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The first and second law analysis on an organic Rankine cycle with ejector
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Solar Energy 93 (2013) 100–108 www.elsevier.com/locate/solener
The first and second law analysis on an organic Rankine cycle with ejector Xinguo Li ⇑, Xiajie Li, Qilin Zhang Department of Thermal Engineering, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China Received 1 December 2012; received in revised form 19 March 2013; accepted 3 April 2013 Available online 4 May 2013 Communicated by: Associate Editor Yogi Goswami
Abstract In consideration of the low efficiency of the organic Rankine cycle (ORC) with low-grade heat source (LGHS), an organic Rankine cycle with ejector (EORC) and a double organic Rankine cycle (DORC) based on the ORC is introduced in this paper. The thermodynamic first law and second law analysis and comparison on the ORC, EORC and DORC cycles are conducted on the cycle’s power output, thermal efficiency, exergy loss and exergy efficiency. Water is chosen as the LGHS fluid, and the same temperature and mass flow rate of the water is the standard condition for the comparative analysis on the cycles. The emphasis is on the thermodynamic performance at the maximum net power output of the cycles. The results show the power output is higher in the EORC and DORC compared to the ORC. And the cycle’s exergy efficiency could be ranked from high to low: DORC > EORC > ORC. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Organic Rankine cycle with ejector (EORC); Double organic Rankine cycle (DORC); Ejector; Thermodynamic analysis
1. Introduction The low-grade heat source (LGHS), such as solar energy, geothermal energy, biomass energy, and waste heat from various thermal processes, exists in the world extensively. Generally, the LGHS could be converted to power by the organic Rankine cycle (ORC), but the low efficiency of the ORC with LGHS has limited its wide use. The research on the ORC is mainly focused on the thermodynamic analysis, the selection of the working fluids, and the optimization of the system. The selection of the working fluids is very important and significant to the research and application of the ORC (Lakew and Bolland, 2010; Roy et al., 2010; Hettiarachchi et al., 2007; Saleh et al., 2007; Heberle et al., 2012; Chen et al., 2010; He et al., 2012; Wang et al., 2013; Li et al., 2012). Chen et al. (2010) presented a review of the ORC and supercritical Rankine cycle for the conversion of low-grade ⇑ Corresponding author. Tel.: +86 022 27890058.
E-mail address: [email protected] (X. Li). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.04.003
heat into power, as well as selection criteria of potential working fluids. The thermodynamic and physical properties and environmental impacts, etc. of the working fluids were evaluated. He et al. (2012) calculated the optimal evaporation temperature of the ORC that the larger net power output would be produced when the critical temperature of working fluid approached to the temperature of the waste heat source. Wang et al. (2013) analyzed the influence of working fluid properties on the thermal efficiency of ORC, and the optimal operation condition and exergy destruction for various heat source temperatures. It was unadvisable to always pursue high thermal efficiency for LGHS. Li et al. (2012) investigated the energetic and exergetic performance of the ORC at different heat source temperatures. A combined ORC or Rankine cycle and ejector refrigeration cycle by LGHS was investigated. This combined power and cooling cycle originally was proposed by Xu et al. (2000), and Tamm et al. (2004) that the cycle could produce both power and refrigeration simultaneously and achieved high thermal efficiency.
X. Li et al. / Solar Energy 93 (2013) 100–108
101
Nomenclature E h m Q r s T u W
exergy (kW) specific enthalpy (kJ kg1) mass flow rate (kg s1) heat transfer (kW) exergy loss ratio specific entropy (kJ kg1 K1) temperature (K) mass flow ratio in the first-stage evaporator or the entrainment ratio of the ejector power output (kW)
Greek symbols g efficiency (%) Subscripts cond (c) condensation eje ejector
Wang et al. (2009), and Dai et al. (2009) proposed a combined the Rankine cycle and the ejector-absorption refrigeration cycle, in which an ejector was introduced between the rectifier and the condenser to provide a performance improvement. Optimal thermal parameters were done using genetic algorithm and the optimized exergy efficiency was 43% for a given condition. And the biggest exergy loss was due to the irreversibility occurred in the heat addition processes, and the ejector caused the next largest exergy loss. Zheng and Weng (2010) proposed a combined the ORC and the ejector refrigeration cycle. The ejector was driven by the exhausts from the turbine to produce power and refrigeration simultaneously, and most exergy losses took place in the ejector. Xu and He (2011) proposed a regenerative organic Rankine cycle (RORC) that used a vapor injector as the regenerator. Results indicated that there existed the inlet vapor pressure regions for the injector that allowed the RORC performed better than the basic ORC. Habibzadeh et al. (2013) presented a thermodynamic study on the combined ORC and the ejector refrigeration cycle with working fluids of R123, R141b, R245fa, R600a, R601a for the power to refrigeration ratio of 10. R141b had the lowest optimum pressure and smallest total thermal conductance, and R601a had the highest thermal efficiency and lowest total exergy destruction. Khaliq et al. (2012) proposed a cogeneration cycle with a LiB–H2O absorption refrigeration cycle employed to the combined power and ejector refrigeration cycle. Results showed that around 53.6% of the total input exergy was destroyed due to irreversibilities in the components, 22.7% was available as a useful exergy output, and 23.7% was exhaust exergy lost to the environment, whereas energy distribution showed 44% was exhaust energy and 19.7% was useful energy output. The low efficiency of ORC with LGHS has limited its wide use in industry. Increasing the ORC’s power output
evap (e) evaporation ex exergy exp expander in inlet loss exergy loss max maximum mix mixed fluid in ejector oc environment opt optimal out outlet net net output pf primary fluid in ejector sf secondary fluid in ejector sum sum th thermal w water wf working fluid
and efficiency was the objective of the ORC research. Based on this purpose, an organic Rankine cycle with ejector (EORC) was proposed in our early researches (Li et al., 2012; Li and Jia, 2009). In the reference (Li et al., 2012), the configuration and processes of the EORC was described, and a preliminary first law analysis on the net power output and thermal efficiency was conducted with R600 only at water temperature of 80 °C. A further thermodynamic first law and second law analysis and comparison on the EORC would be necessary especially for the exergy analysis on the ejector in the EORC. 2. Principle of organic Rankine cycle with ejector (EORC) In the EORC, an ejector and a second-stage evaporator are added to the ORC, as shown in Figs. 1 and 2. The
LGHS
Expander
1 First-stage evaporator
6 Second-stage evaporator
3 Fluid pump
2
7 Condenser
5
4
Ejector
Fig. 1. Configuration and processes of organic Rankine cycle with ejector (EORC).
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X. Li et al. / Solar Energy 93 (2013) 100–108
T
T
P e1
P e1
1
P e2
P e2
2
6
1 2
6
7
7 4
Pc
Pc
5
5 3
s
s
Fig. 2. T–S diagram of the EORC.
Fig. 4. T–S diagram of the DORC.
vapor from the second-stage evaporator works as the primary fluid for the ejector to induce the exhaust from the expander so as to decrease the expander backpressure and increase the pressure difference in the expander, which results in an increase of the power output of the ORC. In order to analyze and compare the thermal performance of the EORC, a double organic Rankine cycle (DORC) Li et al., 2012 is also introduced in the paper, as shown in Figs. 3 and 4. 3. Thermodynamic analysis on the ORC, EORC and DORC The thermodynamic analysis and comparison on the ORC, EORC and DORC will be conducted in this paper. An idealized thermodynamic process of the cycles is assumed and considered as no pressure loss, no heat loss, and isentropic processes are assumed for the expander and the pump. The calculation programs for the cycle’s thermodynamic performance are built based on the refrigerant’s physical properties by REFPROP from NIST on Matlab. The calculated thermodynamic performances are: power output from the expander (Wout), pumping power (Wpump), net power output (Wnet), thermal efficiency (gth), exergy loss
1
LGHS
(Eloss) and exergy efficiency (gex), and operating condition parameters. 3.1. Specifications and conditions for calculation (1) R245fa is chosen as the working fluid for it is a generally accepted working fluid for the ORC. (2) Water is chosen as the LGHS fluid, and the water temperature is selected in a range of 95–150 °C and a typical temperature of 95 °C, and the mass flow rate of water is 1 kg/s. The same temperature and mass flow rate of the water is the standard condition for the comparative analysis on the cycles. (3) The outlet of the working fluid from the evaporator is set to saturated vapor. (4) In the evaporator, the bubble point of the working fluid is set as the pinch point, and the pinch point temperature difference between the heat source water and the working fluid is set to 5 °C. (5) The outlet of working fluid from the condenser is set to saturated liquid, and the bubble temperature of working fluid in the condenser is set to 35 °C. (6) The environment state is set to: poc = 101.325 kPa, Toc = 298.15 K.
3.2. First law analysis
First-stage evaporator
2 6
3 3' 4
The evaporation heat (Qevap) from the heat source water in the evaporator is:
Expander
Qevap ¼ mwf ðhevap– out hevap– in Þ
Second-stage evaporator
ð1Þ
The condensation heat (Qcond) in the condenser is: 7
3'
Fluid pump
5
Condenser
3
4
Qcond ¼ mwf ðhcond– in hcond– out Þ
ð2Þ
The power output (Wout) from the expander is: W out ¼ mwf ðhexp– in hexp– out Þ
ð3Þ
The pumping power (Wpump) by the pump is: Fig. 3. Configuration and processes of double organic Rankine cycle (DORC).
W pump ¼ mwf ðhpump– out hpump– in Þ
ð4Þ
X. Li et al. / Solar Energy 93 (2013) 100–108
103
8
90
7
12
Entrainment ratio
Net power output (kW)
Entrainment efficiency
10 8 DORC
6
EORC ORC
4
80
Entrainment ratio
70
6
60
5
50 4 40 3
30
2
20
1
10 0
0 50
2 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
)
)
Fig. 5. Net power output with Te1 at water temperature of 95 °C.
Fig. 8. Entrainment ratio and entrainment efficiency with Te1 at water temperature of 95 °C.
12
1 ORC
10
Exhaust water
0.9
Exergy loss rate in ORC
Thermal efficiency (%)
Entrainment efficiency (%)
14
DORC EORC
8
6
4
Evaporator
0.8
Condenser
0.7 0.6 0.5 0.4 0.3 0.2 0.1
2 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
0
85
50
55
)
60
65
70
75
Evaporation temperature of Te1 (
Fig. 6. Thermal efficiency with Te1 at water temperature of 95 °C.
80
85
)
Fig. 9. Exergy loss ratio in each component of the ORC with Te1 at the Wnet_max at water temperature of 95 °C.
220 0.6
Exergy loss rate in EORC
Evaporation heat (kW)
190 160 Qe1 or ORC_Qe
130
EORC_Qe_sum EORC_Qe2
100
DORC_Qe_sum
70
DORC_Qe2
40
First-stage evaporator Second-stage evaporator
0.5
Ejector Condenser
0.4
Exhaust water
0.3 0.2 0.1
10 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
0 50
)
55
60
65
70
75
Evaporation temperature of Te1 (
Fig. 7. Evaporation heat with Te1 at water temperature of 95 °C.
80
85
)
Fig. 10. Exergy loss ratio in each component of the EORC with Te1 at the Wnet_max at water temperature of 95 °C.
The net power output (Wnet) of the cycle is: W net ¼ W out W pump
Exergy equations: ð5Þ (1) The exergy of heat source water inlet to the evaporator is:
The thermal efficiency (gth) of the cycle is: gth ¼ W net =Qevap
ð6Þ
3.3. Second law analysis The concept of exergy related to the maximum work (or power) output that could theoretically be obtained from any state of the system relative to the given environment.
Ew– in ¼ mw ðhw– in hoc T oc ðsw– in soc ÞÞ
ð7Þ
(2) The exergy of heat source water outlet from the evaporator is: Ew– out ¼ mw ðhw– out hoc T oc ðsw– out soc ÞÞ
ð8Þ
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X. Li et al. / Solar Energy 93 (2013) 100–108 45
First-stage evaporator Second-stage evaporator Condenser Exhaust water
0.5
40
Exergy efficiency (%)
Exergy loss rate in DORC
0.6
0.4 0.3 0.2
35 30 25 DORC
20
EORC
15
0.1
ORC
10
0 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
50
85
55
60
65
70
75
Evaporation temperature of Te1 (
)
Fig. 11. Exergy loss ratio in each component of the DORC with Te1 at the Wnet_max at water temperature of 95 °C.
(3) The exergy loss in the evaporator, including the exergy loss in the working fluid and the heat source water:
80
85
)
Fig. 12. Exergy efficiency of the ORC, EORC and DORC with Te1 at the Wnet_max at water temperature of 95 °C.
ri ¼ Eloss– i =Eloss– total
ð13Þ
(8) The exergy efficiency of the cycle is: Eloss– evap ¼ exergy loss in the working fluid þ exergy loss in the heat source water ¼ T oc ðmwf ðsevap– out sevap– in Þ þ mw ðsw– out sw– in ÞÞ
gex ¼ 1 Eloss– total =Ew– in ð9Þ
(4) The exergy loss in the condenser, calculated by the exergy difference of the inlet to the outlet of the condenser by the working fluid, included the heat exergy by the condensation heat released to the environment: Eloss– cond ¼ exergy inlet to the condenser exergy outlet from the condenser ¼ mwf ððhcond– in hoc Þ T oc ðscond– in soc ÞÞ mwf ððhcond– out hoc Þ T oc ðscond– out soc ÞÞ ¼ mwf ððhcond– in hcond– out Þ T oc ðscond– in scond– out ÞÞ
ð10Þ
(5) The exergy loss in the ejector, calculated by the entropy increase from the inlet to the outlet in the ejection process by the working fluid: Eloss– eje ¼ mwf T oc ðseje– mix seje– sf u=ðu þ 1Þ seje– pf =ðu þ 1ÞÞ
ð11Þ
(6) The total exergy loss of the cycle is: Eloss– total ¼ Eloss– evap þ Eloss– cond þ Eloss– eje þ Ew– out
ð12Þ
(7) The exergy loss ratio in each component of the cycle is:
ð14Þ
4. Results and discussion 4.1. Performance and comparison at water temperature of 95 °C Figs. 5–12 present the net power output (Wnet), thermal efficiency (gth) and the exergy analyses on the ORC, EORC and DORC with the first-stage evaporation temperature (Te1) at the same water temperature of 95 °C. 4.1.1. Net power output (Wnet) The Wnet of cycles increases and then decreases with the first-stage evaporation temperature (Te1), and there exists the maximum net power output (Wnet_max), as shown in Fig. 5, which is 10.57 kW for ORC, 11.68 kW for EORC, 12.80 kW for DORC respectively, and the corresponding optimal first-stage evaporation temperature (Te1_opt) is 63.11 °C, 65.61 °C, 71.63 °C, as shown in Table 1. And the Wnet of the cycles can be ranked from high to low: DORC > EORC > ORC. 4.1.2. Thermal efficiency (gth) As shown in Fig. 6, the thermal efficiency (gth) of the ORC increases with the Te1 almost linearly. The gth of EORC and DORC increases and then decreases with the Te1, and there also exists the maximum of gth (gth_max), which is 6.21% for EORC and 7.81% for DORC, and its corresponding Te1 is 69.32 °C, 82.54 °C respectively. In summary, the power output is higher in the EORC and DORC compared to the ORC. The power output and thermal efficiency of the DORC is superior to the EORC, but another expander-generator and its auxiliary equipments is required for DORC led to the increase of
X. Li et al. / Solar Energy 93 (2013) 100–108
105
Table 1 Performance comparison between ORC, EORC and DORC at the maximum net power output (Wnet_max) at water temperature of 95 °C. Unit
ORC
EORC
DORC
kg/s °C °C °C
1 95 61.81 /
1 95 64.31 49.55
1 95 70.75 53.68
Temperature (Te1) Pressure (Pe1) Mass flow rate (mwf1) Temperature (Te2) Pressure (Pe2) Mass flow rate (mwf2) Temperature (Tc) Pressure (Pc) Mass flow rate
°C bar kg/s °C bar kg/s °C bar kg/s /
63.11 5.05 0.68 / / / 35 2.12 0.68 /
65.61 5.41 0.63 45.66 3.01 0.32 35 2.12 0.95 1.95
71.63 6.37 0.49 50.52 3.50 0.37 35 2.12 0.85 1.33
Pressure Temperature Pressure Temperature Pressure Temperature
bar °C bar °C bar °C /
/ / / / / / 2.38
3.01 45.66 1.90 37.19 2.12 39.61 2.85
/ / / / / / 3 and 1.65
First-stage (Qe1) Second-stage (Qe2) The sum (Qe_sum)
Condensation heat (Qcond) Power output from expander (Wout) Pumping power (Wpump) Maximum net power output (Wnet_max) Thermal efficiency (gth) Exergy efficiency (gex)
kW kW kW kW kW kW kW % %
139.26 / 139.26 128.69 10.72 0.15 10.57 7.59 35.38
128.83 61.72 190.55 178.87 11.86 0.18 11.68 6.13 39.13
101.85 71.46 173.31 160.51 12.99 0.20 12.80 7.38 42.87
4. The increase Increase of the Increase of the Increase of the
% % %
/ / /
10.50 19.24 10.6
21.10 -2.77 21.17
1. Water’s parameters Water mass flow rate Water temperature inlet to evaporator Water temperature outlet from evaporator 2. Cycle parameters of R245fa as the working fluid First-stage evaporation
Second-stage evaporation
Condensation
First-stage Second-stage
Mass flow ratio in the first-stage evaporator or the entrainment ratio of the ejector (u) Ejector Primary fluid Second fluid Mixed fluid Pressure ratio (inlet/outlet) in expander 3. Performance of the cycles Evaporation heat (Qe)
of performance compared to ORC Wnet_max gth gex
the investment and operation management compared to the EORC. 4.1.3. Evaporation heat (Qe) and effect on the thermal efficiency (gth) Fig. 7 presents the variation of the evaporation heat (Qe) with the Te1. At the same Te1, the evaporation heat in the first-stage (Qe1) for the EORC and DORC is the same as the evaporation heat in the ORC. The variation of the evaporation heat in the second-stage (Qe2) for EORC and DORC is very similar, but the Qe2 in the EORC is higher than that in the DORC in most evaporation temperature range, so the sum evaporation heat (Qe_sum) in the EORC is higher than the DORC. The variation of thermal efficiency (gth) of the ORC is different from the EORC and DORC, as shown in Fig. 6, which could be derived and explained from the combination of the net power output (Wnet) and the evaporation heat (Qe) for the gth is the Wnet divided by the Qe.
It is found that the negative slope or the decrease tendency of the evaporation heat in the ORC is higher than that in the EORC and DORC due to the Qe2. And the positive slope of the Qe2 increases with the Te1 that causes the negative slope of the Qe_sum in the EORC and DORC not to increase, but maintain almost the same. Especially the negative slope of the Qe in the ORC increases with the evaporation temperature. With the Te1 higher than the optimal Te1_opt, which is 63.11 °C, 65.61 °C, 71.63 °C for the ORC, EORC and DORC respectively, the Wnet decreases, but the negative slope of the Qe in the ORC is higher than the negative slope of the Wnet with the evaporation temperature, the gth of the ORC does not decrease, but increase. For the negative slope of the Qe_sum in the EORC and DORC does not to increase, but maintain almost the same, that makes the gth of the EORC and DORC different from the ORC, and exists the maximum of gth_max, which is similar as the variation of the Wnet.
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X. Li et al. / Solar Energy 93 (2013) 100–108
Table 2 Exergy loss in each component of the ORC, EORC and DORC at the maximum net power output (Wnet_max) at water temperature of 95 °C. Exergy loss
ORC
EORC
Eloss (kW)
r
Ranking
Eloss (kW)
r
Ranking
Eloss (kW)
r
Ranking
First-stage evaporator Second-stage evaporator Total exergy loss in the two evaporators Condenser Ejector Exhaust water Total exergy loss
6.310 / 6.310 4.197 / 8.789 19.296
0.327 / 0.327 0.218 / 0.455 1
2 / / 3 / 1 /
5.55 2.04 7.57 5.84 0.75 4.01 18.17
0.31 0.11 0.42 0.32 0.04 0.22 1
2 4 / 1 5 3 /
3.95 2.46 6.41 5.24 / 5.42 17.07
0.23 0.14 0.37 0.31 / 0.32 1
3 4 / 2 / 1 /
4.1.4. Entrainment ratio and entrainment efficiency of the ejector in EORC Fig. 8 presents the entrainment ratio and the entrainment efficiency of the ejector in EORC with the Te1 at water temperature of 95 °C. The ranges of the entrainment ratio and the entrainment efficiency are 0.26–7.46 and 21–82.73% respectively within the Te1 of 50–85 °C. At the Wnet_max with the Te1_opt of 65.61 °C, the entrainment ratio and the entrainment efficiency are 1.95% and 61.84% respectively. 4.1.5. Exergy loss At the maximum net power output (Wnet_max) at water temperature of 95 °C, the exergy loss ratio in each component of the ORC, EORC and DORC with the Te1 are shown in Figs. 9–11. The results show that the exergy loss ratio decreases in the evaporator, while it increases in the exhaust water with the Te1. It is found that the increase tendency or the slope of the exhaust water’s exergy loss ratio in the ORC is higher than that in the EORC and DORC with the Te1, as shown in Figs. 9–11. This phenomenon could be explained from the variation of the evaporation heat (Qe), which is presented in Section 4.1.3 with Fig. 7, that the decrease tendency or the negative slope of the ORC’s Qe is higher than that of the EORC and DORC. The less the evaporation heat is consumed from the heat source water, the more the heat with a higher temperature will be remained and discharged in the exhaust water, so that the more exergy loss in the exhaust water is resulted in the ORC compared to the EORC and DORC. 4.1.5.1. Exergy loss in the ORC. As shown in Fig. 9, the exergy loss ratio in the condenser of the ORC decreases with the evaporation temperature due to the decrease of the mass flow rate of the working fluid. 4.1.5.2. Exergy loss in the EORC. As shown in Fig. 10, the exergy loss ratio in the first-stage evaporator decreases with the Te1, while it increases in the ejector and in the exhaust water, and it increases and then decreases in the secondstage evaporator and the condenser, which is due to the flow rate of the working fluid in the two evaporators. At the maximum net power output (Wnet_max), the most exergy losses takes place in the evaporator, condenser and the exhaust water, while it is the smallest in the ejector, and it is only 4% of the total exergy loss, as shown in Table 2.
DORC
The exergy loss in the evaporator and condenser is high due to the high evaporation temperature in the evaporator, and the heat exergy by the condensation heat released to the environment in the condenser. The ejector’s exergy loss is the cause of the irreversible processes in the ejection process. And a further investigation on the ejector’s exergy loss is necessary to verify this calculation. 4.1.5.3. Exergy loss in the DORC. As shown in Fig. 11, the exergy loss ratio in the first-stage evaporator decreases, while it increases in the second-stage evaporator and in the exhaust water, and it increases and then decreases in the condenser. The exergy loss in each component of the ORC, EORC and DORC at the maximum net power output (Wnet_max) is listed in Table 2. The ratio or the weighting of the exergy loss in each component of the cycles is different with the cycle type. Ranking the exergy loss in the evaporator and the condenser of the cycles from high to low is: EORC > DORC > ORC, and it is: ORC > DORC > EORC in the exhaust water. The reasons are that the evaporation heat and the flow rate of the working fluid in EORC are higher than that in DORC, and the temperature inlet to the condenser in the EORC is higher than that in the DORC due to the irreversible ejection process in EORC. The higher the temperature of the exhaust water is, the higher the exergy loss in the exhaust water is. 4.1.6. Exergy efficiency Fig. 12 shows the exergy efficiency (gex) of the ORC, EORC and DORC with the Te1. It reveals that the variation of the gex is consistent with the net power output (Wnet), and there also exists the maximum exergy efficiency (gex_max) with the Te1, which is 35.38% and 63.11 °C for ORC, 39.13% and 65.61 °C for EORC and 42.87% and 71.63 °C for DORC respectively, as shown in Table 1. And this gex_max condition is also the same condition of the maximum net power output (Wnet_max). At the same Te1, the gex of the cycles could be ranked from high to low: DORC > EORC > ORC, which is the same as the Wnet of the cycles. 4.2. Performance and comparison with different water temperature Figs. 13 and 14 present the maximum net power output (Wnet_max) and the corresponding thermal efficiency (gth) of
Maximum net power output (kW)
X. Li et al. / Solar Energy 93 (2013) 100–108
61.84% respectively in the water temperature of 95– 150 °C.
50 DORC
45
EORC
40
ORC
5. Conclusions
35 30 25 20 15 10 95
100
105
110
115
120
125
130
Water temperature (
135
140
145
150
)
Fig. 13. The maximum net power output (Wnet_max) with water temperature.
14 ORC
13
Thermal efficiency (%)
107
DORC
12
EORC
11 10 9
(1) The power output is higher in the EORC and DORC compared to the ORC. The power output and thermal efficiency of the DORC is superior to the EORC, but another expander-generator and its auxiliary equipments is required for the DORC led to the increase of the investment and operation management compared to the EORC. (2) Ranking the exergy loss ratio in the evaporator and the condenser of the cycles from high to low is: EORC > DORC > ORC, and it is: ORC > DORC > EORC in the exhaust water. (3) The cycle’s exergy efficiency can be ranked from high to low: DORC > EORC > ORC. (4) At the maximum net power output, the most exergy losses took place in the evaporator, condenser and the exhaust water, while it is the smallest in the ejector in the EORC cycle.
8 7
Acknowledgement
6 95
100
105
110
115
120
125
130
Water temperature (
135
140
145
150
)
Fig. 14. Thermal efficiency with water temperature at the Wnet_max.
the ORC, EORC and DORC in water temperature of 95– 150 °C. The Wnet_max and gth increase with the water temperature almost linearly, and these results and analyses are similar to the outcomes of the thermal performance of the cycles at water temperature of 95 °C. Fig. 15 shows the entrainment ratio and the entrainment efficiency of the ejector in EORC with water temperature at the Wnet_max. The ranges of the entrainment ratio and the entrainment efficiency are 1.95–3.15% and 60–
3.5
62
Entrainment ratio
Entrainment ratio
3
61.5
61 2.5 60.5 2
60
1.5 95
Entrainment efficiency (%)
Entrainment efficiency
59.5 100 105 110 115 120 125 130 135 140 145 150
Water temperature (
)
Fig. 15. Entrainment ratio and entrainment efficiency with water temperature at the Wnet_max.
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51276122). References Chen, H.J., Goswami, D.Y., Stefanakos, E.K., 2010. A review of thermodynamic cycles and working fluids for the conversion of lowgrade heat. Renew. Sust. Energy Rev. 14, 3059–3067. Dai, Y.P., Wang, J.F., Gao, L., 2009. Exergy analysis, parametric analysis and optimization for a novel combined power and ejector refrigeration cycle. Appl. Therm. Eng. 29, 1983–1990. Habibzadeh, A., Rashidi, M.M., Galanis, N., 2013. Analysis of a combined power and ejector-refrigeration cycle using low temperature heat. Energy Convers. Manage. 65, 381–391. He, C., Liu, C., Gao, H., Xie, H., 2012. The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Energy 38, 136–143. Heberle, F., Preißinger, M., Bru¨ggemann, D., 2012. Zeotropic mixtures as working fluids in Organic Rankine Cycles for low-enthalpy geothermal resources. Renew. Energy 37, 364–370. Hettiarachchi, H.D.M., Golubovic, M., Worek, W.M., Ikegami, Y., 2007. Optimum design criteria for an organic Rankine cycle using lowtemperature geothermal heat sources. Energy 32 (9), 1698–1706. Khaliq, A., Agrawal, B.K., Kumar, R., 2012. First and second law investigation of waste heat based combined power and ejectorabsorption refrigeration cycle. Int. J. Refrig. 35 (1), 88–97. Lakew, A.A., Bolland, O., 2010. Working fluids for low-temperature heat source. Appl. Therm. Eng. 30 (10), 1262–1268. Li, X.G., Jia, Y.M., Increasing the generation capacity of low-grade heat source by ejector in power generation system, China, 2009-10-07, ZL200910070578.3 [P]. Li, X.G., Zhao, C.C., Hu, X.C., 2012. Thermodynamic analysis of Organic Rankine Cycle with Ejector. Energy 42, 342–349.
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Li, J., Pei, G., Li, Y.Z., Wang, D.Y., Ji, J., 2012. Energetic and exergetic investigation of an organic Rankine cycle at different heat source temperatures. Energy 38, 85–95. Roy, J.P., Mishra, M.K., Misra, Ashok, 2010. Parametric optimization and performance analysis of a waste heat recovery system using Organic Rankine Cycle. Energy 35 (12), 5049–5062. Saleh, B., Koglbauer, G., Wendland, M., Fischer, J., 2007. Working fluids for low temperature organic Rankine cycles. Energy 32 (7), 1210–1221. Tamm, G., Goswami, D.Y., Lu, S., Hasan, A.A., 2004. Theoretical and experimental investigation of an ammonia–water power and refrigeration thermodynamic cycle. Sol. Energy 76 (1–3), 217–228.
Wang, J.F., Dai, Y.P., Zhang, T.Y., Ma, S.L., 2009. Parametric analysis for a new combined power and ejector-absorption refrigeration cycle. Energy 34 (10), 1587–1593. Wang, D.X., Ling, X., Peng, H., Liu, L., Tao, L.L., 2013. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy, 1–10. Xu, R.J., He, Y.L., 2011. A vapor injector-based novel regenerative organic Rankine cycle. Appl. Therm. Eng. 31 (6–7), 1238–1243. Xu, F., Goswami, D.Y., Bhagwat, S.S., 2000. A combined power/cooling cycle. Energy 25, 233–246. Zheng, B., Weng, Y.W., 2010. A combined power and ejector refrigeration cycle for low temperature heat sources. Sol. Energy 84 (5), 784–791.
Solar Energy 93 (2013) 100–108 www.elsevier.com/locate/solener
The first and second law analysis on an organic Rankine cycle with ejector Xinguo Li ⇑, Xiajie Li, Qilin Zhang Department of Thermal Engineering, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China Received 1 December 2012; received in revised form 19 March 2013; accepted 3 April 2013 Available online 4 May 2013 Communicated by: Associate Editor Yogi Goswami
Abstract In consideration of the low efficiency of the organic Rankine cycle (ORC) with low-grade heat source (LGHS), an organic Rankine cycle with ejector (EORC) and a double organic Rankine cycle (DORC) based on the ORC is introduced in this paper. The thermodynamic first law and second law analysis and comparison on the ORC, EORC and DORC cycles are conducted on the cycle’s power output, thermal efficiency, exergy loss and exergy efficiency. Water is chosen as the LGHS fluid, and the same temperature and mass flow rate of the water is the standard condition for the comparative analysis on the cycles. The emphasis is on the thermodynamic performance at the maximum net power output of the cycles. The results show the power output is higher in the EORC and DORC compared to the ORC. And the cycle’s exergy efficiency could be ranked from high to low: DORC > EORC > ORC. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Organic Rankine cycle with ejector (EORC); Double organic Rankine cycle (DORC); Ejector; Thermodynamic analysis
1. Introduction The low-grade heat source (LGHS), such as solar energy, geothermal energy, biomass energy, and waste heat from various thermal processes, exists in the world extensively. Generally, the LGHS could be converted to power by the organic Rankine cycle (ORC), but the low efficiency of the ORC with LGHS has limited its wide use. The research on the ORC is mainly focused on the thermodynamic analysis, the selection of the working fluids, and the optimization of the system. The selection of the working fluids is very important and significant to the research and application of the ORC (Lakew and Bolland, 2010; Roy et al., 2010; Hettiarachchi et al., 2007; Saleh et al., 2007; Heberle et al., 2012; Chen et al., 2010; He et al., 2012; Wang et al., 2013; Li et al., 2012). Chen et al. (2010) presented a review of the ORC and supercritical Rankine cycle for the conversion of low-grade ⇑ Corresponding author. Tel.: +86 022 27890058.
E-mail address: [email protected] (X. Li). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.04.003
heat into power, as well as selection criteria of potential working fluids. The thermodynamic and physical properties and environmental impacts, etc. of the working fluids were evaluated. He et al. (2012) calculated the optimal evaporation temperature of the ORC that the larger net power output would be produced when the critical temperature of working fluid approached to the temperature of the waste heat source. Wang et al. (2013) analyzed the influence of working fluid properties on the thermal efficiency of ORC, and the optimal operation condition and exergy destruction for various heat source temperatures. It was unadvisable to always pursue high thermal efficiency for LGHS. Li et al. (2012) investigated the energetic and exergetic performance of the ORC at different heat source temperatures. A combined ORC or Rankine cycle and ejector refrigeration cycle by LGHS was investigated. This combined power and cooling cycle originally was proposed by Xu et al. (2000), and Tamm et al. (2004) that the cycle could produce both power and refrigeration simultaneously and achieved high thermal efficiency.
X. Li et al. / Solar Energy 93 (2013) 100–108
101
Nomenclature E h m Q r s T u W
exergy (kW) specific enthalpy (kJ kg1) mass flow rate (kg s1) heat transfer (kW) exergy loss ratio specific entropy (kJ kg1 K1) temperature (K) mass flow ratio in the first-stage evaporator or the entrainment ratio of the ejector power output (kW)
Greek symbols g efficiency (%) Subscripts cond (c) condensation eje ejector
Wang et al. (2009), and Dai et al. (2009) proposed a combined the Rankine cycle and the ejector-absorption refrigeration cycle, in which an ejector was introduced between the rectifier and the condenser to provide a performance improvement. Optimal thermal parameters were done using genetic algorithm and the optimized exergy efficiency was 43% for a given condition. And the biggest exergy loss was due to the irreversibility occurred in the heat addition processes, and the ejector caused the next largest exergy loss. Zheng and Weng (2010) proposed a combined the ORC and the ejector refrigeration cycle. The ejector was driven by the exhausts from the turbine to produce power and refrigeration simultaneously, and most exergy losses took place in the ejector. Xu and He (2011) proposed a regenerative organic Rankine cycle (RORC) that used a vapor injector as the regenerator. Results indicated that there existed the inlet vapor pressure regions for the injector that allowed the RORC performed better than the basic ORC. Habibzadeh et al. (2013) presented a thermodynamic study on the combined ORC and the ejector refrigeration cycle with working fluids of R123, R141b, R245fa, R600a, R601a for the power to refrigeration ratio of 10. R141b had the lowest optimum pressure and smallest total thermal conductance, and R601a had the highest thermal efficiency and lowest total exergy destruction. Khaliq et al. (2012) proposed a cogeneration cycle with a LiB–H2O absorption refrigeration cycle employed to the combined power and ejector refrigeration cycle. Results showed that around 53.6% of the total input exergy was destroyed due to irreversibilities in the components, 22.7% was available as a useful exergy output, and 23.7% was exhaust exergy lost to the environment, whereas energy distribution showed 44% was exhaust energy and 19.7% was useful energy output. The low efficiency of ORC with LGHS has limited its wide use in industry. Increasing the ORC’s power output
evap (e) evaporation ex exergy exp expander in inlet loss exergy loss max maximum mix mixed fluid in ejector oc environment opt optimal out outlet net net output pf primary fluid in ejector sf secondary fluid in ejector sum sum th thermal w water wf working fluid
and efficiency was the objective of the ORC research. Based on this purpose, an organic Rankine cycle with ejector (EORC) was proposed in our early researches (Li et al., 2012; Li and Jia, 2009). In the reference (Li et al., 2012), the configuration and processes of the EORC was described, and a preliminary first law analysis on the net power output and thermal efficiency was conducted with R600 only at water temperature of 80 °C. A further thermodynamic first law and second law analysis and comparison on the EORC would be necessary especially for the exergy analysis on the ejector in the EORC. 2. Principle of organic Rankine cycle with ejector (EORC) In the EORC, an ejector and a second-stage evaporator are added to the ORC, as shown in Figs. 1 and 2. The
LGHS
Expander
1 First-stage evaporator
6 Second-stage evaporator
3 Fluid pump
2
7 Condenser
5
4
Ejector
Fig. 1. Configuration and processes of organic Rankine cycle with ejector (EORC).
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T
T
P e1
P e1
1
P e2
P e2
2
6
1 2
6
7
7 4
Pc
Pc
5
5 3
s
s
Fig. 2. T–S diagram of the EORC.
Fig. 4. T–S diagram of the DORC.
vapor from the second-stage evaporator works as the primary fluid for the ejector to induce the exhaust from the expander so as to decrease the expander backpressure and increase the pressure difference in the expander, which results in an increase of the power output of the ORC. In order to analyze and compare the thermal performance of the EORC, a double organic Rankine cycle (DORC) Li et al., 2012 is also introduced in the paper, as shown in Figs. 3 and 4. 3. Thermodynamic analysis on the ORC, EORC and DORC The thermodynamic analysis and comparison on the ORC, EORC and DORC will be conducted in this paper. An idealized thermodynamic process of the cycles is assumed and considered as no pressure loss, no heat loss, and isentropic processes are assumed for the expander and the pump. The calculation programs for the cycle’s thermodynamic performance are built based on the refrigerant’s physical properties by REFPROP from NIST on Matlab. The calculated thermodynamic performances are: power output from the expander (Wout), pumping power (Wpump), net power output (Wnet), thermal efficiency (gth), exergy loss
1
LGHS
(Eloss) and exergy efficiency (gex), and operating condition parameters. 3.1. Specifications and conditions for calculation (1) R245fa is chosen as the working fluid for it is a generally accepted working fluid for the ORC. (2) Water is chosen as the LGHS fluid, and the water temperature is selected in a range of 95–150 °C and a typical temperature of 95 °C, and the mass flow rate of water is 1 kg/s. The same temperature and mass flow rate of the water is the standard condition for the comparative analysis on the cycles. (3) The outlet of the working fluid from the evaporator is set to saturated vapor. (4) In the evaporator, the bubble point of the working fluid is set as the pinch point, and the pinch point temperature difference between the heat source water and the working fluid is set to 5 °C. (5) The outlet of working fluid from the condenser is set to saturated liquid, and the bubble temperature of working fluid in the condenser is set to 35 °C. (6) The environment state is set to: poc = 101.325 kPa, Toc = 298.15 K.
3.2. First law analysis
First-stage evaporator
2 6
3 3' 4
The evaporation heat (Qevap) from the heat source water in the evaporator is:
Expander
Qevap ¼ mwf ðhevap– out hevap– in Þ
Second-stage evaporator
ð1Þ
The condensation heat (Qcond) in the condenser is: 7
3'
Fluid pump
5
Condenser
3
4
Qcond ¼ mwf ðhcond– in hcond– out Þ
ð2Þ
The power output (Wout) from the expander is: W out ¼ mwf ðhexp– in hexp– out Þ
ð3Þ
The pumping power (Wpump) by the pump is: Fig. 3. Configuration and processes of double organic Rankine cycle (DORC).
W pump ¼ mwf ðhpump– out hpump– in Þ
ð4Þ
X. Li et al. / Solar Energy 93 (2013) 100–108
103
8
90
7
12
Entrainment ratio
Net power output (kW)
Entrainment efficiency
10 8 DORC
6
EORC ORC
4
80
Entrainment ratio
70
6
60
5
50 4 40 3
30
2
20
1
10 0
0 50
2 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
)
)
Fig. 5. Net power output with Te1 at water temperature of 95 °C.
Fig. 8. Entrainment ratio and entrainment efficiency with Te1 at water temperature of 95 °C.
12
1 ORC
10
Exhaust water
0.9
Exergy loss rate in ORC
Thermal efficiency (%)
Entrainment efficiency (%)
14
DORC EORC
8
6
4
Evaporator
0.8
Condenser
0.7 0.6 0.5 0.4 0.3 0.2 0.1
2 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
0
85
50
55
)
60
65
70
75
Evaporation temperature of Te1 (
Fig. 6. Thermal efficiency with Te1 at water temperature of 95 °C.
80
85
)
Fig. 9. Exergy loss ratio in each component of the ORC with Te1 at the Wnet_max at water temperature of 95 °C.
220 0.6
Exergy loss rate in EORC
Evaporation heat (kW)
190 160 Qe1 or ORC_Qe
130
EORC_Qe_sum EORC_Qe2
100
DORC_Qe_sum
70
DORC_Qe2
40
First-stage evaporator Second-stage evaporator
0.5
Ejector Condenser
0.4
Exhaust water
0.3 0.2 0.1
10 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
85
0 50
)
55
60
65
70
75
Evaporation temperature of Te1 (
Fig. 7. Evaporation heat with Te1 at water temperature of 95 °C.
80
85
)
Fig. 10. Exergy loss ratio in each component of the EORC with Te1 at the Wnet_max at water temperature of 95 °C.
The net power output (Wnet) of the cycle is: W net ¼ W out W pump
Exergy equations: ð5Þ (1) The exergy of heat source water inlet to the evaporator is:
The thermal efficiency (gth) of the cycle is: gth ¼ W net =Qevap
ð6Þ
3.3. Second law analysis The concept of exergy related to the maximum work (or power) output that could theoretically be obtained from any state of the system relative to the given environment.
Ew– in ¼ mw ðhw– in hoc T oc ðsw– in soc ÞÞ
ð7Þ
(2) The exergy of heat source water outlet from the evaporator is: Ew– out ¼ mw ðhw– out hoc T oc ðsw– out soc ÞÞ
ð8Þ
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X. Li et al. / Solar Energy 93 (2013) 100–108 45
First-stage evaporator Second-stage evaporator Condenser Exhaust water
0.5
40
Exergy efficiency (%)
Exergy loss rate in DORC
0.6
0.4 0.3 0.2
35 30 25 DORC
20
EORC
15
0.1
ORC
10
0 50
55
60
65
70
75
Evaporation temperature of Te1 (
80
50
85
55
60
65
70
75
Evaporation temperature of Te1 (
)
Fig. 11. Exergy loss ratio in each component of the DORC with Te1 at the Wnet_max at water temperature of 95 °C.
(3) The exergy loss in the evaporator, including the exergy loss in the working fluid and the heat source water:
80
85
)
Fig. 12. Exergy efficiency of the ORC, EORC and DORC with Te1 at the Wnet_max at water temperature of 95 °C.
ri ¼ Eloss– i =Eloss– total
ð13Þ
(8) The exergy efficiency of the cycle is: Eloss– evap ¼ exergy loss in the working fluid þ exergy loss in the heat source water ¼ T oc ðmwf ðsevap– out sevap– in Þ þ mw ðsw– out sw– in ÞÞ
gex ¼ 1 Eloss– total =Ew– in ð9Þ
(4) The exergy loss in the condenser, calculated by the exergy difference of the inlet to the outlet of the condenser by the working fluid, included the heat exergy by the condensation heat released to the environment: Eloss– cond ¼ exergy inlet to the condenser exergy outlet from the condenser ¼ mwf ððhcond– in hoc Þ T oc ðscond– in soc ÞÞ mwf ððhcond– out hoc Þ T oc ðscond– out soc ÞÞ ¼ mwf ððhcond– in hcond– out Þ T oc ðscond– in scond– out ÞÞ
ð10Þ
(5) The exergy loss in the ejector, calculated by the entropy increase from the inlet to the outlet in the ejection process by the working fluid: Eloss– eje ¼ mwf T oc ðseje– mix seje– sf u=ðu þ 1Þ seje– pf =ðu þ 1ÞÞ
ð11Þ
(6) The total exergy loss of the cycle is: Eloss– total ¼ Eloss– evap þ Eloss– cond þ Eloss– eje þ Ew– out
ð12Þ
(7) The exergy loss ratio in each component of the cycle is:
ð14Þ
4. Results and discussion 4.1. Performance and comparison at water temperature of 95 °C Figs. 5–12 present the net power output (Wnet), thermal efficiency (gth) and the exergy analyses on the ORC, EORC and DORC with the first-stage evaporation temperature (Te1) at the same water temperature of 95 °C. 4.1.1. Net power output (Wnet) The Wnet of cycles increases and then decreases with the first-stage evaporation temperature (Te1), and there exists the maximum net power output (Wnet_max), as shown in Fig. 5, which is 10.57 kW for ORC, 11.68 kW for EORC, 12.80 kW for DORC respectively, and the corresponding optimal first-stage evaporation temperature (Te1_opt) is 63.11 °C, 65.61 °C, 71.63 °C, as shown in Table 1. And the Wnet of the cycles can be ranked from high to low: DORC > EORC > ORC. 4.1.2. Thermal efficiency (gth) As shown in Fig. 6, the thermal efficiency (gth) of the ORC increases with the Te1 almost linearly. The gth of EORC and DORC increases and then decreases with the Te1, and there also exists the maximum of gth (gth_max), which is 6.21% for EORC and 7.81% for DORC, and its corresponding Te1 is 69.32 °C, 82.54 °C respectively. In summary, the power output is higher in the EORC and DORC compared to the ORC. The power output and thermal efficiency of the DORC is superior to the EORC, but another expander-generator and its auxiliary equipments is required for DORC led to the increase of
X. Li et al. / Solar Energy 93 (2013) 100–108
105
Table 1 Performance comparison between ORC, EORC and DORC at the maximum net power output (Wnet_max) at water temperature of 95 °C. Unit
ORC
EORC
DORC
kg/s °C °C °C
1 95 61.81 /
1 95 64.31 49.55
1 95 70.75 53.68
Temperature (Te1) Pressure (Pe1) Mass flow rate (mwf1) Temperature (Te2) Pressure (Pe2) Mass flow rate (mwf2) Temperature (Tc) Pressure (Pc) Mass flow rate
°C bar kg/s °C bar kg/s °C bar kg/s /
63.11 5.05 0.68 / / / 35 2.12 0.68 /
65.61 5.41 0.63 45.66 3.01 0.32 35 2.12 0.95 1.95
71.63 6.37 0.49 50.52 3.50 0.37 35 2.12 0.85 1.33
Pressure Temperature Pressure Temperature Pressure Temperature
bar °C bar °C bar °C /
/ / / / / / 2.38
3.01 45.66 1.90 37.19 2.12 39.61 2.85
/ / / / / / 3 and 1.65
First-stage (Qe1) Second-stage (Qe2) The sum (Qe_sum)
Condensation heat (Qcond) Power output from expander (Wout) Pumping power (Wpump) Maximum net power output (Wnet_max) Thermal efficiency (gth) Exergy efficiency (gex)
kW kW kW kW kW kW kW % %
139.26 / 139.26 128.69 10.72 0.15 10.57 7.59 35.38
128.83 61.72 190.55 178.87 11.86 0.18 11.68 6.13 39.13
101.85 71.46 173.31 160.51 12.99 0.20 12.80 7.38 42.87
4. The increase Increase of the Increase of the Increase of the
% % %
/ / /
10.50 19.24 10.6
21.10 -2.77 21.17
1. Water’s parameters Water mass flow rate Water temperature inlet to evaporator Water temperature outlet from evaporator 2. Cycle parameters of R245fa as the working fluid First-stage evaporation
Second-stage evaporation
Condensation
First-stage Second-stage
Mass flow ratio in the first-stage evaporator or the entrainment ratio of the ejector (u) Ejector Primary fluid Second fluid Mixed fluid Pressure ratio (inlet/outlet) in expander 3. Performance of the cycles Evaporation heat (Qe)
of performance compared to ORC Wnet_max gth gex
the investment and operation management compared to the EORC. 4.1.3. Evaporation heat (Qe) and effect on the thermal efficiency (gth) Fig. 7 presents the variation of the evaporation heat (Qe) with the Te1. At the same Te1, the evaporation heat in the first-stage (Qe1) for the EORC and DORC is the same as the evaporation heat in the ORC. The variation of the evaporation heat in the second-stage (Qe2) for EORC and DORC is very similar, but the Qe2 in the EORC is higher than that in the DORC in most evaporation temperature range, so the sum evaporation heat (Qe_sum) in the EORC is higher than the DORC. The variation of thermal efficiency (gth) of the ORC is different from the EORC and DORC, as shown in Fig. 6, which could be derived and explained from the combination of the net power output (Wnet) and the evaporation heat (Qe) for the gth is the Wnet divided by the Qe.
It is found that the negative slope or the decrease tendency of the evaporation heat in the ORC is higher than that in the EORC and DORC due to the Qe2. And the positive slope of the Qe2 increases with the Te1 that causes the negative slope of the Qe_sum in the EORC and DORC not to increase, but maintain almost the same. Especially the negative slope of the Qe in the ORC increases with the evaporation temperature. With the Te1 higher than the optimal Te1_opt, which is 63.11 °C, 65.61 °C, 71.63 °C for the ORC, EORC and DORC respectively, the Wnet decreases, but the negative slope of the Qe in the ORC is higher than the negative slope of the Wnet with the evaporation temperature, the gth of the ORC does not decrease, but increase. For the negative slope of the Qe_sum in the EORC and DORC does not to increase, but maintain almost the same, that makes the gth of the EORC and DORC different from the ORC, and exists the maximum of gth_max, which is similar as the variation of the Wnet.
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X. Li et al. / Solar Energy 93 (2013) 100–108
Table 2 Exergy loss in each component of the ORC, EORC and DORC at the maximum net power output (Wnet_max) at water temperature of 95 °C. Exergy loss
ORC
EORC
Eloss (kW)
r
Ranking
Eloss (kW)
r
Ranking
Eloss (kW)
r
Ranking
First-stage evaporator Second-stage evaporator Total exergy loss in the two evaporators Condenser Ejector Exhaust water Total exergy loss
6.310 / 6.310 4.197 / 8.789 19.296
0.327 / 0.327 0.218 / 0.455 1
2 / / 3 / 1 /
5.55 2.04 7.57 5.84 0.75 4.01 18.17
0.31 0.11 0.42 0.32 0.04 0.22 1
2 4 / 1 5 3 /
3.95 2.46 6.41 5.24 / 5.42 17.07
0.23 0.14 0.37 0.31 / 0.32 1
3 4 / 2 / 1 /
4.1.4. Entrainment ratio and entrainment efficiency of the ejector in EORC Fig. 8 presents the entrainment ratio and the entrainment efficiency of the ejector in EORC with the Te1 at water temperature of 95 °C. The ranges of the entrainment ratio and the entrainment efficiency are 0.26–7.46 and 21–82.73% respectively within the Te1 of 50–85 °C. At the Wnet_max with the Te1_opt of 65.61 °C, the entrainment ratio and the entrainment efficiency are 1.95% and 61.84% respectively. 4.1.5. Exergy loss At the maximum net power output (Wnet_max) at water temperature of 95 °C, the exergy loss ratio in each component of the ORC, EORC and DORC with the Te1 are shown in Figs. 9–11. The results show that the exergy loss ratio decreases in the evaporator, while it increases in the exhaust water with the Te1. It is found that the increase tendency or the slope of the exhaust water’s exergy loss ratio in the ORC is higher than that in the EORC and DORC with the Te1, as shown in Figs. 9–11. This phenomenon could be explained from the variation of the evaporation heat (Qe), which is presented in Section 4.1.3 with Fig. 7, that the decrease tendency or the negative slope of the ORC’s Qe is higher than that of the EORC and DORC. The less the evaporation heat is consumed from the heat source water, the more the heat with a higher temperature will be remained and discharged in the exhaust water, so that the more exergy loss in the exhaust water is resulted in the ORC compared to the EORC and DORC. 4.1.5.1. Exergy loss in the ORC. As shown in Fig. 9, the exergy loss ratio in the condenser of the ORC decreases with the evaporation temperature due to the decrease of the mass flow rate of the working fluid. 4.1.5.2. Exergy loss in the EORC. As shown in Fig. 10, the exergy loss ratio in the first-stage evaporator decreases with the Te1, while it increases in the ejector and in the exhaust water, and it increases and then decreases in the secondstage evaporator and the condenser, which is due to the flow rate of the working fluid in the two evaporators. At the maximum net power output (Wnet_max), the most exergy losses takes place in the evaporator, condenser and the exhaust water, while it is the smallest in the ejector, and it is only 4% of the total exergy loss, as shown in Table 2.
DORC
The exergy loss in the evaporator and condenser is high due to the high evaporation temperature in the evaporator, and the heat exergy by the condensation heat released to the environment in the condenser. The ejector’s exergy loss is the cause of the irreversible processes in the ejection process. And a further investigation on the ejector’s exergy loss is necessary to verify this calculation. 4.1.5.3. Exergy loss in the DORC. As shown in Fig. 11, the exergy loss ratio in the first-stage evaporator decreases, while it increases in the second-stage evaporator and in the exhaust water, and it increases and then decreases in the condenser. The exergy loss in each component of the ORC, EORC and DORC at the maximum net power output (Wnet_max) is listed in Table 2. The ratio or the weighting of the exergy loss in each component of the cycles is different with the cycle type. Ranking the exergy loss in the evaporator and the condenser of the cycles from high to low is: EORC > DORC > ORC, and it is: ORC > DORC > EORC in the exhaust water. The reasons are that the evaporation heat and the flow rate of the working fluid in EORC are higher than that in DORC, and the temperature inlet to the condenser in the EORC is higher than that in the DORC due to the irreversible ejection process in EORC. The higher the temperature of the exhaust water is, the higher the exergy loss in the exhaust water is. 4.1.6. Exergy efficiency Fig. 12 shows the exergy efficiency (gex) of the ORC, EORC and DORC with the Te1. It reveals that the variation of the gex is consistent with the net power output (Wnet), and there also exists the maximum exergy efficiency (gex_max) with the Te1, which is 35.38% and 63.11 °C for ORC, 39.13% and 65.61 °C for EORC and 42.87% and 71.63 °C for DORC respectively, as shown in Table 1. And this gex_max condition is also the same condition of the maximum net power output (Wnet_max). At the same Te1, the gex of the cycles could be ranked from high to low: DORC > EORC > ORC, which is the same as the Wnet of the cycles. 4.2. Performance and comparison with different water temperature Figs. 13 and 14 present the maximum net power output (Wnet_max) and the corresponding thermal efficiency (gth) of
Maximum net power output (kW)
X. Li et al. / Solar Energy 93 (2013) 100–108
61.84% respectively in the water temperature of 95– 150 °C.
50 DORC
45
EORC
40
ORC
5. Conclusions
35 30 25 20 15 10 95
100
105
110
115
120
125
130
Water temperature (
135
140
145
150
)
Fig. 13. The maximum net power output (Wnet_max) with water temperature.
14 ORC
13
Thermal efficiency (%)
107
DORC
12
EORC
11 10 9
(1) The power output is higher in the EORC and DORC compared to the ORC. The power output and thermal efficiency of the DORC is superior to the EORC, but another expander-generator and its auxiliary equipments is required for the DORC led to the increase of the investment and operation management compared to the EORC. (2) Ranking the exergy loss ratio in the evaporator and the condenser of the cycles from high to low is: EORC > DORC > ORC, and it is: ORC > DORC > EORC in the exhaust water. (3) The cycle’s exergy efficiency can be ranked from high to low: DORC > EORC > ORC. (4) At the maximum net power output, the most exergy losses took place in the evaporator, condenser and the exhaust water, while it is the smallest in the ejector in the EORC cycle.
8 7
Acknowledgement
6 95
100
105
110
115
120
125
130
Water temperature (
135
140
145
150
)
Fig. 14. Thermal efficiency with water temperature at the Wnet_max.
the ORC, EORC and DORC in water temperature of 95– 150 °C. The Wnet_max and gth increase with the water temperature almost linearly, and these results and analyses are similar to the outcomes of the thermal performance of the cycles at water temperature of 95 °C. Fig. 15 shows the entrainment ratio and the entrainment efficiency of the ejector in EORC with water temperature at the Wnet_max. The ranges of the entrainment ratio and the entrainment efficiency are 1.95–3.15% and 60–
3.5
62
Entrainment ratio
Entrainment ratio
3
61.5
61 2.5 60.5 2
60
1.5 95
Entrainment efficiency (%)
Entrainment efficiency
59.5 100 105 110 115 120 125 130 135 140 145 150
Water temperature (
)
Fig. 15. Entrainment ratio and entrainment efficiency with water temperature at the Wnet_max.
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