Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures

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Energy xxx (2015) 1e13

Contents lists available at ScienceDirect

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

Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures Konstantinos Braimakis a, *, Markus Preißinger b, Dieter Brüggemann b, Sotirios Karellas a, Kyriakos Panopoulos c a b c

National Technical University of Athens, Athens, Greece University of Bayreuth, Centre of Energy Technology (ZET), Bayreuth, Germany Centre for Research and Technology Hellas, Athens, Greece

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 November 2014 Received in revised form 19 March 2015 Accepted 23 March 2015 Available online xxx

The Organic Rankine Cycle (ORC) is a promising technology for low temperature waste heat-to-power conversion. This work investigates the waste heat recovery potential of the ORC and some of its innovative variations, such as the supercritical cycle and the use of binary zeotropic mixtures. Focus is given to natural hydrocarbons having low ozone depletion and global warming potential. By performing simulations for heat source temperatures ranging from 150 to 300 C, the optimal operation mode and working ﬂuids are identiﬁed. Meanwhile, several technical parameters (such as the turbine size parameter and rotational speed) are calculated. The system exergetic efﬁciency is affected by the critical temperature of the working ﬂuids and in the case of mixtures by their temperature glide in the condenser. The maximum efﬁciency ranges from 15 to 40% for heat source temperatures between 150 and 300 C, respectively. For temperatures above 170 C, the optimal ﬂuids are mixtures combined with supercritical operation. Compared to the subcritical ORC with R245fa, the achievable efﬁciency improvement ranges between 10 and 45%. Although smaller turbines can be used due to the lower size parameter values of supercritical mixtures, R245fa has lower volume ﬂow ratio, rotational speed and UA values. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Waste heat Organic Rankine Cycle Supercritical Natural refrigerants Zeotropic mixtures Efﬁciency increase

1. Introduction 1.1. Potential of the Organic Rankine Cycle for waste heat recovery Low and medium grade waste heat utilization for electricity production has attracted signiﬁcant interest as one way to alleviate the energy shortage and environmental pollution problems associated with excess CO2 and other air pollutants (NOx, SOx etc) emissions [1]. Most typical sources of abundant waste heat can be found in industrial processes of steel, cement, glass, oil and gas [2]. lez et al. [3] report that the heat rejected by various industrial Ve processes can surpass 50% of the total initial heat produced.

* Corresponding author. E-mail addresses: [email protected] (K. Braimakis), markus.preissinger@ uni-bayreuth.de (M. Preißinger), [email protected] (D. Brüggemann), [email protected] (S. Karellas), [email protected] (K. Panopoulos).

Additionally, remarkable amounts of waste heat are carried by exhaust gases that are rejected from internal combustion engines [4]. Campana et al. [2] have assessed the potential of electricity generation from waste heat in Europe and have estimated that a total of 21.6 TWhel can be produced on an annual basis, with savings amounting to 1.95 billion V and 8.1 million tonnes of Greenhouse Gas (GHG) emissions. Considering the above, it becomes evident that, apart from its positive environmental impact, waste heat recovery (WHR) for the production of electricity can lead to considerable economic beneﬁts for the relevant industries, by helping to reduce energy demands and subsequently allowing to decrease fuel consumption costs. The Organic Rankine Cycle (ORC) has been repeatedly proposed and extensively investigated as an appealing technology for WHRto-power applications [5e9]. Hajabdollahi et al. [6] modelled and optimized an ORC for diesel engine waste heat recovery and identiﬁed R123 and R245fa as the best working ﬂuid candidates from a thermo-economic standpoint. Quoilin et al. [7] developed a

http://dx.doi.org/10.1016/j.energy.2015.03.092 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

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K. Braimakis et al. / Energy xxx (2015) 1e13

Nomenclature A E_ h m_ n p P Q_ s SP T TIT U V_ VFR

heat exchanger surface area, m2 exergy ﬂow rate, kW speciﬁc enthalpy, kJ/kg mass ﬂow rate, kg/s rotational speed, rpm pressure, bar power, kW heat ﬂux, kW speciﬁc entropy, kJ/kgK size parameter of turbine, m temperature, C turbine inlet temperature, C overall heat transfer coefﬁcient, kW/K volume ﬂow rate, m3/s volume ﬂow ratio of expander outlet to inlet stream

Greek symbols D difference h efﬁciency Subscripts 0 ambient cond condenser crit critical cw cooling water el electric evap evaporator ex exergetic G generator

thermo-economic model for evaluating WHR-ORCs. By comparing a number of refrigerants under varying operational conditions, they stressed that the thermo-economic and the thermodynamic optimization of WHR-ORC systems may give different results. Wei et al. [8] underlined the importance of maximizing the utilization of the heat source for increasing the power output of the ORC. Dai et al. [9] compared the conventional wateresteam Rankine cycle with the ORC for low grade (145 C) heat sources. They concluded that an ORC is more efﬁcient, with R236ea exhibiting the highest exergetic efﬁciency among the working ﬂuids which they examined. Some of the ORC's primary advantages compared to the conventional steamewater Rankine cycle include its capability to operate at very low temperatures, reduced cost, smaller component size and simplicity of construction and operation [1,5,10]. 1.2. Working ﬂuids and efﬁciency improvement strategies There is a wide variety of organic ﬂuid candidates for ORC systems, including hydrocarbons, hydroﬂuorocarbons, hydrochloroﬂuorocarbons, perﬂuorocarbons and siloxanes [10]. Although many studies have focused on the selection of the most appropriate ones [1,11,12], no single ﬂuid has been identiﬁed as ultimately optimal for all ORCs. This is in part due to the variability of the characteristics (temperature proﬁle ranges, physicochemical properties etc.) of the several heat sources considered. Furthermore, it can be also attributed to the different cycle working conditions that are assumed in each case, as well as to the different indicators used by various researchers for evaluating the system performance [12].

gl gross heat HS in is lm m M net ORC out pump rec sat T th

temperature glide gross electricity heater heat source inlet isentropic logarithmic mean mechanical motor net electricity working ﬂuid of ORC outlet pump recuperator saturation turbine thermal

Abbreviations C3 propane C4 butane C5 pentane cC5 cyclopentane C6 hexane GHG greenhouse gas GWP global warming potential (relative to carbon dioxide) LMTD logarithmic mean temperature difference ODP ozone depletion potential (relative to R11) ORC Organic Rankine Cycle WHR Waste Heat Recovery

So far a number of refrigerants have already been banned or are to be phased out in the proximate future, in accordance with legislation (e.g. Montreal Protocol [13] and Kyoto Protocol [14]) aiming to restrict the use of high Ozone Depletion Potential (ODP) and Global Warming Potential (GWP) ﬂuids. The European Union through a series of regulations [15,16] aims to progressively decrease the production of certain ﬂuorinated gases (F-gases) by 80% of today's level until 2030. The result of the above policies is a shift of interest towards the use of low ODP and GWP natural refrigerants (such as butane, pentane, hexane etc.) as working ﬂuids. These refrigerants are available at low prices and are viewed as promising options concerning the overall system efﬁciency of the ORC. Meanwhile, a number of studies have suggested that the energetic and exergetic efﬁciency can be further improved when the working ﬂuid is pumped to supercritical pressures before it is heated to its maximum temperature [17e19]. The main concept behind the application of the supercritical ORC relies on the expected minimization of the exergy destruction losses during the heating of the supercritical working ﬂuid, which takes place under a variable temperature (contrary to the subcritical evaporation which occurs isothermally). Schuster et al. [17] showed that for a number of working ﬂuids, the supercritical ORC can lead to an increase of the thermal and overall system efﬁciency of waste heat applications to up to 8%. According to Vetter et al. [18], who performed thermodynamic simulations considering a large number of working ﬂuids, an increase in both thermal efﬁciency and net power output for low enthalpy (~150e170 C) processes is achieved under supercritical operation of the cycle. Mikielewicz and

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

K. Braimakis et al. / Energy xxx (2015) 1e13

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Mikielewicz [19] report that through the implementation of the supercritical ORC, an overall efﬁciency improvement of roughly 5% can be attained in micro cogeneration of heat and power (CHP) applications. Despite these potential efﬁciency beneﬁts, however, it should be noted that in supercritical conditions the necessary heat exchanger surface is generally larger [20], and thus the heat exchange equipment may be more costly and require rigorous design. Another possible improvement of the ORC is the replacement of pure substances with zeotropic mixtures as working ﬂuids [1,21e23]. The temperature glide of these mixtures during their evaporation and condensation permits a better matching of their temperature with the temperature of the heat source (evaporator) and the cooling medium (condenser). This, in turn, can help to reduce the irreversibility that occurs in these process steps of the ORC and increase the exergetic efﬁciency of the system [21,22,24]. Heberle et al. [21] examined the potential of R227ea/R245fa and isobutane/isopentane mixtures for low temperature geothermal applications. They estimated that the use of these zeotropic mixtures can lead to an increase of the exergetic efﬁciency from 4.3 to 15% compared to their most efﬁcient pure components. Liu et al. [22] explored the thermodynamic performance of a number of zeotropic mixtures. Like Heberle et al. [21], they emphasized the matching between the temperature glide of the working ﬂuid and the temperature change of the cooling medium during the condensation of the former as an optimization criterion for selecting the ideal concentration of the mixture components. Based on numerical simulations from Weith et al. [25], the achievable efﬁciency increase by using MM/MDM mixtures compared to pure hexamethyldisiloxane (MM) and octamethyltrisiloxane (MDM) is 1.3 and 3% for an electricity and a combined electricity and heat production scenario respectively in a biogas waste heat recovery plant. Meanwhile, the heat transfer area increase of the preheater and the evaporator for these mixtures was estimated to 0.9 and 11%. 1.3. Scope The present work has a dual purpose. Firstly, it aims to evaluate the performance of the WHR-ORC when using natural hydrocarbons as working ﬂuids compared to benchmark ﬂuid R245fa. The second goal is to investigate the potential increase of the cycle efﬁciency by using binary zeotropic mixtures consisting of these pure natural refrigerants. In both cases, the operation under subcritical and supercritical pressures is simulated by thermodynamically modelling the WHR-ORC system. The investigated cycle conﬁgurations are summarized schematically in Fig. 1. 2. Methodology and assumptions

Fig. 1. a) Supercritical ORC with pure ﬂuid b) subcritical ORC with zeotropic mixture c) Supercritical ORC with zeotropic mixture compared to standard subcritical ORC.

2.1. System description For the numerical simulations a generic waste heat source stream consisting of dry atmospheric air and a regenerative ORC are assumed. The speciﬁc state points of the thermodynamic cycle on a simple process diagram can be seen in Fig. 2. The saturated liquid refrigerant (state point 6) is pressurized with a pump (state point 1). A heat exchanger is used for transferring the energy content of the heat source to the working ﬂuid (state points 2e3). Depending on the maximum operational pressure of the cycle, the working ﬂuid at the turbine inlet (state point 3) is either subcritical vapour or at supercritical phase. Following the expansion process, the superheated ﬂuid stream (state point 4) ﬂows into the recuperator in order to make use of its energy content by preheating the sub-cooled liquid exiting the pump. In the present study the recuperator is only considered for dry ﬂuids (with a positive slope of the saturated vapour curve in the Tes

diagram). This is justiﬁed because in the case of pure wet ﬂuids, there is no or very little potential to recover heat by de-superheating the expanded vapour. Furthermore, for wet mixtures the recuperator would have an extended dual-phase heat transfer area while providing an insigniﬁcant increase of the temperature of the cold stream due to the temperature glide of the hot stream and the location of the pinch point at the cold side of the heat exchanger. After the recuperator (state point 5), the working ﬂuid is cooled down in the condenser by a stream of water and re-enters the pump as saturated liquid, repeating the cycle (state point 6) (Fig. 2). The simulations of the thermodynamic cycle and the calculations of all thermophysical properties were carried out with the AspenPlus™ software by using the PengeRobinson equation of state with BostoneMathias alpha function property method [26]. A steady state operation is assumed, while the heat and pressure losses through piping, ﬁttings and heat exchangers are neglected.

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

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K. Braimakis et al. / Energy xxx (2015) 1e13

Turbine

3

Generator G

Heater HSin

HSout

Heat source stream

2

4

E_ HS ¼ m_ HS hHS;in hHS;0 T0 sHS;in sHS;0

Recuperator

Cooling medium

Cwin

Cwout

hex ¼

hHS;in hHS;0 hex ¼ hth hHS;u hHS;in hHS;0 T0 sHS;in sHS;0

Fig. 2. Schematic process scheme of the WHR-ORC investigated.

2.2. Performance evaluation parameters The net electricity produced by the ORC system is equal to the difference between the gross electricity produced by the generator which is coupled to the turbine and the electricity consumed for pumping the working ﬂuid:

(1)

In the above equation the factors hm, hG and hM stand for the mechanical efﬁciency of the turbine and the efﬁciency of the generator and pump motor, respectively. The heat delivered from the heat source to the working ﬂuid in the heater is given by the equation:

Q_ ORC;in ¼ m_ HS hHS;in hHS;out ¼ m_ ORC ðh3 h2 Þ

(2)

In order to evaluate the exploitation degree of the waste heat, the heat source utilization efﬁciency hHS,u is deﬁned. It is equal to the actual heat recovered, Q_ ORC;in ; divided by the theoretical maximum amount of heat that could have been recovered from the heat source stream if it was cooled down to the ambient temperature:

hHS;u ¼

m_ HS

Q_ ORC;in hHS;in hHS;0

(3)

Two of the most commonly used performance evaluation parameters of thermodynamic cycles and ORCs are the thermal (ﬁrst law) and the exergetic (second law) efﬁciency. The thermal efﬁciency of the cycle is used to indicate the percentage of the heat input to the ORC that is converted to electric power:

hth ¼

Pel Q_ ORC;in

(6)

From the above equation it can be seen that the exergetic efﬁciency directly mirrors the net electric power produced by the system. Combining equations (2)e(6), another expression of the exergetic efﬁciency can be given by:

6

Ppump Pel;net ¼ Pel;gross Pel;pump ¼ hm hG Pexp hМ ðh h6 Þ ¼ m_ ORC hm hG ðh3 h4 Þ 1 hМ

Pel E_

HS

Condenser

Pump

(5)

The subscript 0 refers to the conditions of the environment (T0 ¼ 15 C, p0 ¼ 1 bar). The exergetic efﬁciency of the WHR-ORC is deﬁned as the ratio of the actual power produced by the cycle to the amount of the exergy of the heat source that ﬂows into the system:

5

1

deﬁned as the theoretical (according to the second law of thermodynamics) maximum work that could be produced if the system is brought into equilibrium with its surroundings. In the case of a heat source consisting of a hot ﬂuid stream, its exergy rate E_ HS is given by the expression:

(4)

The thermal efﬁciency is an indicator that takes into account solely the ﬁrst law of thermodynamics (energy balance), without considering the inherent qualitative difference between heat and mechanical power. The exergy of a thermodynamic system is

(7)

According to the above equation, for any heat source stream of a given quality (enthalpy and entropy), the exergetic efﬁciency of the WHR-ORC system is the product of two factors. The ﬁrst one is the thermal efﬁciency of the ORC, which is intrinsic of the thermophysical properties and the operational points (pressures, temperatures) of the working ﬂuid within the cycle. The second one is the heat source utilization efﬁciency and reﬂects the thermal transfer between the working ﬂuid and the heat source ﬂuid stream. Therefore, the optimization of the exergetic efﬁciency of the cycle for a given heat source stream is based on the maximization of the value of the product hthhHS,u. Consequently, both the thermal and heat source utilization efﬁciency parameters are equally important when designing WHR-ORC systems. Thermodynamic efﬁciency (and not necessarily economic) optimization of waste heat recovery schemes is achieved when the net power output (and the concurrent energy savings) is maximized [5]. However, the maximization of the exergetic efﬁciency does not necessarily lead to optimized cost-competitiveness, since it may involve excessively or impractically large and costly heat exchanger surfaces or other equipment (e.g. turbine) and consequently much higher capital costs that can possibly offset the actual beneﬁts derived from the increased electricity generation. However, the exergetic efﬁciency remains a useful tool for the preliminary assessment of waste heat recovery processes, allowing for parametric evaluations and screening of working ﬂuid candidates. Apart from the exergetic efﬁciency, which is used to evaluate the system from a thermodynamic point of view, other parameters provide more insight into the technical feasibility and economic competitiveness of the WHR-ORC. These are the rotational speed n (which is in this study calculated assuming a speciﬁc turbine speed of 0.1 s1, considered as optimal according to Astolﬁ et al. [27]), the size parameter SP of the turbine, the volume ﬂow ratio VFR of the inlet to the outlet stream of the turbine and the UA values (overall heat transfer coefﬁcient U multiplied by the heat exchange surface A) in the heater, the condenser and the recuperator. These parameters are described by the following equations:

n¼

Dh0:75 T;is qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 10 V_ T;out

(8)

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

K. Braimakis et al. / Energy xxx (2015) 1e13

SP ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ V_ T;out Dh0:25 T;is

VFR ¼

V_ T;out V_

(9)

(10)

T;in

UA ¼

Q_ DTlm

(11)

In the above equations DhT,is is the isentropic speciﬁc enthalpy drop in the turbine, V_ T;in and V_ T;out are the volume ﬂow rates of the working ﬂuid at the turbine inlet and outlet, respectively, Q_ is the heat ﬂux of the heat exchanger and DTlm is the logarithmic mean temperature difference (LMTD) between the heat exchange ﬂuid streams. The ﬁrst three parameters concern the operational applicability of the turbine and are related to its cost. Extremely high rotor speeds may result in impossible or expensive turbine conﬁgurations (involving magnetic bearings for the turbine shaft), while increased VFR and SP values are associated with larger turbine sizes and technical complexity. More speciﬁcally, the size parameter, introduced by Macchi and Perdichizzi [28] as a key efﬁciency optimization parameter for turbines operating with nonconventional ﬂuids, inﬂuences the turbine's actual dimensions (such as blade height). Furthermore, the VFR is inversely correlated with the isentropic efﬁciency of the expansion. It has been reported that for achieving, for instance, isentropic efﬁciencies higher than 80%, the VFR value must be lower than 50 [29]. The UA value of a heat exchange process is roughly indicating the heat transfer equipment required. A high UA value means that more heat needs to be transferred between the heat exchange streams for the desired temperature increase/decrease to be accomplished, with implications on the total surface of the heat exchanger and its cost. 2.3. Boundary conditions 2.3.1. Heat source The heat source stream inlet temperature in the heater is varied from 150 to 300 C in steps of 10 K. Since it is modelled as dry atmospheric air, there are no practical limitations on the minimum temperature of the heat source stream at the heater outlet (due to condensation or other thermo-chemical phenomena). Note that this is not always the case for waste heat recovery applications. For example, when the heat source consists of ﬂue gases or geothermal water, it often cannot be cooled below a certain temperature to avoid problems such as corrosion of the heat exchange surfaces and other equipment. The characteristics of the heat source stream of the present work are summarized in Table 1. 2.3.2. Working ﬂuids The set of the examined pure working ﬂuids and their critical temperatures and pressures is given in Table 2. Additional information included is the ODP, the GWP and the ASHRAE Safety Group for each ﬂuid [30]. The working ﬂuids include the natural refrigerants butane, cyclopentane, hexane, pentane and propane

5

(Fig. 3), along with R245fa, which is used as a benchmark ﬂuid. Heptane, octane etc. are not examined due to their signiﬁcantly higher critical temperatures. Methane, on the other hand, was excluded from the study because of its extremely low critical temperature (83.59 C) which results in an entirely different cycle conﬁguration (the condensation is replaced by supercritical cooling). R245fa is selected for benchmarking due to its reported favourable environmental properties and good thermodynamic performance in low/mid temperature ORC applications [3,5,11]. The pure working ﬂuids of Table 2 result in 10 possible binary mixture combinations, summarized in Table 3. For the present study, the molar fraction of each of the binary mixtures is varied from 10/90 to 90/10 in steps of 10%. As a result, a total of 95 working ﬂuids (5 pure and 90 mixtures) are simulated. 2.3.3. ORC One of the main parameters of ORC systems is the pinch point of the heat exchangers, deﬁned as the minimum temperature difference between the hot and cold ﬂuid streams in the heater, the condenser and the recuperator. Smaller pinch point values lead to higher heat exchange efﬁciency, since the amount of heat transferred increases. However, due to the limited LMTD a larger surface may be required (equation (11)). The isentropic efﬁciencies of the pump and the turbine indicate the deviation of the actual compression/expansion that takes place from the theoretical isentropic process. In the case of the WHR-ORC investigated, they are given by the equations:

his;pump ¼

his;T ¼

h1;is h6 h1 h6

h3 h4 h3 h4;is

(12)

(13)

For each value of the heat source inlet temperature, the ORC is simulated for every working ﬂuid by varying its high pressure level within a speciﬁed range. For the dry ﬂuids the maximum subcritical operating pressure corresponds to the point of the maximum entropy smax of the saturated vapour curve of the Tes diagram. For the wet ﬂuids, it is set to 90% of their critical pressure. For the supercritical ORC, the maximum pressure is set to 130% of pcrit for both dry and wet ﬂuids. The above assumptions are represented graphically in Fig. 4. The limitations on the pressure range of the system are based on two reasons. Firstly, it has been shown that near the critical point of the working ﬂuid its thermophysical properties become unstable [20,33]. Secondly, an upper limit to the maximum operating pressure of the ORC is posed in order to maintain applicable pressure ratio values. For the subcritical dry ﬂuids, the turbine inlet temperature (TIT) is equal to the temperature of the saturated vapour for each operating pressure. In all other cases, the working ﬂuids are superheated until their entropy is equal to smax (as deﬁned in Fig. 4 for dry and wet ﬂuids) [23]. This superheating is necessary to ensure that no liquid phase occurs at the outlet of the turbine, an effect highly detrimental to its operation. The boundary conditions chosen for the simulations are summarized in Table 4. 3. Results and discussion

Table 1 Heat source characteristics. Mass ﬂow rate Temperature Pressure Composition (mole fractions)

3.1. Optimization of exergetic efﬁciency 5 kg/s 150e300 C 2 bar 78% N2, 21% O2, 1% Ar

The maximum exergetic efﬁciency that can be attained by using each one of the working ﬂuids for a heat source temperature between 150 and 300 C is illustrated in Fig. 5. In Fig. 5 and all

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

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K. Braimakis et al. / Energy xxx (2015) 1e13

Table 2 Properties of the pure organic ﬂuids that are examined.

Butane Cyclopentane Hexane Pentane Propane R245fa

pcrit (bar) [26]

Tcrit ( C) [26]

ODP [31]

GWP [31]

ASHRAE Safety Group [30]

Molecular weight (kg/kmol) [32]

37.35 45.77 30.05 33.42 41.95 35.72

151.98 238.54 234.67 196.55 96.74 153.01

0 0 0 0 0 0

3.3 <25 3 <25 3.3 950e1020

A3 e e A3 A3 A1

58.1 70.1 86.2 72.1 44.1 134.1

Fig. 3. Tes saturation curves of the natural refrigerants investigated (as calculated by Aspen Plus™ [26]).

Table 3 Properties of binary mixtures at 50/50 molar concentration (data from Aspen Plus™ [26]).

Butaneecyclopentane Butaneehexane Butaneepentane Butaneepropane Cyclopentaneehexane Cyclopentaneepentane Cyclopentaneepropane Hexaneepentane Hexaneepropane Pentaneepropane

pcrit (bar)

Tcrit ( C)

39.41 35.97 32.43 37.64 31.48 33.94 52.46 28.38 43.23 41.81

197.39 198.72 168.33 123.18 223.85 204.89 184.17 207.92 192.01 158.44

subsequent ﬁgures, the abbreviations C3, C4, C5, cC5 and C6 (signifying the number of carbon atoms in the molecule) stand for propane, butane, pentane, cyclopentane and hexane, respectively. In the case of zeotropic working ﬂuids, the plotted exergetic

efﬁciency corresponds to the mixture component ratio of the ﬂuid that maximizes the performance of the cycle. As can be observed from Fig. 5, the working ﬂuid selection for optimizing the WHR-ORC largely depends on the temperature of the waste heat stream. Concerning the supercritical ORC, some refrigerants can be used only for high heat source temperature ranges, depending on their Tcrit and the pinch point value in the heater. In general, the exergetic efﬁciency initially tends to increase along with THS. Beyond a certain heat source temperature, however, it reaches a peak value and then starts to slightly decrease to lower values. Reasons for this behaviour are described in the following. As the heat source temperature increases, so does the mass ﬂow rate of the working ﬂuid, until the pinch point in the heater shifts from the inlet of the evaporator (or close to the point of the phase transition for the supercritical ORC) to the cold side of the preheater. This leads to an increased heat source utilization efﬁciency which is almost independent of the operating pressure of the cycle. For the lower heat source temperature range the operating pressure (and in turn the turbine inlet temperature) of the working ﬂuids has an intermediate optimal value. This happens because of the competing effects of the increasing hth and decreasing hHS,u on the overall efﬁciency of the system at higher operating pressures. The optimal operating pressure tends to increase together with the THS, with a subsequent increase of the exergetic efﬁciency of the cycle. For higher temperatures, on the other hand, the optimal operating pressure and temperature (and so the thermal efﬁciency of the cycle) stop increasing and adopt their maximum values (as deﬁned in Table 4). This happens because due to the relatively pressure-independent heat source utilization efﬁciency, the ﬁrst law efﬁciency becomes the determining factor for maximizing hex. Meanwhile, for increasing heat source temperatures, the growth rate of the heat source utilization efﬁciency is not sufﬁcient to compensate for the decrease rate of the factor (hHS,in hHS,0)/ [(hHS,in hHS,0) T0(sHS,in sHS,0)], which is due to the exergy increase of the heat source stream. This ultimately leads to the observed slight decline in the overall system performance. The result is the existence of an “optimal” heat source temperature for

Fig. 4. Upper limits of the maximum cycle operation pressure investigated and deﬁnition of the turbine inlet temperature TIT for dry and wet ﬂuids.

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

K. Braimakis et al. / Energy xxx (2015) 1e13 Table 4 ORC simulation parameters. Efﬁciencies Turbine isentropic efﬁciency (his,T) Pump isentropic efﬁciency (his,pump) Electromechanical efﬁciency (hmhG) Pump motor efﬁciency (hM) Heat exchangers Pinch point heater Pinch point condenser Pinch point recuperator Cooling water inlet temperature Cooling water temperature increase Maximum operating pressures Subcritical ORC Supercritical ORC Maximum operating temperatures Subcritical ORC

Supercritical ORC

75% 80% 95% 85% 35 10 10 20 15

K K K C K

Dry ﬂuids: p(smax) Wet ﬂuids: 90% pcrit 130% of pcrit Dry ﬂuids: Saturation temperature at operating pressure Wet ﬂuids: T(smax) T(smax)

each working ﬂuid beyond which the exergetic efﬁciency either decreases or increases at a considerably low rate. Among the pure ﬂuids, for the subcritical (Fig. 5a)) and supercritical (Fig. 5c)) ORC, propane is mostly favourable at low temperatures (below 180 C). In fact, propane is the only pure ﬂuid that can be used for supercritical operation in this temperature range. Butane and pentane exhibit the highest exergetic efﬁciency for moderate and higher heat source temperature levels, respectively. Hexane and cyclopentane tend to perform better for even higher

7

temperatures (beyond 300 C) that are not included in this study. R245fa is moderately efﬁcient compared to the pure ﬂuids and its efﬁciency curve strongly resembles the one of butane. As far as the subcritical mixtures are concerned (Fig. 5b)), butaneepropane, butaneecyclopentane and pentaneepropane are more efﬁcient for the lower (<200 C) heat source temperature range. Butaneecyclopentane mixtures also present a high performance for medium to high temperatures along with butaneepentane and butaneehexane mixtures. Despite being less C, efﬁcient below 270 cyclopentaneepentane, cyclopentaneehexane and hexaneepentane mixtures are becoming remarkably efﬁcient close to 300 C. However, their efﬁciency is still lower than the one achieved by butaneecyclopentane. The situation is not much different for the supercritical ORC (Fig. 5d)). Butaneepropane and pentaneepropane mixtures are preferable below 200 C, while butaneehexane, butaneepentane and butaneecyclopentane mixtures are more attractive when the waste heat stream is above 220 C. Cyclopentaneepentane, cyclopentaneehexane and hexaneepentane ﬂuids tend to optimize the WHR-ORC for heat source temperatures of at least equal to 300 C. Compared to natural refrigerant mixtures, R245fa is more competitive within the temperature range between 200 and 230 C, where its exergetic efﬁciency reaches its maximum value. From the above results, it can be established that there is a strong correlation between the critical temperature of each working ﬂuid and the heat source temperature under which its performance is optimized (and the pinch point shift occurs). Propane, for example, having the lowest Tcrit, is more efﬁcient for low waste heat temperatures. Hexane and cyclopentane, on the other hand, tend to perform better in higher heat source temperature levels close or

Fig. 5. Exergetic efﬁciency of the WHR-ORC as a function of the temperature of the heat source for a) pure ﬂuids, subcritical ORC, b) mixtures (optimal component ratio), subcritical ORC, c) pure ﬂuids, supercritical ORC and d) mixtures (optimal component ratio), supercritical ORC.

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K. Braimakis et al. / Energy xxx (2015) 1e13

even beyond 300 C. Working ﬂuids having intermediate critical temperatures are generally favourable from 200 to 250 C. Furthermore, the efﬁciency curves of R245fa (Tcrit ¼ 153.01 C) and butane (Tcrit ¼ 151.98 C) as well as those of hexane (Tcrit ¼ 234.67 C) and cyclopentane (Tcrit ¼ 238.54 C) are almost identical. The same observation is also valid for the binary mixtures (for example butaneepropane mixtures are most efﬁcient close to 150e200 C and cyclopentaneehexane close to 300 C). This can be attributed to the fact that for ﬂuids with high Tcrit the shifting of the pinch point in the heater occurs at higher heat source temperatures and, as a result, the exergetic efﬁciency can reach even higher values before starting to plateau. The interdependence between the optimum temperature for maximizing hex and the Tcrit of the working ﬂuids can also explain the way in which the optimal composition of the binary mixtures varies in accordance with the heat source temperature, when the critical temperatures of their parent pure components differ signiﬁcantly. For example, if the subcritical mixture of cyclopentane (Tcrit ¼ 238.54 C) and propane (Tcrit ¼ 96.74 C) is considered, the optimal composition for THS ¼ 150 C is 10/90, while for 300 C it is 90/10. A similar effect can be observed for butaneehexane (Fig. 6) and also hexaneepropane and pentaneepropane for the subcritical and the supercritical ORC. In the above cases, the heat source temperature under which the optimal composition changes from favouring one component to another depends on the optimal heat source temperature of each ﬂuid. Note that the change of the optimal composition of mixtures is often not gradual, since its value can considerably vary even within a 10 K increment of the THS. On the other hand, when the difference between Tcrit of the pure constituents of a mixture is not very high, the optimal component ratio adopts intermediate values and its variation is smoother (as is the case for cyclopentaneehexane and butaneepentane in Fig. 6). Despite the described trends, it should be stated that it is difﬁcult to draw a general rule which precisely predicts the optimal component ratio of binary mixtures, as can be seen from Fig. 6 and Table 5. This is because the performance of the system is also inﬂuenced by the exergy destruction rate in the condenser, which depends on the temperature glide of the working ﬂuid during its phase change. When the temperature glide approaches the temperature difference of the cooling water required for the condensation of the working ﬂuid (and thus jDΤcw DΤgl,ORCj/0), the irreversibility is minimized to the beneﬁt of the exergetic efﬁciency. The variation of the jDΤcw DΤgl,ORCj value in the condenser depends on the total DΤ (corresponding to both the desuperheating and the condensation of the working ﬂuid) of the cooling water (set in this study to 15 K), on the slope of the isobaric condensation curve of the mixture (directly related to its component ratio) but also on the temperature and the vapour fraction of the hot stream at the outlet of the recuperator if it is in operation. Depending on the above conditions, there can be one, two or even three local minima of the absolute difference of the temperature glide of the working ﬂuid and the DT of the cooling water during the condensation. The temperature glide of mixtures becomes generally higher when the overall deviation between the Tes saturation curves (Fig. 3) of their pure components increases and is in principle positively correlated with the difference between the critical temperatures of their parent components. When the saturation curves of two dry pure ﬂuids are close to one another, the temperature glide is smaller than 15 K and the jDΤcw DΤgl,ORCj value has one minimum, usually between 40/60 and 60/40 (line a) in Fig. 7). If their saturation curves are further apart, the temperature glide may exceed 15 K and there will usually be two local minima of jDΤcw DΤgl,ORCj for the relative concentrations where the temperature glide of the working ﬂuid is equal to the temperature

change of the cooling water, usually around 20/80 and 80/20 (line b) in Fig. 7). For propane mixtures, a third local minimum occurs as the mixture turns from dry to wet, usually when the composition of propane is around 60e70% (line c) in Fig. 7) and the recuperator stops operating, resulting in the increase of the temperature glide of the working ﬂuid and thus to an increase of the jDΤcw DΤgl,ORCj given that, for these mixtures, DΤgl,ORC > DΤcw. From the above considerations, it becomes clear that the inﬂuence of both the critical temperature and the irreversibility in the condenser should be examined when searching for the optimal component ratio of zeotropic mixtures. While it is sometimes possible to alter the mixture composition so that these two effects do not contradict each other, this is not always the case, since the minimization of the jDΤcw DΤgl,ORCj does not necessarily coincide with favourable Tcrit values and the maximization of the exergetic efﬁciency. 3.2. Analysis of efﬁciency improvement strategies In Fig. 8 the efﬁciency increase potential of the supercritical ORC as a percentage of the subcritical cycle exergetic efﬁciency is plotted for a) pure ﬂuids and b) binary mixtures. In the case of pure ﬂuids, the supercritical ORC is either impossible to realize or procures a negligible beneﬁt for high Tcrit ﬂuids such as cyclopentane, hexane and pentane. For butane and propane, however, an efﬁciency increase between 12 and 18% can be achieved when the heat source temperature is higher than 250 and 200 C, respectively. For most of the zeotropic ﬂuids the supercritical ORC can be beneﬁcial for an interval of intermediate heat source temperatures whose range greatly depends on the type of the binary mixture. For most of the cases the expected exergetic efﬁciency increase of the cycle is not higher than 10%. Butaneepropane mixtures constitute an exception, with an efﬁciency increase approaching 14%. Similarly to the case of the pure ﬂuids, for high critical temperature mixtures such as cyclopentaneehexane, cyclopentaneepentane and hexaneepentane, the potential of enhancing the performance of the cycle through supercritical operation is insigniﬁcant. From the above discussion it can be concluded that the use of the supercritical ORC is more beneﬁcial when the critical temperature of the working ﬂuid is substantially lower than the temperature of the heat source. In Fig. 9 the effect of replacing pure ﬂuids with binary mixtures as working ﬂuids on the performance of the system is plotted for a) subcritical and b) supercritical pressures. For the subcritical ORC, the potential of the second law efﬁciency enhancement by using zeotropic mixtures is substantially dependent on the heat source temperature. As illustrated in Fig. 9, the exergetic efﬁciency increase of each mixture compared to the highest exergy of its most efﬁcient pure component at a given THS can vary widely from zero to even 35%. For all of the mixtures there are two peaks of the exergetic efﬁciency increase, one at 150 C and a second at a heat source temperature between 180 and 300 C. In general, the greatest beneﬁts for the performance of the subcritical WHR-ORC can be attained for lower to moderate heat source temperatures. In contrast with the subcritical ORC, there is one temperature under which the potential efﬁciency increase is maximized for every supercritical zeotropic mixture. This temperature can vary from 200 C (butaneepropane) to 300 C (cyclopentaneepentane). However, the biggest efﬁciency improvement can be achieved for moderate to high THS values and can exceed 60% (as is the case of cyclopentaneepropane at 270 C). To summarize, the supercritical ORC for the ﬂuids examined can be justiﬁed only for ﬂuids of a relatively low critical temperature at higher (pure ﬂuids) and moderate (ﬂuid mixtures) heat source

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Fig. 6. The variation of the optimal composition of each mixture as a function of the heat source temperature for a) Subcritical and b) Supercritical ORC.

temperatures. Nonetheless, the use of mixtures instead of pure ﬂuids can have a signiﬁcantly positive effect on the cycle performance under speciﬁc waste heat temperature ranges, especially when combined with the supercritical operation. 3.3. Overview In Fig. 10 the maximum exergetic efﬁciency that can be achieved by the WHR-ORC under the four different investigated modes of operation and for the benchmark ﬂuid is plotted as a function of the temperature of the heat source. While for the two lowest waste heat temperature levels the subcritical mixture ﬂuids exhibit the best performance, for THS values higher than 170 C the second law efﬁciency of the system is always maximized when a zeotropic mixture is used in combination with the supercritical ORC. In fact,

the use of zeotropic mixtures instead of pure refrigerants as working ﬂuids can improve the exergetic efﬁciency of the system for the whole range of the investigated heat source temperatures. Moreover, the beneﬁts of implementing supercritical operation pressures are mainly incremental in the case of pure ﬂuids, while they become more important for the mixtures. Compared to R245fa, the use of natural refrigerants or their binary mixtures (under sub- or supercritical pressures), can actually lead to a performance improvement especially near the lower and higher ends of the THS range considered in the present study. Between roughly 200 C and 240 C the exergetic efﬁciency of all modes and of the benchmark ﬂuid converges to around 30%. Table 6 summarizes the exergetic efﬁciency as well as the technical evaluation parameters of the optimal ﬂuid together with those corresponding to the optimal subcritical operation pressure

Table 5 The variation of the optimal composition of each mixture as a function of the heat source temperature for subcritical (upper row) and supercritical (lower row) ORC. THS ( C)

C4/cC5

C4/C6

C4/C5

C4/C3

cC5/C6

cC5/C5

cC5/C3

C6/C5

C6/C3

C5/C3

150

60/40 e 60/40 e 60/40 e 60/40 e 70/30 e 80/20 e 90/10 e 90/10 e 90/10 90/10 80/20 90/10 70/30 90/10 70/30 90/10 60/40 90/10 50/50 90/10 30/70 90/10 20/80 90/10

80/20 e 80/20 e 80/20 e 90/10 e 90/10 e 90/10 e 90/10 e 90/10 e 90/10 90/10 90/10 90/10 80/20 90/10 80/20 90/10 70/30 90/10 10/90 90/10 10/90 90/10 10/90 90/10

60/40 e 60/40 e 60/40 e 60/40 e 60/40 90/10 70/30 90/10 90/10 90/10 80/20 90/10 70/30 80/20 60/40 80/20 50/50 80/20 40/60 80/20 20/80 80/20 20/80 80/20 10/90 80/20 10/90 80/20

30/70 10/90 30/70 10/90 30/70 10/90 30/70 10/90 30/70 30/70 30/70 30/70 90/10 30/70 90/10 30/70 90/10 80/20 90/10 80/20 90/10 80/20 90/10 80/20 90/10 80/20 90/10 80/20 90/10 80/20 90/10 80/20

50/50 e 40/60 e 50/50 e 40/60 e 40/60 e 40/60 e 40/60 e 40/60 e 40/60 e 30/70 e 40/60 e 30/70 e 40/60 e 20/80 e 40/60 e 60/40 e

40/60 e 40/60 e 40/60 e 20/80 e 20/80 e 10/90 e 10/90 e 10/90 e 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 30/70 10/90 40/60 10/90 60/40 10/90

10/90 e 10/90 e 10/90 e 10/90 e 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 20/80 10/90 20/80 10/90 30/70 10/90 30/70 10/90 30/70 10/90 80/20 10/90 80/20 10/90 90/10 10/90

50/50 e 50/50 e 40/60 e 40/60 e 40/60 e 40/60 e 40/60 e 30/70 e 30/70 e 30/70 e 10/90 e 10/90 e 10/90 e 20/80 e 30/70 e 40/60 e

10/90 e 10/90 e 10/90 e 10/90 e 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 10/90 20/80 10/90 20/80 10/90 20/80 10/90 20/80 10/90 90/10 10/90 90/10 10/90 90/10 10/90

10/90 e 10/90 e 10/90 e 10/90 e 10/90 10/90 20/80 10/90 20/80 10/90 20/80 10/90 20/80 20/80 90/10 20/80 90/10 20/80 90/10 20/80 90/10 20/80 90/10 20/80 90/10 20/80 90/10 20/80

160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

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Fig. 7. Qualitative illustration of the jDΤcw DΤgl,ORCj difference as a function of the component ratio of the mixture for a) dry ﬂuids of close Tes saturation curves, b) dry ﬂuids of distant Tes saturation curves, c) wet ﬂuids.

for R245fa under each heat source temperature. The relative difference of the hex, VFR, n, SP and UA values in the heat exchangers between the optimal and the benchmark ﬂuid is plotted in Fig. 11. As far as the exergetic efﬁciency is concerned (Fig. 11a)), the greatest increase is estimated to occur for heat source temperatures

from 270 to 300 C, reaching a maximum of 45%. Another area of potential performance improvement is within the lower temperature range between 150 and 190 C (around 30%). The exergetic efﬁciency increase is lowest around 220 C at about 10%. The VFR difference between the optimal ﬂuids and R245fa (Fig. 11b)) is relatively stable until 220 C, where it is always below 25%. At and above this THS it grows very rapidly, reaching the value of 500% for the heat source temperature of 300 C. The calculated increase in the VFR difference occurs because the high pressure level and therefore the pressure ratio of the supercritical working ﬂuids keep increasing along with the heat source temperature, whereas for the subcritical R245fa it assumes its maximum value when THS ¼ 200 C. As shown in Table 6, the VFR values for the optimal working ﬂuids surpass the limit of 50 at around 270 C and, in this case, special care has to be taken for the design of the turbine in order to achieve the isentropic efﬁciency of 75% which is assumed in this study. R245fa has consistently a much lower rotational speed. This is an expected result as can be derived from equation (8). The optimal ﬂuids operate mostly under supercritical conditions, which result in a greater enthalpy drop in the turbine due to the increasing pressure ratio and turbine inlet temperature. Moreover, because of the increasing speciﬁc enthalpy difference between state points 3 and 2 of the supercritical ORC (Fig. 2), the mass ﬂow rate of the optimal working ﬂuids increases at a smaller rate than in the case of R245fa. Having a maximum of 177% when THS is 170 C, the relative difference of the rotational speed steadily drops to lower values at

Fig. 8. Relative difference of the maximum exergetic efﬁciency of the supercritical compared to the subcritical ORC for a) pure ﬂuids and b) mixtures (optimal component ratio) as a function of the heat source temperature.

Fig. 9. Relative difference of the maximum exergetic efﬁciency of the binary mixtures (optimal component ratio) compared to their most efﬁcient pure component for a) subcritical and b) supercritical ORC.

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Fig. 10. Overview of the maximum exergetic efﬁciency of the WHR-ORC for each one of the operation modes investigated as a function of the heat source temperature. In each case the optimal working ﬂuid is identiﬁed.

around 120% as the waste heat temperature increases. This decline can be explained by the decreasing value of the low pressure level of the ORC and thus the decline of the mass density of the working ﬂuid at the turbine outlet as the critical temperature of the optimal working ﬂuid increases, in accordance with the discussion made in Section 3.1. Because of the signiﬁcantly high rotational speeds (which do never drop below 60,000 rpm), associated with using supercritical zeotropic mixtures, it is expected that high speed turbines would be required for these working ﬂuids. Furthermore, costly electromagnetic bearings would be necessary for the operation of the turbine shaft. Note that the values for the rotational speed were calculated assuming an optimal speciﬁc speed of 0.1 s1 [27]. Consequently, if the speed of the turbine for the supercritical ﬂuid mixtures is to be reduced, it would operate under non-optimal conditions, with an anticipated decrease of its isentropic efﬁciency which would be different from the ﬁxed value assumed in this study. Since the SP is inversely related to the rotational speed of the turbine, R245fa exhibits high size parameter values for most of the

heat source temperatures investigated. This means that the actual dimensions of the turbine are expected to be larger, thus increasing its design complexity. The optimal ﬂuids selected for the WHR-ORC are associated with substantially higher UA values in the heat exchangers, especially in the condenser and the recuperator. This can be explained by the non-isothermal heat transfer of these ﬂuids during their supercritical heating and their condensation which results in lower LMTD values. Note that in some cases, such as for the benchmark ﬂuid when the heat source temperature is at 150 C, the temperature increase of the cold stream in the recuperator is insigniﬁcant (about 2 K) and therefore the heat duty and the UA value adopt very low values. Of course, the required heat transfer surface is not necessarily reﬂected by the UA values due to the variability of the overall heat transfer coefﬁcient for different working ﬂuids. For this reason, it is important that the UA values are only interpreted as preliminary indicators of the heat transfer intensity, since they cannot provide conclusive information. Taking into account the above considerations, despite the appealing theoretical performance increase of the zeotropic ﬂuids

Table 6 Comparison of the exergetic efﬁciency and the technical evaluation parameters between the optimal ﬂuid and the benchmark ﬂuid (R245fa) for each heat source temperature.

hex (%)

UAevap (kW/m2) UAcond (kW/m2) UArec (kW/m2)

VFR

SP (m)

N (rpm)

THS ( C) Optimal ﬂuid

Optimal Bench. Optimal Bench. Optimal Bench. Optimal Bench. Optimal Bench. Optimal Bench. Optimal Bench.

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

15.53 17.53 20.82 23.53 25.91 27.68 29.47 30.50 31.94 33.99 35.65 36.72 37.79 38.57 39.14 39.77

ButaneeCyclopentane (60/40)-Sub ButaneePropane (30/70)-Sub ButaneePropane (20/80)-Super ButaneePropane (30/70)-Super ButaneePropane (30/70)-Super ButaneePropane (40/60)-Super ButaneePropane (60/40)-Super ButaneePropane (60/40)-Super ButaneeHexane (90/10)-Super ButaneeHexane (90/10)-Super ButaneeCyclopentane (80/20)-Super ButaneeCyclopentane (70/30)-Super ButaneeCyclopentane (70/30)-Super ButaneeCyclopentane (60/40)-Super ButaneeCyclopentane (50/50)-Super ButaneeCyclopentane (30/70)-Super

11.93 13.91 15.84 17.90 20.03 22.44 25.67 27.80 28.76 29.05 28.86 28.61 28.35 28.10 27.83 27.57

5.26 7.06 9.30 10.82 13.11 14.24 15.03 16.62 14.79 17.03 18.04 19.02 20.41 21.08 21.82 21.89

4.78 5.44 6.11 6.97 7.90 9.13 11.52 13.85 15.27 15.87 15.84 15.71 15.62 15.60 15.58 15.58

20.48 27.62 30.50 37.76 43.29 46.68 45.80 51.45 44.95 49.82 57.09 59.25 65.16 65.16 62.77 58.47

13.87 16.00 17.78 20.37 22.61 24.90 29.01 34.31 38.49 42.11 44.90 47.83 50.79 53.70 56.57 59.47

1.84 0.00 0.00 0.00 0.00 58.12 3.34 3.71 7.07 7.69 6.65 8.14 8.93 10.15 10.76 10.61

0.29 0.58 0.92 1.31 1.76 2.27 2.82 3.33 3.73 4.08 4.36 4.64 4.91 5.20 5.48 5.75

3.12 3.51 4.51 5.98 7.46 8.90 11.10 11.32 18.37 24.85 26.71 34.34 35.10 41.27 49.16 62.38

2.84 3.36 4.07 4.85 6.06 8.05 10.35 10.37 10.36 10.38 10.36 10.37 10.38 10.38 10.37 10.38

0.0240 0.0142 0.0139 0.0154 0.0162 0.0177 0.0195 0.0206 0.0260 0.0270 0.0286 0.0306 0.0320 0.0343 0.0365 0.0411

0.0239 54,517 34,233 0.0248 92,545 35,501 0.0254 103,059 37,123 0.0265 98,173 37,563 0.0272 98,334 38,781 0.0279 92,878 40,266 0.0295 88,652 39,578 0.0321 84,087 36,439 0.0340 74,057 34,391 0.0355 73,396 32,926 0.0367 70,942 31,828 0.0379 69,441 30,864 0.0390 66,442 29,981 0.0401 63,838 29,160 0.0412 61,497 28,408 0.0422 56,852 27,708

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Fig. 11. Relative difference between a) the exergetic efﬁciency, b) the volume ﬂow ratio, c) the rotational speed and size parameter and d) the UA values of the heat exchangers between the optimal ﬂuid (maximum hex) and the benchmark ﬂuid R245fa.

combined with the supercritical ORC, it is not possible to deﬁnitively decide on their practical superiority in real WHR-ORC systems. This is in part because of their exceptionally high turbine rotational speeds and volume ﬂow ratios (mainly for higher heat source temperatures), which may induce efﬁciency penalties. The use of supercritical zeotropic ﬂuids is also associated with additional economic challenges, due to the expected cost of electromagnetic bearings and heat exchangers. 4. Conclusions In this study, ﬁve natural refrigerants and their binary mixtures were evaluated as working ﬂuids for a waste heat recovery Organic Rankine Cycle, considering subcritical and supercritical operation. A strong positive correlation between the optimal heat source temperature of the working ﬂuids (pure and mixtures) and their critical temperature was observed. Another key parameter affecting the performance of mixtures is their temperature glide and its relation to the temperature change of the cooling water during their condensation. Their optimal component ratio for maximizing the exergetic efﬁciency thus depends on the combined inﬂuence of these two effects. Compared to the subcritical ORC, the supercritical ORC can lead to improved exergetic efﬁciency mainly for low critical temperature ﬂuids for medium and high waste heat temperatures. The maximum efﬁciency increase was estimated equal to 18% in the case of propane. The substitution of pure ﬂuids by zeotropic binary mixtures has the potential to greatly enhance the performance of the cycle for both subcritical and supercritical conditions. The

estimated increase of the second law efﬁciency by using mixtures instead of their most efﬁcient pure component depends on the heat source temperature and, in the case of supercritical cyclopentaneepropane mixtures, it surpasses 60%. Among all the investigated working ﬂuids, the supercritical mixtures of butaneepropane, butaneehexane and butaneecyclopentane exhibit the highest exergetic efﬁciency for the lower, moderate and high heat source temperature range respectively. It is notable that for heat source temperatures of 170 C and higher, the maximum exergetic efﬁciency is always exhibited by a mixture under supercritical cycle operation. This veriﬁes the capability of the examined efﬁciency improvement strategies of the ORC to enhance the overall system thermodynamic performance. Furthermore, the natural refrigerants and their mixtures have in general a better second law efﬁciency (increased by 10e45 %) than the benchmark ﬂuid R245fa and lower turbine size parameter values. Nevertheless, R245fa has a signiﬁcantly lower volume ﬂow ratio especially for higher temperatures and also lower rotational speed of the turbine and UA values (mainly in the condenser). For this reason, detailed techno-economic investigations should be carried out to determine at which extent the favourable exergetic efﬁciency of the supercritical natural refrigerant mixtures can compensate for the technical challenges associated with their implementation as working ﬂuids for waste heat recovery ORCs. Acknowledgements The work documented in this publication has been funded by the 2013 Scholarship of the Knowledge Center on Organic Rankine

Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092

K. Braimakis et al. / Energy xxx (2015) 1e13

Cycle technology (www.kcorc.org), the organization formed by the members of the ORC Power Systems committee of the ASME International Gas Turbine Institute (IGTI). The results were obtained by the collaboration of the Centre of Energy Technology (ZET) of the University of Bayreuth, Germany and the Laboratory of Steam Boilers and Thermal Plants (LSBTP) of the National Technical University of Athens, Greece.

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Please cite this article in press as: Braimakis K, et al., Low grade waste heat recovery with subcritical and supercritical Organic Rankine Cycle based on natural refrigerants and their binary mixtures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.03.092