Accepted Manuscript Novel classification of pure working fluids for Organic Rankine Cycle Gábor Györke, Ulrich K. Deiters, Axel Groniewsky, Imre Lassu, Attila R. Imre PII:
S03605442(17)321783
DOI:
10.1016/j.energy.2017.12.135
Reference:
EGY 12084
To appear in:
Energy
Received Date: 6 September 2017 Revised Date:
21 November 2017
Accepted Date: 26 December 2017
Please cite this article as: Györke Gá, Deiters UK, Groniewsky A, Lassu I, Imre AR, Novel classification of pure working fluids for Organic Rankine Cycle, Energy (2018), doi: 10.1016/j.energy.2017.12.135. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Novel Classification of Pure Working Fluids for Organic Rankine Cycle Gábor Györke1, Ulrich K. Deiters2, Axel Groniewsky1, Imre Lassu1, Attila R. Imre1,3,* 1
Budapest University of Technology and Economics, Department of Energy Engineering
Muegyetem rkp. 3, H1111 Budapest, Hungary 2
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Institute of Physical Chemistry, University of Cologne, Luxemburger Str. 116, D50939 Köln, Germany Thermohydraulics Department, MTA Centre for Energy Research, P.O. Box 49, Budapest 1525, Hungary
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* corresponding author,
[email protected]
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Abstract

The need for a refined classification for working fluids (beyond the classical categories wet/isentropic/dry) is demonstrated. A novel classification based on characteristic points is introduced. Potential technical applications for the new classification are presented. Categories and characteristic points for 57 pure working fluids are provided.
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Power generation from lowtemperature heat sources (80300 °C) like thermal solar, geothermal, biomass or waste heat has been becoming more and more significant in the last few decades. Organic Rankine Cycle (ORC) uses organic working fluids, obtaining higher thermal efficiency than with water used in traditional Rankine Cycles, because of the physical (thermodynamic) properties of these fluids. The traditional classification of pure (onecomponent) working fluids is based on the quality of the expanded vapour after an isentropic (adiabatic and reversible) expansion from saturated vapour state, and distinguishes merely three categories: wet, dry and isentropic working fluids. The purpose of this paper is to show the deficiencies of this traditional classification and to introduce novel categorisation mostly to help in finding the thermodynamically optimal working fluid for a given heat source.
Keywords: specific entropy, Ts diagram, droplet formation, quality, qT diagram, isentropes
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Subscripts s isentropic T isothermal
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Abbreviation ORC Organic Rankine Cycle ECO economizer EVAP evaporator SH superheater C condenser P pump T turbine G generator H heat source R recuperator (preheater)
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primary characteristic point on saturated liquid curve critical point secondary characteristic point on saturated vapour curve (higher temperature) secondary characteristic point on saturated vapour curve (lower temperature) vapour quality, mol mol1 specific entropy, J mol1 K1 absolute temperature, K primary characteristic point on saturated vapour curve
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A C M N q s T Z
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Superscripts u higher entropy d lower entropy or temperature * technical temperature limit
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ACCEPTED MANUSCRIPT 1. Introduction
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For the past few decades, power generation tends to turn to alternative energy sources; wind energy, photovoltaics, but also unconventional sources of thermal energy. Examples for the latter are geothermal energy, solar heat, biomassbased heat production, or waste heat from other industrial processes. Usually these unconventional sources of thermal energy do not have as high energy densities as the socalled conventional ones, and the heat is supplied at a lower temperature. Power plants based on the conventional Rankine cycle, using water as working fluid, cannot exploit such heat sources efficiently. An alternative solution is the socalled Organic Rankine Cycle (ORC), which uses nonconventional working fluids (mostly organic ones, although some of them are inorganic, like carbon dioxide) and which are suitable for power generation from various lowtemperature heat sources [1,2]. According to the ORC World Map [3], the number of installed major ORC units in mid2016 exceeded 700.
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The traditional classification of the working fluids [4,5] is based on the quality of the expanded vapour at the outlet of the turbine, which is often referred to as expander in ORC applications. According to this approach, the categories of ORC working fluids are wet, dry and isentropic [68]. • For a wet working fluid, an isentropic (adiabatic and reversible) expansion starting from a saturated vapour state will end in the twophase region, which is also called “wet vapour region”. In a temperature–entropy diagram, the saturated vapour curve of a wet fluid has a negative slope at each point (dT/ds < 0), which means that the entropy increases with decrease of saturation temperature. • In contrast to this, a similar isentropic expansion of a dry fluid leads to a final state in the singlephase region, which is also called “superheated vapour region” or “dry region”. The saturated vapour curve of a dry fluid has mainly a positive slope (dT/ds > 0). At high temperatures, the curve passes through an entropy maximum (ds/dT = 0) and then has a small portion with negative slope. • For an isentropic fluid, an isentropic expansion starting from a saturated vapour state will end in saturated vapour state. The saturated vapour curve of an ideal isentropic fluid has an infinite slope (dT/ds → ∞) at each point after reaching the first (highest temperature) point where ds/dT = 0; this point is similar to the point of entropy maximum in case of dry fluids. Figs. 1a, c and e show the traditional three categories, marking the ideal steps of the Organic Rankine Cycle, including the adiabatic expansion. Each type of working fluid needs a special cycle layout as explained in Figs. 1b, d and f. • When wettype working fluids (Figs. 1a and b) are used, it might be necessary to superheat the fluid (see process 45 in Fig. 1a), because the formation of liquid droplets in the lowpressure stage of the turbine has to be kept within limits to avoid erosion of the blades. Minimising the droplet formation is also beneficial to the isentropic efficiency of the turbine, as it decreases the twophase (wet) steam energy loss. Moreover, superheating increases greatly the average temperature, at which the 3
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heat is added to the cycle, which consequently increases the Carnot efficiency. It makes, however, the working fluid less desirable for lowgrade waste heat recovery. Besides, in some cases the superheater can be the most expensive heat exchanger among the ones that are responsible for vapour generation, since here occurs the highest temperature values in the cycle – on both heat source and working fluid sides – so it may require special alloys, although this is usually not true for lowtemperature heat sources. The superheater also needs a relatively larger effective heat transfer surface compared to economiser (ECO) and evaporator (EVAP), because the heat transfer coefficient in the case of a liquid flow and boiling fluid is much larger than in the case of a vapour (superheated steam) flow. Fig. 1a shows that the expansion can start from any state between the ones marked as 4 and 5, but the closer the initial state is to state 4, the higher is the rate of blade erosion in the turbine, and also the more energy loss occurs. • Drytype working fluids do not require superheating to avoid droplet formation in the turbine because of the shape of their saturated vapour curve. Moreover, expanded vapour exits the turbine in considerably superheated state. The layout and the Ts diagram for the ORC cycle can be seen in Figs. 1c and d. Superheated vapour is disadvantageous for the condenser, since it can significantly increase the cooling load and decrease its overall heat transfer coefficient by negatively affecting the film condensation on the outer surface of cooling pipes. Therefore, a recuperative heat exchanger, also called preheater, can be placed before the condenser to eliminate these disadvantages by cooling the superheated vapour almost to the saturated state (see process 67 in Fig. 1c). On the other side, saturated or slightly subcooled liquid is pumped from the condenser to the preheater, which serves the same purpose as a feedwater heater in conventional steam power plants. This method also improves the thermal efficiency of the ORC by increasing the average temperature during heat input, so that the energy of the superheating is not rejected from the cycle, but recovered. • For isentropic working fluids, neither superheating nor recuperative cooling are necessary, because theoretically the expansion line coincides with the saturated vapour curve in the Ts diagram. On the other hand, in real systems – as it can be seen in Figs. 1e and f – a slight superheating occurs before the expansion, which means that the expansion line runs slightly on the highentropy side of the saturation curve and does not penetrate deeply into the superheated zone. In this case, superheating is a safety measure rather than improvement of thermal efficiency, as it merely serves to avoid unwanted condensation of the fluid before it enters the turbine. It should be noted that there is no need for this measure in case of real expansion processes (ds > 0) or for socalled real isentropic working fluids, which we discuss in the following sections. Evidently, the shape and slope of the saturated vapour curve of the Ts diagram appear to be very important for the selection of working fluids [7–9]. Therefore any classification for these fluids should be based on the properties of this curve. Of course, the selection of working fluids cannot be based on the saturated vapour curve alone; often chemical or other nonphysical criteria must be taken into consideration [10–14] as well. 4
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2. Shortcomings of the traditional categories Although from a pure technological viewpoint, traditional (wetdryisentropic) categories seem to be sufficient, there are at least two cases where these simple classes are not enough [9,15].
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One of them can be observed in the case of dry fluids. Fig. 2 shows the T–s diagrams of two dry working fluids with an isentropic expansion starting from a saturated liquid state (indicated as 12). Three characteristic points have been marked; the initial and final point of the Ts diagram (marked as A and Z) and the critical point (C). In case (a) the expansion from the saturated liquid state can only end in the twophase (wet vapour) zone, whereas in case (b), the expansion can end not just in the twophase zone (2*), but even in the superheated vapour zone (2), assuming that the entropy of the initial liquid state was larger than sZ, the entropy at point Z. So the difference is whether we can get singlephase (quality = 1) vapour by expanding liquid isentropically or not. This is rather of theoretical than practical significance for ORC technology, but for other technologies which use fast evaporation of liquids – for example the TFC, trilateral flash cycle [16]  this distinction may be important.
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In the same figure, compression processes (34) starting from the saturated vapour state are shown as well. In case (a), the dry steam cannot be liquefied completely. Depending on the extent of compression, both twophase (4*) and superheated vapour (4) states can be reached. In case (b), after passing the twophase region (4*), further compression leads to the pressurized liquid region (4). This distinction has a practical importance in refrigeration cycles, too. The compressor increases the pressure of saturated – or, for the safety of the machine, slightly superheated – vapour. Even if we assume a real adiabatic process in the compressor, which means entropy production during compression, (b)type fluids almost certainly cannot be used because of the liquid formation during the compression process, whereas (a)type fluids – depending on the isentropic efficiency of the equipment – could be potential candidates as refrigerants. Moreover, using (a)type fluids leads into a slight superheating at the end of the compression, which is beneficial for the operation of the compressor as well as for the condenser. Another kind of problem arises in case of isentropic fluids. First of all, one can say that a fluid with exactly isentropic behaviour does not exist. By “exactly isentropic” we mean that the saturatedvapour curve in temperature–entropy space has an infinite (more precisely a negative infinite) slope; such a fluid could be called “ideal” isentropic fluid. There are, however, some fluids which come close to ideal isentropic behaviour, as a considerable part of their saturated vapour curve exhibits a nearly constant entropy. Fig. 1e is the T–s diagram of trichlorofluoromethane (CCl3F, R11), which is a good example for ideal isentropic behaviour. In reality, these working fluids have an Sshaped saturated vapour curve with two parts of negative and one part of positive slope. Directly below the critical point the curve must have a negative slope, then, after passing through a local entropy maximum, a positive 5
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part, and finally, “bend” back to negative slope. In contrast to this behaviour, dry fluids have one part with negative and one with positive slope, and wet fluids have negative slope throughout. Analysis of experimental data of fluids considered isentropic (like R11) as well as a theoretical study based on the van der Waals equation of state [9] show that probably all isentropic fluids have an Sshaped vapour saturation curve (negativepositivenegative slopes in sequence). Some further consideration about having an infinite slope part in a Ts diagram can be found in the following section as well as in Appendix A.
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Fig. 3 shows T–s diagrams of “real isentropic” fluids in as well as some isentropic expansions (ideal process in turbines) from a saturated vapour state. Although these types of fluids could be considered as dry at high temperature and wet at low temperature, it is preferable to keep the isentropic category. In these cases it is also possible to start the isentropic expansion on the saturated vapour curve and terminate it on it as illustrated by the 12 and 34 expansion lines in Fig. 3a. Therefore – replacing the traditional definition – the fluid is isentropic, if it is possible to find an isentropic expansion line starting from and ending in a saturated vapour state in such a way that the expansion line does not enter the twophase (wet) region. It can be easily realised that this is just a modified definition; it does not overwrite the traditional one, but merely makes it applicable to real fluids. Figs. 3b and c demonstrate that the shape of the saturated vapour curve greatly affects the outcome of the isentropic expansion process in turbines. The most important issue is whether the formation of liquid droplets occurs during the expansion, and if so, to what degree. While for fluids represented by Fig. 3c, expansions starting from a wide range of possible states can be kept superheated (singlephase) during the process, this cannot be done for fluids represented by Fig. 3b, unless the expansion is terminated at higher pressure. This, however, would eventually decrease the thermal efficiency of the cycle.
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Because of these important theoretical and practical differences between working fluids within the same categories, a new and extended classification is necessary, which is compatible with the traditional one (wet, dry and isentropic), but provides more accurate definitions and categories.
3. Novel classification
3.1. Characteristic points
In order to classify saturation curves of working fluids we define five characteristic points on these curves – three primary and two secondary ones. The relative location or even the existence of these points will be the base of the new categories. The primary points always exist (they were already mentioned briefly in Section 2); the secondary ones exist for dry and isentropic working fluids only. The characteristic points are illustrated in Fig. 4, which shows the Ts diagram of three alkanes (data are taken from the NIST Chemistry WebBook [17]).
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The primary points A and Z are defined as the points with the lowest temperature on the saturated liquid and vapour curve respectively. The lowest temperature may be chosen for physical reasons (e.g., the temperature of the melting point or the triple point) or technical reasons (e.g. environmental temperature). Points A and Z can be characterized by the specific entropy of saturated liquid and vapour at the same reference temperature. The primary point C indicates the critical point of the working fluid. Here the slope of the saturation curve becomes zero (dT/ds = 0). The secondary points M and N are defined as the local entropy extrema on the saturated vapour curve. M can be a local entropy maximum for the Ts curve, while N represents a local minimum. Both are mathematically characterized by (ds/dT)M,N = 0. According to the definition, the traditional “wet” category has no secondary characteristic points, whereas category dry has one secondary point (M), and isentropic fluids have both M and N secondary characteristic points. A graphical visualisation of all the above can be seen in Figs 4ac.
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One can also define socalled tertiary characteristic points. Since they are not relevant for this classification, they will not be included in our description, but their relative position can be technologically important, therefore we give their definition in Appendix B.
3.2. Constraints on characteristic points
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As stated above, the new classification is based on the location of the characteristic points relative to each other. The ascending order of the characteristic points according to their specific entropy seems to be the most appropriate to serve this purpose, since the relative order of the temperatures is always the same: TA = TZ < (TN < TM <) TC (the parentheses refers to whether these secondary points exist or not).
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The existence of the characteristic points is decided by the following rules: a) Primary points A, C and Z can be defined for all working fluids. b) Wet working fluids do not have secondary points. c) Dry working fluids have only the secondary point M. d) Isentropic working fluids have both M and N secondary points. e) If point N exists, then point M also exists, but the opposite is not true. Furthermore, the following constraints on specific entropy of the points have to be taken into consideration, as they affect the total number of possible new categories. 1) 2) 3) 4)
Point A is the lowermost in entropy. Point M – if it exists – has a larger entropy than point C. If point N does not exist, point M has the largest entropy, Point N – if it exists – has a lower entropy than points M and Z.
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ACCEPTED MANUSCRIPT 3.3. New categories Since the traditional categories are compatible with the new ones, they provide a solid foundation for them. As already mentioned, the new categories are defined according to the order of specific entropy of the characteristic points, so later we can refer to them with these entropy sequences.
Rule b from section 3.2 restricts the number of wettype sequences to 1, because without point M, at which the saturated vapour line has a maximum value (ds/dT = 0), the entropy of point Z must always be greater than that of point C. Therefore, we can define only one wettype sequence, namely ACZ (excluding AZC). Fig. 4a shows the T–s diagram of methane as a typical example for this case. Constraint 2, which imposes that point M always has larger entropy than point C, reduces the number of possible sequences in category “dry” from 6 to 2. Point M must not follow point A immediately, which excludes 2 sequences, namely AMCZ and AMZC. If point A is followed by point Z, only one sequence remains possible, namely AZCM, and we can exclude one more ordering (AZMC). If point A is followed by point C, Constraint 3 excludes one more sequence, namely ACMZ, because if there is no point N, point M must have the largest entropy. The total number of drytype sequences is therefore 2, namely AZCM and ACZM. Of the 4!=24 sequence permutation of the “isentropic” type, where both secondary points exist, Constraint 2 excludes the sequences in which point M follows directly point A. This reduces the possible number of sequences by 6 (3!), from 24 to 18. Constraint 4 excludes 6 (3!) further sequences, in which point Z immediately follows directly point A. Applying Constraints 2) and 4) to the remaining 12 permutation, we obtain merely 5 possible isentropictype sequences.
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According to Constraint 1) from section 3.2 , sequences always start with point A. By merely considering the permutations of the other characteristic points, we could – in principle – define 2! = 2 wet, 3! = 6 dry and 4! = 24 isentropic subcategories making a total of 32. The other constraints and rules, however, decrease the number of possible sequences.
Fig. 5 shows all the possible sequences in a tree diagram, while Fig. 6 displays their T–s and qT (qualitytemperature, explained below) diagrams. We propose to extend the traditional classification of working fluids (wet/dry/isentropic) by introducing eight subclasses based on the possible sequences of characteristic points. We use the sequences (without the hyphens) as labels of these classes, for instance ACZ or ACZM. It should be mentioned here, that although it might be theoretically possible to have equality for the entropy values (for example sZ=sC), we are ignoring these cases for two reasons. First, they can be included into the existing categories, then in those cases, some of the tertiary points would coincide with the primary or secondary ones, but our classification would not be affected. The other reason is that, in real fluids, such an exact equality is forbidden by Gibbs’ 8
ACCEPTED MANUSCRIPT phase rule. On the other hand, to have a closed theoretical framework, these cases should be also considered, therefore as theoretical possibilities, discussed in Appendix B.
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We should mention here that, although a significant amount of pure working fluid have been considered in the literature, only a very small fraction of them meets the criteria of industrial applications. The most commonly used – not patent protected – ORC working fluids are R245fa (ACNMZ), toluene (ANZCM), npentane (ANCMZ), R134a (ACZ), ammonia (ACZ) and CO2 (ACZ). More detailed list can be found in the Supplementary Material.
4. Analysis of the new categories
q=
amount of vapour total amount of the fluid
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Avoiding droplet formation or keeping it within strict limits is one of the most crucial issues in design process of ORC plants. It is therefore useful to discuss qualitytemperature (qT) diagrams of various expansion processes. The quality of vapour in the twophase fluid is defined as: [mol/mol] or [kg/kg]
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The liquid content of the twophased fluid is therefore 1−q. The domain of quality is the range between liquid and vapour saturation curve, and by definition, saturated liquid is 0 and saturated vapour is 1 in quality. We consider the quality of singlephase subcooled and superheated fluid undefined, although sometimes they are defined as 0 and 1, respectively. Here, all qT diagrams are equilibrium diagrams; it is possible that, during fast expansion, the fluid crosses the phase boundary, but remains in metastable (dry) vapour condition for significant period of time. In this work, metastable states [18,19] are not considered.
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It should be noted that, during an adiabatic expansion in the single as well as the twophase state, the pressure can be uniquely calculated from the temperature and the initial conditions, so that the discussion of twodimensional q–T diagrams is sufficient, instead of threedimensional pqT ones [15]. The qT diagrams for the eight categories can be seen in Fig. 6, together with the corresponding Ts diagrams. The qvalues are shown along ten different isentropic lines; their corresponding entropyvalues are marked on the Ts diagrams. For clarity, the liquidonly and vapouronly values (where q is 0 or 1 over a finite temperature range) are not shown (except for Appendix A to show the peculiar features). Figs. 6a and b shows the Ts diagram of the only one wettype class, with the corresponding qT diagram. In the former, the isentropic lines are evenly spaced between points A and Z. Wet working fluids can be classified as ACZtype in the new classification scheme. It is evident that using wet fluids always necessitate fluid superheating to avoid hazardous droplet
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Figs. 6cf show the two drytype classes, namely ACZM and AZCM. The q–T diagrams (Fig. 6d,f) clearly demonstrate the difference between the two classes, as well as the need for making the distinction (already mentioned in Section 2). There is no isentropic curve in class ACZM, which runs from quality 0 to 1. This means that it is not possible to evaporate the liquid completely by an isentropic expansion. On the other hand, class AZCM has such isentropic lines, for example the ones with square, diamond, triangle and pentagram markers (orange, turquoise, pink and brown). In contrast to wet (ACZ) fluid, both dry classes (ACZM as well as AZCM) show isentropic lines crossing the vapour saturation curve between points C and M, passing through a maximum in liquid content and then crossing the vapour saturation curve somewhat below TM; this is a socalled reentrant phase transition. Beyond this crossing, the fluid (now in singlephase state) becomes more and more superheated, hence the general need for preheater (recuperator) for this class of fluids.
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Figs. 6go show the classes for isentropic fluids. The existence of isentropes running from 0 (singlephase liquid) to 1 (singlephase vapour) depends on whether point N precedes or follows point C in entropy. If it precedes (as for class ANZCM, Figs. 6g,h) , it is possible to evaporate liquid completely by an isentropic expansion. But while for some isentropes a complete evaporation is possible by expanding the fluid even down to TA, for others it must be ended a a slightly higher temperature. In the qT diagram, these isentropes start on the liquid side (q=0), run to the vapour side, and then reenter the diagram at lower temperature. The other two classes where N precedes C behave similarly, but of course the relative position of point Z influences the q range of isentropic curves with complete evaporation. For the turbine process, class ANZCM (Figs. 6g,h) seems the most favourable, but also necessitates a preheater to decrease superheating before the fluid enters the condenser. In case of class ANCZM (Figs. 6i,j) droplet formation in the lowpressure stage (end of expansion) can be completely avoided by choosing, for instance, the last, triangle marked isentropic line. In case of class ANCMZ (Fig. 6k,l) it is possible to achieve this only by applying superheating or terminating the expansion on higher temperature/pressure. Otherwise, the isentropic expansion (if it reaches TA or other low temperatures) always ends in the twophase region. Isentropic classes where point N follows C in entropy seem to be the closest to ideal isentropic fluid behaviour (Figs. 6/m,n). One can eliminate droplet formation in class ACNZM by choosing isentropic lines running very close to M, and then there will be no need for superheating. Nevertheless, choosing isentropic lines starting at temperature between those of M and C (TM < T < TC), and entropies between those of N and M (sN < s < sM) results in relatively small amount of liquid formation in the lowpressure stage (see Fig. 6n) between TA and TN. For class ACNMZ (Figs. 6o,p) liquid droplet formation is expected in the lowpressure stage if superheating is omitted. If sZ is not much larger than sM, the liquid formation can be kept within acceptable limits (<8%) which is usually considered tolerable (Chen et al. 2010). However, the more sZ exceeds sM, the more superheating is required to protect the 10
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For each of the new classes, examples are given in Table 1. For dry and isentropic working fluids, however, the classification is ambiguous, as it depends on the choice of TA — triple point temperature or a technically reasonable environmental temperature. A good example is butane, which, in principle, should be in an isentropic ACNMZ class if the point Z defined by the triple point temperature (ca. 135 K). At the more practical reference temperature of 25 °C, which can be taken as environmental temperature, however, point N has already disappeared, and the point Z at this temperature has an entropy less than that of M. Consequently, butane is practically in the dry ACZM class for most applications, except for the ones where low temperatures are relevant, like cryogenic power cycles with regasification processes [20]. In cases where the distinction matters, we propose to use the symbols A and Z when TA has been set to the triple point or melting point temperature, but A* and Z* when another, technically more convenient temperature has been used.
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A similar example is hexane, which is, in principle, an ANZCM fluid. But its TN, the temperature of the local entropy minimum, is around –11.5 °C (261.7 K) — below typical environmental temperatures, therefore using hexane as working fluid in a power plant, a higher (environmental) temperature has to be used as lower temperature limit. If here, too, the bottom part of the Ts diagram is disregarded, the remaining part belongs to the dry class A*Z*CM. This is demonstrated in Fig. 7.
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Although it would be tempting to elect one of the novel class as the “best one” for ORCapplications, but it cannot be done here. According to traditional classification, isentropic fluids were thought to be the best (as far as thermodynamic properties are concerned), therefore one might expect that one of the isentropic subclasses (ANZCM, ANCZM, ANCMZ, ACNZM and ACNMZ) could be the “ultimate” working fluid. However, as it can be seen on Figure 3, the choice of the “best” expansion (from hightemperature saturated vapour state to a lowtemperature saturated vapour state) strongly depends on the maximal and minimal temperature values of the given thermodynamic cycle. Therefore, a class, which is optimal for one heat source, might score worse for an other heat source. This lack of a clear recommendation should not be regarded as a shortcoming of the new classification; on the contrary, it is a consequence of its better, more detailed representation of the thermodynamics of the working fluids.
5. Summary The traditional classification of working fluids, with merely three categories (wet, dry, isentropic), is not sufficient to reliably predict or exclude the formation of liquid droplets in the lowpressure stage of the turbine of an ORC power plant. In this paper, a novel, refined classification is proposed, which overcomes this problem and which makes it easier to select working fluids for ORC applications. 11
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The new classification scheme is based on the existence and relative location of some characteristic points of the vapour–liquid coexistence curve in T–s diagram: the equilibrium states at low temperature (depending on the application, the triple point temperature or a conveniently chosen environmental temperature), the critical point, and – if they exist – the entropy extrema of the saturated vapour curve. The sequences, in which these points appear, when ordered with respect to increasing entropy, are used to construct the labels of the categories. This makes it easy to determine the category label for a given fluid and on the other side allows the qualitative reconstruction of the T–s diagram from the label.
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The classification contains eight categories. These categories have different thermodynamic characteristics (e.g., the possibility to achieve total evaporation by adiabatic expansion or to end in a twophase state), and they require different layouts for ORC machinery. This should make it easier to find the thermodynamically optimal working fluids for ORC applications.
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For each of the new categories, real working fluids are given as examples. An extensive list of working fluids and their categories can be found in the Supplementary material.
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Acknowledgements This work was supported by the Hungarian National Innovation Office (NKFIH, grant No. K116375) and by the Hungarian Higher Education and Industry Cooperation Center (FIEK, grant. No. 16120160007). A.R.I gratefully acknowledges an “Albert’s reunion grant” of the University of Cologne. Special thanks to one of the unknown referees for giving several suggestions, especially for the ones concerning cryogenic cycles and alternative special points for Ts diagrams.
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Supplementary material: In the supplementary material, 57 pure working fluids are tabulated, together with their primary and secondary characteristic points (when available). Temperature and specific entropy data were taken from the NIST Chemistry Webbook (2017). The traditional (wet/isentropic/dry) and the novel (sequencebased) categories are indicated. References
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ACCEPTED MANUSCRIPT Appendix. A. Ideal isentropic sequences
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As already mentioned in Section 3, the entropy values for some of the primary and secondary characteristic points can theoretically be equal (without violating the constraints introduced in Section 3.2.). When these are neighbouring points (like MN or NZ), a finite part on the saturated vapour curve must be ideal isentropic (ds/dT=0). These parts can be the MN, and NZ sequences. The entropy for NZ can be either higher or lower than the entropy of C; Figs. A1a and c show these two version (the corresponding diagrams can be seen in Figs. A1b,d).
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In case of triple equality (sM=sN=sZ), the ideal isentropic part can extend from M to Z; in that case, point N is undefined, this can be seen in Figs. A1e, f. Finally, the case when the entropy values of N and M are equal can be seen in Figs. A1g,h.
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We indicate equalities in the category labels by placing parentheses around symbols of the characteristic points with equal entropies, listing primary points first and secondary points second; when there are more than one secondary point inside of the parentheses, alphabetical order is used (e.f. ZMN)). The peculiarity of these types is the existence of isentropic lines where the entropy is smaller than sZ but q=1 within a finite temperature range, see for example in Fig. A1f.
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As for the existence of these types of fluids, recent calculations with simple van der Waals fluids show that the slope of the saturated vapour curve is always negative at low temperatures, for example, sZ is always above sN [9]. This excludes the existence of classes A(ZN)CM, AC(ZN)M and AC(ZMN), leaving only AC(MN)Z (Figs. B1g and h).
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Further studies about the possibility of ideal isentropic parts are in progress.
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ACCEPTED MANUSCRIPT Appendix B. Tertiary characteristic points
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Tertiary characteristic points are the points defined by isothermal or isentropic processes starting at primary and secondary points. These processes (represented by horizontal or vertical lines on Ts diagram) can be reversible adiabatic expansion or compression (constant s) or any isothermal process (like isothermal heat rejection or addition, constant T). The points are labelled with the letter of the projected point (like M), with a subscript indicating the constant quantity of the process (for example s for isentropic expansion or compression). Finally, superscripts indicate the direction of the process; “u” (up) is for increasing s or T and “d” (down) for decreasing s or T. The tertiary characteristic point are the intersections of the lines of these processes with the Ts curve. In some situations, two intersections are possible. Then double indices (like “uu”) are used. The possible ternary points for the ANCMZ class are shown in Figs. B1a and b.
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It should be noted, that isothermal tertiary points cannot exist for A and Z primary points, although theoretically A should be considered as , while Z can be considered as . For Z, isentropic tertiary points might exist (subscript s), but their temperature is always larger than for the original Z point (superscript u). For C, only isentropic (subscript s) tertiary points can exist; depending on the sequence, they can be single or double indexed, but always at a lower temperature than the original point C (superscript d or dd). For M and N, both isothermal and isentropic tertiary points can exist. Concerning isentropic ones, they can be only singleindexed with a lower entropy for M (superscript d) and higher entropy for N (superscript u). A detailed list can be found in Table B1; the l and v in parentheses indicate whether the point is located on the liquid or on the vapour curve.
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The existence/nonexistence of these points can be used for some technical considerations. If, for example for dry fluids (ACZM or AZCM), exists in the form of () (i.e. in class AZCM), the lowtemperature dry vapour can be completely liquefied by reversible adiabatic (i.e. isentropic) compression. Similarly, if the temperature of is larger than the ambient temperature, full liquidization/vapourization is possible by isentropic expansion/compression in the temperature range between these two values. On the other hand, when the temperature corresponding to is lower than the ambient temperature, only a partial liquidization/vapourization is possible by isentropic expansion/compression. For further characterization of the Ts diagrams, points representing d2s/dT2 states might be used, but probably they do not have significance in expansion and compression processes, hence we are neglecting them in this study.
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Figure 1. Traditional categories, corresponding cycle layouts and processes in T–s diagrams of Organic Rankine Cycles of wet (a,b), dry (c,d) and ideal isentropic (e,f) working fluids. C: condenser, ECO: economiser, EVAP: evaporator, G: generator, H: heat source, P: pump, R: recuperator, SH: superheater, T: turbine
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Figure 2. Demonstration of the existence of subcategories within category “dry” showing the different outcome upon isentropic expansion of saturated liquid (a) and upon isentropic compression of saturated vapour (b).
Figure 3. Demonstration of the existence of subcategories within category “isentropic” showing the different outcome during various processes.
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Figure 4. Introduction of the primary and secondary characteristic points in case of traditional category wet (a), dry (b) and real isentropic (c) working fluids using data of real fluids taken from the NIST Chemistry WebBook [17].
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Figure 5. Possible sequences of the novel classification.
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Figure 7. Ts diagram of hexane representing the change of sequences by choosing a technical limit (here it is 15 0C) for the lowest temperature, instead of using the triplepoint temperature. Here hexane switch from ANZCM (isentropic) to A*Z*CM (dry), where stars mark the redefined points.
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Figure B1: Potential tertiary points (isentropic: a; isothermal: b) of an ANCMZtype working fluid.
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ACCEPTED MANUSCRIPT Table 1. Examples for the novel categories.
lowermost temperature triple point environmental temperature triple point triple point triple point triple point triple point triple point
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Material water, carbon dioxide butane (R600) 1,2dichlorotetrafluoroethane (R114) heptane benzene pentane (R601) 1,1,1,3,3,3hexafluoropropane (R236fa) butane (R600)
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Novel category ACZ A*CZ*M AZCM ANZCM ANCZM ANCMZ ACNZM ACNMZ
Table B1: Tertiary points for the eight types of working fluids, with their location given in parentheses (l: on the liquid curve; v: on the vapour curve).
traditional category
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ACCEPTED MANUSCRIPT Highlights for Györke et al. “Novel Classification of Pure Working Fluids for Organic Rankine Cycle”
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The need for a refined classification for working fluids (beyond the classical categories wet/isentropic/dry) is demonstrated. A novel classification based on characteristic points is introduced. Potential technical applications for the new classification are presented. Categories and characteristic points for 57 pure working fluids are provided.
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