energies

Article A Simple Method of Finding New Dry and Isentropic Working Fluids for Organic

Gábor Györke 1, Axel Groniewsky 1 and Attila R. Imre 1,2,* 1 Budapest University of Technology and Economics, Department of Energy Engineering, Muegyetem rkp. 3, H-1111 Budapest, Hungary; [email protected] (G.G.); [email protected] (A.G.) 2 MTA Centre for Energy Research, Department of Thermohydraulics, POB. 49, H-1525 Budapest, Hungary * Correspondence: [email protected]

 Received: 17 January 2019; Accepted: 1 February 2019; Published: 1 February 2019 

Abstract: One of the most crucial challenges of sustainable development is the use of low-temperature sources (60–200 ◦C), such as thermal solar, geothermal, biomass, or , for electricity production. Since conventional -based thermodynamic cycles are not suitable in this temperature range or at least operate with very low efficiency, other working fluids need to be applied. Organic Rankine Cycle (ORC) uses organic working fluids, which results in higher thermal efficiency for low-temperature heat sources. Traditionally, new working fluids are found using a trial-and-error procedure through experience among chemically similar materials. This approach, however, carries a high risk of excluding the ideal working fluid. Therefore, a new method and a simple rule of thumb—based on a correlation related to molar isochoric specific heat capacity of saturated vapor states—were developed. With the application of this thumb rule, novel isentropic and dry working fluids can be found applicable for given low-temperature heat sources. Additionally, the importance of molar quantities—usually ignored by energy engineers—was demonstrated.

Keywords: ORC; saturated vapor curve; T–s diagram; isentropic expansion; low-temperature heat sources; droplet formation; isochoric heat capacity; molar quantities; characteristic points

1. Introduction In the last few decades, power generation started to turn to alternative energy sources, such as wind energy and photovoltaics, as well as unconventional sources of heat, such as , solar heat, biomass-firing plants, or waste heat from other industrial processes. Generally, these unconventional heat sources do not have as high energy density as the conventional ones nor a high cycle efficiency, since the heat is supplied at a lower temperature level. Nevertheless, they can perform better under specific circumstances. Conventional Rankine Cycle-based thermal power plants use water as working fluid. Because of the thermal properties of the water, the cycle cannot exploit such unconventional heat sources efficiently. Organic Rankine Cycle (ORC) provides an alternative solution, because it uses non-conventional working fluids, mainly organic ones. These unconventional working fluids are suitable for power generation from various low-temperature heat sources [1,2], including geothermal heat [3,4] or low-temperature industrial waste heat [5]. According to the ORC World Map [6], in the middle of 2016, the number of installed major ORC units exceeded 700. Obviously, using different working fluids would also influence the actual layout. In some cases, it requires a superheater, a recuperator, or other auxiliary units [7]. Also, the type of expander in use depends on the fluid properties [8–11], but this problem is not addressed in this paper. Traditionally, the working fluid for a given ORC is selected using a trial-and-error procedure through experience from chemically similar materials, although recently there were more and more

Energies 2019, 12, 480; doi:10.3390/en12030480 www.mdpi.com/journal/energies Energies 2019, 12, 480 2 of 11 attempts to use chemical or physical properties to predict the applicability of a given fluid as an ORC working fluid. In some cases, simple optimization algorithms are used to select the ideal existing working fluid, while, in other cases, the optimization is based on molecular or equation-of-state parameters [12–17]. Usually, possible candidates are identified using information collected from similar systems. In this way, one might risk excluding novel, previously unused working fluids, which could be better than any traditional ones. A novel classification method was developed by us [18] not only to describe and categorize all the potential working fluids, but also to use some elements of the classification as a tool for finding the best working fluid for a given heat source. A short review of the novel classification is given in Section3. The basis of the new classification is the relative location of some characteristic points on the saturation curve of a given material in specific –temperature diagram. Using one or two of these points and correlating them with the isochoric molar specific heat capacities of the equilibrium vapor , we are able to give a “rule of thumb” to select working fluids, where droplet formation during expansion and, hence, the potentially harmful droplet erosion of turbine blades—common for traditional and some organic Rankine processes using wet working fluids [19,20]—can be avoided. In this way, several new potential working fluids can be found and used for further evaluation, using general criteria for ORC working fluid selection including thermodynamics [18,21], safety and environmental impact [22,23], availability, compatibility, and cost-effectiveness [24], or most often, a combination of these criteria.

2. Traditional Classification The widespread traditional classification of working fluids is based on the shape of the vapor saturation curve of the fluids and, hence, the quality of the expanded vapor at the outlet of the turbine [21,25]. Expander is a more common term in ORC technology, which refers to the differences in size and construction compared to steam turbines. The traditional classification of ORC working fluids differentiates three categories, namely wet, dry, and isentropic, usually with a smooth transition between them [12,24,26–28]. The is called wet or wet-type if an isentropic (adiabatic and reversible) expansion starting from a saturated vapor state will end in the two-phase region, which is also called “saturated liquid vapor region” or “wet region”. The vapor curve of a wet fluid in a temperature–entropy diagram has a negative slope at each point (dT/ds < 0). The working fluid is called dry if an isentropic expansion starting from a saturated vapor state will end in the single-phase vapor region, which is also called “superheated vapor region” or sometimes simply “dry region”. The vapor curve of dry fluids has mainly a positive slope (dT/ds > 0). At high temperatures, the vapor curve has necessarily a negative slope, where the entropy increases until reaching a maximum value (ds/dT = 0), and then the curve bends back to smaller entropy values. Finally, the working fluid is called isentropic if an isentropic expansion starts and ends in a saturated vapor state. The saturated vapor curve of an ideal isentropic fluid has an infinite slope (dT/ds → ∞) at each point after reaching the point where ds/dT = 0. The visualization of the three traditional categories can be seen in Figure1, marking isentropic expansion processes with initial (1) and final (2) states.

Deficiencies in Traditional Classification Owing to the spread of ORC technology and, hence, the application of new working fluids, the traditional classification is deemed narrow and does not reflect significant differences between fluids from the same categories. These differences have theoretical and even practical significance. The development and the wide variety of applied working fluids raise the need for a more sophisticated classification, which contains more precise information about the applicability of the fluid. Energies 2019, 12, 480 3 of 11 Energies 2019, 12, x 3 of 12 T Temperature -

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FigureFigure 1.1. TraditionalTraditional categorization: categorization: wet, wet, dry, dry, and and isentropic. isentropic. Curves Curves represent represent saturated saturated states. states. One- One-phasephase states states are located are located above above the saturation the saturation curves curves (liquid (liquid states: states: low-entropy low-entropy side; vapor side; vaporstates: states:high-entropy high-entropy side). Two-phase side). Two-phase states (liquid states (liquid+ vapor) + vapor)are located are locatedbelow the below saturation the saturation curve. Lines curve. 1 Linesand 2 1represent and 2 represent isentropic isentropic expansion expansion processes processes (see corresponding (see corresponding text). text).

ConcerningConcerning drydry fluids,fluids, thethe “dryness”“dryness” hashas practicalpractical significancesignificance andand anan effecteffect onon thethe layoutlayout ofof thethe ORCORC powerpower plant.plant. AfterAfter thethe isentropicisentropic expansionexpansion ofof thethe fluidfluid inin thethe expanderexpander (turbine),(turbine), thethe vaporvapor isis inin aa superheatedsuperheated state.state. TheThe extentextent ofof superheatingsuperheating alsoalso hashas aa greatgreat effecteffect onon thethe thermalthermal efficiencyefficiency ofof thethe cycle.cycle. Also,Also, therethere isis aa mainlymainly theoreticaltheoretical issueissue relatingrelating toto thethe drynessdryness ofof thethe fluid.fluid. IfIf thethe fluidfluid isis “very“very dry”,dry”, itit bendsbends backback greatlygreatly toto lowerlower ;entropies; however,however, atat leastleast underneathunderneath thethe criticalcritical point,point, itit becomesbecomes possiblepossible toto fullyfully liquefyliquefy vaporvapor usingusing anan isentropicisentropic compressioncompression andand vicevice versaversa (to(to fullyfully evaporateevaporate liquidliquid usingusing anan isentropicisentropic expansion)expansion) [[18].18]. AnotherAnother very significant significant issue issue relates relates to to the the isentropic isentropic category. category. It is It not is not proven, proven, but butneither neither real realfluid fluid properties properties available available in inthe the NIST NIST Chemistry Chemistry Webbook Webbook database database (NIST) (NIST) Chemistry WebbookWebbook databasedatabase [[29]29] nornor theoreticaltheoretical analysesanalyses ofof modelmodel fluidsfluids [[7,30]7,30] confirmconfirm thethe existenceexistence ofof anyany fluidsfluids withwith aa perfectlyperfectly isentropicisentropic saturationsaturation vaporvapor curve.curve. It meansmeans that,that, forfor realreal oror eveneven modelmodel fluids,fluids, entropyentropy cannotcannot bebe constantconstant inin aa finitefinite temperaturetemperature range.range. TheseThese theoreticaltheoretical analysesanalyses alsoalso showshow thatthat probablyprobably allall isentropicisentropic fluidsfluids havehave anan S-shapedS-shaped vaporvapor saturationsaturation curvecurve (negative–positive–negative(negative–positive–negative slopesslopes inin sequence).sequence). InIn practice,practice, we we can can find find some some fluids fluids that that approach approach the the “ideal” “ideal” isentropic isentropic behavior behavior at leastat least in ain smaller a smaller part part of the of vapor the vapor curve, curve, for instance, for instance, a common a common , refrigerant, trichlorofluoromethane trichlorofluoromethane (CCl3F, R-11).(CCl3F, These R-11). facts These inspired facts the inspired authors the to redefineauthors tothe redefine meaning the of isentropic-type meaning of isentropic-type fluids. According fluids. to theAccording new definition, to the new the definition, fluid is isentropic the fluid if is it isentropic is possible if toit findis possible an isentropic to find an expansion isentropic line expansion starting fromline starting and ending from in and a saturated ending in vapor a saturated state, whereby vapor state, the expansion whereby linethe expansion does not enter line thedoes two-phase not enter (wet)the two-phase region. A(wet) “real” region. isentropic-type A “real” isentropic-type working fluid working can be fluid seen can in Figure be seen2 (biggestin Figure diagram), 2 (biggest whichdiagram), shows which the importanceshows the importance of the reverse of the S-shaped reverse vapor S-shaped curve vapor by displaying curve by displayingthree isentropic three expansionisentropic linesexpansion (blue, lines red, and(blue, green). red, and In thegreen). first In case the (blue), first case the working(blue), the fluid working behaves fluid like behaves a wet like a wet type, because the expansion ends in the wet region. In the second case (red), isentropic

Energies 2019, 12, 480 4 of 11 type, because the expansion ends in the wet region. In the second case (red), isentropic behavior can be observed (initial and final points of the expansion located on the saturation curve). In the third case Energies 2019, 12, x 5 of 12 (green), the fluid shows dry behavior,

FigureFigure 2. Novel 2. Novel classification: classification: visualizationvisualization of of characteristic characteristic points points and andthe novel the novel eight eightcategories categories (sequences).(sequences). a detailed a detailed description, description, seesee corresponding text text below below or for or further for further details, details, Reference Reference [18]. [18].

Energies 2019, 12, 480 5 of 11

Since the expansion ends in the dry (superheated vapor) region. The quality of the vapor during the expansion is maybe the most crucial issue when designing a power plant, since it has strict limits regarding the extent of liquid droplet formation in the expander for safety and lifetime reasons.

3. Novel Classification

3.1. Characteristic Points The basis of the novel classification is five well-definable characteristic points located on the T–s saturation curve. The relative location or even the existence of these points defines the categories (sequences) and gives them their names. These characteristic points marked by A, C, M, N, and Z can be seen in Figure2. Points A and Z are defined as points with the lowest temperature on the saturated liquid and vapor curve, respectively. This temperature is chosen to be the triple-point temperature of the fluid as a physical property, although one might choose another limit which fits more to the given application (for example, environmental temperature, in the case of air-cooled processes). Point C indicates the critical point of the working fluid, which is also a well-defined physical property. Points M and N are defined as the local or even global entropy extrema on the saturated vapor curve. Point M is the one with a higher temperature. Points A, C, and Z can be defined for every working fluid; however, this is not true for points M and N. Wet-type fluids have only points A, C, and Z, while dry-type fluids have point M, but do not have point N. Isentropic-type fluids have both points M and N.

3.2. Sequences (Categories) According to the relative location and existence of the characteristic points, eight sequences (categories) can be defined, based on the increasing order of corresponding entropy values, namely ACZ, ACZM, AZCM, ANZCM, ANCMZ, ANCZM, ANCMZ, ACNZM, and ACNMZ. There are some more mathematically, but not physically possible sequences forbidden by certain constraints on characteristic points [18]. The names of the sequences mirror the entropy of the characteristic points in ascending order. For a better understanding, see Figure2. The novel classification is compatible with the traditional one. Only one wet-type sequence exists, namely ACZ. Two dry-type sequences exist, namely ACZM and AZCM. Five isentropic-type sequences exist, namely ANZCM, ANCZM, ANCMZ, ACNZM, and ACNMZ. The compatibility can be followed in Table1. All of the listed sequences can be seen in Figure2. Further information about the characteristic points and a detailed analysis of the sequences can be found in Reference [18].

Table 1. Examples of the new categories.

Novel Classification Traditional Category Working Fluid ACZ wet water, carbon dioxide ACZM dry — AZCM dry neopentane, dodecane ANZCM isentropic hexane, heptane ANCZM isentropic benzene ANCMZ isentropic pentane, toluene ACNZM isentropic — ACNMZ isentropic butane, trichlorofluoromethane

Table1 gives examples for most of the sequences. The data for the temperature–entropy diagrams and other physical properties of the fluids are from the NIST database [29]. The database (Table S1, Supplementary Materials) contains 74 working fluids with their saturation curve properties, but no examples of ACZM and ACNZM sequences could be found. Theoretical analyses of the shape of the saturation curve using two equations of state, namely van der Waals [7] and Redlich–Kwong [29], also indicate that there is no working fluid which can be sorted into sequences ACZM or ACNMZ. Energies 2019, 12, 480 6 of 11

The two categories, however, could be important if the environmental temperature (for example 15 ◦C) is used as the lower limit, instead of the . This way, two new practical end-points should be defined for the T–s curve as A* and Z*, corresponding to the state at 15 ◦C. Then, some of the fluids might show AC*Z*M- and A*CNZ*M-type curves (butane for the first, 1,1-dichloro-1-fluoroethane (R-141b) for the second). These types of transitions are discussed elsewhere [18]. It should be clarified here that, when we use the term “isentropic” for a given class, it does not mean that the corresponding T–s diagram has any non-zero temperature range, where the entropy of the saturated steam is constant. We use “isentropic” in the sense that, for the given T–s curve, it is possible to define a finite isentropic expansion step from a saturated vapor state to another saturated vapor state. On one hand, in a strict sense, it would be better to call these types “pseudo-isentropic”. On the other hand, neither real nor model fluids (see, for example, References [18,28]) can be found with a real isentropic T–s diagram; even the “nearest” ones (like R-11) show a reversed S-shaped saturated vapor curve, yet they are still labeled as isentropic. This is the reason why we use the term “isentropic” instead of creating a new one (pseudo-isentropic) for all categories, where the abovementioned finite isentropic expansion step is possible.

4. Application and Correlations Novel classification can help in finding thermodynamically optimal working fluids for a given heat source. Since other thermodynamic cycles use various types of working fluids such as cycles or heat , creation of a database that contains the main thermodynamic properties and the sequence of the working fluids or makes the search even easier and faster. Our database includes 74 working fluids (data taken from the NIST [29]), and continuous updates and expansions can make it valuable not only for researchers, but also for the industry. Since the triple-point temperature of some working fluids is far below the normal environmental circumstances, the database also includes ◦ ◦ the sequence of all 74 working fluids at 15 C ambient temperature (TA = 15 C), as well for a more realistic limit for most applications (except cryogenic cycles [31] where temperature can approach the triple point of most relevant working fluids). The present form of the database is included in Table S1 (Supplementary Materials). After introducing the novel classification, our research turned to finding a simple, measurable physical property with the help of which it is possible to easily differentiate the eight sequences or at least the traditional categories (dry, wet, and isentropic). Based on the results of studies on model fluids [7], isochoric molar specific heat capacity (cV) seemed to be a proper candidate to establish some correlation with the novel classes. Therefore, our research focused on examining the cV of the saturated vapor curve of real working fluids [32] from the NIST database. Figure3 displays the isochoric specific heat capacity values (given in mass-related kJ/kg ·K units) of the saturated vapor curve of working fluids available in the NIST database with respect to their reduced temperature (defined as actual temperature in Kelvin divided by the critical temperature of the given fluid, also in Kelvin). Blue lines represent wet-type, red lines represent isentropic-type, and green lines represents dry-type sequences. Circles and squares mark points M and N, previously defined on the temperature–entropy curve of the given material. No correlation between the fluid categories (wet, dry, and isentropic) and the isochoric specific heat capacity values can be seen here. On the other hand, a strong correlation between categories and the isochoric “molar” specific heat capacity was reported for model fluids [7,30]. Using molar heat capacity values might be unusual for engineering applications, but one should be aware that, in several cases, when comparing materials with the same mass—instead of the same mole number—it might be misleading. For example, the isochoric heat capacity of helium—expressed in J/g·K or kJ/kg·K—is one order of magnitude higher than that of argon; however, while using J/mol·K or kJ/kmol·K, these quantities are equal. The reason for this difference is that the molar mass of argon is ten times higher than the molar mass of helium and, accordingly, in the same mass, one can find ten times more helium atoms than argon ones. Therefore, in certain analyses, the use of properties Energies 2019, 12, x 8 of 12 Energies 2019, 12, 480 7 of 11 quantities with mol, instead of kg). Figure 4 displays the molar isochoric specific heat capacity values relatedof the tosaturated the same vapor amount curve (instead of working of the fluids same with mass) respect of substances to their reduced is advised temperature (i.e., using quantities(circles and withsquares mol, mark instead points of kg). M and Figure N; blue4 displays lines represent the molar wet isochoric-type, red specific lines re heatpresent capacity isentropic values-type of the, and saturatedgreen lines vapor represent curve of dry working-type sequences). fluids with respectHere, one to theircan see reduced a strong temperature correlation (circles between and squaresthe fluid markcategory points and M the and molar N; blue heat lines capacity. represent It can wet-type, easily be red seen lines that represent wet-type isentropic-type, fluids, i.e., ACZ and sequences, green linesare representlocated exclusively dry-type sequences).at the bottom Here, part one of the can diagram. see a strong Above correlation this ACZ between region, the there fluid is categorya narrow andtransition the molar zone heat where capacity. isentropic It can- easilytype fluids, be seen i.e., that ACNMZ wet-type sequences, fluids, i.e., appear. ACZ sequences, ACNMZ aremay located be said exclusivelyto be the closest at the in bottom behavior part to of wet the-type diagram. fluids Above (see Figure this ACZ 2). Ri region,ght until there the isappe a narrowarance transitionof the first zonedry- wheretype fluid isentropic-type (AZCM), only fluids, sequence i.e., ACNMZ ACNMZ sequences, of isentropic appear.-type ACNMZfluids can may be found. be said Above to be the this closestregion in, only behavior sequences to wet-type starting fluids with (seeAN, Figurewhere2 the). Right characteristic until the point appearance N has a of lower the first entropy dry-type value fluidthan (AZCM), point C, onlyexist. sequence The disappearance ACNMZ of isentropic-typeof sequences starting fluids canwith be AC found. can Abovebe explained this region, by the only fact sequencesthat, if we starting consider with a AN,wet– wheredry global the characteristic transition, then point isentropic N has a lowerfluids entropyhave to valuereflect than this point in some C, exist.intermediate The disappearance steps; thus, of with sequences the increase starting of with cV, they AC canbecome be explained closer and by closer the fact to that, dry- iftype we considerbehavior, awith wet–dry point global N shifting transition, below then point isentropic C in the fluids entropy have scale. to reflect As we this go inhigher some with intermediate cV, only the steps; dry thus,-type sequence AZCM and isentropic-type sequence ANZCM exist. The NIST database seems to have a with the increase of cV, they become closer and closer to dry-type behavior, with point N shifting shortage in dry-type fluids, but it is probable that, above a certain cV value, only dry-type fluids with below point C in the entropy scale. As we go higher with cV, only the dry-type sequence AZCM and isentropic-typesequence AZCM sequence can exist. ANZCM Nevertheless, exist. The there NIST are databasesome sequences seems to(AZCM) have a mixed shortage with in isentropic dry-type - type fluids; it can also be observed that these fluids have a high triple-point temperature compared fluids, but it is probable that, above a certain cV value, only dry-type fluids with sequence AZCM can exist.to their Nevertheless, critical temperature. there are some sequences (AZCM) mixed with isentropic-type fluids; it can also be observed that these fluids have a high triple-point temperature compared to their critical temperature.

Figure 3. Isochoric specific heat capacity (kJ/kg·K) curves of various working fluids in saturated Figure 3. Isochoric specific heat capacity (kJ/kg·K) curves of various working fluids in saturated vapor vapor conditions; blue, red, and green curves represent wet, isentropic, and dry materials, respectively. conditions; blue, red, and green curves represent wet, isentropic, and dry materials, respectively. Squares and circles represent points N (lower temperature) and M (higher temperature). Squares and circles represent points N (lower temperature) and M (higher temperature). In Figure4, square markers represent characteristic points N, while circle markers represent points M of each fluid. Although a kind of regularity (U-shape) can be discovered in the relative location of the characteristic points, it is still not clear how to find the right way to describe them with a trend line, since these measured values should be supported with theoretical explanation as well. Nevertheless, an outer envelope (dotted curve) can be drawn, and a rule of thumb can be established by appointing the minimum of this envelope as a border point between wet and non-wet fluids. This point is plotted in Figure3 and is indicated by a triangle marker at the lowest molar isochoric specific heat capacity value of the envelope; here, points M and N are identical. According to this rule, if the isochoric specific heat capacity of a fluid in a saturated vapor state is smaller than 80 J/(mol·K) at its reduced temperature of 0.74 (0.74·TC), corresponding to the minimum on the dotted envelope, marked with

Energies 2019, 12, 480 8 of 11 a triangle, then the fluid is very possibly a wet-type one (ACZ). However, when it is higher than 80 J/(mol·K), then the fluid is most probably isentropic or dry.

cV (T = 0.74 · Tc) < 80 J/(mol·K) → wet−type fluid, cV (T = 0.74 · Tc) ≥ 80 J/(mol·K) → dry− or isentropic−type fluid. Energies 2019, 12, x 9 of 12

Figure 4.4.Molar Molar isochoric isochoric specific specific heat heat capacity capacity (kJ/mol (kJ/mol·K) curves·K) curves of various of various working working fluids in saturatedfluids in vaporsaturated conditions; vapor condition blue, red,s; andblue, green red, curvesand green represent curves wet, represent isentropic, wet, andisentropic dry materials,, and dry respectively. materials, respectively.Squares and circlesSquares represent and circles points represent N (lower points temperature) N (lower temperature) and M (higher and temperature). M (higher temperature). The triangle Tshowshe triangle the border shows between the border wet between and non-wet wet and fluids, non located-wet fluids at Tr, =located 0.74 and at TcVr == 0.74 80 J/mol and c·VK. = 80 The J/mol∙K dotted. Thecurve dotted represents curve therepresent outer envelopes the outer for envelope points M for and points N. M and N.

InThis Figure value 4 almost, square coincides markers withrepresent characteristic characteristic point Npoints of trichlorofluoromethane N, while circle markers (CCl represent3F) that waspoints already M of saideach tofluid. be practically Although ana kind “ideal” of regularity isentropic (U fluid;-shape) thus, can it is be one discovered of the best in examples the relative for locationdescribing of the characteristic start of the wet points, isentropic it is still transition not clear region. how to The find difference the right betweenway to describe the molar them entropy with aof trend the characteristic line, since these points measured M and N values of CCl should3F is approximately be supported 0.12 with J/(mol theoretical·K); hence, explanation they are as almost well. Nevertheless,identical. A similar an outer rule envelope of thumb (dotted can curve) be established can be drawn for the, and relative a rule positionof thumb of can points be established C and N; byhowever, appointing so far, the it hasminimum been made of this only envelope for model as a fluidsborder [33 point]. between wet and non-wet fluids. This pointIn is additionplotted in to Figure this rule 3 and of thumb,is indicated two by other a triangle results marker can be deducedat the lowest from molar the presentation isochoric specific used heatin Figure capacity4. All valuecV linesof the are enve plottedlope; here from, points the triple-point M and N are temperature identical. toAccording the critical to this one. rule, It can if the be isochoricseen that, specific for dry heat working capacity fluids of a (green fluid lines),in a saturated the absence vapor of state point is Nsmaller is simply than caused 80 J/(mol∙K) by the at fact its that freezing happens at temperatures higher than the expected crossing of the c line and the outer reduced temperature of 0.74 (0.74∙TC), corresponding to the minimum on theV dotted envelope, markedenvelope with (represented a triangle by, then the the dotted fluid line) is very of points possibly N anda wet M.-type It means one (ACZ). that, by However, using dry when working it is higher than 80 J/(mol∙K), then the fluid is most probably isentropic or dry. cV (T = 0.74 · Tc) < 80 J/(mol∙K) → wet−type fluid,

cV (T = 0.74 · Tc) ≥ 80 J/(mol∙K) → dry− or isentropic−type fluid. This value almost coincides with characteristic point N of trichlorofluoromethane (CCl3F) that was already said to be practically an “ideal” isentropic fluid; thus, it is one of the best examples for describing the start of the wet isentropic transition region. The difference between the molar entropy of the characteristic points M and N of CCl3F is approximately 0.12 J/(mol∙K); hence, they are almost identical. A similar rule of thumb can be established for the relative position of points C and N; however, so far, it has been made only for model fluids [33].

Energies 2019, 12, 480 9 of 11

fluids, which have the tendency to supercool (i.e., remain liquid for a while below the freezing point, e.g., glycerol), one might obtain wet vapor during expansion instead of the expected dry one. For model fluids (i.e., for fluids described by van der Waals of by Redlich–Kwong equations of state) the presence of this low-temperature local entropy minimum (point N) can be found for all substances [7,30,33], but this is the first indirect experimental proof for its general existence in real fluids. Finally, one can see that sharp borders between various novel working fluid classes do not exist. However, taking a fixed reduced temperature value (for example, T = 0.74·Tc, given above), one can assume that all fluids with cV > 165 J/(mol·K) should be either dry or ANZCM-type, while those with 80 J/(mol·K) < cV < 105 J/(mol·K) are probably ACNZM-type. These differences are crucial not only for ORC applications, but also for other thermodynamic cycles such as the Trilateral Flash Cycle (TFC) [33].

5. Conclusions The traditional classification of working fluids with its three categories (wet, dry, isentropic), is not sufficient to reliably predict or exclude the formation of liquid droplets in the low-pressure stage of the expander of an ORC power plant. In this paper, a brief overview is given for a novel and more sophisticated classification [17], which eliminates these deficiencies and makes it easier to select working fluids for ORC applications. The novel classification contains eight categories, also called sequences. These categories have different thermodynamic characteristics and they require different layouts for ORC machinery. A database was created to make the choice of optimal working fluid even easier and faster. The database contains 74 fluids (so far) with their significant thermodynamic properties and their traditional and novel classifications. Using the location of two of these characteristic points in isochoric (molar) heat capacity–reduced temperature space, a rule of thumb can be defined to distinguish between wet and non-wet working fluids. If the molar isochoric heat capacity of the saturated vapor phase of the given working fluid is smaller than 80 J/(mol·K) at a temperature 0.74·Tc, then it is most likely a wet fluid (or ACZ according to the novel classification), while fluids with heat capacity values above this limit (at this temperature) are very likely dry or isentropic. Real fluids show the theoretically proven trend that, with the increase of molar isochoric heat capacity, the fluid is more and more probably isentropic or dry. In a similar way, one can assume that all fluids with cV > 165 J/(mol·K) at T = 0.74·Tc temperature are either dry or ANZCM-type, while the ones with 80 J/(mol·K) < cV < 105 J/(mol·K) are probably ACNZM-type. These correlations can be seen only when isochoric heat capacities are plotted in molar units (in J/(mol·K)), which shows the importance of molar quantities in comparative analysis. There are other methods—developed by Garrido et al. [12,13] and White et al. [27]—to separate wet fluids from dry (and isentropic) ones, using various quantities. Combining the criterion of isochoric molar heat capacity given in this paper with the other two criteria (given for critical molar volume [27] and for a material-dependent generalized psi-function [12,13]) should give an even more accurate selection method for classifying a fluid as wet or dry/isentropic. Therefore, the usage of the three methods in combination is strongly advised. Finally, it was shown that, even for the so-called dry fluids, a local entropy maximum (point N) might exist, i.e., they might have a low-temperature part on their saturated vapor line (in the T–s diagram) with a negative slope. Therefore, having a properly deep expansion in these dry fluids, the final state might be wet. Since this part of the saturation curves usually “hides” below the freezing point, it can be relevant only for fluids where supercooling of the liquid phase is possible.

Supplementary Materials: The following are available online at http://www.mdpi.com/1996-1073/12/3/ 480/s1: Table S1: Temperature and entropy data of characteristic points used for novel classification, novel (sequence-based) classification for the whole temperature range (from triple point to critical point), or the “realistic” temperature range (from 15 ◦C to critical point), former classification (wet, dry, isentropic). Author Contributions: G.G., A.G., and A.R.I. developed the concept and worked on the research project; G.G. collected the data; G.G. and A.R.I. performed the calculations; G.G., A.G., and A.R.I. wrote the paper. Energies 2019, 12, 480 10 of 11

Funding: This work was performed in the framework of the FIEK_16-1-2016-0007 project, implemented with the support provided from the National Research, Development, and Innovation Fund of Hungary, financed under the FIEK_16 funding scheme. Acknowledgments: The APC was covered with the help of the Open Access publication program of the Hungarian Academy of Science. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

ORC—Organic Rankine Cycle TFC—Trilateral Flash Cycle A—characteristic point A, related to the low-temperature, low-entropy end of the temperature–entropy curve C—characteristic point C, refers to critical point of the fluid M—characteristic point M, related to the local entropy maximum on the saturated vapor curve N—characteristic point N, related to the local entropy minimum on the saturated vapor curve Z—characteristic point Z, related to the low-temperature, high-entropy end of the temperature–entropy curve cV—isochoric molar heat capacity; J/(mol·K) or isochoric heat capacity J/(kg·K) s—molar entropy; J/(mol·K) T—temperature; K Tc—critical temperature; K Tr—reduced temperature; K/K

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