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A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power
Energy 36 (2011) 549e555
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Energy journal homepage: www.elsevier.com/locate/energy
A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power Huijuan Chen, D. Yogi Goswami*, Muhammad M. Rahman, Elias K. Stefanakos Clean Energy Research Center, College of Engineering, ENB 118, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 March 2010 Received in revised form 30 September 2010 Accepted 2 October 2010 Available online 30 October 2010
A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power is proposed and analyzed in this paper. Unlike a conventional organic Rankine cycle, a supercritical Rankine cycle does not go through the two-phase region during the heating process. By adopting zeotropic mixtures as the working fluids, the condensation process also happens nonisothermally. Both of these features create a potential for reducing the irreversibilities and improving the system efficiency. A comparative study between an organic Rankine cycle and the proposed supercritical Rankine cycle shows that the proposed cycle can achieve thermal efficiencies of 10.8e13.4% with the cycle high temperature of 393 Ke473 K as compared to 9.7e10.1% for the organic Rankine cycle, which is an improvement of 10e30% over the organic Rankine cycle. When including the heating and condensation processes in the system, the system exergy efficiency is 38.6% for the proposed supercritical Rankine cycle as compared to 24.1% for the organic Rankine cycle. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Supercritical Rankine cycle Zeotropic mixture Organic Rankine cycle Low-grade heat
1. Introduction Low-grade heat such as geothermal, waste heat, and heat from low to mid temperature solar collectors, accounts for 50% or more of the total heat generated worldwide [1]. Due to the fact that conventional steam Rankine cycle does not allow efficient energy conversion at low temperatures [1e5], organic Rankine cycle (ORC) has been extensively studied for the conversion of low-grade heat into power for its simplicity and relatively high efficiency [1e15]. However, an important limitation of the ORC with a pure working fluid is the isothermal boiling, which creates a bad thermal match between the working fluid and the heat source due to the pinch point, leading to large irreversibilities. Use of mixtures [16e23] and supercritical fluids [24e26] can reduce this problem. Supercritical Rankine cycles (SRC) have been studied to improve the performance of the energy conversion at low temperatures [26e29]. In contrast to a conventional ORC, the working fluid of an SRC is heated directly from liquid state into supercritical state, bypassing the two-phase region, which allows it to have a better thermal match with the heat source, resulting in less exergy destruction [28]. Furthermore, in a conventional ORC, the boiling
* Corresponding author. Tel.: þ1 813 974 0956; fax: þ1 813 974 5250. E-mail address: [email protected] (D.Y. Goswami). 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.006
system requires specialized equipment to separate the vapor phase from the liquid phase, while a supercritical system simplifies that. The choice of working fluids is of key importance for the performance of an SRC. Carbon dioxide has been studied as the working fluid of SRCs by a number of investigators [25,30,31]. Zhang et al. [32,33] conducted research on a CO2-based SRC, and reported the power generation efficiency of the cycle to be 8.0%e 11.4%, depending on the working condition. Chen et al. [29] did a comparative study between a CO2-based SRC and an R123-based ORC, finding that under the same thermodynamic mean heat rejection temperature, the CO2-based SRC gives a slightly higher power output than the R123-based ORC. However, the CO2-based SRC operates under pressures as high as 16 MPa, while condensing the carbon dioxide is also a challenge due to its low condensation temperature. Beside carbon dioxide, fluids such as hydrocarbons [32] and refrigerants R134a, R227ea, R236fa and R245fa have also been studied as the working fluids in SRCs, and the results showed that the thermal efficiency could improve by 10%e20%, compared to the same working fluids used in ORCs [4,28,33e35]. A review of the literature shows that all of the research on SRCs has been limited to pure fluids. While SRC using a pure working fluid does overcome the pinch point limitations of ORCs during the heating process, the condensation process is still isothermal. Our research introduces the novel concept of using zeotropic mixtures as the working fluids in an SRC, which results in much lower exergy destruction during both boiling and condensation, and, therefore,
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higher efficiencies. This study compares the performance of a conventional ORC with a zeotropic mixture-based SRC under the same temperature limits, which shows the advantages of the zeotropic mixture-based SRC. 2. Zeotropic mixture-based supercritical Rankine cycle 2.1. Cycle configuration and processes Fig. 1 shows the basic configuration and a T-s diagram of the proposed SRC. The working fluid is pumped above its critical pressure, and then heated from the liquid to the supercritical state directly; the supercritical fluid expands in the turbine, generating power; the exhaust fluid from the turbine is condensed, thus completing the cycle. The proposed SRC using zeotropic mixtures as the working fluids has two important features: in the heating process (process 2/3 in Fig. 1(b)), the working fluid is heated directly to a supercritical state from the liquid phase; and in the condensation process (process 4/1 in Fig. 1(b)), the working fluid is condensed isobarically but non-isothermally. Both of these features results in temperature glides which allow us to reduce irrversibilities of the heat transfer processes during the heating and condensation. 2.2. Zeotropic mixtures as the working fluids Zeotropic mixtures of refrigerants are the potential candidates for the proposed SRC due to their thermophysical properties and stability. Over 50 refrigerants were considered, however, some of them were rejected due to environmental concerns [36]. Beside the environmental concerns, some refrigerants are not suitable because of their thermophysical properties, such as a low critical temperature, which would be a challenge for the condensation process [37]. In consideration of their environmental impacts and thermophysical properties, 22 refrigerants, listed in Table 1, are screened as the potential candidates for designing the zeotropic mixtures. In order to take advantage of non-isothermal condensation, only those mixtures that can create thermal glides greater than 3 K during the condensation process are considered. 3. Comparative study of an organic Rankine cycle and the proposed supercritical Rankine cycle In order to investigate the performance of the proposed SRC with zeotropic mixture working fluids, it was compared with an ORC over the same temperature range. A zeotropic mixture of R134a and R32 (0.7/0.3, mass fraction) is used as the working fluid
of the SRC, while pure R134a is considered as the working fluid of the ORC. A zeotropic mixture of 0.7R134a and 0.3R32 is considered safe and environmentally friendly and has been used in refrigeration systems [36], while pure R134a is often used as the working fluid of ORCs [1,9,38] and refrigeration cycles. A T-s diagram of an ORC using R134a as the working fluid is shown in Fig. 2, while an SRC using the zeotropic mixture of 0.7R134a/0.3R32 is shown in Fig. 3. The thermal efficiencies and the net work output of the thermodynamic cycles, the exergy efficiencies of the condensing processes, and the exergy efficiencies of the heating processes are analyzed in this section for both cycles with the cycle high temperature in the range of 393 Ke473 K. Properties of the working fluids for this simulation are obtained by process simulation software ChemCADÒ and NIST database. 3.1. Thermal efficiencies and net work outputs of the cycles The thermal efficiencies and the net work outputs of the two cycles are investigated for the turbine inlet temperature of 393 Ke473 K and average condensing temperature of 309.5 K. The pump and turbine efficiencies are set both at 85% for both cycles. The cycle high pressure of the 134a-based ORC is set to be 3.3 MPa (critical pressure 4.06 MPa), and that of the zeotropic mixture-based SRC is 7 MPa (critical pressure 5.13 MPa) in the simulation. The low pressures of the cycles are determined by the average condensation temperature of 309.5 K. The computed thermal efficiencies of the ORC and the SRC are shown in Fig. 4(a). Over the investigated cycle high temperature range (393 Ke473 K), the thermal efficiency of the ORC using pure R134a is 9.70e10.13%, while that of the SRC using the zeotropic mixture is 10.77e13.35%, showing 10e30% increase over the R134a-based ORC. Fig. 4(a) also shows that the thermal efficiency of the R134a-based ORC has no significant increase as the cycle high temperature is increased from 393 K to 473 K. The above simulations were based on constant cycle high pressures. Computations were also made with changing cycle high pressures in order to optimize the cycle thermal efficiencies. Assuming the minimum vapor quality at the turbine exit is 90%, the optimized thermal efficiency of the SRC is shown with a dotted line in Fig. 4(a). Comparing it with the efficiency of the SRC working at 7 MPa (continuous line in Fig. 4(a)), it is seen that there is a significant improvement at higher cycle temperatures. Fig. 4(b) shows the cycle high pressure of the SRC for optimized thermal efficiency. It is observed that in order to get the optimized thermal efficiency of 15.08% at 473 K, the pressure of the cycle is as high as 33 MPa. A high pressure like that could be a concern in real practice. The analysis of optimized thermal efficiency is only to show that there is a potential
Fig. 1. Configuration and processes of a zeotropic mixture supercritical Rankine cycle.
H. Chen et al. / Energy 36 (2011) 549e555
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Table 1 The screened 22 refrigerants for synthesizing zeotropic mixtures. ASHRAE Number
Name
Molecular Weight
Critical Temperature (K)
Critical Pressure (MPa)
GWP 100yra
ODPb
R-21 R-22 R-23 R-32 R-41 R-116 R-123 R-124 R-125 R-134a R-141b R-142b R-143a R-152a R-218 R-227ea R-236ea R-245ca R-245fa R-C318 R-3-1-10 FC-4-1-12
Dichlorofluoromethane Chlorodifluoromethane Trifluoromethane Difluoromethane Fluoromethane Hexafluoroethane 2,2-Dichloro-1,1,1-trifluoroethane 2-Chloro-1,1,1,2-tetrafluoroethane Pentafluoroethane 1,1,1,2-Tetrafluoroethane 1,1-Dichloro-1-fluoroethane 1-Chloro-1,1-difluoroethane 1,1,1-Trifluoroethane 1,1-Difluoroethane Octafluoropropane 1,1,1,2,3,3,3-Heptafluoropropane 1,1,1,2,3,3-Hexafluoropropane 1,1,2,2,3-Pentafluoropropane 1,1,1,3,3-Pentafluoropropane Octafluorocyclobutane Decafluorobutane Dodecafluoropentane
102.92 86.47 70.01 52.02 34.03 138.01 152.93 136.48 120.02 102.03 116.95 100.50 84.04 66.05 188.02 170.03 152.04 134.05 134.05 200.03 238.03 288.03
451.48 369.30 299.29 351.26 317.28 293.03 456.83 395.43 339.17 374.21 477.50 410.26 345.86 386.41 345.02 375.95 412.44 447.57 427.20 388.38 386.33 420.56
5.18 4.99 4.83 5.78 5.90 3.05 3.66 3.62 3.62 4.06 4.21 4.06 3.76 4.52 2.64 3.00 3.50 3.93 3.64 2.78 2.32 2.05
210 1700 N/A 550 97 11,900 120 620 3400 1300 700 2400 4300 120 8600 3500 9400 560 900 10,000 8600 9160
0.01 0.03 0.00 0.00 0.00 0.00 0.01 0.03 0.00 0.02 0.09 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
a GWP (Global Warming Potential) 100 yr, is a measure of how much a given mass of a gas contributes to global warming over 100 years. GWP is a relative scale which compares the greenhouse gas to Carbon dioxide where GWP by definition is 1. b ODP (Ozone Depletion Potential), is the relative amount of degradation a chemical compound can cause to the ozone layer.
for improvement of the SRC. However, the following analysis of the SRC is still based on a constant cycle high pressure of 7 MPa. The net work outputs per unit mass of working fluid of the two cycles are shown in Fig. 5. It is seen that the net work output of the SRC is higher than that of the ORC and the difference between them increases with the increase of the cycle high temperature. At 473 K, the SRC provides 38.9% more net work compared to the ORC.
3.2. Exergy efficiency of the condensing process Exergy analyses are conducted in this section to study the condensation processes of pure R134a in the ORC and the zeotropic mixture of 0.7R134a/0.3R32 in the SRC, which processes are shown in Figs. 6 and 7, respectively. The working fluids are condensed from
Fig. 2. Processes of an organic Rankine cycle using R134a as the working fluid (ⓐ/ⓑ/ⓒ/ⓓ0 /ⓓ).
saturated vapor at point ⓓ to saturated liquid at point ⓐ by dissipating the heat to the cooling fluid. The thermal matches between the working fluids and the cooling fluids are shown at on the top left corners of the figures. For the purpose of calculation, water is used as the cooling fluid in this study. The exergy analyses of the condensation processes in the two cycles are conducted under the average condensation temperature of 309.5 K. The mass flow rate of the working fluids is set at 1 kg/s, and the heat exchanger pinch limitation is set at 8 K. Based on the average condensing temperature of 309.5 K, the pure R134a is condensed isobarically at 0.92 MPa (Fig. 6), while the zeotropic mixture is condensed isobarically at 1.4 MPa with the condensation commencing at a temperature of 312.37 K (point ⓓ in Fig. 7) and ending at a temperature of 306.6 K (point ⓐ in Fig. 7).
Fig. 3. Processes of a supercritical Rankine cycle using the zeotropic mixture of R134a and R32 as the working fluid (ⓐ/ⓑ/ⓒ/ⓓ0 /ⓓ).
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Fig. 5. Net work outputs of the R134a-based organic Rankine cycle (ORC) and the zeotropic mixture-based supercritical Rankine cycle (SRC).
their temperatures and fluid types. The flow rate of the cooling water is calculated to be 8.37 kg/s from equation (1). The net change in the flow exergy rate from saturated vapor (point ⓓ in Fig. 7 to saturated liquid point ⓐ in Fig. 7) for the zeotropic mixture is computed to be 383.05 kW using the following equation, neglecting the effects of motion and gravity [39]: ˇ
ˇ
ⓓa
h d T0 s s ⓐa
ˇ
ˇ
ⓐa
_ zeo ¼ m
ⓓa
ˇ
a ⓐ
ˇ
_ zeo e e DE_ zeo ¼ m
ⓓa
(2) where T0 is the dead-state temperature, 273K. Similarly, the change in the flow exergy rate from the inlet to the outlet for the cooling water is found to be 312.72 kW by using the following equation (3):
Fig. 4. Thermal efficiencies of the R134a-based organic Rankine cycle (ORC) and the zeotropic mixture-based supercritical Rankine cycle (SRC).
Since the zeotropic mixture creates a thermal glide when condensed isobarically, the heat exchange process can be designed such that the temperature profile of the cooling water parallels that of the working fluid to obtain the best thermal match. Under this design, the mass flow rate of cooling water can be found from the energy balance of the condenser at steady state:
_ zeo h h _ water h h þ m ¼ 0 m ˇ
ˇ
a ②
ⓓa
ˇ
ˇ
a ①
ⓐa
(1)
_ water is the mass flow rate of the cooling water, h① and h② where m denote the enthalpies of the cooling water at points ① and ②, _ zeo is the mass flow rate of the respectively (See Fig. 7). Similarly, m zeotropic mixture being condensed; hⓓ and hⓐ are the enthalpies of the zeotropic mixture at points ⓓ and ⓐ, respectively. The enthalpy values of all the four points can be obtained according to
Fig. 6. Condensing process of R134a and its thermal match with the cooling fluid.
H. Chen et al. / Energy 36 (2011) 549e555
553
Table 2 Comparison of the condensation process of the two working fluids in the cycles. Working Fluid Working fluid Temperature (K) Cooling Water Temperature (K)
Point Point Point Point
Exergy Efficiency (%) a b
Fig. 7. Condensing process of the zeotropic mixture of R134a and R32 and its thermal match with the cooling fluid.
ˇ
ˇ
①a
h h ②a
ˇ
ˇ
②a
_ water ¼ m
①a
T0 s s ˇ
②a
ˇ
_ water e e DE_ water ¼ m
①a
(3) The exergetic efficiency of the heat exchange process for condensing the zeotropic mixture can then be calculated from the following equation to be 81.64%:
ˇ
ˇ
(4)
ˇ
ⓐa
ⓓa
With the same flow rate of cooling water and the aforesaid design and operating parameters, the enthalpy of the inlet cooling water (h①) in the R134a-based ORC can be found by the following equation:
_ water h h þ m _ R134a h h m ¼ 0 ˇ
ˇ
a ②
ⓓa
ˇ
ˇ
a ①
ⓓ ⓐa ①a ②a
R134a
Zeotropic mixtureb
309.5 309.5 293.7 301.5 66.55
312.4 306.6 298.6 304.4 81.64
Refer to Figs. 6 and 7 for point ⓓ, ⓐ, ② and ①. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
processes of the two cycles with the thermal match shown on the top left corners. The working fluids are heated from state ⓑ to state ⓒ by a sensible heat source in counterflow heat exchangers in both cycles. Pressurized hot water (P ¼ 0.5 MPa) at 410 K is applied as the heat source for the sake of this simulation. The working fluids in both cycles with mass flow rates of 1 kg/s are heated to 400 K, and the pinch limitation is set at 10 K. The mass flow rate of the heat source is just enough to heat the working fluids to 400 K and meet the pinch limitation of 10 K throughout the heat exchange process. In the ORC, the pinch limitation is reached at the saturated liquid point during the heating process (Fig. 8). Since there is no obvious pinch point for the zeotropic mixture, multiple points are tested during the calculation. The heating processes of the pure R134a in the ORC and the zeotropic mixture of 0.7 R134a/0.3R32 in the SRC are analyzed and the results listed in Table 3. It is seen from Table 3 that the discharge temperature of the heat source in the R134a-based ORC is 24 K higher than that in the zeotropic mixture-based SRC (point ④ in ④ Figs. 8 and 9), which indicates that the effective utilization of the heat source is much less in the R134a-based ORC than that of the 0.7R134a/0.3R32based SRC. Such result is also obvious by comparing the exergy efficiencies of the heating process of the two cycles with the SRC showing 7.30% higher exergy efficiency of the heating process than that of the pure R134a in the ORC.
ˇ
DE_ e ¼ _water DEzeo
_ water e e m a ② ①a ¼ _ mzeo e e
a
ⓐa
4. System results and discussion For a system composed of a heat source, a power cycle and a heat sink, the two systems have been studied for their performance in the heat transfer from the heat source to the power cycle, the thermal efficiency of power cycle, and the heat dissipation from the power
(5)
The net changes in the flow exergy rate of the pure R134a and its cooling water can be found through Equations (2) and (3), except that the working fluid is pure R134a. The exergetic efficiency of the heat exchange process for condensing pure R134a is calculated to be 66.55%. Detailed results of the condensation processes in both cycles are listed in Table 2. It can be observed from Table 2 that the thermal glide of the zeotropic mixture is 312.4K 306.6 K ¼ 5.8 K, while there is no thermal glide created by pure R134a. The cooling water temperature required by pure R134a is 293.7 K, which is 4.8 K lower than that of the zeotropic mixture. Exergy efficiency indicates the percentage of usable energy conserved during the condensation process. It is seen that the exergy efficiency of the 0.7R134a/0.3R32 condensation process is 22.67% higher than that of pure R134a.
3.3. Exergy efficiency of the heating process In this section, exergy analyses of the heating processes of the two cycles are carried out. Figs. 8 and 9 present the heating
Fig. 8. Heating process of R134a and its thermal match with the heat source.
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H. Chen et al. / Energy 36 (2011) 549e555 Table 4 Comparison of the efficiency between the organic Rankine cycle and the supercritical Rankine cycle.a Working fluid & Thermodynamic cycle
R134a, ORC Zeotropic mixture,b SRC
Cycle exergy efficiency(%) Condensing process exergy efficiency(%) Heating process exergy efficiency(%) System total exergy efficiency(%) a b
43.82 66.55 82.64 24.10
53.28 81.64 88.67 38.57
Computation based on the cycle high temperature of 400 K. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
5. Conclusions
Fig. 9. Heating process of the zeotropic mixture of R134a and R32 and its thermal match with the heat source.
cycle to the heat sink. The 0.7R134a/0.3R32 zeotropic mixture-based SRC shows advantages over the pure R134a-based ORC in all of the aspects that have been analyzed, the results being summarized in Table 4. Comparing the two cycles, the SRC improves the cycle thermal efficiency, exergy efficiency of the condensation process and the exergy efficiency of the heating process by 21.57%, 22.67%, and 7.30%, respectively over the ORC using R134a. The exergy efficiencies of the two systems are also calculated by multiplying the exergy efficiencies of the heating processes, the energy conversion cycle and the condensation processes of the respective system, which results are also listed in Table 4. It is noticed that the total exergy efficiency of the SRC system is 38.57%, which is a 60.04% improvement over that of the ORC (24.10%). The zeotropic mixture of 0.7R134a/0.3R32 considered as the working fluid of the SRC in this study may not always be the best choice. It can be observed from Fig. 4 that there is little gain in thermal efficiency when the cycle high temperature is beyond 433 K, which indicates that the zeotropic mixture of 0.7R134a/ 0.3R32 may be a good choice for heat sources with temperatures below 433 K, while there may be other mixtures which could perform better above 433 K. One should be able to compose other zeotropic mixtures from the screened 22 fluids in Table 1 for different temperature applications. More detailed discussion on the working fluids is given in our review on thermodynamic cycles for low-grade heat conversion [37]. Beside the temperature considerations, it is recommended that a zeotropic mixture to be used as the working fluid of an SRC should have a thermal glide during the condensation process in order to take advantage of non-isothermal condensation. Table 3 Comparison of the heating process of the two working fluids in the cycles. Working Fluid Heat Source Temperature (K) Working Fluid Temperature (K) Exergy Efficiency (%) a b
Point Point Point Point
a
③ ④a ⓑa ⓒa
R134a
Zeotropic mixtureb
410.0 355.7 309.5 400.0 82.64
410.0 331.7 306.6 400.0 88.67
Refer to Figs. 8 and 9 for point ③, ④, ⓑ and ⓒ. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
A supercritical Rankine cycle (SRC) using a zeotropic mixture as the working fluid has been proposed in this paper. The performance of the proposed cycle is investigated through a comparative study of a SRC and an ORC working under the same thermal conditions. It was found that the SRC using a zeotropic mixture of 0.7R134a/ 0.3R32 can achieve thermal efficiency of 10.77e13.35% with the cycle high temperature of 393e453 K as compared to 9.70e10.13% from an ORC using pure R134a working fluid under the same thermal conditions. The SRC using the zeotropic mixture also improves the heat exchange processes: the exergy efficiencies of the heating and condensation processes for the zeotropic mixture are 88.67% and 81.64%, respectively, as compared to 82.65% and 66.55% for the pure R134a in ORC. Overall, the system exergy efficiency of the SRC using the zeotropic mixture of 0.7R134a/0.3R32 is 38.57%, while that of the ORC using pure R134a is 24.10%. From the more than 50 refrigerants considered, 22 fluids were screened out as the potential candidates for composing zeotropic mixtures in consideration of their environmental impacts and thermophysical properties. One should be able to compose various zeotropic mixtures from these fluids for different temperature applications. It is recommended that a zeotropic mixture to be used as the working fluid of a supercritical Rankine cycle should have a certain thermal glide in the condensation process in order to take advantage of non-isothermal condensation. Acknowledgement The research leading to this paper was funded by the State of Florida through the Florida Energy Systems Consortium (FESC) funds. Appendix. Error analysis PengeRobinson Equation of State [40] was used to get the properties of the working fluid, which is:
P ¼
RT aðTÞ V b VðV þ bÞ þ bðV bÞ
where
R2 T2c aðTÞ ¼ 0:45724 alphaðTÞ Pc RTc b ¼ 0:07780 Pc 2 T alphaðTÞ ¼ 1 þ k 1 squrt Tc k ¼ 0:37464 þ 1:54226w 0:26992w2 Substituting a(T), b, alpha(T),and k into the equation of state gives:
H. Chen et al. / Energy 36 (2011) 549e555
P ¼
RT C V 0:07780RT PC
T 2 þ 0:37464 þ 1:54226w 0:26992w2 1 squrtTC RTC C C V 0:07780RT V V þ 0:07780RT RC þ 0:07780 PC PC
0:45724
R2 T2C PC 1
The acentric factor w is a constant, 0.7. Thus the equation of state of a fluid is a function of its critical temperature Tc, and critical pressure Pc. In order to validate the property of the working fluids that used in the investigation, a comparison between the data from NIST and ChemCAD is carried out in the following. The critical temperature and critical pressure data from the two data sources are tabulated below.
Data Source
NIST ChemCAD
555
R134a
R32
Tc (K)
Pc (MPa)
Tc (K)
Pc (MPa)
374.21 374.23
4.0593 4.0603
351.26 351.60
5.7820 5.8302
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 The standard division of Tc is sTc ¼ The standard division of Pc is sPc ¼
k
ðTck Tc Þ N
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 k
ðPck Pc Þ N
¼ 0:34K. ¼ 0:0482MPa.
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[17] Gawlik K, Hassani V. Advanced binary cycles: optimum working fluids. In: Energy Conversion Engineering Conference. Honolulu, HI, USA. 1997; 3:1809e1814. [18] Maizza V, Maizza A. Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems. Applied Thermal Engineering 2001;21 (3):381e90. [19] Angelino G, Colonna di Paliano P. Multicomponent working fluids for organic Rankine cycles (ORCs). Energy 1998;23(6):449e63. [20] Bliem CJ, Mines G. Supercritical binary geothermal cycle experiments with mixedhydrocarbon working fluids and a near-horizontal in-tube condenser. Report. See also: http://www.osti.gov/bridge/purl.cover.jsp;jsessionid¼05CACF73F9FBDCBD F0BAFB25CAED1A47?purl¼/6532956-3iBCz7/native/; 1989. [21] Wang X, Zhao L. Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation. Solar Energy 2009;83(5):605e13. [22] Borsukiewicz-Gozdur A, Nowak W. Comparative analysis of natural and synthetic refrigerants in application to low temperature Clausius-Rankine cycle. Energy 2007;32(4):344e52. [23] Radermacher R. Thermodynamic and heat transfer implications of working fluid mixtures in Rankine cycles. International Journal of Heat and Fluid Flow 1989;10(2):90e102. [24] Chen Y. Novel cycles using carbon dioxide as working fluid: new ways to utilize energy from low-grade heat sources. Thesis. Stockholm, Sweden: KTH; 2006. [25] Chen Y, Lundqvist P, Platell P. Theoretical research of carbon dioxide power cycle application in automobile industry to reduce vehicle’s fuel consumption. Applied Thermal Engineering 2005;25(14e15):2041e53. [26] Chen Y, Lundqvist P, Johansson A, Platell P. A comparative study of the carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working fluid in waste heat recovery. Applied Thermal Engineering 2006;26(17e18):2142e7. [27] McClanahan TS, Crim MC. Simple and compact low-temperature power cycle. U.S. patent US 2004/0,107,700 A1, Dec. 2004. [28] Karellas S, Schuster A. Supercritical fluid parameters in organic Rankine cycle applications. International Journal of Thermodynamics 2008;11 (3):101e8. [29] Zhang XR, Yamaguchi H, Uneno D, Fujima K, Enomoto M, Sawada N. Analysis of a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide. Renewable Energy 2006;31 (12):1839e54. [30] Zhang XR, Yamaguchi H, Fujima K. A feasibility study of CO2-based Rankine cycle powered by solar energy. JSME International Journal Series B (Japan Society Mechanical Engineering) 2005;48(3):540e7. [31] Cayer E, Galanis N, Desilets M, Nesreddine H, Roy P. Analysis of a carbon dioxide transcritical power cycle using a low temperature source. Applied Energy 2009;86(7e8):1055e63. [32] Ochs TL, O’Connor WK. Energy recovery during expansion of compressed gas using power plant low-quality heat sources. U.S. patent US 7,007,474 B1, Mar. 2006. [33] Chacartegui R, Sánchez D, Muñoz J, Sánchez T. Alternative ORC bottoming cycles for combined cycle power plants. Applied Energy 2009;86 (10):2162e70. [34] McMahan A, Klein SA, Reindl DT. A finite-time thermodynamic framework for optimizing solar-thermal power plants. Journal of Solar Energy Engineering 2007;129(4):355e62. [35] Etemoglu AB. Thermodynamic evaluation of geothermal power generation systems in Turkey. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 2008;30(10):905e16. [36] Powell RL. CFC phase-out: have we met the challenge? Journal of Fluorine Chemistry 2002;114(2):237e50. [37] Chen H, Goswami DY, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renewable and Sustainable Energy Reviews 2010;14(9):3059e67. [38] Kosmadakis G, Manolakos D, Kyritsis S, Papadakis G. Economic assessment of a two-stage solar organic Rankine cycle for reverse osmosis desalination. Renewable Energy 2009;34(6):1579e86. [39] Moran MJ, Shapiro HN. Fundamentals of engineering thermodynamics. 6th ed. New York: Wiley; 2007. [40] Vitu S, Jaubert J, Mutelet F. Extension of the PPR78 model (Predictive 1978, Peng-Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing naphtenic compounds. Fluid Phase Equilibria 2006;243(1):9e28.
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A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power Huijuan Chen, D. Yogi Goswami*, Muhammad M. Rahman, Elias K. Stefanakos Clean Energy Research Center, College of Engineering, ENB 118, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 March 2010 Received in revised form 30 September 2010 Accepted 2 October 2010 Available online 30 October 2010
A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power is proposed and analyzed in this paper. Unlike a conventional organic Rankine cycle, a supercritical Rankine cycle does not go through the two-phase region during the heating process. By adopting zeotropic mixtures as the working fluids, the condensation process also happens nonisothermally. Both of these features create a potential for reducing the irreversibilities and improving the system efficiency. A comparative study between an organic Rankine cycle and the proposed supercritical Rankine cycle shows that the proposed cycle can achieve thermal efficiencies of 10.8e13.4% with the cycle high temperature of 393 Ke473 K as compared to 9.7e10.1% for the organic Rankine cycle, which is an improvement of 10e30% over the organic Rankine cycle. When including the heating and condensation processes in the system, the system exergy efficiency is 38.6% for the proposed supercritical Rankine cycle as compared to 24.1% for the organic Rankine cycle. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Supercritical Rankine cycle Zeotropic mixture Organic Rankine cycle Low-grade heat
1. Introduction Low-grade heat such as geothermal, waste heat, and heat from low to mid temperature solar collectors, accounts for 50% or more of the total heat generated worldwide [1]. Due to the fact that conventional steam Rankine cycle does not allow efficient energy conversion at low temperatures [1e5], organic Rankine cycle (ORC) has been extensively studied for the conversion of low-grade heat into power for its simplicity and relatively high efficiency [1e15]. However, an important limitation of the ORC with a pure working fluid is the isothermal boiling, which creates a bad thermal match between the working fluid and the heat source due to the pinch point, leading to large irreversibilities. Use of mixtures [16e23] and supercritical fluids [24e26] can reduce this problem. Supercritical Rankine cycles (SRC) have been studied to improve the performance of the energy conversion at low temperatures [26e29]. In contrast to a conventional ORC, the working fluid of an SRC is heated directly from liquid state into supercritical state, bypassing the two-phase region, which allows it to have a better thermal match with the heat source, resulting in less exergy destruction [28]. Furthermore, in a conventional ORC, the boiling
* Corresponding author. Tel.: þ1 813 974 0956; fax: þ1 813 974 5250. E-mail address: [email protected] (D.Y. Goswami). 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.006
system requires specialized equipment to separate the vapor phase from the liquid phase, while a supercritical system simplifies that. The choice of working fluids is of key importance for the performance of an SRC. Carbon dioxide has been studied as the working fluid of SRCs by a number of investigators [25,30,31]. Zhang et al. [32,33] conducted research on a CO2-based SRC, and reported the power generation efficiency of the cycle to be 8.0%e 11.4%, depending on the working condition. Chen et al. [29] did a comparative study between a CO2-based SRC and an R123-based ORC, finding that under the same thermodynamic mean heat rejection temperature, the CO2-based SRC gives a slightly higher power output than the R123-based ORC. However, the CO2-based SRC operates under pressures as high as 16 MPa, while condensing the carbon dioxide is also a challenge due to its low condensation temperature. Beside carbon dioxide, fluids such as hydrocarbons [32] and refrigerants R134a, R227ea, R236fa and R245fa have also been studied as the working fluids in SRCs, and the results showed that the thermal efficiency could improve by 10%e20%, compared to the same working fluids used in ORCs [4,28,33e35]. A review of the literature shows that all of the research on SRCs has been limited to pure fluids. While SRC using a pure working fluid does overcome the pinch point limitations of ORCs during the heating process, the condensation process is still isothermal. Our research introduces the novel concept of using zeotropic mixtures as the working fluids in an SRC, which results in much lower exergy destruction during both boiling and condensation, and, therefore,
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higher efficiencies. This study compares the performance of a conventional ORC with a zeotropic mixture-based SRC under the same temperature limits, which shows the advantages of the zeotropic mixture-based SRC. 2. Zeotropic mixture-based supercritical Rankine cycle 2.1. Cycle configuration and processes Fig. 1 shows the basic configuration and a T-s diagram of the proposed SRC. The working fluid is pumped above its critical pressure, and then heated from the liquid to the supercritical state directly; the supercritical fluid expands in the turbine, generating power; the exhaust fluid from the turbine is condensed, thus completing the cycle. The proposed SRC using zeotropic mixtures as the working fluids has two important features: in the heating process (process 2/3 in Fig. 1(b)), the working fluid is heated directly to a supercritical state from the liquid phase; and in the condensation process (process 4/1 in Fig. 1(b)), the working fluid is condensed isobarically but non-isothermally. Both of these features results in temperature glides which allow us to reduce irrversibilities of the heat transfer processes during the heating and condensation. 2.2. Zeotropic mixtures as the working fluids Zeotropic mixtures of refrigerants are the potential candidates for the proposed SRC due to their thermophysical properties and stability. Over 50 refrigerants were considered, however, some of them were rejected due to environmental concerns [36]. Beside the environmental concerns, some refrigerants are not suitable because of their thermophysical properties, such as a low critical temperature, which would be a challenge for the condensation process [37]. In consideration of their environmental impacts and thermophysical properties, 22 refrigerants, listed in Table 1, are screened as the potential candidates for designing the zeotropic mixtures. In order to take advantage of non-isothermal condensation, only those mixtures that can create thermal glides greater than 3 K during the condensation process are considered. 3. Comparative study of an organic Rankine cycle and the proposed supercritical Rankine cycle In order to investigate the performance of the proposed SRC with zeotropic mixture working fluids, it was compared with an ORC over the same temperature range. A zeotropic mixture of R134a and R32 (0.7/0.3, mass fraction) is used as the working fluid
of the SRC, while pure R134a is considered as the working fluid of the ORC. A zeotropic mixture of 0.7R134a and 0.3R32 is considered safe and environmentally friendly and has been used in refrigeration systems [36], while pure R134a is often used as the working fluid of ORCs [1,9,38] and refrigeration cycles. A T-s diagram of an ORC using R134a as the working fluid is shown in Fig. 2, while an SRC using the zeotropic mixture of 0.7R134a/0.3R32 is shown in Fig. 3. The thermal efficiencies and the net work output of the thermodynamic cycles, the exergy efficiencies of the condensing processes, and the exergy efficiencies of the heating processes are analyzed in this section for both cycles with the cycle high temperature in the range of 393 Ke473 K. Properties of the working fluids for this simulation are obtained by process simulation software ChemCADÒ and NIST database. 3.1. Thermal efficiencies and net work outputs of the cycles The thermal efficiencies and the net work outputs of the two cycles are investigated for the turbine inlet temperature of 393 Ke473 K and average condensing temperature of 309.5 K. The pump and turbine efficiencies are set both at 85% for both cycles. The cycle high pressure of the 134a-based ORC is set to be 3.3 MPa (critical pressure 4.06 MPa), and that of the zeotropic mixture-based SRC is 7 MPa (critical pressure 5.13 MPa) in the simulation. The low pressures of the cycles are determined by the average condensation temperature of 309.5 K. The computed thermal efficiencies of the ORC and the SRC are shown in Fig. 4(a). Over the investigated cycle high temperature range (393 Ke473 K), the thermal efficiency of the ORC using pure R134a is 9.70e10.13%, while that of the SRC using the zeotropic mixture is 10.77e13.35%, showing 10e30% increase over the R134a-based ORC. Fig. 4(a) also shows that the thermal efficiency of the R134a-based ORC has no significant increase as the cycle high temperature is increased from 393 K to 473 K. The above simulations were based on constant cycle high pressures. Computations were also made with changing cycle high pressures in order to optimize the cycle thermal efficiencies. Assuming the minimum vapor quality at the turbine exit is 90%, the optimized thermal efficiency of the SRC is shown with a dotted line in Fig. 4(a). Comparing it with the efficiency of the SRC working at 7 MPa (continuous line in Fig. 4(a)), it is seen that there is a significant improvement at higher cycle temperatures. Fig. 4(b) shows the cycle high pressure of the SRC for optimized thermal efficiency. It is observed that in order to get the optimized thermal efficiency of 15.08% at 473 K, the pressure of the cycle is as high as 33 MPa. A high pressure like that could be a concern in real practice. The analysis of optimized thermal efficiency is only to show that there is a potential
Fig. 1. Configuration and processes of a zeotropic mixture supercritical Rankine cycle.
H. Chen et al. / Energy 36 (2011) 549e555
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Table 1 The screened 22 refrigerants for synthesizing zeotropic mixtures. ASHRAE Number
Name
Molecular Weight
Critical Temperature (K)
Critical Pressure (MPa)
GWP 100yra
ODPb
R-21 R-22 R-23 R-32 R-41 R-116 R-123 R-124 R-125 R-134a R-141b R-142b R-143a R-152a R-218 R-227ea R-236ea R-245ca R-245fa R-C318 R-3-1-10 FC-4-1-12
Dichlorofluoromethane Chlorodifluoromethane Trifluoromethane Difluoromethane Fluoromethane Hexafluoroethane 2,2-Dichloro-1,1,1-trifluoroethane 2-Chloro-1,1,1,2-tetrafluoroethane Pentafluoroethane 1,1,1,2-Tetrafluoroethane 1,1-Dichloro-1-fluoroethane 1-Chloro-1,1-difluoroethane 1,1,1-Trifluoroethane 1,1-Difluoroethane Octafluoropropane 1,1,1,2,3,3,3-Heptafluoropropane 1,1,1,2,3,3-Hexafluoropropane 1,1,2,2,3-Pentafluoropropane 1,1,1,3,3-Pentafluoropropane Octafluorocyclobutane Decafluorobutane Dodecafluoropentane
102.92 86.47 70.01 52.02 34.03 138.01 152.93 136.48 120.02 102.03 116.95 100.50 84.04 66.05 188.02 170.03 152.04 134.05 134.05 200.03 238.03 288.03
451.48 369.30 299.29 351.26 317.28 293.03 456.83 395.43 339.17 374.21 477.50 410.26 345.86 386.41 345.02 375.95 412.44 447.57 427.20 388.38 386.33 420.56
5.18 4.99 4.83 5.78 5.90 3.05 3.66 3.62 3.62 4.06 4.21 4.06 3.76 4.52 2.64 3.00 3.50 3.93 3.64 2.78 2.32 2.05
210 1700 N/A 550 97 11,900 120 620 3400 1300 700 2400 4300 120 8600 3500 9400 560 900 10,000 8600 9160
0.01 0.03 0.00 0.00 0.00 0.00 0.01 0.03 0.00 0.02 0.09 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
a GWP (Global Warming Potential) 100 yr, is a measure of how much a given mass of a gas contributes to global warming over 100 years. GWP is a relative scale which compares the greenhouse gas to Carbon dioxide where GWP by definition is 1. b ODP (Ozone Depletion Potential), is the relative amount of degradation a chemical compound can cause to the ozone layer.
for improvement of the SRC. However, the following analysis of the SRC is still based on a constant cycle high pressure of 7 MPa. The net work outputs per unit mass of working fluid of the two cycles are shown in Fig. 5. It is seen that the net work output of the SRC is higher than that of the ORC and the difference between them increases with the increase of the cycle high temperature. At 473 K, the SRC provides 38.9% more net work compared to the ORC.
3.2. Exergy efficiency of the condensing process Exergy analyses are conducted in this section to study the condensation processes of pure R134a in the ORC and the zeotropic mixture of 0.7R134a/0.3R32 in the SRC, which processes are shown in Figs. 6 and 7, respectively. The working fluids are condensed from
Fig. 2. Processes of an organic Rankine cycle using R134a as the working fluid (ⓐ/ⓑ/ⓒ/ⓓ0 /ⓓ).
saturated vapor at point ⓓ to saturated liquid at point ⓐ by dissipating the heat to the cooling fluid. The thermal matches between the working fluids and the cooling fluids are shown at on the top left corners of the figures. For the purpose of calculation, water is used as the cooling fluid in this study. The exergy analyses of the condensation processes in the two cycles are conducted under the average condensation temperature of 309.5 K. The mass flow rate of the working fluids is set at 1 kg/s, and the heat exchanger pinch limitation is set at 8 K. Based on the average condensing temperature of 309.5 K, the pure R134a is condensed isobarically at 0.92 MPa (Fig. 6), while the zeotropic mixture is condensed isobarically at 1.4 MPa with the condensation commencing at a temperature of 312.37 K (point ⓓ in Fig. 7) and ending at a temperature of 306.6 K (point ⓐ in Fig. 7).
Fig. 3. Processes of a supercritical Rankine cycle using the zeotropic mixture of R134a and R32 as the working fluid (ⓐ/ⓑ/ⓒ/ⓓ0 /ⓓ).
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Fig. 5. Net work outputs of the R134a-based organic Rankine cycle (ORC) and the zeotropic mixture-based supercritical Rankine cycle (SRC).
their temperatures and fluid types. The flow rate of the cooling water is calculated to be 8.37 kg/s from equation (1). The net change in the flow exergy rate from saturated vapor (point ⓓ in Fig. 7 to saturated liquid point ⓐ in Fig. 7) for the zeotropic mixture is computed to be 383.05 kW using the following equation, neglecting the effects of motion and gravity [39]: ˇ
ˇ
ⓓa
h d T0 s s ⓐa
ˇ
ˇ
ⓐa
_ zeo ¼ m
ⓓa
ˇ
a ⓐ
ˇ
_ zeo e e DE_ zeo ¼ m
ⓓa
(2) where T0 is the dead-state temperature, 273K. Similarly, the change in the flow exergy rate from the inlet to the outlet for the cooling water is found to be 312.72 kW by using the following equation (3):
Fig. 4. Thermal efficiencies of the R134a-based organic Rankine cycle (ORC) and the zeotropic mixture-based supercritical Rankine cycle (SRC).
Since the zeotropic mixture creates a thermal glide when condensed isobarically, the heat exchange process can be designed such that the temperature profile of the cooling water parallels that of the working fluid to obtain the best thermal match. Under this design, the mass flow rate of cooling water can be found from the energy balance of the condenser at steady state:
_ zeo h h _ water h h þ m ¼ 0 m ˇ
ˇ
a ②
ⓓa
ˇ
ˇ
a ①
ⓐa
(1)
_ water is the mass flow rate of the cooling water, h① and h② where m denote the enthalpies of the cooling water at points ① and ②, _ zeo is the mass flow rate of the respectively (See Fig. 7). Similarly, m zeotropic mixture being condensed; hⓓ and hⓐ are the enthalpies of the zeotropic mixture at points ⓓ and ⓐ, respectively. The enthalpy values of all the four points can be obtained according to
Fig. 6. Condensing process of R134a and its thermal match with the cooling fluid.
H. Chen et al. / Energy 36 (2011) 549e555
553
Table 2 Comparison of the condensation process of the two working fluids in the cycles. Working Fluid Working fluid Temperature (K) Cooling Water Temperature (K)
Point Point Point Point
Exergy Efficiency (%) a b
Fig. 7. Condensing process of the zeotropic mixture of R134a and R32 and its thermal match with the cooling fluid.
ˇ
ˇ
①a
h h ②a
ˇ
ˇ
②a
_ water ¼ m
①a
T0 s s ˇ
②a
ˇ
_ water e e DE_ water ¼ m
①a
(3) The exergetic efficiency of the heat exchange process for condensing the zeotropic mixture can then be calculated from the following equation to be 81.64%:
ˇ
ˇ
(4)
ˇ
ⓐa
ⓓa
With the same flow rate of cooling water and the aforesaid design and operating parameters, the enthalpy of the inlet cooling water (h①) in the R134a-based ORC can be found by the following equation:
_ water h h þ m _ R134a h h m ¼ 0 ˇ
ˇ
a ②
ⓓa
ˇ
ˇ
a ①
ⓓ ⓐa ①a ②a
R134a
Zeotropic mixtureb
309.5 309.5 293.7 301.5 66.55
312.4 306.6 298.6 304.4 81.64
Refer to Figs. 6 and 7 for point ⓓ, ⓐ, ② and ①. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
processes of the two cycles with the thermal match shown on the top left corners. The working fluids are heated from state ⓑ to state ⓒ by a sensible heat source in counterflow heat exchangers in both cycles. Pressurized hot water (P ¼ 0.5 MPa) at 410 K is applied as the heat source for the sake of this simulation. The working fluids in both cycles with mass flow rates of 1 kg/s are heated to 400 K, and the pinch limitation is set at 10 K. The mass flow rate of the heat source is just enough to heat the working fluids to 400 K and meet the pinch limitation of 10 K throughout the heat exchange process. In the ORC, the pinch limitation is reached at the saturated liquid point during the heating process (Fig. 8). Since there is no obvious pinch point for the zeotropic mixture, multiple points are tested during the calculation. The heating processes of the pure R134a in the ORC and the zeotropic mixture of 0.7 R134a/0.3R32 in the SRC are analyzed and the results listed in Table 3. It is seen from Table 3 that the discharge temperature of the heat source in the R134a-based ORC is 24 K higher than that in the zeotropic mixture-based SRC (point ④ in ④ Figs. 8 and 9), which indicates that the effective utilization of the heat source is much less in the R134a-based ORC than that of the 0.7R134a/0.3R32based SRC. Such result is also obvious by comparing the exergy efficiencies of the heating process of the two cycles with the SRC showing 7.30% higher exergy efficiency of the heating process than that of the pure R134a in the ORC.
ˇ
DE_ e ¼ _water DEzeo
_ water e e m a ② ①a ¼ _ mzeo e e
a
ⓐa
4. System results and discussion For a system composed of a heat source, a power cycle and a heat sink, the two systems have been studied for their performance in the heat transfer from the heat source to the power cycle, the thermal efficiency of power cycle, and the heat dissipation from the power
(5)
The net changes in the flow exergy rate of the pure R134a and its cooling water can be found through Equations (2) and (3), except that the working fluid is pure R134a. The exergetic efficiency of the heat exchange process for condensing pure R134a is calculated to be 66.55%. Detailed results of the condensation processes in both cycles are listed in Table 2. It can be observed from Table 2 that the thermal glide of the zeotropic mixture is 312.4K 306.6 K ¼ 5.8 K, while there is no thermal glide created by pure R134a. The cooling water temperature required by pure R134a is 293.7 K, which is 4.8 K lower than that of the zeotropic mixture. Exergy efficiency indicates the percentage of usable energy conserved during the condensation process. It is seen that the exergy efficiency of the 0.7R134a/0.3R32 condensation process is 22.67% higher than that of pure R134a.
3.3. Exergy efficiency of the heating process In this section, exergy analyses of the heating processes of the two cycles are carried out. Figs. 8 and 9 present the heating
Fig. 8. Heating process of R134a and its thermal match with the heat source.
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H. Chen et al. / Energy 36 (2011) 549e555 Table 4 Comparison of the efficiency between the organic Rankine cycle and the supercritical Rankine cycle.a Working fluid & Thermodynamic cycle
R134a, ORC Zeotropic mixture,b SRC
Cycle exergy efficiency(%) Condensing process exergy efficiency(%) Heating process exergy efficiency(%) System total exergy efficiency(%) a b
43.82 66.55 82.64 24.10
53.28 81.64 88.67 38.57
Computation based on the cycle high temperature of 400 K. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
5. Conclusions
Fig. 9. Heating process of the zeotropic mixture of R134a and R32 and its thermal match with the heat source.
cycle to the heat sink. The 0.7R134a/0.3R32 zeotropic mixture-based SRC shows advantages over the pure R134a-based ORC in all of the aspects that have been analyzed, the results being summarized in Table 4. Comparing the two cycles, the SRC improves the cycle thermal efficiency, exergy efficiency of the condensation process and the exergy efficiency of the heating process by 21.57%, 22.67%, and 7.30%, respectively over the ORC using R134a. The exergy efficiencies of the two systems are also calculated by multiplying the exergy efficiencies of the heating processes, the energy conversion cycle and the condensation processes of the respective system, which results are also listed in Table 4. It is noticed that the total exergy efficiency of the SRC system is 38.57%, which is a 60.04% improvement over that of the ORC (24.10%). The zeotropic mixture of 0.7R134a/0.3R32 considered as the working fluid of the SRC in this study may not always be the best choice. It can be observed from Fig. 4 that there is little gain in thermal efficiency when the cycle high temperature is beyond 433 K, which indicates that the zeotropic mixture of 0.7R134a/ 0.3R32 may be a good choice for heat sources with temperatures below 433 K, while there may be other mixtures which could perform better above 433 K. One should be able to compose other zeotropic mixtures from the screened 22 fluids in Table 1 for different temperature applications. More detailed discussion on the working fluids is given in our review on thermodynamic cycles for low-grade heat conversion [37]. Beside the temperature considerations, it is recommended that a zeotropic mixture to be used as the working fluid of an SRC should have a thermal glide during the condensation process in order to take advantage of non-isothermal condensation. Table 3 Comparison of the heating process of the two working fluids in the cycles. Working Fluid Heat Source Temperature (K) Working Fluid Temperature (K) Exergy Efficiency (%) a b
Point Point Point Point
a
③ ④a ⓑa ⓒa
R134a
Zeotropic mixtureb
410.0 355.7 309.5 400.0 82.64
410.0 331.7 306.6 400.0 88.67
Refer to Figs. 8 and 9 for point ③, ④, ⓑ and ⓒ. Zeotropic mixture of R32 and R134a (0.3/0.7, mass fraction).
A supercritical Rankine cycle (SRC) using a zeotropic mixture as the working fluid has been proposed in this paper. The performance of the proposed cycle is investigated through a comparative study of a SRC and an ORC working under the same thermal conditions. It was found that the SRC using a zeotropic mixture of 0.7R134a/ 0.3R32 can achieve thermal efficiency of 10.77e13.35% with the cycle high temperature of 393e453 K as compared to 9.70e10.13% from an ORC using pure R134a working fluid under the same thermal conditions. The SRC using the zeotropic mixture also improves the heat exchange processes: the exergy efficiencies of the heating and condensation processes for the zeotropic mixture are 88.67% and 81.64%, respectively, as compared to 82.65% and 66.55% for the pure R134a in ORC. Overall, the system exergy efficiency of the SRC using the zeotropic mixture of 0.7R134a/0.3R32 is 38.57%, while that of the ORC using pure R134a is 24.10%. From the more than 50 refrigerants considered, 22 fluids were screened out as the potential candidates for composing zeotropic mixtures in consideration of their environmental impacts and thermophysical properties. One should be able to compose various zeotropic mixtures from these fluids for different temperature applications. It is recommended that a zeotropic mixture to be used as the working fluid of a supercritical Rankine cycle should have a certain thermal glide in the condensation process in order to take advantage of non-isothermal condensation. Acknowledgement The research leading to this paper was funded by the State of Florida through the Florida Energy Systems Consortium (FESC) funds. Appendix. Error analysis PengeRobinson Equation of State [40] was used to get the properties of the working fluid, which is:
P ¼
RT aðTÞ V b VðV þ bÞ þ bðV bÞ
where
R2 T2c aðTÞ ¼ 0:45724 alphaðTÞ Pc RTc b ¼ 0:07780 Pc 2 T alphaðTÞ ¼ 1 þ k 1 squrt Tc k ¼ 0:37464 þ 1:54226w 0:26992w2 Substituting a(T), b, alpha(T),and k into the equation of state gives:
H. Chen et al. / Energy 36 (2011) 549e555
P ¼
RT C V 0:07780RT PC
T 2 þ 0:37464 þ 1:54226w 0:26992w2 1 squrtTC RTC C C V 0:07780RT V V þ 0:07780RT RC þ 0:07780 PC PC
0:45724
R2 T2C PC 1
The acentric factor w is a constant, 0.7. Thus the equation of state of a fluid is a function of its critical temperature Tc, and critical pressure Pc. In order to validate the property of the working fluids that used in the investigation, a comparison between the data from NIST and ChemCAD is carried out in the following. The critical temperature and critical pressure data from the two data sources are tabulated below.
Data Source
NIST ChemCAD
555
R134a
R32
Tc (K)
Pc (MPa)
Tc (K)
Pc (MPa)
374.21 374.23
4.0593 4.0603
351.26 351.60
5.7820 5.8302
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 The standard division of Tc is sTc ¼ The standard division of Pc is sPc ¼
k
ðTck Tc Þ N
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 k
ðPck Pc Þ N
¼ 0:34K. ¼ 0:0482MPa.
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