Methodical thermodynamic analysis and regression models of organic Rankine cycle architectures for waste heat recovery

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Energy 87 (2015) 60e76

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Methodical thermodynamic analysis and regression models of organic Rankine cycle architectures for waste heat recovery S. Lecompte*, H. Huisseune, M. van den Broek, M. De Paepe Department of Flow, Heat, and Combustion Mechanics, Ghent University e UGent, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 January 2015 Received in revised form 25 March 2015 Accepted 21 April 2015 Available online 27 May 2015

The ORC (organic Rankine cycle) is an established technology for converting low temperature heat to electricity. Knowing that most of the commercially available ORCs are of the subcritical type, there is potential for improvement by implementing new cycle architectures. The cycles under consideration are: the SCORC (subcritical ORC), the TCORC (transcritical ORC) and the PEORC (partial evaporation ORC). Care is taken to develop an optimization strategy considering various boundary conditions. The analysis and comparison is based on an exergy approach. Initially 67 possible working ﬂuids are investigated. In successive stages design constraints are added. First, only environmentally friendly working ﬂuids are retained. Next, the turbine outlet is constrained to a superheated state. Finally, the heat carrier exit temperature is restricted and addition of a recuperator is considered. Regression models with low computational cost are provided to quickly evaluate each design implications. The results indicate that the PEORC clearly outperforms the TCORC by up to 25.6% in second law efﬁciency, while the TCORC outperforms the SCORC by up to 10.8%. For high waste heat carrier inlet temperatures the performance gain becomes small. Additionally, a high performing environmentally friendly working ﬂuid for the TCORC is missing at low heat carrier temperatures (100 C). © 2015 Elsevier Ltd. All rights reserved.

Keywords: organic Rankine cycle Cycle architectures Working ﬂuids Optimization Exergy Second law efﬁciency

1. Introduction The ORC (organic Rankine cycle) is considered a mature technology for low to medium temperature heat to electricity conversion. Besides the capability to operate at low temperatures, the highlights of the ORC include: low maintenance cost, autonomous operation and favourable operating pressures [1]. Commercial ORC installations typically operate with pure working ﬂuids under subcritical conditions [2]. Therefore the heat carrier and working ﬂuid temperature proﬁle have a suboptimal match due to the isothermal evaporation [3]. Advanced cycle architectures have the potential to improve this match by effectively reducing exergy losses associated to ﬁnite temperature heat transfer [4]. Performance gains over the subcritical ORC are reported for, amongst others, multi-pressure cycles [5e8], trilateral [3,9e12] and transcritical cycles [3,13e17]. Considering the above, advances in cycle architectures can further push adoption of ORC technologies for low temperature heat conversion. The TLC (trilateral cycle) and the TCORC (transcritical cycle) are further investigated in this work. * Corresponding author. E-mail address: [email protected] (S. Lecompte). http://dx.doi.org/10.1016/j.energy.2015.04.094 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Furthermore, they share the same component arrangement with the SCORC (subcritical ORC). Only the operating regime is different, necessitating technical modiﬁcations. Also a generalization of the TLC, named the PEORC (partial evaporating ORC) [18] is studied. In contrast to a TLC, the working ﬂuid is allowed to partially evaporate. The working ﬂuid in a TLC, in contrast to the SCORC, does not undergo isothermal boiling but is only heated to a saturated liquid state. An ideal TLC would have a perfect triangular shape with the expansion process stopping in the two-phase region. If the expansion process stops in the dry region, the TLC is sometimes called a quadrilateral cycle [11]. Smith et al. [9] were amongst the ﬁrst to extensively investigate the TLC. The optimization potential of modiﬁed ORC cycles can be appreciated by comparing the Carnot cycle and the ideal TLC. Evaluating the ideal TLC and Carnot cycle with ﬁnite heat capacity streams in their optimal upper cycle temperature results in an ideal conversion efﬁciency of the TLC which is roughly twice that of the Carnot cycle [9,19]. For a TCORC, the working ﬂuid is brought to supercritical pressure and heated to a supercritical state. The heat rejection process is still done by condensing the working ﬂuid. Both the TLC and TCORC approach a triangular shape in a T-s diagram, providing a good match with a ﬁnite capacity heat source [3].

S. Lecompte et al. / Energy 87 (2015) 60e76

Nomenclature E_ e h I_

exergy ﬂow, kW speciﬁc exergy, kJ/(kg) speciﬁc enthalpy, kJ/(kg)

m_ N PP Q_ 2

R s _ W

x yD yL

irreversibility rate, kW mass ﬂow rate, kg/s number of segments, e pinch point temperature difference, C heat transfer rate, kW coefﬁcient of determination, e speciﬁc entropy, kJ/(kgK) work, kW vapour quality, e exergy destruction ratio, e exergy loss ratio, e

Abbreviations ASHRAE American Society of Heating, Refrigerating, and Air-Conditioning Engineers AWF all working ﬂuids CHP combined heat and power EWF environmentally friendly working ﬂuids GWP global warming potential NFPA National Fire Protection Agency ODP ozone depletion potential PEORC partial evaporation organic Rankine cycle

However, there is no general consensus in scientiﬁc literature on the best performing cycle type. Schuster et al. [3] recommends a TCORC to approximate the ideal trilateral cycle. While in a study by Fischer et al. [10], the TLC had an improved net power output over both the SCORC and TCORC. In the latter study the TLC worked with water as working ﬂuid while the TCORC employed R141b, R123, R245ca or R21. The inlet temperature pairs of heat carrier and condenser cooling ﬂuid were (350 C, 62 C), (280 C, 62 C), (280 C, 15 C), (220 C, 15 C) and (150 C, 15 C). Yamada et al. [20] also investigated the SCORC, TLC and TCORC for the working ﬂuid R1234yf. In their simulations the heat carrier stream is however neglected. The highest thermal efﬁciency was found for a supercritical cycle, however nothing is mentioned about the point of maximum net power output. Furthermore, several papers study either the TCORC or TLC, see Table 1 for a non exhaustive overview. To the authors' knowledge no paper: Compared and analysed the three cycle architectures; SCORC, TCORC and PEORC considering a large set of boundary conditions.

Table 1 Articles which investigate either the TLC or TCORC. Reference

Cycle

Topic

[9,45] [46] [11] [47] [48] [49] [50] [51] [52] [53]

TLC TLC TLC TLC TLC TCORC TCORC TCORC TCORC TCORC

Analysis and working ﬂuid selection Development of a screw expander Comparison of TLCs Piston engine as expander Analysis of an ammonia-water TLC Parametric study Plate heat exchanger design Performance analysis in near-critical conditions Working ﬂuid selection Working ﬂuid selection

SCORC SSE TCORC TLC

61

subcritical organic Rankine cycle sum of squares due to error transcritical organic Rankine cycle trilateral cycle

Greek symbols efﬁciency, e ε effectiveness, e

h

Subscripts 0 dead state I ﬁrst law II second law cf cold ﬂuid crit critical evap evaporator ext external hf heat carrier ﬂuid in inlet int internal isen isentropic liq liquid out outlet rec recuperator sat saturated wf working ﬂuid

Includes a systematic analysis of the constraints: restriction to environmentally friendly working ﬂuids, superheated state after the expander, restriction on the heat carrier outlet temperature and the effect of the recuperator. Provides regression models for the three ORC architectures under consideration. Because scattered boundary conditions and assumptions are used in literature, it is hard to make a fair comparison between different working ﬂuids and cycle architectures. Therefore the effort was set up to analyse a large set of working ﬂuids for several waste heat and cooling conditions in a methodological approach and this for the SCORC, PEORC and TCORC. Another challenge is the availability of high performing ORC working ﬂuids in the near future. From an environmental viewpoint several working ﬂuids are a priori ﬂagged as unsuitable. The ODP (ozone depletion potential) and GWP (global warming potential) are typically employed to assess respectively the impact on the ozone layer and the greenhouse effect. Working ﬂuids with an ODP > 0 are banned by the Montreal protocol [21]. In anticipation of new European F-gas regulations [22] the incentive is launched to ban ﬂuids with a GWP value of >150. By 2015 this rule would apply to domestic freezers and refrigerators and by 2022 in extension to some commercial installations. While the current rules apply for refrigerators and freezers an analogues restriction can be expected for power producing cycles. In addition to environmental constraints, safety is a main concern. The ASHRAE 34 standard provides a classiﬁcation system which takes into account toxicity and ﬂammability for refrigerants. Working ﬂuids with a classiﬁcation of A1 are preferred. These are non toxic and non ﬂammable when tested in air at 21 C and 101 kPa. However, in contrast to ODP and GWP regulations, there is no general consensus on acceptable or permitted working ﬂuids concerning safety. For example, both

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S. Lecompte et al. / Energy 87 (2015) 60e76

Fig. 1. (a) Basic ORC layout. (b) ORC layout with recuperator.

n-pentane and toluene are commercially [2,23] used in ORC installations but are not classiﬁed in the ASHRAE 34 database. However, they are classiﬁed under the NFPA 704 [24] standard. This standard categorizes hazardous materials to quickly identify their risks. Under NFPA 704, toluene is marked as level 31 ﬂammability and level 22 toxicity. Cyclopentane is marked as level 43 ﬂammability and level 14 toxicity. Both are highly ﬂammable, yet are used in ORC systems. This work explicitly focuses on waste heat recovery applications. For these applications maximization of the net power output is the main objective. Typical applications for the low to medium temperature regime are water jacket cooling [25], cooling of furnaces [26] or bottoming cycles [27]. The high temperature cases typically consist of cooling of high temperature ﬂue gas [1]. In order to address the concerns listed above the following topics are tackled in this work: 1. The TCORC, PEORC, and SCORC are analysed and compared for heat sources with low to medium temperatures (100 Ce250 C) and high temperatures (250 Ce350 C). 2. The performance potential of the TCORC, PEORC and SCORC is highlighted by using an exergy analysis and rigorously applying the set of boundary conditions on each cycle type. 3. A large set (67) of refrigerants is selected for the study. 4. The PEORC is considered, investigating the region between the TLC and the SCORC. 5. The impact of successive constraints is analysed: limitation to environmentally friendly working ﬂuids, enforced superheated state after the expander and upper cooling limit of the heat carrier. 6. Addition of a recuperator to the SCORC and TCORC is discussed. 7. Simple regression models are provided to quickly assess design implications.

2. Cycle arrangements In this section the different cycles under investigation are brieﬂy introduced and visualised in a T-s diagram. Three closed cycle arrangements are investigated in this work: the SCORC (subcritical

1 Liquids and solids (including ﬁnely divided suspended solids) that can be ignited under almost all ambient temperature conditions. Liquids having a ﬂash point below 23 C and having a boiling point at or above 38 C or having a ﬂash point between 23 C and 38 C. 2 Intense or continued but not chronic exposure could cause temporary incapacitation or possible residual injury. 3 Will rapidly or completely vaporize at normal atmospheric pressure and temperature, or is readily dispersed in air and will burn readily. Includes pyrophoric substances. Flash point below 23 C. 4 Exposure would cause irritation with only minor residual injury.

ORC), the TCORC (transcritical ORC) and the PEORC (partial evaporating ORC). The PEORC is a generalization of the TLC. The component arrangements are identical for all of these cycles and corresponds with that of Fig. 1. The working ﬂuid passes successively trough the pump, evaporator, expander and condenser. For the TCORC, the evaporator is typically called a vapour generator because two-phase boiling is omitted. For the TLC, the evaporator only includes the pre-heating and ends at a saturated liquid state. The T-s diagram for each of the four cycles (without recuperator) are given in Fig. 2. 3. Thermodynamic model and assumptions The analysis is done for waste heat recovery applications. The heat carrier temperature varies between 100 C and 350 C. The cooling water inlet temperature ranges between 15 C and 30 C. A matrix with waste heat inlet temperature Thf,in and water cooling loop inlet temperature Tcf,in is constructed. Thf,in and Tcf,in respectively take the values [100, 120, 140, 160, 180, 200, 225, 250, 275, 300, 325, 350] C and [15, 20, 25, 30] C. The cycles are modelled under the assumption of steady state operation, no heat losses to the environment (i.e. well insulated heat exchangers) and no pressure drops in the heat exchangers (these pressure drops can in ﬁrst instance be neglected compared to the pressure changes in the expander). The developed code supports a continuous transition between the three investigated cycles. The evaporators are modelled by discretizing them in N segments. In this way changing ﬂuid properties are taken into account. This is especially crucial for modelling the TCORC. The error analysis indicates that net power output of the TCORC changes less than 0.1% when going from N ¼ 20 to N ¼ 100. To keep an acceptable calculation time a discretization with N ¼ 20 segments is chosen. The condenser is only divided into three zones. A cooling, condensing and subcooling zone. More information about the modelling approach is provided by Lecompte et al. [28] in a previous work. The assumptions and parameters of the model are summarized in Table 2. Thermophysical data is taken from CoolProp [29]. Only pure working ﬂuids are considered in this study, working ﬂuid mixtures are out of scope. As additional criterion, the working ﬂuids should have a critical temperature above 60 C to make sure two-phase condensation occurs. Furthermore, for the SCORC the maximum pressure is 0.9 times the critical pressure [28,30]. This to avoid unstable operation in near critical conditions. The complete list of working ﬂuids and their characteristics are provided in Appendix A. The total heat input to the cycle follows from:

Q_ evap ¼

N X hevap ·m_ wf hevap wf ;x wf ;ðx1Þ x¼1

(1)

S. Lecompte et al. / Energy 87 (2015) 60e76

63

Fig. 2. T-s diagrams for the subcritical ORC (SCORC), transcritical ORC (TCORC), trilateral cycle (TLC) and partial evaporating ORC (PEORC) with as working ﬂuid R143a.

Table 2 Assumptions and parameters for the thermodynamic model.

hI ¼

Description

Value

hpump hturbine

Isentropic efﬁciency pump [%] Isentropic efﬁciency turbine [%] DT pinch evaporator [ C] DT pinch condenser [ C] Heat carrier medium Cooling loop medium Heat carrier inlet temperature [ C] Heat carrier mass ﬂow rate [kg/s] Inlet temperature cooling water [ C] Temperature rise cooling loop [ C] Effectiveness recuperator [e]

70 80 5 5 Air Water 100e350 1 15e30 10 0.8

With hwf,x evaluated at the evaporation pressure Pwf,evap. Furthermore, hwf,N is ﬁxed by the state variables Pwf,evap and swf,evap,out as discussed in Section 4. The effectiveness of the recuperator is deﬁned as:

. h h4 ε ¼ Q_ rec Q_ max ¼ 3 h3 h40

(2)

with h40 evaluated at (p ¼ P4, T ¼ T1). The turbine and pump are characterized by their isentropic efﬁciency:

_ pump ¼ m_ · W wf

hisen pump;out

hpump;in

hpump

_ _ wf ·hturbine hturbine;in hisen W turbine ¼ m turbine;out

The thermal efﬁciency is deﬁned as:

3.1. Performance evaluation criteria An exergy analysis is done to assess the performance potential of the cycles. In order to calculate the exergy, a dead state (P0,T0) is speciﬁed. This is typically the ambient conditions or the inlet temperature of the condenser cooling loop. The latter is used in this work. The work potential is lost when the system reaches thermal and mechanical equilibrium with the dead state. When potential and kinetic contributions to the ﬂow energies are assumed negligible, the speciﬁc exergy e for a steady state stream is given by:

e ¼ h h0 T0 ðs s0 Þ

_ E_ ¼ me

(7)

The irreversibilities rates I_ of the components for a steady state ﬂow are evaluated as follows:

0¼

X

! X X T0 _ _ þ m_ in ein m_ out eout I_component 1 Qj W Tj out in (8)

(3a)

(3b)

(4)

(6)

The exergy ﬂow E_ is obtained by multiplying the speciﬁc exergy with the mass ﬂow rate:

j

and hturbine,in ¼ hwf,N. The net power output is given as:

_ _ _ net ¼ W W turbine W pump

(5)

evap

Variable

PPevap PPcond hf cf Thf,in m_ hf Tcf,in DTcf εrec

_ net W _ Q

with the index j referring to an equal temperature section of the system boundary. The performance is assessed in relation to the maximum work potential available from the heat carrier stream. _ net . The useful output is W The internal second law efﬁciency is given as:

hII;int ¼

_ net W _ Ehf ;in E_ hf ;out

And the external second law efﬁciency as:

(9)

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S. Lecompte et al. / Energy 87 (2015) 60e76

hII;ext ¼

E_ hf ;in E_ hf ;out E_

(10)

hf ;in

Thus the second law efﬁciency hII is given as:

_ net W hII ¼ ¼ hII;int ·hII;ext _ E

(11)

hf ;in

The exergy ﬂow into the system E_ hf ;in can also be written as:

_ net þ E_ _ _ _ _ E_ hf ;in ¼ W hf ;out þ Ecf ;out þ I pump þ I turbine þ I condensor þ I_evaporator þ I_recuperator (12) The exergy loss, subscript L, is deﬁned as exergy which is unused and discarded into the atmosphere. There are two main exergy losses in this work. The exergy loss associated to the hot stream outlet of the evaporator E_ hf ;out and the one associated to the cooling ﬂuid outlet of the condenser E_ cf ;out . Unlike CHP (Combined Heat and Power) applications, these streams are not used for heating purposes and thus are considered losses in this work. Exergy destruction, subscript D, is deﬁned as exergy which is unavoidably lost in the cycle during the conversion from heat to electricity. These are the irreversibilities during ﬁnite temperature heat transfer (I_condensor , I_evaporator , I_recuperator ) and the irreversibilities associated to the pump (I_pump ) and turbine (I_turbine ). The exergy destruction and loss ratio is respectively given as:

yD ¼

I_component Ehf ;in

(13)

and

yL ¼

E_ stream Ehf ;in

(14)

4. Optimization algorithm and strategy From the model in Section 3 follows that there are two degrees of freedom left which can be optimized. These are generally ﬁxed as follows: for the SCORC, evaporation pressure and superheating, for the TLC, evaporation pressure and vapour quality at the outlet of the evaporator and for the TCORC evaporation pressure and temperature at the outlet of the evaporator. In this work however, the degrees of freedom are ﬁxed by deﬁning two independent dimensionless parameters Fp and Fs:

Fp ¼

Pwf ;evap Pmin Pmax Pmin

(15a)

Pmax ¼ 1:3·Pwf ;crit if Thf ;in PPevap > Twf ;crit

(15b)

Pmax ¼ Pwf ;sat T ¼ Thf ;in PPevap if Thf ;in PPevap < Twf ;crit Pmin ¼ Pwf ;sat T ¼ Tcf ;out þ PPcd Fs ¼

swf ;evap;out smin smax smin

smin ¼ swf ;sat;liq P ¼ Pwf ;evap if Pwf ;evap < Pwf ;crit

(16b)

smin ¼ swf ;crit if Pwf ;evap > Pwf ;crit

(16c)

smax ¼ swf P ¼ Pwf ;evap ; T ¼ Thf ;in PPevap

(16d)

Both parameters have a range [0,1]. The parameter Fp is directly related to the evaporation pressure. For a TCORC the maximum pressure is limited to 1.3 times the critical pressure. For the other cycles, the maximum pressure is limited to the saturation pressure at the heat input temperature corrected with the pinch point temperature difference. The parameter Fs determines the amount of superheating (SCORC), the vapour quality (TLC) or the turbine inlet temperature (TCORC). The maximum value corresponds to a pinch point which is located at the evaporator heat carrier inlet. For the SCORC, the minimum lies at the saturated liquid state at a given evaporation pressure. For the TCORC, the minimum corresponds to the critical point. The beneﬁt of employing these parameters is a more robust optimization process. The model based on the parameters Fp and Fs permits to deﬁne the search space based on only two unique variables. The two state variables Fp and Fs ﬁx the evaporator (or vapour generator) outlet state. In Fig. 3 the effect of Fp and Fs on the second law efﬁciency is shown for the working ﬂuid R1234yf. In respectively Fig. 3a and b a waste heat carrier with Thf,in ¼ 140 C and Thf,in ¼ 90 C is used. The three different architectures: SCORC, TCORC and PEORC can be easily distinguished. For the case Thf,in ¼ 90 C, a supercritical regime is not attainable due to the critical temperature of R1234yf (Tcrit ¼ 94.7 C). This is because the waste heat inlet temperature corrected with the minimum pinch point temperature is lower than the critical temperature. The supercritical regime is bounded by a straight line with a ﬁxed value of Fp. The interface between PEORC and SCORC is explained by the saturation vapour curve; as such both Fp and Fs vary. The ﬁnal goal is to optimize the second law efﬁciency hII for different working ﬂuids and cycle constraints. In Fig. 3a (Thf,in ¼ 140 C) the global maximum for the second law efﬁciency is 0.437 and corresponds to a TCORC. In Fig. 3b (Thf,in ¼ 90 C) the global maximum for the second law efﬁciency is 0.284 and corresponds to a PEORC. The operating conditions for both cases are summarized in Table 3. However, as can be seen from Fig. 3b, there is a risk that the optimization algorithm gets stuck at a local optimum. Therefore a simple multi-start algorithm is employed [31]. This is a global optimization algorithm which is partially heuristic. The fundamental idea is to construct an initial grid on which a local solver is applied. The global optimization algorithm starts with a randomly distributed set of start points in the search space (Fs, Fp). Initially 20 start points were used. Subsequently, a local solver based on a trust-region algorithm [32] starts at these trail points and the best solution is retained. The investigated problem for the local solver is given below:

maximize hII Fs ; Fp Fs ;Fp

0 Fs 1 and 0 Fp 1

(17)

(15c)

subject to

(15d)

The optimization can also be limited to certain ORC architectures by further constraining Fs and Fp as illustrated in Fig. 3. The termination conditions are listed in Table 4. To assess the inﬂuence of the number of start points, the calculations were repeated with 40 start points. This however gave identical results.

(16a)

S. Lecompte et al. / Energy 87 (2015) 60e76

65

Fig. 3. Second law efﬁciency hII in function of Fp and Fs for R1234yf, Tcf,in ¼ 25 C and (a) Thf,in ¼ 140 C, (b) Thf,in ¼ 90 C.

Table 3 Maximum second law efﬁciency for Thf,in ¼ 90 C and Thf,in ¼ 140 C for R1234yf with Tcf,in ¼ 25 C.

Cycle type hII [e] Fs [e] Fp [e] Pwf,evap [bar] Pwf,cond [bar] Tturbine,in [ C]

Thf,in ¼ 140 C

Thf,in ¼ 90 C

TCORC 0.437 0.7205 1 43.97 9.86 120.78

PEORC 0.284 0.1394 0.6242 21.23 10.18 71.76

Table 4 Termination conditions trust-region algorithm. Maximum function evaluations Tolerance on objective function Tolerance on input variables

3000 1e-6 1e-6

The investigation strategy consists of the following steps: ﬁrst, AWF (all working ﬂuids) from Appendix A are considered (Case 1). Afterwards the analysis is repeated for the subset which is assumed EWF (environmentally friendly working ﬂuids) (Case 2). Next, the turbine outlet is constrained to a superheated state, this results in an added constraint xturbine,out ¼ 1 (Case 3). In a following step the heat carrier outlet temperature is restricted, resulting in an added constraint on Thf,out (Case 4). Finally, the addition of a recuperator is considered (Case 5). For each analysis the second law efﬁciency hII is maximized by employing the global optimization algorithm. With this strategy a maximum attainable performance is reported in each consecutive step. As such, the consequence of each design choice is clearly analysed and this for the three different cycles under consideration. 5. Results and discussion 5.1. Regression models First, regression models are compiled for each of the cycle types and cases under consideration. These regression models express the maximal second law efﬁciency hII as function of temperatures Thf,in and Tcf,in. The proposed regression models are useful for predicting the impact of design constraints and this with a low computational cost. Several linear regression models up to third

order were tried. However, the ﬁnal proposed regression model which best captures the trends is non-linear:

. hII;max ¼ a þ b· c·Tcf ;in þ 1 d·Thf ;in þ 1

(18)

Corresponding parameter estimates for each of the cycle types are provided in Table 5. Goodness-of-ﬁt statistics [33] are provided in Table 6. A SSE (Sum of Squares Due to Error) closer to zero means that the ﬁt is more useful for prediction (interpolation). While a high adjusted R2 value indicates a successful ﬁt in explaining the variation of the data. The SSE and adjusted R2 ranges respectively between 0.0006e0.0041 and 0.992e0.999. Both SSE and adjusted R2 can be considered highly satisfactory. The residuals have been visually analysed on quantileequantile (QeQ) plots [33] and appear normally distributed around zero. All the coefﬁcients are signiﬁcant from a t-test [33] with 5% signiﬁcance level. Contour plots of these surface ﬁts are plotted for: 1. Case 1: the full set of working ﬂuids (AWF) (Fig. 4). 2. Case 2: the EWF (environmentally friendly working ﬂuids) set of working ﬂuids (Fig. 5). 3. Case 3: the EWF set with xturbine,out ¼ 1 (Fig. 6). 4. Case 4: the EWF set with xturbine,out ¼ 1 and Thf,out ¼ 130 C (Fig. 7).

Table 5 Parameter estimates for hII surface ﬁts. Type SCORC TCORC PEORC SCORC TCORC PEORC SCORC TCORC SCORC TCORC SCORC TCORC

a

b

c

AWF 0.7548 1.315 0.01180 0.7405 0.791 0.01265 0.7408 0.4796 0.01286 EWF 0.7531 1.66 0.00933 0.7247 0.371 0.01058 0.7408 0.4796 0.01286 EWF, xturbine,out ¼ 1 0.7548 1.735 0.009109 0.7228 0.3061 0.01042 EWF, xturbine,out ¼ 1, Thf,out ¼ 130 C 0.7532 1.695 0.002262 0.8410 14.981 0.001937 EWF, xturbine,out ¼ 1, RC, Thf,out ¼ 130 C 0.7303 1.433 0.001919 0.8303 9.997 0.001922

d 0.04730 0.03490 0.02996 0.05206 0.01960 0.02996 0.05345 0.01693 0.02434 0.1382 0.02230 0.09669

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S. Lecompte et al. / Energy 87 (2015) 60e76

5.2. Full set of working ﬂuids (Case 1)

Table 6 Goodness-of-ﬁt statistics for hII surface ﬁts. Cycle type SCORC TCORC PEORC SCORC TCORC PEORC SCORC TCORC SCORC TCORC SCORC TCORC

Adjusted R2

SSE

AWF 0.994 0.995 0.998 EWF 0.993 0.996 0.998 EWF, xturbine,out ¼ 1 0.992 0.994 EWF, xturbine,out ¼ 1, Thf,out ¼ 130 C 0.999 0.996 EWF, xturbine,out ¼ 1, RC, Thf,out ¼ 130 C 0.999 0.996

0.0032 0.0022 0.0006 0.0040 0.0023 0.0006 0.0041 0.0018 0.0007 0.0029 0.0006 0.0030

5. Case 5: the EWF set with xturbine,out ¼ 1, Thf,out ¼ 130 C and recuperator (Fig. 8). The marker type indicates the cycle architecture, while the colour of the marker indicates the working ﬂuid name. An overview of the optimal working ﬂuids with the corresponding cases and cycles is listed in Table 7. In the presented overview we also give the recommendations made by other authors. Looking ahead at the results, see Table 7, we see that several combinations of cycle architecture and working ﬂuid can be ﬂagged as optimal. Many of these thermodynamic optimal combinations can also be retrieved from literature. Note that we only considered articles on waste heat recovery. However, due to different modelling constraints and assumptions between the works, it was not straightforward to interpret the results. In this work, a rigorous set of boundary conditions and assumptions is used, facilitating the analysis and discussion of the results below.

We start by discussing the results for the full set of working ﬂuids. From Fig. 4 can be seen that the PEORC consistently has a higher hII than the SCORC and TCORC. Up to Thf,in ¼ 250 C partial evaporation is largely omitted and the cycle corresponds to a TLC. The vapour quality at turbine inlet for each of the calculated working points is visualised in Fig. 13. For increasing temperature Thf,in, the vapour quality at turbine inlet increases slightly but does not exceed 9%. From a thermodynamic point of view the pure TLC is thus a favourable choice. Furthermore, measuring the vapour quality for control purposes could be tedious in practical applications. The resulting optimal ﬂuids for the PEORC are: D4, D6, MD2M, MD3M, water, n-dodecane, o-xylene. All these working ﬂuids have a high critical temperature in common. As such there is a large increase in speciﬁc volume over the expander, indicating that optimal design of volumetric machines is challenging. While turbines can provide an alternative, there is the problem of the erosion of the turbine blades. Therefore, optimizing solely hII will not necessarily result in technically feasible solutions. Still, these results are valuable to deﬁne an upper region in which a technical solution can be found. The optimal ﬂuids for the TCORC are: acetone, neopentane, R113, R218, R227ea, R236fa, R245fa, RC318, toluene and n-pentane. All these working ﬂuids, except neopentane and toluene, are also found in the SCORC list of optimal ﬂuids. Furthermore, the corresponding working ﬂuids share the same boundary conditions. The resulting optimal ﬂuids for the SCORC are highly sensitive to the heat carrier inlet temperature Thf,in. This is explained by the strong correlation between the critical temperature of the working ﬂuid and the net power output for a ﬁxed Thf,in [34e36]. A critical temperature closer to Thf,in results in larger net power output [34]. Due to the large variations in critical temperature for the working ﬂuids under consideration, the resulting optimal working ﬂuids often change for varying Thf,in. In total, 15 working ﬂuids result from optimizing the SCORC, compared to 10 and 7 for respectively the TCORC and PEORC.

Fig. 4. Contour plot hII, full set of working ﬂuids (Case 1).

S. Lecompte et al. / Energy 87 (2015) 60e76

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Fig. 5. Contour plot hII, environmentally friendly set of working ﬂuids (Case 2).

Fig. 6. Contour plot hII, environmentally friendly set of working ﬂuids and xturbine,out ¼ 1 (Case 3).

For the PEORC typically siloxanes appear to give the best second law efﬁciency. Furthermore all of the optimal working ﬂuids, except water, are very dry ﬂuids [1]. These ﬂuids have a positive evaporation saturation slope in a T-s diagram. Wet ﬂuids on the other hand have a negative slope while isentropic ﬂuids have approximately constant

speciﬁc entropy. For the TCORC several chemical groups of working ﬂuids are found. These are amongst others: alkanes, chloroﬂuorocarbons, ﬂuorocarbons, halocarbons and hydroﬂuorocarbons. However all of the resulting working ﬂuids are of the dry type. Also for the SCORC most of the ﬂuids are of the dry type. The only

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Fig. 7. Contour plot hII, environmentally friendly set of working ﬂuids, xturbine,out ¼ 1 and Thf,out ¼ 130 C (Case 4).

Fig. 8. Contour plot hII, environmentally friendly set of working ﬂuids, xturbine,out ¼ 1, Thf,out ¼ 130 C and recuperator (Case 5).

exceptions are R1234yf and acetone which are isentropic ﬂuids and R143 which is a wet ﬂuid. For comparison purposes, the relative difference in hII between PEORC-TCORC and TCORC-SCORC are given respectively in Fig. 9a and b. These plots clearly indicate a larger difference for low heat carrier inlet temperatures Thf,in. Comparing the TCORC with the PEORC, the relative difference in hII is always lower than 26%. For temperatures Thf,in of 350 C the relative difference in hII already reduces to less than 5%. On the other hand, comparing the TCORC with the SCORC, the relative difference of hII is always lower than

11%. While at temperatures of 350 C the relative difference is less than 3%. Thus advanced cycle architectures like the PEORC and TCORC, have foremost potential in low temperature waste heat recovery applications. The exergy content for the processes of the three cycle types is shown in Fig. 10a for Tcf,in ¼ 20 C. With increasing Tcf,in mainly yD,condensor and yL,condensor increase while reducing hII (see Fig. 4). For high Thf,in, the expander is the main source of exergy destruction. In contrast, for decreasing Thf,in, the share yD,evaporator and yL,evaporator increase and become the dominant sources of exergy destruction

S. Lecompte et al. / Energy 87 (2015) 60e76

69

Table 7 Overview optimal working ﬂuids and comparison with scientiﬁc literature. Working ﬂuid

Acetone Butene Cyclopentane cis-2-Butene D4 D6 Ethanol Isobutane Isohexane MD2M MD3M Neopentane m-Xylene n-Nonane n-Dodecane n-Hexane n-Pentane o-Xylene R113 R114 R123 R1233zde R1234yf R1234zee R141b R143a R152a R218 R227ea R236fa R245fa R365mfc RC318 Toluene Water

Recommended as working ﬂuid for

Case SCORC

TCORC

PEORC

SCORC

TCORC

TLC or PEORC

1,2,3,4,5

1,2,3,4,5 4,5 3,4,5 4,5 e e 4,5 2 e e e 1,3 e e e e 1,3,4 e 1 e e 2 2,3 2,3 e e 4,5 1 1 1 1 e 1 2,3 e

e e e e 1,2 1,2

[54,55] e [30,54,56e58] [59] [60] e [61,62] [13,40,63] e [60] e e e e [64] [35,64] [34,64e66] [67,68] [34,61,69,70] [34] [34,66,68,70e72] [73] [20,74,75] [74] [34,41,66,70,77,78] [75] [25] [81] [65,83,84] [84,85] [34,58,65,70] [58] [84] [27,64,71] e

e e [30] e [60] e e e e e e e e e e e e e e e e e [20] [76] e [13,53,75,79,80] [53] [81,82] [80] [36] e [3] e e e

e e [11] e e e e e e e e e e e e e [9] e [9] e e e e e e e e e e e e e e e [10]

1,2,3,4 e e e 4 2,3 2,3 e e 3 4 4 e 2,3 1,3 e e 1 1 1,2,3 1,2,3 2,3 1 1 e 1 1 1 1 1 1 1 e

e e 1,2 1,2 e e e 1,2 e e 1,2 e e e e e e e e e e e e e e e e 1,2

Fig. 9. Relative cycle results hII, (a) (Case 1, PEORC - TCORC), (b) (Case 1, TCORC - SCORC), (c) (Case 2, TCORC - SCORC), (d) (Case 3, TCORC - SCORC), (e) (Case 4, TCORC - SCORC), (f) (Case 5, TCORC - SCORC).

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Fig. 10. Exergy content (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5 with Tcf,in ¼ 20 C.

Fig. 11. Relative cycle results hII for SCORC architecture, (a) (Case 1 e Case 2), (b) (Case2 e Case 3), (c) (Case 3 e Case 4), (d) (Case 4 e Case 5).

and losses. This occurs around Thf,in ¼ 140 C. Consequently, for low Thf,in, it is beneﬁcial to look further at strategies to decrease yD,evaporator and yL,evaporator. In contrast, for high Thf,in, the exergy loss yL,evaporator and exergy destruction yD,evaporator become insigniﬁcant.

Improving the turbine efﬁciency is thus more gainful. The increased

hII when going from SCORC to TCORC or from TCORC to PEORC can clearly be associated to a reduction in exergy destruction yD,evaporator and exergy losses yL,evaporator. The PEORC always boosts the highest

S. Lecompte et al. / Energy 87 (2015) 60e76

71

Fig. 12. Relative cycle results hII for TCORC architecture, (a) (Case 1 e Case 2), (b) (Case2 e Case 3), (c) (Case 3 e Case 4), (d) (Case 4 e Case 5).

Fig. 13. xturbine,in for the PEORC.

reduction in exergy losses yL,evaporator. As expected for the TCORC, the exergy destruction associated to the pump is always higher in comparison to the PEORC or the SCORC. Especially for low Thf,in the share of exergy destruction yD,pump is signiﬁcant at the expense of a low hII. 5.3. Environmentally friendly set of working ﬂuids (Case 2) In a following step, the working ﬂuid set is constrained to environmentally friendly ones. This means an ODP equal to zero and a GWP equal or lower than 150. The results of the hII maximization are plotted in Fig. 5. The results for the PEORC are completely identical with those discussed for the full set of working ﬂuids. For the SCORC only 10 working ﬂuids remain. This is to be expected considering the reduced variation in critical temperature along the remaining working ﬂuids. From these working ﬂuids acetone, cyclopentane, R1233zde, R1234yf and n-pentane are shared with Case 1. For the TCORC there are now 9 optimal working ﬂuids. From these, 4 are shared with Case 1: acetone, neopentane, toluene and n-pentane.

For the SCORC and TCORC most of the working ﬂuids are of the dry type. The only exceptions are acetone (isentropic), R1234yf (isentropic), R1234zee (isentropic) and propylene (wet). Again several chemical categories of working ﬂuids are found. Plots of the relative performance between the SCORC-TCORC are given in Fig. 9c. For the temperature Thf,in ¼ 100 C, hII for the TOCRC is reduced by 15.3% relatively to the SCORC. Yet, when looking at Case 1, R218 was ﬂagged as optimal and performed up to 10.8% better than an SCORC. Therefore an environmentally friendly working ﬂuid resembling the characteristics of R218 could resolve this gap. The poor performance of the environmentally friendly equivalent, propylene, is partly due to the high supercritical pressure of 1.7 times that of R218. For Thf,in ¼ 120 C the TCORC again shows a relative hII increase over the SCORC by up to 6.8%. The performance gain again gradually reduces for increasing heat carrier temperature. A detailed comparison between Case 1 and Case 2 is provided in Fig. 11a for the SCORC and Fig. 12a for the TCORC. For both the SCORC and TCORC there is a reduction in hII for the low temperature regimes. Again, the highest reductions, up to 14.3% for the SCORC and 27.9% for the TCORC, are found for Thf,in ¼ 100 C. However, as can be seen from Figs. 11a and 12b, going to environmentally friendly working ﬂuids does not necessarily lead to large detriments in performance. There are also some interesting changes in the exergy distribution shown in Fig. 10b. For Thf,in ¼ 100 C, the poor performance of both the TCORC and SCORC can be linked to high exergy losses yL,evaporator. Indicating that both the SCORC and TCORC are not able to effectively cool down the heat carrier. In summary, there is still a gap for high performing environmentally friendly working ﬂuids for low temperature applications (Thf,in ¼ 100 C) and this both for sub- and transcritical operation. 5.4. Restriction to superheated state after the expander (Case 3) In the foregoing discussion wet expansion was permitted. The SCORC and TCORC cycles which have wet vapour after the turbine are listed in Table 8. For the full set of working ﬂuids (Case 1), most of the SCORC and TCORC would end in a superheated state after the expander. However, when limited to environmentally friendly working ﬂuids (Case 2), the expansion process of the TCORC mostly ends in the two-phase region. In general, the vapour quality at the

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Table 8 SCORC and TCORC working ﬂuids with expansion ending in two-phase region. Cycle type Working ﬂuid Thf,in [ C] Tcf,in [ C] SCORC TCORC TCORC TCORC

R1234yf R227ea acetone acetone

120 120 275 300

SCORC SCORC TCORC TCORC TCORC TCORC TCORC TCORC TCORC

R1234yf R1234zee propylene R1234yf R1234zee isobutane R1233zde acetone acetone

120 140 100 120 140 160 200 275 300

AWF 15, 20, 15, 20, 15, 20, 15, 20, EWF 15, 20, 15, 20 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20,

xturbine,out [e]

25 0.972, 0.9699, 0.957 25, 30 0.913, 0.902, 0.891, 0.881 25, 30 0.855, 0.859, 0.861, 0.862 25, 30 0.931, 0.933, 0.936, 0.938 25, 30 0.972, 0.994, 25, 30 0.631, 25, 30 0.838, 25, 30 0.912, 25, 30 0.920, 25, 30 0.968, 25, 30 0.855, 25, 30 0.931,

0.970, 0.992 0.676, 0.835, 0.908, 0.917, 0.964, 0.859, 0.933,

0.957, 0.996 0.603, 0.843, 0.904, 0.917, 0.961, 0.861, 0.936,

0.631 0.846 0.911 0.909 0.956 0.862 0.938

outlet of the expander is consistently higher than 0.855 for the full set of working ﬂuids and higher than 0.631 for the environmentally friendly set. While wet expansion is feasible for volumetric machines, it is not an option in turbomachinery due to erosion of the turbine blades. Therefore, in a following step, the outlet of the expander is constrained to a superheated state. The results of the hII maximisation are plotted in Fig. 6. The exergy distribution is given in Fig. 10c. The optimal working ﬂuids for the SCORC are identical to those of Case 2. Only the operating parameters have changed so that a superheated stated is obtained after the turbine. The results from Fig. 11b conﬁrm that there is only a limited performance loss when restricting the expander outlet to superheated state. For the TCORC some of the working ﬂuids have changed compared to Case 2 and 6 optimal working ﬂuids remain. Isobutane, propylene and R1233zde are removed while cyclopentane is added. For both the TCORC and SCORC all the working ﬂuids are of the dry or isentropic type. In contrast to the SCORC, hII for the TCORC is further reduced for low Thf,in. This by up to 10.2% for Thf,in ¼ 120 C as noted in Fig. 12b. Furthermore, there are no suitable transcritical ﬂuids found for Thf,in ¼ 100 C. From Fig. 9d a signiﬁcant improvement of the TCORC over the SCORC is observed starting from Thf,in ¼ 140 C. Thus, while the TCORC is mainly beneﬁcial in low temperature applications (Case 1), under the common restrictions applied in Case 3 only the smaller performance beneﬁt at high Thf,in remains.

Fig. 14. hII, hII,int and hII,ext for Case 4 with Thf,in ¼ 160 C.

n-pentane. For the SCORC most of the working ﬂuids are still of the dry type, except ethanol (wet) and acetone (isentropic). For the TCORC, dry working ﬂuids are not dominant anymore. Notable is the increased second law efﬁciency for increasing Tcf,in as opposed to the above cases. This is due to choice of the dead state T0, which is equal to Tcf,in. Thus hII,ext increases for rising Tcf,in because less of the available heat after the evaporator is considered useful. In contrast, hII,int decreases as expected, corresponding with a lower cycle efﬁciency. Yet, the resulting product results in an increased second law efﬁciency as can be seen from Fig. 14. In Fig. 9e the optimized hII for SCORC and TCORC are compared for this case. For almost no boundary condition the TCORC provides a thermodynamic beneﬁt over the SCORC. Only starting from Thf,in ¼ 300 C there is a small improvement by going to a TCORC. This can be further explained with the help of the exergy distribution plot of Fig. 10d. Up to Thf,in ¼ 350 C the evaporator exergy loss yL,evaporator has the highest share in the exergy distribution. The absolute evaporator exergy losses are however ﬁxed by the constant Thf,out. Thus cycle architectures which have as main effect a reduction in yL,evaporator, have no direct beneﬁt under the constraints of this case. The only possible beneﬁt can be associated to a reduction in yD,evaporator. For high temperatures Thf,in there is indeed a small reduction of yD,evaporator in comparison to the SCORC.

5.5. Restriction with upper cooling limit (Case 4) 5.6. Addition of a recuperator (Case 5) In heat recovery from hot ﬂue gasses there is often an upper cooling limit. When ﬂue gasses, which contain water and sulphur trioxide, are cooled below the acid dew point sulphuric acid vapour condenses. These acids potentially lead to corrosion and damage of the heat exchanger. The temperature of the acid dew point varies with the composition of the ﬂue gas. Typical values range from around 100 C to 130 C [37e39]. In practice manufactures want to reduce the risk of corrosion, therefore the higher value of Thf,out ¼ 130 C is chosen in this work. The results of the hII maximisation are plotted in Fig. 7. Optimal working ﬂuids for the SCORC are found from Thf,in ¼ 140 C. Yet, many of the optimal SCORC working ﬂuids from Case 3 have been replaced. Only acetone and cyclopentane remain. Furthermore the list of optimal SCORC working ﬂuids has shrunk drastically to 5: acetone, cyclopentane, ethanol, m-xylene and n-nonane. For the TCORC, only acetone, cyclopentane and n-pentane are shared between case 3 and case 4. 7 working ﬂuids are ﬂagged as optimal for the TCORC: acetone, butene, cyclopentane, ethanol, R152a, cis-2-butene and

Under the constraints of Case 4 a recuperator could be beneﬁcial according to the scientiﬁc literature [30,40,41]. A recuperator essentially increases the thermal efﬁciency [13]. Thus a high power output can be maintained for a decreased heat input to the ORC. The resulting contour plots of the regression model and the optimized working ﬂuids are given in Fig. 8. For the SCORC acetone, cyclopentane, ethanol and methanol result from the optimization. For the TCORC the optimal working ﬂuids are acetone, butane, cyclopentane, ethanol, R152a and cis-2-butene. For both the TCORC and SCORC the optimal working ﬂuids are either dry, isentropic or wet ﬂuids. As in case 4, an increased second law efﬁciency is observed for increasing Tcf,in. The relative comparison of hII with case 4 for the TCORC and SCORC is given in respectively Figs. 12d and 11d. For most boundary condition pairs inclusion of a recuperator results in a decreased hII. Maraver et al. [39] also reported similar decreased second law efﬁciencies in their cases. Yet, they state that the addition of a

S. Lecompte et al. / Energy 87 (2015) 60e76 Table 9 Description of two representative waste heat recovery cases A and B. Case Description A B

Tcf,in [ C] Thf,in,average [ C] Thf,out [ C]

Flue gas from drying process 25 Flue gas from electric arc furnace 25

240 305

e 130

recuperator will in theory not decrease the second law efﬁciency of the cycle. It should at least be the same as for a non-recuperative cycle. They explain the observed reduction to discretization errors. However, the observed reduction is a result of the ﬁxed temperature glide of the secondary medium in the condenser. With a recuperator, to keep the outlet temperature of the secondary medium ﬁxed, the condenser pressure rises. While also the condenser exergy destruction yd,condenser decreases slightly (see Fig. 10d and e), the net effect is a decreased second law efﬁciency. This suggests that, when investigating the effect of the recuperator, also the condenser side should be optimized taking into account fan and pumping power. 5.7. Application of regression models on waste heat recovery cases The beneﬁt of using the proposed regression models is the low computational cost in making an initial appraisal between different cycle architectures. Furthermore, the models can easily be used with a wide variety of cases. In this section, the effectiveness of the regression models based on Eq. (18) are assessed by application on two waste heat recovery cases. A medium temperature (Thf,in ¼ 150250 C) and a high temperature (Thf,in ¼ 250350 C) waste heat recovery group are deﬁned. The low temperature group is representative for drying processes [42] and annealing furnaces [1]. The high temperature group includes, amongst others, exhaust gases from gas turbines or internal combustion engines [1] and electric arc furnaces [43]. One representative case is selected for each group. Details are provided in Table 9. The proposed cases and classiﬁcation are based on data gathered from the industrial advisory board of the ORCNext project [44]. For both cases, the performance potential of the different cycle architectures is investigated by employing the regression models. The regression models corresponding to environmentally friendly working ﬂuids and a superheated state after the expander are used. An exception is made for the PEORC where no superheated state is required after the expander. For Case B, an additional minimum Thf,out of 130 C is imposed. In this case the PEORC is not considered. The results are plotted in Fig. 15. For Case A going to a TCORC or

Fig. 15. Results of applying the regression models on waste heat recovery cases A and B.

73

PEORC is clearly advantageous in terms of hII. A respective increase of 3.51% and 10.66% in second law efﬁciency is attained compared to the SCORC. However, as expected from the discussion in Section 5.5, in Case B the TCORC does not lead to an increased hII compared to the SCORC. Therefore, going to advanced cycle architectures for case B could already be discouraged only from the thermodynamic viewpoint. 6. Conclusions In this work regression models were formulated to quickly assess design constraints for the SCORC, TCORC and PEORC. In the ﬁrst step we included all 67 working ﬂuids. Especially for low temperature waste heat, alternative architectures like TCORC and PEORC show improved second law efﬁciency. The PEORC clearly outperforms the TCORC in second law efﬁciency by up to 25.6%, while the TCORC outperforms the SCORC in second law efﬁciency by up to 10.8%. For high Thf,in the performance gain becomes small. Furthermore, the choice of optimal working ﬂuid is highly dependent on the boundary conditions of cooling loop and heat carrier. For the PEORC typically siloxanes appear to give the best second law efﬁciency. Furthermore all of the working ﬂuids, except water, are strong dry ﬂuids. Also for the SCORC and TCORC most of the working ﬂuids are of the dry type. There is however no clear chemical group of working ﬂuids which provides the best performance. When restricting the working ﬂuids to environmentally friendly ones there is still a gap for high performing working ﬂuids around Thf,in ¼ 100 C and this both for the SCORC and TCORC. For Thf,in ¼ 100 C the SCORC even outperforms the TCORC. There is only a small impact on hII when further limiting the expander outlet to a superheated state. A signiﬁcant improvement of the TCORC over the SCORC is again observed starting from Thf,in ¼ 140 C. Restricting Thf,out to 130 C results in an almost completely different set of optimal ﬂuids. In this case the TCORC provides no beneﬁt over a SCORC. Acknowledgements The results presented in this paper have been obtained within the frame of the IWT SBO-110006 project The Next Generation Organic Rankine Cycles (www.orcnext.be), funded by the Institute for the Promotion and Innovation by Science and Technology in Flanders. This ﬁnancial support is gratefully acknowledged. Appendix A. Working ﬂuids list Working ﬂuid

Tcrit [ C]

Pcrit [kPa]

R11 R113 R114 R12 R123 R1233zde R1234yf R1234zee R125 R134a R141b R142b R143a R152a R161 R21 R218 R22

197.91 214.06 145.68 111.97 183.67 165.6 94.7 109.37 66.023 101.06 204.35 137.11 72.707 113.261 102.1 178.66 71.87 96.145

4394 3392 3257 4136 3672 3570 3382 3636 3617 4059 4212 4055 3761 4520 5010 5181 2640 4990

GWP

ODP

Environmentally friendly

4750 6130 10,000 10,900 77 6 4 6 3500 1430 725 2310 4470 124 10 151 8830 1810

1 1 1 1 0.02 0 0 0 0 0 0.12 0.07 0 0 0 0.04 0 0.05

e e e e e X X X e e e e e X X e e e

(continued on next page)

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(continued )

Working ﬂuid

Tcrit [ C]

Pcrit [kPa]

GWP

ODP

Environmentally friendly

R227ea R236ea R236fa R245fa R32 R365mfc RC318 SES36 Ammonia Acetone Butene CycloHexane CycloPropane Cyclopentane D4 D5 D6 Ethanol HFE143m IsoButane IsoButene Isohexane Isopentane MD2M MD3M MD4M MDM MM Methanol Neopentane Propylene Propyne Toluene Water cis-2-Butene m-Xylene n-Butane n-Decane n-Dodecane n-Heptane n-Hexane n-Nonane n-Octane n-Pentane n-Propane n-Undecane o-Xylene p-Xylene trans-2-Butene

101.75 139.29 124.92 154.01 78.105 186.85 115.23 177.55 132.25 234.95 146.14 280.49 125.15 238.57 313.35 346 372.63 241.56 104.77 134.67 144.94 224.55 187.2 326.25 355.21 380.05 290.94 245.6 239.35 160.59 91.06 129.23 318.6 373.94 162.6 343.74 151.975 344.55 384.95 266.98 234.67 321.4 296.17 196.55 96.74 365.65 357.109 343.018 155.46

2925 342 3200 3651 5782 3266 2777 2849 11,333 4700 4005 4075 5579 4571 1332 1160 961 6268 3635 3629 4009 3040 3378 1227 945 877 1415 1939 8103 3196 4555 5626 4126 22,064 4225 3534 3796 2103 1817 2736 3034 2281 2497 3370 4251 1990 3737 3531 4027

3220 1200 9810 1030 675 794 10,300 3710 0 0.5 3 n.a 20 11 n.a n.a n.a 0 347 3 n.a n.a 2 0 0 0 0 0 2.8 n.a 3.1 n.a 3.3 0.2 2 3 3 2 2 3 3.1 2 3 2 3 2 1 3 n.a

0 0 0 0 0 0 0 0 0 0 0 0 0 0 n.a n.a n.a 0 0 0 n.a n.a 0 0 0 0 0 0 0 0 0 0 0 0 0 n.a 0 0 0 0 0 0 0 0 0 0 n.a n.a n.a

e e e e e e e e X X X X X X X X X X e X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

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