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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

332

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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.

334

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.

338

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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H. Yu et al. / Energy 160 (2018) 330e340

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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