1、230 2008 ASHRAE ABSTRACT This paper demonstrates, through several examples ofpotential R-114 replacement refrigerants, the step-by-stepprocedure to implement the methodology described in, forexample, Reid et al. (1987) and Poling et al. (2001)and illus-trated in recent publications by Brown (2007a,
2、2007b)forevaluating the thermodynamic performance potentials ofalternative refrigerants. This methodology allows one to esti-mate quickly and easily several key thermodynamic parame-tersnamely, critical temperature, critical pressure, criticaldensity, ideal gas specific heat at constant pressure, an
3、d acen-tric factorfrom knowing only a refrigerants normal boilingpoint temperature and its molecular structure. Once these keyparameters are known, the Peng-Robinson equation-of-stateformulation implemented in REFPROP 8.0 (Lemmon et al.2007) easily can be used to predict a refrigerants heating orcoo
4、ling coefficient of performance and volumetric heating orcooling capacity. The power of this methodology is that onecan predict easily and quickly the performance potentials of alarge number of refrigerants that are not-so-well-described, aswell as ones that are, limiting the need for expensive and
5、time-consuming experimentation or detailed equation-of-statemodeling. Then, once this preliminary investigation iscomplete, one could focus on a shortened, much more limitedlist of potential replacement refrigerants.INTRODUCTIONTwo recent publications by Brown (2007a, 2007b) illus-trate the methodol
6、ogy outlined in, for example, Reid et al.(1987) and Poling et al. (2001) for evaluating the performancepotentials of refrigerants, both well-described ones and not-so-well-described ones. Using their methodology, one onlyneeds to know a refrigerants normal boiling point temperature(NBP) and its mole
7、cular structure to obtain quite a good esti-mate of its performance potential (heating or cooling coeffi-cient of performance COPHor COPC and volumetric heatingor cooling capacity VHC or VCC) in an idealized vapor-compression refrigeration cycle. Similar approaches to theone presented in this paper
8、have been discussed by severalauthors. For example, McLinden (1990) attempted to design“optimum” refrigerants for non-ideal cycles. In particular, heused the principle of corresponding states to determine theoptimum critical temperature and optimum ideal gas specificheat at constant pressure for ref
9、rigerator applications. Severalpublications from researchers at Oak Ridge National Labora-tory in the early to mid-1990s also used approaches similar tothe one outlined in this paper. Some representative examplesfrom this research group include (1) Fischer and Sand (1993),who used the Lee-Kessler-Pl
10、cker equation of state to inves-tigate the performances of over 57,000 combinations of 22pure refrigerants as possible R-22 substitutes in air-condition-ing applications and (2) Sand and Fischer (1994), who used theCarnahan-Starling-DeSantis and Lee-Kessler-Plcker equa-tions of state to investigate
11、the performances of non-chlori-nated alternatives for R-11 and R-12 in centrifugal chillersusing the property estimation techniques outlined in Reid et al.(1987) when the necessary property data were not knownexperimentally. Following the particular approach presented in this paperand using only kno
12、wn NBP and molecular structures, Brown(2007a) was able to predict the COPCand VCC for a group of24 refrigerants with absolute errors of 2.0% and 10.6%,respectively, compared to the values calculated usingREFPROP 8.0 (Lemmon et al. 2007). If, in addition to NBPMethodology for Estimating Thermodynamic
13、 Parameters and Performance of Alternative RefrigerantsJ. Steven Brown, PhD, PEMember ASHRAEJ. Steven Brown is an associate professor and Chair of Mechanical Engineering, Department of Mechanical Engineering, The Catholic Univer-sity of America, Washington, DC.NY-08-029 (RP-1308)2008, American Socie
14、ty of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permi
15、ssion.ASHRAE Transactions 231and molecular structure, known values for critical tempera-ture, critical pressure, and critical density were included, theCOPCand VCC for the same group of 24 refrigerants werepredicted with absolute errors of 1.8% and 3.7%, respectively,compared to the values calculate
16、d using REFPROP 8.0. This present paper intends to be didactic, providingseveral step-by-step, detailed examples illustrating the meth-odology outlined in Reid et al. (1987) and Poling et al. (2001)and as implemented in Brown (2007a, 2007b). An accompa-nying paper by Brown (2008) uses this same meth
17、odology toanalyze 56 potential R-114 replacement refrigerants for high-temperature heat pumping applications.METHODOLOGYEstimation of Thermodynamic Parameters for Pure FluidsBrown (2007a, 2007b) used the Peng-Robinson (P-R)equation of state (EoS) as implemented in REFPROP 8.0(Lemmon et al. 2007) to
18、estimate the performance potentials(COPHor COPC and VHC or VCC) of over 40 differentrefrigerants. He used this formulation because (1) it is simpleand easy to use, even for persons without EoS modeling expe-rience; (2) it provides acceptable accuracy, allowing one toeasily screen a large number of p
19、otential fluids; (3) it requiresvery little information be known about a refrigerant, makinganalysis of not-so-well-described refrigerants possible; (4) itcan be used to parametrically design an “ideal” refrigerant fora particular application; and (5) because REFPROP is widelyused, making the proced
20、ure accessible to a wide audiencewithout a user needing to resort to extensive computerprogramming or EoS modeling.To use the P-R EoS, one needs to know a refrigerants crit-ical temperature (Tc), critical pressure (Pc), critical density(c), acentric factor (), and ideal gas specific heat at constant
21、pressure ( ). While all these parameters may be known for aparticular refrigerant, often less is known about alternativerefrigerants. The methodology described below can be used insuch cases to predict the performance potentials of these not-so-well-described refrigerants. In particular, one only ne
22、eds toknow a refrigerants NBP and its molecular structure. Then,from these, one can use group contribution methods to predictTc, Pc, c, , and .There are several group contribution methods that can beused to predict Tc, Pc, and c(see, for example, the discussionsin Reid et al. 1987 and Poling et al.
23、2001). Here, theAmbrose Group Contribution Method (Reid et al. 1987) isapplied because of its acceptable accuracy and ease of imple-mentation. Equations 13 relate Tc, Pc, and cto NBP, molec-ular weight (MW), and the Ambrose Group Contributions, andTable 1 provides the contributions for several atomi
24、c or molec-ular groups.(1)(2)(3)For Equations 13, NBP is in K, MW is in kgkmol1K1,Tcis in K, Pcis in kPa, and cis in kgm3.Once these properties have been determined, one can usethe method of Reid et al. (1987) to determine the acentricfactor:(4)Just as for Tc, Pc, and c, several group contributionme
25、thods exist for determining (again, see the discussionsin Reid et al. 1987 and Poling et al. 2001). Here, theJoback Group Contribution Method (Reid et al. 1987 orPoling et al. 2001) is used. Equation 5, together withTable 2, relates the group contributions of various atomic ormolecular groups to .(5
26、)where T is in K and is in kJkmol1K1. To convert theresults of Equations 13 and 5 to IP unitsnamely, in F,in psia, in lbmft3, and in Btulbmol1F1multi-ply Equation 1 by 1.8 and then subtract 459.67 from the result,divide Equation 2 by 6.894, divide Equation 3 by 16.02, anddivide Equation 5 by 4.18.Fi
27、gure 1 presents a schematic of the methodologydescribed above. It also shows the linkage to REFPROP 8.0,which allows one to determine the other relevant thermody-cpocpoTcNBP 111.242 Tc+-+=Table 1. Ambrose Group Contributions for Critical Constants (Reid et al. 1987)Atomic orMolecular Group values fo
28、rTcPcVcC 0.138 0.226 55.1Cl 0.055 0.318 45.0F 0.055 0.223 14.0F correction 0.125 0.000 0.0H 0.000 0.000 0.0I 0.055 0.000 90.0N 0.088 0.170 30.0NH20.208 0.095 30.0O 0.138 0.160 20.0S 0.105 0.270 55.0CH ring 0.030 0.182 44.5CH2ring 0.090 0.182 44.5PcMW0.0339 0.1 Pc+()2-=c1000MW40 Vc+-=37-NBPTc- 1NBPTc
29、-1log10Pc101.13-1=cpocpocponjaj37.93njbj0.21+T+=njcj3.91 104T2njdj2.06 107+T3+cpoTcPcccpo232 ASHRAE Transactionsnamic properties. The use of REFPROP will be describedmore fully in the following sections.Estimation of Thermodynamic Properties Using REFPROPPure Fluids. Once Tc, Pc, c, , and are known,
30、REFPROP 8.0 can be used to predict the other thermodynamicproperties needed to calculate COPHand VHC. In particular,one needs to know temperature (T), pressure (P), density (),quality (x), enthalpy (h), and entropy (s) at several state pointsaround the cycle. To this end, one could use, for example,
31、 theP-R EoS as implemented in REFPROP 8.0 to model the fluidsbehavior. To do so, one must create an FLD file (the file thatsupplies fluid-specific information to the main algorithms ofREFPROP). Figure 2 shows an example FLD file for R-114for the P-R EoS. The sixteen items shown in bold, in slightlyl
32、arger font, are the items that would need to change in order tocreate an FLD file for a different fluid. Note: when using theP-R EoS as implemented in REFPROP, only Tcand Pcareactually used, whereas cis not. That is, the P-R EoS fixes thecritical compressibility factor, Zc, at a value of 0.307, allo
33、wingfor only two degrees of freedom in specifying the critical state. Mixtures. The method of Lemmon and Jacobsen (1999)is used to predict the mixture EoS. This model is the defaultone used by REFPROP 8.0 for binary pairs if the mixingparameters have not been determined already experimentally.The mo
34、del is somewhat complex, but in essence it relates theHelmholtz energy to one generalized function valid for a widerange of fluids as well as three mixture-dependent parameters,which can be correlated to experimental data. However, in theabsence of experimental data, the model sets two of the threem
35、ixture-dependent parameters to zero and then correlates theremaining and most important of the three to the criticaltemperatures, critical pressures, and acentric factors of thebinary pair. A REFPROP user does not need to do anythingparticular to implement this mixture model for unknownbinary pairs;
36、 it is implemented automatically by default. Oncea REFPROP user selects the mixture components, he or shewould proceed as for pure fluids to predict T, P, , x, h, and s.EXAMPLES ILLUSTRATING THE METHODOLOGYExamples of the Estimation of Thermodynamic Parameters for Pure FluidsIn this section, the abo
37、ve-described methodology is illus-trated through several detailed examples, in particular(1) twelve pure refrigerants, one of which is R-114, nine ofwhich are potential R-114 replacements, and two of which arethe components of R-410A and (2) one binary mixture (R-410A). Of the twelve pure fluids, on
38、ly four (R-114, R-32, R-125, and R-C270) are included in REFPROP 8.0; therefore,the examples of the other eight pure fluids demonstrate thepower and ease of the methodology for investigating refriger-ants that are not-so-well described. Table 3 lists the 12 pureTable 2. Joback Group Contributions fo
39、r Ideal Gas Specific Heats at Constant Pressure (Reid et al. 1987 or Poling et al. 2001)Atomic or Molecular GroupabcdC 6.62E+01 4.27E01 6.41E04 3.01E07Cl 3.33E+01 9.63E02 1.87E04 9.96E08F 2.65E+01 9.13E02 1.91E04 1.03E07I 3.21E+01 6.41E02 1.26E04 6.87E08N 3.11E+01 2.27E01 3.20E04 1.46E07NH22.69E+01
40、4.12E02 1.64E04 9.76E08O 2.55E+01 6.32E02 1.11E04 5.48E08S 1.96E+01 5.61E03 4.02E05 2.76E08CH 2.30E+01 2.04E01 2.65E04 1.20E07CH29.09E01 9.50E02 5.44E05 1.19E08CH31.95E+01 8.08E03 1.53E04 9.67E08CH2ring 6.03E+00 8.54E02 8.00E06 1.80E08cpoFigure 1 Schematic describing the methodology aspresented in t
41、his paper.ASHRAE Transactions 233fluids, their molecular structures, and their NBP. The first fluidlisted is R-114, and then the other 11 are listed in order ofincreasing NBP. In order to illustrate the methodology, Table 4 showsdetailed calculations of the Ambrose Group Contributions forthe critica
42、l constants of the 12 pure fluids. The particular fluidswere chosen to demonstrate a range of issues and subtletiesencountered when using the methodology. The values ofTable 4 then are used in conjunction with Equations 14 tocalculate Tc, Pc, c, and . Table 5 shows these calculatedparameters for the
43、 12 pure fluids, together with any knownvalues, and Table 6 shows the percentage errors between thepredicted and known values. Table 7 shows detailed calculations of the Joback GroupContributions for the ideal gas specific heats at constant pres-sures of the 12 pure fluids. Then, these values are us
44、ed inconjunction with Equation 5 to calculate . Table 8 providespolynomial expressions for for the 12 fluids and, in addi-tion, for six of the fluids provides comparisons betweenpredicted and known values evaluated at the critical tempera-ture. Finally, Table 9 provides the reference sources for the
45、known data used in Tables 38.Examples of the Estimation of Thermodynamic Properties and Performances of Both Pure Fluids and Mixtures Using REFROPOnce Tc, Pc, c, , and are established using the above-described methodology, other relevant thermodynamic prop-erties, i.e., T, P, , x, h, and s, can be e
46、stimated. These valuescould then be used in a cycle calculation to determine its ther-modynamic performance. As an example of how the imple-mentation of this methodology would proceed in predictingthermodynamic properties, Figure 3 shows percentage errorsas a function of reduced temperature (T/Tc) f
47、or some R-114property values calculated using the P-R EoS.Figure 3 begs an obvious question: how do errors in esti-mating Tc, Pc, , and affect COPHand VHC predictions?(Recall that cis not used.) Figures 47 show the impacts ofthese parameter estimation errors on COPHand VHC calcu-lations for the exam
48、ple of R-114. In each figure, only oneparticular parameter is varied while the other three are heldfixed at their known values. In general, inaccuracies in theparameter estimations have more of an effect on VHC thanthey do on COPH. To improve the VHC predictive capabilityof the P-R EoS one could, of course, include as much knownfluid information as possible in the relevant REFPROP FLDFigure 2 Example REFPROP 8.0 FLD file.Table 3. Normal Boiling Point Temperatures for Several RefrigerantsRefrigerant Formula NBP, K (F)R-114 CClF2CClF2276.7 (
