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A new selection principle of working fluids for subcritical organic Rankine cycle coupling with different heat sources
Energy 68 (2014) 283e291
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A new selection principle of working fluids for subcritical organic Rankine cycle coupling with different heat sources Chao He a, b, Chao Liu a, *, Mengtong Zhou c, Hui Xie a, Xiaoxiao Xu a, Shuangying Wu a, Yourong Li a a Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400030, China b Key Laboratory of Renewable Energy of Agricultural Ministry, College of Mechanical & Electrical Engineering, Henan Agricultural University, Zhengzhou 450002, China c College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 August 2013 Received in revised form 11 February 2014 Accepted 13 February 2014 Available online 14 March 2014
The low-grade heat sources coupled by ORC (organic Rankine cycle) are categorized into two groups. For the first one, the inlet temperature and the mass flow rate are known, and the working mass of the heat source is directly discharged after being used. For the second, the heat release is specific and the working mass of the heat source is usually recycled after releasing heat. The theoretical formulas of net power output and thermal efficiency for subcritical ORC coupling with the two kinds of heat source are proposed to elucidate the selection criteria of working fluids. The new mathematical relation of working fluid selection is given out. The selection of working fluids for subcritical ORC should couple with the types of low-grade heat sources. For the first heat source, both the theoretical analysis and numerical simulation results show that the working fluids with high liquid specific heat and low latent heat of evaporation should be selected as the working fluids. In contrast, the working fluids with low liquid specific heat and the high latent heat of evaporation are better for the second heat source. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Net power output Thermal efficiency Subcritical ORC Liquid specific heat Latent heat of evaporation
1. Introduction The increasingly serious energy and environmental issues have become attracted much attention with the rapid increasing of the energy consumption. The energy shortage problem is mainly caused by the limitation of traditional energy resources, and the environmental problems mainly refers to the greenhouse gas emission, thermal pollution, and other environment pollution because of the burning of the fossil energy resources and lots of waste emissions. To solve the two major issues, on the one hand, vigorous developing and utilizing the renewable energy such as solar energy, geothermal energy and biomass energy, is of key importance. On the other hand, recovering the low-grade waste heat from the industrial process and utility boiler, are of great significance for energy saving and emission reduction. The ORC (organic Rankine cycle) shows great potential both in using renewable energy and recovering the low-grade waste heat.
* Corresponding author. Tel./fax: þ86 023 65112469. E-mail address: [email protected] (C. Liu). http://dx.doi.org/10.1016/j.energy.2014.02.050 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
Therefore, the research on the ORC has become a hot topic and much work has been done in recently years. ORC possesses the capability to couple with different forms of low-grade heat sources to generate power. Some researchers [1e6] focused on the ORC using solar energy and some [7e10] conducted the study on the ORC with low-temperature geothermal energy. Besides, there were some others [11e13] revolving about the ORC for agricultural residues and biomass-based power generation. Additionally, some others [14e26] showed their interest in the ORC for the low-grade waste heat recovery. Owing to the different characteristics of different types of low-grade heat sources, the suitable working fluids for the ORC with these types of low-grade heat sources may be different. The appropriate working fluids play a key role in the ORC, and numbers of researches have been done in terms of the working fluid selection for ORC. According to the slope of saturation steam curve of working fluids in T-s diagram, the working fluids can be grouped into three categories: dry, isentropic and wet fluids corresponding to the positive, infinite and negative slope of saturation curve respectively [24,27]. With respect to the effect of working fluids categories on the performance of ORC, the researchers
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[24,28e30] obtained the consistent conclusion. Liu et al. [24] examined the effect of pure working fluids on the performance of ORC and pointed out that the wet fluids were unsuitable to use in ORC. Hung et al. [28,29] investigated the effect of dry, isentropic and wet fluids on the system efficiency and indicated that the wet fluids were easy to form droplets during the vapor expansion in the expander, the dry fluids were usually superheated vapor at the expander exit, making the net power output reduced, and the isentropic or nearly isentropic fluids avoided the disadvantages of dry and wet fluids and they were regarded as the most suitable working fluids for low-grade heat source. Mago et al. [30] presented the second law analysis of ORC with dry and wet fluids. Their work showed that dry fluids exhibited better performance than wet fluids. However, with respect to the effect of working fluids physical properties on the performance of ORC, different researchers [19,29,31e35] may get different conclusions and even opposite conclusions. In the aspect of studying on physical properties, the most obvious inconsistencies happened on the selection principle concerning with the specific heat, latent heat of evaporation. Hung et al. [29]noted that high latent heat working fluids were expected to improve the heat recovery efficiency of ORC and the working fluids with low specific heat should be adopted in order to reduce the load of the condenser. Yamamoto et al. [31] pointed out that the expander inlet temperature, the pressure ratio of cycle and the mass flow rate of working fluid were the most important factors to affect the expander power output. For the ORC with low-grade heat source, in order to increase the expander inlet mass flow rate, the cycle required the working fluids with low latent heat. Tchanche et al. [32] indicated that the good working fluids should have high latent heat of vaporization and high specific heat. Maizza V and Maizza A [33] stated that the characteristics of high latent heat and low specific heat helped the working fluids to absorb more heat during the evaporation. To elaborate the effect of latent heat and specific heat on the unit expander work output based on the assumption of the ideal gas, Chen et al. [34]proposed a theoretical analysis formula as following:
h
Dhisentropic ¼ Cp Tin 1 egð1=Ta 1=Tb Þ=Cp Þ
i
(1)
From Eq. (1), they explained that the working fluids with high latent heat and low liquid specific heat exhibited high unit mass work output. Wang et al. [19] also proposed a theoretical equation which reads:
hth ¼ 1
ðTEC 1Þ1 lnðTECÞ þ ðTEC$JaÞ1 1 þ Ja1
Fig. 1. Schematic diagram of the subcritical ORC.
evaluate the performance of ORC are different. Some preferred to use thermal efficiency to evaluate the performance of ORC while others may prefer to use the power output. Few reports [19,34] contribute to the theoretical analysis. In order to resolve this contradiction, firstly, the types of lowgrade heat sources are grouped into two categories: the first one is that the inlet temperature and mass flow rate are given; the second one is that the heat released is given. The geothermal energy and most of the waste heat belong to the first kind of heat source while the solar energy used by solar collector and a few waste heat source belong to the second kind of heat source. For the first kind of heat source, the net power output should be selected as the indicator to evaluate the performance of ORC while the maximizing of the thermal efficiency does not make sense any more. This is because the heat supplied to the ORC varies and it will appear that the thermal efficiency is very high while the net output power is very low. For the second kind of heat source, maximizing the net power output is equal to maximizing the thermal efficiency. Secondly, the theoretical models of net power output and thermal efficiency for subcritical ORC are proposed to prove the effect of latent heat and liquid specific heat on the system performance and the corresponding simulation is also completed. 2. Theoretical model and analysis 2.1. Subcritical ORC For the subcritical ORC, the system schematic and temperatureentropy diagram are shown in Figs. 1 and 2 respectively. The working fluid is saturated vapor at the expander inlet. Superheated ORC is not considered here because the subcritical ORC exhibits the
(2)
The thermal efficiency of ORC is related to the latent heat and specific heat of working fluids under the same conditions. Their simulation results showed that the thermal efficiency decreased with the increase of Jacob number. That meant the working fluids required high latent heat and low liquid specific heat based on the thermal efficiency. Kuo et al. [35] also obtained the same conclusions as Wang et al. [19] through the numerical simulation for the ORC of 50 kW. Obviously, for subcritical ORC, the criteria of screening working fluids about latent heat and liquid specific heat are appreciable inconsistencies. The reasons for this contradiction can be summarized into the following two aspects. Firstly, the types of low-grade heat source are different, which means that the initial conditions of the heat source are different among the researches. Few work [36] focuses on the types of heat source. Secondly, the indicators used to
Fig. 2. Tes diagram of the subcritical ORC.
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optimal thermal efficiency (net power output) at the saturated or slightly-superheated vapor state at the expander inlet [37]. In the simulation, the hypotheses are introduced as follows: the system is at the steady state; the pressure drops in evaporator, condenser and all the pipes are not considered; all the components are adiabatic; the isentropic efficiencies of the pump and the expander are constant. The detailed thermodynamic description of a subcritical ORC is shown in the previous work [38] and is summarized as follows. The heat absorption:
_ wf ðh1 h4 Þ _ h ðT5 T6 Þ ¼ m Q_ evp ¼ Cph m
(3)
The expander work:
_ t ¼ m _ wf ðh1 h2 Þhg ¼ m _ wf ðh1 h2s Þhs hg W
(4)
The pump work:
_ wf ðh4s h3 Þ _ p ¼ m _ wf ðh4 h3 Þ ¼ m W
hp
(5)
The net power output:
_ tW _ p _ net ¼ W W
(6)
The thermal efficiency of system:
_ W
hth ¼ _ net Q evp
(7)
The net power model theoretically based on the subcritical ORC has been proposed in the previous work [38]. The theoretical formula is described as follows:
_ hh D _ net zCph mh s g ðT5 T1 T1 Þ ðT T Þ 1 þ Cpl T1 ln T1 W 1 3 T1 2g T3
(8)
The detailed derivation process is shown in Ref. [38]. And Eq. (8) can be further organized into the following form:
h i Ja 1 _ net z C m hc þ ln hs hg W ph _ h ðT5 T1 DT1 Þ 2 1 hc
(9)
where hc ¼ 1 T3/T1 and Ja ¼ Cpl(T1 T3)/g ¼ (T1 þ DT1 T6)/ (T5 T1 DT1), which denote the Carnot cycle efficiency and Jacob number respectively. By substituting Eqs. (3) and (9) into (7), the thermal efficiency of the subcritical ORC can be approximately obtained as follows:
hc þ Ja2 ln 11hc hth z hs hg 1 þ Ja
(10)
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output and Jacob number. For the subcritical ORC with different working fluids, from Eq. (9), the net power output is a single function of Jacob number. Thus, the working fluid selection criteria can be determined by the following expressions (11) and (12).
_ net dW 1 1 _ h hs hg ðT5 T1 DT1 Þln ¼ Cph m 2 1 hc dJa
(11)
_ net dW >0 dJa
(12)
It is easy to prove that the derivative of net power to Ja is positive, so the net power output increases with the rise of Jacob number. That means that working fluids with high liquid specific heat and low latent heat of evaporation are preferable for subcritical ORC. The net power output should be regarded as the objective function to screen the working fluids. Additionally, for the same working fluid, Eq. (9) can be used to analyze the effect of cycle parameters on the performance of ORC. With the increase of evaporation temperature (T1) of ORC, both the Carnot cycle efficiency (hc) and Jacob number (Ja) will increase, leading to the increment of the term in the second square bracket in Eq. (9) and the decrease of the term in the first square bracket. Therefore, there may exist an optimal evaporation temperature to maximize the net power output. This optimal evaporation temperature has been stated in detail in the previous work [38]. In order to investigate the influence of condensation temperature (T3) on the performance of ORC, the derivative of net power is obtained as follows.
_ net dW 1 Cpl T1 T 1 _ h hs hg ðT5 T1 DT1 Þ ¼ Cph m þ þ ln 1 T1 2g T3 dT3 T3 T1 (13) In Eq. (13), the evaporation temperature T1 is higher than condensation temperature T3, and hence T1/T3 þ lnT1/T3 1/T3 > 0. It is obvious that the derivative of net power to T3 is negative.
_ net dW <0 dT3
(14)
That indicates the net power output will decrease with the increase of condensation temperature. Similar to the condensation temperature, the derivative of net power to the pinch temperature difference in the evaporator is obtained as follows. Obviously, the derivative of net power to DT1 is negative.
_ net C T dW T _ h hs hg hc 1 þ pl 1 ln 1 ¼ Cph m dDT1 2g T3
(15)
_ net dW <0 dDT1
(16)
Obviously, it is found that the net power output and thermal efficiency for subcritical ORC are related to the Jacob number. These relations are helpful to analyze the selection criteria for the two kinds of low-grade heat source.
From expression (16), it means that the net power output will decrease with the increase of the pinch temperature difference in the evaporator.
2.1.1. Subcritical ORC coupling with the first kind of low-grade heat source For the first kind of heat source, the inlet temperature (T5) and mass flow rate (mh) of the heat source are given. When the pinch temperature difference in the evaporator (DT1), the expander isentropic efficiency (hs), the generator efficiency (hg), evaporation temperature (T1) and condensation temperature (T3) are fixed, Eq. (9) can be used to reflect the relationship between the net power
2.1.2. Subcritical ORC coupling with the second kind of low-grade heat source For the second kind of heat source, the heat supplied to ORC is given. The change trends of net power and thermal efficiency are consistent because of the fixed heat absorption. So regarding the net power or thermal efficiency as the objective function is no difference. For the second kind of heat source, the expression (9) is not suitable to analyze the selection criteria about Ja because the
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Fig. 3. The relationship between the heat sources and expected working fluids.
net power output is not a single function of Jacob number any more. Hence, it is necessary to make further analysis in terms of the thermal efficiency. For the subcritical ORC with different working fluids, when the expander isentropic efficiency (hs), the generator efficiency (hg), evaporation temperature (T1) and condensation temperature (T3) are given, the thermal efficiency is a single function of Jacob number in Eq. (10). Thus, the selection criteria of working fluid can be determined by the following expression.
dhth ¼ dJa
1 ln 1 2 1hc
hc
ð1 þ JaÞ2
hs hg
(17)
In order to determine the sign of this expression, it is necessary to discuss the monotonicity of the function f(hc).
f ðhc Þ ¼
1 1 ln hc ð0 < hc < 1Þ 2 1 hc
(18)
The first and second derivatives of the function f(hc) are respectively given by:
f 0 ðhc Þ ¼
f 00 ðhc Þ ¼
1 1 2ð1 hc Þ 1 2ð1 hc Þ2
(19)
>0
(20)
From Eq. (20), it is obvious that the first derivative of the function f(hc) is a monotonously increasing function of hc. On the other hand, f 0 ð1=2Þ ¼ 0, hence, f 0 ðhc Þ < 0ð0 < hc < ð1=2ÞÞ. That implies the function f(hc) is a monotonously decreasing function when hc
changes from 0 to 0.5. Additionally, f(½) ¼ 0.153 and f(0) ¼ 0. Therefore, f(hc) < 0(0 < hc < ½). When hc exceeds 0.5, the evaporation temperature of ORC will be more than twice as the condensation temperature. This case exceeds the temperature range researched in the ORC using low-grade heat source, which is usually lower than 600 K. Accordingly, the situation that hc exceeds 0.5 is not considered. From the discussion above, the expression (21) can be obtained. Obviously, the thermal efficiency will increase with the decrease of Jacob number. That indicates working fluids with low liquid specific heat and high latent heat of evaporation are preferred to adopt in subcritical ORC.
dhth 1 < 0 0 < hc < 2 dJa
(21)
For the subcritical ORC coupling with the first kind of heat source, from expressions (12) and (21), it is obvious that the inconsistent requirements on the working fluids are obtained when selecting working fluids based on net power and thermal efficiency respectively. The net power output should be selected as the objective function and the thermal efficiency is misleading for the first kind of heat source. By theoretical analysis above, the conclusions are obtained as following: the selection standard of working fluids in subcritical ORC is different for the two different kinds of heat source. The net power output should be selected as the objective function for the first kind of heat source, and the thermal efficiency does for the second kind of heat source. In addition, the required working fluids in terms of liquid specific heat and latent heat of evaporation are different for the two different kinds of heat source.
Table 1 Properties of working fluids. Working fluids
Type of fluids
Molecular weight (g/mol)
Normal boiling point (K)
Critical temperature (K)
Critical pressure (kPa)
ODP
GWP
R717 R600a R142b R114 R600 R245fa R123 R601a R601 R141b R113
Wet Dry Isentropic Isentropic Isentropic Isentropic Isentropic Dry Dry Isentropic Isentropic
17.03 58.12 100.5 170.92 58.12 134.05 152.93 72.15 72.15 116.95 187.38
239.82 261.48 264 276.74 272.6 288.05 300.97 300.95 309.21 305.2 320.74
405.4 407.85 410.26 418.83 425.13 427.2 456.83 460.4 469.7 479.96 487.21
11,333 3640 4070 3257 3700 3600 3600 3370 3370 4460 3392
0 0 0.07 1 0 0 0.02 0 0 0.12 1
<1 w20 2310 10.04 w20 1030 77 w20 w20 725 6130
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2.2. The difference between the two kinds of heat sources From the above mathematical analysis, the expected working fluids, which are decided by the kinds of heat sources, are different. Fig. 3 depicts the relationship between the heat sources and expected working fluids. For the subcritical ORC coupled with the first kind of heat source, in order to obtain more power the outlet temperature of heat source will be reduced (T60 ) as shown in Fig. 3(a). The pinch point in evaporator will shift and this will lead to the mismatch of liquid absorption heat line of a to the heat source. The liquid absorption heat line of b will replace one of a and the cycle will become triangular cycle when the limitation reaches. However, when the subcritical ORC coupled with the second kind of heat source, the situation is different as shown in Fig. 3(b). In later situation, the heat source is kept fixed, and the shift of pinch point in evaporator will lead to the expansion of cycle area in the T-s diagram. The liquid absorption heat line of b will be substituted by one of a in order to obtain higher efficiency. This cycle will become Carnot cycle when the limitation reaches. 3. Simulated results and discussion 3.1. Subcritical ORC coupling with the first kind of low-grade heat source In the front part, for subcritical ORC coupling with the first kind of low-grade heat source, it has been proved that the working fluids with high liquid specific heat and low latent heat of evaporation exhibit the greater net power output from theory aspects. In this part, that will be elaborated in the terms of numerical simulation results. The specific conditions of ORC system with the first kind of lowgrade heat source are as follows: the inlet temperature and mass flow rate of waste heat source are 423.15 K and 10 kg/s, respectively; the cooling water temperature is 293.15 K; the pinch temperature differences in evaporator and condenser are 5 K; the isentropic efficiencies of expander and pump are 80% and 75%, respectively; and the generator efficiency is 96%. The thermodynamic properties of working fluids and the ORC performance are evaluated with EES (Engineering Equation Solver). The working fluids considered here include wet, isentropic and dry fluids based on the previous work [38]. Table 1 presents the physical properties of all the working fluids.
Fig. 4. Comparison with numerical results and theoretical results for the first kind of heat source.
Fig. 5. The net power output with Jacob number for different working fluids at the same evaporation temperature.
In order to compare the analytical results with numerical results, taking the working fluid R123 as an example, the net power output and thermal efficiency are calculated by the two means as shown in Fig. 4. The predicted values of the theoretical analysis show excellent agreements with the numerical results. When the condensation temperature is constant at 301 K and the evaporation temperature changes from 333 K to 393 K with the intervals of 20 K, the relationship between the net power output and Jacob number for different working fluids is shown in Fig. 5. From Fig. 5, for different working fluids at the evaporation temperatures of 333, 353, 373 and 393 K respectively, the net power output increases with the rise of Jacob number from the overall trend. This illustrates that working fluids with high liquid specific heat and low latent heat of evaporation are expected from the point of net power output. These results are consistent with the preceding theoretical analysis. For the four evaporation temperatures, Fig. 5 also shows that the ORC with R600a, R114, R245fa or R142b usually exhibits the greatest net power while the ORC with R717 or R141b does the lowest net power. Hence, among the working fluids investigated, R600a R114, R245fa and R142b are better to be used in ORC coupling with the first kind of low-grade heat source.
Fig. 6. The thermal efficiency with Jacob number for different working fluids at the same evaporation temperature.
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Fig. 7. The net power output with Jacob number for different working fluids at the same condensation temperature.
Fig. 9. The net power output with Jacob number for the same working fluid at various evaporation temperatures.
From the preceding theoretical analysis, for the first kind of lowgrade heat source, the working fluids with low liquid specific heat and high latent heat of evaporation are expected for maximizing thermal efficiency of ORC, which has also been illustrated by the simulated results as shown in Fig. 6. Fig. 6 depicts the thermal efficiency with Jacob number for different working fluids at the evaporation temperatures of 333, 353, 373 and 393 K, respectively. It’s obvious that the thermal efficiency decreases with the increment of Jacob number from the overall trend. This means the ORC requires working fluids with low liquid specific heat and high latent heat of evaporation based on thermal efficiency. However, it does not make sense to pursue the thermal efficiency of ORC coupling with the first kind of low-grade heat source. Because there may exist the case that the thermal efficiency is very high while the net power output is very low. Not only the evaporation temperature but also the condensation temperature can have an effect on the Jacob number. When the evaporation temperature is constant at 353 K and condensation temperatures change from 303 K to 309 K with the intervals of 2 K, the relationship between the net power output and Jacob number for different working fluids is shown in Fig. 7. For the condensation temperatures of 303, 305, 307 and 309 K respectively, the net
power output increases with the increase of the Jacob number. This is the same as the theoretical analysis. Fig. 8 illustrates the thermal efficiency with Jacob number for different working fluids at the condensation temperatures of 303, 305, 307 and 309 K, respectively. Analogously, the thermal efficiency decreases with the rise of Jacob number from the overall trend. For different working fluids, the influence of Jacob number on the net power and thermal efficiency is discussed above. For the same working fluid, the effects of evaporation temperature, condensation temperature and pinch temperature difference in evaporator on the net power will be addressed from the numerical computation. Fig. 9 elucidates the variation of net power output with Jacob number for the same working fluid when the evaporation temperature changes from 333 K to 393 K. The change of Jacob number is caused by the change of evaporation temperature. For each working fluid investigated, there is an optimal Jacob number corresponding to a maximum net power. This illustrates that it is failed to use Jacob number to judge the performance of ORC coupling with the first kind of heat source for the same working fluid at different operation conditions. This also implies there is an optimal evaporation temperature corresponding to a maximum net power. This
Fig. 8. The thermal efficiency with Jacob number for different working fluids at the same condensation temperature.
Fig. 10. The net power output with the condensation temperature for each working fluid.
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Fig. 11. The net power output with pinch temperature difference in evaporator.
result is consistent with the theoretical analysis. The issue of the optimal evaporation temperature has been addressed in the previous work [38]. Fig. 10 shows the net power output with the condensation temperature for each working fluid. The net power output linearly reduces with the increasing of the condensation temperature for each working fluid investigated. These results are consistent with the theoretical analysis. Fig. 11 depicts the net power output with pinch temperature difference in evaporator for each working fluid when the evaporation temperature and condensation temperature are kept at 353 K and 301 K, respectively. It is obvious that the net power output linearly reduces with the linearly increasing of the pinch temperature difference in evaporator. These results show good agreements with the theoretical analysis. 3.2. Subcritical ORC coupling with the second kind of low-grade heat source In the second part, for subcritical ORC coupling with the second kind of low-grade heat source, it has proved that the working fluids with low liquid specific heat and high latent heat of evaporation show greater net power output from theory analysis. In this part, that will be expounded in the terms of numerical simulation results.
Fig. 12. Comparison with numerical results and theoretical results for the second kind of heat source.
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Fig. 13. The thermal efficiency with Jacob number for different working fluids at the same evaporation temperature.
The specific conditions of the second kind of low-grade heat source are the same as the first kind of low-grade heat source except that the outlet temperature of waste heat source is fixed at the temperature of 343.15 K. In order to fix the heat absorbed by the ORC, the inlet and outlet temperature and the mass flow rate of the heat source are provided. The thermodynamic properties of working fluid and the ORC performance are evaluated with EES. The working fluids in Table 1 are also adopted here. For the second kind of heat source, the analytical results are compared with numerical results as shown in Fig. 12. Taking the working fluid R123 as an example, the net power output and thermal efficiency are calculated by the two means. The predicted values of the theoretical analysis show good agreements with the numerical results. Fig. 13 presents the thermal efficiency with Jacob number for different working fluids at the evaporation temperature of 353, 358, 363 and 368 K separately when the condensation temperature is kept at 301 K. Obviously, as the theoretical analysis, with the increase of Jacob number, the thermal efficiency decreases. As it is shown in Fig. 14, the net power output has the same trend as the thermal efficiency with the variation of Jacob number. From Figs. 13 and 14, it can be seen that for the four evaporation temperatures, R717 and R141b generally exhibit the greatest
Fig. 14. The net power output with Jacob number for different working fluids at the same evaporation temperature.
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Fig. 15. The thermal efficiency with Jacob number for different working fluids at the same condensation temperature.
Fig. 17. The thermal efficiency with Jacob number for the same working fluid at various evaporation temperatures.
4. Conclusions thermal efficiency (net power output) while R114, R600a and R245fa do the lowest thermal efficiency (net power output). Therefore, R717 and R141b are expected to be adopted in the ORC coupling with the second kind of heat source. Obviously, the working fluids selected for the second kind of heat source are contrary to that for the first kind of heat source based on the net power output. When the evaporation temperature is kept at 353 K, the thermal efficiency and net power output with Jacob number for different working fluids at the condensation temperatures of 303, 305, 307 and 309 K are shown in Figs. 15 and 16 respectively. The same trend can be obtained as compared to Figs. 10 and 11. For the same working fluid operated at different evaporation temperatures (from 353 K to 388 K), the variation of thermal efficiency with the Jacob number is described in Fig. 17 when the condensation temperature is kept at 301 K. Obviously, for each working fluid, a higher Jacob number results in a higher thermal efficiency. It illustrates that for the same working fluid operated at different evaporation temperatures, it is still effective to use Jacob number to judge the performance of ORC coupling with the second kind of heat source.
The low-grade heat sources coupled with ORC were divided into two categories. The net power output and thermal efficiency models were proposed to analyze the required working fluids in terms of latent heat and liquid specific heat for subcritical ORC coupling with the two different heat sources. The specific working fluids were used to state the results of theoretical analysis. A new selection principle of working fluids for subcritical ORC coupling with different heat sources was established. The main conclusions can be made as following: (1) The selection of working fluids for subcritical ORC should consider the types of low-grade heat sources. Low-grade heat sources coupled by ORC can be categorized into two groups. (2) For the subcritical ORC coupling with the first kind of lowgrade heat source, it is better to adopt the working fluids with high liquid specific heat and low latent heat of evaporation based on the net power output. The inconsistent requirements on the working fluids are obtained when selecting working fluids based on net power and thermal efficiency respectively. Net power output should be regarded as the objective function. The increase of condensation temperature and pinch temperature difference in evaporator will lead to the decrease of net power output. For the same working fluid operated at different evaporation temperatures, it is not suitable to use Jacob number to judge the performance of ORC (3) For the subcritical ORC coupling with the second kind of lowgrade heat source, the working fluids with low liquid specific heat and high latent heat of evaporation are expected, based on the thermal efficiency (net power output). For the same working fluid operated at different evaporation temperatures, it is effective to use Jacob number to judge the performance of ORC. Acknowledgments This work was supported by National Basic Research Program of China (973 Program) under Grant No.2011CB710701.
Fig. 16. The net power output with Jacob number for different working fluids at the same condensation temperature.
Nomenclature Cp fluid specific heat capacity (kJ kg1K1) h specific enthalpy(kJ kg1)
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Dh Ja _ m Q_ s T Ta, Tb TEC
DT1 w _ W
unit enthalpy drop (kJ kg1) Jacob number (dimensionless) mass flow rate (kg s1) the heat rate injected (kW) specific entropy (kJ kg1 K1) temperature (K) the high and low saturation temperatures of two points on the coexistence line (K) the ratio of evaporation temperature and heat rejected temperature (dimensionless) the pinch temperature difference in evaporator (K) specific work (kJ kg1) power output or input (kW)
Greek symbols g latent heat of fluid (kJ kg1) h efficiency (dimensionless) Subscripts c carnot cycle evp evaporator g generator h waste heat source in inlet l liquid net net p pump s isentropic t expander th thermal wf working fluid 1e8 state points 2s,4s stat points for the ideal case References [1] He YL, Mei DH, Tao WQ, Yang WW, Liu HL. Simulation of the parabolic trough solar energy generation system with Organic Rankine Cycle. Appl Energy 2012;97:630e41. [2] Wang JL, Zhao L, Wang XD. A comparative study of pure and zeotropic mixtures in low-temperature solar Rankine cycle. Appl Energy 2010;87:3366e73. [3] Wang JL, Zhao L, Wang XD. An experimental study on the recuperative low temperature solar Rankine cycle using R245fa. Appl Energy 2012;94:34e40. [4] Tchanche BF, Lambrinos G, Frangoudakis A, Papadakis G. Exergy analysis of micro-organic Rankine power cycles for a small scale solar driven reverse osmosis desalination system. Appl Energy 2010;87:1295e306. [5] Tchanche BF, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a low-temperature solar organic Rankine cycle. Appl Therm Eng 2009;29: 2468e76. [6] Marion M, Voicu I, Tiffonnet A-L. Study and optimization of a solar subcritical organic Rankine cycle. Renew Energy 2012;48:100e9. [7] Zhang SJ, Wang HX, Guo T. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740e54. [8] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy 2011;36:2639e49. [9] Baik YJ, Kim M, Chang KC, Lee YS, Yoon HK. Power enhancement potential of a mixture transcritical cycle for a low-temperature geothermal power generation. Energy 2012;47:70e6. [10] Mago PJ, Srinivasan KK, Chamra LM, Somayaji C. An examination of exergy destruction in organic Rankine cycles. Int J Energy Res 2008;32:926e38. [11] Algieri A, Morrone P. Comparative energetic analysis of high-temperature subcritical and transcritical Organic Rankine Cycle (ORC). A biomass application in the Sibari district. Appl Therm Eng 2012;36:236e44.
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[12] Al-Sulaiman FA, Hamdullahpur F, Dincer I. Greenhouse gas emission and exergy assessments of an integrated organic Rankine cycle with a biomass combustor for combined cooling, heating and power production. Appl Therm Eng 2011;31:439e46. [13] Chinese D, Meneghetti A, Nardin G. Diffused introduction of Organic Rankine Cycle for biomass-based power generation in an industrial district: a systems analysis. Int J Energy Res 2004;28:1003e21. [14] Zhang HG, Wang EH, Fan BY. A performance analysis of a novel system of a dual loop bottoming organic Rankine cycle (ORC) with a light-duty diesel engine. Appl Energy 2013;102:1504e13. [15] Wang ZQ, Zhou NJ, Guo J, Wang XY. Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat. Energy 2012;40:107e15. [16] Yu G, Shu G, Tian H, Wei H, Liu L. Simulation and thermodynamic analysis of a bottoming Organic Rankine Cycle (ORC) of diesel engine (DE). Energy 2013;51:281e90. [17] Wei D, Lu X, Lu Z, Gu J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manag 2007;48: 1113e9. [18] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36:3406e18. [19] Wang D, Ling X, Peng H, Liu L, Tao L. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy 2013;50:343e52. [20] Wang D, Ling X, Peng H. Performance analysis of double organic Rankine cycle for discontinuous low temperature waste heat recovery. Appl Therm Eng 2012;48:63e71. [21] Roy JP, Misra A. Parametric optimization and performance analysis of a regenerative Organic Rankine Cycle using R-123 for waste heat recovery. Energy 2012;39:227e35. [22] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery Organic Rankine Cycles. Appl Therm Eng 2011;31: 2885e93. [23] Macián V, Serrano JR, Dolz V, Sánchez J. Methodology to design a bottoming Rankine cycle, as a waste energy recovering system in vehicles. Study in a HDD engine. Appl Energy 2013;104:758e71. [24] Liu BT, Chien KH, Wang CC. Effect of working fluids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207e17. [25] Wang J, Yan Z, Wang M, Li M, Dai Y. Multi-objective optimization of an organic Rankine cycle (ORC) for low grade waste heat recovery using evolutionary algorithm. Energy Convers Manag 2013;71:146e58. [26] Wang T, Zhang Y, Peng Z, Shu G. A review of researches on thermal exhaust heat recovery with Rankine cycle. Renew Sustain Energy Rev 2011;15: 2862e71. [27] Badr O, Probert SD, Ocallaghan PW. Selecting a working fluid for a Rankinecycle engine. Appl Energy 1985;21:1e42. [28] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661e7. [29] Hung TC, Wang SK, Kuo CH, Pei BS, Tsai KF. A study of organic working fluids on system efficiency of an ORC using low-grade energy sources. Energy 2010;35:1403e11. [30] Mago PJ, Chamra LM, Somayaji C. Performance analysis of different working fluids for use in organic Rankine cycles. Proc Inst Mech Eng Part A J Power Energy 2007;221:255e64. [31] Yamamoto T, Furuhata T, Arai N, Mori K. Design and testing of the Organic Rankine Cycle. Energy 2001;26:239e51. [32] Tchanche BF, Lambrinos G, Frangoudakis A, Papadakis G. Low-grade heat conversion into power using organic Rankine cycles e a review of various applications. Renew Sustain Energy Rev 2011;15:3963e79. [33] Maizza V, Maizza A. Working fluids in non-steady flows for waste energy recovery systems. Appl Therm Eng 1996;16:579e90. [34] Chen H, Goswami DY, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew Sustain Energy Rev 2010;14:3059e67. [35] Kuo C-R, Hsu S-W, Chang K-H, Wang C-C. Analysis of a 50kW organic Rankine cycle system. Energy 2011;36:5877e85. [36] Borsukiewicz-Gozdur A. Exergy analysis for maximizing power of organic Rankine cycle power plant driven by open type energy source. Energy 2013;62:73e81. [37] Chen Q, Xu J, Chen H. A new design method for Organic Rankine Cycles with constraint of inlet and outlet heat carrier fluid temperatures coupling with the heat source. Appl Energy 2012;98:562e73. [38] He C, Liu C, Gao H, Xie H, Li YR, Wu SY, et al. The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Energy 2012;38:136e43.
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A new selection principle of working fluids for subcritical organic Rankine cycle coupling with different heat sources Chao He a, b, Chao Liu a, *, Mengtong Zhou c, Hui Xie a, Xiaoxiao Xu a, Shuangying Wu a, Yourong Li a a Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400030, China b Key Laboratory of Renewable Energy of Agricultural Ministry, College of Mechanical & Electrical Engineering, Henan Agricultural University, Zhengzhou 450002, China c College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 August 2013 Received in revised form 11 February 2014 Accepted 13 February 2014 Available online 14 March 2014
The low-grade heat sources coupled by ORC (organic Rankine cycle) are categorized into two groups. For the first one, the inlet temperature and the mass flow rate are known, and the working mass of the heat source is directly discharged after being used. For the second, the heat release is specific and the working mass of the heat source is usually recycled after releasing heat. The theoretical formulas of net power output and thermal efficiency for subcritical ORC coupling with the two kinds of heat source are proposed to elucidate the selection criteria of working fluids. The new mathematical relation of working fluid selection is given out. The selection of working fluids for subcritical ORC should couple with the types of low-grade heat sources. For the first heat source, both the theoretical analysis and numerical simulation results show that the working fluids with high liquid specific heat and low latent heat of evaporation should be selected as the working fluids. In contrast, the working fluids with low liquid specific heat and the high latent heat of evaporation are better for the second heat source. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Net power output Thermal efficiency Subcritical ORC Liquid specific heat Latent heat of evaporation
1. Introduction The increasingly serious energy and environmental issues have become attracted much attention with the rapid increasing of the energy consumption. The energy shortage problem is mainly caused by the limitation of traditional energy resources, and the environmental problems mainly refers to the greenhouse gas emission, thermal pollution, and other environment pollution because of the burning of the fossil energy resources and lots of waste emissions. To solve the two major issues, on the one hand, vigorous developing and utilizing the renewable energy such as solar energy, geothermal energy and biomass energy, is of key importance. On the other hand, recovering the low-grade waste heat from the industrial process and utility boiler, are of great significance for energy saving and emission reduction. The ORC (organic Rankine cycle) shows great potential both in using renewable energy and recovering the low-grade waste heat.
* Corresponding author. Tel./fax: þ86 023 65112469. E-mail address: [email protected] (C. Liu). http://dx.doi.org/10.1016/j.energy.2014.02.050 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
Therefore, the research on the ORC has become a hot topic and much work has been done in recently years. ORC possesses the capability to couple with different forms of low-grade heat sources to generate power. Some researchers [1e6] focused on the ORC using solar energy and some [7e10] conducted the study on the ORC with low-temperature geothermal energy. Besides, there were some others [11e13] revolving about the ORC for agricultural residues and biomass-based power generation. Additionally, some others [14e26] showed their interest in the ORC for the low-grade waste heat recovery. Owing to the different characteristics of different types of low-grade heat sources, the suitable working fluids for the ORC with these types of low-grade heat sources may be different. The appropriate working fluids play a key role in the ORC, and numbers of researches have been done in terms of the working fluid selection for ORC. According to the slope of saturation steam curve of working fluids in T-s diagram, the working fluids can be grouped into three categories: dry, isentropic and wet fluids corresponding to the positive, infinite and negative slope of saturation curve respectively [24,27]. With respect to the effect of working fluids categories on the performance of ORC, the researchers
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[24,28e30] obtained the consistent conclusion. Liu et al. [24] examined the effect of pure working fluids on the performance of ORC and pointed out that the wet fluids were unsuitable to use in ORC. Hung et al. [28,29] investigated the effect of dry, isentropic and wet fluids on the system efficiency and indicated that the wet fluids were easy to form droplets during the vapor expansion in the expander, the dry fluids were usually superheated vapor at the expander exit, making the net power output reduced, and the isentropic or nearly isentropic fluids avoided the disadvantages of dry and wet fluids and they were regarded as the most suitable working fluids for low-grade heat source. Mago et al. [30] presented the second law analysis of ORC with dry and wet fluids. Their work showed that dry fluids exhibited better performance than wet fluids. However, with respect to the effect of working fluids physical properties on the performance of ORC, different researchers [19,29,31e35] may get different conclusions and even opposite conclusions. In the aspect of studying on physical properties, the most obvious inconsistencies happened on the selection principle concerning with the specific heat, latent heat of evaporation. Hung et al. [29]noted that high latent heat working fluids were expected to improve the heat recovery efficiency of ORC and the working fluids with low specific heat should be adopted in order to reduce the load of the condenser. Yamamoto et al. [31] pointed out that the expander inlet temperature, the pressure ratio of cycle and the mass flow rate of working fluid were the most important factors to affect the expander power output. For the ORC with low-grade heat source, in order to increase the expander inlet mass flow rate, the cycle required the working fluids with low latent heat. Tchanche et al. [32] indicated that the good working fluids should have high latent heat of vaporization and high specific heat. Maizza V and Maizza A [33] stated that the characteristics of high latent heat and low specific heat helped the working fluids to absorb more heat during the evaporation. To elaborate the effect of latent heat and specific heat on the unit expander work output based on the assumption of the ideal gas, Chen et al. [34]proposed a theoretical analysis formula as following:
h
Dhisentropic ¼ Cp Tin 1 egð1=Ta 1=Tb Þ=Cp Þ
i
(1)
From Eq. (1), they explained that the working fluids with high latent heat and low liquid specific heat exhibited high unit mass work output. Wang et al. [19] also proposed a theoretical equation which reads:
hth ¼ 1
ðTEC 1Þ1 lnðTECÞ þ ðTEC$JaÞ1 1 þ Ja1
Fig. 1. Schematic diagram of the subcritical ORC.
evaluate the performance of ORC are different. Some preferred to use thermal efficiency to evaluate the performance of ORC while others may prefer to use the power output. Few reports [19,34] contribute to the theoretical analysis. In order to resolve this contradiction, firstly, the types of lowgrade heat sources are grouped into two categories: the first one is that the inlet temperature and mass flow rate are given; the second one is that the heat released is given. The geothermal energy and most of the waste heat belong to the first kind of heat source while the solar energy used by solar collector and a few waste heat source belong to the second kind of heat source. For the first kind of heat source, the net power output should be selected as the indicator to evaluate the performance of ORC while the maximizing of the thermal efficiency does not make sense any more. This is because the heat supplied to the ORC varies and it will appear that the thermal efficiency is very high while the net output power is very low. For the second kind of heat source, maximizing the net power output is equal to maximizing the thermal efficiency. Secondly, the theoretical models of net power output and thermal efficiency for subcritical ORC are proposed to prove the effect of latent heat and liquid specific heat on the system performance and the corresponding simulation is also completed. 2. Theoretical model and analysis 2.1. Subcritical ORC For the subcritical ORC, the system schematic and temperatureentropy diagram are shown in Figs. 1 and 2 respectively. The working fluid is saturated vapor at the expander inlet. Superheated ORC is not considered here because the subcritical ORC exhibits the
(2)
The thermal efficiency of ORC is related to the latent heat and specific heat of working fluids under the same conditions. Their simulation results showed that the thermal efficiency decreased with the increase of Jacob number. That meant the working fluids required high latent heat and low liquid specific heat based on the thermal efficiency. Kuo et al. [35] also obtained the same conclusions as Wang et al. [19] through the numerical simulation for the ORC of 50 kW. Obviously, for subcritical ORC, the criteria of screening working fluids about latent heat and liquid specific heat are appreciable inconsistencies. The reasons for this contradiction can be summarized into the following two aspects. Firstly, the types of low-grade heat source are different, which means that the initial conditions of the heat source are different among the researches. Few work [36] focuses on the types of heat source. Secondly, the indicators used to
Fig. 2. Tes diagram of the subcritical ORC.
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optimal thermal efficiency (net power output) at the saturated or slightly-superheated vapor state at the expander inlet [37]. In the simulation, the hypotheses are introduced as follows: the system is at the steady state; the pressure drops in evaporator, condenser and all the pipes are not considered; all the components are adiabatic; the isentropic efficiencies of the pump and the expander are constant. The detailed thermodynamic description of a subcritical ORC is shown in the previous work [38] and is summarized as follows. The heat absorption:
_ wf ðh1 h4 Þ _ h ðT5 T6 Þ ¼ m Q_ evp ¼ Cph m
(3)
The expander work:
_ t ¼ m _ wf ðh1 h2 Þhg ¼ m _ wf ðh1 h2s Þhs hg W
(4)
The pump work:
_ wf ðh4s h3 Þ _ p ¼ m _ wf ðh4 h3 Þ ¼ m W
hp
(5)
The net power output:
_ tW _ p _ net ¼ W W
(6)
The thermal efficiency of system:
_ W
hth ¼ _ net Q evp
(7)
The net power model theoretically based on the subcritical ORC has been proposed in the previous work [38]. The theoretical formula is described as follows:
_ hh D _ net zCph mh s g ðT5 T1 T1 Þ ðT T Þ 1 þ Cpl T1 ln T1 W 1 3 T1 2g T3
(8)
The detailed derivation process is shown in Ref. [38]. And Eq. (8) can be further organized into the following form:
h i Ja 1 _ net z C m hc þ ln hs hg W ph _ h ðT5 T1 DT1 Þ 2 1 hc
(9)
where hc ¼ 1 T3/T1 and Ja ¼ Cpl(T1 T3)/g ¼ (T1 þ DT1 T6)/ (T5 T1 DT1), which denote the Carnot cycle efficiency and Jacob number respectively. By substituting Eqs. (3) and (9) into (7), the thermal efficiency of the subcritical ORC can be approximately obtained as follows:
hc þ Ja2 ln 11hc hth z hs hg 1 þ Ja
(10)
285
output and Jacob number. For the subcritical ORC with different working fluids, from Eq. (9), the net power output is a single function of Jacob number. Thus, the working fluid selection criteria can be determined by the following expressions (11) and (12).
_ net dW 1 1 _ h hs hg ðT5 T1 DT1 Þln ¼ Cph m 2 1 hc dJa
(11)
_ net dW >0 dJa
(12)
It is easy to prove that the derivative of net power to Ja is positive, so the net power output increases with the rise of Jacob number. That means that working fluids with high liquid specific heat and low latent heat of evaporation are preferable for subcritical ORC. The net power output should be regarded as the objective function to screen the working fluids. Additionally, for the same working fluid, Eq. (9) can be used to analyze the effect of cycle parameters on the performance of ORC. With the increase of evaporation temperature (T1) of ORC, both the Carnot cycle efficiency (hc) and Jacob number (Ja) will increase, leading to the increment of the term in the second square bracket in Eq. (9) and the decrease of the term in the first square bracket. Therefore, there may exist an optimal evaporation temperature to maximize the net power output. This optimal evaporation temperature has been stated in detail in the previous work [38]. In order to investigate the influence of condensation temperature (T3) on the performance of ORC, the derivative of net power is obtained as follows.
_ net dW 1 Cpl T1 T 1 _ h hs hg ðT5 T1 DT1 Þ ¼ Cph m þ þ ln 1 T1 2g T3 dT3 T3 T1 (13) In Eq. (13), the evaporation temperature T1 is higher than condensation temperature T3, and hence T1/T3 þ lnT1/T3 1/T3 > 0. It is obvious that the derivative of net power to T3 is negative.
_ net dW <0 dT3
(14)
That indicates the net power output will decrease with the increase of condensation temperature. Similar to the condensation temperature, the derivative of net power to the pinch temperature difference in the evaporator is obtained as follows. Obviously, the derivative of net power to DT1 is negative.
_ net C T dW T _ h hs hg hc 1 þ pl 1 ln 1 ¼ Cph m dDT1 2g T3
(15)
_ net dW <0 dDT1
(16)
Obviously, it is found that the net power output and thermal efficiency for subcritical ORC are related to the Jacob number. These relations are helpful to analyze the selection criteria for the two kinds of low-grade heat source.
From expression (16), it means that the net power output will decrease with the increase of the pinch temperature difference in the evaporator.
2.1.1. Subcritical ORC coupling with the first kind of low-grade heat source For the first kind of heat source, the inlet temperature (T5) and mass flow rate (mh) of the heat source are given. When the pinch temperature difference in the evaporator (DT1), the expander isentropic efficiency (hs), the generator efficiency (hg), evaporation temperature (T1) and condensation temperature (T3) are fixed, Eq. (9) can be used to reflect the relationship between the net power
2.1.2. Subcritical ORC coupling with the second kind of low-grade heat source For the second kind of heat source, the heat supplied to ORC is given. The change trends of net power and thermal efficiency are consistent because of the fixed heat absorption. So regarding the net power or thermal efficiency as the objective function is no difference. For the second kind of heat source, the expression (9) is not suitable to analyze the selection criteria about Ja because the
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Fig. 3. The relationship between the heat sources and expected working fluids.
net power output is not a single function of Jacob number any more. Hence, it is necessary to make further analysis in terms of the thermal efficiency. For the subcritical ORC with different working fluids, when the expander isentropic efficiency (hs), the generator efficiency (hg), evaporation temperature (T1) and condensation temperature (T3) are given, the thermal efficiency is a single function of Jacob number in Eq. (10). Thus, the selection criteria of working fluid can be determined by the following expression.
dhth ¼ dJa
1 ln 1 2 1hc
hc
ð1 þ JaÞ2
hs hg
(17)
In order to determine the sign of this expression, it is necessary to discuss the monotonicity of the function f(hc).
f ðhc Þ ¼
1 1 ln hc ð0 < hc < 1Þ 2 1 hc
(18)
The first and second derivatives of the function f(hc) are respectively given by:
f 0 ðhc Þ ¼
f 00 ðhc Þ ¼
1 1 2ð1 hc Þ 1 2ð1 hc Þ2
(19)
>0
(20)
From Eq. (20), it is obvious that the first derivative of the function f(hc) is a monotonously increasing function of hc. On the other hand, f 0 ð1=2Þ ¼ 0, hence, f 0 ðhc Þ < 0ð0 < hc < ð1=2ÞÞ. That implies the function f(hc) is a monotonously decreasing function when hc
changes from 0 to 0.5. Additionally, f(½) ¼ 0.153 and f(0) ¼ 0. Therefore, f(hc) < 0(0 < hc < ½). When hc exceeds 0.5, the evaporation temperature of ORC will be more than twice as the condensation temperature. This case exceeds the temperature range researched in the ORC using low-grade heat source, which is usually lower than 600 K. Accordingly, the situation that hc exceeds 0.5 is not considered. From the discussion above, the expression (21) can be obtained. Obviously, the thermal efficiency will increase with the decrease of Jacob number. That indicates working fluids with low liquid specific heat and high latent heat of evaporation are preferred to adopt in subcritical ORC.
dhth 1 < 0 0 < hc < 2 dJa
(21)
For the subcritical ORC coupling with the first kind of heat source, from expressions (12) and (21), it is obvious that the inconsistent requirements on the working fluids are obtained when selecting working fluids based on net power and thermal efficiency respectively. The net power output should be selected as the objective function and the thermal efficiency is misleading for the first kind of heat source. By theoretical analysis above, the conclusions are obtained as following: the selection standard of working fluids in subcritical ORC is different for the two different kinds of heat source. The net power output should be selected as the objective function for the first kind of heat source, and the thermal efficiency does for the second kind of heat source. In addition, the required working fluids in terms of liquid specific heat and latent heat of evaporation are different for the two different kinds of heat source.
Table 1 Properties of working fluids. Working fluids
Type of fluids
Molecular weight (g/mol)
Normal boiling point (K)
Critical temperature (K)
Critical pressure (kPa)
ODP
GWP
R717 R600a R142b R114 R600 R245fa R123 R601a R601 R141b R113
Wet Dry Isentropic Isentropic Isentropic Isentropic Isentropic Dry Dry Isentropic Isentropic
17.03 58.12 100.5 170.92 58.12 134.05 152.93 72.15 72.15 116.95 187.38
239.82 261.48 264 276.74 272.6 288.05 300.97 300.95 309.21 305.2 320.74
405.4 407.85 410.26 418.83 425.13 427.2 456.83 460.4 469.7 479.96 487.21
11,333 3640 4070 3257 3700 3600 3600 3370 3370 4460 3392
0 0 0.07 1 0 0 0.02 0 0 0.12 1
<1 w20 2310 10.04 w20 1030 77 w20 w20 725 6130
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2.2. The difference between the two kinds of heat sources From the above mathematical analysis, the expected working fluids, which are decided by the kinds of heat sources, are different. Fig. 3 depicts the relationship between the heat sources and expected working fluids. For the subcritical ORC coupled with the first kind of heat source, in order to obtain more power the outlet temperature of heat source will be reduced (T60 ) as shown in Fig. 3(a). The pinch point in evaporator will shift and this will lead to the mismatch of liquid absorption heat line of a to the heat source. The liquid absorption heat line of b will replace one of a and the cycle will become triangular cycle when the limitation reaches. However, when the subcritical ORC coupled with the second kind of heat source, the situation is different as shown in Fig. 3(b). In later situation, the heat source is kept fixed, and the shift of pinch point in evaporator will lead to the expansion of cycle area in the T-s diagram. The liquid absorption heat line of b will be substituted by one of a in order to obtain higher efficiency. This cycle will become Carnot cycle when the limitation reaches. 3. Simulated results and discussion 3.1. Subcritical ORC coupling with the first kind of low-grade heat source In the front part, for subcritical ORC coupling with the first kind of low-grade heat source, it has been proved that the working fluids with high liquid specific heat and low latent heat of evaporation exhibit the greater net power output from theory aspects. In this part, that will be elaborated in the terms of numerical simulation results. The specific conditions of ORC system with the first kind of lowgrade heat source are as follows: the inlet temperature and mass flow rate of waste heat source are 423.15 K and 10 kg/s, respectively; the cooling water temperature is 293.15 K; the pinch temperature differences in evaporator and condenser are 5 K; the isentropic efficiencies of expander and pump are 80% and 75%, respectively; and the generator efficiency is 96%. The thermodynamic properties of working fluids and the ORC performance are evaluated with EES (Engineering Equation Solver). The working fluids considered here include wet, isentropic and dry fluids based on the previous work [38]. Table 1 presents the physical properties of all the working fluids.
Fig. 4. Comparison with numerical results and theoretical results for the first kind of heat source.
Fig. 5. The net power output with Jacob number for different working fluids at the same evaporation temperature.
In order to compare the analytical results with numerical results, taking the working fluid R123 as an example, the net power output and thermal efficiency are calculated by the two means as shown in Fig. 4. The predicted values of the theoretical analysis show excellent agreements with the numerical results. When the condensation temperature is constant at 301 K and the evaporation temperature changes from 333 K to 393 K with the intervals of 20 K, the relationship between the net power output and Jacob number for different working fluids is shown in Fig. 5. From Fig. 5, for different working fluids at the evaporation temperatures of 333, 353, 373 and 393 K respectively, the net power output increases with the rise of Jacob number from the overall trend. This illustrates that working fluids with high liquid specific heat and low latent heat of evaporation are expected from the point of net power output. These results are consistent with the preceding theoretical analysis. For the four evaporation temperatures, Fig. 5 also shows that the ORC with R600a, R114, R245fa or R142b usually exhibits the greatest net power while the ORC with R717 or R141b does the lowest net power. Hence, among the working fluids investigated, R600a R114, R245fa and R142b are better to be used in ORC coupling with the first kind of low-grade heat source.
Fig. 6. The thermal efficiency with Jacob number for different working fluids at the same evaporation temperature.
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Fig. 7. The net power output with Jacob number for different working fluids at the same condensation temperature.
Fig. 9. The net power output with Jacob number for the same working fluid at various evaporation temperatures.
From the preceding theoretical analysis, for the first kind of lowgrade heat source, the working fluids with low liquid specific heat and high latent heat of evaporation are expected for maximizing thermal efficiency of ORC, which has also been illustrated by the simulated results as shown in Fig. 6. Fig. 6 depicts the thermal efficiency with Jacob number for different working fluids at the evaporation temperatures of 333, 353, 373 and 393 K, respectively. It’s obvious that the thermal efficiency decreases with the increment of Jacob number from the overall trend. This means the ORC requires working fluids with low liquid specific heat and high latent heat of evaporation based on thermal efficiency. However, it does not make sense to pursue the thermal efficiency of ORC coupling with the first kind of low-grade heat source. Because there may exist the case that the thermal efficiency is very high while the net power output is very low. Not only the evaporation temperature but also the condensation temperature can have an effect on the Jacob number. When the evaporation temperature is constant at 353 K and condensation temperatures change from 303 K to 309 K with the intervals of 2 K, the relationship between the net power output and Jacob number for different working fluids is shown in Fig. 7. For the condensation temperatures of 303, 305, 307 and 309 K respectively, the net
power output increases with the increase of the Jacob number. This is the same as the theoretical analysis. Fig. 8 illustrates the thermal efficiency with Jacob number for different working fluids at the condensation temperatures of 303, 305, 307 and 309 K, respectively. Analogously, the thermal efficiency decreases with the rise of Jacob number from the overall trend. For different working fluids, the influence of Jacob number on the net power and thermal efficiency is discussed above. For the same working fluid, the effects of evaporation temperature, condensation temperature and pinch temperature difference in evaporator on the net power will be addressed from the numerical computation. Fig. 9 elucidates the variation of net power output with Jacob number for the same working fluid when the evaporation temperature changes from 333 K to 393 K. The change of Jacob number is caused by the change of evaporation temperature. For each working fluid investigated, there is an optimal Jacob number corresponding to a maximum net power. This illustrates that it is failed to use Jacob number to judge the performance of ORC coupling with the first kind of heat source for the same working fluid at different operation conditions. This also implies there is an optimal evaporation temperature corresponding to a maximum net power. This
Fig. 8. The thermal efficiency with Jacob number for different working fluids at the same condensation temperature.
Fig. 10. The net power output with the condensation temperature for each working fluid.
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Fig. 11. The net power output with pinch temperature difference in evaporator.
result is consistent with the theoretical analysis. The issue of the optimal evaporation temperature has been addressed in the previous work [38]. Fig. 10 shows the net power output with the condensation temperature for each working fluid. The net power output linearly reduces with the increasing of the condensation temperature for each working fluid investigated. These results are consistent with the theoretical analysis. Fig. 11 depicts the net power output with pinch temperature difference in evaporator for each working fluid when the evaporation temperature and condensation temperature are kept at 353 K and 301 K, respectively. It is obvious that the net power output linearly reduces with the linearly increasing of the pinch temperature difference in evaporator. These results show good agreements with the theoretical analysis. 3.2. Subcritical ORC coupling with the second kind of low-grade heat source In the second part, for subcritical ORC coupling with the second kind of low-grade heat source, it has proved that the working fluids with low liquid specific heat and high latent heat of evaporation show greater net power output from theory analysis. In this part, that will be expounded in the terms of numerical simulation results.
Fig. 12. Comparison with numerical results and theoretical results for the second kind of heat source.
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Fig. 13. The thermal efficiency with Jacob number for different working fluids at the same evaporation temperature.
The specific conditions of the second kind of low-grade heat source are the same as the first kind of low-grade heat source except that the outlet temperature of waste heat source is fixed at the temperature of 343.15 K. In order to fix the heat absorbed by the ORC, the inlet and outlet temperature and the mass flow rate of the heat source are provided. The thermodynamic properties of working fluid and the ORC performance are evaluated with EES. The working fluids in Table 1 are also adopted here. For the second kind of heat source, the analytical results are compared with numerical results as shown in Fig. 12. Taking the working fluid R123 as an example, the net power output and thermal efficiency are calculated by the two means. The predicted values of the theoretical analysis show good agreements with the numerical results. Fig. 13 presents the thermal efficiency with Jacob number for different working fluids at the evaporation temperature of 353, 358, 363 and 368 K separately when the condensation temperature is kept at 301 K. Obviously, as the theoretical analysis, with the increase of Jacob number, the thermal efficiency decreases. As it is shown in Fig. 14, the net power output has the same trend as the thermal efficiency with the variation of Jacob number. From Figs. 13 and 14, it can be seen that for the four evaporation temperatures, R717 and R141b generally exhibit the greatest
Fig. 14. The net power output with Jacob number for different working fluids at the same evaporation temperature.
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Fig. 15. The thermal efficiency with Jacob number for different working fluids at the same condensation temperature.
Fig. 17. The thermal efficiency with Jacob number for the same working fluid at various evaporation temperatures.
4. Conclusions thermal efficiency (net power output) while R114, R600a and R245fa do the lowest thermal efficiency (net power output). Therefore, R717 and R141b are expected to be adopted in the ORC coupling with the second kind of heat source. Obviously, the working fluids selected for the second kind of heat source are contrary to that for the first kind of heat source based on the net power output. When the evaporation temperature is kept at 353 K, the thermal efficiency and net power output with Jacob number for different working fluids at the condensation temperatures of 303, 305, 307 and 309 K are shown in Figs. 15 and 16 respectively. The same trend can be obtained as compared to Figs. 10 and 11. For the same working fluid operated at different evaporation temperatures (from 353 K to 388 K), the variation of thermal efficiency with the Jacob number is described in Fig. 17 when the condensation temperature is kept at 301 K. Obviously, for each working fluid, a higher Jacob number results in a higher thermal efficiency. It illustrates that for the same working fluid operated at different evaporation temperatures, it is still effective to use Jacob number to judge the performance of ORC coupling with the second kind of heat source.
The low-grade heat sources coupled with ORC were divided into two categories. The net power output and thermal efficiency models were proposed to analyze the required working fluids in terms of latent heat and liquid specific heat for subcritical ORC coupling with the two different heat sources. The specific working fluids were used to state the results of theoretical analysis. A new selection principle of working fluids for subcritical ORC coupling with different heat sources was established. The main conclusions can be made as following: (1) The selection of working fluids for subcritical ORC should consider the types of low-grade heat sources. Low-grade heat sources coupled by ORC can be categorized into two groups. (2) For the subcritical ORC coupling with the first kind of lowgrade heat source, it is better to adopt the working fluids with high liquid specific heat and low latent heat of evaporation based on the net power output. The inconsistent requirements on the working fluids are obtained when selecting working fluids based on net power and thermal efficiency respectively. Net power output should be regarded as the objective function. The increase of condensation temperature and pinch temperature difference in evaporator will lead to the decrease of net power output. For the same working fluid operated at different evaporation temperatures, it is not suitable to use Jacob number to judge the performance of ORC (3) For the subcritical ORC coupling with the second kind of lowgrade heat source, the working fluids with low liquid specific heat and high latent heat of evaporation are expected, based on the thermal efficiency (net power output). For the same working fluid operated at different evaporation temperatures, it is effective to use Jacob number to judge the performance of ORC. Acknowledgments This work was supported by National Basic Research Program of China (973 Program) under Grant No.2011CB710701.
Fig. 16. The net power output with Jacob number for different working fluids at the same condensation temperature.
Nomenclature Cp fluid specific heat capacity (kJ kg1K1) h specific enthalpy(kJ kg1)
C. He et al. / Energy 68 (2014) 283e291
Dh Ja _ m Q_ s T Ta, Tb TEC
DT1 w _ W
unit enthalpy drop (kJ kg1) Jacob number (dimensionless) mass flow rate (kg s1) the heat rate injected (kW) specific entropy (kJ kg1 K1) temperature (K) the high and low saturation temperatures of two points on the coexistence line (K) the ratio of evaporation temperature and heat rejected temperature (dimensionless) the pinch temperature difference in evaporator (K) specific work (kJ kg1) power output or input (kW)
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