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Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle
Energy 42 (2012) 503e509
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Energy journal homepage: www.elsevier.com/locate/energy
Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle You-Rong Li*, Jian-Ning Wang, Mei-Tang Du Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 January 2012 Accepted 4 March 2012 Available online 11 April 2012
This paper presented the analysis on the influence of the pinch point temperature difference (PPTD) and the evaporation temperature on the performance of organic Rankine cycle (ORC) in recovering the low temperature waste heat of the flue gas. Both the net power output and the heat transfer area of the evaporator and condenser were evaluated for dry and isentropic working fluids. When the heat and cold source conditions were given, the maximum net power output and the heat transfer area were obtained. The results show that some organic working fluids cannot reach the maximum net power output to avoid the low temperature corrosion. With the increase of the PPTD of the evaporator at a given total temperature difference, the total heat transfer area decreases first and then increases, while the corresponding cost-effective performance (ratio of the net power output to total heat transfer area) displays almost the opposite variation tendency. The PPTD of the evaporator for the optimization cost-effective performance is approximately the same for different organic working fluids. Meanwhile, the isentropic working fluids show better cost-effective performance than dry working fluids. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Pinch point temperature difference Evaporation temperature Low temperature waste heat Flue gas
1. Introduction Due to the rapid increase of the energy consumption in recent years, how to effectively utilize the low temperature waste heat, which was directly discharged to atmosphere in the industrial production, has attracted the considerable interest. It has been found that more than half of the total industrial waste heat was the low temperature heat energy and most of that was wasted in the form of flue gas [1]. Therefore, converting waste heat into electricity not only saves the fossil fuel but also contributes to reduce the thermal pollution. Nevertheless, a great quantity of waste heat with the temperature below 200 C is not suitable to be recovered by the traditional Rankine cycle [2]. As one of the most promising technologies in recovering this kind of waste heat, the organic Rankin cycle (ORC) with organic working fluids, which occurs phase change at relative low temperature, has been increasingly paid attention and gradually used in practical industrial applications. In addition, the ORC system has many advantages in making full use of the low temperature waste heat, for example, flexibility, safety and maintenance requirements etc [3,4]. So far, many investigations on the ORC system has been performed, including the working fluid selection [5e9], the optimum
* Corresponding author. Tel.: þ86 23 6511 2284; fax: þ86 23 6510 2473. E-mail address: [email protected] (Y.-R. Li). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.03.018
design for improving the system efficiency [10e13] and the system operating optimization etc [14e18]. Internal heat exchanger (IHE) was suggested to be equipped to improve the ORC efficiency in some conditions, however, Dai and Li pointed out that the IHE could not increase the net power output at a given heat source condition [19e22] and even not consider the extra investment. Besides, it was also certified that the superheating and supercooling of the working fluids lead to an increase of the system irreversibility [23,24]. Therefore, the basic ORC system was considered in present study. Evaporation temperature and condensation temperature are two main control parameters and have an important impact on the ORC performance. According to the second law of thermodynamics, both the higher evaporation temperature and the lower condensation temperature lead to an increase of the system thermal efficiency [25]. However, the evaporation temperature and condensation temperature are restricted by the critical temperature of the organic working fluid and the ambient temperature, respectively. The increasing evaporation temperature will reduce the heat transfer flux in the evaporator, which may lead to a decrease of the net power output finally. At the same time, the PPTD of the heat exchanger not only influences the evaporation temperature and condensation temperature but also plays an essential role in the cost-efficiency tradeoff [26]. With the decrease of the PPTD, higher evaporation temperature and lower condensation temperature can be achieved between the inlet temperature
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Nomenclature A cp h m Ja K Q T W
heat transfer area (m2) specific heat capacity (J kg1 K1) specific enthalpy (J kg1) mass flow rate (kg s1) Jacob number () heat transfer coefficient (W m2 K1) heat transfer flux (W) temperature ( C) power (W)
Greek symbols h isentropic efficiency
of waste heat and the heat sink temperature. Meanwhile, more heat transfer area is required with the decrease of the PPTD, which results in an increase of cost for the ORC system. Although there were many investigations associated with the optimization of the ORC system, detailed influence of the PPTD on the ORC performance was rarely found. Hence the main objective of this study is to analyze the influences of the coupled evaporation temperature and the PPTD on the net power output and the costeffective performance. The lowest temperature of the flue gas at the evaporator outlet should exceed 90 C in order to avoid the low temperature corrosion. At the given external heat and cold source conditions, the optimum performance of the ORC system is evaluated with different working fluids including R123, R11, R245fa and R113 etc. The physical properties of organic working fluids and the system performance were calculated with Engineering Equation Solver (EES) [27].
ε
ratio of the net power output to heat transfer area (W m2)
Subscripts a cooling air c condenser e evaporator g flue gas p pump s single-phase region t two-phase region T total tur turbine wf working fluid
The heat transfer area can be obtained when the heat transfer coefficient and state parameters of the organic working fluid are determined. Meanwhile, cost-effective performance for the ORC system would be worked out. A simple description of the thermodynamic modeling procedure of the basic ORC system, as shown in Ref. [20], was summarized as following:
2. Thermodynamic model of the ORC system The layout of the basic ORC system and the T-S diagram are shown in Fig. 1. It can be found that the ORC system uses the same thermodynamic principles as the traditional steam Rankine cycle. The difference is that the ORC system employs the low boiling point organic working fluid to recover the low temperature waste heat. The organic working fluid absorbs heat from the flue gas in the evaporator and becomes saturated vapor used to drive turbine. After leaving turbine, the organic working fluid is condensed to saturated liquid in the condenser and pumped back to the evaporator to close the cycle. The steady operation state of the cycle is assumed in this work and pressure drop in the evaporator, condenser and pipes can be neglected. Specific heat capacities of the flue gas and cooling air are assumed to be constant. The ORC specifications in this work are listed in Table 1. The detailed procedures of calculation are outlined as follows: At the given conditions of heat and cold sources, the physical properties at the two-phase region of the evaporator and the mass flow rate of the working fluid are obtained from the prescribed evaporation temperature and the PPTD of the evaporator. The state of the organic working fluid at condenser outlet is assumed to be saturated liquid. Therefore, the condensation temperature can be calculated after iterating to meet the PPTD of the condenser and the given isentropic efficiencies of turbine and pump. In addition, the outlet temperatures of the flue gas and cooling air, and the net power output are determined by state parameters of the working fluid at operation points.
Fig. 1. The basic ORC system.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Ref.
The calculation method is completely adapted to the condenser and the heat released of the organic working fluid in condenser can be obtained easily as:
[20,25]
Qc ¼ ma cpa Tc DTc Ta;in ð1 þ Jac Þ;
Table 1 Specifications of the ORC considered. Items
Value
Ambient temperature ( C) Flue gas temperature ( C) Flue gas flow rate (kg s1) Cooling air temperature ( C) Cooling air flow rate (kg s1) Pump isentropic efficiency Turbine isentropic efficiency Minimum allowed discharge temperature ( C) Heat transfer coefficient in evaporator (W m2 K1) Heat transfer coefficient in condenser (W m2 K1)
20 160 10.47 20 52.35 0.8 0.85 90 70 50
Jac ¼
(1)
h1 h1a Ta;out Tc þ DTc ¼ : h1a h2 Tc DTc Ta;in
(12)
DTc is the PPTD of the condenser and the Jac denotes the ratio of the sensible heat to the latent heat of the working fluid in condenser. Therefore, the net power output of the ORC system can be determined as following: Wnet ¼ Wtur Wp ¼ Qe Qc :
Pump, 2-3,
Wp ¼ mwf ðh3 h2 Þ ¼ mwf ðh2a h2 Þ=hp :
(11)
where, [31] [3] [3] [31] [30] [30]
Condenser, 1-2,
Qc ¼ mwf ðh1 h2 Þ:
505
(13)
Substituting Eqs. (10) and (11) into Eq. (13) yields:
(2)
Wnet ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ ma cpa Tc DTc Ta;in ð1 þ Jac Þ:
ð14Þ
Evaporator, 3-4, 2.2. Heat transfer area
Qe ¼ mwf ðh4 h3 Þ:
(3)
mwf ðh4 h3a Þ ¼ mg cpg Tg;in Tg;e ;
(5)
There have been many formulas which used to calculate the heat transfer coefficient of the heat exchanger in the published literatures [2,15,28,29]. Shell-and-tube heat exchanger of the counter-current design is employed, and the heat transfer coefficients in evaporator and condenser are directly given in Table 1. Both heat transfer procedures of the single-phase region and the two-phase region were considered in evaporator and condenser. As the thermal resistances of gas side and air side in evaporator and condenser are much larger than those of the working fluid side, respectively, heat transfer coefficients of evaporator and condenser could be regarded as constant [30]. Based on the heat transfer equations, the heat transfer area of the single-phase region in the evaporator can be calculated as following:
mwf ðh3a h3 Þ ¼ mg cpg Tg;e Tg;out ;
(6)
Ae;s ¼
Turbine, 4-1,
Wtur ¼ mwf ðh4 h1 Þ ¼ mwf ðh4 h4a Þhtur :
(4)
2.1. Net power output When the viscous dissipation and heat losses of the heat exchanger are neglected, energy balance in single-phase and twophase region of evaporator can be expressed as following, respectively,
where
(15)
where,
Tg;e ¼ Te þ DTe :
(7)
The h4 and h3a are the enthalpies of the organic working fluid at the saturated vapor and saturated liquid conditions, respectively. DTe is the smallest temperature difference in evaporator, which is defined as the difference between the flue gas temperature where the organic fluid begins to evaporate and the evaporation temperature. In evaporator, the ratio of the sensible heat to the latent heat of the working fluid is defined as
Jae ¼
mg cpg Te þ DTe Tg;out : Ke DTm;e;s
Te þ DTe Tg;out h3a h3 ¼ : h4 h3a Tg;in Te DTe
(8)
The total absorbed heat of the organic working fluid in the evaporator can be expressed as:
Qe ¼ mwf ðh4 h3 Þ ¼ mg cpg Tg;in Tg;out :
Ae;s ¼
(16)
mg cpg Te þ DTe Tg;out Tg;out T3 ln : DTe Ke Tg;out Tc DTe
(17)
Set ze ¼ Jae ðTg;in Te DTe Þ, the above equation can be written as:
Ae;s ¼ (10)
Tg;out T3 DTe : Tg;out T3 ln DTe
DTm,e,s is the logarithmic mean temperature difference of the single-phase region in evaporator and Ke is the heat transfer coefficient. In the basic ORC system, Tc is very close to T3 and the difference between Tc and T3 is negligible, and therefore, using Tc to replace T3 is reasonable. In this case, the heat transfer area can be determined as:
(9)
Substituting Eqs. (5), (6) and (8) into Eq. (9) yields:
Qe ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ:
DTm;e;s ¼
mg cpg ze ðTe Tc þ DTe Þ ze ln : DTe Ke Te Tc ze
(18)
Using the similar method, the heat transfer area of the singlephase region in the condenser can be expressed as
506
Ac;s
Y.-R. Li et al. / Energy 42 (2012) 503e509
ma cpa zc ðT þ Tc DTc Þ zc ¼ ln 1 ; DTc Kc T1 Tc zc
(19)
where, zc ¼ Jac ðTc DTc Ta;in Þ. T1 mainly depends on Te and Tc with the constant isentropic efficiency of turbine. The value of T1 will slightly increase with the increase of Te and the decrease of Tc. For a near-isentropic fluid, the difference between T1 and Tc can be neglected [7]. In two-phase region, the areas of the heat exchanger for the evaporator and condenser can be written as, respectively,
Ae;t
Tg;in Te mg cpg ¼ ln ; DTe Ke
(20)
Tc Ta;in ma cpa ln : DTc Kc
(21)
Ac;t ¼
The total heat transfer area in the evaporator and condenser can be obtained as:
AT ¼ Ae þ Ac :
(22)
where, Ae ¼ Ae,s þ Ae,t and Ac ¼ Ac,s þ Ac,t. Thereby, the net power output per heat transfer area can be obtained as:
ε ¼ Wnet =AT :
(23)
Based on above analyses, it can be known that both the net power output and the heat transfer area of the ORC system are mainly associated with Te, Tc, DTe and DTc. At the given heat and cold sources, matching those key parameters to improve the ORC system performance is the main target of this work. The previous published papers have researched the ORC at some certain PPTD, as shown in Table 2, however, the effect of the PPTD on the ORC performance is not considered. Consequently, this paper will focus much attention on the influence of the PPTD of the evaporation on the cost-effective optimization at a given total PPTD (DTT). In order to check the validation of the present model, we carried out some calculations of the basic ORC for the various fluids under the same operation conditions as Dai et al. [22]. The comparison of the net power output was shown in Table 3. A good agreement was achieved and the relative error was less 1%.
Table 3 The comparison of the net power output. Working fluids
R11
R123
R141b
R113
Wnet (kW)
149.9 151.34 0.95
157.8 156.91 0.57
152.4 152.8 0.26
155.8 155.77 0.02
This work Dai et al. [22] Relative error (%)
3.1. Effect of the PPTD on the net power output Fig. 2 shows the variation of the net power output with the PPTD of the evaporator at DTT ¼ 20 C. It can be found that the net power output increases first, and then decreases with the increase of the PPTD of the evaporator at a fixed evaporation temperature Te. This is mainly because the increase of the PPTD of the evaporator causes the decrease of the heat transfer flux, which results in a reduction of the mass flow rate of the organic working fluids. On the other hand, at a given total PPTD (DTT), the condensation temperature decreases to meet the decrease of the PPTD of the condenser. As a result, the difference between the evaporation temperature and the condensation temperature increases, which leads to the increase of the specific enthalpy drop in turbine. Therefore, there is an optimal PPTD of the evaporator to maximize the net power output. Comparison with other waste heat resources like the geothermal energy, the low temperature flue gas has several distinct features in the waste heat recovery system. Of which, the temperature of the flue gas at the evaporator outlet should exceed 90 C to avoid the low temperature corrosion. Therefore, organic
a
3. Results and discussion The cost-effective performance is determined by the electric energy production and investment of the ORC system, which can be measured by the net power output and the heat transfer area. In this work, we focused on the dry and isentropic organic working fluids.
b
Table 2 Selections of pinch point temperature difference in references. Fluids
Heat source
Cold source
DTe DTc Ref.
R134a, R123, R227ea, R245fa, R290, n-pentane R113, R245ca, isobutene, R123 Water, ammonia, Butane, Isobutene, R11, R236EA R123, R141B, R113, R245CA R134a R227ea, Isobutane, R245fa, opentane
Hot air
Water
10
5
[6]
Water Flue gas
Water e
15 8
15 e
[14] [22]
Water/steam Hot water
11 5
6 5
[31] [13]
R123
Flue gas
Air Cold water e
10
10
[20]
Fig. 2. Variation of the net power output with the PPTD of the evaporator at DTT ¼ 20 C. Solid lines correspond to Tg,out 90 C and dashed lines Tg,out < 90 C. (a) R245fa; 1: Te ¼ 108 C; 2: Te ¼ 110 C; 3: Te ¼ 112 C; (b) R123; 1: Te ¼ 105 C; 2: Te ¼ 107 C; 3: Te ¼ 109 C.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Fig. 3. The variations of the maximum net power output and the optimal evaporation temperature with the PPTD of the evaporator at DTT ¼ 20 C. Solid line: Wnet,max; Dashed line: Te,opt. 1: R245fa; 2: R114; 3: R123; 4: R11.
working fluids can be categorized into two groups at the given operation conditions according to whether they can achieve the maximum net power output. With the increase of the PPTD of the evaporator, isentropic working fluids, for example R245fa and R114, cannot achieve the maximum value of the net power output at the restrict condition, as shown in Fig. 2(a). Some attention should be paid when they are used to recovery the low temperature waste heat of the flue gas. On the contrary, R123 and R11 belong to the kind of organic working fluids which can achieve the maximum net power output at certain evaporation temperature, as shown in Fig. 2(b). When the PPTD is determined, the net power output increases first, and then decreases with the increase of the evaporation temperature [25]. Therefore, there has been an optimal evaporation temperature for each PPTD of the evaporator to maximize the net power output at a fixed total PPTD. The linear relations of the maximum net power output and the optimal evaporation temperature with the PPTD of the evaporator at DTT ¼ 20 C are shown in Fig. 3. It can be found that the organic working fluids including R114 and R245fa which cannot achieve the maximum net power output present better performance than R123 and R11. The area of heat exchangers contributes largely to the total cost of the ORC system, therefore, it is necessary to discuss the effect of the PPTD on the heat transfer area, which has the advantage to analyze the performance of the ORC. When the total PPTD is given, with the variation of the PPTD of the evaporator, the heat transfer area of evaporator and condenser would change simultaneously. It means that the variation of the PPTD of the evaporator affects the area of not only evaporator but also condenser. The heat transfer areas corresponding to the maximum net power output are calculated at the given conditions shown in Table 1. In general, the area of the heat exchanger decreases with the increase of the PPTD at the same heat transfer flux. The rational allocation of the PPTDs in evaporator and condenser to achieve more net power output with less heat transfer area by reducing the system irreversibility is the main task in the optimization process. As shown in Fig. 4, the area of the evaporator decreases and the area of condenser increases with the increase of the PPTD of the evaporator. Because the heat transfer coefficient of evaporator is generally larger than that of condenser, and the temperature variation of cooling air between the inlet and outlet is less than that of the flue gas in evaporator, and therefore, the area of condenser is the major source of the total heat transfer area. As a result, the total area of the heat exchanger is decreasing slightly first and then increasing gradually after reaching the minimum value at the PPTD of the evaporator about 7 C.
507
Fig. 4. Variation of the heat transfer area with the PPTD of the evaporator at DTT ¼ 20 C.
Fig. 5 shows that the variation tendencies of the heat transfer area for different organic working fluids are the approximate same. The difference of the total area of the heat exchanger between two arbitrary organic working fluids decreases with the increase of the PPTD of the evaporator. It means the choice of the organic working fluid has a little influence on the heat transfer area. The total area of the heat exchanger decreases with the increase of the total PPTD for all organic working fluids. This is because the increase of the PPTD of the condenser reduces the area of condenser, which is the major factor of the total heat transfer area. The good linear relationship between the maximum net power output and the PPTD of the evaporator is found in the previous part. However, the growth rate of the total heat transfer area is
a
b
Fig. 5. Variation of the heat transfer area with the PPTD of the evaporator. (a) DTT ¼ 20 C; (b) DTT ¼ 30 C. 1: R123; 2: R11; 3: R245fa; 4: R114.
508
Y.-R. Li et al. / Energy 42 (2012) 503e509
Fig. 6. Variations of the total heat transfer area and the net power output with the PPTD of the evaporator at DTT ¼ 20 C.
increasing gradually with the increase of the PPTD of the evaporator. Both the above relationships for R123 can be seen in Fig. 6. 3.2. Cost-effective optimum Pure pursuit of the net power output is meaningless without considering the investment in utilizing the low temperature waste heat effectively. The optimum of the net power output per heat transfer area has a very important practical significance. The heat transfer area can be reduced to some extent by matching the system parameter with the exterior condition for the same power output. In addition, the above analyses show that both the total area of heat exchangers and the net power output increase with the increase of the PPTD of the evaporator. Therefore, it’s necessary to evaluate the cost-effective performance of the ORC system by ε,
a
b
which is defined as the ratio of the net power output to the total heat transfer area. The ratio of the net power output to heat transfer area increases first, and then decreases for all organic working fluids, as shown in Fig. 7. Meanwhile, we can see that the ORC system using R11 as the working fluid always has the best cost-effective performance although it presents the lowest net power output, as shown in Fig. 3, compared to other organic working fluids. It hints that the maximum net power output and the best costeffective performance cannot be achieved at the same time. Those two aspects should be considered simultaneously in choosing the most suitable organic working fluids in different designs. Further, the less system irreversibility is generated in condenser when isentropic fluids are used. Therefore, we can come to a conclusion that isentropic fluids show better cost-effective performance than dry fluids. As shown in Fig. 7, the isentropic fluids including R11 and R123 present better cost-effective performance than dry working fluids including R114 and R245fa. The differences of the performance for organic working fluids are reducing along with the increase of the PPTD of the evaporator. Taking the total PPTD of 20 C as an example, when the PPTD of the evaporator exceeds to 14 C, the difference of ε among the isentropic and dry working fluids is very small. 4. Conclusions In this study, we have analyzed the influence of the evaporation temperature and the PPTD on the performance of the ORC system in recovering the low temperature waste heat of the flue gas. Based on the present analysis, the main conclusions can be summarized as follows: (1) In order to avoid the low temperature corrosion, some organic working fluids, such as R114 and R245fa, cannot achieve their maximum net power output, which should be paid attention to recover waste heat of the flue gas. Furthermore, it is found that there has been a linear relationship between the PPTD of the evaporator and the corresponding maximum net power output. (2) The total heat transfer area is decreasing first and then increasing with the increase of the PPTD of the evaporator. The differences of the heat transfer area between two arbitrarily organic working fluids diminish gradually with the increase of the PPTD of the evaporator. In this case, the choice of organic working fluids has little difference. (3) The ratio of the net power output to the heat transfer area is increasing first, and then decreasing after reaching its maximum value at an optimal PPTD of the evaporator which are almost equal to all the organic working fluids studied in the work. The calculation presents that the ORC system using R11 as the working fluid achieves the largest value of the net power output per heat transfer area, followed by R123, R245fa and R114. Acknowledgment This work is supported by National Basic Research Program of China (973 Program, Grant No. 2011CB710701). References
Fig. 7. Variations of ε with the PPTD of the evaporator. (a) DTT ¼ 20 C; (b) DTT ¼ 30 C. 1: R123; 2: R11; 3: R245fa; 4: R114.
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Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle You-Rong Li*, Jian-Ning Wang, Mei-Tang Du Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 January 2012 Accepted 4 March 2012 Available online 11 April 2012
This paper presented the analysis on the influence of the pinch point temperature difference (PPTD) and the evaporation temperature on the performance of organic Rankine cycle (ORC) in recovering the low temperature waste heat of the flue gas. Both the net power output and the heat transfer area of the evaporator and condenser were evaluated for dry and isentropic working fluids. When the heat and cold source conditions were given, the maximum net power output and the heat transfer area were obtained. The results show that some organic working fluids cannot reach the maximum net power output to avoid the low temperature corrosion. With the increase of the PPTD of the evaporator at a given total temperature difference, the total heat transfer area decreases first and then increases, while the corresponding cost-effective performance (ratio of the net power output to total heat transfer area) displays almost the opposite variation tendency. The PPTD of the evaporator for the optimization cost-effective performance is approximately the same for different organic working fluids. Meanwhile, the isentropic working fluids show better cost-effective performance than dry working fluids. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Pinch point temperature difference Evaporation temperature Low temperature waste heat Flue gas
1. Introduction Due to the rapid increase of the energy consumption in recent years, how to effectively utilize the low temperature waste heat, which was directly discharged to atmosphere in the industrial production, has attracted the considerable interest. It has been found that more than half of the total industrial waste heat was the low temperature heat energy and most of that was wasted in the form of flue gas [1]. Therefore, converting waste heat into electricity not only saves the fossil fuel but also contributes to reduce the thermal pollution. Nevertheless, a great quantity of waste heat with the temperature below 200 C is not suitable to be recovered by the traditional Rankine cycle [2]. As one of the most promising technologies in recovering this kind of waste heat, the organic Rankin cycle (ORC) with organic working fluids, which occurs phase change at relative low temperature, has been increasingly paid attention and gradually used in practical industrial applications. In addition, the ORC system has many advantages in making full use of the low temperature waste heat, for example, flexibility, safety and maintenance requirements etc [3,4]. So far, many investigations on the ORC system has been performed, including the working fluid selection [5e9], the optimum
* Corresponding author. Tel.: þ86 23 6511 2284; fax: þ86 23 6510 2473. E-mail address: [email protected] (Y.-R. Li). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.03.018
design for improving the system efficiency [10e13] and the system operating optimization etc [14e18]. Internal heat exchanger (IHE) was suggested to be equipped to improve the ORC efficiency in some conditions, however, Dai and Li pointed out that the IHE could not increase the net power output at a given heat source condition [19e22] and even not consider the extra investment. Besides, it was also certified that the superheating and supercooling of the working fluids lead to an increase of the system irreversibility [23,24]. Therefore, the basic ORC system was considered in present study. Evaporation temperature and condensation temperature are two main control parameters and have an important impact on the ORC performance. According to the second law of thermodynamics, both the higher evaporation temperature and the lower condensation temperature lead to an increase of the system thermal efficiency [25]. However, the evaporation temperature and condensation temperature are restricted by the critical temperature of the organic working fluid and the ambient temperature, respectively. The increasing evaporation temperature will reduce the heat transfer flux in the evaporator, which may lead to a decrease of the net power output finally. At the same time, the PPTD of the heat exchanger not only influences the evaporation temperature and condensation temperature but also plays an essential role in the cost-efficiency tradeoff [26]. With the decrease of the PPTD, higher evaporation temperature and lower condensation temperature can be achieved between the inlet temperature
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Nomenclature A cp h m Ja K Q T W
heat transfer area (m2) specific heat capacity (J kg1 K1) specific enthalpy (J kg1) mass flow rate (kg s1) Jacob number () heat transfer coefficient (W m2 K1) heat transfer flux (W) temperature ( C) power (W)
Greek symbols h isentropic efficiency
of waste heat and the heat sink temperature. Meanwhile, more heat transfer area is required with the decrease of the PPTD, which results in an increase of cost for the ORC system. Although there were many investigations associated with the optimization of the ORC system, detailed influence of the PPTD on the ORC performance was rarely found. Hence the main objective of this study is to analyze the influences of the coupled evaporation temperature and the PPTD on the net power output and the costeffective performance. The lowest temperature of the flue gas at the evaporator outlet should exceed 90 C in order to avoid the low temperature corrosion. At the given external heat and cold source conditions, the optimum performance of the ORC system is evaluated with different working fluids including R123, R11, R245fa and R113 etc. The physical properties of organic working fluids and the system performance were calculated with Engineering Equation Solver (EES) [27].
ε
ratio of the net power output to heat transfer area (W m2)
Subscripts a cooling air c condenser e evaporator g flue gas p pump s single-phase region t two-phase region T total tur turbine wf working fluid
The heat transfer area can be obtained when the heat transfer coefficient and state parameters of the organic working fluid are determined. Meanwhile, cost-effective performance for the ORC system would be worked out. A simple description of the thermodynamic modeling procedure of the basic ORC system, as shown in Ref. [20], was summarized as following:
2. Thermodynamic model of the ORC system The layout of the basic ORC system and the T-S diagram are shown in Fig. 1. It can be found that the ORC system uses the same thermodynamic principles as the traditional steam Rankine cycle. The difference is that the ORC system employs the low boiling point organic working fluid to recover the low temperature waste heat. The organic working fluid absorbs heat from the flue gas in the evaporator and becomes saturated vapor used to drive turbine. After leaving turbine, the organic working fluid is condensed to saturated liquid in the condenser and pumped back to the evaporator to close the cycle. The steady operation state of the cycle is assumed in this work and pressure drop in the evaporator, condenser and pipes can be neglected. Specific heat capacities of the flue gas and cooling air are assumed to be constant. The ORC specifications in this work are listed in Table 1. The detailed procedures of calculation are outlined as follows: At the given conditions of heat and cold sources, the physical properties at the two-phase region of the evaporator and the mass flow rate of the working fluid are obtained from the prescribed evaporation temperature and the PPTD of the evaporator. The state of the organic working fluid at condenser outlet is assumed to be saturated liquid. Therefore, the condensation temperature can be calculated after iterating to meet the PPTD of the condenser and the given isentropic efficiencies of turbine and pump. In addition, the outlet temperatures of the flue gas and cooling air, and the net power output are determined by state parameters of the working fluid at operation points.
Fig. 1. The basic ORC system.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Ref.
The calculation method is completely adapted to the condenser and the heat released of the organic working fluid in condenser can be obtained easily as:
[20,25]
Qc ¼ ma cpa Tc DTc Ta;in ð1 þ Jac Þ;
Table 1 Specifications of the ORC considered. Items
Value
Ambient temperature ( C) Flue gas temperature ( C) Flue gas flow rate (kg s1) Cooling air temperature ( C) Cooling air flow rate (kg s1) Pump isentropic efficiency Turbine isentropic efficiency Minimum allowed discharge temperature ( C) Heat transfer coefficient in evaporator (W m2 K1) Heat transfer coefficient in condenser (W m2 K1)
20 160 10.47 20 52.35 0.8 0.85 90 70 50
Jac ¼
(1)
h1 h1a Ta;out Tc þ DTc ¼ : h1a h2 Tc DTc Ta;in
(12)
DTc is the PPTD of the condenser and the Jac denotes the ratio of the sensible heat to the latent heat of the working fluid in condenser. Therefore, the net power output of the ORC system can be determined as following: Wnet ¼ Wtur Wp ¼ Qe Qc :
Pump, 2-3,
Wp ¼ mwf ðh3 h2 Þ ¼ mwf ðh2a h2 Þ=hp :
(11)
where, [31] [3] [3] [31] [30] [30]
Condenser, 1-2,
Qc ¼ mwf ðh1 h2 Þ:
505
(13)
Substituting Eqs. (10) and (11) into Eq. (13) yields:
(2)
Wnet ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ ma cpa Tc DTc Ta;in ð1 þ Jac Þ:
ð14Þ
Evaporator, 3-4, 2.2. Heat transfer area
Qe ¼ mwf ðh4 h3 Þ:
(3)
mwf ðh4 h3a Þ ¼ mg cpg Tg;in Tg;e ;
(5)
There have been many formulas which used to calculate the heat transfer coefficient of the heat exchanger in the published literatures [2,15,28,29]. Shell-and-tube heat exchanger of the counter-current design is employed, and the heat transfer coefficients in evaporator and condenser are directly given in Table 1. Both heat transfer procedures of the single-phase region and the two-phase region were considered in evaporator and condenser. As the thermal resistances of gas side and air side in evaporator and condenser are much larger than those of the working fluid side, respectively, heat transfer coefficients of evaporator and condenser could be regarded as constant [30]. Based on the heat transfer equations, the heat transfer area of the single-phase region in the evaporator can be calculated as following:
mwf ðh3a h3 Þ ¼ mg cpg Tg;e Tg;out ;
(6)
Ae;s ¼
Turbine, 4-1,
Wtur ¼ mwf ðh4 h1 Þ ¼ mwf ðh4 h4a Þhtur :
(4)
2.1. Net power output When the viscous dissipation and heat losses of the heat exchanger are neglected, energy balance in single-phase and twophase region of evaporator can be expressed as following, respectively,
where
(15)
where,
Tg;e ¼ Te þ DTe :
(7)
The h4 and h3a are the enthalpies of the organic working fluid at the saturated vapor and saturated liquid conditions, respectively. DTe is the smallest temperature difference in evaporator, which is defined as the difference between the flue gas temperature where the organic fluid begins to evaporate and the evaporation temperature. In evaporator, the ratio of the sensible heat to the latent heat of the working fluid is defined as
Jae ¼
mg cpg Te þ DTe Tg;out : Ke DTm;e;s
Te þ DTe Tg;out h3a h3 ¼ : h4 h3a Tg;in Te DTe
(8)
The total absorbed heat of the organic working fluid in the evaporator can be expressed as:
Qe ¼ mwf ðh4 h3 Þ ¼ mg cpg Tg;in Tg;out :
Ae;s ¼
(16)
mg cpg Te þ DTe Tg;out Tg;out T3 ln : DTe Ke Tg;out Tc DTe
(17)
Set ze ¼ Jae ðTg;in Te DTe Þ, the above equation can be written as:
Ae;s ¼ (10)
Tg;out T3 DTe : Tg;out T3 ln DTe
DTm,e,s is the logarithmic mean temperature difference of the single-phase region in evaporator and Ke is the heat transfer coefficient. In the basic ORC system, Tc is very close to T3 and the difference between Tc and T3 is negligible, and therefore, using Tc to replace T3 is reasonable. In this case, the heat transfer area can be determined as:
(9)
Substituting Eqs. (5), (6) and (8) into Eq. (9) yields:
Qe ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ:
DTm;e;s ¼
mg cpg ze ðTe Tc þ DTe Þ ze ln : DTe Ke Te Tc ze
(18)
Using the similar method, the heat transfer area of the singlephase region in the condenser can be expressed as
506
Ac;s
Y.-R. Li et al. / Energy 42 (2012) 503e509
ma cpa zc ðT þ Tc DTc Þ zc ¼ ln 1 ; DTc Kc T1 Tc zc
(19)
where, zc ¼ Jac ðTc DTc Ta;in Þ. T1 mainly depends on Te and Tc with the constant isentropic efficiency of turbine. The value of T1 will slightly increase with the increase of Te and the decrease of Tc. For a near-isentropic fluid, the difference between T1 and Tc can be neglected [7]. In two-phase region, the areas of the heat exchanger for the evaporator and condenser can be written as, respectively,
Ae;t
Tg;in Te mg cpg ¼ ln ; DTe Ke
(20)
Tc Ta;in ma cpa ln : DTc Kc
(21)
Ac;t ¼
The total heat transfer area in the evaporator and condenser can be obtained as:
AT ¼ Ae þ Ac :
(22)
where, Ae ¼ Ae,s þ Ae,t and Ac ¼ Ac,s þ Ac,t. Thereby, the net power output per heat transfer area can be obtained as:
ε ¼ Wnet =AT :
(23)
Based on above analyses, it can be known that both the net power output and the heat transfer area of the ORC system are mainly associated with Te, Tc, DTe and DTc. At the given heat and cold sources, matching those key parameters to improve the ORC system performance is the main target of this work. The previous published papers have researched the ORC at some certain PPTD, as shown in Table 2, however, the effect of the PPTD on the ORC performance is not considered. Consequently, this paper will focus much attention on the influence of the PPTD of the evaporation on the cost-effective optimization at a given total PPTD (DTT). In order to check the validation of the present model, we carried out some calculations of the basic ORC for the various fluids under the same operation conditions as Dai et al. [22]. The comparison of the net power output was shown in Table 3. A good agreement was achieved and the relative error was less 1%.
Table 3 The comparison of the net power output. Working fluids
R11
R123
R141b
R113
Wnet (kW)
149.9 151.34 0.95
157.8 156.91 0.57
152.4 152.8 0.26
155.8 155.77 0.02
This work Dai et al. [22] Relative error (%)
3.1. Effect of the PPTD on the net power output Fig. 2 shows the variation of the net power output with the PPTD of the evaporator at DTT ¼ 20 C. It can be found that the net power output increases first, and then decreases with the increase of the PPTD of the evaporator at a fixed evaporation temperature Te. This is mainly because the increase of the PPTD of the evaporator causes the decrease of the heat transfer flux, which results in a reduction of the mass flow rate of the organic working fluids. On the other hand, at a given total PPTD (DTT), the condensation temperature decreases to meet the decrease of the PPTD of the condenser. As a result, the difference between the evaporation temperature and the condensation temperature increases, which leads to the increase of the specific enthalpy drop in turbine. Therefore, there is an optimal PPTD of the evaporator to maximize the net power output. Comparison with other waste heat resources like the geothermal energy, the low temperature flue gas has several distinct features in the waste heat recovery system. Of which, the temperature of the flue gas at the evaporator outlet should exceed 90 C to avoid the low temperature corrosion. Therefore, organic
a
3. Results and discussion The cost-effective performance is determined by the electric energy production and investment of the ORC system, which can be measured by the net power output and the heat transfer area. In this work, we focused on the dry and isentropic organic working fluids.
b
Table 2 Selections of pinch point temperature difference in references. Fluids
Heat source
Cold source
DTe DTc Ref.
R134a, R123, R227ea, R245fa, R290, n-pentane R113, R245ca, isobutene, R123 Water, ammonia, Butane, Isobutene, R11, R236EA R123, R141B, R113, R245CA R134a R227ea, Isobutane, R245fa, opentane
Hot air
Water
10
5
[6]
Water Flue gas
Water e
15 8
15 e
[14] [22]
Water/steam Hot water
11 5
6 5
[31] [13]
R123
Flue gas
Air Cold water e
10
10
[20]
Fig. 2. Variation of the net power output with the PPTD of the evaporator at DTT ¼ 20 C. Solid lines correspond to Tg,out 90 C and dashed lines Tg,out < 90 C. (a) R245fa; 1: Te ¼ 108 C; 2: Te ¼ 110 C; 3: Te ¼ 112 C; (b) R123; 1: Te ¼ 105 C; 2: Te ¼ 107 C; 3: Te ¼ 109 C.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Fig. 3. The variations of the maximum net power output and the optimal evaporation temperature with the PPTD of the evaporator at DTT ¼ 20 C. Solid line: Wnet,max; Dashed line: Te,opt. 1: R245fa; 2: R114; 3: R123; 4: R11.
working fluids can be categorized into two groups at the given operation conditions according to whether they can achieve the maximum net power output. With the increase of the PPTD of the evaporator, isentropic working fluids, for example R245fa and R114, cannot achieve the maximum value of the net power output at the restrict condition, as shown in Fig. 2(a). Some attention should be paid when they are used to recovery the low temperature waste heat of the flue gas. On the contrary, R123 and R11 belong to the kind of organic working fluids which can achieve the maximum net power output at certain evaporation temperature, as shown in Fig. 2(b). When the PPTD is determined, the net power output increases first, and then decreases with the increase of the evaporation temperature [25]. Therefore, there has been an optimal evaporation temperature for each PPTD of the evaporator to maximize the net power output at a fixed total PPTD. The linear relations of the maximum net power output and the optimal evaporation temperature with the PPTD of the evaporator at DTT ¼ 20 C are shown in Fig. 3. It can be found that the organic working fluids including R114 and R245fa which cannot achieve the maximum net power output present better performance than R123 and R11. The area of heat exchangers contributes largely to the total cost of the ORC system, therefore, it is necessary to discuss the effect of the PPTD on the heat transfer area, which has the advantage to analyze the performance of the ORC. When the total PPTD is given, with the variation of the PPTD of the evaporator, the heat transfer area of evaporator and condenser would change simultaneously. It means that the variation of the PPTD of the evaporator affects the area of not only evaporator but also condenser. The heat transfer areas corresponding to the maximum net power output are calculated at the given conditions shown in Table 1. In general, the area of the heat exchanger decreases with the increase of the PPTD at the same heat transfer flux. The rational allocation of the PPTDs in evaporator and condenser to achieve more net power output with less heat transfer area by reducing the system irreversibility is the main task in the optimization process. As shown in Fig. 4, the area of the evaporator decreases and the area of condenser increases with the increase of the PPTD of the evaporator. Because the heat transfer coefficient of evaporator is generally larger than that of condenser, and the temperature variation of cooling air between the inlet and outlet is less than that of the flue gas in evaporator, and therefore, the area of condenser is the major source of the total heat transfer area. As a result, the total area of the heat exchanger is decreasing slightly first and then increasing gradually after reaching the minimum value at the PPTD of the evaporator about 7 C.
507
Fig. 4. Variation of the heat transfer area with the PPTD of the evaporator at DTT ¼ 20 C.
Fig. 5 shows that the variation tendencies of the heat transfer area for different organic working fluids are the approximate same. The difference of the total area of the heat exchanger between two arbitrary organic working fluids decreases with the increase of the PPTD of the evaporator. It means the choice of the organic working fluid has a little influence on the heat transfer area. The total area of the heat exchanger decreases with the increase of the total PPTD for all organic working fluids. This is because the increase of the PPTD of the condenser reduces the area of condenser, which is the major factor of the total heat transfer area. The good linear relationship between the maximum net power output and the PPTD of the evaporator is found in the previous part. However, the growth rate of the total heat transfer area is
a
b
Fig. 5. Variation of the heat transfer area with the PPTD of the evaporator. (a) DTT ¼ 20 C; (b) DTT ¼ 30 C. 1: R123; 2: R11; 3: R245fa; 4: R114.
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Fig. 6. Variations of the total heat transfer area and the net power output with the PPTD of the evaporator at DTT ¼ 20 C.
increasing gradually with the increase of the PPTD of the evaporator. Both the above relationships for R123 can be seen in Fig. 6. 3.2. Cost-effective optimum Pure pursuit of the net power output is meaningless without considering the investment in utilizing the low temperature waste heat effectively. The optimum of the net power output per heat transfer area has a very important practical significance. The heat transfer area can be reduced to some extent by matching the system parameter with the exterior condition for the same power output. In addition, the above analyses show that both the total area of heat exchangers and the net power output increase with the increase of the PPTD of the evaporator. Therefore, it’s necessary to evaluate the cost-effective performance of the ORC system by ε,
a
b
which is defined as the ratio of the net power output to the total heat transfer area. The ratio of the net power output to heat transfer area increases first, and then decreases for all organic working fluids, as shown in Fig. 7. Meanwhile, we can see that the ORC system using R11 as the working fluid always has the best cost-effective performance although it presents the lowest net power output, as shown in Fig. 3, compared to other organic working fluids. It hints that the maximum net power output and the best costeffective performance cannot be achieved at the same time. Those two aspects should be considered simultaneously in choosing the most suitable organic working fluids in different designs. Further, the less system irreversibility is generated in condenser when isentropic fluids are used. Therefore, we can come to a conclusion that isentropic fluids show better cost-effective performance than dry fluids. As shown in Fig. 7, the isentropic fluids including R11 and R123 present better cost-effective performance than dry working fluids including R114 and R245fa. The differences of the performance for organic working fluids are reducing along with the increase of the PPTD of the evaporator. Taking the total PPTD of 20 C as an example, when the PPTD of the evaporator exceeds to 14 C, the difference of ε among the isentropic and dry working fluids is very small. 4. Conclusions In this study, we have analyzed the influence of the evaporation temperature and the PPTD on the performance of the ORC system in recovering the low temperature waste heat of the flue gas. Based on the present analysis, the main conclusions can be summarized as follows: (1) In order to avoid the low temperature corrosion, some organic working fluids, such as R114 and R245fa, cannot achieve their maximum net power output, which should be paid attention to recover waste heat of the flue gas. Furthermore, it is found that there has been a linear relationship between the PPTD of the evaporator and the corresponding maximum net power output. (2) The total heat transfer area is decreasing first and then increasing with the increase of the PPTD of the evaporator. The differences of the heat transfer area between two arbitrarily organic working fluids diminish gradually with the increase of the PPTD of the evaporator. In this case, the choice of organic working fluids has little difference. (3) The ratio of the net power output to the heat transfer area is increasing first, and then decreasing after reaching its maximum value at an optimal PPTD of the evaporator which are almost equal to all the organic working fluids studied in the work. The calculation presents that the ORC system using R11 as the working fluid achieves the largest value of the net power output per heat transfer area, followed by R123, R245fa and R114. Acknowledgment This work is supported by National Basic Research Program of China (973 Program, Grant No. 2011CB710701). References
Fig. 7. Variations of ε with the PPTD of the evaporator. (a) DTT ¼ 20 C; (b) DTT ¼ 30 C. 1: R123; 2: R11; 3: R245fa; 4: R114.
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