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Temperature matching method of selecting working fluids for geothermal heat pumps
Applied Thermal Engineering 23 (2003) 179–195 www.elsevier.com/locate/apthermeng
Temperature matching method of selecting working fluids for geothermal heat pumps P.C. Zhao, L. Zhao, G.L. Ding *, C.L. Zhang Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, No. 1954, Huashan Road, Shanghai 200030, China Received 8 February 2002; accepted 15 September 2002
Abstract The fact, that some areas need district heating through heat pumps and at the same time recover residual heat from geothermal water, presents a new working condition: feed water temperature of heat network 80 °C, return water temperature 65 °C; discarded geothermal water temperature 40 °C and its emission standard temperature below 30 °C. But none of known pure refrigerants and mixtures can meet this requirement. The paper introduces a novel approach named temperature-matching method, which provides a direction in selecting high-performance working fluids for further research. It is shown from the results that the mean COPs of binary and ternary mixtures are 4.85 and 4.74 respectively, but that of pure refrigerants is 4.12 under the same ambient condition. This point indicates that temperature matching contributes to energy saving. The novel approach to high-performance working fluids can be conveniently introduced into other working conditions. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Temperature matching; Method; Non-azeotropic; Exergy loss; COP; Geothermal
1. Introduction Some areas, such as Tianjin China, need district heating [1–5], and at the same time recover residual heat from low-temperature geothermal water of about 40 °C. If the geothermal water is directly discharged to the environment, it will result in not only low efficiency of using geothermal energy resources but also pollution to the Earth surface [4].
*
Corresponding author. Tel.: +86-21-62932110; fax: +86-21-62932601. E-mail address: [email protected] (G.L. Ding).
1359-4311/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 1 7 1 - 0
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Nomenclature cp specific heat at constant pressure (kJ kg1 K1 ) COP coefficient of performance Ex exergy loss (kJ) Fx ; F heat transfer area (m2 ) h specific enthalpy (kJ kg1 ) LMTD log mean temperature difference (°C or K) m mass flow rate (kg s1 ) p pressure (kPa) q specific heating capacity (kJ kg1 ) volumetric heating capacity (kJ m3 ) qv Q heating capacity (kW) T Kelvin temperature (K) t Celsius temperature (°C) ambient temperature (K) T0 U overall heat transfer coefficient (W m2 K1 ) v specific volume (m3 kg1 ) w specific work (kJ kg1 ) l defined in Eq. (9) g compressor isentropic efficiency Subscripts bubble, bub bubble-point dew dew-point crit (pseudo) critical point evap evaporator cond condenser com compressor cool cool side hot hot side in inlet side out outlet side Abbreviation HC hydrocarbon HFC hydrofluorocarbon CFC chlorofluorocarbon HCFC hydrochlorofluorocarbon SHTF second heat transfer fluid HTF heat transfer fluid GHPS geothermal heat pump system
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The problem can be solved through heat pumps. The heat pumps have two main functions: district heating and heat recovery from discarded geothermal water, which can raise the utility rate of geothermal energy and prevent surface pollution. This new working condition requires: feed water temperature of heat network 80 °C, return water temperature 65 °C; discarded geothermal water temperature 40 °C and its emission standard temperature below 30 °C. However, none of known pure refrigerants and mixtures can meet this requirement. It can be easily understood that working fluids are very important to GHPS. Currently R22 is used in the GHPS [6], but it has the following undesirable aspects: (1) R22 is a kind of HCFCs; (2) heating water temperature reaches only 45 °C; (3) COP reaches only 2.8. Sometimes, when a new working condition is presented, it is difficult to find its proper pure working fluids, which meet environmental requirement and meanwhile is thermodynamically high performance. But mixtures of the pure refrigerants can suit many conditions because of their variability. Another advantage of mixtures is that they can suit ambient temperature, approaching Lorentz cycle and behaving well in performance. Up to now, it has been shown in some papers [7–10] that temperature matching can help to increase efficiency. For example, Jung [9] concluded that the high performance (20–30% increase in COP under proper operating conditions) of his system contributes mainly to temperature matching between refrigerant mixtures and the SHTF, and then recommended that the first step in selecting a proper mixture be to compare the gliding TD of that mixture against the available TD of SHTF in the heat exchanger. For the purpose of temperature matching, counter flow must be used in heat exchangers. In this study, a novel approach named temperature-matching method is used to select those mixtures that can work in GHPS. This method chiefly aims at highest efficiency, and provides a direction in selecting high-performance mixtures. Twenty pure refrigerants discussed in the paper are listed in Table 1, which can be available from Refprop 6.1 [11]. Arbitrary binary and ternary compounds of the 20 pure refrigerants are made with different mass ratio at intervals of 10% at a time over the entire spectrum, and as a result, 1710 binary and 41 040 ternary mixtures can be attained theoretically. From the list of 33 pure refrigerants provided in Refprop 6.1, 6 CFCs (R11, R113, R114, R115, R12 and R13) and 5 HCFCs (R22, R123, R124, R141b and R142b), which have a value of ODP, and are forbidden by Montreal Protocol, and then they are not included in Table 1. What is more, there are two inorganic compounds, ammonia and carbon dioxide, excluded from the table. Table 1 Pure refrigerants analyzed in the study HC Ethane Propane Butane Isobutene Propylene
HFC R116 R125 R134a R14 R143a R152a R227ea R23
R236ea R236fa R245ca R245fa R32 R41 RC318
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2. Optimal temperature matching It is well known that there is exergy loss wherever there is TD, but TD is necessary to heat transfer. That is to say, exergy loss is simultaneous with heat transfer. Fig. 1 shows the process of heat transfer between two heat transfer fluids (HTFs). The exergy loss in the process is calculated as follows: dEx ¼ T0
Thot Tcool dQ Thot Tcool
ð1Þ
where T0 is the ambient temperature (assumed as constant). Thot and Tcool are the temperatures of hot fluid and cool fluid respectively. dEx represents the exergy loss during heat transfer of dQ. From the expression, it is apparent that exergy loss increases with a lift in TD between the two HTFs. But TD needs to be kept at a proper value to assure certain capability of heat transfer. The rate of heat transfer dQ through infinitesimal heat transfer area dF can be expressed: dQ ¼ U ðThot Tcool Þ dFx
ð2Þ
Hot fluid dQ ¼ ðmcp Þhot dThot
ð3Þ
Cool fluid dQ ¼ ðmcp Þcool dTcool
ð4Þ
where ðmcp Þhot ðmcp Þcool are heat capacities of hot and cool fluids, respectively. The two negative signs in the above expressions represent that temperature decreases with heat transfer area increasing. As for non-azeotropes, cp is defined equivalently as follow: cp ¼
hdew hbubble Tdew Tbubble
ð5Þ
Fig. 1. Derivation of exergy loss in counter-flow exchanger.
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Take a water-source heat pump for example. In practical application, working conditions often confines water temperature. And its TD is required to be set at a proper value. So, for instance as the condenser, the following parameters can be assumed as constant: Tin;cool ; Tout;cool LMTD, overall heat transfer coefficient in the whole area U , and constant-pressure specific heat of both fluids. LMTD is deduced from Eqs. (2)–(4): LMTD ¼
ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ T Tout;cool ln Tin;hot out;hot Tin;cool
ð6Þ
The two temperature curves of HTFs are exponential and their expressions are given as follows: Hot fluid Thot ¼ Tin;hot þ
Tin;hot Tout;cool ½expðlUFx Þ 1 lðmcp Þhot
ð7Þ
Cool fluid Tcool ¼ Tin;hot þ
Tin;hot Tout;cool ðTin;hot Tout;cool Þ ðTin;hot Tout;cool Þ expðlUFx Þ lðmcp Þhot lðmcp Þhot
ð8Þ
where l¼
1 1 ðmcp Þhot ðmcp Þcool
ð9Þ
When l equals zero, (Tin;hot Tout;cool ) equals (Tout;hot Tin;cool ). So Eqs. (6)–(8) are no longer adaptive. For the case where l ¼ 0, three corresponding equations are shown below: LMTD ¼ Tin;hot Tout;cool ¼ Tout;hot Tin;cool Thot ¼ Tin;hot ðTout;cool Tin;cool Þ
Fx F
Fx F Substituting Eqs. (2), (7) and (8), or Eqs. (2), (70 ) and (80 ) into Eq. (1) gives Tout;cool ðmcp Þcool T0 ðTout;cool Tin;cool Þ Tin;hot ln Ex ¼ ðmcp Þcool T0 ln Tin;hot Tout;hot Tin;cool Tout;hot Tcool ¼ Tout;cool ðTout;cool Tin;cool Þ
0
ð6 Þ 0
ð7 Þ 0
ð8 Þ
ð10Þ
where Tin;hot and Tout;hot are relevant though Eq. (6). It is shown from Eqs. (6) and (10) that Ex is only the function of Tin;hot but the function is very complex. It can be illustrated [see Appendix A] that exergy loss Ex reaches the minimum when Tin;hot ¼ Tout;cool þ LMTD
ð11Þ
and then the hot fluid temperature at the outlet is deduced Tout;hot ¼ Tin;cool þ LMTD
ð12Þ
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Fig. 2. Schematic of optimal temperature matching in counter-flow heat exchanger.
Now we can find that TDs at both sides of heat exchanger are equal to LMTD, and TDs over the entire spectrum of heat exchanger are all equal to LMTD. Hence, the two curves are straight lines. Schematic of optimal temperature matching is shown in Fig. 2. An instruction to find appropriate working fluids for a working condition can be deduced form the analysis above: as for a certain working condition, those non-azeotropic mixtures are the most proper whose temperature glide is as approximate to TD of SHTF as possible, and whose dewpoint temperature under condensation pressure is the sum of the water outlet temperature and LMTD. Meanwhile, for the purpose of high heat efficiency in the evaporator, the dew-point temperature under evaporation pressure is approximate to the difference between the water inlet temperature and LMTD. In practical operation, a certain LMTD can be achieved by adjusting heat transfer area and mass flow rates of both HTFs.
3. Definition of working condition The new condition of geothermal heat pumps requires new working fluids to meet the following aspects: (1) environmental compatibility, the value of ODP is zero; (2) condensation pressure lower than 2500 kPa for fear of unwieldiness of equipment; (3) evaporation pressure higher than 100 kPa for fear that air seeps in the system; (4) compressor discharge temperature (peak temperature) lower than 120 °C; (5) large volumetric heating capacity to lessen the compressor displacement; (6) high COP; (7) inflammability because of large charge quantity. In order to assure certain rate of heat transfer and, at the same time, to lessen exergy loss during heat transfer, LMTD is defined as an appropriate value of 5 °C. When the working fluid is a non-azeotropic mixture and temperature matching is optimal, its dew-point and bubble-point temperatures under condensation pressure are 85 and 70 °C respectively, and its dew-point temperatures under evaporation pressure are 35 °C. At the same
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time, working fluid temperature at evaporator inlet is required to be below 25 °C (meanwhile above 20 °C). When a pure refrigerant is used, its condensation and evaporation temperatures are needed to be controlled at 80.79 and 26.38 °C to assure the same heat exchanging effect under the same condition of 5 °C LMTD. It is necessarily stated that the definition of working condition is in the viewpoint of water temperature but in that of refrigerant temperature, as the purpose is to get water, but refrigerant, of a certain temperature. Sometimes different water temperatures may be acquired in spite of the same bubble-point or dew-point temperature for different mixtures. 4. Cycle analysis and selecting results The specific work done by the compressor, specific heating capacity, volumetric heating capacity and COP are calculated for each pure refrigerant and their mixtures. A compressor isentropic efficiency g of 0.8 is used, and both the condenser subcooling degree and evaporator superheating degree are assumed to be 6.0 °C. Isenthalpic expansion is also used for refrigerants and zero pressure drop is assumed to be through the condenser and the evaporator. The performance of the different refrigerants is calculated as follows (see Figs. 3 and 4): The compressor specific work w is calculated as ð13Þ w ¼ h2 h1 ¼ ðh2s h1 Þ=g The specific heating capacity q is given by q ¼ h2 h4 The volumetric heating capacity qv is given by q qv ¼ v1 where v1 is the specific volume at the compressor suction point.
Fig. 3. Vapour–compression cycle for pure refrigerants or azeotropic mixtures.
ð14Þ
ð15Þ
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Fig. 4. Vapour–compression cycle for non-azeotropic mixtures.
The heating coefficient of performance COP is COP ¼
q w
ð16Þ
The compressor discharge temperature tout;com can also be obtained from the condensation pressure and enthalpy at point 2. 4.1. Pure refrigerants Table 2 gives the performance of 12 pure refrigerants under the condition. Those pure ones, whose critical temperatures are below 81 °C, are listed: ethane R116, R125, R14, R143a, R23, R32 Table 2 Performance of 12 pure refrigerants in the working condition Pure refrigerants
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tout;com (°C)
tcrit (°C)
Butane Isobutane Propane Propylene R134a R152a R227ea R236ea R236fa R245ca R245fa RC318
4.44 4.28 3.87 3.81 4.03 4.31 3.66 4.26 4.11 4.54 4.43 3.72
2029.3 2603.6 5641.2 6781.8 4800.8 4764.2 2839 1799.5 2169.4 1064.9 1460.8 2044.8
1030.3 1363.7 3178 3778.5 2677.8 2381.7 1890.6 1021.2 1272.1 581.4 804.5 1367.2
254.4 364.6 985.7 1197.9 693.2 621.2 474.6 216 285.2 106.3 157.2 326.5
83.7 83.3 95.8 102.2 96.5 105.7 80.8 80.8 80.8 82.6 81.5 80.8
152 134.7 96.7 92.4 101.1 113.3 101.7 139.3 124.9 174.4 154.1 115.2
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187
and R41, and they are excluded from the table. The common parameters are: condensation temperature 80.79 °C, evaporation temperature 26.38 °C. From the data in Table 2, the mean COP of pure refrigerants is 4.12. Only one (R152a) meets the requirements (qv > 3000 kJ/m3 and pcond < 2500 kPa); but it is flammable. 4.2. Binary mixtures A computer program assists the selecting process of mixtures. Table 3 gives the eight qualified binary mixtures, their working pressures, COPs and volumetric heating capacities. The common parameters of these working fluids are given below: Dew-point temperature under condensation pressure: 85 °C; Bubble-point temperature under condensation pressure: 70 °C, (inaccuracy 1.0 °C, the reason for the inaccuracy is given in Section 5 (5)); Dew-point temperature under evaporation pressure: 35 °C. And their temperatures at the evaporator inlet are kept between 25 and 20 °C to make waste water achieve the drainage standard. Their condensation pressure is controlled below 2500 kPa, and evaporation pressure above 100 kPa. From the data in Table 3, the mean COP of these binary mixtures is 4.85. In the table, R125/ R236ea (0.5/0.5) is composed of two kinds of inflammable substance. 4.3. Ternary mixtures Ternary mixtures have even larger variability than binary ones, so the number of qualified working fluids is even larger, too. Tables 4 and 5 give the qualified ternary mixtures, their working Table 3 Eight qualified binary mixtures and their performances in the working condition Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/R143a (0.4/0.6) Butane/R143a (0.7/0.3) Isobutane/R125 (0.5/0.5) R125/R236ea (0.5/0.5) R143a/R236ea (0.3/0.7) R152a/R245ca (0.2/0.8) R152a/R245ca (0.3/0.7) R152a/R245ca (0.4/0.6)
4.66
4429.3
2158.7
617.9
20.8
96.5
111.7
5.18
3332.7
1446.6
419
24.8
90.8
133.9
4.7
4554.4
2227.6
671.4
24.4
91.4
112.3
4.39
4288.7
2330.9
594.4
20.7
92.7
98.4
4.67
3697.2
1860.1
476.3
22.4
92.4
110.3
5.2
2028.2
912.6
208.5
22.7
93.2
153.8
5.07
2345
1073.4
248.8
20.4
96.5
146.0
4.93
2683.9
1257.1
296.1
20.1
99.6
139.3
188
P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
Table 4 Performance of 12 ternary mixtures whose volumetric heating capacities are larger than 4000 kJ/m3 Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/propylene/R125 (0.5/0.4/0.1) Butane/R125/R134a (0.4/0.3/0.3) Butane/R125/R152a (0.3/0.6/0.1) Butane/R125/R245fa (0.2/0.6/0.2) Butane/R143a/R227ea (0.4/0.4/0.2) Butane/R236fa/R32 (0.2/0.6/0.2) Isobutane/propane/ R125 (0.5/0.1/0.4) Isobutane/propylene/ R116 (0.5/0.2/0.3) Propane/R116/R236fa (0.1/0.1/0.8) Propane/R236fa/R32 (0.1/0.8/0.1) R125/R236ea/RC318 (0.4/0.5/0.1) R236ea/R236fa/R32 (0.3/0.5/0.2)
4.74
4437.4
2086.3
616.8
21.4
97.7
118.3
4.83
4069.3
1919.5
548.9
23.1
92.8
122.5
4.57
4673.9
2348.4
669.3
21.7
95.1
110.2
4.55
4518.2
2310.3
641.9
22.2
93.1
109.1
4.8
4024.6
1910
550
23
92.9
118
4.73
4623.2
2234.1
620.6
23.2
98.2
117.2
4.72
4659
2253.1
686.9
24.6
92.2
111
4.69
4892.9
2367.5
732.3
24.2
93.9
105.7
4.4
4094.2
2224.5
582.6
23.4
92.6
108
4.44
4551.5
2405.6
634.2
21.9
97.6
106.2
4.51
4012.1
2119.7
546.1
22.4
90.4
103.4
4.72
4425.3
2167.3
565.1
22.5
99.3
108.3
pressures, COPs and volumetric heating capacities. The common parameters of these working fluids are given below: Dew-point temperature under condensation pressure: 85 °C; Bubble-point temperature under condensation pressure: 70 °C (inaccuracy 0.25 °C); Dew-point temperature under evaporation pressure: 35 °C. And their temperatures at the evaporator inlet are kept below 25 °C to make waste water meet the drainage standard. Their condensation pressure is controlled below 2500 kPa, and evaporation pressure above 100 kPa. From the data in Tables 4 and 5, the mean COP of these ternary mixtures is 4.74. An interesting phenomenon can be found through the comparison between the data in Table 2 and those in Tables 3–5: the mean COPs of pure refrigerants are 4.12, however, those of binary and ternary mixtures are 4.85 and 4.74, respectively. What conclusion can be drawn from the phenomenon? Under the same temperature level, COP is in inverse proportion to exergy loss. Therefore, such a conclusion can be drawn that the system with non-azeotropic mixtures reduces exergy loss and enhances heat efficiency through temperature matching.
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189
Table 5 Performance of 31 ternary mixtures whose volumetric heating capacities are between 3000 and 4000 kJ/m3 Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/isobutane/ R143a (0.3/0.3/0.4) Butane/propane/R116 (0.6/0.3/0.1) Butane/propane/R143a (0.6/0.2/0.2) Butane/propylene/ R134a (0.6/0.2/0.2) Butane/R125/R134a (0.5/0.2/0.3) Butane/R125/R152a (0.5/0.3/0.2) Butane/R125/R236fa (0.3/0.4/0.3) Butane/R125/R245fa (0.2/0.3/0.5) Butane/R134a/R143a (0.5/0.2/0.3) Butane/R134a/R143a (0.6/0.2/0.2) Butane/R143a/R245fa (0.4/0.4/0.2) Isobutane/R116/R245ca (0.4/0.2/0.4) Isobutane/R125/R245ca (0.3/0.3/0.4) Isobutane/R125/R245ca (0.3/0.4/0.3) Propane/R152a/R236ea (0.1/0.1/0.8) Propane/R236ea/ R236fa (0.1/0.7/0.2) Propylene/R227ea/ R236ea (0.1/0.3/0.6) Propylene/R227ea/ R245fa (0.1/0.5/0.4) R125/R134a/R236ea (0.3/0.1/0.6) R125/R134a/R245fa (0.1/0.3/0.6) R125/R134a/R245fa (0.3/0.3/0.4) R125/R143a/R236ea (0.2/0.2/0.6) R125/R227ea/R245fa (0.4/0.3/0.3)
4.9
3987.5
1838.5
543.7
23.9
92.6
121.2
5.03
3722.2
1657.4
489.8
25.0
92.5
127.6
5.0
3719.5
1667
489.1
24.1
93.0
127.7
4.96
3797.7
1714.6
499.8
23.2
94.1
128.2
4.97
3689.8
1681.3
480.3
23.9
91.6
129.9
4.97
3832.2
1738.4
501.1
23.8
93.1
128.5
4.84
3980.4
1895.7
541
24.4
90.3
119.6
4.9
3350.7
1585.9
418.2
24.2
89.7
130.6
4.91
3858.7
1776.6
510.8
23.1
93.5
125.1
5.05
3503.2
1562.1
450.5
24.6
91.7
132.4
4.89
3863.2
1795.6
512.3
23.7
92.9
123.6
4.85
3407.7
1624.1
447.9
23.6
89.3
130.5
4.66
3425
1714.6
447.1
20.5
91.8
129.8
4.61
3919.3
1976.7
539.4
21.7
92.0
121.7
4.69
3577.8
1781.3
457.1
22.4
92.3
124.3
5.41
3242.9
1681.3
430.3
23.8
85.6
125.2
4.55
3713.9
1929.1
498.9
22.7
90.5
117.3
4.46
3598.8
1919.5
480.6
20.9
91.5
117.9
4.67
3791.2
1919.5
491.4
23.1
90.8
109.7
4.92
3066.6
1462
355.3
22.6
92.2
126.3
4.57
3927.2
2024.4
501.5
20.4
95.6
109.5
4.54
3999
2081.6
533.5
21.4
93.0
104.4
4.34
3994.9
2215
551.2
20.5
92.0
101.5
(continued on next page)
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Table 5 (continued) Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
R125/R236ea/R236fa (0.3/0.5/0.2) R125/R236fa/R245fa (0.3/0.5/0.2) R125/R236fa/R245fa (0.4/0.4/0.2) R143a/R227ea/R245fa (0.3/0.3/0.4) R143a/R236ea/R245fa (0.2/0.6/0.2) R143a/R236fa/R245fa (0.2/0.4/0.4) R143a/R245ca/RC318 (0.2/0.2/0.6) R227ea/R245fa/R32 (0.6/0.3/0.1)
4.72
3626.2
1824.2
468.4
24.2
89.0
110.9
4.7
3602.3
1824.2
465
24.0
90.0
110.7
4.52
3919.1
2072
523.5
22.0
92.0
104.5
4.51
3729.9
1957.7
490.7
20.6
93.5
108.1
4.92
3163.3
1509.7
381.6
24.6
89.5
121.9
4.86
3171.3
1538.3
384.8
23.9
90.7
120.3
4.57
3237.1
1700.3
428.1
22.4
87.8
113.4
4.6
3927.5
2024.4
516.7
22.6
92.5
111.1
5. Discussion (1) It is difficult to acquire the accurate databases about properties of mixtures, even though by using the authoritative databases of Refprop 6.1. Moreover, when the selected mixtures are put into use, some other aspects, such as oil solubility and safety, may become restrictive factors. Therefore, temperature-matching method can only serve as the initial step in selecting working fluids. It provides the direction in acquiring high-efficiency working fluids for further research. The next step is to examine their other properties of these selected mixtures and finally put them into experimental research [5]. (2) The charge quantity of working fluids in this kind of system is usually large, and therefore working fluids are required to be inflammable. Table 6 summarizes the toxicity and flammability characteristics of some refrigerants. In ANSI/ASHRAE Standard 15-1992 [12], refrigerants are classified according to the hazard involved in their use. Group A1 refrigerants are the least hazardous, Group B3 the most hazardous. The safety characteristic of mixtures is complex and not discussed in detail here. The following mixtures are probably safe by roughly examining their proportion of non-combustible compositions to combustible ones: R125/R236ea (0.5/0.5), propane/R116/R236fa (0.1/0.1/ 0.8), propane/R236fa/R32 (0.1/0.8/0.1), R125/R236ea/RC318 (0.4/0.5/0.1) and R236ea/ R236fa/R32 (0.3/0.5/0.2). (3) In two-phase region, an equivalent specific heat cp is used in Eq. (5) for non-azeotropic mixtures, and is assumed as constant. In reality, cp will vary through two-phase region. Therefore, even though temperature gliding of mixtures is equal to TD of water, optimal temperature matching will not be acquired. However, the assumption brings the following great advantage: proper working fluids can be selected just through fixing some points of working condition, and the method is qualitatively accurate. If variation of cp is to be considered, it is suggested to adopt a distributed parameter model. The work in the paper can serve as its preliminary
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Table 6 Comparison of safety group classification to those under ASHRAE standard 34-1989 Refrigerant R14 R134a R152a Ethane Propane RC318
Safety group Old
New
1
A1 A1 A2 A3 A3 A1
3b 3a 3a 1
research. On the basis of acquired mixtures, the mass ratio wants to be adjusted somewhat according to the analysis of the model. (4) In Tables 3–5, the variation step of mass ratio is 10%, but in practical application, more careful search should be made on their mass ratio to find the optimum ratio. Here R125/R236ea is discussed in detail as a demonstration. Fig. 5 gives its performances varying with the mass ratio of R125. The figure shows that its COP decreases but its volumetric heating capacity increases with the mass ratio of R125 increasing. So, for various requirements its mass ratio is somewhat different. In Fig. 5, there are some peaks and dips in the two lines. The reason for these types of peaks and dips is unclear and is not investigated in detail; however, it might be from inaccurate thermodynamic properties predicted by REFPROP or from inaccurate interaction parameters for each binary pair of components in the mixture. (5) When qualified mixtures cannot be found under the condition of optimal temperature matching, the restrictive parameters should be eased somewhat. Now, the temperature matching is not optimal, but it is near the optimal value and its COP decreases only a little. (6) In this work, pressure drop of working fluids through heat exchangers is ignored, so there may be some deviation from the reality. In the condenser, temperature glide becomes larger as a
Fig. 5. COP and qv varying with the mass ratio of R125 (R125/R236ea).
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result of pressure drop, but the inverse case appears in the evaporator. Consequently, the mass ratio should be properly adjusted on the basis of actual pressure drop to achieve the optimal temperature matching. Even if not adjusted, it has approximately optimal temperature matching, because pressure drop usually makes the temperature deviation of <1 °C. (7) Because of partial pressure of lubricant oil, the real pressure is always higher the calculated value [5]. So, those mixtures whose calculated peak pressure is a little lower than the limit will really be qualified. (8) As compared to pure refrigerants, mixtures have the following main disadvantages: they have many trivial details in the design of the system, in the charge and management of working fluids and in the influence of leakage.
6. Conclusions A novel method of selecting proper working fluids for geothermal heat pumps is discussed in the paper. The method mainly aims at their thermodynamic property, and provides a direction in selecting high-performance mixtures. The definition of the working condition is not in the viewpoint of working fluid side but in that of SHTF side, for which one reason is that our real interest is the temperature of SHTF, and the other is that there are temperature glides for mixtures. It is shown from the results that the mean COPs of binary and ternary mixtures are 4.85 and 4.74 respectively, but that of pure refrigerants is 4.12 under the same ambient condition. Then, the following conclusions can be drawn from the work: (1) The system with non-azeotropic mixtures reduces exergy loss through temperature matching and then enhances heat efficiency. (2) Based on the analysis of the environmental and thermodynamic aspects, and the rough analysis of safety, the following mixtures can be recommended as candidate working fluids for further research: R125/R236ea (0.5/0.5), propane/R116/R236fa (0.1/0.1/0.8), propane/R236fa/ R32 (0.1/0.8/0.1), R125/R236ea/RC318 (0.4/0.5/0.1) and R236ea/R236fa/R32 (0.3/0.5/0.2). The sequent work is to examine their other properties and finally put them into experimental research. (3) The novel method of selecting appropriate working fluids is of catholicity and can be extended to other cases. In some special cases where an even bigger TD of SHTF is needed, the predominance of temperature matching of mixtures will be more distinct.
Appendix A. Illustration of the minimum exergy loss Optimization object function Ex ¼ ðmcp Þcool T0 ln
Tout;cool Tin;cool
ðmcp Þcool T0 ðTout;cool Tin;cool Þ ln Tin;hot Tout;hot
Tin;hot Tout;hot
ðA:1Þ
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193
subject to LMTD ¼
ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ Tin;hot Tout;cool ln Tout;hot Tin;cool
ðA:2Þ
In order to include the special case where TDs of both HTFs are equal, Eqs. (A.2) and (A.20 ) is rewritten into the following form. ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ ¼ LMTD½lnðTin;hot Tout;cool Þ lnðTout;hot Tin;cool Þ 0
ðA:2 Þ In the above equations, Ex is the object function, and Tin;hot and Tout;hot are independent variables, and the others are all given constants. Now, for the purpose of simplified representation, Eqs. (A.1) and (A.20 ) are abstracted into the following form. Optimization object function z¼
ln x ln y xy
ðA:3Þ
subject to ðx bÞ ðy aÞ ¼ c½lnðx bÞ lnðy aÞ
ðA:4Þ
Solution: The problem can be treated as follows: z is only the function of x, and y is the intermediate variable, that is to say, y is the implicit function of x though Eq. (A.4). Differentiation of Eq. (A.3) yields 1 1 dy ðx yÞ ðln x ln yÞ 1 dy x y dx dx dz ðA:5Þ ¼ 2 dx ðx yÞ Eq. (A.5) is assumed zero, hence x dy y ¼ ln x ln y þ 1 ln x ln y þ 1 y dx x
ðA:6Þ
Differentiation of Eq. (A.4) yields dy c c dy ¼ dx x b y a dx
ðA:7Þ
c dy c ¼ 1 1 ya dx x b
ðA:8Þ
1 Hence
From (A.6) and (A.8), we obtain x y ln x ln y þ 1 ðb þ c xÞðy aÞ ¼ ln x ln y þ 1 ða þ c yÞðx bÞ y x
ðA:9Þ
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Fig. 6. Exergy loss and TDcool varying with TDhot (LMTD ¼ 5 K).
From (A.4) and (A.9), we obtain the following solution. x¼bþc y ¼aþc
ðA:10Þ
Now, the remaining problem is: Eqs. (A.4) and (A.9) make up transcendental equations set, so it is difficult to prove in usual methods that the achieved solution is the minimum solution. In the section, an illustration of the problem is given. Some constants are given as follows: Tin;cool ¼ 273:15 þ 65:0 K;
Tout;cool ¼ 273:15 þ 80:0 K;
ðmcp Þcool ¼ 0:1 kg=s 4187:0 J=ðkg KÞ;
T0 ¼ 273:15 K
Other variables are defined as follows: Heating capacity: Q ¼ ðmcp Þcool ðTout;cool Tin;cool Þ TD in the hot side of heat exchanger: TDhot ¼ Tin;hot Tout;cool TD in the cool side of heat exchanger: TDcool ¼ Tout;hot Tin;cool The examined range of temperature glide is from 0 to 50 K. When the temperature glide is equal to zero, the working fluid is pure or azeotropic. Note that hot fluid temperature at the inlet is always higher than or equal to that at the outlet as the fluid releases heat. Fig. 6 shows that when TDcool and TDhot are equal to LMTD, exergy loss reaches the minimum. References [1] J.W. Lund, D.H. Freeston, World-wide direct uses of geothermal energy 2000, Geothermics 30 (1) (2001) 29–68. [2] J. Tomasson, P. Arason, Evidence for thermal mining in low temperature geothermal areas in Iceland, Geothermics 29 (6) (2000) 723–735. [3] Z. Agioutantis, A. Bekas, The potential of district heating using geothermal energy. A case study, Greece, Geothermics 29 (1) (2000) 51–64.
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[4] S. Simsek, G. G€ unay, H. Elhatip, M. Ekmekcßi, Environmental protection of geothermal waters and travertines at Pamukkale, Geothermics 29 (4/5) (2000) 557–572. [5] P.C. Zhao, L. Zhao, G.L. Ding, C.L. Zhang, Experimental research on geothermal heat pump system with nonazeotropic working fluids, Applied Thermal Engineering 22 (15) (2002) 1749–1761. [6] Y.A. Kara, B. Yuksel, Evaluation of low temperature geothermal energy through the use of heat pump, Energy Conversion and Management 42 (6) (2001) 773–781. [7] M.O. McLinden, R. Radermacher, Methods for comparing the performance of pure and mixed refrigerants in the vapor compression cycle, International Journal of Refrigeration 10 (6) (1987) 318–325. [8] M. H€ ogberg, L. Vamling, T. Berntsson, Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications, International Journal of Refrigeration 16 (6) (1993) 403–413. [9] D. Jung, H.J. Kim, O. Kim, A study on the performance of multi-stage heat pumps using mixtures, International Journal of Refrigeration 22 (5) (1999) 402–413. [10] Y.S. Chang, M.S. Kim, S.T. Ro, Performance and heat transfer characteristics of hydrocarbon refrigerants in heat pump system, International Journal of Refrigeration 23 (3) (2000) 232–242. [11] NIST REFPROP standard reference database 23, NIST Thermodynamic properties of refrigerants and refrigerant mixtures, version 6.1, Thermophysics Division, National Institute of Standards and Technology, November 1998; Gaithersburg, MD 20899. [12] Ga. Atlanta, ASHRAE Handbook 1993 Fundamentals.
Temperature matching method of selecting working fluids for geothermal heat pumps P.C. Zhao, L. Zhao, G.L. Ding *, C.L. Zhang Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, No. 1954, Huashan Road, Shanghai 200030, China Received 8 February 2002; accepted 15 September 2002
Abstract The fact, that some areas need district heating through heat pumps and at the same time recover residual heat from geothermal water, presents a new working condition: feed water temperature of heat network 80 °C, return water temperature 65 °C; discarded geothermal water temperature 40 °C and its emission standard temperature below 30 °C. But none of known pure refrigerants and mixtures can meet this requirement. The paper introduces a novel approach named temperature-matching method, which provides a direction in selecting high-performance working fluids for further research. It is shown from the results that the mean COPs of binary and ternary mixtures are 4.85 and 4.74 respectively, but that of pure refrigerants is 4.12 under the same ambient condition. This point indicates that temperature matching contributes to energy saving. The novel approach to high-performance working fluids can be conveniently introduced into other working conditions. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Temperature matching; Method; Non-azeotropic; Exergy loss; COP; Geothermal
1. Introduction Some areas, such as Tianjin China, need district heating [1–5], and at the same time recover residual heat from low-temperature geothermal water of about 40 °C. If the geothermal water is directly discharged to the environment, it will result in not only low efficiency of using geothermal energy resources but also pollution to the Earth surface [4].
*
Corresponding author. Tel.: +86-21-62932110; fax: +86-21-62932601. E-mail address: [email protected] (G.L. Ding).
1359-4311/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 1 7 1 - 0
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Nomenclature cp specific heat at constant pressure (kJ kg1 K1 ) COP coefficient of performance Ex exergy loss (kJ) Fx ; F heat transfer area (m2 ) h specific enthalpy (kJ kg1 ) LMTD log mean temperature difference (°C or K) m mass flow rate (kg s1 ) p pressure (kPa) q specific heating capacity (kJ kg1 ) volumetric heating capacity (kJ m3 ) qv Q heating capacity (kW) T Kelvin temperature (K) t Celsius temperature (°C) ambient temperature (K) T0 U overall heat transfer coefficient (W m2 K1 ) v specific volume (m3 kg1 ) w specific work (kJ kg1 ) l defined in Eq. (9) g compressor isentropic efficiency Subscripts bubble, bub bubble-point dew dew-point crit (pseudo) critical point evap evaporator cond condenser com compressor cool cool side hot hot side in inlet side out outlet side Abbreviation HC hydrocarbon HFC hydrofluorocarbon CFC chlorofluorocarbon HCFC hydrochlorofluorocarbon SHTF second heat transfer fluid HTF heat transfer fluid GHPS geothermal heat pump system
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The problem can be solved through heat pumps. The heat pumps have two main functions: district heating and heat recovery from discarded geothermal water, which can raise the utility rate of geothermal energy and prevent surface pollution. This new working condition requires: feed water temperature of heat network 80 °C, return water temperature 65 °C; discarded geothermal water temperature 40 °C and its emission standard temperature below 30 °C. However, none of known pure refrigerants and mixtures can meet this requirement. It can be easily understood that working fluids are very important to GHPS. Currently R22 is used in the GHPS [6], but it has the following undesirable aspects: (1) R22 is a kind of HCFCs; (2) heating water temperature reaches only 45 °C; (3) COP reaches only 2.8. Sometimes, when a new working condition is presented, it is difficult to find its proper pure working fluids, which meet environmental requirement and meanwhile is thermodynamically high performance. But mixtures of the pure refrigerants can suit many conditions because of their variability. Another advantage of mixtures is that they can suit ambient temperature, approaching Lorentz cycle and behaving well in performance. Up to now, it has been shown in some papers [7–10] that temperature matching can help to increase efficiency. For example, Jung [9] concluded that the high performance (20–30% increase in COP under proper operating conditions) of his system contributes mainly to temperature matching between refrigerant mixtures and the SHTF, and then recommended that the first step in selecting a proper mixture be to compare the gliding TD of that mixture against the available TD of SHTF in the heat exchanger. For the purpose of temperature matching, counter flow must be used in heat exchangers. In this study, a novel approach named temperature-matching method is used to select those mixtures that can work in GHPS. This method chiefly aims at highest efficiency, and provides a direction in selecting high-performance mixtures. Twenty pure refrigerants discussed in the paper are listed in Table 1, which can be available from Refprop 6.1 [11]. Arbitrary binary and ternary compounds of the 20 pure refrigerants are made with different mass ratio at intervals of 10% at a time over the entire spectrum, and as a result, 1710 binary and 41 040 ternary mixtures can be attained theoretically. From the list of 33 pure refrigerants provided in Refprop 6.1, 6 CFCs (R11, R113, R114, R115, R12 and R13) and 5 HCFCs (R22, R123, R124, R141b and R142b), which have a value of ODP, and are forbidden by Montreal Protocol, and then they are not included in Table 1. What is more, there are two inorganic compounds, ammonia and carbon dioxide, excluded from the table. Table 1 Pure refrigerants analyzed in the study HC Ethane Propane Butane Isobutene Propylene
HFC R116 R125 R134a R14 R143a R152a R227ea R23
R236ea R236fa R245ca R245fa R32 R41 RC318
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2. Optimal temperature matching It is well known that there is exergy loss wherever there is TD, but TD is necessary to heat transfer. That is to say, exergy loss is simultaneous with heat transfer. Fig. 1 shows the process of heat transfer between two heat transfer fluids (HTFs). The exergy loss in the process is calculated as follows: dEx ¼ T0
Thot Tcool dQ Thot Tcool
ð1Þ
where T0 is the ambient temperature (assumed as constant). Thot and Tcool are the temperatures of hot fluid and cool fluid respectively. dEx represents the exergy loss during heat transfer of dQ. From the expression, it is apparent that exergy loss increases with a lift in TD between the two HTFs. But TD needs to be kept at a proper value to assure certain capability of heat transfer. The rate of heat transfer dQ through infinitesimal heat transfer area dF can be expressed: dQ ¼ U ðThot Tcool Þ dFx
ð2Þ
Hot fluid dQ ¼ ðmcp Þhot dThot
ð3Þ
Cool fluid dQ ¼ ðmcp Þcool dTcool
ð4Þ
where ðmcp Þhot ðmcp Þcool are heat capacities of hot and cool fluids, respectively. The two negative signs in the above expressions represent that temperature decreases with heat transfer area increasing. As for non-azeotropes, cp is defined equivalently as follow: cp ¼
hdew hbubble Tdew Tbubble
ð5Þ
Fig. 1. Derivation of exergy loss in counter-flow exchanger.
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Take a water-source heat pump for example. In practical application, working conditions often confines water temperature. And its TD is required to be set at a proper value. So, for instance as the condenser, the following parameters can be assumed as constant: Tin;cool ; Tout;cool LMTD, overall heat transfer coefficient in the whole area U , and constant-pressure specific heat of both fluids. LMTD is deduced from Eqs. (2)–(4): LMTD ¼
ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ T Tout;cool ln Tin;hot out;hot Tin;cool
ð6Þ
The two temperature curves of HTFs are exponential and their expressions are given as follows: Hot fluid Thot ¼ Tin;hot þ
Tin;hot Tout;cool ½expðlUFx Þ 1 lðmcp Þhot
ð7Þ
Cool fluid Tcool ¼ Tin;hot þ
Tin;hot Tout;cool ðTin;hot Tout;cool Þ ðTin;hot Tout;cool Þ expðlUFx Þ lðmcp Þhot lðmcp Þhot
ð8Þ
where l¼
1 1 ðmcp Þhot ðmcp Þcool
ð9Þ
When l equals zero, (Tin;hot Tout;cool ) equals (Tout;hot Tin;cool ). So Eqs. (6)–(8) are no longer adaptive. For the case where l ¼ 0, three corresponding equations are shown below: LMTD ¼ Tin;hot Tout;cool ¼ Tout;hot Tin;cool Thot ¼ Tin;hot ðTout;cool Tin;cool Þ
Fx F
Fx F Substituting Eqs. (2), (7) and (8), or Eqs. (2), (70 ) and (80 ) into Eq. (1) gives Tout;cool ðmcp Þcool T0 ðTout;cool Tin;cool Þ Tin;hot ln Ex ¼ ðmcp Þcool T0 ln Tin;hot Tout;hot Tin;cool Tout;hot Tcool ¼ Tout;cool ðTout;cool Tin;cool Þ
0
ð6 Þ 0
ð7 Þ 0
ð8 Þ
ð10Þ
where Tin;hot and Tout;hot are relevant though Eq. (6). It is shown from Eqs. (6) and (10) that Ex is only the function of Tin;hot but the function is very complex. It can be illustrated [see Appendix A] that exergy loss Ex reaches the minimum when Tin;hot ¼ Tout;cool þ LMTD
ð11Þ
and then the hot fluid temperature at the outlet is deduced Tout;hot ¼ Tin;cool þ LMTD
ð12Þ
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Fig. 2. Schematic of optimal temperature matching in counter-flow heat exchanger.
Now we can find that TDs at both sides of heat exchanger are equal to LMTD, and TDs over the entire spectrum of heat exchanger are all equal to LMTD. Hence, the two curves are straight lines. Schematic of optimal temperature matching is shown in Fig. 2. An instruction to find appropriate working fluids for a working condition can be deduced form the analysis above: as for a certain working condition, those non-azeotropic mixtures are the most proper whose temperature glide is as approximate to TD of SHTF as possible, and whose dewpoint temperature under condensation pressure is the sum of the water outlet temperature and LMTD. Meanwhile, for the purpose of high heat efficiency in the evaporator, the dew-point temperature under evaporation pressure is approximate to the difference between the water inlet temperature and LMTD. In practical operation, a certain LMTD can be achieved by adjusting heat transfer area and mass flow rates of both HTFs.
3. Definition of working condition The new condition of geothermal heat pumps requires new working fluids to meet the following aspects: (1) environmental compatibility, the value of ODP is zero; (2) condensation pressure lower than 2500 kPa for fear of unwieldiness of equipment; (3) evaporation pressure higher than 100 kPa for fear that air seeps in the system; (4) compressor discharge temperature (peak temperature) lower than 120 °C; (5) large volumetric heating capacity to lessen the compressor displacement; (6) high COP; (7) inflammability because of large charge quantity. In order to assure certain rate of heat transfer and, at the same time, to lessen exergy loss during heat transfer, LMTD is defined as an appropriate value of 5 °C. When the working fluid is a non-azeotropic mixture and temperature matching is optimal, its dew-point and bubble-point temperatures under condensation pressure are 85 and 70 °C respectively, and its dew-point temperatures under evaporation pressure are 35 °C. At the same
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time, working fluid temperature at evaporator inlet is required to be below 25 °C (meanwhile above 20 °C). When a pure refrigerant is used, its condensation and evaporation temperatures are needed to be controlled at 80.79 and 26.38 °C to assure the same heat exchanging effect under the same condition of 5 °C LMTD. It is necessarily stated that the definition of working condition is in the viewpoint of water temperature but in that of refrigerant temperature, as the purpose is to get water, but refrigerant, of a certain temperature. Sometimes different water temperatures may be acquired in spite of the same bubble-point or dew-point temperature for different mixtures. 4. Cycle analysis and selecting results The specific work done by the compressor, specific heating capacity, volumetric heating capacity and COP are calculated for each pure refrigerant and their mixtures. A compressor isentropic efficiency g of 0.8 is used, and both the condenser subcooling degree and evaporator superheating degree are assumed to be 6.0 °C. Isenthalpic expansion is also used for refrigerants and zero pressure drop is assumed to be through the condenser and the evaporator. The performance of the different refrigerants is calculated as follows (see Figs. 3 and 4): The compressor specific work w is calculated as ð13Þ w ¼ h2 h1 ¼ ðh2s h1 Þ=g The specific heating capacity q is given by q ¼ h2 h4 The volumetric heating capacity qv is given by q qv ¼ v1 where v1 is the specific volume at the compressor suction point.
Fig. 3. Vapour–compression cycle for pure refrigerants or azeotropic mixtures.
ð14Þ
ð15Þ
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Fig. 4. Vapour–compression cycle for non-azeotropic mixtures.
The heating coefficient of performance COP is COP ¼
q w
ð16Þ
The compressor discharge temperature tout;com can also be obtained from the condensation pressure and enthalpy at point 2. 4.1. Pure refrigerants Table 2 gives the performance of 12 pure refrigerants under the condition. Those pure ones, whose critical temperatures are below 81 °C, are listed: ethane R116, R125, R14, R143a, R23, R32 Table 2 Performance of 12 pure refrigerants in the working condition Pure refrigerants
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tout;com (°C)
tcrit (°C)
Butane Isobutane Propane Propylene R134a R152a R227ea R236ea R236fa R245ca R245fa RC318
4.44 4.28 3.87 3.81 4.03 4.31 3.66 4.26 4.11 4.54 4.43 3.72
2029.3 2603.6 5641.2 6781.8 4800.8 4764.2 2839 1799.5 2169.4 1064.9 1460.8 2044.8
1030.3 1363.7 3178 3778.5 2677.8 2381.7 1890.6 1021.2 1272.1 581.4 804.5 1367.2
254.4 364.6 985.7 1197.9 693.2 621.2 474.6 216 285.2 106.3 157.2 326.5
83.7 83.3 95.8 102.2 96.5 105.7 80.8 80.8 80.8 82.6 81.5 80.8
152 134.7 96.7 92.4 101.1 113.3 101.7 139.3 124.9 174.4 154.1 115.2
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187
and R41, and they are excluded from the table. The common parameters are: condensation temperature 80.79 °C, evaporation temperature 26.38 °C. From the data in Table 2, the mean COP of pure refrigerants is 4.12. Only one (R152a) meets the requirements (qv > 3000 kJ/m3 and pcond < 2500 kPa); but it is flammable. 4.2. Binary mixtures A computer program assists the selecting process of mixtures. Table 3 gives the eight qualified binary mixtures, their working pressures, COPs and volumetric heating capacities. The common parameters of these working fluids are given below: Dew-point temperature under condensation pressure: 85 °C; Bubble-point temperature under condensation pressure: 70 °C, (inaccuracy 1.0 °C, the reason for the inaccuracy is given in Section 5 (5)); Dew-point temperature under evaporation pressure: 35 °C. And their temperatures at the evaporator inlet are kept between 25 and 20 °C to make waste water achieve the drainage standard. Their condensation pressure is controlled below 2500 kPa, and evaporation pressure above 100 kPa. From the data in Table 3, the mean COP of these binary mixtures is 4.85. In the table, R125/ R236ea (0.5/0.5) is composed of two kinds of inflammable substance. 4.3. Ternary mixtures Ternary mixtures have even larger variability than binary ones, so the number of qualified working fluids is even larger, too. Tables 4 and 5 give the qualified ternary mixtures, their working Table 3 Eight qualified binary mixtures and their performances in the working condition Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/R143a (0.4/0.6) Butane/R143a (0.7/0.3) Isobutane/R125 (0.5/0.5) R125/R236ea (0.5/0.5) R143a/R236ea (0.3/0.7) R152a/R245ca (0.2/0.8) R152a/R245ca (0.3/0.7) R152a/R245ca (0.4/0.6)
4.66
4429.3
2158.7
617.9
20.8
96.5
111.7
5.18
3332.7
1446.6
419
24.8
90.8
133.9
4.7
4554.4
2227.6
671.4
24.4
91.4
112.3
4.39
4288.7
2330.9
594.4
20.7
92.7
98.4
4.67
3697.2
1860.1
476.3
22.4
92.4
110.3
5.2
2028.2
912.6
208.5
22.7
93.2
153.8
5.07
2345
1073.4
248.8
20.4
96.5
146.0
4.93
2683.9
1257.1
296.1
20.1
99.6
139.3
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Table 4 Performance of 12 ternary mixtures whose volumetric heating capacities are larger than 4000 kJ/m3 Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/propylene/R125 (0.5/0.4/0.1) Butane/R125/R134a (0.4/0.3/0.3) Butane/R125/R152a (0.3/0.6/0.1) Butane/R125/R245fa (0.2/0.6/0.2) Butane/R143a/R227ea (0.4/0.4/0.2) Butane/R236fa/R32 (0.2/0.6/0.2) Isobutane/propane/ R125 (0.5/0.1/0.4) Isobutane/propylene/ R116 (0.5/0.2/0.3) Propane/R116/R236fa (0.1/0.1/0.8) Propane/R236fa/R32 (0.1/0.8/0.1) R125/R236ea/RC318 (0.4/0.5/0.1) R236ea/R236fa/R32 (0.3/0.5/0.2)
4.74
4437.4
2086.3
616.8
21.4
97.7
118.3
4.83
4069.3
1919.5
548.9
23.1
92.8
122.5
4.57
4673.9
2348.4
669.3
21.7
95.1
110.2
4.55
4518.2
2310.3
641.9
22.2
93.1
109.1
4.8
4024.6
1910
550
23
92.9
118
4.73
4623.2
2234.1
620.6
23.2
98.2
117.2
4.72
4659
2253.1
686.9
24.6
92.2
111
4.69
4892.9
2367.5
732.3
24.2
93.9
105.7
4.4
4094.2
2224.5
582.6
23.4
92.6
108
4.44
4551.5
2405.6
634.2
21.9
97.6
106.2
4.51
4012.1
2119.7
546.1
22.4
90.4
103.4
4.72
4425.3
2167.3
565.1
22.5
99.3
108.3
pressures, COPs and volumetric heating capacities. The common parameters of these working fluids are given below: Dew-point temperature under condensation pressure: 85 °C; Bubble-point temperature under condensation pressure: 70 °C (inaccuracy 0.25 °C); Dew-point temperature under evaporation pressure: 35 °C. And their temperatures at the evaporator inlet are kept below 25 °C to make waste water meet the drainage standard. Their condensation pressure is controlled below 2500 kPa, and evaporation pressure above 100 kPa. From the data in Tables 4 and 5, the mean COP of these ternary mixtures is 4.74. An interesting phenomenon can be found through the comparison between the data in Table 2 and those in Tables 3–5: the mean COPs of pure refrigerants are 4.12, however, those of binary and ternary mixtures are 4.85 and 4.74, respectively. What conclusion can be drawn from the phenomenon? Under the same temperature level, COP is in inverse proportion to exergy loss. Therefore, such a conclusion can be drawn that the system with non-azeotropic mixtures reduces exergy loss and enhances heat efficiency through temperature matching.
P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
189
Table 5 Performance of 31 ternary mixtures whose volumetric heating capacities are between 3000 and 4000 kJ/m3 Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
Butane/isobutane/ R143a (0.3/0.3/0.4) Butane/propane/R116 (0.6/0.3/0.1) Butane/propane/R143a (0.6/0.2/0.2) Butane/propylene/ R134a (0.6/0.2/0.2) Butane/R125/R134a (0.5/0.2/0.3) Butane/R125/R152a (0.5/0.3/0.2) Butane/R125/R236fa (0.3/0.4/0.3) Butane/R125/R245fa (0.2/0.3/0.5) Butane/R134a/R143a (0.5/0.2/0.3) Butane/R134a/R143a (0.6/0.2/0.2) Butane/R143a/R245fa (0.4/0.4/0.2) Isobutane/R116/R245ca (0.4/0.2/0.4) Isobutane/R125/R245ca (0.3/0.3/0.4) Isobutane/R125/R245ca (0.3/0.4/0.3) Propane/R152a/R236ea (0.1/0.1/0.8) Propane/R236ea/ R236fa (0.1/0.7/0.2) Propylene/R227ea/ R236ea (0.1/0.3/0.6) Propylene/R227ea/ R245fa (0.1/0.5/0.4) R125/R134a/R236ea (0.3/0.1/0.6) R125/R134a/R245fa (0.1/0.3/0.6) R125/R134a/R245fa (0.3/0.3/0.4) R125/R143a/R236ea (0.2/0.2/0.6) R125/R227ea/R245fa (0.4/0.3/0.3)
4.9
3987.5
1838.5
543.7
23.9
92.6
121.2
5.03
3722.2
1657.4
489.8
25.0
92.5
127.6
5.0
3719.5
1667
489.1
24.1
93.0
127.7
4.96
3797.7
1714.6
499.8
23.2
94.1
128.2
4.97
3689.8
1681.3
480.3
23.9
91.6
129.9
4.97
3832.2
1738.4
501.1
23.8
93.1
128.5
4.84
3980.4
1895.7
541
24.4
90.3
119.6
4.9
3350.7
1585.9
418.2
24.2
89.7
130.6
4.91
3858.7
1776.6
510.8
23.1
93.5
125.1
5.05
3503.2
1562.1
450.5
24.6
91.7
132.4
4.89
3863.2
1795.6
512.3
23.7
92.9
123.6
4.85
3407.7
1624.1
447.9
23.6
89.3
130.5
4.66
3425
1714.6
447.1
20.5
91.8
129.8
4.61
3919.3
1976.7
539.4
21.7
92.0
121.7
4.69
3577.8
1781.3
457.1
22.4
92.3
124.3
5.41
3242.9
1681.3
430.3
23.8
85.6
125.2
4.55
3713.9
1929.1
498.9
22.7
90.5
117.3
4.46
3598.8
1919.5
480.6
20.9
91.5
117.9
4.67
3791.2
1919.5
491.4
23.1
90.8
109.7
4.92
3066.6
1462
355.3
22.6
92.2
126.3
4.57
3927.2
2024.4
501.5
20.4
95.6
109.5
4.54
3999
2081.6
533.5
21.4
93.0
104.4
4.34
3994.9
2215
551.2
20.5
92.0
101.5
(continued on next page)
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P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
Table 5 (continued) Working fluids (by mass)
COP
qv (kJ/m3 )
pcond (kPa)
pevap (kPa)
tin;evap (°C)
tout;com (°C)
tcrit (°C)
R125/R236ea/R236fa (0.3/0.5/0.2) R125/R236fa/R245fa (0.3/0.5/0.2) R125/R236fa/R245fa (0.4/0.4/0.2) R143a/R227ea/R245fa (0.3/0.3/0.4) R143a/R236ea/R245fa (0.2/0.6/0.2) R143a/R236fa/R245fa (0.2/0.4/0.4) R143a/R245ca/RC318 (0.2/0.2/0.6) R227ea/R245fa/R32 (0.6/0.3/0.1)
4.72
3626.2
1824.2
468.4
24.2
89.0
110.9
4.7
3602.3
1824.2
465
24.0
90.0
110.7
4.52
3919.1
2072
523.5
22.0
92.0
104.5
4.51
3729.9
1957.7
490.7
20.6
93.5
108.1
4.92
3163.3
1509.7
381.6
24.6
89.5
121.9
4.86
3171.3
1538.3
384.8
23.9
90.7
120.3
4.57
3237.1
1700.3
428.1
22.4
87.8
113.4
4.6
3927.5
2024.4
516.7
22.6
92.5
111.1
5. Discussion (1) It is difficult to acquire the accurate databases about properties of mixtures, even though by using the authoritative databases of Refprop 6.1. Moreover, when the selected mixtures are put into use, some other aspects, such as oil solubility and safety, may become restrictive factors. Therefore, temperature-matching method can only serve as the initial step in selecting working fluids. It provides the direction in acquiring high-efficiency working fluids for further research. The next step is to examine their other properties of these selected mixtures and finally put them into experimental research [5]. (2) The charge quantity of working fluids in this kind of system is usually large, and therefore working fluids are required to be inflammable. Table 6 summarizes the toxicity and flammability characteristics of some refrigerants. In ANSI/ASHRAE Standard 15-1992 [12], refrigerants are classified according to the hazard involved in their use. Group A1 refrigerants are the least hazardous, Group B3 the most hazardous. The safety characteristic of mixtures is complex and not discussed in detail here. The following mixtures are probably safe by roughly examining their proportion of non-combustible compositions to combustible ones: R125/R236ea (0.5/0.5), propane/R116/R236fa (0.1/0.1/ 0.8), propane/R236fa/R32 (0.1/0.8/0.1), R125/R236ea/RC318 (0.4/0.5/0.1) and R236ea/ R236fa/R32 (0.3/0.5/0.2). (3) In two-phase region, an equivalent specific heat cp is used in Eq. (5) for non-azeotropic mixtures, and is assumed as constant. In reality, cp will vary through two-phase region. Therefore, even though temperature gliding of mixtures is equal to TD of water, optimal temperature matching will not be acquired. However, the assumption brings the following great advantage: proper working fluids can be selected just through fixing some points of working condition, and the method is qualitatively accurate. If variation of cp is to be considered, it is suggested to adopt a distributed parameter model. The work in the paper can serve as its preliminary
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191
Table 6 Comparison of safety group classification to those under ASHRAE standard 34-1989 Refrigerant R14 R134a R152a Ethane Propane RC318
Safety group Old
New
1
A1 A1 A2 A3 A3 A1
3b 3a 3a 1
research. On the basis of acquired mixtures, the mass ratio wants to be adjusted somewhat according to the analysis of the model. (4) In Tables 3–5, the variation step of mass ratio is 10%, but in practical application, more careful search should be made on their mass ratio to find the optimum ratio. Here R125/R236ea is discussed in detail as a demonstration. Fig. 5 gives its performances varying with the mass ratio of R125. The figure shows that its COP decreases but its volumetric heating capacity increases with the mass ratio of R125 increasing. So, for various requirements its mass ratio is somewhat different. In Fig. 5, there are some peaks and dips in the two lines. The reason for these types of peaks and dips is unclear and is not investigated in detail; however, it might be from inaccurate thermodynamic properties predicted by REFPROP or from inaccurate interaction parameters for each binary pair of components in the mixture. (5) When qualified mixtures cannot be found under the condition of optimal temperature matching, the restrictive parameters should be eased somewhat. Now, the temperature matching is not optimal, but it is near the optimal value and its COP decreases only a little. (6) In this work, pressure drop of working fluids through heat exchangers is ignored, so there may be some deviation from the reality. In the condenser, temperature glide becomes larger as a
Fig. 5. COP and qv varying with the mass ratio of R125 (R125/R236ea).
192
P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
result of pressure drop, but the inverse case appears in the evaporator. Consequently, the mass ratio should be properly adjusted on the basis of actual pressure drop to achieve the optimal temperature matching. Even if not adjusted, it has approximately optimal temperature matching, because pressure drop usually makes the temperature deviation of <1 °C. (7) Because of partial pressure of lubricant oil, the real pressure is always higher the calculated value [5]. So, those mixtures whose calculated peak pressure is a little lower than the limit will really be qualified. (8) As compared to pure refrigerants, mixtures have the following main disadvantages: they have many trivial details in the design of the system, in the charge and management of working fluids and in the influence of leakage.
6. Conclusions A novel method of selecting proper working fluids for geothermal heat pumps is discussed in the paper. The method mainly aims at their thermodynamic property, and provides a direction in selecting high-performance mixtures. The definition of the working condition is not in the viewpoint of working fluid side but in that of SHTF side, for which one reason is that our real interest is the temperature of SHTF, and the other is that there are temperature glides for mixtures. It is shown from the results that the mean COPs of binary and ternary mixtures are 4.85 and 4.74 respectively, but that of pure refrigerants is 4.12 under the same ambient condition. Then, the following conclusions can be drawn from the work: (1) The system with non-azeotropic mixtures reduces exergy loss through temperature matching and then enhances heat efficiency. (2) Based on the analysis of the environmental and thermodynamic aspects, and the rough analysis of safety, the following mixtures can be recommended as candidate working fluids for further research: R125/R236ea (0.5/0.5), propane/R116/R236fa (0.1/0.1/0.8), propane/R236fa/ R32 (0.1/0.8/0.1), R125/R236ea/RC318 (0.4/0.5/0.1) and R236ea/R236fa/R32 (0.3/0.5/0.2). The sequent work is to examine their other properties and finally put them into experimental research. (3) The novel method of selecting appropriate working fluids is of catholicity and can be extended to other cases. In some special cases where an even bigger TD of SHTF is needed, the predominance of temperature matching of mixtures will be more distinct.
Appendix A. Illustration of the minimum exergy loss Optimization object function Ex ¼ ðmcp Þcool T0 ln
Tout;cool Tin;cool
ðmcp Þcool T0 ðTout;cool Tin;cool Þ ln Tin;hot Tout;hot
Tin;hot Tout;hot
ðA:1Þ
P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
193
subject to LMTD ¼
ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ Tin;hot Tout;cool ln Tout;hot Tin;cool
ðA:2Þ
In order to include the special case where TDs of both HTFs are equal, Eqs. (A.2) and (A.20 ) is rewritten into the following form. ðTin;hot Tout;cool Þ ðTout;hot Tin;cool Þ ¼ LMTD½lnðTin;hot Tout;cool Þ lnðTout;hot Tin;cool Þ 0
ðA:2 Þ In the above equations, Ex is the object function, and Tin;hot and Tout;hot are independent variables, and the others are all given constants. Now, for the purpose of simplified representation, Eqs. (A.1) and (A.20 ) are abstracted into the following form. Optimization object function z¼
ln x ln y xy
ðA:3Þ
subject to ðx bÞ ðy aÞ ¼ c½lnðx bÞ lnðy aÞ
ðA:4Þ
Solution: The problem can be treated as follows: z is only the function of x, and y is the intermediate variable, that is to say, y is the implicit function of x though Eq. (A.4). Differentiation of Eq. (A.3) yields 1 1 dy ðx yÞ ðln x ln yÞ 1 dy x y dx dx dz ðA:5Þ ¼ 2 dx ðx yÞ Eq. (A.5) is assumed zero, hence x dy y ¼ ln x ln y þ 1 ln x ln y þ 1 y dx x
ðA:6Þ
Differentiation of Eq. (A.4) yields dy c c dy ¼ dx x b y a dx
ðA:7Þ
c dy c ¼ 1 1 ya dx x b
ðA:8Þ
1 Hence
From (A.6) and (A.8), we obtain x y ln x ln y þ 1 ðb þ c xÞðy aÞ ¼ ln x ln y þ 1 ða þ c yÞðx bÞ y x
ðA:9Þ
194
P.C. Zhao et al. / Applied Thermal Engineering 23 (2003) 179–195
Fig. 6. Exergy loss and TDcool varying with TDhot (LMTD ¼ 5 K).
From (A.4) and (A.9), we obtain the following solution. x¼bþc y ¼aþc
ðA:10Þ
Now, the remaining problem is: Eqs. (A.4) and (A.9) make up transcendental equations set, so it is difficult to prove in usual methods that the achieved solution is the minimum solution. In the section, an illustration of the problem is given. Some constants are given as follows: Tin;cool ¼ 273:15 þ 65:0 K;
Tout;cool ¼ 273:15 þ 80:0 K;
ðmcp Þcool ¼ 0:1 kg=s 4187:0 J=ðkg KÞ;
T0 ¼ 273:15 K
Other variables are defined as follows: Heating capacity: Q ¼ ðmcp Þcool ðTout;cool Tin;cool Þ TD in the hot side of heat exchanger: TDhot ¼ Tin;hot Tout;cool TD in the cool side of heat exchanger: TDcool ¼ Tout;hot Tin;cool The examined range of temperature glide is from 0 to 50 K. When the temperature glide is equal to zero, the working fluid is pure or azeotropic. Note that hot fluid temperature at the inlet is always higher than or equal to that at the outlet as the fluid releases heat. Fig. 6 shows that when TDcool and TDhot are equal to LMTD, exergy loss reaches the minimum. References [1] J.W. Lund, D.H. Freeston, World-wide direct uses of geothermal energy 2000, Geothermics 30 (1) (2001) 29–68. [2] J. Tomasson, P. Arason, Evidence for thermal mining in low temperature geothermal areas in Iceland, Geothermics 29 (6) (2000) 723–735. [3] Z. Agioutantis, A. Bekas, The potential of district heating using geothermal energy. A case study, Greece, Geothermics 29 (1) (2000) 51–64.
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[4] S. Simsek, G. G€ unay, H. Elhatip, M. Ekmekcßi, Environmental protection of geothermal waters and travertines at Pamukkale, Geothermics 29 (4/5) (2000) 557–572. [5] P.C. Zhao, L. Zhao, G.L. Ding, C.L. Zhang, Experimental research on geothermal heat pump system with nonazeotropic working fluids, Applied Thermal Engineering 22 (15) (2002) 1749–1761. [6] Y.A. Kara, B. Yuksel, Evaluation of low temperature geothermal energy through the use of heat pump, Energy Conversion and Management 42 (6) (2001) 773–781. [7] M.O. McLinden, R. Radermacher, Methods for comparing the performance of pure and mixed refrigerants in the vapor compression cycle, International Journal of Refrigeration 10 (6) (1987) 318–325. [8] M. H€ ogberg, L. Vamling, T. Berntsson, Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications, International Journal of Refrigeration 16 (6) (1993) 403–413. [9] D. Jung, H.J. Kim, O. Kim, A study on the performance of multi-stage heat pumps using mixtures, International Journal of Refrigeration 22 (5) (1999) 402–413. [10] Y.S. Chang, M.S. Kim, S.T. Ro, Performance and heat transfer characteristics of hydrocarbon refrigerants in heat pump system, International Journal of Refrigeration 23 (3) (2000) 232–242. [11] NIST REFPROP standard reference database 23, NIST Thermodynamic properties of refrigerants and refrigerant mixtures, version 6.1, Thermophysics Division, National Institute of Standards and Technology, November 1998; Gaithersburg, MD 20899. [12] Ga. Atlanta, ASHRAE Handbook 1993 Fundamentals.