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Zeotropic mixture active design method for organic Rankine cycle
Accepted Manuscript Research Paper Zeotropic mixture active design method for organic Rankine cycle Huixing Zhai, Qingsong An, Lin Shi PII: DOI: Reference:
S1359-4311(17)33066-1 https://doi.org/10.1016/j.applthermaleng.2017.10.027 ATE 11225
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
5 May 2017 21 September 2017 4 October 2017
Please cite this article as: H. Zhai, Q. An, L. Shi, Zeotropic mixture active design method for organic Rankine cycle, Applied Thermal Engineering (2017), doi: https://doi.org/10.1016/j.applthermaleng.2017.10.027
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Title of the article: Zeotropic mixture active design method for organic Rankine cycle
Authors: Huixing ZHAIa,b, Qingsong ANc, Lin SHIb First author’s surname: ZHAI
Affiliations: a. School of Environment and Energy Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China E-mail address:
[email protected]
b. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China E-mail address:
[email protected]
c. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy of Ministry of Education, Tianjin University, Tianjin 300072, China E-mail address:
[email protected]
Corresponding author information:
Name:
Lin SHI
Postal address: Department of Thermal Engineering, Tsinghua University, Haidian District, Beijing 1
100084, China
Tel: +861062787613
Fax: +861062787613
E-mail address: [email protected]
2
Zeotropic mixture active design method for organic Rankine cycle Huixing ZHAIa,b, Qingsong ANc , Lin SHIb* a. School of Environment and Energy Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China b. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China c. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy of Ministry of Education, Tianjin University, Tianjin 300072, China
Abstract Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC) system. Instead of recommending mixtures or compositions for a specific heat source, this work is focused on providing preliminary design guidelines of zeotropic mixture working fluids for ORC. The zeotropic mixture active design method is provided for mixture selection without massive calculation or blind trial. The designed mixtures have better performance than the optimal pure working fluid. The designed zeotropic mixtures should have the same key properties as the optimal pure working fluids and also have temperature glide matching with the cooling source. Firstly, the authors’ previous study on the optimal pure working fluid screen criteria is simply reviewed. Then, how the mixture’s temperature glide influencing on the cycle performance is analyzed. Finally, the zeotropic mixture active design method is provided and verified. Some debatable questions regarding to the mixtures are also answered.
Key words: 3
Active design; Mixtures; Temperature glide; Organic Rankine cycle; ORC
1. Introduction Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC). Researchers have recommended mixtures for different heat sources. Chys et al. [1] found that a potential increase of 16% and 6% in cycle efficiency is gained using mixtures for 150 °C and 250 °C heat sources. Heberle et al. [2] studied the performance of R227ea, isobutane, R245fa, isopentane and their mixtures for the heat source temperature below 120°C and gave the conclusion that the second law efficiency of the mixtures increased in range of 4.3% and 15% compared to the most efficient pure component. Lecompte et al. [3] analyzed the performance of eight pure working fluids and their mixtures for a 150°C heat source and the results showed that an increase in the second law efficiency in range of 7.1% and 14.2 was obtained by the mixtures compared to pure working fluids. Song et al. [4] studied R141b and R11 blended with the hydrocarbons as zeotropic mixtures and recommended cyclohexane/R141b (0.5/0.5) for the waste heat recovery of a diesel engine. Kang et al. [5] found that R245fa/R600a (0.9/0.1) was the best mixtures among 10 groups of mixtures for a 120°C geothermal heat source. Sadeghi et al. [6] found that using zeotropic mixtures as the working fluid instead of a pure fluid such as R245fa, leads to more than 24% improvement in power generation for ORC with 100°C geothermal water. Wu et al. [7] analyzed the performance of ORC using zeotropic mixtures of R227ea/R245fa, Butane/R245fa and RC318/R245fa for a 120°C hot air heat source. Results showed that the mixtures may provide high thermal efficiency but bad economic performance. However, Xi et al. [8] found that mixture working fluid is more economic-efficient than pure working fluid and R245fa/Isopentane and 4
R245fa/Pentane were recommended for 100-180°C heat sources among 4 mixture and 5 pure working fluids. Garg et al. [9] evaluated isopentane, R245fa and their mixtures’ performance in ORC for 106-151°C heat sources and recommended isopentane/R245fa (0.7/0.3). For higher temperature heat sources, Dong et al. [10] studied MM/MDM as ORC working fluids for the heat source with 280°C inlet temperature and 240°C outlet temperature. For more mixture recommendation, Bao et al. [11] and Gholamreza et al. [12] gave an overview of the mixtures used in ORC. The previous studies recommended mixtures for the specific heat source and only a couple of mixtures were analyzed. Whether the mixture is better than the optimal pure working fluid has not been proven. The mixture selection is quite different from the pure working fluid selection. There are around fifty pure working fluids commonly used in the field of organic Rankine cycles, making it is feasible to compare all the pure working fluids and find the optimal one. However, the mixtures are uncountable as there could be different compositions and proportions. Thus, it is difficult to compare all the mixtures for the optimal mixture selection. The Computer Aided Molecular Design (CAMD) [13-18] is studied for the optimal pure working fluid and mixture selection. In this paper, a zeotropic mixture active design method is provided. Instead of selecting the optimal mixtures, this method is to design mixtures which have better performance than the optimal pure working fluids without massive calculation or blind trial. The analysis of the temperature glide of this method could also be part of CAMD. The idea of this method is: as the mixtures’ properties are adjustable, the designed mixtures could have the same key property of the optimal pure working fluid and have the condensation temperature glide matching with the cooling sources at the same time. As a result, the designed mixtures have 5
better performance than all the other pure working fluids. In this paper, the zeotropic mixture active design method is introduced taking the subcritical ORC with heat sources without outlet temperature limitation as an example. The following debatable questions are also answered, •
In what condition, the mixtures are superior to the pure working fluids?
•
Why the mixtures are superior to the pure working fluids? Is it only to decrease the evaporation and condensation exergy losses?
•
What is the proper temperature glide of the mixture?
•
Does the temperature glide matching with the evaporator or the condenser provide more improvement for the cycle performance?
•
What is the mixture design method?
2. Model description of the subcritical ORC using mixtures 2.1. Subcritical ORC using mixtures
Fig. 1 ORC configuration
Fig. 2 T-s diagram of subcritical ORC using mixtures
The ORC is a simple four-component system as shown in Fig. 1. The working fluid is pumped to the
6
evaporator to be vaporized by the heat source and then expands in the expander to generate work. The vapor or liquid out of the expander goes into the condenser to total condensed to liquid. Then the liquid working fluid goes to the pump and begins a new circulation. Evaporating pressure is controlled to be lower than 0.9Pc or the saturate pressure of (T5-Tp) to guarantee a subcritical cycle as shown in Fig. 2. 2.2. Subcritical ORC model using mixtures 2.2.1. Model assumptions There is no pressure drop during the working fluid flowing in the system. Because the pressure drop is not easy to calculate accurately. The cycle is running at steady state. These assumptions may make the cycle efficiency higher than the actual condition, however, have little influence on the working fluid selection. The heat exchangers are in counter flow layout. Compared with the parallel flow layout, the counter flow layout has larger logarithmic mean temperature difference so that the heat exchanger is more compact. 2.2.2. First law of thermodynamics analysis The subscript of the parameters are referred to Fig. 2. The cycle efficiency is calculated by,
wt wpp qeva
(1)
where wt is the work output of the expander, wpp is the work consumed by the pump and qeva is the heat absorbed by the working fluid. And,
wt h3 h4 7
(2)
wpp h2 h1
(3)
qeva h3 h2
(4)
The cycle work output is calculated by,
.
W net mwf (wt wpp ) Q
(5)
where m wf is the mass flow rate of the working fluid and Q is the heat absorbed by the cycle.
And Q is calculated by,
.
Q mhs (h5 h6 )
(6)
where m hs is the mass flow rate of the working fluid. 2.2.3. Second law of thermodynamic analysis The reference state is as follows, T0 = 293.15 K, P0=0.1 MPa
(7)
The exergy of a thermodynamic system is defined as the theoretical maximum work that could be produced if the system is brought into equilibrium with its surroundings. The exergy of the heat source without an outlet temperature limitation is given by,
E hs mhs [h5 h0 T0 (s5 s0 )]
(8)
In general, the ORC system cannot decrease the heat source temperature into the temperature of the environment and only part of the heat source exergy can be transferred to the ORC working fluid. The exergy transferred to the working fluid is given by,
E hs _tra mhs [h5 h6 T0 ( s5 s6 )]
(9)
The exergy obtained by the working fluid during the evaporation process is calculated by,
E wf_eva mwf [h3 h2 T0 ( s3 s2 )] 8
(10)
The exergy loss during the evaporation process is calculated by,
I eva E hs _in E wf_eva_in T0 [mwf ( s3 s2 ) mhs (s5 s6 )]
(11)
The exergy loss during the expansion process is calculated by,
I exp mwf T0 ( s4 s3 )
(12)
As all the exergy during the condensation process is released to the environment, the exergy loss during the condensation process is calculated by,
I cd mwf [h4 h1 T0 ( s4 s1 )]
(13)
The exergy loss in the pump is calculated by,
I pp mwf T0 ( s2 s1 )
(14)
The exergy balance is given as the follows,
E hs_tra I W net
(15)
which means that the exergy of the heat source that transferred to the ORC working fluid covers all the exergy deduction and the net work output. The system performance metrics is the exergy efficiency of the heat source energy recovery which is defined by,
ex
W net
(16)
E hs
As the E hs of a specific heat source is fixed, from Eqs. 15 and 16, it could be found that the more
exergy transferred to the working fluid from the heat source E hs _tra and less total exergy losses
I give higer exergy efficiencyex . 2.3. Working conditions The calculations were done with the working conditions listed in Table 1. The mass flow rate of the 9
heat source was set to be 1kg/s. The pinch temperature difference is different according to the source heat transfer capability. Typical pinch point temperature difference in the heat exchanger is 10°C for liquid sources [19] and 30°C for gas sources [20]. The outlet temperature of the cooling source is 30°C for the natural cooling condition and 60°C for the combined heat and power system. The expander isentropic efficiency is around 0.75 to 0.8 and the pump isentropic efficiency is around 0.6 to 0.8 [3, 21, 22]. However, the expander and pump isentropic efficiencies would not affect the working fluid selection. The expander and pump isentropic efficiencies need to be unified when compare the working fluids’ cycle performance. If not otherwise specified, the expander and pump isentropic efficiencies are chosen as Table 1 shows. The results were obtained using Matlab together with Refprop 9.1 [23]. In Refprop 9.1, the properties for working pairs without experiment data are estimated by the modified Helmoltz equation. The model in this paper is verified with other works [22].
Table 1 Operating condition of the model Part
Parameter
Assumption
Pinch temperature difference in the evaporator Tp_eva
10 K for water, 30 K for air
Pinch temperature difference in the condenser Tp_cd
10 K
Superheating degree ΔTsup
5K
Subcooling degree ΔT sub
5K
ORC cycle
Expander isentropic efficiency Pump isentropic efficiency
exp
0.8
pp
0.65
10
Heat source fluid mass flow rate m hs
1 kg/s
Heat source inlet temperature Ths
Water: 150°C; Air: 210°C
Outlet temperature of cooling water Tcf_out
30°C-60°C
Heat source
Heat sink
Difference between inlet and outlet temperature of 5 K, 10 K, 15 K, 20 K cooling water ΔTcf
2.4. Working fluids The common used pure working fluids and their key properties are displayed in Table 2, mainly including HFCs, HCs, siloxanes and benzenes. CFCs and HCFCs whose ODP values are not zero are not included for the environment requirement. The thermal properties of the working fluids are referred to Refprop 9.1[23]. The common used pure working fluids have clear thermal properties and are easy to obtain. Thus, the mixtures designed in this paper are consisted of these common used pure working fluids. Table 2 Properties of pure working fluids (ranked by Tc) Working fluid
Molecular formula
Molecular
Tc (°C)
Pc (Mpa)
weight(kg/kmol) R125
CHF2CF3
120.02
66.02
3.6177
R218
CF3CF2CF3
188.02
71.87
2.64
R143a
CF3CH3
84.041
72.71
3.761
R32
CH2F2
52.024
78.11
5.782
propylene
CH2=CH-CH3
42.08
91.06
4.555
R1234yf
CF3CF=CH2
114.04
94.70
3.38
11
propane
CH3CH2CH3
44.096
96.74
4.2512
R134a
CF3CH2F
102.03
101.06
4.0593
R227ea
CF3CHFCF3
170.03
101.75
2.92
R161
C2H5F
48.06
102.15
5.091
R1234ze(E)
CHF=CHCF3(trans)
114.04
109.37
3.6363
perfluorobutane
C4F10
238.03
113.18
2.32
R152a
CHF2CH3
66.051
113.26
4.5168
RC318
cyclo-C4F8
200.03
115.23
2.77
R236fa
CF3CH2CF3
152.04
124.92
3.20
cyclopropane
cyclo-C3H6
42.081
125.15
5.5797
propyne
CH3CCH
40.06
129.23
5.626
isobutane
CH(CH3)3
58.122
134.66
3.63
R236ea
CF3CHFCHF2
152.04
139.29
3.50
isobutene
CH2-C(CH3)2
56.106
144.94
4.01
butene
CH3-CH2-CH=CH2
56.106
146.14
4.01
perfluoropentane
C5F12
288.03
147.41
2.05
butane
CH3-2(CH2)-CH3
58.122
151.98
3.80
R245fa
CF3CH2CHF2
134.05
154.01
3.65
trans-butene
CH3-CH=CH-CH3
56.106
155.46
4.03
neopentane
C(CH3)4
72.149
160.59
3.20
cis-butene
CH3-CH=CH-CH3
56.106
162.60
4.23
12
R245ca
CHF2CF2CH2F
134.05
174.42
3.93
R365mfc
CF3CH2CF2CH3
148.07
186.85
3.27
isopentane
(CH3)2CHCH2CH3
72.149
187.20
3.38
pentane
CH3-3(CH2)-CH3
72.149
196.55
3.37
isohexane
(CH3)2CH(CH2)2CH3
86.175
224.55
3.04
hexane
CH3-4(CH2)-CH3
86.175
234.67
3.03
cyclopentane
cyclo-C5H10
70.133
238.54
4.52
MM
C6H18OSi2
162.38
245.60
1.94
heptane
CH3-5(CH2)-CH3
100.2
266.98
2.74
cyclohexane
cyclo-C6H12
84.161
280.49
4.08
dimethyl carbonate
C3H6O3
90.078
284.23
4.84
benzene
C6H6
78.112
288.87
4.91
MDM
C8H24O2Si3
236.53
290.94
1.42
octane
CH3-6(CH2)-CH3
114.23
296.17
2.50
methylcyclohexane
C6H11(CH3)
98.186
299.05
3.47
D4
C8H24O4Si4
296.62
313.35
1.33
toluene
CH3-C6H5
92.138
318.60
4.13
nonane
CH3-7(CH2)-CH3
128.26
321.40
2.28
MD2M
C10H30Si4O3
310.69
326.25
1.23
decane
CH3-8(CH2)-CH3
142.28
344.55
2.10
propylcyclohexane
(C6H11)CH2CH2CH3
126.24
357.65
2.86
13
3. Zeotropic mixture active design method There are around fifty pure working fluids commonly used in the field of organic Rankine cycles, making it is feasible to calculate all the common used pure working fluids’ cycle performance and choose the optimal one. However, mixtures have different components and proportions, it is not convenient to calculate all the mixtures for the mixture selection. Thus, the mixture active design method is needed for quick and simple mixture selection. The mixture design idea of this paper is that: the mixture fluids are regarded as special pure fluids with the advantage of adjustable properties and temperature glides at the same time; the mixture is designed actively to have the appropriate properties and temperature glides so that the cycle performance is improved. Figure 3 displays the general idea of the zeotropic mixture active design method.
Fig. 3 General idea of the zeotropic mixture active design method Firstly, the key properties which mainly influence the cycle performance of the optimal pure working fluid should be obtained. The designed mixtures’ properties should have the same key properties as
14
the optimal pure working fluid so that the mixtures’ performance is no worse than the optimal pure working fluid. These will be analyzed in detail in part 3.1. Secondly, the mixtures’ condensation temperature glides should match with the cooling source so that the mixtures’ performance is better than the optimal pure working fluid. In part 3.2, how the temperature glides’ influence on the cycle performance and under which condition the mixtures match with the cooling source are analyzed. Finally, based on the analysis of part 3.1 and 3.2, the detailed design procedures are provided in part 3.3. Through this method, the mixtures which have better performance than the optimal pure working fluids could be designed without massive calculation. The common used pure working fluids displayed in Table 2 are used to apply the zeotropic mixture design.
3.1. The key properties of the optimal pure working fluid The key properties of the work fluids influencing the cycle performance could be different for different cycle types and heat source types. The organic Rankine cycles could be subcritical or trans-critical. The heat sources could be divided into the finite capacity heat source without an outlet temperature limitation, the finite capacity heat source with an outlet temperature limitation and the infinite heat capacity heat source [24]. The quantitative conclusion of the optimal pure working fluid’s key property is needed for the mixture design. Take the subcritical ORC with the heat sources without an outlet temperature limitation as an example. For the subcritical ORC with heat sources without outlet temperature limitation, the key property of the optimal pure working fluid is the critical temperature Tc. When the heat source 15
temperatures are between 150-350°C and the outlet temperatures of the cooling sources are between 30-60°C, the key property Tc of the pure optimal working fluid has the quantitative relation with the source temperature Ths and the evaporation pinch temperature difference Tp_eva as displayed in Eq. 17. The detailed analysis could be referred in the authors’ previous work [25].
Th s T p _ e v2a 9 . 0 2 6 T h T 2a0 . 1 6 9 s p_ e v Tc 1.0669 1.0982
（17）
The unit in Eq.17 is °C. With the same Ths and Tp_eva, Tc is lower when the outlet temperature of the cooling source is near 30°C while Tc is higher when the outlet temperature of the cooling source is near 60°C. The mixture’s Tc follows the Kay rule as shown in Eq.18 [26]. Tcm is the mixture’s Tc, Tcj is the Tc of one component and yj is this component’s molar mass fraction. The deviation between the mixture’s Tc calculated by the Kay rule and other more complex rules is less than 2%.
Tcm y jTcj
( 0.5
j
Pci Tci 2) 2 and 0.5 Pcj Tcj
（18）
The designed mixtures satisfy Eq.17, so that their cycle performance will be no worse than the optimal pure working fluid. What’s more, the pure working fluid’s property is fixed while the mixtures’ properties are adjustable by changing the components and proportions which can be closer to the key property. 3.2. Analysis of the temperature glide influence on the cycle performance The largest difference between mixtures and pure working fluids are that mixtures have temperature glides during the evaporation and condensation processes as shown in Fig. 2. The degree of the temperature glide decreases as the phase change pressure increases. Thus, for one mixture, the degree of the temperature glide during the condensation process is larger than that during the 16
evaporation process. In addition, for the subcritical ORC, the proportion of the latent evaporation part is less than that of the latent condensation part. And for the trans-critical ORC, the evaporation temperature glide plays a small role during the supercritical evaporation process. Therefore, the temperature glides during the condensation process have larger influence on improving the cycle performance and the following parts are focusing on the condensation temperature glide matching with the cooling source. 3.2.1. Matching condition during the condensation process According to the working fluid condensation temperature glide degree and the cooling source inlet and outlet temperature difference, the four matching conditions are displayed in Fig. 4. In Fig. 4, Tcd_in is the inlet temperature and Tcd_out is the outlet temperature of the working fluid during the condensation process; the condensation temperature glide ΔTglide=Tcd_in-Tcd_out; Tcf_in is the inlet temperature and Tcf_out is the outlet temperature of the cooling source during the condensation process; ΔTcf=Tcf_out-Tcf_in. If the temperature difference between the working fluid and the cooling source is large, the exergy loss during the condensation process is large. If the working fluid temperature increased by the pump from the condenser outlet is neglected, the allowed lowest heat source outlet temperature is approximately equal to the summation of the condenser outlet temperature of the working fluid Tcd_out and the condensation pinch temperature difference Tp_cd. Thus, if Tcd_out is lower, the heat source outlet temperature may decrease to a lower temperature so that increasing the heat source utilization.
17
(a)
(b)
(c)
(d)
Fig. 4 Matching condition between the working fluid and cooling source during the condensation process
The four matching conditions are illustrated as the follows: 1) No condensation temperature glides as shown in Fig. 4a: ΔTglide=0, this is using a pure working fluid. The pinch point appears in the condenser inlet of the working fluid. The condensation exergy loss is large and the heat source utilization could not be improved. 2) Perfect condensation temperature glides as shown in Fig. 4b: ΔTglide=ΔTcf. The working fluid and 18
the cooling source keep the minimum pinch temperature difference all along the condenser. The condensation exergy loss is the lowest and Tcd_out is the lowest so that the heat source utilization could be improved. 3) Small condensation temperature glides as shown in Fig. 4c: ΔTglide<ΔTcf. The pinch point appears in the condenser inlet of the working fluid. The condensation exergy loss is lower than the pure working fluid and Tcd_out is lower than the pure working fluid so that the heat source utilization could be improved compared to the pure working fluid. 4) Overlarge condensation temperature glides as shown in Fig. 4d: ΔTglide>ΔTcf. The pinch point appears in the condenser outlet of the working fluid. Tcd_out is already the lowest so that the heat source utilization could be improved. As the ΔTglide is becoming larger, the heat source utilization will not increase, however, the condensation exergy loss will increase. It can be seen from the analysis above that mixtures can improve the cycle performance by decreasing the condensation exergy loss and increasing the heat source utilization for the heat source without an outlet temperature limitation. The perfect matching condition is: ΔTglide=ΔTcf
（19）
For the real cycle, the working fluid in the condenser has three sections: the superheat inlet section, the latent heat exchange section and the subcooling outlet section. The condensation temperature glide only exists in the latent heat exchange section. The superheat degree of the expander inlet ΔTsup is close to the superheat degree of the condenser inlet. If the expander inlet ΔTsup and the subcooling degree of the condenser outlet ΔTsub is given, the matching condition is: overall ΔTglide = ΔTcf 19
（20)
The overall ΔTglide is equal to ΔTsup+ΔTglide+ΔTsub. It is not easy to make the overall ΔTglide right equals to ΔTcf. The closer of the overall ΔTglide and ΔTcf, the better of the cycle performance. 3.2.2. Verification of the matching condition The condensation temperature glide’s influence on the cycle performance and the matching condition are verified by the following calculation cases. The cooling source outlet temperature Tcf_out is 30°C and the cooling source inlet temperature Tcf_in is 10°C, 15°C, 20°C and 25°C, respectively. Correspondingly, the difference between inlet and outlet temperature of cooling water ΔTcf are 20 K, 15 K, 10 K and 5 K, respectively. The temperature glide degrees of the isobutane/isopentane mixtures using the 150°C heat source are listed in Tables 3 and 4. As the increase of the pressure, the temperature glide decreases significantly. So the condensation temperature glide is larger than the evaporation temperature glide. For higher temperature heat sources, the evaporation temperature glide could be smaller. Table 3 Evaporation temperature glide using the 150°C heat source ΔTcf (°C)
Isobutane/Isopentane 0.9/0.1
0.8/0.2
0.7/0.3
0.6/0.4
0.5/0.5
0.4/0.6
0.3/0.7
0.2/0.8
0.1/0.9
20
2.16
4.94
6.98
8.47
9.39
9.58
8.86
7.38
4.51
15
2.59
4.98
6.94
8.38
9.26
9.47
8.88
7.33
4.49
10
2.60
4.91
6.82
8.26
9.14
9.37
8.78
7.24
4.46
5
2.55
4.81
6.71
8.13
9.01
9.24
8.68
7.15
4.41
Table 4 Condensation temperature glide using the 150°C heat source ΔTcf (°C)
Isobutane/Isopentane 20
0.9/0.1
0.8/0.2
0.7/0.3
0.6/0.4
0.5/0.5
0.4/0.6
0.3/0.7
0.2/0.8
0.1/0.9
20
3.85
7.00
9.42
11.11
12.03
12.15
11.34
9.33
5.77
15
3.84
6.98
9.35
10.97
11.87
11.99
11.19
9.27
5.76
10
3.83
6.88
9.19
10.81
11.70
11.82
11.04
9.12
5.7
5
3.74
6.73
9.02
10.62
11.51
11.64
10.86
8.97
5.59
The exergy efficiency of different mixtures with different ΔTcf is shown in Fig. 5. For 5 K ΔTsup and 5 K ΔTsub, 20 K ΔTcf is always larger or approximately equals to the overall ΔTglide. The matching conditions are as shown in Fig.4b and Fig.4c. Thus, the mixtures’ cycle performance is better than the pure working fluids. 0.6 isobutane/0.4 isopentane provides the best cycle performance. However, for the 5 K ΔTcf, ΔTsup+ΔTsub is already larger than 5 K ΔTcf. The matching condition of mixtures is as shown in Fig.4d. Additional condensation temperature glides will increase the condensation exergy loss. Thus, the mixtures’ cycle performance cannot surpass the pure working fluids. For 15 K ΔTcf, using 0.8 isobutane/0.2 isopentane provides the best optimal cycle performance because the overall ΔTglide matches well with the ΔTcf. However, the overall ΔTglide is much higher than the ΔTcf and the matching condition is as shown in Fig.4d when using larger condensation temperature glide mixtures, such as 0.4 isobutane/0.6 isopentane, leading to high condensation exergy loss and low exergy efficiency. Thus, the exergy efficiency curve presents a spike up to 0.8 isobutane/0.2 isopentane and then bends inwards when move toward 0.4 isobutane/0.6 isopentane. For 10 K ΔTcf, the exergy efficiency curve presents a spike up to 0.9 isobutane/0.1 isopentane and then bends inwards when move toward 0.4 isobutane/0.6 isopentane for the similar reason.
21
Fig. 5 Exergy efficiency using isobutane/isopentane mixtures for 150oC heat source Figures 6 and 7 display the mixtures’ influence on the heat source utilization and exergy loss in detail, respectively. Figure 6 shows the heat source utilization rate using isobutane/isopentane mixtures for the 150oC heat source. For ΔTcf =20 K, the overall ΔTglide are less than ΔTcf, the heat source utilization rate increases as the overall ΔTglide increases. For ΔTcf =15 K, the mixtures from 0.8 isobutane/0.2 isopentane to 0.2 isobutane/0.8 isopentane, the overall ΔTglide is higher than ΔTcf. The heat source utilization rate reaches the maximum value. For ΔTcf =10 K, the mixtures from 0.9 isobutane/0.1 isopentane to 0.1 isobutane/0.9 isopentane, the overall ΔTglide is higher than ΔTcf. The heat source utilization rate reaches the maximum value. For ΔTcf =5 K, the overall ΔTglide are all larger than ΔTcf, the heat source utilization rates of the pure working fluids already reaches the maximum value and will not be increased by using mixtures.
22
Fig. 6 Heat source utilization rate using isobutane/isopentane mixtures for 150oC heat source Figure 7 shows the exergy loss of different ORC components using isobutane/isopentane mixtures for the 150oC heat source. It can be seen that the exergy losses of the pump and the expander are relatively small and have no obvious differences between the pure working fluids and mixtures. Mixtures mainly influence on the exergy losses of the evaporator and the condenser. In Fig. 7a, for 20 K ΔTcf, the evaporation exergy loss of the mixtures are higher than that of the pure working fluids. The increase of the evaporation exergy loss is because the heat source utilization rate is increased when using mixtures. The mixtures’ condensation exergy losses are lower than the pure working fluids. Thus, the total exergy loss of the system using mixtures are not much higher than the pure working fluids. In Fig. 7d, when the “overall ΔTglide” is much larger than ΔTcf (ΔTcf = 5 K), the evaporation exergy losses are almost the same for all the fluids as the heat source utilization is almost the same. However, mixtures have larger condensation exergy losses than the pure working fluid for the mismatching with the cooling source. 23
For all these four ΔTcf, the pure working fluids have lower total system exergy loss than the mixtures. Thus, the reason why mixtures provide a better performance than the pure working fluids is not because of the decrease of the exergy loss but the increase of the heat source utilization rate.
(a)
(b)
(c)
(d)
Fig. 7 Exergy loss of ORC components with different ΔTcf 3.3. Zeotropic mixture active design procedures Based on the analysis above, the design procedures of mixture active design method is composed of three consecutive steps: 1) Satisfy the key properties of the optimal pure working fluid. This design procedure guarantees that the mixtures’ cycle performance is as good as the optimal pure working fluids’. For subcritical ORC 24
with heat source without an outlet temperature limitation, the mixtures’ critical temperature Tc should satisfy Eq.17. 2) Satisfy the matching condition during the condensation process. The mixtures’ condensation temperature glide should satisfy the matching condition with the cooling source (Eq. 20): ΔTglide= Tcf_out-Tcf_in-ΔTsup -ΔTsub. If Tcf_out-Tcf_in-ΔTsup -ΔTsub<0, mixtures should not be used. 3) Satisfy the environment, safety and cost requirements. Environment requirements mainly include the value of ODP and GWP. The working fluids should satisfy 0 ODP value and low GWP value. Perfluoro-hydrocarbon or working fluids contain more fluorine atoms, such as R227ea, usually have high GWP values. They are not highly recommended in the pure working fluid screen. The mixture’s GWP value is the mass weighted mean value of every component’s GWP value. Thus, the working fluids have good cycle performance but with high GWP value can be used by mixing with working fluids with low GWP value. Safety requirements such as toxicity and flammability are not very important for the industry system. The industry system should make sure the working fluid leakage and the fire prevention under control. There is no doubt that low toxicity and low flammability working fluids are more promising. Economic analysis should be done to balance the thermal performance and the cost of the mixtures.
4. Application of the zeotropic mixture active design method The three consecutive steps of zeotropic mixture active design will be illustrated below. The first step (matching the properties of the optimal pure working fluid) and second step (matching condition with the cooling source) focus on the mixtures’ thermal properties. The third step consists of
25
boundary conditions which can be quite different from one project to another. The binary mixtures can already reflect the thermodynamic advantage of the mixtures. Thus, the mixture active design method application here takes the binary mixtures as an example. The component of the designed mixtures are all from the common used pure working fluids displayed in Table 2. The ternary and multiple mixtures may play a role when considering the environment, safety and cost requirements. The readers could design ternary and multiple mixtures according to their own environment, safety and cost requirements. The design process using the mixture active design method is providing in detail for subcritical ORC with 210ºC heat source without an outlet temperature limitation. The inlet and outlet temperature difference of the cooling source ΔTcf is 20 K. The outlet temperature of the cooling source Tcf_out is 30ºC. Other cycle operating conditions are shown in Table 1. 1) Satisfy the key properties of the optimal pure working fluid. For subcritical ORC with heat source without an outlet temperature limitation, the critical temperature Tc of the optimal working fluid should satisfy Eq. 17. The Tc calculated by Eq. 17 is 414.65 K. Choose one working fluid whose Tc is lower than 414.65 K and another working fluid whose Tc is higher than 414.65 K. The proportions of the two working fluids are decided by Eq. 18. 0.2R227ea/0.8R245fa (mass fraction) and 0.3R1234ze(E)/0.7R245fa (mass fraction) have Tc close to 414.65 K. 2) Satisfy the matching condition between the condensation temperature glide and the cooling source as shown in Eq. 20. Thus, ΔTglide=ΔTcf - ΔTsup - ΔTsub =10 K. The condensation temperature glide of 0.2R227ea/0.8R245fa is 7.39 K which is a little lower than 10 K. The condensation temperature 26
glide of 0.3R1234ze(E)/0.7R245fa is 10.48 K and matches better with the cooling source. The results of the designed mixtures are shown in Table 5. It can be seen from Table 5 that the mixtures increase the heat source utilization Ehs_tra and reduce the condensation exergy losses Icd. The exergy efficiency of the heat source recovery ηex is improved more than 6% by the mixtures compared with the optimal pure working fluid R236ea.
Table 5 Cycle performance improvement by the mixtures for subcritical ORC with 210ºC heat source
Teva
Tc
ΔTglide
ηex
Icd
Ieva
Ehs_tra
ηex improvement
(K)
(K)
(K)
(%)
(J/kg)
(J/kg)
(J/kg)
rate
R236ea
406.88
412.44
0
41.77
7800.73
9851.01
41335.04
-
0.2R227ea/0.8R245fa
411.95
416.70
7.39
44.30
6967.84
9501.83
41600.49
6.1%
0.3R1234ze(E)/0.7R245fa
405.17
412.20
10.48
44.45
6613.67
10200.3
42274.54
6.4%
Working fluids
3) Satisfy the environment, safety and cost requirements. In this case, the system is for industry use. The safety indicators such as the working fluid leakage and the fire prevention are under control. The environmental indicators [27] and cost [28] of the working fluids used in this case are displayed in Table 6. 0.2R227ea/0.8R245fa seems to be very promising as it has almost the same GWP value and lower cost when compared with R236ea. 0.3R1234ze(E)/0.7R245fa has the best environment performance among these three candidates, however, at the expense of higher cost. Even though these working fluids are industrially produced, the product quantity is still limited. As the environmental policy becomes more and more strict and the demand for environment friendly working fluids becomes larger, the cost of R1234ze(E) is expected to become lower in the future. 27
Table 6 Environmental indicators and cost of the working fluids for subcritical ORC with 210ºC heat source
GWP
ODP
Cost
m wf
Cost
value
value
(￥/kg)
(kg/s for 1kg/s m hs )
(￥ for 1kg/s m hs )
R236ea
1410
0
200
0.7
140
R227ea
3580
0
200
-
-
6
0
1000
-
-
R245fa
1050
0
200
-
-
0.2R227ea/0.8R245fa
1556
0
200
0.63
126
0.3R1234ze(E)/0.7R245fa
736.8
0
440
0.65
286
Working fluids
R1234ze(E)
5. Conclusions Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC). In this paper, a zeotropic mixture active design method is provided for mixture selection without massive calculation or blind trial. The zeotropic mixture active design work is pushed forward based on the previous work of the quantitative criteria of the optimal pure working fluid selection. The mixture fluids are regarded as special pure fluids with the advantage of adjustable properties and temperature glide at the same time. The designed mixtures have the key property of the optimal pure working fluid and match better with the cooling source so that having better performance than the optimal pure working fluid. 28
The debatable questions referred in the introduction are answered through this work, •
The match condition of the condensation temperature glide and the cooling source is that ΔTglide approximately equals to “ΔTcf - ΔTsup - ΔTsub”. Thus, if ΔTcf is already smaller than “ΔTsup +ΔTsub”, mixtures should not be used.
•
The mixtures could improve the ORC performance not only because the mixtures decrease the exergy loss in the evaporator and condenser, but also because the mixtures increase the heat source utilization rate.
•
The mixtures’ temperature glides matching with the cooling source in the condenser is more important than matching with the heat source in the evaporator for the cycle performance improvement. Thus, mixtures are also suggested to be used in the trans-critical ORC to improve the cycle performance.
•
The zeotropic mixture active design method: mixtures should firstly have the optimal pure working fluids’ key properties and then satisfy the condensation match requirement. Mixtures designed by this method can provide much better performance than the optimal pure fluids.
Acknowledgement This work was supported by the State Key Program of the National Natural Science Foundation of China (No. 51236004),the Science Fund for Creative Research Group (No. 51321002),the Beijing Scholars Program and Beijing Advanced Innovation Center for Future Urban Design (UDC2016040200).
29
Nomenclature E
exergy (kJ)
h
enthalpy (kJ/kg)
I
exergy loss (kJ/kg)
m
mass flow rate (kg/s)
P
pressure (kPa)
Q
heat (kJ)
q
heat per unit mass flow rate of the working fluid (kJ/kg)
s
entropy (kJ/kg/K)
T
temperature (K)
W
work output (kW)
w
work output per unit mas flow rate working fluid (kJ/kg)
Greek symbols η
efficiency
Subscripts and superscripts 0
reference state
c
critical
cd
condensation
cf
cooling fluid 30
eva
evaporation
ex
exergy
exp
expander
hs
heat source
in
inlet
out
outlet
p
pinch
pp
pump
sub
subcooling
sup
superheating
t
turbine
tra
transfer
wf
working fluid
References [1] Chys M, Broek M, Vanslambrouck B, Paepe M. Potential of zeotropic mixtures as working fluids in organic Rankine cycles. Energy, 44(2012): 623-632. [2] Heberle F, Preissinger M, Brueggemann D. Zeotropic mixtures as working fluids in Organic Rankine Cycles for low-enthalpy geothermal resources. Renew. Energy, 37(2012): 364-370. [3] Lecompte S, Ameel B, Ziviani D, Broek M. Exergy analysis of zeotropic mixtures as working 31
fluids in Organic Rankine Cycles. Energy Convers. Manage., 85(2014): 727-739. [4] Song J, Gu C W. Analysis of ORC (Organic Rankine Cycle) systems with pure hydrocarbons and mixtures of hydrocarbon and retardant for engine waste heat recovery. Appl. Therm. Eng., 89(2015): 693-702. [5] Kang Z H, Zhu J L, Lu X L,Li T L, Wu X J. Parametric optimization and performance analysis of zeotropic mixtures for an organic Rankine cycle driven by low-medium temperature geothermal fluids. Appl. Therm. Eng., 89(2015): 323-331. [6] Sadeghi M, Nemati A, Ghavimi A, Yari M. Thermodynamic analysis and multi-objective optimization of various ORC (organic Rankine cycle) configurations using zeotropic mixtures. Energy, 109(2016): 791-802. [7] Wu Y D, Zhu Y D, Yu L J. Thermal and economic performance analysis of zeotropic mixtures for Organic Rankine Cycles. Appl. Therm. Eng., 96(2016): 57–63. [8] Xi H, Li M J, He Y L, Zhang Y W. Economical evaluation and optimization of organic Rankine cycle with mixture working fluids using R245fa as flame retardant. Appl. Therm. Eng., 113(2017): 1056–1070. [9] Garg P, Kumar P, Srinivasan K, Dutta P. Evaluation of isopentane, R-245fa and their mixtures as working fluids for organic Rankine cycles. Appl. Therm. Eng., 51(2013): 292-300. [10] Dong B S, Xu G Q, Cai Y, Li H W. Analysis of zeotropic mixtures used in high-temperature Organic Rankine cycle. Energy Convers. Manage., 84(2014): 253-260. [11] Bao J J, Zhao L. A review of working fluid and expander selections for organic Rankine cycle. Renew. Sust. Eng. Rev., 24(2013): 325-342. 32
[12] Gholamreza B A, Kyung C K. Investigation of organic Rankine cycles with zeotropic mixtures as a working fluid: Advantages and issues. Renew. Sust. Eng. Rev., 73(2017): 1000-1013. [13] Papadopoulos A I, Stijepovic M, Linke P, Seferlis P, Voutetakis S. Power Generation from Low Enthalpy Geothermal Fields by Design and Selection of Efficient Working Fluids for Organic Rankine Cycles. 13th International Conference on Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction, 2010: 61-66. [14] Papadopoulos A I, Stijepovic M, Linke P. On the systematic design and selection of optimal working fluids for Organic Rankine Cycles. Appl. Therm. Eng., 30(2010): 760-769. [15] Papadopoulos A I, Stijepovic M, Linke P, Seferlis P, Voutetakis S. Multi-level Design and Selection of Optimum Working Fluids and ORC Systems for Power and Heat Cogeneration from Low Enthalpy Renewable Sources. 22 European Symposium on Computer Aided Process Engineering, 2012: 66-70. [16] Papadopoulos A I, Stijepovic M, Linke P, Seferlis P, Voutetakis S. Toward Optimum Working Fluid Mixtures for Organic Rankine Cycles using Molecular Design and Sensitivity Analysis. Ind. Eng. Chem. Res., 52(2013): 12116-12133. [17] Oscar P F, Antonio F T, Graciela C M. Optimal molecular design of working fluids for sustainable low-temperature energy recovery. Comput. Chem. Eng., 72(2015): 334-349. [18] Linke P, Papadopoulos A I, Seferlis P. Systematic methods for working fluid selection and the design, integration and control of organic Rankine cycles: A Review. Energies, 8(2015): 4755-4801. [19] Maraver D, Royo J, Lemort V, Quoilin S. Systematic optimization of subcritical and transcritical 33
organic Rankine cycles (ORCs) constrained by technical parameters in multiple applications. Appl. Energy, 117(2014): 11-29. [20] Vaja I, Gambarotta A. Internal Combustion Engine (ICE) bottoming with Organic Rankine Cycles (ORCs). Energy, 35(2010): 1084-1093. [21] Zhao L, Bao J J. The influence of composition shift on organic Rankine cycle (ORC) with zeotropic mixtures. Energy Convers. Manage., 83(2014): 203-211. [22] Zhai H X, Shi L, An Q S. Influence of working fluid properties on system performance and screen evaluation indicators for geothermal ORC (organic Rankine cycle) system. Energy, 74(2014): 2-11. [23] Lemmon E W, Mclinden M O, Huber M L. NIST reference Fluid Thermodynamic and Transport Properties REFPROP, Version 9.1 [DB/DK]. National Institute of Standard Technology, 2013. [24] Zhai H X, Shi L, An Q S, V Lemort V, S Quoilin. Categorization and analysis of heat sources for ORC systems. Renew. Sust. Eng. Rev.,, 64(2016): 790-805. [25] Zhai H X, An Q S, Shi L. Analysis of the quantitative correlation between the heat source temperature and the critical temperature of the optimal pure working fluid for subcritical organic Rankine cycles. Appl. Therm. Eng., 99(2016) 383-91. [26] Kay W B. Ind. Eng. Chem. 1936, 28: 1014. [27] Calm J M, Hourahan G C. Physical, safety and environmental data for current and alternative refrigerants. Proceedings of the 23rd International Congress of Refrigeration (ICR), August 21-26th , 2011, Prague, Czech Republic. [28] http://www.crrchina.com/contact.html 34
35
Table Captions Table 1 Operating condition of the model Table 2 Properties of pure working fluids (ranked by Tc) Table 3 Evaporation temperature glide using the 150°C heat source Table 4 Condensation temperature glide using the 150°C heat source Table 5 Cycle performance improvement by the mixtures for subcritical ORC with 210ºC heat source Table 6 Environmental indicators and cost of the working fluids for subcritical ORC with 210ºC heat source
36
Figure Captions Fig. 1 ORC configuration Fig. 2 T-s diagram of subcritical ORC using mixtures Fig. 3 General idea of the zeotropic mixture active design method Fig. 4 Matching condition between the working fluid and cooling source during the condensation process Fig. 5 Exergy efficiency using isobutane/isopentane mixtures for 150oC heat source Fig. 6 Heat source utilization rate using isobutane/isopentane mixtures for 150oC heat source Fig. 7 Exergy loss of ORC components with different ΔTcf
37
Highlights
A zeotropic mixture active design method is provided for organic Rankine cycle
The designed mixtures have better performance than the optimal pure working fluid
Mixtures can increase the heat source utilization rate
Using this active design method can avoid massive calculation for mixture selection
38
S1359-4311(17)33066-1 https://doi.org/10.1016/j.applthermaleng.2017.10.027 ATE 11225
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
5 May 2017 21 September 2017 4 October 2017
Please cite this article as: H. Zhai, Q. An, L. Shi, Zeotropic mixture active design method for organic Rankine cycle, Applied Thermal Engineering (2017), doi: https://doi.org/10.1016/j.applthermaleng.2017.10.027
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Title of the article: Zeotropic mixture active design method for organic Rankine cycle
Authors: Huixing ZHAIa,b, Qingsong ANc, Lin SHIb First author’s surname: ZHAI
Affiliations: a. School of Environment and Energy Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China E-mail address:
[email protected]
b. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China E-mail address:
[email protected]
c. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy of Ministry of Education, Tianjin University, Tianjin 300072, China E-mail address:
[email protected]
Corresponding author information:
Name:
Lin SHI
Postal address: Department of Thermal Engineering, Tsinghua University, Haidian District, Beijing 1
100084, China
Tel: +861062787613
Fax: +861062787613
E-mail address: [email protected]
2
Zeotropic mixture active design method for organic Rankine cycle Huixing ZHAIa,b, Qingsong ANc , Lin SHIb* a. School of Environment and Energy Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China b. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China c. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy of Ministry of Education, Tianjin University, Tianjin 300072, China
Abstract Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC) system. Instead of recommending mixtures or compositions for a specific heat source, this work is focused on providing preliminary design guidelines of zeotropic mixture working fluids for ORC. The zeotropic mixture active design method is provided for mixture selection without massive calculation or blind trial. The designed mixtures have better performance than the optimal pure working fluid. The designed zeotropic mixtures should have the same key properties as the optimal pure working fluids and also have temperature glide matching with the cooling source. Firstly, the authors’ previous study on the optimal pure working fluid screen criteria is simply reviewed. Then, how the mixture’s temperature glide influencing on the cycle performance is analyzed. Finally, the zeotropic mixture active design method is provided and verified. Some debatable questions regarding to the mixtures are also answered.
Key words: 3
Active design; Mixtures; Temperature glide; Organic Rankine cycle; ORC
1. Introduction Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC). Researchers have recommended mixtures for different heat sources. Chys et al. [1] found that a potential increase of 16% and 6% in cycle efficiency is gained using mixtures for 150 °C and 250 °C heat sources. Heberle et al. [2] studied the performance of R227ea, isobutane, R245fa, isopentane and their mixtures for the heat source temperature below 120°C and gave the conclusion that the second law efficiency of the mixtures increased in range of 4.3% and 15% compared to the most efficient pure component. Lecompte et al. [3] analyzed the performance of eight pure working fluids and their mixtures for a 150°C heat source and the results showed that an increase in the second law efficiency in range of 7.1% and 14.2 was obtained by the mixtures compared to pure working fluids. Song et al. [4] studied R141b and R11 blended with the hydrocarbons as zeotropic mixtures and recommended cyclohexane/R141b (0.5/0.5) for the waste heat recovery of a diesel engine. Kang et al. [5] found that R245fa/R600a (0.9/0.1) was the best mixtures among 10 groups of mixtures for a 120°C geothermal heat source. Sadeghi et al. [6] found that using zeotropic mixtures as the working fluid instead of a pure fluid such as R245fa, leads to more than 24% improvement in power generation for ORC with 100°C geothermal water. Wu et al. [7] analyzed the performance of ORC using zeotropic mixtures of R227ea/R245fa, Butane/R245fa and RC318/R245fa for a 120°C hot air heat source. Results showed that the mixtures may provide high thermal efficiency but bad economic performance. However, Xi et al. [8] found that mixture working fluid is more economic-efficient than pure working fluid and R245fa/Isopentane and 4
R245fa/Pentane were recommended for 100-180°C heat sources among 4 mixture and 5 pure working fluids. Garg et al. [9] evaluated isopentane, R245fa and their mixtures’ performance in ORC for 106-151°C heat sources and recommended isopentane/R245fa (0.7/0.3). For higher temperature heat sources, Dong et al. [10] studied MM/MDM as ORC working fluids for the heat source with 280°C inlet temperature and 240°C outlet temperature. For more mixture recommendation, Bao et al. [11] and Gholamreza et al. [12] gave an overview of the mixtures used in ORC. The previous studies recommended mixtures for the specific heat source and only a couple of mixtures were analyzed. Whether the mixture is better than the optimal pure working fluid has not been proven. The mixture selection is quite different from the pure working fluid selection. There are around fifty pure working fluids commonly used in the field of organic Rankine cycles, making it is feasible to compare all the pure working fluids and find the optimal one. However, the mixtures are uncountable as there could be different compositions and proportions. Thus, it is difficult to compare all the mixtures for the optimal mixture selection. The Computer Aided Molecular Design (CAMD) [13-18] is studied for the optimal pure working fluid and mixture selection. In this paper, a zeotropic mixture active design method is provided. Instead of selecting the optimal mixtures, this method is to design mixtures which have better performance than the optimal pure working fluids without massive calculation or blind trial. The analysis of the temperature glide of this method could also be part of CAMD. The idea of this method is: as the mixtures’ properties are adjustable, the designed mixtures could have the same key property of the optimal pure working fluid and have the condensation temperature glide matching with the cooling sources at the same time. As a result, the designed mixtures have 5
better performance than all the other pure working fluids. In this paper, the zeotropic mixture active design method is introduced taking the subcritical ORC with heat sources without outlet temperature limitation as an example. The following debatable questions are also answered, •
In what condition, the mixtures are superior to the pure working fluids?
•
Why the mixtures are superior to the pure working fluids? Is it only to decrease the evaporation and condensation exergy losses?
•
What is the proper temperature glide of the mixture?
•
Does the temperature glide matching with the evaporator or the condenser provide more improvement for the cycle performance?
•
What is the mixture design method?
2. Model description of the subcritical ORC using mixtures 2.1. Subcritical ORC using mixtures
Fig. 1 ORC configuration
Fig. 2 T-s diagram of subcritical ORC using mixtures
The ORC is a simple four-component system as shown in Fig. 1. The working fluid is pumped to the
6
evaporator to be vaporized by the heat source and then expands in the expander to generate work. The vapor or liquid out of the expander goes into the condenser to total condensed to liquid. Then the liquid working fluid goes to the pump and begins a new circulation. Evaporating pressure is controlled to be lower than 0.9Pc or the saturate pressure of (T5-Tp) to guarantee a subcritical cycle as shown in Fig. 2. 2.2. Subcritical ORC model using mixtures 2.2.1. Model assumptions There is no pressure drop during the working fluid flowing in the system. Because the pressure drop is not easy to calculate accurately. The cycle is running at steady state. These assumptions may make the cycle efficiency higher than the actual condition, however, have little influence on the working fluid selection. The heat exchangers are in counter flow layout. Compared with the parallel flow layout, the counter flow layout has larger logarithmic mean temperature difference so that the heat exchanger is more compact. 2.2.2. First law of thermodynamics analysis The subscript of the parameters are referred to Fig. 2. The cycle efficiency is calculated by,
wt wpp qeva
(1)
where wt is the work output of the expander, wpp is the work consumed by the pump and qeva is the heat absorbed by the working fluid. And,
wt h3 h4 7
(2)
wpp h2 h1
(3)
qeva h3 h2
(4)
The cycle work output is calculated by,
.
W net mwf (wt wpp ) Q
(5)
where m wf is the mass flow rate of the working fluid and Q is the heat absorbed by the cycle.
And Q is calculated by,
.
Q mhs (h5 h6 )
(6)
where m hs is the mass flow rate of the working fluid. 2.2.3. Second law of thermodynamic analysis The reference state is as follows, T0 = 293.15 K, P0=0.1 MPa
(7)
The exergy of a thermodynamic system is defined as the theoretical maximum work that could be produced if the system is brought into equilibrium with its surroundings. The exergy of the heat source without an outlet temperature limitation is given by,
E hs mhs [h5 h0 T0 (s5 s0 )]
(8)
In general, the ORC system cannot decrease the heat source temperature into the temperature of the environment and only part of the heat source exergy can be transferred to the ORC working fluid. The exergy transferred to the working fluid is given by,
E hs _tra mhs [h5 h6 T0 ( s5 s6 )]
(9)
The exergy obtained by the working fluid during the evaporation process is calculated by,
E wf_eva mwf [h3 h2 T0 ( s3 s2 )] 8
(10)
The exergy loss during the evaporation process is calculated by,
I eva E hs _in E wf_eva_in T0 [mwf ( s3 s2 ) mhs (s5 s6 )]
(11)
The exergy loss during the expansion process is calculated by,
I exp mwf T0 ( s4 s3 )
(12)
As all the exergy during the condensation process is released to the environment, the exergy loss during the condensation process is calculated by,
I cd mwf [h4 h1 T0 ( s4 s1 )]
(13)
The exergy loss in the pump is calculated by,
I pp mwf T0 ( s2 s1 )
(14)
The exergy balance is given as the follows,
E hs_tra I W net
(15)
which means that the exergy of the heat source that transferred to the ORC working fluid covers all the exergy deduction and the net work output. The system performance metrics is the exergy efficiency of the heat source energy recovery which is defined by,
ex
W net
(16)
E hs
As the E hs of a specific heat source is fixed, from Eqs. 15 and 16, it could be found that the more
exergy transferred to the working fluid from the heat source E hs _tra and less total exergy losses
I give higer exergy efficiencyex . 2.3. Working conditions The calculations were done with the working conditions listed in Table 1. The mass flow rate of the 9
heat source was set to be 1kg/s. The pinch temperature difference is different according to the source heat transfer capability. Typical pinch point temperature difference in the heat exchanger is 10°C for liquid sources [19] and 30°C for gas sources [20]. The outlet temperature of the cooling source is 30°C for the natural cooling condition and 60°C for the combined heat and power system. The expander isentropic efficiency is around 0.75 to 0.8 and the pump isentropic efficiency is around 0.6 to 0.8 [3, 21, 22]. However, the expander and pump isentropic efficiencies would not affect the working fluid selection. The expander and pump isentropic efficiencies need to be unified when compare the working fluids’ cycle performance. If not otherwise specified, the expander and pump isentropic efficiencies are chosen as Table 1 shows. The results were obtained using Matlab together with Refprop 9.1 [23]. In Refprop 9.1, the properties for working pairs without experiment data are estimated by the modified Helmoltz equation. The model in this paper is verified with other works [22].
Table 1 Operating condition of the model Part
Parameter
Assumption
Pinch temperature difference in the evaporator Tp_eva
10 K for water, 30 K for air
Pinch temperature difference in the condenser Tp_cd
10 K
Superheating degree ΔTsup
5K
Subcooling degree ΔT sub
5K
ORC cycle
Expander isentropic efficiency Pump isentropic efficiency
exp
0.8
pp
0.65
10
Heat source fluid mass flow rate m hs
1 kg/s
Heat source inlet temperature Ths
Water: 150°C; Air: 210°C
Outlet temperature of cooling water Tcf_out
30°C-60°C
Heat source
Heat sink
Difference between inlet and outlet temperature of 5 K, 10 K, 15 K, 20 K cooling water ΔTcf
2.4. Working fluids The common used pure working fluids and their key properties are displayed in Table 2, mainly including HFCs, HCs, siloxanes and benzenes. CFCs and HCFCs whose ODP values are not zero are not included for the environment requirement. The thermal properties of the working fluids are referred to Refprop 9.1[23]. The common used pure working fluids have clear thermal properties and are easy to obtain. Thus, the mixtures designed in this paper are consisted of these common used pure working fluids. Table 2 Properties of pure working fluids (ranked by Tc) Working fluid
Molecular formula
Molecular
Tc (°C)
Pc (Mpa)
weight(kg/kmol) R125
CHF2CF3
120.02
66.02
3.6177
R218
CF3CF2CF3
188.02
71.87
2.64
R143a
CF3CH3
84.041
72.71
3.761
R32
CH2F2
52.024
78.11
5.782
propylene
CH2=CH-CH3
42.08
91.06
4.555
R1234yf
CF3CF=CH2
114.04
94.70
3.38
11
propane
CH3CH2CH3
44.096
96.74
4.2512
R134a
CF3CH2F
102.03
101.06
4.0593
R227ea
CF3CHFCF3
170.03
101.75
2.92
R161
C2H5F
48.06
102.15
5.091
R1234ze(E)
CHF=CHCF3(trans)
114.04
109.37
3.6363
perfluorobutane
C4F10
238.03
113.18
2.32
R152a
CHF2CH3
66.051
113.26
4.5168
RC318
cyclo-C4F8
200.03
115.23
2.77
R236fa
CF3CH2CF3
152.04
124.92
3.20
cyclopropane
cyclo-C3H6
42.081
125.15
5.5797
propyne
CH3CCH
40.06
129.23
5.626
isobutane
CH(CH3)3
58.122
134.66
3.63
R236ea
CF3CHFCHF2
152.04
139.29
3.50
isobutene
CH2-C(CH3)2
56.106
144.94
4.01
butene
CH3-CH2-CH=CH2
56.106
146.14
4.01
perfluoropentane
C5F12
288.03
147.41
2.05
butane
CH3-2(CH2)-CH3
58.122
151.98
3.80
R245fa
CF3CH2CHF2
134.05
154.01
3.65
trans-butene
CH3-CH=CH-CH3
56.106
155.46
4.03
neopentane
C(CH3)4
72.149
160.59
3.20
cis-butene
CH3-CH=CH-CH3
56.106
162.60
4.23
12
R245ca
CHF2CF2CH2F
134.05
174.42
3.93
R365mfc
CF3CH2CF2CH3
148.07
186.85
3.27
isopentane
(CH3)2CHCH2CH3
72.149
187.20
3.38
pentane
CH3-3(CH2)-CH3
72.149
196.55
3.37
isohexane
(CH3)2CH(CH2)2CH3
86.175
224.55
3.04
hexane
CH3-4(CH2)-CH3
86.175
234.67
3.03
cyclopentane
cyclo-C5H10
70.133
238.54
4.52
MM
C6H18OSi2
162.38
245.60
1.94
heptane
CH3-5(CH2)-CH3
100.2
266.98
2.74
cyclohexane
cyclo-C6H12
84.161
280.49
4.08
dimethyl carbonate
C3H6O3
90.078
284.23
4.84
benzene
C6H6
78.112
288.87
4.91
MDM
C8H24O2Si3
236.53
290.94
1.42
octane
CH3-6(CH2)-CH3
114.23
296.17
2.50
methylcyclohexane
C6H11(CH3)
98.186
299.05
3.47
D4
C8H24O4Si4
296.62
313.35
1.33
toluene
CH3-C6H5
92.138
318.60
4.13
nonane
CH3-7(CH2)-CH3
128.26
321.40
2.28
MD2M
C10H30Si4O3
310.69
326.25
1.23
decane
CH3-8(CH2)-CH3
142.28
344.55
2.10
propylcyclohexane
(C6H11)CH2CH2CH3
126.24
357.65
2.86
13
3. Zeotropic mixture active design method There are around fifty pure working fluids commonly used in the field of organic Rankine cycles, making it is feasible to calculate all the common used pure working fluids’ cycle performance and choose the optimal one. However, mixtures have different components and proportions, it is not convenient to calculate all the mixtures for the mixture selection. Thus, the mixture active design method is needed for quick and simple mixture selection. The mixture design idea of this paper is that: the mixture fluids are regarded as special pure fluids with the advantage of adjustable properties and temperature glides at the same time; the mixture is designed actively to have the appropriate properties and temperature glides so that the cycle performance is improved. Figure 3 displays the general idea of the zeotropic mixture active design method.
Fig. 3 General idea of the zeotropic mixture active design method Firstly, the key properties which mainly influence the cycle performance of the optimal pure working fluid should be obtained. The designed mixtures’ properties should have the same key properties as
14
the optimal pure working fluid so that the mixtures’ performance is no worse than the optimal pure working fluid. These will be analyzed in detail in part 3.1. Secondly, the mixtures’ condensation temperature glides should match with the cooling source so that the mixtures’ performance is better than the optimal pure working fluid. In part 3.2, how the temperature glides’ influence on the cycle performance and under which condition the mixtures match with the cooling source are analyzed. Finally, based on the analysis of part 3.1 and 3.2, the detailed design procedures are provided in part 3.3. Through this method, the mixtures which have better performance than the optimal pure working fluids could be designed without massive calculation. The common used pure working fluids displayed in Table 2 are used to apply the zeotropic mixture design.
3.1. The key properties of the optimal pure working fluid The key properties of the work fluids influencing the cycle performance could be different for different cycle types and heat source types. The organic Rankine cycles could be subcritical or trans-critical. The heat sources could be divided into the finite capacity heat source without an outlet temperature limitation, the finite capacity heat source with an outlet temperature limitation and the infinite heat capacity heat source [24]. The quantitative conclusion of the optimal pure working fluid’s key property is needed for the mixture design. Take the subcritical ORC with the heat sources without an outlet temperature limitation as an example. For the subcritical ORC with heat sources without outlet temperature limitation, the key property of the optimal pure working fluid is the critical temperature Tc. When the heat source 15
temperatures are between 150-350°C and the outlet temperatures of the cooling sources are between 30-60°C, the key property Tc of the pure optimal working fluid has the quantitative relation with the source temperature Ths and the evaporation pinch temperature difference Tp_eva as displayed in Eq. 17. The detailed analysis could be referred in the authors’ previous work [25].
Th s T p _ e v2a 9 . 0 2 6 T h T 2a0 . 1 6 9 s p_ e v Tc 1.0669 1.0982
（17）
The unit in Eq.17 is °C. With the same Ths and Tp_eva, Tc is lower when the outlet temperature of the cooling source is near 30°C while Tc is higher when the outlet temperature of the cooling source is near 60°C. The mixture’s Tc follows the Kay rule as shown in Eq.18 [26]. Tcm is the mixture’s Tc, Tcj is the Tc of one component and yj is this component’s molar mass fraction. The deviation between the mixture’s Tc calculated by the Kay rule and other more complex rules is less than 2%.
Tcm y jTcj
( 0.5
j
Pci Tci 2) 2 and 0.5 Pcj Tcj
（18）
The designed mixtures satisfy Eq.17, so that their cycle performance will be no worse than the optimal pure working fluid. What’s more, the pure working fluid’s property is fixed while the mixtures’ properties are adjustable by changing the components and proportions which can be closer to the key property. 3.2. Analysis of the temperature glide influence on the cycle performance The largest difference between mixtures and pure working fluids are that mixtures have temperature glides during the evaporation and condensation processes as shown in Fig. 2. The degree of the temperature glide decreases as the phase change pressure increases. Thus, for one mixture, the degree of the temperature glide during the condensation process is larger than that during the 16
evaporation process. In addition, for the subcritical ORC, the proportion of the latent evaporation part is less than that of the latent condensation part. And for the trans-critical ORC, the evaporation temperature glide plays a small role during the supercritical evaporation process. Therefore, the temperature glides during the condensation process have larger influence on improving the cycle performance and the following parts are focusing on the condensation temperature glide matching with the cooling source. 3.2.1. Matching condition during the condensation process According to the working fluid condensation temperature glide degree and the cooling source inlet and outlet temperature difference, the four matching conditions are displayed in Fig. 4. In Fig. 4, Tcd_in is the inlet temperature and Tcd_out is the outlet temperature of the working fluid during the condensation process; the condensation temperature glide ΔTglide=Tcd_in-Tcd_out; Tcf_in is the inlet temperature and Tcf_out is the outlet temperature of the cooling source during the condensation process; ΔTcf=Tcf_out-Tcf_in. If the temperature difference between the working fluid and the cooling source is large, the exergy loss during the condensation process is large. If the working fluid temperature increased by the pump from the condenser outlet is neglected, the allowed lowest heat source outlet temperature is approximately equal to the summation of the condenser outlet temperature of the working fluid Tcd_out and the condensation pinch temperature difference Tp_cd. Thus, if Tcd_out is lower, the heat source outlet temperature may decrease to a lower temperature so that increasing the heat source utilization.
17
(a)
(b)
(c)
(d)
Fig. 4 Matching condition between the working fluid and cooling source during the condensation process
The four matching conditions are illustrated as the follows: 1) No condensation temperature glides as shown in Fig. 4a: ΔTglide=0, this is using a pure working fluid. The pinch point appears in the condenser inlet of the working fluid. The condensation exergy loss is large and the heat source utilization could not be improved. 2) Perfect condensation temperature glides as shown in Fig. 4b: ΔTglide=ΔTcf. The working fluid and 18
the cooling source keep the minimum pinch temperature difference all along the condenser. The condensation exergy loss is the lowest and Tcd_out is the lowest so that the heat source utilization could be improved. 3) Small condensation temperature glides as shown in Fig. 4c: ΔTglide<ΔTcf. The pinch point appears in the condenser inlet of the working fluid. The condensation exergy loss is lower than the pure working fluid and Tcd_out is lower than the pure working fluid so that the heat source utilization could be improved compared to the pure working fluid. 4) Overlarge condensation temperature glides as shown in Fig. 4d: ΔTglide>ΔTcf. The pinch point appears in the condenser outlet of the working fluid. Tcd_out is already the lowest so that the heat source utilization could be improved. As the ΔTglide is becoming larger, the heat source utilization will not increase, however, the condensation exergy loss will increase. It can be seen from the analysis above that mixtures can improve the cycle performance by decreasing the condensation exergy loss and increasing the heat source utilization for the heat source without an outlet temperature limitation. The perfect matching condition is: ΔTglide=ΔTcf
（19）
For the real cycle, the working fluid in the condenser has three sections: the superheat inlet section, the latent heat exchange section and the subcooling outlet section. The condensation temperature glide only exists in the latent heat exchange section. The superheat degree of the expander inlet ΔTsup is close to the superheat degree of the condenser inlet. If the expander inlet ΔTsup and the subcooling degree of the condenser outlet ΔTsub is given, the matching condition is: overall ΔTglide = ΔTcf 19
（20)
The overall ΔTglide is equal to ΔTsup+ΔTglide+ΔTsub. It is not easy to make the overall ΔTglide right equals to ΔTcf. The closer of the overall ΔTglide and ΔTcf, the better of the cycle performance. 3.2.2. Verification of the matching condition The condensation temperature glide’s influence on the cycle performance and the matching condition are verified by the following calculation cases. The cooling source outlet temperature Tcf_out is 30°C and the cooling source inlet temperature Tcf_in is 10°C, 15°C, 20°C and 25°C, respectively. Correspondingly, the difference between inlet and outlet temperature of cooling water ΔTcf are 20 K, 15 K, 10 K and 5 K, respectively. The temperature glide degrees of the isobutane/isopentane mixtures using the 150°C heat source are listed in Tables 3 and 4. As the increase of the pressure, the temperature glide decreases significantly. So the condensation temperature glide is larger than the evaporation temperature glide. For higher temperature heat sources, the evaporation temperature glide could be smaller. Table 3 Evaporation temperature glide using the 150°C heat source ΔTcf (°C)
Isobutane/Isopentane 0.9/0.1
0.8/0.2
0.7/0.3
0.6/0.4
0.5/0.5
0.4/0.6
0.3/0.7
0.2/0.8
0.1/0.9
20
2.16
4.94
6.98
8.47
9.39
9.58
8.86
7.38
4.51
15
2.59
4.98
6.94
8.38
9.26
9.47
8.88
7.33
4.49
10
2.60
4.91
6.82
8.26
9.14
9.37
8.78
7.24
4.46
5
2.55
4.81
6.71
8.13
9.01
9.24
8.68
7.15
4.41
Table 4 Condensation temperature glide using the 150°C heat source ΔTcf (°C)
Isobutane/Isopentane 20
0.9/0.1
0.8/0.2
0.7/0.3
0.6/0.4
0.5/0.5
0.4/0.6
0.3/0.7
0.2/0.8
0.1/0.9
20
3.85
7.00
9.42
11.11
12.03
12.15
11.34
9.33
5.77
15
3.84
6.98
9.35
10.97
11.87
11.99
11.19
9.27
5.76
10
3.83
6.88
9.19
10.81
11.70
11.82
11.04
9.12
5.7
5
3.74
6.73
9.02
10.62
11.51
11.64
10.86
8.97
5.59
The exergy efficiency of different mixtures with different ΔTcf is shown in Fig. 5. For 5 K ΔTsup and 5 K ΔTsub, 20 K ΔTcf is always larger or approximately equals to the overall ΔTglide. The matching conditions are as shown in Fig.4b and Fig.4c. Thus, the mixtures’ cycle performance is better than the pure working fluids. 0.6 isobutane/0.4 isopentane provides the best cycle performance. However, for the 5 K ΔTcf, ΔTsup+ΔTsub is already larger than 5 K ΔTcf. The matching condition of mixtures is as shown in Fig.4d. Additional condensation temperature glides will increase the condensation exergy loss. Thus, the mixtures’ cycle performance cannot surpass the pure working fluids. For 15 K ΔTcf, using 0.8 isobutane/0.2 isopentane provides the best optimal cycle performance because the overall ΔTglide matches well with the ΔTcf. However, the overall ΔTglide is much higher than the ΔTcf and the matching condition is as shown in Fig.4d when using larger condensation temperature glide mixtures, such as 0.4 isobutane/0.6 isopentane, leading to high condensation exergy loss and low exergy efficiency. Thus, the exergy efficiency curve presents a spike up to 0.8 isobutane/0.2 isopentane and then bends inwards when move toward 0.4 isobutane/0.6 isopentane. For 10 K ΔTcf, the exergy efficiency curve presents a spike up to 0.9 isobutane/0.1 isopentane and then bends inwards when move toward 0.4 isobutane/0.6 isopentane for the similar reason.
21
Fig. 5 Exergy efficiency using isobutane/isopentane mixtures for 150oC heat source Figures 6 and 7 display the mixtures’ influence on the heat source utilization and exergy loss in detail, respectively. Figure 6 shows the heat source utilization rate using isobutane/isopentane mixtures for the 150oC heat source. For ΔTcf =20 K, the overall ΔTglide are less than ΔTcf, the heat source utilization rate increases as the overall ΔTglide increases. For ΔTcf =15 K, the mixtures from 0.8 isobutane/0.2 isopentane to 0.2 isobutane/0.8 isopentane, the overall ΔTglide is higher than ΔTcf. The heat source utilization rate reaches the maximum value. For ΔTcf =10 K, the mixtures from 0.9 isobutane/0.1 isopentane to 0.1 isobutane/0.9 isopentane, the overall ΔTglide is higher than ΔTcf. The heat source utilization rate reaches the maximum value. For ΔTcf =5 K, the overall ΔTglide are all larger than ΔTcf, the heat source utilization rates of the pure working fluids already reaches the maximum value and will not be increased by using mixtures.
22
Fig. 6 Heat source utilization rate using isobutane/isopentane mixtures for 150oC heat source Figure 7 shows the exergy loss of different ORC components using isobutane/isopentane mixtures for the 150oC heat source. It can be seen that the exergy losses of the pump and the expander are relatively small and have no obvious differences between the pure working fluids and mixtures. Mixtures mainly influence on the exergy losses of the evaporator and the condenser. In Fig. 7a, for 20 K ΔTcf, the evaporation exergy loss of the mixtures are higher than that of the pure working fluids. The increase of the evaporation exergy loss is because the heat source utilization rate is increased when using mixtures. The mixtures’ condensation exergy losses are lower than the pure working fluids. Thus, the total exergy loss of the system using mixtures are not much higher than the pure working fluids. In Fig. 7d, when the “overall ΔTglide” is much larger than ΔTcf (ΔTcf = 5 K), the evaporation exergy losses are almost the same for all the fluids as the heat source utilization is almost the same. However, mixtures have larger condensation exergy losses than the pure working fluid for the mismatching with the cooling source. 23
For all these four ΔTcf, the pure working fluids have lower total system exergy loss than the mixtures. Thus, the reason why mixtures provide a better performance than the pure working fluids is not because of the decrease of the exergy loss but the increase of the heat source utilization rate.
(a)
(b)
(c)
(d)
Fig. 7 Exergy loss of ORC components with different ΔTcf 3.3. Zeotropic mixture active design procedures Based on the analysis above, the design procedures of mixture active design method is composed of three consecutive steps: 1) Satisfy the key properties of the optimal pure working fluid. This design procedure guarantees that the mixtures’ cycle performance is as good as the optimal pure working fluids’. For subcritical ORC 24
with heat source without an outlet temperature limitation, the mixtures’ critical temperature Tc should satisfy Eq.17. 2) Satisfy the matching condition during the condensation process. The mixtures’ condensation temperature glide should satisfy the matching condition with the cooling source (Eq. 20): ΔTglide= Tcf_out-Tcf_in-ΔTsup -ΔTsub. If Tcf_out-Tcf_in-ΔTsup -ΔTsub<0, mixtures should not be used. 3) Satisfy the environment, safety and cost requirements. Environment requirements mainly include the value of ODP and GWP. The working fluids should satisfy 0 ODP value and low GWP value. Perfluoro-hydrocarbon or working fluids contain more fluorine atoms, such as R227ea, usually have high GWP values. They are not highly recommended in the pure working fluid screen. The mixture’s GWP value is the mass weighted mean value of every component’s GWP value. Thus, the working fluids have good cycle performance but with high GWP value can be used by mixing with working fluids with low GWP value. Safety requirements such as toxicity and flammability are not very important for the industry system. The industry system should make sure the working fluid leakage and the fire prevention under control. There is no doubt that low toxicity and low flammability working fluids are more promising. Economic analysis should be done to balance the thermal performance and the cost of the mixtures.
4. Application of the zeotropic mixture active design method The three consecutive steps of zeotropic mixture active design will be illustrated below. The first step (matching the properties of the optimal pure working fluid) and second step (matching condition with the cooling source) focus on the mixtures’ thermal properties. The third step consists of
25
boundary conditions which can be quite different from one project to another. The binary mixtures can already reflect the thermodynamic advantage of the mixtures. Thus, the mixture active design method application here takes the binary mixtures as an example. The component of the designed mixtures are all from the common used pure working fluids displayed in Table 2. The ternary and multiple mixtures may play a role when considering the environment, safety and cost requirements. The readers could design ternary and multiple mixtures according to their own environment, safety and cost requirements. The design process using the mixture active design method is providing in detail for subcritical ORC with 210ºC heat source without an outlet temperature limitation. The inlet and outlet temperature difference of the cooling source ΔTcf is 20 K. The outlet temperature of the cooling source Tcf_out is 30ºC. Other cycle operating conditions are shown in Table 1. 1) Satisfy the key properties of the optimal pure working fluid. For subcritical ORC with heat source without an outlet temperature limitation, the critical temperature Tc of the optimal working fluid should satisfy Eq. 17. The Tc calculated by Eq. 17 is 414.65 K. Choose one working fluid whose Tc is lower than 414.65 K and another working fluid whose Tc is higher than 414.65 K. The proportions of the two working fluids are decided by Eq. 18. 0.2R227ea/0.8R245fa (mass fraction) and 0.3R1234ze(E)/0.7R245fa (mass fraction) have Tc close to 414.65 K. 2) Satisfy the matching condition between the condensation temperature glide and the cooling source as shown in Eq. 20. Thus, ΔTglide=ΔTcf - ΔTsup - ΔTsub =10 K. The condensation temperature glide of 0.2R227ea/0.8R245fa is 7.39 K which is a little lower than 10 K. The condensation temperature 26
glide of 0.3R1234ze(E)/0.7R245fa is 10.48 K and matches better with the cooling source. The results of the designed mixtures are shown in Table 5. It can be seen from Table 5 that the mixtures increase the heat source utilization Ehs_tra and reduce the condensation exergy losses Icd. The exergy efficiency of the heat source recovery ηex is improved more than 6% by the mixtures compared with the optimal pure working fluid R236ea.
Table 5 Cycle performance improvement by the mixtures for subcritical ORC with 210ºC heat source
Teva
Tc
ΔTglide
ηex
Icd
Ieva
Ehs_tra
ηex improvement
(K)
(K)
(K)
(%)
(J/kg)
(J/kg)
(J/kg)
rate
R236ea
406.88
412.44
0
41.77
7800.73
9851.01
41335.04
-
0.2R227ea/0.8R245fa
411.95
416.70
7.39
44.30
6967.84
9501.83
41600.49
6.1%
0.3R1234ze(E)/0.7R245fa
405.17
412.20
10.48
44.45
6613.67
10200.3
42274.54
6.4%
Working fluids
3) Satisfy the environment, safety and cost requirements. In this case, the system is for industry use. The safety indicators such as the working fluid leakage and the fire prevention are under control. The environmental indicators [27] and cost [28] of the working fluids used in this case are displayed in Table 6. 0.2R227ea/0.8R245fa seems to be very promising as it has almost the same GWP value and lower cost when compared with R236ea. 0.3R1234ze(E)/0.7R245fa has the best environment performance among these three candidates, however, at the expense of higher cost. Even though these working fluids are industrially produced, the product quantity is still limited. As the environmental policy becomes more and more strict and the demand for environment friendly working fluids becomes larger, the cost of R1234ze(E) is expected to become lower in the future. 27
Table 6 Environmental indicators and cost of the working fluids for subcritical ORC with 210ºC heat source
GWP
ODP
Cost
m wf
Cost
value
value
(￥/kg)
(kg/s for 1kg/s m hs )
(￥ for 1kg/s m hs )
R236ea
1410
0
200
0.7
140
R227ea
3580
0
200
-
-
6
0
1000
-
-
R245fa
1050
0
200
-
-
0.2R227ea/0.8R245fa
1556
0
200
0.63
126
0.3R1234ze(E)/0.7R245fa
736.8
0
440
0.65
286
Working fluids
R1234ze(E)
5. Conclusions Using mixture working fluids has been proven to be an effective way to improve the performance of organic Rankine cycles (ORC). In this paper, a zeotropic mixture active design method is provided for mixture selection without massive calculation or blind trial. The zeotropic mixture active design work is pushed forward based on the previous work of the quantitative criteria of the optimal pure working fluid selection. The mixture fluids are regarded as special pure fluids with the advantage of adjustable properties and temperature glide at the same time. The designed mixtures have the key property of the optimal pure working fluid and match better with the cooling source so that having better performance than the optimal pure working fluid. 28
The debatable questions referred in the introduction are answered through this work, •
The match condition of the condensation temperature glide and the cooling source is that ΔTglide approximately equals to “ΔTcf - ΔTsup - ΔTsub”. Thus, if ΔTcf is already smaller than “ΔTsup +ΔTsub”, mixtures should not be used.
•
The mixtures could improve the ORC performance not only because the mixtures decrease the exergy loss in the evaporator and condenser, but also because the mixtures increase the heat source utilization rate.
•
The mixtures’ temperature glides matching with the cooling source in the condenser is more important than matching with the heat source in the evaporator for the cycle performance improvement. Thus, mixtures are also suggested to be used in the trans-critical ORC to improve the cycle performance.
•
The zeotropic mixture active design method: mixtures should firstly have the optimal pure working fluids’ key properties and then satisfy the condensation match requirement. Mixtures designed by this method can provide much better performance than the optimal pure fluids.
Acknowledgement This work was supported by the State Key Program of the National Natural Science Foundation of China (No. 51236004),the Science Fund for Creative Research Group (No. 51321002),the Beijing Scholars Program and Beijing Advanced Innovation Center for Future Urban Design (UDC2016040200).
29
Nomenclature E
exergy (kJ)
h
enthalpy (kJ/kg)
I
exergy loss (kJ/kg)
m
mass flow rate (kg/s)
P
pressure (kPa)
Q
heat (kJ)
q
heat per unit mass flow rate of the working fluid (kJ/kg)
s
entropy (kJ/kg/K)
T
temperature (K)
W
work output (kW)
w
work output per unit mas flow rate working fluid (kJ/kg)
Greek symbols η
efficiency
Subscripts and superscripts 0
reference state
c
critical
cd
condensation
cf
cooling fluid 30
eva
evaporation
ex
exergy
exp
expander
hs
heat source
in
inlet
out
outlet
p
pinch
pp
pump
sub
subcooling
sup
superheating
t
turbine
tra
transfer
wf
working fluid
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Table Captions Table 1 Operating condition of the model Table 2 Properties of pure working fluids (ranked by Tc) Table 3 Evaporation temperature glide using the 150°C heat source Table 4 Condensation temperature glide using the 150°C heat source Table 5 Cycle performance improvement by the mixtures for subcritical ORC with 210ºC heat source Table 6 Environmental indicators and cost of the working fluids for subcritical ORC with 210ºC heat source
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Figure Captions Fig. 1 ORC configuration Fig. 2 T-s diagram of subcritical ORC using mixtures Fig. 3 General idea of the zeotropic mixture active design method Fig. 4 Matching condition between the working fluid and cooling source during the condensation process Fig. 5 Exergy efficiency using isobutane/isopentane mixtures for 150oC heat source Fig. 6 Heat source utilization rate using isobutane/isopentane mixtures for 150oC heat source Fig. 7 Exergy loss of ORC components with different ΔTcf
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Highlights
A zeotropic mixture active design method is provided for organic Rankine cycle
The designed mixtures have better performance than the optimal pure working fluid
Mixtures can increase the heat source utilization rate
Using this active design method can avoid massive calculation for mixture selection
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