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Process integration of organic Rankine cycle (ORC) and heat pump for low temperature waste heat recovery
Energy 160 (2018) 330e340
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Process integration of organic Rankine cycle (ORC) and heat pump for low temperature waste heat recovery Haoshui Yu a, Truls Gundersen a, Xiao Feng b, * a b
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjoern Hejes v. 1A, NO-7491 Trondheim, Norway School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2017 Received in revised form 15 May 2018 Accepted 8 July 2018 Available online 11 July 2018
Organic Rankine cycles (ORCs) have been a mature technology for low temperature waste heat utilization. However, the relatively low thermal efficiency and incomplete waste heat recovery limit the power output of ORC systems. The reason for the above two problems is that the temperature-enthalpy (T-H) profile of waste heat sources does not match well with the organic working fluid in an ORC system. Heat pumps may reinforce the match between the waste heat carrier and the organic working fluid of the ORC. The condensation heat released by a heat pump can be used to evaporate the organic working fluid during phase change. Thus, a better thermal match between waste heat and the organic working fluid in the ORC can be obtained. Due to the possibility to improve power output, the integration of an ORC and a heat pump is investigated in this study. Proper working fluids in ORCs and heat pumps are chosen simultaneously. The integration between ORCs and heat pumps presents significant power output increases for special cases and deserves to be popularized in practical applications. However, the integrated system does not always lead to an increase in power output. The integration is profitable only when the following pre-conditions are satisfied simultaneously: (a) poor thermal match between working fluid and waste heat for standalone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. A systematic procedure to determine the optimal operating conditions of the system is proposed in this study. A case study adopted from literature demonstrates the potential benefits of the integration of heat pumps and ORCs. The results show that the net power output and the amount of waste heat recovered increase by 9.37% and 12.04% respectively. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Heat pump Process integration Low temperature waste heat Thermal match
1. Introduction Organic Rankine cycles have received widespread attention since the 1970s. ORCs represent a promising way to convert low to medium temperature heat into power [1]. The choice of working fluid [2], operating conditions [3] and the integration of an ORC with the background process [4] exert great influence on the net power output of ORC systems. Organic Rankine cycle modifications, such as recuperation and turbine bleeding [5], can improve the thermal efficiency of the ORC system. Working fluid selection [6] and operating condition determination [7] affect both thermal efficiency and the amount of waste heat recovered. Applying optimization methods to process integration can explore the trade-offs
* Corresponding author. E-mail address: [email protected] (X. Feng). https://doi.org/10.1016/j.energy.2018.07.028 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
between thermal efficiency, amount of waste heat recovered and economic factors [8]. Yu et al. [9] proposed a new method for simultaneous working fluid selection and determination of operating conditions. This method is based on a newly defined parameter to locate the pinch point. Chen et al. [10] proposed a new method based on mathematical programming to simultaneously optimize the ORC and synthesize the heat exchanger network. Yu et al. [11] proposed a superstructure to integrate an ORC into a background process considering turbine bleeding, superheating and regeneration. However, all of these studies aim at improving the power output of a standalone ORC. If a heat pump is integrated with the ORC, it is possible to increase the overall net power output of the integrated system. According to pinch analysis, heat pumps should be placed across the pinch point in a system [12]. This concept has been applied to distillation processes successfully with substantial energy savings [13]. Heat pumps can be classified into closed and open heat pumps
H. Yu et al. / Energy 160 (2018) 330e340
respectively according to whether the process stream and the working fluid are the same [14]. From a thermodynamic point of view, heat pumps can also be classified into reversed Rankine cycles and Brayton cycles [15]. Reversed Brayton cycle heat pumps operate in vapor phase without phase change, thus this kind of heat pump is also called a sensible heat pump. For a reversed Rankine cycle heat pump, isothermal phase change takes place in the condenser. This isothermal condensation heat can match perfectly with the evaporation process of an ORC. Therefore, integration of closed reversed Rankine cycle heat pumps with an ORC for low temperature waste heat utilization is investigated in this study. At first sight, it seems unreasonable to upgrade waste heat consuming power by a heat pump, and then to generate power by an ORC from the perspective of thermodynamics. However, the involvement of a heat pump may result in better thermal match between the waste heat source and the organic working fluid in some cases. As long as the power increase of an ORC overweighs the power consumed by the heat pump, the integration of the heat pump and the ORC is profitable. In organic Rankine cycles with pure working fluids, the isothermal phase transition will cause a pinch point between the working fluid and the heat source [9]. This pinch point limits the amount of waste heat recovered by an ORC system. The pinch point limitation is caused by the improper ratio of latent to sensible heat of the working fluid, which is dependent on the thermodynamic properties of the working fluid. Therefore, attention should be paid to changing the profile of the waste heat with the help of a heat pump to enhance the thermal match between the waste heat source and the working fluid. A thorough literature search did not identify any papers on the integration of heat pumps with ORCs to increase the net power output of the whole system recovering waste heat. In some specific cases, the integration of a heat pump and an ORC has the potential to increase the net power output of the whole system. This study focuses on integrating an ORC and a heat pump into one system, where the heat pump upgrades part of the waste heat to drive an ORC with increased power production at the cost of power consumption in the heat pump, in order to increase the overall net power output of the system. 2. Motivation and theory There are generally two ways to increase the net power output from an ORC, namely increasing thermal efficiency and increasing the amount of waste heat recovered by the organic working fluid.
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Working fluid selection and ORC modifications aim at increasing the thermal efficiency [16]. The operating conditions also exert a great influence on the thermal efficiency. The optimal operating conditions can be determined from the trade-off between thermal efficiency and the amount of waste heat recovered [17]. However, the effect that thermal efficiency and amount of waste heat recovered have on the net power output depends on the character of waste heat. The waste heat can be classified into two categories according to the target temperature of waste heat as shown in Fig. 1. Nonconstrained waste heat refers to the waste heat whose target temperature is not constrained, and the target temperature can be as low as ambient temperature. Constrained waste heat refers to the waste heat whose target temperature is much higher than the ambient temperature and the target temperature has to meet some specifications. For example, the target temperature of flue gas cannot be lower than the acid dew point to avoid corrosion. The working fluid selection criteria are different for the two kinds of waste heat sources. For non-constrained heat sources, it is obvious that different operating conditions or working fluids exhibit large difference in the amount of waste heat recovered. The net power output depends on both thermal efficiency and the amount of waste heat recovered. However, the amount of waste heat recovered exerts much greater influence on the net power output. Yu et al. [9] proposed a parameter PREDICTOR to determine the pinch point and calculate the amount of waste heat recovered. They found that for non-constrained waste heat recovery, the amount of waste heat is more sensitive to the variation of operating conditions compared with thermal efficiency. Therefore, the amount of waste heat recovered is the primal factor to be considered. For constrained waste heat sources, the waste heat can be recovered totally to heat the working fluid in the ORC as shown in Fig. 1(b). There is no difference in the amount of waste heat recovered for different working fluids or different operating conditions. The net power output only depends on thermal efficiency. Therefore, thermal efficiency is the criteria for working fluid selection. Since the constrained waste heat can be totally recovered, it is not necessary to integrate a heat pump to increase the waste heat recovery. Hence, this study only investigates non-constrained waste heat sources. For non-constrained waste heat recovery, an important limitation of an ORC with pure component working fluid is the isothermal boiling process, which creates pinch points and leads to poor thermal match between the working fluid and waste heat [18]. The “pinch limitation” problem in organic Rankine cycles is
T
T Pinch limitation
Pinch limitation
high evaporating temperature
Optimal design
high evaporating temperature
medium evaporating temperature Tmin=55 Tcon=45
Qre
medium evaporating temperature
low evaporating temperature Tcon=45 Qre
Qre Qmax
(a) Non-constrained waste heat
low evaporating temperature
H
Qmax
(b) Constrained waste heat
Fig. 1. Waste heat classification and pinch limitation for non-constrained waste heat.
H
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supposed to be eliminated or alleviated to improve the net power output. If the evaporation temperature is close to the critical temperature of the working fluid, the evaporation latent heat is very small, which may alleviate the pinch limitation [9]. In the limiting case, as the evaporation temperature approaches the critical temperature, the latent heat approaches zero and the isothermal phase change of the working fluid disappears. Then the working fluid line becomes an oblique line instead of a polygonal line. The “pinch limitation” is eliminated and waste heat can be recovered totally to heat the working fluid in the ORC. On the other hand, some researchers have proposed to use supercritical ORCs to avoid the pinch limitation and the results show that supercritical ORCs perform better than subcritical ORCs [19]. However, due to operational issues, safety concern and investment cost, supercritical ORCs have not yet been implemented in practice [20]. Subcritical ORCs still have predominance in practical applications. To guarantee stable operation, the evaporation temperature should not be very close to the critical temperature; therefore, the “pinch limitation” problem is a critical problem engineers have to face. Fig. 1(a) illustrates the “pinch limitation” on the T-H diagram of
an ORC system for non-constrained waste heat recovery. In this study, the working fluid in the ORC is assumed to be cooled down to 45 C by cooling water in the condenser. Therefore, the minimum waste heat outlet temperature is 55 C assuming the minimum approach temperature is 10 C. The purple line in Fig. 1(a) demonstrates a working fluid evaporating at low temperature. There is no pinch limitation and all of the waste heat can be recovered, but the thermal efficiency is very low and the power output may be not satisfactory. When the evaporation temperature is high, as shown by the green line in Fig. 1(a), the thermal efficiency is high, but the pinch point severely limits heat recovery. The power output is restricted by pinch limitation in this case. To trade-off thermal efficiency and the amount of waste heat recovered, optimal operating conditions can be determined as the blue line indicated in Fig. 1(a). Under optimal operating conditions, the thermal efficiency is less than the green line and greater than the purple line, and the amount of waste heat recovered is less than the purple line and greater than the green line. The pinch limitation for the blue line is worse than the purple line, but better than the green line. The thermal efficiency and amount of waste heat recovered are both moderate under the optimal condition, but this often provides maximum power output. It is noticeable that under the optimal condition, the waste heat is not totally recovered. Therefore, it is possible to increase the power output if the amount of waste heat recovered can be further improved. If a heat pump is introduced, the profile of waste heat can be changed and the amount of waste heat recovered may be improved. Fig. 2 shows the T-S diagram of an ORC and reversed Rankine cycle heat pump. The condensation heat from the heat pump can be used to heat the organic working fluid during phase change attaining good thermal match between isothermal phase transitions in the heat pump and the ORC. Fig. 3 illustrates the flowsheet of the integrated system. Waste heat is recovered and utilized in two ways, namely one part is used to heat the organic working fluid in the ORC system, and the other part is upgraded by the heat pump first and released to the organic working fluid of the ORC at a higher temperature. Fig. 4 illustrates the T-H diagram of the integrated system. The red line, green line and blue line denote waste heat, working fluid in the heat pump and working fluid in the ORC respectively. The yellow shaded area indicates the evaporator of the heat pump. The choice of working fluids for both the ORC and the heat pump are very important decisions. The corresponding operating conditions
T
III Heat Pump
IV 4
3 I
5
1
II
6 Organic Rankine Cycle
s Fig. 2. TeS diagram of ORC and heat pump.
III 5
4
Turbine
Evaporator II
Valve
3
IV
Evaporator
Condensor
Compressor
Condensor
2
Evaporator
Pump 2
I
Waste heat Fig. 3. The layout of the integrated system.
6
1
H. Yu et al. / Energy 160 (2018) 330e340
T
333
Upgraded by heat pump and released to ORC at higher temperature +w
Temperature range of upgraded waste heat Pinch limitations
Teva,hp Tmin=55 Tcon=45
Qre,integrated H Qmax+W Fig. 4. TeH diagram of the integrated system.
should be determined appropriately as well. Without considering capital investment, the integration of a heat pump is beneficial as long as the increase of power output from the ORC overweighs the power consumed by the heat pump. While integrating a heat pump with an ORC, the following challenges should be addressed: (1) When is it worthwhile to integrate a heat pump with an ORC? (2) If a heat pump is to be included, which part of the waste heat should be upgraded by the heat pump? (3) What working fluids should be selected for the ORC and the heat pump respectively? (4) What are the optimal operating conditions of the ORC and the heat pump? This paper aims at answering the above questions based on a proposed systematic procedure. 3. Methodology To integrate a heat pump into the system, one should first check whether there is potential to increase the power output of the ORC. If an ORC can recover nearly all of the waste heat and the evaporation temperature is high enough, the potential to further increase the power output through the integration of a heat pump is limited. On the contrary, if a large portion of waste heat is not recovered, as shown by the blue line in Fig. 1(a), the integration of a heat pump may increase the net power output. As the choice of working fluid exerts great influence on the performance of heat pumps and ORCs, working fluids for both cycles should be determined with care. If there are very good working fluids, the integration may be more profitable. However, the criteria for working fluid selection for an ORC and a heat pump are different in this study and will be discussed in Section 3.1 and 3.2 respectively. After working fluids are determined for both ORC and heat pump, the optimal operating conditions can be determined by the mathematical model discussed in Section 3.3.
environmental concerns [21]. For a sensible waste heat source, a working fluid whose critical temperature is slightly lower than the inlet temperature of the waste heat source performs well due to a less serious pinch limitation [22]. For standalone ORCs, the optimum working fluid and corresponding operating conditions can be determined using the procedures proposed by Rayegan and Tao [23] or a method based on critical temperatures [24]. Thermal efficiency of the working fluid is related to the critical temperature, but the difference between the working fluids is marginal under the same evaporation temperature as shown in Fig. 5, especially in the low temperature range. For non-constrained waste heat, the working fluid with the maximum net power output is generally the one that can recover more waste heat. If heat pump integration is considered, the optimum working fluid in an ORC may change. The purpose of integrating a heat pump into this system is to get a better thermal match between the waste heat source and the working fluid. As discussed earlier, for the non-
3.1. Working fluid selection for organic Rankine cycle (ORC) Working fluid selection for ORCs relies on the temperature of waste heat, type of waste heat (latent, sensible or combined), and practical considerations such as operability, safety and
Fig. 5. Thermal efficiency vs. evaporation temperature for all the pre-selected working fluids with condensation temperature 45 C.
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H. Yu et al. / Energy 160 (2018) 330e340
constrained waste heat recovery, the thermal efficiency has weaker influence on the power output compared with the amount of waste heat recovered, which is related to the ability of the working fluid to recover waste heat. The ratio of latent to sensible heat reflects the ability of the working fluid to recover waste heat. In addition, the smaller the ratio of latent to sensible heat of the working fluid is in an ORC, the less heat needs to be upgraded by the heat pump to get better thermal match of the system. This means that the amount of waste heat recovered can be increased to the same extent with less power consumption by the heat pump. The optimal working fluid for the integrated ORC system is the working fluid with the smallest ratio of latent to sensible heat. For the same working fluid, the ratio of latent to sensible heat is different under different evaporation temperatures. The higher the evaporation temperature, the smaller the ratio of latent to sensible heat. Therefore, the ratio of latent to sensible heat is a performance indicator considering both the working fluid properties and the operating conditions. The integration of a heat pump is worthwhile when the ratio of latent to sensible heat is small. The working fluid with the minimum ratio of latent to sensible heat is the most promising candidate for an ORC. It should be noted that the ratio of latent to sensible heat of the working fluid is a function of condensation temperature and evaporation temperature of the ORC. In this study, the condensation temperature of the ORC is assumed to be 45 C, then the ratio of latent to sensible heat only relies on the evaporation temperature. The preselected working fluids for ORC in this study are listed in Table 1.
3.2. Working fluid selection for heat pump As for the working fluid selection for a heat pump, there are two main concerns, namely the operability of the system and the coefficient of performance (COP). Operability means that the condensation temperature of the heat pump should be higher than the evaporation temperature of the ORC as shown in Fig. 2. Therefore, the critical temperature of working fluids in heat pumps cannot be lower than the evaporation temperature of the ORC to ensure the operability of the system. Several working fluid candidates for heat pumps whose critical temperatures are higher than 130 C are considered in this study as shown in Table 2. The second concern is the COP. Unlike ORCs, the evaporation process of the heat pump is a purely isothermal process, thus no “pinch limitation” takes place in the evaporator. The condensation heat of a heat pump can be totally transferred to the working fluid in the ORC without pinch limitation as well. Then only the thermal efficiency matters, thus COP is the working fluid selection criteria for the heat pump. For working fluid selection in the ORC, the ratio of latent to sensible heat is chosen as the criteria for the working fluid since less waste heat needs to be upgraded to get a better thermal match. For the integrated system proposed in this study, COP is extremely important in determining whether it is worthwhile to integrate a heat pump with an ORC.
Table 2 Pre-selected working fluids for heat pumps. Working fluids
Chemical formula
Tc ( C)
Pc（bar）
ODP
Type
R600a R236ea R600 R245fa R123 R601 n-hexane
C4H10-2 C3H2F6 C4H10-1 C3H3F5-D1 C2HCL2F3-D1 C5H12-1 C6H14-1
134.65 139.23 151.97 154.05 183.79 196.55 234.45
36.40 34.12 37.96 36.40 36.76 33.70 30.25
0.0 0.0 0.0 0.0 0.02 0.0 0.0
Dry Dry Dry Isentropic Dry Dry e
A heat pump operated under various evaporation temperatures with constant condensation temperature (130 C) is simulated in Aspen Plus [25]. The isentropic efficiency of the compressor is assumed to be 85%. Fig. 6 illustrates the variation of the COP with the evaporation temperature. It is clear that n-hexane has the largest COP among all the pre-selected working fluids. Even though the results are based on a fixed condensation temperature, the trend is the same under other operating conditions. Therefore, nhexane is chosen as the working fluid in the heat pump in this study.
3.3. The determination of operating conditions for the integrated system The procedure to determine the operating conditions of the combined ORC and heat pump system is presented in this section and is shown in Fig. 7. First, set the evaporation temperature of the ORC. The evaporation temperature may be constrained by the waste heat inlet temperature or the critical temperature of the working fluid for a subcritical ORC. To guarantee an acceptable thermal efficiency of the ORC, the evaporation temperature is set high at first. The higher the evaporation temperature, the smaller the latent heat of the working fluid in the ORC, the smaller the ratio of latent to sensible heat, and the more chances of profitable integration of a heat pump. Once the evaporation temperature is determined, the corresponding heat pump condensation temperature can be determined. It is clear that the condensation temperature of the heat pump should be DTmin higher than the evaporation temperature of the ORC in order to minimize the power consumption by the heat
Table 1 Pre-selected working fluids for ORC. Working fluids
Chemical formula
Tc ( C)
Pc（bar）
ODP
Type
R227ea R236fa R600a R236ea R600 R245fa R601a R601
C3HF7 C3H2F6-D1 C4H10-2 C3H2F6 C4H10-1 C3H3F5-D1 C5H12-2 C5H12-1
101.68 124.92 134.65 139.23 151.97 154.05 187.25 196.55
29.12 32.19 36.40 34.12 37.96 36.40 33.80 33.70
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Dry Dry Dry Dry Dry Isentropic Dry Dry
Fig. 6. COP of various working fluids with fixed condensation temperature (130 C).
H. Yu et al. / Energy 160 (2018) 330e340
Set ORC evaporation temperature and heat pump condensation temperature
Determine the working fluid in the ORC and the heat pump
Apply Eqs. (1)-(17) to various heat pump evaporation temperatures Decrease the evaporation temperature Obtain the optimal heat pump evaporation temperature and the corresponding operating conditons
Is waste heat recovery satisfactory?
No
Yes
Is net power output increased?
No
Not profitable to integrate heat pump
Yes Profitable integration
Fig. 7. Procedure for integrating heat pump with ORC.
pump. Second, according to the evaporation temperature of the ORC, the working fluid with the smallest ratio of latent to sensible heat is chosen as the working fluid in the ORC and the working fluid for the heat pump is n-hexane due to its highest COP. Once the working fluids are determined, the mathematical model is applied to various heat pump evaporation temperatures. The mathematical model will be discussed later. Afterwards, the optimal heat pump evaporation temperature can be determined. If the waste heat recovery is satisfactory, the integration procedure will terminate. If the power output is increased, then it is profitable to integrate a heat pump with the ORC. If the waste heat recovery is not satisfactory, the evaporation temperature of the ORC should be decreased. It is noticeable that some working fluids cannot evaporate at very high temperature due to the critical temperature limitation. Therefore,
335
with decreasing evaporation temperature, other working fluids with smaller ratio of latent to sensible heat will become the new working fluids in the ORC. Under a specific ORC evaporation temperature, the greatest challenge is to determine the evaporation temperature of heat pump. The evaporation temperature of the heat pump not only affects the COP as shown in Fig. 6, but also determines which part of the waste heat should be upgraded. The waste heat absorbed by the ORC is also related to the evaporation temperature of the heat pump. When the evaporation temperature of the heat pump is 45 C, waste heat above 55 C can be upgraded. The waste heat can be recovered totally by the ORC if the heat pump load is large enough. This is not worthwhile in most cases since the evaporation temperature of the heat pump is too low to justify the integration of a heat pump. Fig. 8 shows the detailed notation of the parameters in the integrated system, which will be used in the mathematical equations later. The waste heat above the heat pump evaporation temperature plus minimum temperature approach ðTeva;hp þ DTmin Þ can be upgraded by the heat pump. Then a “cliff” ðTcliff Þ is formed in the waste heat curve as shown in Fig. 8. As part of the waste heat is upgraded by the heat pump, the cliff will become a new potential pinch limitation. Then how much waste heat should be upgraded? When three pinches develop simultaneously as shown in Fig. 8, the amount of waste heat to be upgraded under the specified evaporation temperature reaches an optimum. The reason is that if more waste heat is upgraded, pinch point I will not exist, in essence more waste heat is upgraded than necessary. Pinch point II limits the amount of waste heat recovered under this circumstance. When the amount of waste heat upgraded is less, Pinch point II will not develop, and Pinch point I limits the amount of waste heat recovered. As the main purpose of integration with a heat pump is to increase the total amount of waste heat recovered, the function of increasing the amount of waste heat recovered is limited under this circumstance. As long as the integration of the heat pump can increase both the waste heat recovered and net power output, it is supposed to increase the amount of waste heat upgraded until three pinch points develop simultaneously. With three pinch points, the potential of increased power output reaches the limit if the integration is profitable. Therefore, under specified evaporation temperature, the optimal amount of waste heat to be upgraded can be calculated, determining Tcliff (namely the waste heat temperature at the inlet of the heat pump evaporator) as shown in Fig. 8. Then the corresponding operating conditions can be determined. The above circumstance only guarantees the optimal amount of waste heat to be upgraded under a specific evaporation temperature. To get the final optimal operating conditions, a heat pump at various evaporation temperatures should be integrated. The heat pump changes the ratio of latent to sensible heat of the waste heat source to get a better match between the waste heat source and the working fluid in the ORC. Theoretically, one should try other ORC evaporation temperatures and determine the corresponding optimal evaporation temperatures of the heat pump and the optimal amount of waste heat upgraded using the above procedure. However, as shown in the case study, only when the evaporation temperature exhibits small ratio of latent to sensible heat, the integration of a heat pump is profitable. Once the waste heat recovery is satisfactory, namely waste heat is totally or near totally recovered, the integration procedure terminates as shown in Fig. 7. Through the proposed method, the optimal design of the integrated system can be obtained. The mathematical model to determine the optimal operating conditions under specified evaporation temperature of the heat pump is presented in the following. The COP of a heat pump is the ratio of heat released in the condenser ðQout;hp Þ to the power consumed ðWÞ as defined by Eq.
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H. Yu et al. / Energy 160 (2018) 330e340
T
Tin,wh
Upgraded by heat pump and released to the ORC at higher temperature
Teva,orc+ Tmin +W
Qout,hp
Teva,orc Tcliff
I
III
Teva,hp+ Tmin Teva,hp Tout,wh
Pinch limitations II
Tout,wh,min=55 Qin,hp Tcon,orc=45
Qsensible
Qlatent Qre,integrated H
Qmax+W Fig. 8. TeH diagram of the integrated system with detailed notation.
(1).
COP ¼
Qout;hp Whp
When pinch I and pinch II occur simultaneously, the optimal new cliff temperature ðTcliff Þ should satisfy Eq. (6)
(1)
Eq. (2) is the energy balance for the heat pump system.
Qin;hp þ Whp ¼ Qout;hp
(2)
where Qin;hp represents waste heat to be upgraded, Whp represents the power consumed by the heat pump and Qout;hp represents total heat released by the heat pump condenser. Then the heat released ðQout;hp Þ and absorbed ðQin;hp Þ by the heat pump satisfy Eq. (3).
1 Qin;hp ¼ Qout;hp 1 COP
rl=s
(4)
When all the three pinches develop, pinch II and pinch I can be used to calculate the maximum organic working fluid flowrate. Referring to the notations in Fig. 8, the sensible heat of the working fluid ðRs;cliff Þ between the new cliff temperature ðTcliff Þ and evaporation temperature ðTeva;orc Þ can be calculated by Eq. (5).
Rs;cliff Teva;orc Teva;hp ¼ Rs Teva;orc Tcon;orc
(6)
From Eqs. (1)e(6), and eliminating the sensible heat of the working fluid ðRs;cliff Þ between the new cliff temperature ðTcliff Þ and evaporation temperature ðTeva;orc Þ, the waste heat to be upgraded ðQin;hp Þ can be calculated by Eq. (7).
h i FCpwh Teva;orc Tcon;orc Rl=s Tin;wh Teva;orc DTmin Qin;hp ¼ . Rl=s Teva;orc Tcon;orc Teva;orc Teva;hp þ½COP=ðCOP1Þ (7)
(3)
The ratio of latent heat to sensible heat ðrl=s Þ for the working fluid is a constant under specified evaporation and condensation temperatures as shown by Eq. (4), where Rl ; Rs ; Ql ; Qs denote molar latent heat, molar sensible heat, total latent heat and total sensible heat respectively.
R Q ¼ l ¼ l ¼ Constant Rs Qs
FCpwh Teva;orc þ DTmin Tcliff Rs;cliff ¼ Rl FCpwh Tin;wh Teva;orc DTmin þ Qout;hp
(5)
Then the power consumed by heat pump ðWhp Þ can be calculated by Eq. (8).
Whp ¼ ðCOP 1ÞQin;hp
(8)
The “cliff” temperature ðTcliff Þ can be obtained from Eq. (9).
. Tcliff ¼ Teva;hp þ DTmin þ Qin;hp FCpwh
(9)
The heat capacity flowrate of the organic working fluid ðFCporc Þ is determined by Pinch I and II and can be calculated by Eq. (10).
FCporc ¼
FCpwh Teva;orc þ DTmin Tcliff Teva;orc Teva;hp
(10)
The heat capacity flowrate of the organic working fluid ðFCporc Þ must be less than that of waste heat ðFCpwh Þ as indicated by Eq. (11), which is consistent with Fig. 8.
H. Yu et al. / Energy 160 (2018) 330e340
Teva;orc þ DTmin Tcliff FCporc ¼ Teva;orc Teva;hp FCpwh . Teva;orc Teva;hp Qin;hp FCpwh ¼ <1 Teva;orc Teva;hp
(11)
Then the total sensible heat of the organic working fluid ðQorc;s Þ can be calculated by Eq. (12).
Qorc;s ¼ FCporc Teva;orc Tcon;orc
(12)
The waste heat that cannot be recovered is the maximum waste heat load below the shifted ORC evaporation temperature ðTeva;orc þ DTmin Þ minus the sensible heat recovered by the organic working fluid ðQorc;s Þ, which is shown Eq. (13).
Qwh;unre ¼ FCpwh Teva;orc þ DTmin Tcliff þ Teva;hp þ DTmin Tout;wh;min Qorc;s (13) Then the outlet temperature of waste heat ðTout;wh Þ can be calculated by Eq. (14).
Tout;wh ¼ Tout;wh;min þ Qwh;unre FCpwh
(14)
The total recovered waste heat load ðQwh;re Þ is the sum of the maximum recoverable waste heat and the power consumed by the heat pump ðWhp Þ minus the unrecovered waste heat load ðQwh;unre Þ as shown in Eq. (15).
Qwh;re ¼ FCpwh Tin;wh Tout;wh;min þ Whp Qwh;unre
(15)
Then the power output of the ORC ðPorc Þ is given by Eq. (16).
Porc ¼ horc Qwh;re
(16)
The net power output ðPnet Þ of the system is given by Eq. (17)
Pnet ¼ Porc Whp
(17)
All the important parameters of the integrated system can be determined by the above equations with given evaporation temperature of the heat pump and the ORC. These equations guarantee that three pinch points develop simultaneously, which will result in the maximum net power output. The above equations only guarantee the optimal condition under fixed heat pump evaporation temperature. The evaporation temperature of the heat pump is a free variable. To find the optimal evaporation temperature of the heat pump, Eqs. (1)-(17) should be solved under various evaporation temperatures. With the mathematical model and integration procedure in Fig. 7, the optimal operating conditions of the integrated system can be determined.
The heat capacity flowrate of waste heat is assumed to be 100 kW/ C Minimum heat transfer approach temperature is assumed to be 10 C The isentropic efficiency of the compressor in the heat pump is assumed to be 85% The isentropic efficiencies of the turbine and the pump in the ORC are assumed to be 80% Pressure drop and heat loss is neglected In this case, the inlet temperature of the waste heat source is 150 C. Then the maximum available waste heat is 100*(15055) ¼ 9500 kW. Fig. 9 shows the variation of net power output and the amount of waste heat recovered with evaporation temperature for a standalone ORC. It is apparent that R236fa gives the largest power output of 805 kW. Thus, the optimum working fluid is R236fa and the optimal evaporation temperature is 120 C. With the increase of evaporation temperature, the amount of waste heat recovered decreases for all the working fluids except for R227ea and R236fa. There is no pinch limitation for R227ea due to its low critical temperature. Even though R227ea can recover the waste heat totally under all the evaporation temperatures, the low critical temperature limits the evaporation temperature and thermal efficiency. For R236fa, the amount of waste heat first decreases and then increases. The reason is that with the evaporation temperature approaching the critical temperature of R236fa, the latent heat of R236fa decreases drastically. Then the pinch limitation is alleviated. Much more waste heat can be recovered with the increase of evaporation temperature. Since both the thermal efficiency and the amount of waste heat recovered increase with the evaporation temperature, the net power output increases drastically near the critical point. The results indicate that the working fluid evaporating at near critical temperature has a small ratio of latent to sensible heat and can recover more waste heat. Fig. 10 shows the T-H diagram for a waste heat source and the organic working fluid R236fa under optimal operating conditions. The amount of waste heat recovered is 7987 kW, which takes up only 84% of the maximum available waste heat (9500 kW). In addition, the optimal evaporation temperature is only 120 C, which is limited by the critical temperature of R236fa. Due to the waste heat inlet temperature of 150 C, the evaporation temperature may be increased, so there is room for increasing the amount of waste recovered or the thermal efficiency of the ORC. Thus, it may be profitable to integrate a heat pump into the system. Based on the results shown in Fig. 6, n-hexane is selected as the working fluid in the heat pump. As discussed in Section 3.1, the working fluid in the ORC should be the one with the smallest ratio of latent to sensible heat. Table 3 lists the ratio of latent heat to sensible heat of several working fluids under specific evaporation temperatures. When the evaporation temperature is 130 C, R600a exhibits the smallest ratio of latent to sensible heat. When the evaporation temperature is 120 C, R236fa exhibits the smallest
4. Case study A case from a previous study [22] is adopted to illustrate how to optimally integrate a heat pump with an ORC with the proposed method in this study. The ORC and the heat pump are simulated in Aspen Plus [25] with Peng-Robinson equation of state. The thermodynamic properties of the working fluids are retrieved from Aspen Plus [25] as well. The following assumptions and parameters in the original study are adopted in this study. The condensation temperature of the ORC is assumed to be 45 C
337
Fig. 9. Net power output and waste heat recovered for standalone ORC.
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Fig. 10. TeH diagram of standalone ORC under optimal operating conditions.
Table 3 The ratio of latent to sensible heat of working fluids under various conditions. Working fluids
Evaporation temperature ( C)
Rl (kJ/kg)
Rs (kJ/kg)
Ratio rl=s
R236fa R600a R600a R236ea R236ea R600 R600 R245fa R245fa R601a R601a R601 R601
120 120 130 120 130 120 130 120 130 120 130 120 130
38.72 150.20 97.18 79.40 63.43 213.34 184.01 111.76 97.31 248.48 233.26 271.13 256.72
115.91 221.86 265.61 106.50 123.88 213.70 248.08 111.63 128.99 195.41 224.61 196.47 225.57
0.33 0.68 0.37 0.75 0.51 1.00 0.74 1.00 0.75 1.27 1.04 1.38 1.14
ratio of latent to sensible heat. The integration is first performed at high evaporation temperature (130 C).
Fig. 11. Integrated system performance as function of heat pump evaporation temperature with R600a as working fluid.
4.2. R236fa as the working fluid in the ORC As the critical temperature of R236fa is 124.92 C, the evaporation temperature is limited to 120 C. R236fa evaporating at 120 C exhibits the smallest ratio of latent to sensible heat among all the working fluids, which makes it the most promising working fluid candidate for ORC in the integrated system. Then the condensation temperature of the heat pump is 130 C in this case. Fig. 12 shows the variation of upgraded waste heat load, unrecovered waste heat load, heat load absorbed by the ORC, and waste heat outlet temperature with increasing heat pump evaporation temperature. Fig. 13 illustrates the variation of net power output, heat pump power consumption, and ORC power output with evaporation temperature of the heat pump. The integration of the heat pump improves the net power output of the system. When the evaporation temperature of the heat pump is 45 C, the COP of the heat pump is 2.65. Based on Eqs. (1)e(3), the amount of waste heat to be upgraded is 280 kW, the power consumed is 169 kW, and the total available heat load is 9669 kW. The thermal efficiency of an ORC with R236fa evaporating at 120 C is about 10.07%, hence the net power output is about 805 kW, which is the same as that of the
4.1. R600a as the working fluid in the ORC When the evaporation temperature is set as 130 C, the condensation temperature of the heat pump is 140 C accordingly. Since R600a exhibits the smallest ratio of latent to sensible heat among all the working fluids, R600a is chosen as the working fluid in the ORC. It should be noted that higher evaporation temperature in the ORC indicates higher condensation temperature of the heat pump, which means lower COP of the heat pump and more power consumption. Fig. 11 shows the net power output of the integrated system under various evaporation temperatures of the heat pump. The horizontal dashed line indicates the maximum power output (805 kW) of a standalone ORC recovering waste heat. It is obvious that the net power output is less than the original standalone ORC. Thus, it is not profitable to integrate a heat pump into the system with the ORC evaporation temperature being 130 C. As R600a is the most promising working fluid for evaporation temperature 130 C, other working fluids with larger ratio of latent to sensible heat will perform worse. When the evaporation temperature is 98 C, the amount of heat recovered is 8050 kW, which is not satisfactory. According to the procedure in Fig. 7, the evaporation temperature should be decreased next.
Fig. 12. Key parameters as function of heat pump evaporation temperature.
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Fig. 13. Integrated system performance as function of heat pump evaporation temperature with R236fa as working fluid.
original standalone ORC. Thus, it is not profitable to integrate the heat pump at the evaporation temperature of 45 C. The reason is that the COP is too low to justify the integration of a heat pump for this evaporation temperature. With increasing evaporation temperature for the heat pump, the COP of the heat pump increases, and the amount of waste heat to be upgraded first increases and then decreases. Both the power consumed by the heat pump and the power output from the ORC decrease. When the evaporation temperature of the heat pump is 90 C, the net power output reaches a maximum of 880.5 kW. The heat pump upgrades the waste heat between 100 C and 102.52 Ce130 C consuming 42.2 kW of power. The COP of the heat pump is 6.97 at this point. Then the total available heat load is 9542.2 kW and the amount of heat recovered by the ORC is 9164 kW, which takes up 96.04% of the total available heat load. The final outlet temperature of the waste heat source is 58.78 C. For the standalone ORC, only 7897 kW waste heat is recovered and the outlet temperature of the waste heat is 70 C. At the expense of 42.2 kW power consumption, the amount of waste heat is increased by 12.04%, and the power output is increased by 9.37%. Fig. 14 illustrates the optimal T-H diagram of the integrated system. Compared with the T-H diagram of the stand-alone ORC system in Fig. 10, the waste heat matches much better with the working fluid after the heat pump is integrated. The waste heat recovery is satisfactory, and then the integration of a heat pump and an ORC is profitable for this case. If the integration at 120 C is not profitable, it is not necessary to continue decreasing the evaporation temperature of the ORC. Since the waste heat recovery is already 96.04%, the thermal match between the working fluid and the waste heat is satisfactory. Based on the analysis of the results in the study, it is noticeable that the minimum ratio of R600a and R236fa are quite similar, but the evaporation temperature is different. The reason is that if the evaporation temperature of the ORC is set too high (for example 130 C for R600a), the COP of the heat pump is lower, and the amount of waste heat above the ORC evaporation temperature is small, thus more waste heat needs to be upgraded by the heat pump to get a better thermal match. These factors result in more power consumption by the heat pump through the comparison of Figs. 11 and 13. When the evaporation temperature is set appropriately and there is a working fluid with small ratio of latent to sensible heat, the integration is profitable. Therefore, whether it is profitable to integrate a heat pump relies on the evaporation temperature of the ORC, the ratio of latent to
339
Fig. 14. TeH diagram of integrated system under optimal operating conditions.
sensible heat of the ORC working fluid, and the COP of the heat pump. The integration is profitable only when the following preconditions are satisfied simultaneously: (a) poor thermal match between working fluid and waste heat for standalone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. Therefore, the evaporation temperature of the ORC working fluid, the waste heat inlet temperature, and the COP of the heat pump jointly determine the performance of the integrated system. 5. Conclusion This study presents a methodology to integrate a heat pump with an ORC to improve the net power output of the system. Integrating a heat pump into the system does not always result in an increase of net power output. When the critical temperature of the working fluid is lower than the inlet temperature of the waste heat source and the ratio of latent to sensible heat is small, then the integration is probably profitable. If the COP of the heat pump is improved, the likelihood to profitably integrate the heat pump will be larger. A systematic method to determine the working fluid in both the ORC and the heat pump, as well as the optimal operating conditions of the integrated system is presented. The case study shows that the net power output and the amount of waste heat recovered are increased by 9.37% and 12.04% respectively. The integration is profitable only when the following pre-conditions are satisfied simultaneously: (a) poor thermal match between the working fluid and the waste heat for stand-alone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. Even though the integration of a heat pump is energy profitable in some special cases, detailed techno-economic analysis should be performed to decide whether it is economically profitable to implement in practice. Several topics are suggested for future work. First, techno-economic analysis of the integrated system should be performed. Although the integration of a heat pump can boost the power output in the case study, the feasibility of the process should be verified from techno-economic analysis. Also, a working fluid in the heat pump with higher COP will enhance the performance of the integrated system. The working fluid in the heat pump is also an
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important impetus for successful implementation of the proposed integrated system. Other cycles with modifications to increase the COP of the heat pump cycle such as closed compression cycles with economizer, cascade configuration, and mechanical vapor recompression are also promising alternatives to enhance the system performance.
[2]
[3]
[4]
Acknowledgement This publication has been funded by HighEFF e Centre for an Energy Efficient and Competitive Industry for the Future. The authors gratefully acknowledge the financial support from the Research Council of Norway and user partners of HighEFF, an 8 year Research Centre under the FME-scheme (Centre for Environmentfriendly Energy Research, 257632/E20). Thanks to Ph.D. candidate John Eason at Carnegie Mellon University for his kind help with a meaningful discussion and suggestions.
[5] [6]
[7]
[8]
[9]
Nomenclature [10]
COP FCp H ORC ODP P Q r R S T W
h
coefficient of performance heat capacity flowrate enthalpy organic Rankine cycle ozone depletion potential power output and pressure heat load ratio heat content entropy temperature electricity consumption thermal efficiency
Subscript c cliff con eva hp in l max min orc out re s unre wh
critical cliff formed in the T-H diagram condensation/condenser evaporation/evaporator heat pump Inlet/absorbed heat latent maximum minimum organic Rankine cycle outlet/released heat recovered sensible unrecovered waste heat
[11]
[12]
[13] [14] [15] [16]
[17]
[18]
[19]
[20]
[21]
[22]
[23] [24] [25]
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conversion into power using organic Rankine cycleseA review of various applications. Renew Sustain Energy Rev 2011;15(8):3963e79. Meinel D, Wieland C, Spliethoff H. Effect and comparison of different working fluids on a two-stage organic rankine cycle (ORC) concept. Appl Therm Eng 2014;63(1):246e53. He C, Liu C, Gao H, Xu X, Xie H. Parameters optimization and performance analysis of organic rankine cycle for industrial waste heat recovery. J Eng Thermophys 2012;33(12):2042e6. Yu H, Feng X, Wang Y, Biegler LT, Eason J. A systematic method to customize an efficient organic Rankine cycle (ORC) to recover waste heat in refineries. Appl Energy 2016;179:302e15. Desai NB, Bandyopadhyay S. Process integration of organic Rankine cycle. Energy 2009;34(10):1674e86. He S, Chang H, Zhang X, Shu S, Duan C. Working fluid selection for an Organic Rankine Cycle utilizing high and low temperature energy of an LNG engine. Appl Therm Eng 2015;90:579e89. Li Y-R, Wang J-N, Du M-T. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy 2012;42(1):503e9. Yu H, Eason J, Biegler LT, Feng X. Simultaneous heat integration and technoeconomic optimization of Organic Rankine Cycle (ORC) for multiple waste heat stream recovery. Energy 2017;119:322e33. Yu H, Feng X, Wang Y. A new pinch based method for simultaneous selection of working fluid and operating conditions in an ORC (Organic Rankine Cycle) recovering waste heat. Energy 2015;90:36e46. Chen C-L, Chang F-Y, Chao T-H, Chen H-C, Lee J-Y. Heat-exchanger network synthesis involving organic rankine cycle for waste heat recovery. Ind Eng Chem Res 2014;53(44):16924e36. Yu H, Eason J, Biegler LT, Feng X. Process integration and superstructure optimization of Organic Rankine Cycles (ORCs) with heat exchanger network synthesis. Comput Chem Eng 2017;107:14. Townsend DW, Linnhoff B. Heat and power networks in process design, Part I: criteria for placement of heat engines and heat pumps in process networks. AIChE J 1983;29(5):742e8. Fu C, Gundersen T. Recuperative vapor recompression heat pumps in cryogenic air separation processes. Energy 2013;59:708e18. Fu C, Gundersen T. A novel sensible heat pump scheme for industrial heat recovery. Ind Eng Chem Res 2016;55(4):967e77. Angelino G, Invernizzi C. Prospects for real-gas reversed Brayton cycle heat pumps. Int J Refrig 1995;18(4):272e80. Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manag 2009;50(3):576e82. He C, Liu C, Gao H, Xie H, Li Y, Wu S, et al. The optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Energy 2012;38(1):136e43. Chen H, Goswami DY, Rahman MM, Stefanakos EK. A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power. Energy 2011;36(1):549e55. lı H, Koç Y, Koç A, Go €rgülü A, Tandirog lu A. Parametric optimization and Yag exergetic analysis comparison of subcritical and supercritical organic Rankine cycle (ORC) for biogas fuelled combined heat and power (CHP) engine exhaust gas waste heat. Energy 2016;111:923e32. 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(9):3059e67. Wang E, Zhang H, Fan B, Ouyang M, Zhao Y, Mu Q. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36(5):3406e18. Yu H, Feng X, Wang Y. Working fluid selection for organic Rankine cycle (ORC) considering the characteristics of waste heat sources. Ind Eng Chem Res 2016;55(5):1309e21. Rayegan R, Tao YX. A procedure to select working fluids for Solar Organic Rankine Cycles (ORCs). Renew Energy 2011;36(2):659e70. Xu J, Yu C. Critical temperature criterion for selection of working fluids for subcritical pressure Organic Rankine cycles. Energy 2014;74(0):719e33. Aspen plus V8.8. United States: Aspen Technology Incorporation; 2015.
Contents lists available at ScienceDirect
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Process integration of organic Rankine cycle (ORC) and heat pump for low temperature waste heat recovery Haoshui Yu a, Truls Gundersen a, Xiao Feng b, * a b
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjoern Hejes v. 1A, NO-7491 Trondheim, Norway School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2017 Received in revised form 15 May 2018 Accepted 8 July 2018 Available online 11 July 2018
Organic Rankine cycles (ORCs) have been a mature technology for low temperature waste heat utilization. However, the relatively low thermal efficiency and incomplete waste heat recovery limit the power output of ORC systems. The reason for the above two problems is that the temperature-enthalpy (T-H) profile of waste heat sources does not match well with the organic working fluid in an ORC system. Heat pumps may reinforce the match between the waste heat carrier and the organic working fluid of the ORC. The condensation heat released by a heat pump can be used to evaporate the organic working fluid during phase change. Thus, a better thermal match between waste heat and the organic working fluid in the ORC can be obtained. Due to the possibility to improve power output, the integration of an ORC and a heat pump is investigated in this study. Proper working fluids in ORCs and heat pumps are chosen simultaneously. The integration between ORCs and heat pumps presents significant power output increases for special cases and deserves to be popularized in practical applications. However, the integrated system does not always lead to an increase in power output. The integration is profitable only when the following pre-conditions are satisfied simultaneously: (a) poor thermal match between working fluid and waste heat for standalone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. A systematic procedure to determine the optimal operating conditions of the system is proposed in this study. A case study adopted from literature demonstrates the potential benefits of the integration of heat pumps and ORCs. The results show that the net power output and the amount of waste heat recovered increase by 9.37% and 12.04% respectively. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Heat pump Process integration Low temperature waste heat Thermal match
1. Introduction Organic Rankine cycles have received widespread attention since the 1970s. ORCs represent a promising way to convert low to medium temperature heat into power [1]. The choice of working fluid [2], operating conditions [3] and the integration of an ORC with the background process [4] exert great influence on the net power output of ORC systems. Organic Rankine cycle modifications, such as recuperation and turbine bleeding [5], can improve the thermal efficiency of the ORC system. Working fluid selection [6] and operating condition determination [7] affect both thermal efficiency and the amount of waste heat recovered. Applying optimization methods to process integration can explore the trade-offs
* Corresponding author. E-mail address: [email protected] (X. Feng). https://doi.org/10.1016/j.energy.2018.07.028 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
between thermal efficiency, amount of waste heat recovered and economic factors [8]. Yu et al. [9] proposed a new method for simultaneous working fluid selection and determination of operating conditions. This method is based on a newly defined parameter to locate the pinch point. Chen et al. [10] proposed a new method based on mathematical programming to simultaneously optimize the ORC and synthesize the heat exchanger network. Yu et al. [11] proposed a superstructure to integrate an ORC into a background process considering turbine bleeding, superheating and regeneration. However, all of these studies aim at improving the power output of a standalone ORC. If a heat pump is integrated with the ORC, it is possible to increase the overall net power output of the integrated system. According to pinch analysis, heat pumps should be placed across the pinch point in a system [12]. This concept has been applied to distillation processes successfully with substantial energy savings [13]. Heat pumps can be classified into closed and open heat pumps
H. Yu et al. / Energy 160 (2018) 330e340
respectively according to whether the process stream and the working fluid are the same [14]. From a thermodynamic point of view, heat pumps can also be classified into reversed Rankine cycles and Brayton cycles [15]. Reversed Brayton cycle heat pumps operate in vapor phase without phase change, thus this kind of heat pump is also called a sensible heat pump. For a reversed Rankine cycle heat pump, isothermal phase change takes place in the condenser. This isothermal condensation heat can match perfectly with the evaporation process of an ORC. Therefore, integration of closed reversed Rankine cycle heat pumps with an ORC for low temperature waste heat utilization is investigated in this study. At first sight, it seems unreasonable to upgrade waste heat consuming power by a heat pump, and then to generate power by an ORC from the perspective of thermodynamics. However, the involvement of a heat pump may result in better thermal match between the waste heat source and the organic working fluid in some cases. As long as the power increase of an ORC overweighs the power consumed by the heat pump, the integration of the heat pump and the ORC is profitable. In organic Rankine cycles with pure working fluids, the isothermal phase transition will cause a pinch point between the working fluid and the heat source [9]. This pinch point limits the amount of waste heat recovered by an ORC system. The pinch point limitation is caused by the improper ratio of latent to sensible heat of the working fluid, which is dependent on the thermodynamic properties of the working fluid. Therefore, attention should be paid to changing the profile of the waste heat with the help of a heat pump to enhance the thermal match between the waste heat source and the working fluid. A thorough literature search did not identify any papers on the integration of heat pumps with ORCs to increase the net power output of the whole system recovering waste heat. In some specific cases, the integration of a heat pump and an ORC has the potential to increase the net power output of the whole system. This study focuses on integrating an ORC and a heat pump into one system, where the heat pump upgrades part of the waste heat to drive an ORC with increased power production at the cost of power consumption in the heat pump, in order to increase the overall net power output of the system. 2. Motivation and theory There are generally two ways to increase the net power output from an ORC, namely increasing thermal efficiency and increasing the amount of waste heat recovered by the organic working fluid.
331
Working fluid selection and ORC modifications aim at increasing the thermal efficiency [16]. The operating conditions also exert a great influence on the thermal efficiency. The optimal operating conditions can be determined from the trade-off between thermal efficiency and the amount of waste heat recovered [17]. However, the effect that thermal efficiency and amount of waste heat recovered have on the net power output depends on the character of waste heat. The waste heat can be classified into two categories according to the target temperature of waste heat as shown in Fig. 1. Nonconstrained waste heat refers to the waste heat whose target temperature is not constrained, and the target temperature can be as low as ambient temperature. Constrained waste heat refers to the waste heat whose target temperature is much higher than the ambient temperature and the target temperature has to meet some specifications. For example, the target temperature of flue gas cannot be lower than the acid dew point to avoid corrosion. The working fluid selection criteria are different for the two kinds of waste heat sources. For non-constrained heat sources, it is obvious that different operating conditions or working fluids exhibit large difference in the amount of waste heat recovered. The net power output depends on both thermal efficiency and the amount of waste heat recovered. However, the amount of waste heat recovered exerts much greater influence on the net power output. Yu et al. [9] proposed a parameter PREDICTOR to determine the pinch point and calculate the amount of waste heat recovered. They found that for non-constrained waste heat recovery, the amount of waste heat is more sensitive to the variation of operating conditions compared with thermal efficiency. Therefore, the amount of waste heat recovered is the primal factor to be considered. For constrained waste heat sources, the waste heat can be recovered totally to heat the working fluid in the ORC as shown in Fig. 1(b). There is no difference in the amount of waste heat recovered for different working fluids or different operating conditions. The net power output only depends on thermal efficiency. Therefore, thermal efficiency is the criteria for working fluid selection. Since the constrained waste heat can be totally recovered, it is not necessary to integrate a heat pump to increase the waste heat recovery. Hence, this study only investigates non-constrained waste heat sources. For non-constrained waste heat recovery, an important limitation of an ORC with pure component working fluid is the isothermal boiling process, which creates pinch points and leads to poor thermal match between the working fluid and waste heat [18]. The “pinch limitation” problem in organic Rankine cycles is
T
T Pinch limitation
Pinch limitation
high evaporating temperature
Optimal design
high evaporating temperature
medium evaporating temperature Tmin=55 Tcon=45
Qre
medium evaporating temperature
low evaporating temperature Tcon=45 Qre
Qre Qmax
(a) Non-constrained waste heat
low evaporating temperature
H
Qmax
(b) Constrained waste heat
Fig. 1. Waste heat classification and pinch limitation for non-constrained waste heat.
H
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supposed to be eliminated or alleviated to improve the net power output. If the evaporation temperature is close to the critical temperature of the working fluid, the evaporation latent heat is very small, which may alleviate the pinch limitation [9]. In the limiting case, as the evaporation temperature approaches the critical temperature, the latent heat approaches zero and the isothermal phase change of the working fluid disappears. Then the working fluid line becomes an oblique line instead of a polygonal line. The “pinch limitation” is eliminated and waste heat can be recovered totally to heat the working fluid in the ORC. On the other hand, some researchers have proposed to use supercritical ORCs to avoid the pinch limitation and the results show that supercritical ORCs perform better than subcritical ORCs [19]. However, due to operational issues, safety concern and investment cost, supercritical ORCs have not yet been implemented in practice [20]. Subcritical ORCs still have predominance in practical applications. To guarantee stable operation, the evaporation temperature should not be very close to the critical temperature; therefore, the “pinch limitation” problem is a critical problem engineers have to face. Fig. 1(a) illustrates the “pinch limitation” on the T-H diagram of
an ORC system for non-constrained waste heat recovery. In this study, the working fluid in the ORC is assumed to be cooled down to 45 C by cooling water in the condenser. Therefore, the minimum waste heat outlet temperature is 55 C assuming the minimum approach temperature is 10 C. The purple line in Fig. 1(a) demonstrates a working fluid evaporating at low temperature. There is no pinch limitation and all of the waste heat can be recovered, but the thermal efficiency is very low and the power output may be not satisfactory. When the evaporation temperature is high, as shown by the green line in Fig. 1(a), the thermal efficiency is high, but the pinch point severely limits heat recovery. The power output is restricted by pinch limitation in this case. To trade-off thermal efficiency and the amount of waste heat recovered, optimal operating conditions can be determined as the blue line indicated in Fig. 1(a). Under optimal operating conditions, the thermal efficiency is less than the green line and greater than the purple line, and the amount of waste heat recovered is less than the purple line and greater than the green line. The pinch limitation for the blue line is worse than the purple line, but better than the green line. The thermal efficiency and amount of waste heat recovered are both moderate under the optimal condition, but this often provides maximum power output. It is noticeable that under the optimal condition, the waste heat is not totally recovered. Therefore, it is possible to increase the power output if the amount of waste heat recovered can be further improved. If a heat pump is introduced, the profile of waste heat can be changed and the amount of waste heat recovered may be improved. Fig. 2 shows the T-S diagram of an ORC and reversed Rankine cycle heat pump. The condensation heat from the heat pump can be used to heat the organic working fluid during phase change attaining good thermal match between isothermal phase transitions in the heat pump and the ORC. Fig. 3 illustrates the flowsheet of the integrated system. Waste heat is recovered and utilized in two ways, namely one part is used to heat the organic working fluid in the ORC system, and the other part is upgraded by the heat pump first and released to the organic working fluid of the ORC at a higher temperature. Fig. 4 illustrates the T-H diagram of the integrated system. The red line, green line and blue line denote waste heat, working fluid in the heat pump and working fluid in the ORC respectively. The yellow shaded area indicates the evaporator of the heat pump. The choice of working fluids for both the ORC and the heat pump are very important decisions. The corresponding operating conditions
T
III Heat Pump
IV 4
3 I
5
1
II
6 Organic Rankine Cycle
s Fig. 2. TeS diagram of ORC and heat pump.
III 5
4
Turbine
Evaporator II
Valve
3
IV
Evaporator
Condensor
Compressor
Condensor
2
Evaporator
Pump 2
I
Waste heat Fig. 3. The layout of the integrated system.
6
1
H. Yu et al. / Energy 160 (2018) 330e340
T
333
Upgraded by heat pump and released to ORC at higher temperature +w
Temperature range of upgraded waste heat Pinch limitations
Teva,hp Tmin=55 Tcon=45
Qre,integrated H Qmax+W Fig. 4. TeH diagram of the integrated system.
should be determined appropriately as well. Without considering capital investment, the integration of a heat pump is beneficial as long as the increase of power output from the ORC overweighs the power consumed by the heat pump. While integrating a heat pump with an ORC, the following challenges should be addressed: (1) When is it worthwhile to integrate a heat pump with an ORC? (2) If a heat pump is to be included, which part of the waste heat should be upgraded by the heat pump? (3) What working fluids should be selected for the ORC and the heat pump respectively? (4) What are the optimal operating conditions of the ORC and the heat pump? This paper aims at answering the above questions based on a proposed systematic procedure. 3. Methodology To integrate a heat pump into the system, one should first check whether there is potential to increase the power output of the ORC. If an ORC can recover nearly all of the waste heat and the evaporation temperature is high enough, the potential to further increase the power output through the integration of a heat pump is limited. On the contrary, if a large portion of waste heat is not recovered, as shown by the blue line in Fig. 1(a), the integration of a heat pump may increase the net power output. As the choice of working fluid exerts great influence on the performance of heat pumps and ORCs, working fluids for both cycles should be determined with care. If there are very good working fluids, the integration may be more profitable. However, the criteria for working fluid selection for an ORC and a heat pump are different in this study and will be discussed in Section 3.1 and 3.2 respectively. After working fluids are determined for both ORC and heat pump, the optimal operating conditions can be determined by the mathematical model discussed in Section 3.3.
environmental concerns [21]. For a sensible waste heat source, a working fluid whose critical temperature is slightly lower than the inlet temperature of the waste heat source performs well due to a less serious pinch limitation [22]. For standalone ORCs, the optimum working fluid and corresponding operating conditions can be determined using the procedures proposed by Rayegan and Tao [23] or a method based on critical temperatures [24]. Thermal efficiency of the working fluid is related to the critical temperature, but the difference between the working fluids is marginal under the same evaporation temperature as shown in Fig. 5, especially in the low temperature range. For non-constrained waste heat, the working fluid with the maximum net power output is generally the one that can recover more waste heat. If heat pump integration is considered, the optimum working fluid in an ORC may change. The purpose of integrating a heat pump into this system is to get a better thermal match between the waste heat source and the working fluid. As discussed earlier, for the non-
3.1. Working fluid selection for organic Rankine cycle (ORC) Working fluid selection for ORCs relies on the temperature of waste heat, type of waste heat (latent, sensible or combined), and practical considerations such as operability, safety and
Fig. 5. Thermal efficiency vs. evaporation temperature for all the pre-selected working fluids with condensation temperature 45 C.
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constrained waste heat recovery, the thermal efficiency has weaker influence on the power output compared with the amount of waste heat recovered, which is related to the ability of the working fluid to recover waste heat. The ratio of latent to sensible heat reflects the ability of the working fluid to recover waste heat. In addition, the smaller the ratio of latent to sensible heat of the working fluid is in an ORC, the less heat needs to be upgraded by the heat pump to get better thermal match of the system. This means that the amount of waste heat recovered can be increased to the same extent with less power consumption by the heat pump. The optimal working fluid for the integrated ORC system is the working fluid with the smallest ratio of latent to sensible heat. For the same working fluid, the ratio of latent to sensible heat is different under different evaporation temperatures. The higher the evaporation temperature, the smaller the ratio of latent to sensible heat. Therefore, the ratio of latent to sensible heat is a performance indicator considering both the working fluid properties and the operating conditions. The integration of a heat pump is worthwhile when the ratio of latent to sensible heat is small. The working fluid with the minimum ratio of latent to sensible heat is the most promising candidate for an ORC. It should be noted that the ratio of latent to sensible heat of the working fluid is a function of condensation temperature and evaporation temperature of the ORC. In this study, the condensation temperature of the ORC is assumed to be 45 C, then the ratio of latent to sensible heat only relies on the evaporation temperature. The preselected working fluids for ORC in this study are listed in Table 1.
3.2. Working fluid selection for heat pump As for the working fluid selection for a heat pump, there are two main concerns, namely the operability of the system and the coefficient of performance (COP). Operability means that the condensation temperature of the heat pump should be higher than the evaporation temperature of the ORC as shown in Fig. 2. Therefore, the critical temperature of working fluids in heat pumps cannot be lower than the evaporation temperature of the ORC to ensure the operability of the system. Several working fluid candidates for heat pumps whose critical temperatures are higher than 130 C are considered in this study as shown in Table 2. The second concern is the COP. Unlike ORCs, the evaporation process of the heat pump is a purely isothermal process, thus no “pinch limitation” takes place in the evaporator. The condensation heat of a heat pump can be totally transferred to the working fluid in the ORC without pinch limitation as well. Then only the thermal efficiency matters, thus COP is the working fluid selection criteria for the heat pump. For working fluid selection in the ORC, the ratio of latent to sensible heat is chosen as the criteria for the working fluid since less waste heat needs to be upgraded to get a better thermal match. For the integrated system proposed in this study, COP is extremely important in determining whether it is worthwhile to integrate a heat pump with an ORC.
Table 2 Pre-selected working fluids for heat pumps. Working fluids
Chemical formula
Tc ( C)
Pc（bar）
ODP
Type
R600a R236ea R600 R245fa R123 R601 n-hexane
C4H10-2 C3H2F6 C4H10-1 C3H3F5-D1 C2HCL2F3-D1 C5H12-1 C6H14-1
134.65 139.23 151.97 154.05 183.79 196.55 234.45
36.40 34.12 37.96 36.40 36.76 33.70 30.25
0.0 0.0 0.0 0.0 0.02 0.0 0.0
Dry Dry Dry Isentropic Dry Dry e
A heat pump operated under various evaporation temperatures with constant condensation temperature (130 C) is simulated in Aspen Plus [25]. The isentropic efficiency of the compressor is assumed to be 85%. Fig. 6 illustrates the variation of the COP with the evaporation temperature. It is clear that n-hexane has the largest COP among all the pre-selected working fluids. Even though the results are based on a fixed condensation temperature, the trend is the same under other operating conditions. Therefore, nhexane is chosen as the working fluid in the heat pump in this study.
3.3. The determination of operating conditions for the integrated system The procedure to determine the operating conditions of the combined ORC and heat pump system is presented in this section and is shown in Fig. 7. First, set the evaporation temperature of the ORC. The evaporation temperature may be constrained by the waste heat inlet temperature or the critical temperature of the working fluid for a subcritical ORC. To guarantee an acceptable thermal efficiency of the ORC, the evaporation temperature is set high at first. The higher the evaporation temperature, the smaller the latent heat of the working fluid in the ORC, the smaller the ratio of latent to sensible heat, and the more chances of profitable integration of a heat pump. Once the evaporation temperature is determined, the corresponding heat pump condensation temperature can be determined. It is clear that the condensation temperature of the heat pump should be DTmin higher than the evaporation temperature of the ORC in order to minimize the power consumption by the heat
Table 1 Pre-selected working fluids for ORC. Working fluids
Chemical formula
Tc ( C)
Pc（bar）
ODP
Type
R227ea R236fa R600a R236ea R600 R245fa R601a R601
C3HF7 C3H2F6-D1 C4H10-2 C3H2F6 C4H10-1 C3H3F5-D1 C5H12-2 C5H12-1
101.68 124.92 134.65 139.23 151.97 154.05 187.25 196.55
29.12 32.19 36.40 34.12 37.96 36.40 33.80 33.70
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Dry Dry Dry Dry Dry Isentropic Dry Dry
Fig. 6. COP of various working fluids with fixed condensation temperature (130 C).
H. Yu et al. / Energy 160 (2018) 330e340
Set ORC evaporation temperature and heat pump condensation temperature
Determine the working fluid in the ORC and the heat pump
Apply Eqs. (1)-(17) to various heat pump evaporation temperatures Decrease the evaporation temperature Obtain the optimal heat pump evaporation temperature and the corresponding operating conditons
Is waste heat recovery satisfactory?
No
Yes
Is net power output increased?
No
Not profitable to integrate heat pump
Yes Profitable integration
Fig. 7. Procedure for integrating heat pump with ORC.
pump. Second, according to the evaporation temperature of the ORC, the working fluid with the smallest ratio of latent to sensible heat is chosen as the working fluid in the ORC and the working fluid for the heat pump is n-hexane due to its highest COP. Once the working fluids are determined, the mathematical model is applied to various heat pump evaporation temperatures. The mathematical model will be discussed later. Afterwards, the optimal heat pump evaporation temperature can be determined. If the waste heat recovery is satisfactory, the integration procedure will terminate. If the power output is increased, then it is profitable to integrate a heat pump with the ORC. If the waste heat recovery is not satisfactory, the evaporation temperature of the ORC should be decreased. It is noticeable that some working fluids cannot evaporate at very high temperature due to the critical temperature limitation. Therefore,
335
with decreasing evaporation temperature, other working fluids with smaller ratio of latent to sensible heat will become the new working fluids in the ORC. Under a specific ORC evaporation temperature, the greatest challenge is to determine the evaporation temperature of heat pump. The evaporation temperature of the heat pump not only affects the COP as shown in Fig. 6, but also determines which part of the waste heat should be upgraded. The waste heat absorbed by the ORC is also related to the evaporation temperature of the heat pump. When the evaporation temperature of the heat pump is 45 C, waste heat above 55 C can be upgraded. The waste heat can be recovered totally by the ORC if the heat pump load is large enough. This is not worthwhile in most cases since the evaporation temperature of the heat pump is too low to justify the integration of a heat pump. Fig. 8 shows the detailed notation of the parameters in the integrated system, which will be used in the mathematical equations later. The waste heat above the heat pump evaporation temperature plus minimum temperature approach ðTeva;hp þ DTmin Þ can be upgraded by the heat pump. Then a “cliff” ðTcliff Þ is formed in the waste heat curve as shown in Fig. 8. As part of the waste heat is upgraded by the heat pump, the cliff will become a new potential pinch limitation. Then how much waste heat should be upgraded? When three pinches develop simultaneously as shown in Fig. 8, the amount of waste heat to be upgraded under the specified evaporation temperature reaches an optimum. The reason is that if more waste heat is upgraded, pinch point I will not exist, in essence more waste heat is upgraded than necessary. Pinch point II limits the amount of waste heat recovered under this circumstance. When the amount of waste heat upgraded is less, Pinch point II will not develop, and Pinch point I limits the amount of waste heat recovered. As the main purpose of integration with a heat pump is to increase the total amount of waste heat recovered, the function of increasing the amount of waste heat recovered is limited under this circumstance. As long as the integration of the heat pump can increase both the waste heat recovered and net power output, it is supposed to increase the amount of waste heat upgraded until three pinch points develop simultaneously. With three pinch points, the potential of increased power output reaches the limit if the integration is profitable. Therefore, under specified evaporation temperature, the optimal amount of waste heat to be upgraded can be calculated, determining Tcliff (namely the waste heat temperature at the inlet of the heat pump evaporator) as shown in Fig. 8. Then the corresponding operating conditions can be determined. The above circumstance only guarantees the optimal amount of waste heat to be upgraded under a specific evaporation temperature. To get the final optimal operating conditions, a heat pump at various evaporation temperatures should be integrated. The heat pump changes the ratio of latent to sensible heat of the waste heat source to get a better match between the waste heat source and the working fluid in the ORC. Theoretically, one should try other ORC evaporation temperatures and determine the corresponding optimal evaporation temperatures of the heat pump and the optimal amount of waste heat upgraded using the above procedure. However, as shown in the case study, only when the evaporation temperature exhibits small ratio of latent to sensible heat, the integration of a heat pump is profitable. Once the waste heat recovery is satisfactory, namely waste heat is totally or near totally recovered, the integration procedure terminates as shown in Fig. 7. Through the proposed method, the optimal design of the integrated system can be obtained. The mathematical model to determine the optimal operating conditions under specified evaporation temperature of the heat pump is presented in the following. The COP of a heat pump is the ratio of heat released in the condenser ðQout;hp Þ to the power consumed ðWÞ as defined by Eq.
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H. Yu et al. / Energy 160 (2018) 330e340
T
Tin,wh
Upgraded by heat pump and released to the ORC at higher temperature
Teva,orc+ Tmin +W
Qout,hp
Teva,orc Tcliff
I
III
Teva,hp+ Tmin Teva,hp Tout,wh
Pinch limitations II
Tout,wh,min=55 Qin,hp Tcon,orc=45
Qsensible
Qlatent Qre,integrated H
Qmax+W Fig. 8. TeH diagram of the integrated system with detailed notation.
(1).
COP ¼
Qout;hp Whp
When pinch I and pinch II occur simultaneously, the optimal new cliff temperature ðTcliff Þ should satisfy Eq. (6)
(1)
Eq. (2) is the energy balance for the heat pump system.
Qin;hp þ Whp ¼ Qout;hp
(2)
where Qin;hp represents waste heat to be upgraded, Whp represents the power consumed by the heat pump and Qout;hp represents total heat released by the heat pump condenser. Then the heat released ðQout;hp Þ and absorbed ðQin;hp Þ by the heat pump satisfy Eq. (3).
1 Qin;hp ¼ Qout;hp 1 COP
rl=s
(4)
When all the three pinches develop, pinch II and pinch I can be used to calculate the maximum organic working fluid flowrate. Referring to the notations in Fig. 8, the sensible heat of the working fluid ðRs;cliff Þ between the new cliff temperature ðTcliff Þ and evaporation temperature ðTeva;orc Þ can be calculated by Eq. (5).
Rs;cliff Teva;orc Teva;hp ¼ Rs Teva;orc Tcon;orc
(6)
From Eqs. (1)e(6), and eliminating the sensible heat of the working fluid ðRs;cliff Þ between the new cliff temperature ðTcliff Þ and evaporation temperature ðTeva;orc Þ, the waste heat to be upgraded ðQin;hp Þ can be calculated by Eq. (7).
h i FCpwh Teva;orc Tcon;orc Rl=s Tin;wh Teva;orc DTmin Qin;hp ¼ . Rl=s Teva;orc Tcon;orc Teva;orc Teva;hp þ½COP=ðCOP1Þ (7)
(3)
The ratio of latent heat to sensible heat ðrl=s Þ for the working fluid is a constant under specified evaporation and condensation temperatures as shown by Eq. (4), where Rl ; Rs ; Ql ; Qs denote molar latent heat, molar sensible heat, total latent heat and total sensible heat respectively.
R Q ¼ l ¼ l ¼ Constant Rs Qs
FCpwh Teva;orc þ DTmin Tcliff Rs;cliff ¼ Rl FCpwh Tin;wh Teva;orc DTmin þ Qout;hp
(5)
Then the power consumed by heat pump ðWhp Þ can be calculated by Eq. (8).
Whp ¼ ðCOP 1ÞQin;hp
(8)
The “cliff” temperature ðTcliff Þ can be obtained from Eq. (9).
. Tcliff ¼ Teva;hp þ DTmin þ Qin;hp FCpwh
(9)
The heat capacity flowrate of the organic working fluid ðFCporc Þ is determined by Pinch I and II and can be calculated by Eq. (10).
FCporc ¼
FCpwh Teva;orc þ DTmin Tcliff Teva;orc Teva;hp
(10)
The heat capacity flowrate of the organic working fluid ðFCporc Þ must be less than that of waste heat ðFCpwh Þ as indicated by Eq. (11), which is consistent with Fig. 8.
H. Yu et al. / Energy 160 (2018) 330e340
Teva;orc þ DTmin Tcliff FCporc ¼ Teva;orc Teva;hp FCpwh . Teva;orc Teva;hp Qin;hp FCpwh ¼ <1 Teva;orc Teva;hp
(11)
Then the total sensible heat of the organic working fluid ðQorc;s Þ can be calculated by Eq. (12).
Qorc;s ¼ FCporc Teva;orc Tcon;orc
(12)
The waste heat that cannot be recovered is the maximum waste heat load below the shifted ORC evaporation temperature ðTeva;orc þ DTmin Þ minus the sensible heat recovered by the organic working fluid ðQorc;s Þ, which is shown Eq. (13).
Qwh;unre ¼ FCpwh Teva;orc þ DTmin Tcliff þ Teva;hp þ DTmin Tout;wh;min Qorc;s (13) Then the outlet temperature of waste heat ðTout;wh Þ can be calculated by Eq. (14).
Tout;wh ¼ Tout;wh;min þ Qwh;unre FCpwh
(14)
The total recovered waste heat load ðQwh;re Þ is the sum of the maximum recoverable waste heat and the power consumed by the heat pump ðWhp Þ minus the unrecovered waste heat load ðQwh;unre Þ as shown in Eq. (15).
Qwh;re ¼ FCpwh Tin;wh Tout;wh;min þ Whp Qwh;unre
(15)
Then the power output of the ORC ðPorc Þ is given by Eq. (16).
Porc ¼ horc Qwh;re
(16)
The net power output ðPnet Þ of the system is given by Eq. (17)
Pnet ¼ Porc Whp
(17)
All the important parameters of the integrated system can be determined by the above equations with given evaporation temperature of the heat pump and the ORC. These equations guarantee that three pinch points develop simultaneously, which will result in the maximum net power output. The above equations only guarantee the optimal condition under fixed heat pump evaporation temperature. The evaporation temperature of the heat pump is a free variable. To find the optimal evaporation temperature of the heat pump, Eqs. (1)-(17) should be solved under various evaporation temperatures. With the mathematical model and integration procedure in Fig. 7, the optimal operating conditions of the integrated system can be determined.
The heat capacity flowrate of waste heat is assumed to be 100 kW/ C Minimum heat transfer approach temperature is assumed to be 10 C The isentropic efficiency of the compressor in the heat pump is assumed to be 85% The isentropic efficiencies of the turbine and the pump in the ORC are assumed to be 80% Pressure drop and heat loss is neglected In this case, the inlet temperature of the waste heat source is 150 C. Then the maximum available waste heat is 100*(15055) ¼ 9500 kW. Fig. 9 shows the variation of net power output and the amount of waste heat recovered with evaporation temperature for a standalone ORC. It is apparent that R236fa gives the largest power output of 805 kW. Thus, the optimum working fluid is R236fa and the optimal evaporation temperature is 120 C. With the increase of evaporation temperature, the amount of waste heat recovered decreases for all the working fluids except for R227ea and R236fa. There is no pinch limitation for R227ea due to its low critical temperature. Even though R227ea can recover the waste heat totally under all the evaporation temperatures, the low critical temperature limits the evaporation temperature and thermal efficiency. For R236fa, the amount of waste heat first decreases and then increases. The reason is that with the evaporation temperature approaching the critical temperature of R236fa, the latent heat of R236fa decreases drastically. Then the pinch limitation is alleviated. Much more waste heat can be recovered with the increase of evaporation temperature. Since both the thermal efficiency and the amount of waste heat recovered increase with the evaporation temperature, the net power output increases drastically near the critical point. The results indicate that the working fluid evaporating at near critical temperature has a small ratio of latent to sensible heat and can recover more waste heat. Fig. 10 shows the T-H diagram for a waste heat source and the organic working fluid R236fa under optimal operating conditions. The amount of waste heat recovered is 7987 kW, which takes up only 84% of the maximum available waste heat (9500 kW). In addition, the optimal evaporation temperature is only 120 C, which is limited by the critical temperature of R236fa. Due to the waste heat inlet temperature of 150 C, the evaporation temperature may be increased, so there is room for increasing the amount of waste recovered or the thermal efficiency of the ORC. Thus, it may be profitable to integrate a heat pump into the system. Based on the results shown in Fig. 6, n-hexane is selected as the working fluid in the heat pump. As discussed in Section 3.1, the working fluid in the ORC should be the one with the smallest ratio of latent to sensible heat. Table 3 lists the ratio of latent heat to sensible heat of several working fluids under specific evaporation temperatures. When the evaporation temperature is 130 C, R600a exhibits the smallest ratio of latent to sensible heat. When the evaporation temperature is 120 C, R236fa exhibits the smallest
4. Case study A case from a previous study [22] is adopted to illustrate how to optimally integrate a heat pump with an ORC with the proposed method in this study. The ORC and the heat pump are simulated in Aspen Plus [25] with Peng-Robinson equation of state. The thermodynamic properties of the working fluids are retrieved from Aspen Plus [25] as well. The following assumptions and parameters in the original study are adopted in this study. The condensation temperature of the ORC is assumed to be 45 C
337
Fig. 9. Net power output and waste heat recovered for standalone ORC.
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H. Yu et al. / Energy 160 (2018) 330e340
Fig. 10. TeH diagram of standalone ORC under optimal operating conditions.
Table 3 The ratio of latent to sensible heat of working fluids under various conditions. Working fluids
Evaporation temperature ( C)
Rl (kJ/kg)
Rs (kJ/kg)
Ratio rl=s
R236fa R600a R600a R236ea R236ea R600 R600 R245fa R245fa R601a R601a R601 R601
120 120 130 120 130 120 130 120 130 120 130 120 130
38.72 150.20 97.18 79.40 63.43 213.34 184.01 111.76 97.31 248.48 233.26 271.13 256.72
115.91 221.86 265.61 106.50 123.88 213.70 248.08 111.63 128.99 195.41 224.61 196.47 225.57
0.33 0.68 0.37 0.75 0.51 1.00 0.74 1.00 0.75 1.27 1.04 1.38 1.14
ratio of latent to sensible heat. The integration is first performed at high evaporation temperature (130 C).
Fig. 11. Integrated system performance as function of heat pump evaporation temperature with R600a as working fluid.
4.2. R236fa as the working fluid in the ORC As the critical temperature of R236fa is 124.92 C, the evaporation temperature is limited to 120 C. R236fa evaporating at 120 C exhibits the smallest ratio of latent to sensible heat among all the working fluids, which makes it the most promising working fluid candidate for ORC in the integrated system. Then the condensation temperature of the heat pump is 130 C in this case. Fig. 12 shows the variation of upgraded waste heat load, unrecovered waste heat load, heat load absorbed by the ORC, and waste heat outlet temperature with increasing heat pump evaporation temperature. Fig. 13 illustrates the variation of net power output, heat pump power consumption, and ORC power output with evaporation temperature of the heat pump. The integration of the heat pump improves the net power output of the system. When the evaporation temperature of the heat pump is 45 C, the COP of the heat pump is 2.65. Based on Eqs. (1)e(3), the amount of waste heat to be upgraded is 280 kW, the power consumed is 169 kW, and the total available heat load is 9669 kW. The thermal efficiency of an ORC with R236fa evaporating at 120 C is about 10.07%, hence the net power output is about 805 kW, which is the same as that of the
4.1. R600a as the working fluid in the ORC When the evaporation temperature is set as 130 C, the condensation temperature of the heat pump is 140 C accordingly. Since R600a exhibits the smallest ratio of latent to sensible heat among all the working fluids, R600a is chosen as the working fluid in the ORC. It should be noted that higher evaporation temperature in the ORC indicates higher condensation temperature of the heat pump, which means lower COP of the heat pump and more power consumption. Fig. 11 shows the net power output of the integrated system under various evaporation temperatures of the heat pump. The horizontal dashed line indicates the maximum power output (805 kW) of a standalone ORC recovering waste heat. It is obvious that the net power output is less than the original standalone ORC. Thus, it is not profitable to integrate a heat pump into the system with the ORC evaporation temperature being 130 C. As R600a is the most promising working fluid for evaporation temperature 130 C, other working fluids with larger ratio of latent to sensible heat will perform worse. When the evaporation temperature is 98 C, the amount of heat recovered is 8050 kW, which is not satisfactory. According to the procedure in Fig. 7, the evaporation temperature should be decreased next.
Fig. 12. Key parameters as function of heat pump evaporation temperature.
H. Yu et al. / Energy 160 (2018) 330e340
Fig. 13. Integrated system performance as function of heat pump evaporation temperature with R236fa as working fluid.
original standalone ORC. Thus, it is not profitable to integrate the heat pump at the evaporation temperature of 45 C. The reason is that the COP is too low to justify the integration of a heat pump for this evaporation temperature. With increasing evaporation temperature for the heat pump, the COP of the heat pump increases, and the amount of waste heat to be upgraded first increases and then decreases. Both the power consumed by the heat pump and the power output from the ORC decrease. When the evaporation temperature of the heat pump is 90 C, the net power output reaches a maximum of 880.5 kW. The heat pump upgrades the waste heat between 100 C and 102.52 Ce130 C consuming 42.2 kW of power. The COP of the heat pump is 6.97 at this point. Then the total available heat load is 9542.2 kW and the amount of heat recovered by the ORC is 9164 kW, which takes up 96.04% of the total available heat load. The final outlet temperature of the waste heat source is 58.78 C. For the standalone ORC, only 7897 kW waste heat is recovered and the outlet temperature of the waste heat is 70 C. At the expense of 42.2 kW power consumption, the amount of waste heat is increased by 12.04%, and the power output is increased by 9.37%. Fig. 14 illustrates the optimal T-H diagram of the integrated system. Compared with the T-H diagram of the stand-alone ORC system in Fig. 10, the waste heat matches much better with the working fluid after the heat pump is integrated. The waste heat recovery is satisfactory, and then the integration of a heat pump and an ORC is profitable for this case. If the integration at 120 C is not profitable, it is not necessary to continue decreasing the evaporation temperature of the ORC. Since the waste heat recovery is already 96.04%, the thermal match between the working fluid and the waste heat is satisfactory. Based on the analysis of the results in the study, it is noticeable that the minimum ratio of R600a and R236fa are quite similar, but the evaporation temperature is different. The reason is that if the evaporation temperature of the ORC is set too high (for example 130 C for R600a), the COP of the heat pump is lower, and the amount of waste heat above the ORC evaporation temperature is small, thus more waste heat needs to be upgraded by the heat pump to get a better thermal match. These factors result in more power consumption by the heat pump through the comparison of Figs. 11 and 13. When the evaporation temperature is set appropriately and there is a working fluid with small ratio of latent to sensible heat, the integration is profitable. Therefore, whether it is profitable to integrate a heat pump relies on the evaporation temperature of the ORC, the ratio of latent to
339
Fig. 14. TeH diagram of integrated system under optimal operating conditions.
sensible heat of the ORC working fluid, and the COP of the heat pump. The integration is profitable only when the following preconditions are satisfied simultaneously: (a) poor thermal match between working fluid and waste heat for standalone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. Therefore, the evaporation temperature of the ORC working fluid, the waste heat inlet temperature, and the COP of the heat pump jointly determine the performance of the integrated system. 5. Conclusion This study presents a methodology to integrate a heat pump with an ORC to improve the net power output of the system. Integrating a heat pump into the system does not always result in an increase of net power output. When the critical temperature of the working fluid is lower than the inlet temperature of the waste heat source and the ratio of latent to sensible heat is small, then the integration is probably profitable. If the COP of the heat pump is improved, the likelihood to profitably integrate the heat pump will be larger. A systematic method to determine the working fluid in both the ORC and the heat pump, as well as the optimal operating conditions of the integrated system is presented. The case study shows that the net power output and the amount of waste heat recovered are increased by 9.37% and 12.04% respectively. The integration is profitable only when the following pre-conditions are satisfied simultaneously: (a) poor thermal match between the working fluid and the waste heat for stand-alone ORC; (b) the evaporation temperature of the ORC is set appropriately; (c) the working fluid of the ORC has a small ratio of latent to sensible heat; (d) the COP of the heat pump is satisfactory. Even though the integration of a heat pump is energy profitable in some special cases, detailed techno-economic analysis should be performed to decide whether it is economically profitable to implement in practice. Several topics are suggested for future work. First, techno-economic analysis of the integrated system should be performed. Although the integration of a heat pump can boost the power output in the case study, the feasibility of the process should be verified from techno-economic analysis. Also, a working fluid in the heat pump with higher COP will enhance the performance of the integrated system. The working fluid in the heat pump is also an
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important impetus for successful implementation of the proposed integrated system. Other cycles with modifications to increase the COP of the heat pump cycle such as closed compression cycles with economizer, cascade configuration, and mechanical vapor recompression are also promising alternatives to enhance the system performance.
[2]
[3]
[4]
Acknowledgement This publication has been funded by HighEFF e Centre for an Energy Efficient and Competitive Industry for the Future. The authors gratefully acknowledge the financial support from the Research Council of Norway and user partners of HighEFF, an 8 year Research Centre under the FME-scheme (Centre for Environmentfriendly Energy Research, 257632/E20). Thanks to Ph.D. candidate John Eason at Carnegie Mellon University for his kind help with a meaningful discussion and suggestions.
[5] [6]
[7]
[8]
[9]
Nomenclature [10]
COP FCp H ORC ODP P Q r R S T W
h
coefficient of performance heat capacity flowrate enthalpy organic Rankine cycle ozone depletion potential power output and pressure heat load ratio heat content entropy temperature electricity consumption thermal efficiency
Subscript c cliff con eva hp in l max min orc out re s unre wh
critical cliff formed in the T-H diagram condensation/condenser evaporation/evaporator heat pump Inlet/absorbed heat latent maximum minimum organic Rankine cycle outlet/released heat recovered sensible unrecovered waste heat
[11]
[12]
[13] [14] [15] [16]
[17]
[18]
[19]
[20]
[21]
[22]
[23] [24] [25]
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