w ¼ cw W

ð15Þ

C_ q ¼ cq E_ q

ð16Þ

where ck ; cw ; cq are the average costs per exergy unit, $/GJ. By inserting Eqs. (14)–(16) into Eq. (13), it then follows that

X

_k¼ ðcout E_ out Þk þ cw;k W

X

ðcin E_ in Þk þ cq;k E_ k þ Z_ k

ð17Þ

The term Z_ k in Eq. (17) is the cost rate associated with the capital investment and operation and maintenance costs for the kth component:

_ OM Z_ k ¼ Z_ CI k þ Zk CRF

ð18Þ

where Z_ CI k ¼ s Z k is the annual levelized capital investment, and ck Z_ OM ¼ Z is the annual levelized operating and maintenance cost. k s k The details of factors CRF, s, ck and relations for Z k of each system component are provided in Table 3. It is noted that the cost of the reactor is based on 2003 [35], costs of turbine 1 and compressors are given in mid-1994 dollars [33], costs of heat exchanger are

based on 1986 [36] and costs of turbine 2 and pump are based on 2005 [37]. The cost estimation of heat exchangers is on the basis of heat exchanger area obtained from the logarithmic mean temperature difference and the overall heat transfer coefficient. Compact heat exchangers are selected as the reference heat exchangers for recupeartors and evaporator while shell and tube heat exchangers are used for condenser and pre-cooler. The approximate value of overall heat transfer coefficient is considered as 3.0 kW/m2 K to estimate the size of the HTR [1]. Value of 1.6 kW/m2 K is used for size estimation of the LTR and the evaporator [1]. The value for the pre-cooler and condenser is given as 2.0 kW/m2 K [38]. The cost balance and required auxiliary equations for each system component are listed in Table 4. It should be noted that, the cooling water is considered as a free resource at environmental condition and therefore a negligible value for cost rate of cooling water is assumed, i.e., C_ 05 ¼ C_ 06 ¼ C_ 05a ¼ C_ 06a ¼ 0. The linear system of equations in Table 4 includes 22 equations and 22 unknown variables. The solution to the equations leads to the cost rate for all exergy streams and then the unit exergetic cost of the system product can be obtained. In the solution, the Gauss– Seidel method was used.

4.2. Optimization method In order to recover as much waste heat as possible, it is necessary to perform the optimization of the combined cogeneration

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201

The effects of decision variables on the exergoeconomic performance of the sCO2/ORC have been discussed in [16]. In the present work, more attention is paid to the sCO2/tCO2 cycle and its comparison to the sCO2/ORC. Reference data from the NIST REFPROP database [40] are used to describe the working fluid thermodynamic properties.

5.1. Parametric study

Fig. 6. Effect of evaporator inlet temperature (T 8a ) on the heat transfer in the evaporator.

system. The objective functioncp;tot [16,33,38], as shown below, is defined as the total unit cost of system products, which includes the plant capital investment, operation, maintenance, and fuel costs.

cp;tot ¼

PNK _ _ k¼1 Z k þ C fuel PNP _ Ep i¼1

ð19Þ

i

where NK and NP are the numbers of system components and products, respectively, and E_ pi is the ith exergy rate of system products. The performances of the sCO2/tCO2 and sCO2/ORC cycles are optimized for either maximum exergy efficiency or minimum total product unit cost. The parameters chosen for optimizing the sCO2/tCO2 are pressure ratio of compressor PRc, turbine 2 inlet temperature T 01 and pressure P01 . For the sCO2/ORC the decision parameters are PRc, evaporation temperature T e , pitch point temperature difference DT E and degree of superheat at ORC turbine inlet DT sup . The constraints that set the bounds on each variable will be given after the parametric analysis. Once the mathematical model is established, a complete simulation code can be developed for the combined cogeneration cycle to analyze the exergetic and economic performances. Fig. 4 shows the flow chart for the combined cycle optimization. The genetic algorithm [39] is then applied to find the optimized design. 5. Results and discussion The results of parametric study, comparison and optimization of the sCO2/tCO2 and sCO2/ORC cycles are presented in this section.

A parametric analysis is conducted to study effects of important exergoeconomic parameters on the combined cogeneration system, such as PRc, maximum cycle temperature T max , T e , DT E , T 01 , and P 01 . Four indicators, i.e., net power output, the first law efficiency, the second law efficiency and total product unit cost, are adopted to evaluate performance of the combined cogeneration cycle. When one specific parameter is evaluated, other parameters are kept constant. In order to guarantee that the results are generalized, some measures are taken to reduce the influence of fixed parameters, such as ranking decision variables according to their importance, simultaneously considering comparative decision variables and choosing arbitrary but reasonable values of fixed parameters according to previous literature. Key component data assumptions and input parameters used in the analysis are given in Table 5. The cost of nuclear reactor fuel is taken to be 7.4 $/MW h, which is based on data for the year 2002. Tables 6 and 7 present the values of thermodynamic properties, exergy rates and cost rates of the fluid streams on a typical operating condition for the sCO2/tCO2 and sCO2/ORC cycles, respectively. Fig. 5(a–c) shows the effects of PRc on the first law efficiency, the second law efficiency, net power output and total product unit cost for the sCO2/tCO2 and sCO2/ORC cycles. It can be seen that the sCO2/tCO2 has higher first and second law efficiency values at lower PRc than the sCO2/ORC. For PRc higher than 2.8, however, the sCO2/ORC achieves higher first and second law efficiency values owing to better heat transfer in the evaporator, with lower values of CO2 outlet temperature (T 9 ) as T 8a increases with the PRc in sCO2/tCO2 cycle, as shown in Fig. 6. Since the sCO2 cycle mostly operates at a cycle maximum pressure of around 20 MPa (2.8 of PRc), the tCO2 cycle is preferable to be integrated with the recompression sCO2 cycle considering the off-design conditions. For the maximum cycle pressure higher than the 20 MPa, the cycle components would be too heavy due to the thicker component walls to contain the high pressures, and the cost of the plant would increase, too. Referring to Fig. 5, the first and second law efficiencies are maximized as PRc changes. On the other hand, a lower value of PRc yields a minimum value of total unit cost of products. That is, the optimal value of PRc for minimum cp;tot is lower than that for maximum second law efficiency. Fig. 5(c) also indicates that the optimal total product unit cost of the sCO2/tCO2 cycle is higher than that of the sCO2/ORC cycle. For the sCO2/ORC cycle, the maximum efficiencies and minimum total product unit cost are obtained by using isobutane as the ORC fluid. Fig. 5 also indicates that results of ORC fluids are almost indifferent, even though the fluids used have distinct differences. This is because net power outputs of the ORCs accounted for 8% of that of the sCO2 cycle. Hence, although the organic fluids have distinct differences, their effects on the performance of the combined cycle are limited and almost indifferent. Fig. 7(a–c) shows the influences of turbine 2 inlet temperature (T 01 ) for the sCO2/tCO2 cycle and evaporation temperature (T e ) for the sCO2/ORC cycle on the efficiencies and total product unit cost of the combined cogeneration cycles. Three values of turbine 2 inlet pressures (P01 ) are considered for the sCO2/tCO2 cycle. As the T e increases, the first and second law efficiencies increase

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Fig. 7. Effects of T 01 for the sCO2/tCO2 cycle and T e for the sCO2/ORC cycle on the first law efficiency (a), the second law efficiency (b) and cp;tot (c). (sCO2/tCO2: T max = 550 °C, PRc = 3.2, P 01 = 120 bar; sCO2/ORC: T max = 550 °C, PRc = 3.2, DT E = 3, DT sup = 0).

slightly at first to reach a maximum and then decrease significantly for the sCO2/ORC cycle. This trend is actually related to the ORC performance in the evaporator: an increase in T e leads to an increase in T 9 and then the heat recovery in evaporator is reduced as the CO2 mass flow rate is constant (PRc is constant) [16]. The trend in efficiencies of sCO2/tCO2 cycle with T 01 , however, is totally different. The first and second law efficiencies increase with

Fig. 8. Effect of turbine 2 inlet temperature (T 01 ) on the heat transfer in evaporator.

an increase in T 01 mainly because of the performance of tCO2 (see Fig. 8). This can be explained as follows: an increase in T 01 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 first and second law efficiency. Referring to Fig. 7(c), the cp;tot is minimized at a particular value of evaporation temperature for the sCO2/ORC cycle. It should be noted that the combined cycle with isobutene has the lowest cp;tot in the temperature range under consideration. For the sCO2/ tCO2 cycle, the cp;tot is very high at a lower value of T 01 and decreases when T 01 increases. Fig. 7 also indicates that the efficiencies and the total product unit cost are strongly affected by P 01 for the sCO2/tCO2 cycle. Hence, the effect of P01 on the sCO2/tCO2 performance is separately considered for a constant T 01 , as shown in Fig. 9. As the P 01 increases, the first and second law efficiencies of the combined cycle increase initially to peak and then decrease. 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 pressure P01 . An increase in P 01 leads to an increase and then a decrease in this area that represents the net work of the tCO2 cycle, as shown in Fig. 9(a). Fig. 9(c) indicates that there is an optimum value for P01 with which the cp;tot is minimized.

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Fig. 9. Effects of P 01 on the first law efficiency and net power output (a), the second law efficiency (b) and cp;tot (c) of the sCO2/tCO2 cycle. (T max = 550 °C, PRc = 3.0, T 01 = 100 °C).

Fig. 10 shows the variation in the first and second law efficiencies and total product unit cost of the sCO2/ORC cycle with the DT E and DT sup . This figure indicates that with increasing DT E , the efficiencies decrease and total product unit cost increases. This is expected because as DT E increases, the sCO2/ORC output power decreases due to the worse heat recovery in the evaporator, resulting in the increase in total product unit cost and the decrease in the second law efficiency. As for DT sup , Fig. 10 shows that small differences occur in first law efficiency, second law efficiency and total product unit cost, indicating that these indicators are slightly affected by the degree of superheat. On the other hand, it can be seen that a better thermodynamic and exergoeconomic performance is achieved with a lower value of DT sup . In fact when DT sup increases the turbine 2 inlet temperature increases. A higher turbine 2 inlet temperature brings about a higher value of enthalpy difference for the ORC, resulting in a decrease of mass flow rate in the ORC cycle. With decreasing the ORC mass flow rate, the power output in bottoming cycle is decreased and therefore the efficiencies of the combined cogeneration cycle decrease. It suggests that further superheating of the organic fluid before the turbine 2 inlet is not as effective as running the ORC turbine with saturated vapor. For a more comprehensive analysis of using CO2 and organic fluids as working fluids in the bottoming cycle, Fig. 11 is presented to show the comparison between the efficiencies and total product unit cost of the sCO2/tCO2 vs. sCO2/ORC against the maximum cycle

temperature. The advantage of the sCO2/tCO2 is not apparent. In fact, the sCO2/tCO2 presents slightly higher first and second law efficiency over the sCO2/ORCs at moderate maximum cycle temperatures (up to 650 °C). At higher maximum cycle temperatures, higher first and second law efficiency values are obtained when the sCO2/ORC cycle uses isobutane as the working fluid. It should be noted that the CO2 in the tCO2 cycle operates at higher temperature (110 °C) than the organic fluids (90 °C) in the ORC. From Fig. 11(c) it can be seen that as maximum cycle temperature increases, cp;tot decreases for both sCO2/tCO2 and sCO2/ORC cycles. Moreover, the total product unit cost of sCO2/tCO2 is 0.30–1.12% higher than that of sCO2/ORC cycle depending on the organic fluid. Further, the lowest cp;tot is obtained when a sCO2/ ORC cycle uses isobutane as the working fluid.

5.2. Exergoeconomic optimization As indicated above, the exergoeconomic performance of the combined system varies depending on the decision parameters. In order to obtain the optimized condition for system exergoeconomic performance, these decision parameters need to be analyzed simultaneously. This can be achieved using exergoeconomic optimization. The optimization is performed for either maximizing the second law efficiency or minimizing the total product unit cost, as follows.

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Fig. 10. Effects of DT E and DT sup on the first law efficiency (a), the second law efficiency (b) and cp;tot (c) of the sCO2/ORC cycle. (T max = 550 °C, T e = 90 °C, PRc = 3.0).

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Fig. 11. Effects of maximum cycle temperature on the first law efficiency and net power output (a), the second law efficiency (b) and cp;tot (c) of the sCO2/tCO2 and sCO2/ORC cycles. (sCO2/tCO2: PRc = 2.8, T 01 = 110 °C, P 01 = 120 bar; sCO2/ORC: PRc = 2.8, T e = 90 °C, DT E = 3 °C, DT sup = 0).

Table 8 The results of thermodynamic optimization for the sCO2/tCO2 and sCO2/ORC with different organic fluids. sCO2/tCO2

sCO2/ORCR123

sCO2/ORCR245fa

sCO2/ORCToluene

sCO2/ORCIsobutane

sCO2/ORCIsopentane

sCO2/ORCCyclohexane

PRc Te (°C) DTE DTsup T01 (°C) P01 (bar) gex (%) gth (%) cp,tot ($/GJ) _ net (MW) W

3.61 – – – 129.80 179.63 62.30 44.99 9.98 269.94

3.95 88.57 3.10 0.46 – – 62.24 44.95 9.96 269.68

3.91 84.77 3.02 0.00 – – 62.46 45.11 9.91 270.64

3.90 86.82 3.00 0.03 – – 62.00 44.77 9.96 268.65

3.99 88.51 3.00 0.01 – – 62.64 45.23 9.93 271.40

3.80 78.53 3.00 0.09 – – 62.27 44.97 9.88 269.80

3.84 82.80 3.02 0.32 – – 62.11 44.85 9.92 269.12

Wnet,b (MW) Q_ pc (MW) _ a (kg/s) m _ b (kg/s) m x cwt1 ($/GJ) cwt2 ($/GJ)

18.36 152.58

19.38 184.37

20.12 163.67

18.07 199.81

21.30 156.86

18.81 161.13

18.28 186.42

2664.10 1124.47 0.32 9.20 20.63

2593.92 813.05 0.33 9.44 16.58

2602.33 825.45 0.33 9.35 16.83

2604.58 312.39 0.33 9.48 16.58

2586.84 491.92 0.33 9.37 16.56

2623.64 450.94 0.32 9.30 17.63

2616.04 352.86 0.33 9.40 16.97

For the sCO2/tCO2 cycle, maximize gex or minimize cp;tot (PRc, T 01 , P 01 )

2:2 6 PRc 6 4 80 6 T 01 ð CÞ 6 130 100 6 P01 ðbarÞ 6 180

And for the sCO2/ORC, maximize gex or minimize cp;tot (PRc, T e , DT E , DT sup )

2:2 6 PRc 6 4 70 6 T e ð CÞ 6 130 3 6 DT E ð CÞ 6 15 0 6 DT sup ð CÞ 6 5

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Table 9 The results of exergoeconomic optimization for the sCO2/tCO2 and sCO2/ORC with different organic fluids. sCO2/tCO2

sCO2/ORCR123

sCO2/ORCR245fa

sCO2/ORCToluene

sCO2/ORCIsobutane

sCO2/ORCIsopentane

sCO2/ORCCyclohexane

PRc Te (°C) DTE DTsup T01 (°C) P01 (bar) cp,tot ($/GJ) gex (%) gth (%) _ net (MW) W

2.84 – – – 126.36 144.83 9.75 60.77 43.89 263.32

2.84 71.70 3.00 0.04 – – 9.61 60.83 43.93 263.60

2.84 72.32 3.03 0.09 – – 9.60 60.92 43.99 263.96

2.82 70.29 3.01 1.90 – – 9.62 60.62 43.78 262.68

2.86 75.15 3.00 0.00 – – 9.60 61.03 44.08 264.47

2.82 71.57 3.06 0.00 – – 9.61 60.77 43.89 263.32

2.82 70.60 3.04 0.17 – – 9.62 60.66 43.81 262.86

Wnet,b (MW) Q_ pc (MW) _ a (kg/s) m _ b (kg/s) m x cwt1 ($/GJ) cwt2 ($/GJ)

14.01 173.66

14.32 193.87

14.71 187.46

13.65 203.12

15.01 188.38

14.30 190.86

13.84 200.02

2897.90 991.52 0.29 9.10 21.35

2899.12 809.68 0.29 9.16 17.45

2899.92 751.95 0.29 9.14 17.40

2908.88 321.14 0.29 9.19 17.54

2891.89 428.19 0.29 9.14 17.16

2909.29 394.71 0.29 9.15 17.56

2909.29 340.30 0.29 9.18 17.51

The results of thermodynamic optimization are shown in Table 8 for both the sCO2/tCO2 and sCO2/ORC cycles. The objective in thermodynamic optimization is to maximize the second law efficiency. As can be seen, isobutane and toluene, among other organic fluids, bring about the highest and the lowest second law efficiencies for the sCO2/ORC, respectively. For the sCO2/tCO2 cycle, both the first and second law efficiencies are slightly lower than those of the sCO2/ORC with isobutane as the ORC working fluid. Moreover, the cogeneration cycle has a net power output of about 270 MW, while the bottoming cycle has net power outputs of about 18–21 MW, which accounts for 7% of whole net power output. This may leads to the indifference of different bottoming cycles. Compared to the organic fluids in the sCO2/ORC, the CO2 in the bottoming cycle of the sCO2/tCO2 operates at a higher temperature at the inlet of turbine 2. In addition, the tCO2 cycle mass flow rate is the highest, i.e., 1124.47 kg/s, which is about 2.3 times higher than that of isobutane ORC. It is worth noting that a value of 152.58 MW of cooling capacity (Q_ pc ) is produced by the sCO2/tCO2 cycle in the pre-cooler. This value of energy loss is the lowest compared to that of the sCO2/ORC for all the organic fluids under consideration. The objective in exergoeconomic optimization is to minimize the total product unit cost. The results are shown in Table 9. As can be seen, the total product unit cost of the sCO2/ORC is lower than that of the sCO2/tCO2 by up to 1.56%. Among the considered ORC working fluids, the isobutane brings about the lowest total product unit cost (9.60 $/GJ) and the highest net power output (264.47 MW). The R123, however, has the highest mass flow rate (809.68 kg/s) among the others as its enthalpy difference across the evaporator is the lowest. Compared to the sCO2/ORCs, the sCO2/tCO2 cycle has a lower unit exergy cost of power output in turbine 1 (cwt1 ) but a higher unit cost of power output in turbine 2 (cwt2 ). In addition, a cooling capacity of 173.66 MW is produced by the sCO2/tCO2 cycle, which is also the lowest compared to sCO2/ORCs. Besides, Table 9 shows that ORCs operate at very low evaporation temperatures (T e ), which may not be practical for most ORC fluids. It suggests that the sCO2/tCO2 cycle is preferable when economic operation mode is the objective for a sCO2 Brayton system. A comparison between Tables 8 and 9 reveals that, the values of the first and second law efficiencies obtained for the exergoeconomic optimization are lower than the corresponding values calculated for the thermodynamic optimization. When the sCO2/tCO2 combined system is optimized from the viewpoint of exergoeconomic, a reduction of about 2.3% in the total product unit cost is

achieved at the expense of about 2.45% reduction in the second law efficiency. For the case of sCO2/ORC (with isobutane as the ORC working fluid), a reduction of about 3.36% in the total product unit cost is yielded at the expense of about 2.55% reduction in the second law efficiency. This indicates that more thermodynamically efficient components do not guarantee a cost- optimal design for the combined system.

6. Conclusions In this study, the tCO2 power cycle and the ORC with different organic fluids were studied as the bottoming cycle of a recompression sCO2 Brayton cycle. Detailed thermodynamic and exergoeconomic analyses and comparison have been successfully performed. Parametric studies were carried out for the two combined cycles to study the effects of key thermodynamic parameters on the first and second law efficiencies and total product unit cost. The main conclusions are drawn below:
At lower PRc, the sCO2/tCO2 cycle is desirable and performs better than the sCO2/ORC cycle. Since the sCO2 cycle mostly operates at a cycle maximum pressure of around 20 MPa (2.8 of PRc), the tCO2 cycle is preferable to be integrated with the recompression sCO2 cycle considering the off-design conditions.
Contrary to the sCO2/ORC cycle, a higher turbine 2 inlet temperature improves exergoeconomic performance of the sCO2/tCO2 cycle.
The thermodynamic optimization study reveals that the second law efficiency of sCO2/tCO2 cycle is comparable with that of the sCO2/ORC system. The maximum second law efficiency is obtained by using isobutane as the ORC working fluid, i.e., 62.64%.
The exergoeconomic optimization study indicates that the total product unit cost of the sCO2/ORC is slightly lower than that of the sCO2/tCO2. Among the considered ORC working fluids, the isobutane brings about the lowest total product unit cost (9.60 $/GJ).

References [1] Dostal V. A supercritical carbon dioxide cycle for next generation nuclear reactors. MIT Sc D; 2004. [2] Dostal V, Driscoll MJ, Hejzlar P, Todreas NE. A supercritical CO2 gas turbine power cycle for next-generation nuclear reactors. Proc ICONE 2002;10:14–8.

X. Wang, Y. Dai / Applied Energy 170 (2016) 193–207 [3] Hejzlar P, Dostal V, Driscoll MJ, Dumaz P, Poullennec G, Alpy N. Assessment of gas cooled fast reactor with indirect supercritical CO2 cycle. Nucl Eng Technol 2006;38:109–18. [4] Dostal V, Hejzlar P, Scoll MJ. The supercritical carbon dioxide power cycle: comparison to other advanced power cycles. Nucl Technol 2006;154 (3):283–301. [5] Iverson BD, Conboy TM, Pasch JJ, Kruizenga AM. Supercritical CO2 Brayton cycles for solar-thermal energy. Appl Energy 2013;111(4):957–70. [6] Al-Sulaiman FA, Atif M. Performance comparison of different supercritical carbon dioxide Brayton cycles integrated with a solar power tower. Energy 2015;82:61–71. [7] Padilla RV, Too YCS, Benito R, Stein W. Exergetic analysis of supercritical CO2 Brayton cycles integrated with solar central receivers. Appl Energy 2015;148:348–65. [8] Ahn Y, Lee J, Kim SG, Lee JI, Cha JE, Lee SW. Design consideration of supercritical CO2 power cycle integral experiment loop. Energy 2015;86:115–27. [9] Sarkar J. Second law analysis of supercritical CO2 recompression Brayton cycle. Energy 2009;34:1172–8. [10] Sarkar J, Bhattacharyya S. Optimization of recompression S-CO2 power cycle with reheating. Energy Conver Manage 2009;50:1939–45. [11] Chacartegui R, Sánchez D, Jiménez-Espadafor F, Muñoz A, Sánchez T. Analysis of intermediate temperature combined cycles with a carbon dioxide topping cycle. ASME Turbo Expo 2008: Power for Land, Sea, and Air; 2008. GT200851053. [12] Chacartegui R, Munoz JM, Sánchez D, Monje B, Sánchez T. Alternative cycles based on carbon dioxide for central receiver solar power plants. Appl Therm Eng 2011;31:872–9. [13] Sánchez D, Brenes BM, Munoz JM, Chacartegui R. Non-conventional combined cycle for intermediate temperature systems. Int J Energy Res 2013;37:403–11. [14] Besarati SM, Goswami DY. Analysis of advanced supercritical carbon dioxide power cycles with a bottoming cycle for concentrating solar power applications. ASME J Sol Energy Eng 2013;136(1):010904-010904-7. [15] Zhang HZ, Shao S, Zhao H, Feng ZP. Thermodynamic analysis of a SCO2 partflow cycle combined with an organic Rankine cycle with liquefied natural gas as heat sink. In: ASME Turbo Expo 2014: turbine technical conference and exposition, Düsseldorf, Germany; 2014. GT2014-26500. [16] Akbari Ata D, Mahmoudi Seyed MS. Thermoeconomic analysis & optimization of the combined supercritical CO2 (carbon dioxide) recompression Brayton/ organic Rankine cycle. Energy 2014;78:501–12. [17] Yari M, Sirousazar M. A novel recompression S-CO2 brayton cycle with precooler exergy utilization. Proc Inst Mech Eng Part A J Power Energy 2010;224:931–46. [18] Wang XR, Wu Y, Wang JF, Dai YP, Xie DM. Thermo-economic analysis of a recompression supercritical CO2 cycle combined with a transcritical CO2 cycle. In: Proc ASME Turbo Expo, Montréal 2015; GT2015-42033. [19] Wang XR, Wang JF, Zhao P, Dai YP. Thermodynamic comparison and optimization of supercritical CO2 Brayton cycles with a bottoming transcritical CO2 cycle. J Energy Eng 2015. 04015028-1-11. [20] Freeman J, Hellgardt K, Markides CN. An assessment of solar-powered organic Rankine cycle systems for combined heating and power in UK domestic applications. Appl Energy 2015;138:605–20. [21] Yun E, Kim D, Sang YY, Kim KC. Experimental investigation of an organic Rankine cycle with multiple expanders used in parallel. Appl Energy 2015;145:246–54.

207

[22] Chacartegui R, Sánchez D, Muñoz JM, Sánchez T. Alternative ORC bottoming cycles for combined cycle power plants. Appl Energy 2009;86(10): 2162–70. [23] Chen Y, Lundqvist P, Johansson A, Platell P. A comparative study of the carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working fluid in waste heat recovery. Appl Therm Eng 2006;26:2142–7. [24] Baik YJ, Kim M, Chang KC, Kim SJ. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl Energy 2011;88:892–8. [25] Sarkar J. Review and future trends of supercritical CO2 Rankine cycle for lowgrade heat conversion. Renew Sust Energ Rev 2015;48:434–51. [26] Wang JF, Sun ZX, Dai YP, Ma SL. Parametric optimization design for supercritical CO2 power cycle using genetic algorithm and artificial neural network. Appl Energy 2010;87:1317–24. [27] Wang JF, Zhao P, Niu XQ, Dai YP. Parametric analysis of a new combined cooling, heating and power system with transcritical CO2 driven by solar energy. Appl Energy 2012;94:58–64. [28] Cayer E, Galanisa N, Desilets M, Nesreddine H, Roy P. Analysis of a carbon dioxide transcritical power cycle using a low temperature source. Appl Energy 2009;86:1055–63. [29] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl Energy 2010;87:1349–57. [30] Song YH, Wang JF, Dai YP, Zhou EM. Thermodynamic analysis of a transcritical CO2 power cycle driven by solar energy with liquified natural gas as its heat sink. Appl Energy 2012;92. 194-03.. [31] Yari M, Mahmoudi Seyed MS. Utilization of waste heat from GT-MHR for power generation in organic Rankine cycles. Appl Therm Eng 2010;30: 366–75. [32] Guzovic´ Z, Loncˇar D, Ferdelji N. Possibilities of electricity generation in the Republic of Croatia by means of geothermal energy. Energy 2010;35: 3429–40. [33] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: John Wiley and Sons Inc.; 1996. [34] Ghaebi H, Amidpour M, Karimkashi S, Rezayan O. Energy, exergy and thermoeconomic analysis of a combined cooling, heating and power (CCHP) system with gas turbine prime mover. Int J Energy Res 2011;35. 697-09.. [35] Schultz KR, Brown LC, Besenbruch GE, Hamilton CJ. Large scale production of hydrogen by nuclear energy for the hydrogen economy. General Atomics 2003. GA-A24265.. [36] Zhou GY, Wu E, Tu ST. Techno-economic study on compact heat exchangers. Int J Energy Res 2008;32:1119–27. [37] Dorj P. Thermoeconomic analysis of a new geothermal utilization CHP plant in Tsetserleg, Mongolia. MSc thesis, University of Iceland 2005. [38] Zare V, Mahmoudi Seyed MS, Yari M. An exergoeconomic investigation of waste heat recovery from the Gas Turbine-Modular Helium Reactor (GT-MHR) employing an ammonia–water power/cooling cycle. Energy 2013;61. 397-09. [39] Holland JH. Adaptation in nature and artificial systems: an introductory analysis with applications to biology, control and artificial intelligence. Massachusetts: MIT Press; 1992. [40] Lemmon EW, Huber ML, McLinden MO. NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, version 9.0; 2007.