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Energy 43 (2012) 402e415
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Energy
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Transcritical or supercritical CO2 cycles using both low- and high-temperatureheat sources
Y.M. Kim a,*, C.G. Kim a, D. Favrat b
a ECO Machinery Division, Korea Institute of Machinery and Materials, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, Republic of Koreab Industrial Energy System Laboratory, Swiss Federal Institute of Technology of Lausanne (EPFL), Station 9, CH1015 Lausanne, Switzerland
a r t i c l e i n f o
Article history:Received 17 November 2011Received in revised form26 February 2012Accepted 31 March 2012Available online 4 May 2012
Keywords:Transcritical CO2
Supercritical CO2
Rankine cycleBrayton cycleThermal energy storage (TES)Exergy
* Corresponding author. Tel.: þ82 42 868 7377; faxE-mail addresses: [email protected] (Y.M. Kim), c
[email protected] (D. Favrat).
0360-5442/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.energy.2012.03.076
a b s t r a c t
In CO2 cycles with high-temperature heat sources that are used in applications such as nuclear power,concentrated solar power, and combustion, partial condensation transcritical CO2 (T-CO2) cycles orrecompression supercritical CO2 (S-CO2) cycles are considered to be promising cycles; this is becausethese cycles cause a reduction in the large internal irreversibility in the recuperator owing to the higherspecific heat of the high-pressure side than that of the low-pressure side. However, if heat is available inthe low-temperature range, the T-CO2 Rankine cycles (or fully-cooled S-CO2 cycles) will be more effectivethan the T-CO2 Brayton cycles (or less-cooled S-CO2 cycles) and even than the partial condensation T-CO2
cycles (or recompression S-CO2 cycles). This is because the compression work is reduced while achievingthe same temperature rise by heat recovery through the recuperator before the high-temperature heater.
The proposed T-CO2 Rankine cycles or fully-cooled S-CO2 cycles using both the low- and high-temperature heat sources can maximize the power output of the CO2 power cycle with the givenhigh-temperature heat sources. Moreover, the proposed CO2 cycles combined with the low-temperaturethermal energy storage offer the advantage of load leveling over other CO2 cycles, with the given high-temperature heat sources.
� 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Recently, interest in a supercritical CO2 power cycle hasincreased in conjunction with its application in nuclear reactorsowing to its simplicity, compactness, sustainability, enhancedsafety, and superior economy [1e5]. The supercritical CO2 cycle isexpected to benefit fossil, renewable, and advanced nuclear powerplants because CO2 is an extremely effective working fluid in itssupercritical state.
In the case of CO2 cycles with high-temperature (HT) heatsources such as nuclear power, concentrated solar power, andcombustion, the working fluid goes through both subcritical andsupercritical states (transcritical cycle), or is used entirely above itscritical pressure (supercritical cycle). Further, the CO2 cycles can begas cycles (Brayton cycles) or condensation cycles (Rankinecycles). Feher [6] proposed a supercritical CO2 (S-CO2) power cyclethat operates entirely above the critical pressure of CO2, isregenerative, and ensures the compression in the liquid phase to
: þ82 42 868 [email protected] (C.G. Kim),
All rights reserved.
minimize pump work [1]. Angelino [7] conducted one of the mostdetailed investigations on transcritical CO2 (T-CO2) cycles andprimarily focused on condensation cycles [1]. However, it wasfound that the T-CO2 Rankine cycles exhibited a large internalirreversibility in the recuperator owing to heat transfer from theturbine exhaust stream with a low specific heat to the pump exitstream with a high specific heat [1]. Feher [6] first revealed thesame problem associated with irreversibility in the recuperatorused in the S-CO2 cycles. A recompression cycle was proposed toavoid the problem; the recuperator was divided into low- andhigh-temperature parts, each having different flow rates to copewith a large variation in the heat capacity of the fluid. Thus, onlya fraction of the CO2 fluid flow is bypassed to the recompressingcompressor before pre-cooling and is merged with the rest of thefluid flow, heated through the low-temperature (LT) recuperator,from the main pump (or compressor) before it enters the HTrecuperator. The recompression cycle can be applied to both the S-CO2 and the T-CO2 cycles, and it has been studied as the mostpromising CO2 cycle for HT heat conversion [1e9]. Sarkar et al. [10]studied the effects of various operating conditions and perfor-mance of components on the optimization of the S-CO2 recom-pression cycle. Meanwhile, the T-CO2 Rankine cycles (fullycondensation cycles) have been mostly studied for low-grade heat
Nomenclature
B Braytoncp isobaric specific heat [kJ/(kg K)]e specific exergy (kJ/kg)E exergy (kJ)_E rate of exergy (kW)ε heat exchanger effectivenessh specific enthalpy (kJ/kg)H, HT high-temperatureL, LT low-temperatureL exergy loss (kJ)_L rate of exergy loss (kW)LH both low- and high-temperature heat sourcesm mass (kg)_m mass flow rate (kg/s)max maximumP pressure (kPa)Q heat (kJ)_Q rate of heat (kW)R RankineR Dcp;H�LðTÞ ratio of specific heat difference at Ts specific entropy [kJ/(kg K)]S-CO2 supercritical CO2
T temperature (K)T-CO2 transcritical CO2
TES thermal energy storageTEES thermo-electric energy storageW work (kJ)_W rate of work (kW)y split ratio
h isentropic efficiencyhth thermal efficiencyh*th increased thermal efficiencyhII second law efficiency
Subscriptsa atmospheric (environmental) stateC compressor, condenserCO2 carbon dioxideE expanderH heaterH, C heat source, cooling water (heat sink)H1, H2 LT heat source, HT heat sourceH, L high-pressure, low-pressurei state pointin inletL cool down to lowest temperaturenet net outputout outletP pumpR recuperatorR1, R2 LT recuperator, HT recuperators isentropicT turbinetot totalW waste heatw water
Supercriptsþ input� output
Y.M. Kim et al. / Energy 43 (2012) 402e415 403
conversion such as geothermal energy, waste heat, and LT solarcollectors [11e19]. In the case of the T-CO2 Rankine cycle for HTheat conversion, although the compression work is significantlyreduced, the outlet temperature of CO2 heated through the recu-perator is much lower than that in the T-CO2 Brayton cycle. This isbecause at temperatures below 150 �C, especially below 120 �C,the isobaric specific heat of CO2 in the high-pressure side isconsiderably higher than that in the low-pressure side. Theoperation of the T-CO2 Brayton cycle can escape from thistemperature range, and therefore, the outlet temperature of CO2heated through the recuperator in this cycle is much higher thanthat in the T-CO2 Rankine cycle. However, if heat, which is used tocompensate for the difference in the specific heats of CO2 betweenthe two sides, is available in this LT range, the T-CO2 Rankine cyclewill be more effective than the T-CO2 Brayton cycle and even thanthe recompression T-CO2 cycle. This is because less compressionwork is required while obtaining the same outlet temperature ofCO2 heated through the recuperator before it enters the HT heateras observed in the T-CO2 Brayton cycle. The concept of the T-CO2cycle using both the LT and the HT heat sources can also be appliedto the S-CO2 cycle. Minimizing the irreversibilities while heatingup the working fluid particularly in the lower temperature isa well known challenge with respect to efficiency and specificwork. As an example, the integrated solar combined cycle system(ISCCS) is a steam Rankine cycle using both low- and high-temperature heat sources to improve the cycle efficiency andsystem cost [20].
In this paper, for obtaining themaximumpower output with thegiven HT heat sources, a novel concept of a T-CO2 (or S-CO2) cycleusing both the LT and the HT heat sources and its applications arepresented in comparisonwith the basic T-CO2 Rankine and Brayton
cycles and the partial condensation T-CO2 (or recompression S-CO2)cycle by energy and exergy analyses.
2. Transcritical CO2 cycle using both low- and high-temperature heat sources (LH T-CO2 cycle)
2.1. Energy analysis
The configurations and T-s diagrams of the basic T-CO2 Rankineand Brayton cycles studied here are shown in Figs. 1 and 2 and inFigs. 3 and 4, respectively. The following general assumptions areused in this analysis: the kinetic and potential energies as well asthe heat and friction losses are negligible, isentropic efficiencies ofthe pump or compressor and the turbine are both 90%, effective-ness of the recuperator is 0.95, condensation temperature for CO2 is20 �C, and saturated liquid exits the condenser. For the power rangeof 300e500 MWe considered in this study, the assumed isentropicefficiencies of 90% are reasonable and are based on the values ofconservative turbomachinery deign [2]. In the case of the T-CO2Brayton cycle, saturated vapor, which is about to condense, exitsthe cooler. The properties of CO2 are obtained from REFPROP-NIST[21]. The equations for the different components of the cycle are asfollows.
For the pump or compressor,
hPðCÞ ¼ h1;s � hoh1 � h0
; (1)
_WPðCÞ ¼ _mCO2ðh1 � h0Þ: (2)
WT
WP
QL
HT (TH)Heat Source
Recuperator
QR
Con
dens
er
Heat Sink (T0)
Pump
QH
T 0
5
3
4
12
Turbine
Fig. 1. Schematic of T-CO2 Rankine cycle with HT heat source.
Y.M. Kim et al. / Energy 43 (2012) 402e415404
For the turbine,
hT ¼ h3 � h4h3;s � h4
; (3)
_WT ¼ _mCO2ðh3 � h4Þ: (4)
The efficiency of the recuperator, εR, is expressed as
εR ¼ _mCO2ðh4 � h5Þ_Qmax
¼ _mCO2ðh2 � h1Þ_Qmax
: (5)
The rate of maximum heat exchange, _Qmax, is given as follows:
_Qmax ¼ _mCO2ðh4 � h5Þ assuming T5 ¼ T1: (6)
For the heater,
_QH ¼ _mCO2ðh3 � h2Þ: (7)
For the condenser or cooler,
_QW ¼ _mCO2ðh5 � h0Þ: (8)
The rate of heat wasted to the heat sink, _QW , can be split into therate of heat to cool down, _QL, and the rate of heat to condense, _QC ,as follows:
_QL ¼ _mCO2ðh5 � h6Þ; (9)
where state 6 is the saturated gas state.
Fig. 2. T-s diagram of T-CO2 Rankine cycle with HT heat source.
_QC ¼ _mCO2ðh6 � h0Þ (10)
For the thermal efficiency of the cycle,
hth ¼_WT � _WPðCÞ
_QH: (11)
2.2. Exergy analysis
The purpose of the idea proposed in this paper is to find a novelCO2 cycle that maximizes the power output of the CO2 cycle withthe given HT heat sources by using available LT heat sources. Exergyanalysis is very helpful in understanding the advantages of thenovel CO2 cycle over other CO2 cycles. Although increasing themaximum cycle temperature can increase the cycle efficiency, themaximum cycle temperature is assumed to be 600 �C consideringthe cost and lifetime of materials under the high-pressure condi-tions of CO2 cycles. In this study, the ideal cycle is assumed to bea Carnot cycle operating between an HT (TH ¼ 600 �C) heat sourceand an LT (TC ¼ 15 �C) heat sink with water cooling. Therefore, themaximum work from the Carnot engine can be written as
Wmax ¼�1� TC
TH
�QH : (12)
This work can be assumed to be the exergy input from the HTheat source, EþH , and the exergy losses in the components areinvestigated.
The exergy of a CO2 stream can be expressed as
_ECO2¼ _mCO2
e ¼ _mCO2½h� ha � Taðs� saÞ�; (13)
where e, h, and s are the specific exergy, enthalpy, and entropy,respectively, and the subscript a indicates that the properties aretaken at ambient temperature and pressure (Ta,Pa). The ambienttemperature Ta is assumed to be the temperature of the heat sink,TC, and the ambient pressure Pa is assumed to be the atmosphericpressure.
The general exergy balance can be expressed as a rate equation[22]:
_Eþ � _E
� ¼ _L; (14)
where _Eþis the rate of exergy transfer to the system by heat, work,
and mass; _E�is the rate of exergy transfer from the system; and _L is
the rate of exergy loss.
Fig. 3. Schematic of T-CO2 Brayton cycle with HT heat source.
Y.M. Kim et al. / Energy 43 (2012) 402e415 405
The exergy loss of compression (pumping) is given by
_LCðPÞ ¼ _EþCðPÞ � _mCO2
ðe1 � e0Þ: (15)
The exergy loss of the turbine is given by
_LT ¼ _mCO2ðe3 � e4Þ � _E
�T : (16)
The exergy loss of the recuperator is given by
_LR ¼ _mCO2ðe4 � e5Þ � _mCO2
ðe2 � e1Þ: (17)
Fig. 4. T-s diagram of T-CO2 Brayton cycle with HT heat source.
Fig. 5. Reference cycle of T-CO2 Rankine cycle with HT heat source.
The exergy loss of the heater is given by
_LH ¼ _EþH � _mCO2
ðe3 � e2Þ: (18)
The exergy loss of waste heat to the condenser or cooler is givenas
_LW ¼ _mCO2ðe5 � e0Þ: (19)
The second law (exergy) efficiency of the overall system withtranscritical or supercritical cycles can be defined as
Fig. 6. Reference cycle of T-CO2 Brayton cycle with HT heat source.
Fig. 7. Isobaric specific heats of CO2 in high- and low-pressure sides over temperaturerange of heat recovery.
Table 1Exergy analysis of transcritical CO2 Rankine cycle with HT heat source.
State (i) T (�C) P (bar) ei�e0(kJ/kg)
Q(E), W (kJ/kg) L (kJ/kg)
0 20.0 57.3 0.0 Q�W ¼ 222.7 (E�W ¼ 7.0) LW ¼ 7.0 (7.0%)
1 39.2 200.0 17.6 WþP ¼ 19.4 (EþP ¼ 19.4) LP ¼ 1.8 (1.8%)
2 297.5 200.0 180.7 QþR ¼ 449.0 (EþR ¼ 163.1) LR ¼ 25.2 (25.3%)
3 600.0 200.0 372.8 QþH ¼ 373.1 (EþH ¼ 245.0) LH ¼ 57.9 (58.2%)
4 449.0 57.3 195.3 W�T ¼ 169.9 (E�T ¼ 169.9) LT ¼ 7.6 (7.6%)
5 54.3 57.3 7.0 Q�R ¼ 449.0 (E�R ¼ 188.3) (LR ¼ 25.2)
hII ¼ E�T � EþPEþH
¼ 0.614 EþH ¼ 245.0 Ltot ¼ 99.5 (100%)
Table 2Exergy analysis of transcritical CO2 Brayton cycle with HT heat source.
State (i) T (�C) P (bar) ei�e0(kJ/kg)
Q(E), W(E) (kJ/kg) L (kJ/kg)
0 20.0 57.3 0.0 Q�W ¼ 164.2 (E�W ¼ 23.6) LW ¼ 23.6 (33.4%)
1 114.6 200.0 46.7 WþC ¼ 50.4 (EþC ¼ 50.4) LC ¼ 3.8 (5.4%)
2 370.0 200.0 195.2 QþR ¼ 355.5 (EþR ¼ 148.5) LR ¼ 20.6 (29.2%)
3 600.0 200.0 370.2 QþH ¼ 283.6 (EþH ¼ 190.0) LH ¼ 15.0 (21.2%)
4 449.0 57.3 192.7 W�T ¼ 169.9 (E�T ¼ 169.9) LT ¼ 7.6 (10.8%)
5 131.1 57.3 23.6 Q�R ¼ 355.5 (E�R ¼ 169.1) (LR ¼ 20.6)
hII ¼ E�T � EþCEþH
¼ 0.629 EþH ¼ 190.0 Ltot ¼ 70.6 (100%)
Fig. 9. Reference cycle of LH T-CO2 cycle using both LT and HT heat sources.
Y.M. Kim et al. / Energy 43 (2012) 402e415406
hII ¼_E�T � _E
þCðPÞ
_EþH
: (20)
2.3. Comparison between T-CO2 Rankine cycle and T-CO2 Braytoncycle
To compare the basic two cycles (i.e., the T-CO2 Rankine andBrayton cycles), we assume the following conditions: high-pressureof 200 bar, low-pressure of 57.3 bar (condensation temperature20 �C), and turbine inlet temperature of 600 �C. These conditionsare similar to those in other literature that discuss the use of S-CO2cycles for next-generation nuclear reactors [1e3].
Figs. 5 and 6 show the energy flow per unit mass of the workingfluid on temperature versus entropy (T-s) diagrams of the T-CO2Rankine and Brayton cycles, respectively. The exergy analyses of the
WT
HT (TH2)Heat Source
HT Recuperator
QR2
QH2
T
5
4
3
Turbine
Fig. 8. Schematic of LH T-CO2 cycle us
T-CO2 Rankine and Brayton cycles, expressed on unit mass basis, aresummarized in Tables 1 and 2, respectively. The efficiency of theT-CO2 Rankine cycle is lower than that of the T-CO2 Brayton cycle.Although the compression work of the T-CO2 Rankine cycle issignificantly reduced, the outlet temperature of CO2 heated throughthe recuperator in this cycle is much lower than that of the T-CO2Brayton cycle. This is because below 150 �C and especially below120 �C, the isobaric specific heat, cp, of CO2 in the high-pressure sideis much higher than that in the low-pressure side, as shown inFig. 7. The operation of T-CO2 Brayton cycle can escape from thistemperature range, and therefore, the outlet temperature of CO2heated through the recuperator is much higher in the T-CO2 Bray-ton cycle than in the T-CO2 Rankine cycle. The accumulateddifference in the isobaric specific heat between the high-pressureside (cp,H) and the low-pressure side (cp,L) below a temperature Tthat is over the temperature range for heat recovery in the T-CO2Rankine cycle (from T1 to T4) can be defined as
R Dcp;H�LðTÞh
ZT
T1
�cp;H � cp;L
�dT
ZT4
T1
�cp;H � cp;L
�dT
: (21)
WP
QL+QC
QH1
QR1
LT (TH1)Heat Source
Con
dens
er
LT Recuperator
Heat Sink (T0)
Pump
0
2 1
6
ing both LT and HT heat sources.
Table 3Comparison of performances of different T-CO2 cycles (H: High-temperature of TH2, L: Low-temperature of TH1, R: Rankine, B: Brayton).
Cycle TH1 (�C) QH1 (kJ/kg) TH2 (�C) QH2 (kJ/kg) TR (�C) WP(C) (kJ/kg) WT (kJ/kg) Wnet (kJ/kg) hth h*th
H-R (1) e e 600 373.1 298 19.4 169.9 150.4 0.403 e
H-B (2) e e 600 283.6 370 50.4 169.9 119.4 0.421 e
L-R (3) 112 178.0 e e e 19.4 40.9 21.4 0.120 e
LH-R (4) 112 87.0 600 286.1 368 19.4 169.9 150.4 0.403 0.526L-R (3) þ H-B (2) 112 87.0 600 286.1 370 9.5 þ 50.9 20.0 þ 171.3 10.5 þ 120.5 0.351 e
QH1
QR1
LT (TH1) Heat Source
LT Recuperator
12
6
mw
7
Tw,in Tw,out
1HTΔ
1RTΔPH
PL
T1
= 39.2T2
= 112.2
T7
= 54.3T6
= 128.8
Tw,in
= 117.0T
w,out= 50.1
2310.0 COw mm =
Fig. 10. Mass flow rate and inlet/outlet temperature of hot water required in LT recuperator.
50 100 150 200 250 300 350 400 450280
300
320
340
360
380
400
420
440
460
TR
ηth*
Temperature of LT heat source (T (oC))
TR (
o C)
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
ηth *
Y.M. Kim et al. / Energy 43 (2012) 402e415 407
As shown in Fig. 7, R Dcp;H�LðTÞ is approximately 0.5 at 112 �Cand approximately 0.68 at 150 �C. This indicates that the outlettemperature of CO2 heated through the recuperator is low owing tothe large difference in the specific heat between the high- and low-pressure sides in this LT range.
The exergy analyses of both cycles, expressed on a unit massbasis, are summarized in Tables 1 and 2. The exergy loss of theheater, LH, is larger in the T-CO2 Rankine cycle than in the T-CO2Brayton cycle because of the lower temperature, TR (T2), throughthe recuperator on the high-pressure side. On the other hand, theexergy loss of waste heat, LW, is larger in the T-CO2 Brayton cyclethan in the T-CO2 Rankine cycle because of the higher temperature,T5, through the recuperator on the low-pressure side. The overallexergy efficiency of the T-CO2 Brayton cycle is higher than that ofthe T-CO2 Rankine cycle.
40 50 60 70 80 90 100 110
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
),(),()( TTPCTPCTC LpHpp Δ+−≡Δ
pCΔ
S-
Isob
aric
spe
cific
hea
t (kJ
/kg-
K)
Temperature (oC)
S+
Fig. 11. Isobaric specific heat of LT heat source required to make up for difference inisobaric specific heats between two CO2 streams.
H1
Fig. 12. Temperature TR and thermal efficiency h*th according to temperature of LT heatsource (TH1).
Fig. 13. Reference cycle of T-CO2 cycle with LT heat source.
Fig. 14. Schematic of partial pre-cooling S-CO2 cycle.
Table 4Exergy analysis of transcritical CO2 cycle using both LT and HT heat sources.
State (i) T (�C) P (bar) ei�e0(kJ/kg)
Q(E), W(E) (kJ/kg) L (kJ/kg)
0 20.0 57.3 0.0 Q�W ¼ 222.7 (E�W ¼ 7.0) LW ¼ 7.0 (12.1%)
1 39.2 200.0 17.6 WþP ¼ 19.4 (EþP ¼ 19.4) LP ¼ 1.8 (3.1%)
2 112.2 200.0 48.0 QþR1 ¼ 91.0 (EþR1 ¼ 18.6)
QþH1 ¼ 87.0 (EþH1 ¼ 16.6)
LR1þH1 ¼ 4.8 (8.3%)
3 368.0 200.0 196.4 QþR2 ¼ 358.1 (EþR ¼ 148.4) LR2 ¼ 21.4 (37.0%)
4 600.0 200.0 372.8 QþH2 ¼ 286.1 (EþH2 ¼ 191.7) LH2 ¼ 15.3 (26.4%)
5 449.0 57.3 195.3 W�T ¼ 169.9 (E�T ¼ 169.9) LT ¼ 7.6 (13.1%)
6 128.8 57.3 25.5 Q�R2 ¼ 358.1 (E�R ¼ 169.8) (LR2 ¼ 21.4)
7 54.3 57.3 7.0 Q�R1 ¼ 91.0 (E�R ¼ 18.6) (LR1 ¼ 3.5)
hII ¼ E�T � EþPEþH1 þ EþH2
¼ 0.723EþH1 ¼ 16.6EþH2 ¼ 191.7
Ltot ¼ 57.9 (100%)
Y.M. Kim et al. / Energy 43 (2012) 402e415408
2.4. T-CO2 cycle using both low- and high-temperature heat sources
Asmentioned before, in the case of the T-CO2 Rankine cycle withHT heat sources, although the compressionwork and exergy loss ofwaste heat are significantly reduced, the outlet temperature of CO2heated through the recuperator is much lower than that of theT-CO2 Brayton cycle owing to the large difference in the isobaricspecific heat of CO2 between the high- and low-pressure sides in
Fig. 15. Schematic of LH T-CO2 cycle combined with T-CO
the LT range. Therefore, the thermal efficiency of the T-CO2 Rankinecycle is lower than that of the T-CO2 Brayton cycle.
However, if heat is available from other heat sources in this LTrange, it is possible to make up for the difference in the isobaricspecific heat of CO2 between the high- and low-pressure sides andrectify this imbalance in specific heats. Therefore, a T-CO2 cycleusing both the LT and the HT heat sources (named an LH T-CO2cycle) is proposed. The configuration of the LH T-CO2 cycle system isshown in Fig. 8. The recuperator is divided into two parts: a low-temperature (LT) recuperator and a high-temperature (HT) recu-perator. In the LT recuperator, the supplemental heat is supplied byan LT (TH1) heat source. Fig. 9 shows the energy flow per unit massof the working fluid on the T-s diagram of the system for theprevious T-CO2 Rankine cycle with an additional LT heat source toheat CO2 up to 112 �C. Table 3 compares the performances,expressed on a unit mass basis, of different CO2 cycles. Hot water isused as an example of an LT heat source, and themass flow rate andinlet/outlet temperature of the hot water are shown in Fig. 10. Themass flow rate and inlet/outlet temperature of hot water requiredin the LT recuperator can be calculated from the thermal match ofthree flows as follows. As shown in Fig. 11, DcpðTÞ is the isobaricspecific heat of an LT heat source required to make up for thedifference in the isobaric specific heats between the high-pressure(PH) side and the low-pressure (PL) side. Considering the temper-ature difference, DT, for the heat transfer from the low-pressureside to the high-pressure side, Dcp(T) can be defined as
DcpðTÞhcpðPH; TÞ � cpðPL; T þ DTÞ: (22)
Because the isobaric specific heat of water as an LT heat source isalmost constant, the average isobaric specific heat, DcpðTÞ, to makeup for Dcp(T) over the temperature range of the LT recuperator canbe obtained as shown in Fig. 11, where the area marked Sþ is equalto the area marked S�.
The mass flow rate of hot water can be calculated from theobtained DcpðTÞ as
_mw~cp;w ¼ _mCO2Dcp; (23)
where _mw and ~Cp;w are the mass flow rate and average isobaricspecific heat of water flowing through the LT recuperator,respectively.
2 Brayton cycle and TES, T-CO2 Brayton mode (night).
Fig. 16. Schematic of LH T-CO2 cycle combined with T-CO2 Brayton cycle and TES, LH T-CO2 mode (day).
Y.M. Kim et al. / Energy 43 (2012) 402e415 409
If the minimum temperature difference for heat transfer fromthe hot water to the side with CO2 at high-pressure is assumed to5 �C, the outlet temperature of water can be calculated from a heatbalance equation as
_QH1 ¼ _mw~cp;w�Tw;in � Tw;out
�; (24)
where Tw,in and Tw,out are the inlet and outlet temperatures of waterflowing through the LT recuperator, respectively.
With additional heat, QH1 ¼ 87.0 kJ/kg, provided by the LT heatsource, the temperature after the HT recuperator, TR, can beincreased significantly, and therefore, it is possible to reduce theheat input, QH2, from the HT (TH2) heat source in the T-CO2 Rankinecycle. As compared to the previous T-CO2 Rankine cycle, the LH T-CO2 cycle can achieve the same thermal efficiency using 23.3% ofthe total heat input from the LT heat source, not from the HT heatsource. In order to compare the LH T-CO2 cycle with other CO2cycles, two different thermal efficiencies are defined:
40 50 60 70 80 90 100 110 1200.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
)3.57(2 barPc Lp =×
)3.57( barPc Lp =
)200( barPc Hp =
Isob
aric
spe
cific
hea
t (kJ
/kg-
K)
Temperature (oC)
Fig. 17. Thermal match over low-temperature range in LH T-CO2 cycle combined withT-CO2 Brayton cycle and TES.
hth ¼_WT � _WP_ _
; (25)
QH1 þ QH2h*th ¼_WT � _WP
_QH2: (26)
hth represents general thermal efficiency; however, h*th representsthe increased thermal efficiency with the given heat input from theHT heat source by using the heat available from the LT heat source.As compared to the previous T-CO2 Brayton cycle with the sameheat input QH2 from the HT heat source, the LH T-CO2 cycle canproduce approximately 25% more power by reducing thecompression work and achieve an increased thermal efficiency ofh*th ¼ 0:526. Fig. 12 shows the temperature after the HT recuper-ator, TR, and the increased efficiency, h*th, as functions of thetemperature (TH1) of the LT heat source. It can be seen that the LTheat source below 150 �C aids in increasing TR and h*th of the T-CO2Rankine cycle with the given heat input QH2 from the HT heatsource, despite the low-grade of the heat source.
The LH T-CO2 cycle operates synergistically with the sum of thetwo separate cycles (i.e., a T-CO2 Rankine cycle with the LT (TH1)heat source, as shown in Fig. 13, and a T-CO2 Brayton cycle with theHT (TH2) heat source, as shown in Fig. 6). The LH T-CO2 cycle caneliminate both exergy losses from the turbine in the LT cycle and
Fig. 18. Reference cycle of partial condensation T-CO2 cycle.
Fig. 19. Reference cycle of fully-cooled S-CO2 cycle. Fig. 21. Reference cycle of recompression S-CO2 cycle.
60 70 80 90 100 110 120 130 140 1500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
)77(7.1 barPc Lp =×
)77( barPc Lp =
)200( barPc Hp =
Isob
aric
spe
cific
hea
t (kJ
/kg-
K)
Temperature (oC)
Fig. 22. Thermal match over low-temperature range in recompression S-CO2 cycle.
Y.M. Kim et al. / Energy 43 (2012) 402e415410
the compressor in the HT cycle by combining them; moreover, theLH T-CO2 cycle can utilize the waste heat from the HT cycle for theLT cycle. As shown in Table 3, the LH T-CO2 cycle can produceapproximately 15% more power than the sum of the separate twocycles with the same heat inputs by these synergistic effects. Theexergy analysis of the LH T-CO2 cycle, expressed on a unit massbasis, is summarized in Table 4. The exergy loss of the heater, whichis the main exergy loss in the previous T-CO2 Rankine cycle, isreduced in the LH T-CO2 cycle and the exergy loss of the waste heat,which is themain exergy loss in the previous T-CO2 Brayton cycle, isalso reduced in the LH T-CO2 cycle. The LH T-CO2 cycle has anexergy efficiency of 72%, approximately over 10% higher than thoseof the T-CO2 Rankine and Brayton cycles.
Chen et al. studied transcritical Rankine cycles using CO2 andR32 as the working fluids for converting low-grade heat to power[11] and found that the exergy efficiencies of these cycles are in therange of 50%w60% at the cycle high-temperature of 160 �C. In theiranalysis, the isentropic efficiencies of the compressor and turbinewere fixed at 85% and the condensation temperature for theworking fluids was fixed at 24 �C. Zhao et al. [23] investigated themultiple reheat helium Brayton cycles for sodium-cooled fastreactors. In their analysis, the isentropic efficiencies of thecompressor and turbine were fixed at 88% and 93%, respectively,and the effectiveness of the recuperator was fixed at 0.95. Atturbine inlet temperature of 600 �C and compressor inlet temper-ature of 20 �C, the thermal efficiency of the cycle with threeexpansion stages and six compression stages was approximately47%, which is equivalent to an exergy efficiency of 71% in this study.The exergy efficiency of 72% of the proposed LH T-CO2 cycle in thisstudy is a significant achievement considering the simplicity of thecycle.
Fig. 20. Reference cycle of less-cooled S-CO2 cycle.
3. Applications of LH T-CO2 cycle
3.1. Nuclear power plant
Asmentioned previously, interest in the S-CO2 cycle has recentlybeen revived in conjunction with its application to Generation IVnuclear reactors at the Massachusetts Institute of Technology (MIT)and the Tokyo Institute of Technology (TIT) [1e5]. At the TIT,a partial pre-cooling (or a partial condensation) T-CO2 cycle was
Fig. 23. Reference cycle of LH S-CO2 cycle using both LT and HT heat sources.
Y.M. Kim et al. / Energy 43 (2012) 402e415 411
studied to eliminate the temperature mismatch in the CO2 cyclesbetween the high- and low-pressure sides. As shown in Fig. 14[1e5], if the CO2 flow is bypassed to the compressor before pre-cooling, this temperature mismatch will be avoided. However, thebypassed flow reduces the heat rejected to the cooling waterthrough the pre-cooler and increases the required compressorwork. Despite the opposing effect on the cycle efficiency owing tothe bypassed flow of CO2, the cycle efficiency is enhanced by
Fig. 24. Schematic of thermo-electric energy storage (TEES) system with tr
approximately 4% at 800 �C [1]. The MIT is developing the recom-pression S-CO2 cycle recommended by Feher [6]. However, thecondensation of CO2was eliminated, and the pumpwas replaced bya compressor because condensing CO2 cycles require year-roundsupply of very cold cooling water (10e15 �C), which is not avail-able in all regions worldwide [1].
The LH T-CO2 cycle can also be used to avoid the temperaturemismatch in the CO2 cycles and improve the cycle efficiency with
anscritical CO2 cycles, charging (top) and discharging (bottom) modes.
Fig. 25. Reference cycle of TEES system with transcritical CO2 cycles.
Fig. 26. Schematic of TEES LH T-CO2 cycles, charging mode
Y.M. Kim et al. / Energy 43 (2012) 402e415412
the given heat input from the nuclear reactor. If heat is availablefrom the LT heat source below 120 �C, then our results, which werediscussed previously, suggest that the cycle efficiency can beenhanced by slightly over 10% at 600 �C from the basic T-CO2Rankine and Brayton cycles. However, if no heat is available fromthe LT heat source, the LH T-CO2 cycle combined with the T-CO2Brayton cycle and an LT thermal energy storage (TES) can be used. Aschematic of the cycle is shown in Fig. 15 (night) and Fig. 16 (day).During the night, when the demand for electricity is low, thesystem is operated as the T-CO2 Brayton cycle (Fig. 6) and the wasteheat (QL) is stored in the LT TES using the water flowing from thecold tank to the hot tank. During the day, when the demand forelectricity is high, the system is operated as the LH T-CO2 cycle(Fig. 9) and the supplemental heat needed in the LT range (QH1) issupplied by the LT TES using the water flowing from the hot tank tothe cold tank. The amount of waste heat (QL) from the T-CO2Brayton cycle is larger than the supplemental heat needed in the LTrange (QH1) for the LH T-CO2 cycle. Moreover, as shown in Fig. 17,
(top) and discharging and generation mode (bottom).
Fig. 27. Reference cycle of TEES LH T-CO2 cycle, discharging and generation mode.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00
50
100
150
200
250
300
Hea
t (kJ
/kg)
Split Ratio (y)
QH1
QH2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00
20
40
60
80
100
120
140
160
180
200
220
Wor
k (k
J/kg
)
Split Ratio (y)
Wnet
WT
WE
WP
Fig. 28. Heat input (top) and work input/output (bottom) as a function of split ratio yin TEES LH T-CO2 cycle.
Y.M. Kim et al. / Energy 43 (2012) 402e415 413
twice (currentþ stored) the isobaric specific heat of CO2 in the low-pressure side is well matched to that in the high-pressure, andgiven the unused waste heat from the HT recuperator, it is possibleto supply QH1 for the LH T-CO2 cycle by using QL stored from theprevious T-CO2 Brayton cycle. As shown in our previous results,during the day with high demand for electricity, the LH T-CO2 cyclecan produce approximately 25% more power than during the nightby reducing the compression work and by enhancing the cycleefficiency from 42.1% to 52.6% at 600 �C with the same heat inputfrom the nuclear reactor. The thermal energy storage used is verysimilar to that of a new type of thermo-electric energy storage(TEES) systemwith transcritical CO2 cycles using hot water storage,recently proposed by the ABB Corporate Research Center [19].Water tanks (289MWt, thermal energy storage) similar to that ofthe 50 MWe TEES system are needed for the nuclear power plantoperating from 400 MWe (night) to 500 MWe (day) using theproposed LH T-CO2 cycle.
As shown in Fig. 18, the partial condensation T-CO2 cycle ina study at the TIT is similar to a compound cycle of the T-CO2Rankine and Brayton cycles in this study. The configuration of thesystem is similar to that of the previously combined LH T-CO2 cycleas shown in Figs. 15 and 16; however, no thermal energy is stored,and half a fraction of the fluid flow is bypassed to the compressorbefore it enters the condenser. If the mass flow in the high-pressureside is half of that in the low-pressure side in the LT recuperator, thetemperature mismatch problem in the LT recuperator can beavoided in the sameway as shown in Fig. 17. As shown in Fig.18, thecompression work and the power output of the partial condensa-tion T-CO2 cycle are the mean values of those in the T-CO2 Braytoncycle (night) and the LH T-CO2 cycle with LT TES (day), indicatinga nuclear power plant with a constant power output of 450 MWe.However, the proposed LH T-CO2 cycle combined with the T-CO2Brayton cycle and the LT TES offers the advantage of load levelingfrom 400 MWe to 500 MWe by regulating the split ratio for thebypass CO2 flow and the direction and the quantity of water flow ofthe LT TES. Traditionally, reactor power control has been used inbase-load operating conditions. With the increasing share of powerplant, it seems that the load-follow operating of nuclear reactorswill be inevitable in the future. But, it is hard to get the satisfyingperformance with classic control strategy to control nuclear reactorpower [24,25].
The concept of the LH T-CO2 cycle can also be applied to the S-CO2 cycle. The turbine inlet temperature and pressure in the S-CO2cycle are maintained constant (600 �C and 200 bar); however, thecompressor inlet temperature and pressure are slightly higher thanthose in the T-CO2 cycle (32 �C and 77 bar), which is very close tothe optimal recompression S-CO2 cycle in other literature [1e3].Similar to the previous LH T-CO2 cycle, two S-CO2 cyclesdfully-cooled and less-cooled S-CO2 cycles e can be considered asshown in Figs.19 and Fig. 20, respectively. The recompression S-CO2cycle is similar to a compound cycle of the two S-CO2 cycles, asshown in Fig. 21. If 41% of the fluid flow at point 0A is bypassed tothe compressor before the final cooler (0A-0B), temperaturemismatch in the LT recuperator can be avoided in the same way, asthat shown in Fig. 22, and the cycle efficiency can be increased up to46.4% from the two basic S-CO2 cycles. The present numericalmodel was verified using the same data and operating conditions asthose used by Dostal [2]; these conditions are as follows: maximumcycle temperature of 550 �C, maximum cycle pressure of 200 bar,pressure ratio of 2.6, recompressed mass flow ratio of 0.41, εR of96.3%, and turbine and compressor isentropic efficiencies of 90%and 89%, respectively. The calculated cycle efficiency (45.8%) isslightly higher than that of the reference case (45.3%), consideringthe assumption of zero pressure drop in the primary system in thisstudy.
On the other way, the LH S-CO2 cycle combined with the LT TEScan be used. The system is operated as a less-cooled S-CO2 cycle(Fig. 20), and the waste heat (QL) is stored in the LT TES using thewater flowing from the cold tank to the hot tank. During the day,when the demand for electricity is high, the system is operated as
Table 5Comparison of performances of different T-CO2 cycles with TEES (H: High-temperature of TH2, L: Low-temperature of TH1, R: Rankine, B: Brayton).
Cycle TH1 (�C) QH1 (kJ/kg) TH2 (�C) QH2 (kJ/kg) TR (�C) WP(C) (kJ/kg) WT (kJ/kg) Wnet (kJ/kg) hth h*th
H-R (1) e e 600 456.8 225 14.7 201.5 186.8 0.409 e
H-B (2) e e 600 292.6 360 72.8 201.5 128.7 0.440 e
L-R (3) 122 281.7 e e e 14.7 59.0 44.3 0.157 e
LH-R (4) 122 161.1 600 295.7 357 14.7 201.5 186.8 0.409 0.632L-R (3) þ H-B (2) 122 161.1 600 295.7 360 8.4 þ 73.6 33.7 þ 203.7 25.3 þ 130.1 0.340 e
Y.M. Kim et al. / Energy 43 (2012) 402e415414
an LH S-CO2 cycle (Fig. 23) and the supplemental heat needed in theLT range (QH1) is supplied by the LT TES using the water flowingfrom the hot tank to the cold tank. As shown in Fig. 22, 1.7 times(current þ stored) the isobaric specific heat of CO2 in the low-pressure side is well matched to that in the high-pressure side.For thermal matching, the system is operated as a less-cooled S-CO2cycle (Fig. 20) for 10 h and an LH S-CO2 cycle (Fig. 23) for 14 h.During the day, when there is a high demand for electricity, the LHS-CO2 cycle can produce approximately 40% more power thanduring the night by reducing the compression work and enhancingthe cycle efficiency from 37.6% to 52.5% at 600 �C with the sameheat input from the nuclear reactor. The proposed LH S-CO2 cyclecombined with the LT TES offers the advantages of load levelingfrom 358 MWe to 500 MWe with the constant nuclear reactor byregulating the split ratio for the bypass CO2 flow and the directionand the quantity of water flow of the LT TES.
3.2. Hybrid system of LH transcritical CO2 cycle combined with TEES
As mentioned before, a new type of TEES systemwith reversibleT-CO2 cycles was recently proposed by the ABB Corporate ResearchCenter [19]. The system layout is shown in Fig. 24, and the energyflow per unit mass of working fluid on T-s diagram of the basereference (reversible) cycle is shown in Fig. 25. The concept is basedon heat pump and heat engine (reverse cycle) technologies utilizingT-CO2 cycles, storage of pumped heat in hot water, and ice gener-ation and melting at the cold end of the cycles. Figs. 24 and 25 arebased on the preferred realization of the transcritical cyclewith CO2as the working fluid and hot water and ice as the storage materials.Liquid water has a very high heat capacity, which provides a highenergy density for energy storage. The potential advantages ofusing ice for energy storage are increased site-independence withminimum interaction with the ambient, reduction of back-work,and an increased temperature potential and therefore anincreased storage utilization factor [19].
TEES systems with transcritical CO2 cycles can be used asa hybrid system combined with an LH T-CO2 cycle (we refer to thisas an LH T-CO2 cycle with TEES). The schematic and reference cycleof this system are shown in Figs. 26 and 27, respectively. Thecharging mode of the system is the same as the TEES system.However, in the discharging mode of the system, the high-pressureCO2 gas heated by the LT source (thermal energy storage) is dividedby two parts by a split ratio y, which is controlled according to thedemand for electricity. One portion, y, of the CO2 gas is sent to theHT heater and the other portion,1�y, is sent to the LT expander. Theexpanded hot CO2 gas from the HT turbine transfers its heat to thecompressed CO2 gas through the HT recuperator, where it is cooleddown and combined with the expanded CO2 gas from the LTexpander. The combined, expanded CO2 gas transfers its heat to thecompressed CO2 gas through the LT recuperator. Fig. 28 shows theheat input and the work input/output according to the split ratio,expressed on a unit mass basis. Table 5 compares the performances,expressed on a unit mass basis, of different CO2 cycles based on thereference cycle in Fig. 27 to show the synergistic effects of thehybrid system that combines the TEES system with the LH T-CO2
cycle. During the day with high demand for electricity, incomparison with the T-CO2 Brayton cycle, the LH T-CO2 cycle canproduce approximately 45% more power by reducing thecompression work and improve the cycle efficiency, h*th, byapproximately 19% at 600 �C with the same heat input from the HTheat source.
4. Conclusions
In this paper, a novel transcritical CO2 Rankine cycle using boththe LT and the HT heat sources (LH T-CO2 cycle) is proposed tomaximize the power output of the CO2 power cycle with the givenHT heat sources for use in applications such as nuclear power,concentrated solar power, and combustion. Although thecompression work and exergy loss of waste heat are significantlyreduced in the T-CO2 Rankine cycle with HT heat sources ascompared to the T-CO2 Brayton cycle, the outlet temperature of CO2heated through the recuperator is considerably lower than that inthe T-CO2 Brayton cycle. Therefore, the thermal efficiency of the T-CO2 Rankine cycle is lower than that of the T-CO2 Brayton cycle. Thisis because below 150 �C, particularly below 120 �C, the isobaricspecific heat of CO2 in the high-pressure side is considerably higherthan that in the low-pressure side. However, if heat is available inthis LT range to compensate for the difference in the specific heat ofCO2 between the high- and the low-pressure sides, the T-CO2Rankine cycle will be more effective than the T-CO2 Brayton cycle.Further, the T-CO2 is more effective than the partial condensation T-CO2 cycle, which is a compound cycle of the T-CO2 Rankine andBrayton cycles, because low compression work is required whileobtaining the same outlet temperature of CO2 heated through therecuperator before it enters the HT heater.
As compared to the T-CO2 Brayton cycle with an HT heat source,the proposed LH T-CO2 cycle can produce approximately 25% morepower by reducing the compression work and enhancing the cycleefficiency by approximately 10% at 600 �C with the same heat inputfrom the HT heat source by utilizing an LT heat source. The exergyefficiency of the LH T-CO2 cycle using both the LT and the HT heatsources is approximately 10% higher than that of the T-CO2 Braytoncycle with an HT heat source.
For the application of this novel concept to nuclear powerplants, during the night, when the demand for electricity is low, thesystem is operated as a T-CO2 Brayton cycle, and the waste heat isstored in an LT TES. Further, during the day, when the demand forelectricity is high, the system is operated as an LH T-CO2 cycle usingthe LT TES. During the day, the LH T-CO2 cycle can produceapproximately 25% more power than during the night by reducingthe compression work and enhancing the cycle efficiency from42.1% to 52.6% at 600 �C with the same heat input from the nuclearreactor. The proposed LH T-CO2 cycle combined with the T-CO2Brayton cycle and LT TES offers the advantage of load leveling from400 MWe to 500 MWe over the partial condensation T-CO2 cyclewith a constant power output of 450MWe. The concept of the LH T-CO2 cycle can also be applied to the S-CO2 cycle, and the LH S-CO2cycle combined with the LT TES offers the advantage of loadleveling from 358 MWe for 10 h to 500 MWe for 14 h over the
Y.M. Kim et al. / Energy 43 (2012) 402e415 415
recompression S-CO2 cycle with a constant power output of442 MWe.
Moreover, a new type of thermo-electric energy storage (TEES)system with reversible transcritical CO2 cycles can be used asa hybrid system combined with the LH T-CO2 cycle.
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