lable at ScienceDirect

Energy 36 (2011) 199e211

Contents lists avai

Energy

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

Working fluids for high-temperature organic Rankine cycles

Ngoc Anh Lai 1, Martin Wendland, Johann Fischer*

Institut für Verfahrens-und Energietechnik, Universität für Bodenkultur, Muthgasse 107, A-1190 Wien, Austria

a r t i c l e i n f o

Article history:Received 28 March 2010Received in revised form15 October 2010Accepted 25 October 2010Available online 7 December 2010

Keywords:Energy conversionOrganic Rankine cyclesWorking fluidsCyclopentaneProcess optimization

* Corresponding author. Tel.: þ43 1 3709726 201; fE-mail address: johann.fischer@boku.ac.at (J. Fisch

1 Present address: Heat Engineering Departmentnology, Vietnam.

0360-5442/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.energy.2010.10.051

a b s t r a c t

Alkanes, aromates and linear siloxanes are considered as working fluids for high-temperature organicRankine cycles (ORCs). Case studies are performed using the molecular based equations of state BACK-ONE and PC-SAFT. First, “isolated” ORC processes with maximum temperatures of 250 �C and 300 �C arestudied at sub- or supercritical maximum pressures. With internal heat recovery, the thermal efficiencieshth averaged over all substances amount to about 70% of the Carnot efficiency and increase with thecritical temperature. Second, we include a pinch analysis for the heat transfer from the heat carrier to theORC working fluid by an external heat exchanger (EHE). The question is for the least heat capacity flowrates of the heat carrier required for 1 MW net power output. For the heat carrier inlet temperatures of280 �C and 350 �C are considered. Rankings based on the thermal efficiency of the ORC and on the heatcapacity flow rates of the heat carrier as well as on the volume and the heat flow rates show cyclo-pentane to be the best working fluid for all cases studied.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

OrganicRankine cycles (ORC) can beused for conversionof heat topower. Heat at different temperature levels may be available asgeothermal heat, as biogenic heat from biomass and biogascombustion, as solar or as waste heat. Whilst ORC processes areknown already for some time [1e3] they gain presently a rapidlyincreasing interest. An actual overview was given in [4]. A crucialproblem in designing an ORC process is the selection of the workingfluid where thermodynamic, stability, safety and environmentalaspects have to be considered. A classification of the cycles can bedone according to their maximum working fluid temperature Tmax.Herewe considerworking fluids for cycles with Tmax between 180 �Cand 300 �C to which we refer as high-temperature cycles. Earlierstudies of high-temperature cycles which concentrate mainly on thethermodynamic aspects are given, e.g. in [5e9]. For low temperaturecycles an extensive investigation of working fluids at subcritical andsupercritical pressureswith Tmax up to 100 �Cwas given in [10]. Otherinterestingwork on low temperature cycles is reported in [8,9,11e17].

Regarding the modeling of high-temperature ORC processes,Angelino and Colonna considered first alkanes, aromates and per-fluorinated benzene [5] and then siloxanes [6] as working fluids.

ax: þ43 1 3709726 210.er)., Hanoi University of Tech-

All rights reserved.

Actually, existing high-temperature ORC plants use mainly siloxanes[18e20] and some few also toluene [21,22]. Recently, Drescher andBrüggemann [7] considered about 700 working fluids for the high-temperature range and concluded that the highest thermal effi-ciencies are found for the alkylbenzenes. A certain problemwith thethermodynamic studies in [5e7] is that they are based on cubicequations of state. This was already realized by Colonna et al. [23]who consequently developed multi-parameter equations of statefor the siloxanes. As these equations contain 12 substance parame-ters which are fitted to rather limited experimental datasets, thereremains again some uncertainty. In this situation a promising alter-native is to usemolecular based equations of state like BACKONE [24]or PC-SAFT [25]which need only 3e5 substance-specific parameters.For alkanes BACKONE parameters are available from a previous studyon natural gas [26]. In addition, we determined recently also BACK-ONE parameters for the cycloalkanes cyclopentane and cyclohexane,for the aromates benezene, toluene, ethylbenzene, butylbenze, m-xylene, o-xylene and p-xylene [27] and PC-SAFT parameters for thefirst five linear siloxanes [28]. Instead of the full chemical names ofthe siloxanes we use the abbreviations MM for hexamethyldisilox-ane (C6H18OSi2), MDM for octamethyltrisiloxane (C8H24O2Si3),MD2M for decamethyltetrasiloxane, (C10H30O3Si4), and MD3M fordodecamethylpentasiloxane (C12H36O4Si5).

In the present paper we consider as working fluids (1) thealkanes n-butane, n-pentane, and cyclopentane, (2) the aromatestoluene, ethylbenzene, butylbenze, m-xylene, o-xylene andp-xylene, and (3) the linear siloxanes MM, MDM, MD2M, andMD3M. We first perform thermodynamic case studies of ORC

Nomenclature

A, B, C, D, E ideal gas heat capacity fit coefficientsCHP combined heat power_C heat capacity flow rate [kW/K]cp heat capacity of the heat carrier [kJ/kgK]cp0 ideal gas heat capacity [J/molK]e5 Specific exergy of heat carrier at inlet of the EHE [kJ/kg]_Ec exergy flow rate of heat carrier [kW]EHE external heat exchangerF Helmholtz energyFA, FA1, FA2 attractive dispersion force contributions to FFH hard-body contribution to FFQ quadrupolar contribution to Fh specific enthalpy [kJ/kg]_H enthalpy flow ratek Boltzmann constantIHE internal heat exchanger_m mass flow rate [kg/s]m number of segments in PC-SAFTMD2M decamethyltetrasiloxane, C10H30O3Si4MD3M dodecamethylpentasiloxane, C12H36O4Si5MDM octamethyltrisiloxane, C8H24O2Si3MM hexamethyldisiloxane, C6H18OSi2o2 cycle at subcritical pmax without superheatingo3 cycle at subcritical pmax with superheatingORC organic Rankine cyclep pressure [MPa]_Q heat flow rate [kW]Q*2 reduced squared quadrupole momentR ideal gas constant [J/molK]s specific entropy [kJ/kgK] or [J/molK]s2 cycle at supercritical pmax

T temperature [K]v specific volume [l/kg], 1 l¼ 1� 10�3 m3

_V volume flow rate [l/s], 1 l¼ 1� 10�3 m3

w specific work [kJ/kg]j _Wj net power output of a cycle [kW]

Greek symbolsa anisotropy parameter in BACKONED difference of quantities3 energy parameter in PC-SAFT (3/k in [K])hIHE efficiency of the internal heat exchangerhs,P isentropic pump efficiencyhs,T isentropic turbine efficiencyhth thermal efficiency of the cyclehth,Carnot thermal efficiency of the Carnot cyclehth� thermal efficiency of cycle without IHEhthþ thermal efficiency of cycle with IHExP exergy efficiency for power productionr density [mol/l]s segment diameter in PC-SAFT [nm]

Subscripts0 characteristic quantity in BACKONE1, 2, 2a, 3, 4, 4a state points of ORC working fluid5,6 state points of heat carrierAI auto-ignitionc critical point; heat carrieri state pointIHE internal heat exchangerin ingoing flows; Inlet temperature of heat carriermax maximum quantities of working fluid (state point 3)min minimum quantities of working fluid (state point 1)out outgoing flowsP pump, powerp pinch (hot stream)r reduced with respect to critical quantitys isentropic; saturation stateT turbineu environment state of heat carrier

N.A. Lai et al. / Energy 36 (2011) 199e211200

processes for given maximum and minimum temperatures andpressures. The maximum ORC temperatures are assumed to be250 �C and 300 �C. As we do not include in these systems a pinchanalysis of external heat exchangers (EHEs) for the heat transfer toand from the cycle, we call them “isolated” ORC processes. Theimportance of including such pinch analyses in modeling ORCsystems depends on the specific heat source [10] or the plant design[7]. In many cases, however, e.g. if waste heat is used, the pinchpoint problem in the EHE where the heat is transferred from a heatcarrier to the working fluid (EHE) plays a crucial role for the poweroutput of the system. Hence, we consider in a second step systemsconsisting of an ORC plus an EHE. For these studies heat carrier inlettemperatures Tin of 280 �C and 350 �C are assumed. As it is known[10,29,30] that supercritical pressures of the working fluid mayimprove the heat transfer in the EHE considerably, we will studyprocesses with sub- and supercritical maximum pressures.

In Section 2 we describe ORC processes in general, considerdifferent cycle types and address the heat transfer from the heatcarrier to the working fluid. In Section 3 we select potentialworking fluids for the temperature ranges considered. For theselected working fluids the parameters for BACKONE and PC-SAFTequations are given together with equations for the isobaric idealgas heat capacities. Moreover, we show the reliability of theseequations of state. In Section 4 we give minimum temperaturesTmin and maximum temperatures Tmax and other boundary condi-tions and discuss the selection of the maximum pressures pmax. In

Section 5 the results for the thermal efficiencies and other ther-modynamic properties of “isolated” ORC processes with differentworking fluids are shown for three pairs of (Tmin, Tmax). In Section 6systems including the heat transfer by a single stage EHE to the ORCwill be considered. Heat capacity flow rates for production of 1 MWnet power output are studied for different cycles andworking fluidsand results of optimized EHEþORC systems are presented.

2. Description of ORC processes

2.1. Plant configurations and fluid flows

The ClausiuseRankine cycle is known from the standard text-books of thermodynamics as, e.g. [1]. The plant configuration of anORC with internal heat exchanger (IHE) is shown in Fig. 1. The IHEtransfers heat from (4,4a) to (2,2a) and is not contained in the mostsimple configuration.

Let us first describe the plant and the process without IHE. Theplant consists of a pump, a heater, a turbine and a cooler-condenser.The mass flow rate of the working fluid is denoted by _m. In state 1the working fluid is a saturated liquid with temperature T1 at thepressure p1, where T1¼ Tmin is the minimum temperature andp1¼ pmin is the minimum pressure in the cycle. Then the pressureof the liquid is increased by the pump with isentropic pump effi-ciency hsP to p2¼ pmax, which is themaximum pressure in the cycle.Thereafter, the fluid is heated in an isobaric process to the

Fig. 1. Configuration of an ORC process with internal heat exchanger.

Fig. 2. Cycle o2 in the T,s-diagram with state points as defined in Fig. 1. The maximumpressure pmax is subcritical and the fluid evaporates. The fluid enters the turbine atstate 3 as saturated vapour.

N.A. Lai et al. / Energy 36 (2011) 199e211 201

temperature T3¼ Tmax which is the maximum temperature in thecycle. In case that pmax is lower than the critical pressure pc ofthe working fluid, the process step from 2 to 3 includes heating ofthe liquid to saturation, evaporation of the liquid and eventuallysuperheating of the gas. In case that pmax is higher than pc, there isno phase transition in going from 2 to 3 and the fluid in state 3 issupercritical. At state point 3 the fluid enters the turbine where itexpands with isentropic turbine efficiency hsT to the pressure pminat state 4 and delivers shaft work in this process step. Finally,starting from state 4 the fluid is first cooled to the temperature Tminand then condensed in an isobaric process till it reaches state 1.

We will see in Section 2.2 that for many organic working fluidsthe temperature at state 4 after the turbine is considerably higherthan at state 1. Hence it may be rewarding to implement an IHE forheat recovery within the cycle. The low-pressure vapour coolsdown from state 4 to 4a and the heat is transferred to thecompressed liquid which is heated up from state 2 to state 2a.

In a full thermodynamic description of an ORC plant also theheat transfer to and from the cycle should be considered. In thepresent consideration we include the heat transfer from the heatcarrier to theworking fluid by a pinch analysis. Fig.1 shows that theheat carrier with fluid mass flow _mc enters the EHE at state 5 andleaves it at state 6. The heat transfer from the cold bottom of thecycle should in principle also be considered by a pinch analysis butin order to keep the modelling simple we prescribe here only theminimum temperature of the cycle.

Fig. 3. Cycle o3 in the T,s-diagram with state points as defined in Fig. 1. The maximumpressure pmax is subcritical, the fluid evaporates and is superheated. The fluid entersthe turbine at state 3 as superheated vapour.

2.2. ORC process thermodynamics and thermal efficiencies

The thermodynamics of an ORC process can conveniently be dis-cussed by using a temperature versus entropy (T,s)-diagram.Considering the vapoureliquid coexistence curve it is known thatorganic fluids consisting of larger molecules have an overhangingsaturated vapour line in the T,s-diagram. In order to describe differentpossible cycles we use the nomenclature introduced in Ref. [10].

2.2.1. o2 cycle and o3 cycleThe o2 cycle is schematically represented in the T,s-diagram in

Fig. 2, the o3 cycle in Fig. 3. In both cases the maximum pressurepmax of the working fluid is lower than the critical pressure pc andhence the working fluid evaporates. In case of the o2 cycle the fluidenters the turbine at state 3 as saturated vapour. In case of the o3cycle the fluid is superheated and as such it enters the turbine atstate 3. As the saturated vapour line is overhanging state 4 can in

both cases only be located on the condenser pressure isobar pmin inthe superheated vapour region.

2.2.2. s2 cycleThe s2 cycle is schematically represented in the T,s-diagram in

Fig. 4. The maximum pressure pmax of the working fluid is higherthan the critical pressure pc and hence the working fluid does notundergo a phase transition during heating. The supercritical fluidenters the turbine at state 3. Depending on state 3 and pmin the fluidat the turbine outlet state 4 may be wet or dry vapour [10]. In theexamples considered here, we find only dry vapour at state 4 andthis case is called s2.

From the T,s-diagrams in Figs. 2e4 it can be seen that for thecycles o2, o3, and s2 the temperature T4 at state point 4 can beremarkably higher than the temperature T1 of the condenser. Henceit is rewarding to use an IHE inwhich the hot stream is cooled downfrom T4 to T4a which has to be higher than T2; we callT4a� T2¼DTIHE. The enthalpy difference h4� h4a is transferred tothe cold streamwhich is heated up from T2 to T2a with an enthalpydifference h2a� h2. Following [7], we introduce an efficiency of theinternal heat exchanger hIHE as

hIHE ¼ ðh2a � h2Þ=ðh4 � h4aÞ: (1)

In the cycles without IHE the heat q23 is added to the workingfluid during the process (2e3) and the heat q41 is removed from itduring the process (4e1). The work w34 is taken from the turbineduring the process (3e4) and a small amount of work w12 is

Fig. 4. Cycle s2 in the T,s-diagram with state points as defined in Fig. 1. The maximumpressure pmax is supercritical. During heating the fluid does not undergo a phasetransition. The supercritical fluid enters the turbine at state 3.

N.A. Lai et al. / Energy 36 (2011) 199e211202

required to pump the liquid during the process (1e2). Then thethermal efficiency of the cycle is given as:

hth ¼ �ðw34 þw12Þ=q23¼ �½ðh4 � h3Þ þ ðh2 � h1Þ�=ðh3 � h2Þ; ðwithout IHEÞ (2)

where h1, h2, h3, and h4 are the specific enthalpies in the respectivestate points in Figs. 1 to 4. In the cycles with IHE only the heat q2a3has to be added to the working fluid and hence the thermal effi-ciency is given in these cases as

hth ¼ �ðw34 þw12Þ=q2a3¼ �½ðh4 � h3Þ þ ðh2 � h1Þ�=ðh3 � h2aÞ; ðwith IHEÞ (3)

where h1, h2, h2a, h3, and h4 are the specific enthalpies in therespective state points in Figs. 1e4.

For themass flow rate of theworkingfluid _m the net power outputof a cycle j _Wj is given by j _W j ¼ j _Wout þ _W inj ¼ _mjw34 þw12j, thevolume flow rate at a given state with specific volume v is given by_V ¼ _mv. In the results the flow rates will be given for a net poweroutput j _Wj of 1 MW.

2.3. Systems with heat transfer to the ORC process

A parameter still to be considered is the supply of the heat flux_Q in to the working fluid in the heater, which is _Q in ¼ _Q23 in casewithout IHE and _Q in ¼ _Q2a3 in casewith IHE. In general, this heat issupplied from a heat carrier fluid and the heater of the ORCworkingfluid is the cold side of an EHE as shown in Fig. 1. The supplied heatflux from the heat carrier is _Q56 (takenwith positive sign). Here weassume the EHE to be adiabatic and hence _Q in ¼ _Q56.

The ultimate aim in the design of a power plant is not thehighest thermal efficiency of the ORC process but rathera maximum power output or a certain combination of heat andpower output from a given heat source. This includes considerationof the EHE by a pinch analysis which has to be based on a T,D _H-diagram of the heat carrier fluid and the working fluid in theheater. We call the upper temperature at the pinch point Tp and thetemperature difference at the pinch point DTp. In case of a subcrit-ical maximum pressure as in cases o2 and o3 the fluid evaporatesand the pinch occurs for the working fluid at the saturated liquidstate. The examples given in Figs. 8e10 of [10] for b1, b3, and s2cycles apply equally well for the o2, o3 and s2 cycles of this paper.

From a puristic thermodynamic point of view an exergy analysisof the ORC system should be made which includes the exergy lossof the heat carrier in the EHE, the exergy gain of the coolingmedium in the cooler-condenser and the net power output. From

a practical point of view, however, the exergy contained in the heatcarrier after the EHE and in the cooling agent is in a single-step, i.e.in a non-cascade ORC in general not used any more for powerproduction. Hence, we adopt here a different point of view and askonly for the exergy flow rate _Ec of the heat carrier at the EHE inletwhich is required for the production of a net power output j _Wj of1 MW from the ORC process. In case of a combined heat power(CHP) plant one could also think about an optimized combinationof the net power output and the enthalpy flow increment of thecooling medium, but such a model has too many free parametersand is not considered here.

The exergy flow rate _Ec at the EHE inlet is given as

_Ec ¼ _mce5; (4)

where _mc is the heat carrier mass flow rate and e5 the specificexergy at the inlet of the EHE. The specific exergy e5 is known to be

e5 ¼ ðh5 � huÞ � Tuðs5 � suÞ; (5)

where the subscript u refers to the conditions of the environment. Ifthe flow of the heat carrier is assumed to be isobaric and the heatcapacity of the heat carrier cp is assumed as constant, we have

h5 � hu ¼ cpðT5 � TuÞ (6)

s5 � su ¼ cplnðT5=TuÞ (7)

and there from

_Ec ¼ _mce5 ¼ _mccp½ðT5 � TuÞ � TulnðT5=TuÞ�: (8)

As in our case studies T5 and Tu will be fixed the interestingquantity is _C ¼ _mccp which is called heat capacity flow rate asusual in pinch technology. Hence, the present question is for theheat capacity flow rate _C which at given temperatures T5 andTmin¼T1 yields a net power production j _Wj ¼ 1 MW. Theoptimum case is the one with minimum _C.

As we consider as outgoing exergy flow only the net power j _Wjwe define an exergy efficiency for power production xP by

xP ¼ �� _W��=�_C½ðT5 � TuÞ � TulnðT5=TuÞ�

�: (9)

3. Potential working fluids and their equations of state

3.1. Potential working fluids

In this study we consider pure fluids from the groups of alkanes,aromates and linear siloxanes as working fluids for ORC processeswith maximum temperatures Tmax being between 180 �C and300 �C. For the exploration of optimal maxiumum pressures inSection 4.2 toluene is even considered at Tmax¼ 350 �C. For thepresent selection of aworking fluid all the following criteria have tobe fulfilled: (1) the critical temperature of the fluid has to be higherthan 150 �C. (2) A molecular based fundamental equation of statehas to be available. (3) The auto-ignition temperature TAI has to behigher than 250 �C. These fluids are compiled in Table 1 andordered according to their critical temperatures Tc. Table 1 alsocontains the CAS and the EC number, the critical pressure pc, thetype and source of the equation of state and the auto-ignitiontemperature TAI of each substance. The EC number is the officialseven digit code of substances in the European Union used in theREACH (Registration, Evaluation, Authorisation and Restriction ofChemicals) regulation which aims at improving the protection ofhuman health and the environment through the better and earlieridentification of the intrinsic properties of chemical substances.

Table 2BACKONE parameters of alkanes and aromates.

Substance T0 (K) r0 (mol/l) a Q*2 Source

n-Butane 411.13 3.8553 1.3693 1.7878 [26]n-Pentane 448.96 3.1407 1.4011 2.3962 [26]Cyclopentane 488.9924 3.7524 1.3694 1.9694 [27]Toluene 567.41 3.10164 1.40682 2.47697 [27]Ethylbenzene 585.32 2.62272 1.42411 2.91600 [27]Butylbenzene 598.68 1.94725 1.44871 4.05099 [27]o-Xylene 594.91 2.64340 1.42209 2.99888 [27]m-Xylene 587.69 2.60975 1.43046 2.98906 [27]p-Xylene 588.78 2.59856 1.42988 2.92245 [27]

Table 3PC-SAFT parameters of linear siloxanes [28].

Substance 3/k (K) s (nm) m

MM 209.4933 0.397997 4.24260MDM 213.3824 0.4168933 5.150368MD2M 212.6004 0.424578 6.19610MD3M 215.3387 0.436766 6.95400

Table 1Alkanes, aromates, and linear siloxanes with critical temperatures Tc> 423.15 K(150 �C) and auto-ignition temperatures TAI> 523.15 K (250 �C). The table also givesthe critical pressures pc and the equations of state (EOS) used in this work.

Substance CAS No,EC No

Tc (K) pc (MPa) EOS TAI (K)

423.15 K< Tc< 523.15 Kn-Butane 106-97-8 425.20 3.922 BACK1 [26] 638.15 [31]

203-448-7 703.15 [32]n-Pentane 109-66-0 469.65 3.370 BACK1 [26] 533.15 [32]

203-692-4 558.15 [33]582.15 [31]

Cyclopentane 287-92-3 511.7 4.51 BACK1 [27] 634.15 [31]206-016-6 653.15 [33]

MM 107-46-0 518.70 1.925 PC-SAFT [28] 613.15 [32,33]203-492-7

523.15 K< Tc< 573.15 KMDM 107-51-7 564.13 1.415 PC-SAFT [28] 623.15 [34]

203-497-4

573.15 K< Tc< 623.15 KToluene 108-88-3 591.80 4.109 BACK1 [27] 753.15 [31]

203-625-9 809.15 [32]MD2M 141-62-8 599.40 1.190 PC-SAFT [28] N/A

205-491-7p-Xylene 106-42-3 616.23 3.511 BACK1 [27] 801.15 [31,32]

203-396-5m-Xylene 108-38-3 617.05 3.541 BACK1 [27] 800.15 [31,32]

203-576-3Ethylbenzene 100-41-4 617.20 3.609 BACK1 [27] 705.15 [31,32]

202-849-4

Tc> 623.15 KMD3M 141-63-9 629.00 0.945 PC-SAFT [28] 703.15 [35]

205-492-2o-Xylene 95-47-6 630.33 3.732 BACK1 [27] 736.15 [31,32]

202-422-2Butylbenzene 104-51-8 660.05 2.887 BACK1 [27] 685.15 [32]

203-209-7

N/A: not available.

N.A. Lai et al. / Energy 36 (2011) 199e211 203

3.2. Equations of state

For the thermodynamic description of the working fluids listedin Table 1 we use the molecular based equations of state BACKONE[24] and PC-SAFT [25]. In both equations the configurational part Fof the Helmholtz energy is written as a sum of contributions fromcharacteristic intermolecular interactions.

In the BACKONE version used here F is written as

F ¼ FH þ FA þ FQ ; (10)

where FH is the hard-body contribution, FA the attractive dispersionforce contribution and FQ the quadrupolar contribution. The hard-body term FH is taken from the hard convex body equation ofBoublik [36], the term FQ has been obtained by extensive molecularsimulations [37], and FA was obtained [24] from a simultaneous fitto experimental data of methane, oxygen and ethane aftersubtraction of the hard-body contribution. This version needs foursubstance-specific parameters: a characteristic temperature T0,a characteristic density r0, an anisotropy parameter a and a reducedsquared quadrupole moment Q*2.

In the PC-SAFT version used here F is written as

F ¼ FH þ FA1 þ FA2; (11)

where FH is again a hard-body contribution, and FA1 and FA2 are firstand second order attractive dispersion force contributions, respec-tively. Thehard-body term FH is taken fromthehard associated chaintheory ofWertheim [38], the terms FA1 and FA2 arise from the secondorder perturbation theory of Barker and Henderson [39] and have

been obtained froma simultaneousfit to experimental data of the n-alkanes from C1 to C20 [25]. This version of PC-SAFT equation hasthree substance-specific parameters, the energy parameter e rep-resenting the well depth, the size parameter s representing thesegment diameter and the chain length m.

Comparing BACKONE and PC-SAFT it seems from studies ofother authors [40] and own studies that BACKONE shows betterperformance for compact molecules whilst PC-SAFT is superior forchain molecules. Here we will use BACKONE for the description ofthe alkanes n-butane, n-pentane and cyclopentane [10,26,27] andof the aromates [27] whilst PC-SAFT is used for describing thesiloxanes [28]. The BACKONE parameters are listed in Table 2 andthe PC-SAFT parameters in Table 3.

For the calculation of caloric properties such as the enthalpy andthe entropy, the residual contributions of BACKONE and PC-SAFThave to be supplemented by the ideal gas heat capacities cp0 whichcan be represented by fit polynomials as [41]

c0p=R ¼ Aþ BT þ CT2 þ DT3 þ ET4; (12)

where R is the ideal gas constant, R¼ 8.314472 J/(molK) and A, B, C,D, and E are fit coefficients. The fit coefficients of the ideal gas heatcapacities together with original data sources and temperatureranges are given in Table 4.

For Tmax values above 530 K n-pentane and higher n-alkanesshould not be considered as working fluids any more because oftheir low auto-ignition temperatures. On the other hand,cyclopentane, the siloxanes and the aromates have much higherauto-ignition temperatures and it seems worth to point out thedifferences between these fluids. As representatives we considercyclopentane and MM which have nearly the same criticaltemperature as well as toluene which is the aromate with thelowest critical temperature considered. For these substances weconsider ideal gas heat capacities cp0 and their vapour pressures ps atT/Tc¼ 0.7. Our equations yield for cyclopentane cp

0¼102 J/(mol K)and ps¼ 0.289 MPa, for toluene cp

0¼144 J/(mol K) andps¼ 0.221 MPa, and for MM cp

0¼ 264 J/(mol K) and ps¼ 0.074 MPa.These differences have significant influences on their behaviour asworking fluids. First, as is shown in Fig. 5, the T,s-diagram ofcyclopentane is the least skewed, whilst that of MM is the mostskewed, which is a consequence of the increasing value of cp0. Asa consequence, if one considers two ORC processes of type o2 withthe same turbine inlet temperature T3, the outlet temperature T4

Table 4Ideal gas heat capacity cp

0 coefficients of Eq. (12), temperature ranges and sources.

Substance A B C D E Tmin (K) Tmax (K) cp0 Source

n-Butane 2.5706 3.1702E�02 4.2294E�06 �1.6889E�08 5.8222E�12 200 1500 [42]n-Pentane �0.2584 5.9954E�02 �3.5457E�05 1.0485E�08 �1.2117E�12 298 1500 [43]Cyclopentane 5.0190 �1.9734E�02 1.7917E�04 �2.1696E�07 8.2150E�11 298 800 [44]Toluene �4.7793 7.0821E�02 �4.7711E�05 1.4068E�08 �1.0756E�12 298 1500 [45]Ethylbenzene 2.8611 2.4422E�02 9.8673E�05 �1.5176E�07 6.3489E�11 0 1000 [46]Butylbenzene 6.4900 1.9080E�02 1.5665E�04 �2.2059E�07 8.8870E�11 200 1000 [41]o-Xylene �1.3865 6.8366E�02 �3.4018E�05 2.2944E�09 2.1532E�12 298 1500 [45]m-Xylene �3.4749 7.4572E�02 �4.1203E�05 6.0963E�09 1.3830E�12 298 1500 [45]p-Xylene �2.7508 6.9888E�02 �3.2768E�05 �1.1154E�10 3.0077E�12 298 1500 [45]MM 6.3472 8.5604E�02 �4.6759E�05 1.0523E�08 0.0000Eþ00 298 1400 [47]MDM 9.4056 1.2051E�01 �6.8020E�05 1.5776E�08 0.0000Eþ00 298 1400 [47]MD2M 10.0356 1.5327E�01 �8.6846E�05 2.0222E�08 0.0000Eþ00 298 1400 [47]MD3M 12.8945 2.0199E�01 �1.2386E�04 3.0840E�08 0.0000Eþ00 298 1400 [47]

N.A. Lai et al. / Energy 36 (2011) 199e211204

will be the highest for the siloxane and the lowest for cyclopentane.Second, as the vapour pressures of the siloxanes are the lowest, thevapour volume flows of the siloxanes will be the highest.

3.3. Accuracy of PC-SAFT and BACKONE

In this subsection we want to discuss the accuracy of theequations of state used in this study.

Regarding the siloxanes we have mentioned already that onlylimited experimental data are available and hence there do notexist any reference equations of state. In [28] the three PC-SAFTparameters have been fitted to extrapolated vapour pressure andsaturated liquid density curves. Then, the thermodynamic proper-ties resulting from PC-SAFT have been compared with a variety ofexperimental data and showed good agreement.

Reference equations of state (REOS), however, are available forn-butane [48,49], n-pentane [50] and toluene [49] which are easilyaccessible via the NIST-webbook [51]. Here we perform compari-sons for n-pentane and toluene for ORC example state points andproperties with these reference equations.

Let usfirst consider anORCprocess for n-pentaneof o3-typewithIHE using the boundary conditions Tmin¼ 358.15 K, Tmax¼ 523.15 K,pmax¼ 3.033 MPa (p/pc¼ 0.9), T4a� T2¼10 K, hs,P¼ 0.65, hs,T¼ 0.85,hIHE¼ 1.0. For that cycle we obtained q2a,3¼ 415.54 (416.65) kJ/kg ,w1,2¼7.177 (7.223) kJ/kg, w3,4¼�84.021 (�84.298) kJ/kg,v3¼14.95 (15.19) l/kg, v4¼124.51 (124.09) l/kg and hth¼ 18.5(18.5)%, where the first numbers are those from the REOS [50] andthe bracketed numbers are from BACKONE.

Next, we consider an ORC process for toluene of o2-type with IHEusing the boundary conditions as suggested in [7] Tmin¼ 363.00 K,pmax¼ 2.0 MPa, T4a� T1¼10 K, hs,P¼ 0.80, hs,T¼ 0.80, hIHE¼ 0.95. Forthat cycle we obtained q2a,3¼ 502.12 (506.32) kJ/kg, w1,2¼ 3.039(3.039) kJ/kg, w3,4¼�111.408 (�113.156) kJ/kg, v3¼16.11 (16.87)

Fig. 5. Comparison of T,s-diagrams of cyclopentane, MM, and toluene.

l/kg, v4¼733.35 (738.35) l/kg and hth¼ 21.6 (21.7)%, where the firstnumbers are those from the REOS [49] and the bracketed numbersare from BACKONE. Focussing on the thermal efficiencies, we notethat the results from REOS and BACKONE agree quite well, whilst theresult from [7] is hth¼ 23.2%, which is about 7% higher than thepresent values.

Summarizing, we conclude that the applied molecular basedequations of state BACKONE and PC-SAFT yield reliable values forthe thermodynamic properties of ORC processes.

4. Boundary conditions

4.1. Assumptions

In the following Sections we consider ORC example cases withdifferent boundary conditions for the ORC process and differenttemperatures Tin¼T5 of the heat carrier at the inlet of the EHE.

As already mentioned in the Introductionwe consider first cycleswith maximum ORC temperatures Tmax being 250 �C and 300 �Cwhich are inspired by previous papers [5,6,8,18e20,52e54]. Theminimum temperature Tmin is assumed for both Tmax values to beTmin¼ 85 �C which is appropriate for CHP plants. For Tmax¼ 250 �Cwe assume asminimum temperature alsoTmin¼ 38 �C as an examplefor releasing heat to the environment in warm countries. Hence, weconsider the following three different boundary temperature cases:

Case 1: Tmax¼ T3¼ 523.15 K (250 �C), Tmin¼T1¼358.15 K (85 �C).Case 2: Tmax¼ T3¼ 523.15 K (250 �C), Tmin¼T1¼311.15 K (38 �C).Case 3: Tmax¼ T3¼ 573.15 K (300 �C), Tmin¼T1¼358.15 K (85 �C).The minimum pressures pmin of the working fluids are the

vapour pressures at the minimum cycle temperature Tmin. Themaximum pressures pmax of the working fluids can be subcriticaland supercritical and will be discussed in more detail in thefollowing subsection. Additional boundary conditions are theisentropic pump efficiency hs,P¼ 0.65 and the isentropic turbineefficiency hs,T¼ 0.85.

The ORC processes are considered without internal heatexchangers (�IHE) and with internal heat exchangers (þIHE). Thelatter are adiabatic, i.e. hIHE¼ 1, and have a pinch point temperaturedifference DTIHE¼ T4a� T2¼10 K. Here we consider for o2 and o3cycles only those for which T2a is smaller than the saturationtemperature at the maximum pressure of the investigated cycle.

The calculation of the mass flow rate _m and of the volume rates_V3 and _V4 at the turbine inlet and outlet is based on 1 MW netpower output.

In Section 6 we also consider the heat transfer process from theheat carrier to the working fluid with entrance temperatures of theheat carrier being T5¼ 280 �C and 350 �C. The EHE is also assumedas adiabatic and the temperature difference at the pinch point isDTp¼ 10 K.

Table 5Results for cycles with n-pentane and toluene as function of the maximum pressure pmax. The mass flow rate _m and the volume flow rates _V3 and _V4 refer to 1 MW net poweroutput.

Substance (Cycle type) pmax/pc pmax (MPa) T4 (K) _V3 (l/s) _V4 (l/s) _m (kg/s) hth (%) �IHE hth (%) þIHE

n-Pentane, Tc¼ 469.65 K, pc¼ 3.370 MPa, Tmax¼ 523.15 K, Tmax/Tc¼ 1.11, Tmin¼ 358.15 K, hcarnot¼ 0.315n-Pentane (o3) 0.8 2.70 476.24 238 1684 13.4 11.3 18.0n-Pentane (o3) 0.9 3.03 471.82 197 1609 13.0 11.9 18.5n-Pentane (s2) 1.1 3.71 463.04 142 1513 12.5 12.7 19.0n-Pentane (s2) 1.2 4.04 458.54 122 1484 12.4 13.0 19.1n-Pentane (s2) 1.3 4.38 453.87 107 1464 12.3 13.3 19.1n-Pentane (s2) 1.4 4.72 448.98 93 1452 12.4 13.5 19.0

Toluene, Tc¼ 591.80, pc¼ 4.109 MPa, Tmax¼ 623.15 K,Tmax/Tc¼ 1.05, Tmin¼ 358.15 K, hcarnot¼ 0.425Toluene (o3) 0.5 2.05 532.07 151 6750 6.5 18.7 28.0Toluene (o3) 0.6 2.47 525.63 117 6470 6.3 19.4 28.6Toluene (o3) 0.7 2.88 519.47 94 6298 6.2 19.9 28.9Toluene (o3) 0.8 3.29 513.32 77 6160 6.2 20.4 29.0Toluene (o3) 0.9 3.70 506.96 64 6070 6.1 20.7 29.1Toluene (s2) 1.1 4.52 492.25 44 5922 6.2 21.3 28.8Toluene (s2) 1.2 4.93 482.61 36 5936 6.4 21.4 28.4Toluene (s2) 1.3 5.34 469.10 28 6008 6.6 21.5 27.5Toluene (s2) 1.4 5.75 454.30 22 6208 7.0 21.4 26.5

N.A. Lai et al. / Energy 36 (2011) 199e211 205

4.2. Maximum pressures

Previous works have sometimes considered as maximumpressure for theworking fluid 20 bar or the vapour pressure at Tmax.The 20 bar limit arose from legal prescriptions in some countriesknown as “Dampfkesselverordnung (steam boiler code)”. On theother hand it is known [10,29,30] that supercritical pressures ofthe working fluid improve the heat transfer from the heat carrier tothe working fluid in a pinch analysis. Here we concentrate on thetechnical optimization of the processes and search for optimalmaximum pressures.

In case that the maximum cycle temperature Tmax is less thanthe critical temperature of the working fluid Tc we assume an o2cycle in which the maximum cycle pressure is pmax¼ ps(Tmax) withps being the vapour pressure at Tmax.

In case that the maximum cycle temperature Tmax is higher thanthe critical temperature of the working fluid Tc the selection of themaximum pressure pmax is an open question. Then, an essentialparameter is the ratio pmax/pc. For subcritical pmax or pmax/pc< 1.0the cycle is of o3-type, for supercriticalpmaxorpmax/pc> 1.0 the cycleis of s2-type. Before performing calculations for all substances, weinvestigate the thermal cycle efficiencies of n-pentane and toluenewith various maximum pressures in the range 0.5� pmax/pc� 1.4.The minimum temperature of these cycles is 85 �C. The maximumtemperature of the cycle with n-pentane is 250 �C and that of thecycle with toluene is 350 �C. The latter temperature was chosen forlater extensions of ORC-studies to higher temperatures. The otherboundary conditions are those from Section 4.1. Results for cycleswithout and with IHE are given in Table 5.

We observe from Table 5 that cycles with n-pentane reach thehighest value for the cycle efficiency hth of 19.1% for the case withIHE at pmax between 1.2pc and 1.3pc. Increasing the digits of hth it isseen that the cycle efficiency has its maximum value closer topmax¼ 1.2pc. On the other hand, for toluene the highest cycle effi-ciency is obtained at 0.9pc.

As a consequence of this study, we do not investigate in thefollowing cycle efficiencies with various maximum pressures for allsubstances. We simply choose as maximum pressure for o3 cyclespmax¼ 0.90pc and for s2 cycles pmax¼ 1.2pc for all substances.

5. Thermodynamic results for ORC processes

In this section results for ORC processes with different workingfluids will be presented and discussed. The boundary conditions are

those of Cases 1 to 3 as described in Section 4.1. The cycles arestudied without and with IHE. For simplicity in the discussion, thethermal efficiencies hth of cycles without IHE will be denoted byhth� and those of cycles with IHE by hthþ if it is necessary fordistinction.

Moreover it seems appropriate to give a ranking of the workingfluids for which we take the following criteria.

(1) The thermal efficiency hth for the process with IHE, hthþ, shallbe as large as possible.

(2) The volume flows _V3 and _V4 shall be as small as possible.(3) The heat flux which is transferred in IHE and EHE to the

working fluid is given by _Q23 and shall be as small as possiblefor sizing of the heat exchangers. This heat flux _Q23 is deter-mined by the net power production of 1 MW and the thermalefficiency hth� for the process without IHE as _Q23 ¼ 1=hth�(MW). This means, in order that _Q23 is as small as possible, hth�shall be as large as possible.

(4) The heat flux _Q4a1 which is delivered in the cooler-condenser shallbe as small as possible. As _Q4a1 ¼ _Q2a3 � j _Wj ¼ ½ð1=hthþ � 1Þ�(MW) which is approximately z1/hthþ (MW). Again hthþ shall beas large as possible.

Hence, for a ranking the quantities hthþ, hth�, _V3 and _V4 areconsidered and related to the following maximum or minimumquantities hthþ/hthþ,max, hth�/hth�,max, _V3min

= _V3 and _V4min= _V4, which

all are �1. A number of points is then attributed according to

Points ¼ 100�3hthþ=hthþ;max þ hth�=hth�;max þ _V3min

= _V3

þ _V4min= _V4

��6: (13)

5.1. Case 1

In this case Tmax¼ 523.15 K and Tmin¼ 358.15 K. Table 6 showsinput parameters as Tmax/Tc, pmax/pc, pmax and pmin and results forthe thermal efficiencies hth without andwith IHE, the turbine outlettemperature T4, the mass and volume flow rates _m, _V3 and _V4 for1 MW net power output as well as the number of points accordingto Eq. (13). The substances considered have been selected fromTable 1. The critical temperatures of n-butane, n-pentane, cyclo-pentane and MM are lower than Tmax and hence they should beconsidered at the subcritical pressure pmax/pc¼ 0.9 in o3 cycles andat the supercritical pressure pmax/pc¼ 1.2 in s2 cycles. The problem

Table 6Results for Case 1 (Tmax¼ 523.15 K, Tmin¼ 358.15 K, hth,Carnot¼ 0.315). The mass flow rate _m and the volume flow rates _V3 and _V4 refer to 1 MW net power output.

Substance Tmax/Tc pmax/pc pmax (MPa) pmin (MPa) T4 (K) _V3 (l/s) _V4 (l/s) _m (kg/s) hth, (%) �IHE hth, (%) þIHE Points Eq. (13)

Tmax> Tc, pmax/pc¼ 0.9, Cycle type o3n-Butane 1.23 0.90 3.53 1.13Eþ00 487.21 326 1043 18.2 8.4 14.8 58n-Pentane 1.11 0.90 3.03 4.20E�01 471.82 197 1609 13.0 11.9 18.5 67Cyclopentane 1.02 0.90 4.06 2.89E�01 431.90 99 1764 10.3 16.6 20.2 82MM 1.01 0.90 1.73 6.29E�02 476.28 153 6528 17.1 12.1 20.9 67

Tmax> Tc, pmax/pc¼ 1.2, Cycle type s2n-Butane 1.23 1.20 4.71 1.13Eþ00 475.38 197 886 15.7 10.1 16.6 69n-Pentane 1.11 1.20 4.04 4.20E�01 458.54 122 1484 12.4 13.0 19.1 75

Tmax< Tc, pmax¼ ps(Tmax) Cycle type o2MDM 0.93 0.54 0.76 1.13E�02 482.18 283 26,772 17.9 12.5 22.4 64Toluene 0.88 0.41 1.67 4.60E�02 432.82 182 7289 8.7 19.0 22.6 75MD2M 0.87 0.28 0.33 2.37E�03 487.80 610 103,544 18.9 12.4 22.9 62p-Xylene 0.85 0.28 0.99 1.90E�02 444.21 287 15,700 8.6 18.7 23.2 72m-Xylene 0.85 0.28 0.98 1.84E�02 444.54 288 16,057 8.5 18.7 23.2 72Ethylbenzene 0.85 0.28 1.02 2.03E�02 446.24 278 14,861 8.7 18.5 23.2 72MD3M 0.83 0.16 0.16 5.69E�04 493.46 1219 372,914 19.9 11.6 23.1 60o-Xylene 0.83 0.24 0.88 1.54E�02 445.71 318 18,763 8.3 18.7 23.3 71Butylbenzene 0.79 0.14 0.41 3.94E�03 459.52 603 62,960 8.7 17.9 23.9 69

N.A. Lai et al. / Energy 36 (2011) 199e211206

with cyclopentane and MM, however, is that their critical temper-atures are very close to Tmax. As a consequence state points 3 in thes2 cycles are very close to the critical point and hence we do notshow results for these cycles. For the o3 cycles state points 3 aredefinitely in the vapour and hence these cycles are included in Table6. For all other substances the critical temperatures are higher thanTmax and hence they are considered in o2 cycles.

Important questions for the design of an ORC process concernthe efficiencies and the sizing. Whilst results for the cycle effi-ciencies and for the volume flow rates at the inlet and the outlet ofthe turbine are included in Table 6 we still present two figures fora convenient comparison of different substances. We show in Fig. 6the thermal efficiencies as function of the critical temperatures forcycles without andwith IHE and in Fig. 7 the thermal efficiencies vs.the volume flow rates _V3 at the turbine inlet for cycles with IHE.

Considering Fig. 6 and Table 6 we observe for cycles with IHEthat the thermal efficiencies hthþ increase with the criticaltemperatures Tc of the substances. For n-butane and n-pentanewith Tmax/Tc> 1 the hthþ values of the s2 cycles are somewhathigher than those of the o3 cycles and for both cases a strongincrease in hthþ is observed with the increase of Tc . For cyclo-pentane and MM only the o3 cycle was considered which showsa further increase of hthþ in comparison with the n-alkanes. For theother siloxanes (MDM, MD2M, MD3M) and the aromates with

Fig. 6. Thermal efficiencies hth as function of the critical temperature Tc for Case 1(Tmax¼ 523.15 K, Tmin¼ 358.15 K). 6: Alkanes with IHE (upper s2; lower o3), >:alkanes without IHE (upper s2; lower o3), C: cyclopentane with IHE, 4: cyclopentanewithout IHE, ,: siloxanes with IHE, þ: siloxanes without IHE, B: aromates with IHE,�: aromates without IHE.

Tmax/Tc< 1 the results from o2 cycles are distributed nearly alongone straight line which also includes the cyclopentane and the MMresults from the o3 cycles. This is remarkable as it means that thehthþ values are nearly independent from the groups of substancesbut showan increasewith the critical temperature Tc. Regarding theaverage value <hthþ> of the cycle efficiencies hthþ of all cycles inTable 6 we obtain <hthþ>¼ 21.2%, which amounts to 67% of theCarnot efficiency hth,Carnot¼ 31.5%.

Fig. 6 shows also that the thermal efficiencies hth� of cycleswithout IHE are considerably smaller than the thermal efficiencieshthþ of cycles with IHE. This difference has its origin in the differentshapes of the coexistence curves in the T,s-diagrams shown in Fig. 5.As a consequence the turbine outlet temperatures T4 are ratherhigh for siloxanes as was already discussed in the last paragraph ofSection 3.2 and is confirmed by the results in Table 6. Moreover, thehth� increase with Tc only for the alkanes, but decrease with Tc forthe siloxanes and aromates.

Next, we look in Fig. 7 for fluids with small volume flow rates _V3at the turbine inlet and large thermal cycle efficiencies hthþ. We seethat the n-pentane (o3, s2), cyclopentane (o3), MM (o3) and toluene(o2) have small values for _V3 combined with good thermal effi-ciencies. The picture, however, changes somewhat by consideringthe overall ranking of the working fluids according to the pointsdefined in by Eq. (13) and contained in Table 6.We find 82 points for

Fig. 7. Thermal efficiencies hth vs. volume flow rates _V3 at the turbine inlet for Case 1(Tmax¼ 523.15 K, Tmin¼ 358.15 K) with IHE. >: n-butane, :: n-pentane, C: cyclo-pentane, þ: MM, -: MDM, ,: toluene, ;: MD2M, A: p- and m-xylene, B: ethyl-benzene, 7: o-xylene, and �: butylbenzene.

Table 7Results for Case 2 (Tmax¼ 523.15 K, Tmin¼ 311.15 K, hth,Carnot¼ 0.405). The mass flow rate _m and the volume flow rates _V3 and _V4 refer to 1 MW net power output.

Substance Tmax/Tc pmax/pc pmax (MPa) pmin (MPa) T4 (K) _V3(l/s) _V4 (l/s) _m (kg/s) hth, (%) �IHE hth, (%) þIHE Points Eq. (13)

Tmax> Tc, pmax/pc¼ 0.9, Cycle type o3n-Butane 1.23 0.90 3.53 3.60E�01 457.59 155 1534 8.7 14.9 23.6 70n-Pentane 1.11 0.90 3.03 1.09E�01 445.36 113 3440 7.4 17.5 26.2 70Cyclopentane 1.02 0.90 4.06 6.89E�02 396.71 62 4403 6.5 22.6 26.9 80MM 1.01 0.90 1.73 1.04E�02 458.43 95 23,828 10.6 16.3 28.2 68

Tmax> Tc, pmax/pc¼ 1.2, Cycle type s2n-Butane 1.23 1.20 4.71 3.60E�01 445.78 102 1408 8.2 16.2 24.6 77n-Pentane 1.11 1.20 4.04 1.09E�01 432.17 72 3283 7.3 18.4 26.4 76

Tmax< Tc, pmax¼ ps(Tmax) Cycle type o2MDM 0.93 0.54 0.76 1.20E�03 465.29 182 156,431 11.5 16.3 29.5 64Toluene 0.88 0.41 1.67 7.16E�03 396.10 122 29,021 5.8 24.8 29.0 72MD2M 0.87 0.28 0.33 1.61E�04 471.35 395 954,471 12.2 16.2 30.0 62p-Xylene 0.85 0.28 0.99 2.38E�03 409.80 193 77,850 5.8 24.4 29.8 70m-Xylene 0.85 0.28 0.98 2.28E�03 410.17 193 80,746 5.7 24.4 29.8 70Ethylbenzene 0.85 0.28 1.02 2.58E�03 412.62 186 72,588 5.8 24.2 29.8 70MD3M 0.83 0.16 0.16 2.59E�05 478.69 790 5,154,084 12.9 15.1 30.3 60o-Xylene 0.83 0.24 0.88 1.83E�03 411.45 214 98,556 5.6 24.4 30.0 70Butylbenzene 0.79 0.14 0.41 3.51E�04 429.96 408 447,981 5.9 23.7 31.3 69

N.A. Lai et al. / Energy 36 (2011) 199e211 207

cyclopentane in the o3 cycle, 75 points for n-pentane in the s2 cycleand also 75 points for toluene in the o2 cycle. The siloxanes haveleast satisfying numbers of points because of their large volumeflows at the turbine outlet and the small hth� values which requirelarge heat exchangers.

5.2. Case 2

This case is similar to case 1 with the difference that theminimum temperature is now Tmin¼ 311.15 K whilst the maximumtemperature is again Tmax¼ 523.15 K. We consider here the samesubstances as in Section 5.1 and the results are compiled in Table 7.

From Table 7 we learn that the behaviour of the thermal effi-ciencies as function of the critical temperature Tc and the volumeflowrate _V3 isqualitativelysimilar to thatofcase1. The thermalefficienciesare higher now than in case 1 as had to be expected because of thelower Tmin value. Regarding the average value<hthþ> of all cycles inTable 7 we obtain <hthþ>¼ 28.4%, which amounts to 70% of theCarnot efficiency hth,Carnot¼ 40.5%. Comparing these 70% for case 2with the 67% for case 1, we learn that the ratio <hth,þ>/hth,Carnot isnearly the same which might be taken as a guideline for estimatingcycle efficiencies of processes with related Tmax and Tmin.

The real big difference between cases 1 and 2 is in the volumeflow rates _V4 or the ratios _V4=

_V3. For n-pentane in the s2 cycle onegets now _V4 ¼ 3:283 l=s ¼ 3:3 m3=s, for MM in the o3 cycle

Table 8Results for Case 3 (Tmax¼ 573.15 K, Tmin¼ 358.15 K, hth,Carnot¼ 0.375). The mass flow rate

Substance Tmax/Tc pmax/pc pmax (MPa) pmin (MPa) T4 (K) _V3(

Tmax> Tc, pmax/pc¼ 0.9, Type o3Cyclopentane 1.12 0.9 4.06 2.89E�01 494.21 109MM 1.10 0.9 1.73 6.29E�02 525.40 183MDM 1.02 0.9 1.27 1.13E�02 523.36 140

Tmax> Tc, pmax/pc¼ 1.2, Type s2Cyclopentane 1.12 1.2 5.41 2.89E�01 478.26 70MM 1.10 1.2 2.31 6.29E�02 517.66 117

Tmax< Tc, pmax¼ ps(Tmax), Type o2Toluene 0.97 0.8 3.22 4.60E�02 450.31 64MD2M 0.96 0.7 0.81 2.37E�03 525.08 165p-Xylene 0.93 0.6 2.00 1.90E�02 470.68 104m-Xylene 0.93 0.6 1.99 1.84E�02 471.26 104Ethylbenzene 0.93 0.6 2.06 2.03E�02 473.50 101MD3M 0.91 0.4 0.41 5.69E�04 534.47 331o-Xylene 0.91 0.6 2.00 1.90E�02 470.68 104Butylbenzene 0.87 0.3 0.92 3.94E�03 493.96 212

_V4 ¼ 23:8 m3=s, for toluene _V4 ¼ 29:0 m3=s and for MDM_V4 ¼ 156 m3=s which is already quite large. These large volumeflow rates _V4 are caused by the very low pressures pmin¼ ps(Tmin)and increase up to _V4 ¼ 5:154 m3=s for MD3M.

Summarizing, case 2 with Tmin¼ 311.15 K yields attractivethermal efficiencies hthþ for cycles with IHE but at the prize of largevolume flow rates _V4 at the turbine outlet. The overall ranking ofthe working fluids according to Eq. (13) yields 80 points for cyclo-pentane in the o3 cycle, 77 points for n-butane in the s2 cycle and76 points for n-pentane in the s2 cycle.

5.3. Case 3

For this casewith Tmax¼ 573.15 K and Tmin¼ 358.15 K the resultsare shown in Table 8. We remind that we consider only those o2and o3 cycles for which T2a is smaller than Ts(pmax), the saturationtemperature at the maximum pressure of the investigated cycle.With this criterion the o3 cycles of the n-alkanes drop out and wealso do not include their s2- cycles. The results for the s2 cycle ofMDM are also not shown because its critical temperatureTc¼ 564.13 is very close to Tmax.

The qualitative behaviour of the thermal efficiencies as functionof the critical temperature is similar to the findings of case 1 dis-played in Fig. 6. We observe again for cycles with IHE that thethermal efficiencies hthþ increase in general with the critical

_m and the volume flow rates _V3 and _V4 refer to 1 MW net power output.

l/s) _V4(l/s) _m (kg/s) hth, (%) �IHE hth, (%) þIHE Points Eq. (13)

1678 8.5 16.2 23.6 816225 14.7 11.7 23.5 61

24,329 15.0 12.4 25.6 64

1579 8.3 17.3 23.9 885944 14.3 12.4 24.0 66

6430 7.4 20.7 25.6 8391,262 15.4 12.8 26.6 6513,672 7.1 20.4 26.8 7613,981 7.0 20.4 26.8 7612,947 7.1 20.1 26.8 77

326,054 16.1 11.9 27.1 6213,672 7.1 20.4 26.8 7654,445 7.0 19.4 28.0 71

N.A. Lai et al. / Energy 36 (2011) 199e211208

temperatures Tc of the substances and that there is no remarkabledifference between cyclopentane, the siloxanes and the aromates.Regarding the average value <hthþ> of all cycles in Table 8 weobtain <hth,þ>¼ 25.8%, which amounts to 69% of the Carnot effi-ciency hth,Carnot¼ 37.5% similar as in Cases 1 and 2.

Considering the volume flow rates _V3 we see from Table 8 thatthey amount 70 l/s (s2) and 109 l/s (o3) for cyclopentane. Moreover,they are generally higher for the siloxanes than for the aromatesand range from 64 l/s for toluene to 331 l/s for MD3M. The ratios ofthe volume flow rates _V4=

_V3 range from 15 for cyclopentane in theo3 cycle to about 1000 for MD3M in the o2 cycle. Fig. 8 shows thethermal efficiencies hthþ vs. the volume flow rates _V4 at the turbineoutlet for cycles with IHE. The overall ranking of the working fluidsaccording to Eq. (13) yields 88 points for cyclopentane in the s2cycle, 83 points for toluene in the o2 cycle and 81 points forcyclopentane in the o3 cycle.

6. Power output optimization including heat transfer to theORC

As is known [10,29], the pinch point in the EHE may havea strong influence on the net power output of an ORC process fora given heat carrier which can be characterized by its inlettemperature Tin¼T5 and its heat capacity flow rate _C ¼ _mccp. Inparticular it is known for o2 cycles [29] that by variation of themaximum temperature Tmax of the ORC working fluid the netpower output j _Wj can be optimized for given T5 and _C.

Here, instead of optimizing the net power output of the ORCsystem j _Wj for a given value of the heat capacity flow rate _C, we askfor the minimum value of _C for an assumed value j _W j ¼ 1 MW,which makes comparisons more application oriented. Two heatcarrier inlet temperatures T5¼ 553.15 K (280 �C) and 623.15 K(350 �C) are considered. The minimum temperature of the cycleTmin is assumed as Tmin¼ 358.15 K (85 �C) which corresponds toa CHP process. In order to find theminimum heat capacity flow rate_C a variation of Tmax was made keeping for o3 processes pmax/pc¼ 0.9 and for the s2 processes p/pc¼ 1.2 fixed.

For the definition of a ranking the most interesting quantity isnow the minimised heat capacity flow rate _C. Other quantities ofinterest are again hthþ, hth�, _V3 and _V4. With similar arguments asfor Eq. (13) a number of points is then attributed according to

Points ¼100�2 _Cmin=

_C þ hthþ=hthþmax þ hth�=hth�max

þ _V3min= _V3 þ _V4min

= _V4��6: ð14Þ

Fig. 8. Thermal efficiencies hth vs. volume flow rates _V4 at the turbine outlet for Case 3(Tmax¼ 573.15 K, Tmin¼ 358.15 K) with IHE. C: cyclopentane, þ: MM, -: MDM, ,:toluene, ;: MD2M, A: p-, m-, and o-xylene, B: ethylbenzene, and �: butylbenzene.

The input data and results are given in Table 9 for T5¼ 553.15 Kand in Table 10 for T5¼ 623.15 K. The input data are Tmax and pmax/pc. Results are given for _V3, _V4, hthþ, hth�, _Q22a, _Q2a3, _C and for thenumber of points. The calculations of _C were made for processeswith IHE. In order to calculate the exergy efficiency for powerproduction xP from Eq. (9) we assume Tu¼ 288.15 K (15 �C). Finally,we remind that the outlet temperature of the heat carrier can bereadily obtained from

_Q2a3 ¼ _CðT6 � T5Þ (15)

6.1. Heat carrier inlet temperature Tin¼ 553.15 K

The input data and the results for the heat carrier inlettemperature Tin¼T5¼ 553.15 K (280 �C) are given in Table 9. Forthis case we consider as potential working fluids n-pentane,cyclopentane, MM, MDM, and toluene. For the assumed tempera-tures and j _Wj ¼ 1 MW the explicit relation for xP is obtained fromEq. (9) as xP¼ 12.97[kW/K]/ _C.

For n-pentane the critical temperature Tc is lower than the heatcarrier inlet temperature T5. We consider this case as an examplefor following cases and hence discuss it in more detail. Results forall three cycle types o2, o3, and s2 are shown. First we consideredo2 cycles with increasing temperatures Tmax and consequentlyincreasing pressures pmax starting from Tmax¼ 435.15 K (pmax/pc¼ 0.58). We observed that _C decreases with increasing temper-ature Tmax. As can be seen, however, from Fig. 2, the entropy on thedew line as function the temperature has a maximumvalue. If statepoint 3 of the o2 cycle which has to be on the dew line is shifted toa higher temperatures than that withmaximumdew point entropy,the expansion necessarily goes through the wet vapour regionwhich we want to avoid. Hence, for o2 cycles the temperatureshould only be increased up to the value with maximum dew pointentropy which occurs for pentane at 455.15 K yielding a value_C ¼ 45:3 kW=K. For further increase of the temperature and thecorresponding vapour pressure up to, e.g., pmax/pc¼ 0.90 theexpansion from the dew point goes through the wet region. Thiscan be avoided by superheating the vapour which was made for o3cycles with fixed pressure pmax/pc¼ 0.90 and increasing Tmaxvalues. The lowest _C value was found to be 44.0 kW/K for slightsuperheating by about 6 K to Tmax¼ 470.15 K. Further superheatingincreases _C again. Finally, supercritical cycles at pressures pmax/pc¼ 1.20 are considered. If Tmax is too low the expansion goes againthrough the wet region. With increasing Tmax the expansion leavesthe wet region and the best _C value is found for Tmax¼ 496.80 K as_C ¼ 42:3 kW=K with the exergy efficiency for power productionbeing xP¼ 0.31. Further increase of the temperature increases _C.

For cyclopentane again results for all three cycle types o2, o3,and s2 were obtained. The search for Tmax minimising _C in any ofthe cycles o2, o3 and s2 was done similarly as for n-pentane. Here,contrary to n-pentane the lowest _C value was found for the o2 cycleat Tmax¼ 489.00 K (pmax/pc¼ 0.74) as _C ¼ 39:1 kW=K with anexergy efficiency for power production being xP¼ 0.33.

For MM also results for all three cycle types o2, o3, and s2 areshown. We note that for MM the dew point with the highestentropy is very close to the critical point and hence expansionthrough the wet region did not occur for o2 cycles. Similar as forcyclopentane the lowest _C value was found for the o2 cycle, whichyields for Tmax¼ 493.15 K and pmax/pc¼ 0.69 (pmax¼ 1.33 MPa) theheat capacity flow rate _C ¼ 44:5 kW=K and the exergy efficiencyfor power production xP¼ 0.29.

For MDM the critical temperature Tc is slightly higher than theheat carrier inlet temperature T5 and hence only o2 cycles havebeen considered. The lowest _C value was found for Tmax¼ 477.81 Kand the rather low pressure pmax/pc¼ 0.23 (pmax¼ 0.32 MPa) for

Table 9Results for minimum heat capacity flow rates _C of the heat carrier for a net power output j _W j ¼ 1 MW obtained by variation of Tmax [T5¼ 553.15 K (280�), Tmin¼ 358.15 K(85 �C), _C for ORC with IHE].

Type Tmax (K) pmax/pc _V3 (l/s) _V4 (l/s) hth, (%) �IHE hth, (%) þIHE _Q22a (MW) _Q2a3 (MW) _C (kW/K) Points Eq. (14)

n-Pentane, Tc¼ 469.65 K, pc¼ 3.37 MPa, Tc/T5¼ 0.85o2 455.15 0.79 198 1892 11.9 13.4 0.95 7.46 45.3 70o3 470.15 0.90 167 1766 12.3 14.7 1.32 6.81 44.0 74s2 496.80 1.20 107 1588 13.1 16.7 1.65 5.99 42.3 82

Cyclopentane, Tc¼ 511.7 K, pc¼ 4.51 MPa, Tc/T5¼ 0.93o2 489.00 0.74 121 1937 15.8 17.3 0.53 5.79 39.1 84o3 513.45 0.90 94 1799 16.5 19.2 0.84 5.21 44.6 85s2 529.00 1.20 51 1778 16.9 18.6 0.54 5.37 43.1 94

MM, Tc¼ 518.7 K, pc¼ 1.925 MPa, Tc/T5¼ 0.94o2 493.15 0.69 220 7021 12.4 18.7 2.70 5.34 44.5 64o3 520.00 0.90 151 6548 12.6 20.5 3.06 4.89 49.5 65s2 529.00 1.20 72 6456 13.0 20.4 2.79 4.90 46.5 73

MDM, Tc¼ 564.13 K, pc¼ 1.415 MPa, Tc/T5¼ 1.02o2 477.81 0.23 950 31,761 11.5 18.2 3.17 5.49 47.4 55

Toluene, Tc¼ 591.80 K, pc¼ 4.109 MPa, Tc/T5¼ 1.07o2 456.01 0.13 882 10,266 14.6 16.1 0.61 6.23 47.4 59

N.A. Lai et al. / Energy 36 (2011) 199e211 209

which _C ¼ 47:4 kW=K and the exergy efficiency for powerproduction is xP¼ 0.27.

For toluene the critical temperature Tc is 7% higher than the heatcarrier inlet temperature T5 and hence again only o2 cycles areconsidered. The minimum value of _C is found at Tmax¼ 456.01 Kand pmax/pc¼ 0.13 (pmax¼ 0.53 MPa) for which _C ¼ 47:4 kW=Kand the exergy efficiency for power production is xP¼ 0.27.

The overall ranking of the working fluids for power outputoptimization including heat transfer to the ORC according to Eq.(14) yields 94 points for cyclopentane in the s2 cycle, 85 points forcyclopentane in the o3 cycle and 84 points for cyclopentane in theo2 cycle. In addition, n-pentane shows also a good ranking for thes2 cycle. The best exergy efficiency for power production isobtained with the o2 cycle of cyclopentane as xP¼ 0.33.

6.2. Heat carrier inlet temperature Tin¼ 623.15 K

The input data and the results for the heat carrier inlettemperature Tin¼T5¼ 623.15 K (350 �C) are given in Table 10. Forthis case we consider as potential working fluids n-pentane,cyclopentane, MM, MDM, toluene, and o-xylene. For the assumed

Table 10Results for minimum heat capacity flow rates _C of the heat carrier for a net power outp(85 �C), _C for ORC with IHE].

Type Tmax (K) pmax/pc _V3(l/s) _V4(l/s) hth, (%) �IHE hth

n-Pentane, Tc¼ 469.65 K, pc¼ 3.37 MPa, Tc/T5¼ 0.75o3 485.42 0.90 182 1693 12.2 16s2 496.80 1.20 107 1588 13.1 16

Cyclopentane, Tc¼ 511.7 K, pc¼ 4.51 MPa, Tc/T5¼ 0.82o2 489.00 0.74 121 1937 15.8 17o3 513.45 0.90 94 1799 16.5 19s2 529.00 1.20 51 1778 16.9 18

MM, Tc¼ 518.70 K, pc¼ 1.925 MPa, Tc/T5¼ 0.83o2 513.15 0.95 120 6613 12.8 20s2 529.00 1.20 72 6456 13.0 20

MDM, Tc¼ 564.130 K, pc¼ 1.415 MPa, Tc/T5¼ 0.91o2 514.78 0.47 353 27,502 12.4 21s2 574.00 1.20 56 22,980 12.9 25

Toluene, Tc¼ 591.80 K, pc¼ 4.109 MPa, Tc/T5¼ 0.95o2 510.15 0.33 239 7642 18.3 21

o-Xylene, Tc¼ 630.33 K, pc¼ 3.732 MPa, Tc/T5¼ 1.01o2 500.00 0.16 532 20,598 17.5 21

temperatures and j _Wj ¼ 1 MW the explicit relation for xP isobtained from Eq. (9) as xP¼ 8.87 [kW/K]/ _C.

For n-pentane we present results only for the o3 and s2 cycles.The optimal o3 cycle at the pressure pmax/pc¼ 0.90 is obtained forthe temperature Tmax¼ 485.42 K yielding _C ¼ 29:9 kW=K. Cyclesat the supercritical pressure pmax/pc¼ 1.20 yield an optimum valueof _C ¼ 28:3 kW=K for Tmax¼ 496.80 K. For that s2 cycle the exergyefficiency for power production is xP¼ 0.31.

For cyclopentane results for all three cycle types o2, o3, and s2are shown. The lowest _C value was found for the s2 cycle, whichyields for Tmax¼ 529.00 K and pmax/pc¼ 1.20 the value_C ¼ 23:4 kW=K and an exergy efficiency for power productionbeing xP¼ 0.38.

For MM results for the o2 and s2 cycles are shown. For the o2cycles the _C values decrease with increasing pmax or Tmax till veryclose to the critical point. In order to avoid running into the criticalpoint we stopped the investigation at pmax/pc¼ 0.95(Tmax¼ 513.15 K) where _C ¼ 27:5 kW=k is obtained. Superheatingin an o3 cycle at pmax/pc¼ 0.90 by about 10 K gave a higher _C valuethanwas obtained in the o2 cycle at the same pressure. Consideringthe s2 cycles at pmax/pc¼ 1.20 the expansion goes completely

ut j _Wj ¼ 1 MW obtained by variation of Tmax [T5¼ 623.15 K (350�), Tmin¼ 358.15 K

, (%) þIHE _Q22a (MW) _Q2a3 (MW) _C (kW/K) Points Eq. (14)

.1 1.96 6.21 29.9 68

.7 1.65 5.99 28.3 75

.3 0.53 5.79 24.9 77

.2 0.84 5.21 24.0 84

.6 0.54 5.37 23.4 92

.0 2.78 5.01 27.5 64

.4 2.79 4.90 27.3 69

.7 3.47 4.60 28.4 56

.1 3.77 3.99 29.8 71

.5 0.81 4.64 23.1 71

.1 0.97 4.73 24.0 65

N.A. Lai et al. / Energy 36 (2011) 199e211210

through the dry region for Tmax¼ 529.0 K and yields the best value_C ¼ 27:3 kW=K of all MM cycles with xP¼ 0.32.

For MDM the o2 cycles exhibit a minimum _C ¼ 28:4 at 514.78 K.For the s2 cycle at pmax/pc¼ 1.20 and Tmax¼ 574.00 K the expansiongoes completely through the dry region but the s2 result for_C ¼ 29:8 is worse than that for the best o2 cycle. The disadvantagewith MDM in o2 and s2 cyles is the large volume flow rates of thevapour at the turbine outlet.

For toluene we considered o2 cycles and found the optimum_C ¼ 23:10 for Tmax¼ 510.15 K (pmax¼ 1,3746 MPa) yielding anexergy efficiency for power production xP¼ 0.38. For the super-critical pressure cycles s2 at pmax/pc we found that the expansiongoes through the wet region for lower values of Tmax. If Tmax isincreased to 612.00 K the upper part of T,D _H-diagram comes closeto T5. This moves the pinch point temperature suddenly up toTp¼ 617.2 K which allows only a rather small heat transfer_Q56 ¼ 3:79 MW and hence requires a rather large heat capacityflow rate _C ¼ 52:3 at the inlet of the turbine.

For o-xylene the critical temperature Tc¼ 630.33 K is higher thanthe heat carrier inlet temperature T5 and hence only o2 cycles areconsidered. The minimum value of _C is found to be _C ¼ 24:0 kW=Kat pmax/pc¼ 0.16 (pmax¼ 0.60 MPa) and Tmax¼ 500.00 K yielding anexergy efficiency for power production xP¼ 0.37. Similar to MDM,thedisadvantageofo-xylene in theo2 cycles is the largevolumeflowrates of the vapour at the turbine inlet and outlet.

The overall ranking of the working fluids for power outputoptimization including heat transfer to the ORC according to Eq.(14) yields 92 points for cyclopentane in the s2 cycle, 84 points forcyclopentane in the o3 cycle and 77 points for cyclopentane in theo2 cycle. In addition, n-pentane shows again a good ranking for thes2 cycle. The best exergy efficiency for power production isobtained with the s2 cycle of cyclopentane as xP¼ 0.38.

7. Summary

In the present paper we have investigated potential pureworking fluids for high-temperature ORC processes. The analysis isbased on thermodynamic data derived from the molecular basedequations of state BACKONE and PC-SAFT. The fluids considered arealkanes, linear siloxanes and aromates.

In a first part (Section 5) we considered “isolated”ORC processesat given maximum and minimum temperatures and pressureswithout including a pinch analysis of EHEs. In this part of the studywe found certain systematic trends. In particular it was found thatwith internal heat recovery, the thermal efficiencies <hthþ> aver-aged over all substances amount to about 70% of the Carnot effi-ciency at given Tmax and Tmin. The effect of the individual substancesis reflected in an increase of hthþ with the critical temperature Tcwhich is modest for the aromates and siloxanes.

These results are similar to those from our previous study onworking fluids for low temperature ORC processes [10] in o2 cycleswith Tmax¼ 100 �C and Tmin¼ 30 �C and internal heat recovery.There, the thermal efficiencies hthþ show also a modest butsomewhat scattering increase with the critical temperature Tc.Moreover, the thermal efficiency <hthþ> averaged over allsubstances amounts 13.2% which, trivially, is considerably lowerthan the values found here for the high-temperature ORCprocesses. It is, however, interesting to note that this value is alsojust 70% of the Carnot efficiency.

In the second part (Section 6) we included a pinch analysis forthe heat transfer from the heat carrier to the ORC working fluid byan EHE. For a given inlet temperature Tin of the heat carrier wesearched for ORC working fluids and cycle conditions which giveaminimumvalue of the heat capacity flow rate _C for the productionof 1 MW net power output.

For both parts, “isolated” ORC and ORCþEHE we introduceda ranking which is based on the thermal efficiency of the ORC andon the heat capacity flow rates of the heat carrier as well as on thevolume and the heat flow rates. It was found that cyclopentane isthe best working fluid for all cases studied.

Acknowledgement

The authors gratefully acknowledge fruitful discussions withProfessor Dr.-Ing. Jadran Vrabec and Dipl.-Ing. Frithjof Dubberke,Universitaet Paderborn, and with Dr.-Ing. Wilhelm Althaus,Fraunhofer-Institut UMSICHT Oberhausen. Moreover, Ngoc Anh Laigives thanks to Österreichischer Austauschdienst for financialsupport by a Technologiestipendium.

References

[1] Rogers G, Mayhew Y. Engineering thermodynamics, work and heat transfer.4th ed. Harlow: Longman Scientific & Technical; 1992. pp. 239e243.

[2] ORC-HP-technology. In: VDI-Berichte 539. VDIeVerlag Düsseldorf, ISBN3180905395; 1984. Proceedings of VDI-Seminar 10e12 Sept. 1984 ETH Zürich.

[3] Hammer H, Röhmfeld M. Abwärmenutzung zur Krafterzeugung mittels neuerKreislaufmedien. In: VDI-Bericht 415. VDI-Verlag Düsseldorf; 1981. pp.81e87.

[4] Schuster A, Karellas S, Kakaras E, Spliethoff H. Energetic and economicinvestigation of Organic Rankine Cycle applications. Appl Therm Eng 2009;29:1809e17.

[5] Angelino G, Colonna P. Organic Rankine cycles for energy recovery frommolten carbonate fuel cells. In: 35th Intersociety Energy Conversion Engi-neering Conference and Exhibit, Las Vegas, NV. Reston, VA: AIAA; 2000.

[6] Angelino G, Colonna P. Air cooled siloxane bottoming cycle for moltencarbonate fuel cells. In: 2000 Fuel Cell Seminar, No 114, Portland, OR; 2000.

[7] Drescher U, Brueggemann D. Fluid selection for the Organic Rankine Cycle(ORC) in biomass power and heat plants. Appl Therm Eng 2007;27:223e8.

[8] Wang J, Dai Y, Gao L. Exergy analyses and parametric optimizations fordifferent cogeneration power plants in cement industry. Appl Energy 2009;86:941e8.

[9] Desai NB, Bandyopadhyay S. Process integration of organic Rankine cycle.Energy 2009;34:1674e86.

[10] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low-temperature organic Rankine cycles. Energy 2007;32:1210e21.

[11] Yari M. Performance analysis of the different Organic Rankine Cycles (ORCs)using dry fluids. Int J Exergy 2009;6:323e42.

[12] Kosmadakis G, Manolakos D, Kyritsis S, Papadakis G. Comparative thermo-dynamic study of refrigerants to select the best for use in the high-temper-ature stage of a two-stage organic Rankine cycle for RO desalination.Desalination 2009;243:74e94.

[13] Dai YP, Wang JF, Gao L. Parametric optimization and comparative study oforganic Rankine cycle (ORC) for low grade waste heat recovery. EnergyConvers Manage 2009;50:576e82.

[14] Wang XD, Zhao L. Analysis of zeotropic mixtures used in low-temperaturesolar Rankine cycles for power generation. Solar Energy 2009;83:605e13.

[15] Chacartegui R, Sanchez D, Munoz JM, Sanchez T. Alternative ORC bottomingcycles for combined cycle power plants. Appl Energy 2009;86:2162e70.

[16] Yari M. Exergetic analysis of various types of geothermal power plants. RenewEnergy 2010;35:112e21.

[17] Tchanche BF, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection fora low-temperature solar organic Rankine cycle. Appl Therm Eng 2009;29:2468e76.

[18] Obernberger I, Hammerschmid A, Bini R. Biomasse-Kraft-Wärme-Kopplungenauf Basis des ORC-Prozesses-EU-THERMIE-Projekt Admont (A). In: Proc. VDI-Tagung “Thermische Nutzung von fester Biomasse”, Salzburg, Mai 2001. VDIBericht 1588. VDI-Verlag Düsseldorf, ISBN 3-18-091588-9; 2001. p. 283e302.

[19] Obernberger I, Thonhofer P, Reisenhofer E. Description and evaluation of thenew 1,000 kWel Organic Rankine Cycle process integrated in the biomass CHPplant in Lienz, Austria. Euroheat Power 2002;10:1e17.

[20] Althaus W. ORC-anlagen 20e120 kWel, Abwärmeverstromung bei Bio-gasmotoren, http://www.umsicht.fraunhofer.de/geschaeftsfelder/geschaeftsfeld/downloads/1208164782.pdf.

[21] Larjola J. Electricity from industrial heat using high-speed organic Rankinecycle (ORC). Int J Product Econom 1995;41:227e35.

[22] van Buijtenen J, van Hasselt RJ, Koolwijk E, Lemmens H, Siedlecki M. Hal-baarheidstudie ORC in combinatie met WK. Cogen Projects, http://gasunie.eldoc.ub.rug.nl/FILES/root/2004/3377338/3377338.pdf; 2004.

[23] Colonna P, Nannan NR, Gurdone A, Lemmon EW. Multiparameter equations ofstate for selected siloxanes. Fluid Phase Equilib 2006;244:193e211.

[24] Müller A, Winkelmann J, Fischer J. The Backone family of equations of state: 1.Nonpolar and polar pure fluids. AIChE J 1996;42:1116e26.

N.A. Lai et al. / Energy 36 (2011) 199e211 211

[25] Gross J, Sadowski G. Perturbed-chain SAFT: an equation of state based ona perturbation theory for chain molecules. Ind Eng Chem Res 2001;40:1244e60.

[26] Wendland M, Saleh B, Fischer J. Accurate thermodynamic properties from theBACKONE equation for the processing of natural gas. Energy Fuels 2004;18:938e51.

[27] Lai NA, Wendland M, Fischer J. Description of cyclic alkanes and aromateswith BACKONE equation of state, in preparation.

[28] Lai NA, Wendland M, Fischer J. Description of linear siloxanes with PC-SAFTequation. Fluid Phase Equilib 2009;283:22e30.

[29] Koglbauer G, Saleh B, Wendland M, Fischer J. Arbeitsmedien für Nie-drigtemperatur-ORC-Prozesse. In: Proceedings of the ninth symposiumenergy innovation, 15e17 February 2006, TU Graz. Graz: Verlag der TU Graz,ISBN 3-902465-30-1; 2006. p. 170e1.

[30] Schuster A, Karellas S, Aumann R. Efficiency optimization potential insupercritical Organic Rankine Cycles. Energy 2010;35:1033e9.

[31] International Labour Organization, International Occupation Safety and HealthInformation Centre. International Chemical Safety Cards, http://www.ilo.org/public/english/protection/safework/cis/products/icsc/dtasht/index.htm.

[32] Safety Officer in Physical Chemistry at Oxford University, http://msds.chem.ox.ac.uk/.

[33] Merck Sicherheitsdatenblatt, http://www.merck-chemicals.com.[34] Dow Corning Sicherheitsdatenblatt, http://www2.dowcorning.com/DataFiles/

090007b2810e366c.pdf.[35] Julabo Safety Data Sheet, http://www.julabo.com/Download/Julabo_Thermal_

C2_e.pdf.[36] Boublik T. Hard convex body equation of state. J Chem Phys 1975;63:4084.[37] Saager B, Fischer J. Construction and application of physically based equations

of state, II. The dipolar and quadrupolar contributions to the Helmholtzenergy. Fluid Phase Equilib 1992;72:67e88.

[38] Wertheim MS. Fluids with highly directional attractive forces. I. Statisticalthermodynamics. J Statist Phys 1984;35:19e34.

[39] Barker JA, Henderson D. Perturbation theory and equation of state for fluids. II.A successful theory of liquids. J Chem Phys 1967;47:4714e21.

[40] Castro-Marcano F, Olivera-Fuentes CG, Colina CM. JouleeThomson inversioncurves and third virial coefficients for pure fluids from molecular-basedmodels. Ind Eng Chem Res 2008;47:8894e905.

[41] Prausnitz JM, Poling BE, O’Connell JP. The properties of gases and liquids. 5thed. New York: McGraw-Hill; 2001.

[42] Chen SS, Wilhoit RC, Zwolinski BJ. Ideal gas thermodynamic properties andisomerization of n-butane and isobutene. J Phys Chem Ref Data1975;4:859e69.

[43] Pitzer KS, Kilpatrick JE. The entropies and related properties of branchedparaffin hydrocarbons. Chem Rev 1946;39:435e47.

[44] Dorofeeva OV, Gurvich LV, Jorish VS. Thermodynamic properties of twenty-one monocyclic hydrocarbons. J Phys Chem Ref Data 1986;15:437e64.

[45] Pitzer KS, Scott DW. The thermodynamics and molecular structure of benzeneand its methyl derivatives. J Am Chem Soc 1943;65:803e29.

[46] Miller A, Scott DW. Chemical thermodynamic properties of ethylbenzene.J Chem Phys 1978;68:787e1324.

[47] Nannan NR, Colonna P, Tracy CM, Rowley RL, Hurly JJ. Ideal-gas heat capacitiesof dimethylsiloxanes from speed-of-sound measurements and ab initiocalculations. Fluid Phase Equilib 2007;257:102e13.

[48] Miyamoto H, Watanabe K. A thermodynamic property model for fluid-phasen-butane. Int J Thermophys 2001;22:459e75.

[49] Polt A, Platzer B, Maurer G. Parameter der thermischen Zustandsgleichungvon Bender fuer 14 mehratomige reine Stoffe. Chem Tech (Leipzig) 1992;44:216e24.

[50] Span R. Multiparameter equations of state e an accurate source of thermo-dynamic property data. Berlin: Springer; 2000. 367 pp.

[51] NIST Chemistry WebBook. Thermophysical properties of fluids, http://webbook.nist.gov/chemistry/fluid/.

[52] Obernberger I. Description of the ORC technology for biomass Combined Heatand Power plants as well as further possibilities for process integration. Graz:Bios-Bioenergiesysteme GmbH, http://www.bios-bioenergy.at/en/electricity-from-biomass/orc-process.html; 2008.

[53] Gaderer M. Organic Rankine Cycle (ORC) Kraft-Wärme-Kopplung bei Ver-wendung eines organischen Arbeitsmediums in Kombination mit einer Bio-massefeuerung. Bayerisches Zentrum für angewandte. Energieforschung e.V.(ZAE Bayern), http://www.carmen-ev.de/dt/portrait/sonstiges/gaderer.pdf;2002.

[54] Gaderer M. Stromerzeugung aus Biomasse und Abwärme. Bayerisches Zen-trum für angewandte. Energieforschung e.V. (ZAE Bayern), http://www.carmen-ev.de/dt/hintergrund/vortraege/fg_biogas/1_09_Gaderer.pdf; 2008.