DOE/CE/23810-97
`
`Development of the REFPROP Database
`and Transport Properties of Refrigerants
`
`Final Report
`
`Mark O. McLinden
`
`Physical and Chemical Properties Division
`National Institute of Standards and Technology
`325 Broadway, Mailstop 838.07
`Boulder, CO 80303-3328
`
`July, 1998
`
`Prepared for
`Air-Conditioning and Refrigeration Technology Institute
`Under
`ARTI MCLR Project Number 665-50800
`
`This research project is supported, in whole or in part, by U.S. Department of Energy grant DE-FG02-91CE23810: Materials
`Compatibility and Lubricants Research (MCLR) on CFC-Refrigerant Substitutes. Federal funding supporting this project
`constitutes 93.57% of allowable costs. Funding from non-government sources supporting this project consists of direct cost
`sharing of 6.43% of allowable costs; and in-kind contributions from the air-conditioning and refrigeration industry.
`
`Page 1 of 40
`
`Arkema Exhibit 1126
`
`

`
`DISCLAIMER
`
`The U.S. Department of Energy’s and the air-conditioning industry’s support for the Materials
`Compatibility and Lubricants Research (MCLR) program does not constitute an endorsement by
`the U.S. Department of Energy, nor by the air-conditioning and refrigeration industry, of the
`views expressed herein.
`
`NOTICE
`
`This report was prepared as an account of work sponsored by the United States Government.
`Neither the United States nor the Department of Energy, nor the Air-Conditioning and
`Refrigeration Technology Institute, nor any of their employees, nor any of their contractors,
`subcontractors, or their employees, makes any warranty, expressed or implied, or assumes any
`legal liability or responsibility for the accuracy, completeness, or usefulness of any information,
`apparatus, product or process disclosed or represents that its use would not infringe privately-
`owned rights.
`
`COPYRIGHT NOTICE
`(for journal publication submissions)
`
`By acceptance of this article, the publisher and/or recipient acknowledges the rights of the U.S.
`Government and the Air-Conditioning and Refrigeration Technology Institute, Inc. (ARTI) to
`retain a non-exclusive, royalty-free license in and to any copyrights covering this paper.
`
`Page 2 of 40
`
`

`
`Development of REFPROP
`
`EXECUTIVE SUMMARY
`
`This task consisted of developing Version 6.0 of the NIST Thermodynamic and Transport
`Properties of Refrigerants and Refrigerant Mixtures Database (REFPROP), entailing a complete revision
`of this database. This program is based on the most accurate pure fluid and mixture models currently
`available. It is distributed by the Standard Reference Data Program of NIST. The database development
`is further divided into the development of a graphical user interface and the development of Fortran
`subroutines which implement the property models.
`
`Three models are used for the thermodynamic properties of pure components, depending on the
`availability of data. The first is the modified Benedict-Webb-Rubin (MBWR) equation of state. It is
`capable of accurately representing the properties of a fluid over wide ranges of temperature, pressure,
`and density. The MBWR equation is the basis for the current international standard for the properties of
`R123 (Younglove and McLinden, 1994). The second high-accuracy pure-fluid equation of state is
`written in terms of reduced molar Helmholtz free energy. This “Helmholtz energy model” is the basis for
`the international standard formulation for R134a (Tillner-Roth and Baehr, 1994). The third pure-fluid
`model is the extended corresponding states (ECS) model of Huber and Ely (1994). It is used for fluids
`with limited experimental data.
`
`The thermodynamic properties of mixtures are calculated with a new model which was developed,
`in slightly different forms, independently by Tillner-Roth (1993) and Lemmon (1996) (see also Lemmon
`and Jacobsen, 1997). It applies mixing rules to the Helmholtz energy of the mixture components. The
`Lemmon-Jacobsen model provides a number of advantages. By applying mixing rules to the Helmholtz
`energy of the mixture components, it allows the use of high-accuracy equations of state for the
`components, and the properties of the mixture will reduce exactly to the pure components as the
`composition approaches a mole fraction of 1. Different components in a mixture may be modeled with
`different forms; for example, a MBWR equation may be mixed with a Helmholtz equation of state. The
`mixture is modeled in a fundamental way, and thus the departure function is a relatively small
`contribution to the total Helmholtz energy for most refrigerant mixtures. The great flexibility of the
`adjustable parameters in this model allows an accurate representation of a wide variety of mixtures,
`provided sufficient experimental data are available.
`
`The mixing parameters have been fitted to experimental data for 75 binary pairs. For mixtures
`lacking experimental data a predictive model, based on the fundamental molecular parameters dipole
`moment, acentric factor, and critical parameters, is used. This model is described in Appendix B.
`Mixture properties calculated with this model will have a larger uncertainty than those based on
`experimental data. Furthermore, the data used to develop this predictive model were for mixtures of
`HFCs, CFCs, HCFCs, hydrocarbons, and carbon dioxide. Its applicability to different types of mixtures,
`such as ammonia plus an HFC, is unknown.
`
`The transport properties of pure fluids are modeled with either fluid-specific correlations taken
`from the literature or a new variation on the extended corresponding states model. This new model is
`described below and in Appendix C. Mixtures are modeled with the ECS approach.
`
`The property models described above are implemented as a suite of FORTRAN subroutines.
`These routines have been completely rewritten from earlier versions of REFPROP. Source code is
`provided with the database so that users may link the property routines with their own application. The
`routines are written in ANSI-standard FORTRAN 77 and are compatible with FORTRAN 90. They are
`
`1
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`Page 3 of 40
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`

`
`written in a structured format, are internally documented with extensive comments, and have been tested
`on a variety of compilers.
`
`The fluid or mixture of interest is specified with a (required) call to the subroutine “SETUP.” This
`routine reads the coefficients to the NIST-recommended models for that fluid. Alternative property
`models and/or nonstandard reference states may be specified by calls to additional (optional) setup
`routines. Routines are provided to calculate thermodynamic and transport properties and surface tension
`at a given (T, r, x) state. Iterative routines provide saturation properties at a specified (T, x) or (P, x)
`state. Flash calculations calculate single- or two-phase states at specified (P, h, x), (P, T, x), etc.
`
`The routines mentioned above are independent of the model. Underlying these routines are sets of
`“core” routines for each of the models implemented in the database. Each such set is highly modular and
`is contained in a separate file. Coefficients needed for a particular model are stored in common blocks,
`but these commons are referenced only by routines in the same file. These sets of subroutines, thus,
`resemble “units” in the Pascal language with clearly demarcated “interface” and “local” declarations.
`This structure is intended to simplify the addition of future models to the database and will make such
`additions almost totally transparent to the user.
`
`Numerical coefficients to the property models are stored in text files. There is one file per fluid
`and one file containing coefficients for the mixture departure functions. These files are read (once) upon
`the call to SETUP. NIST REFPROP contains 33 pure fluids and can calculate properties for mixtures
`with up to five components. Fluids in the database include environmentally acceptable HFCs, such as
`R23, R32, R125, R134a, and R245fa; HCFCs, such as R22, R123, R124, R141b, and R142b; traditional
`CFCs, such as R11, R12, R13, R113, R114, and R115; and “natural” refrigerants, such as ammonia,
`carbon dioxide, propane, and isobutane. The fluids included in the database are listed in Table 1. NIST
`will add fluids to the database as commercial interest and the availability of data allow, and we welcome
`suggestions for new fluids.
`
`The user interface provides a convenient means to calculate and display thermodynamic and
`transport properties. It is written for the Windows™ operating system. The interface is written in Pascal;
`it accesses the FORTRAN property subroutines via a dynamic link library. The program is controlled
`through the use of the following pull-down menus:
`
`File provides commands to save and print generated tables and plots. Individual items or
`entire sessions with multiple windows may be saved or recalled. The standard “print setup”
`and “exit” commands are also present.
`
`The Edit menu provides copy and paste commands which allow selected data to be
`exchanged with other applications.
`
`The Options menu provides commands for selecting the unit system, properties of interest,
`and the reference state. These options may be stored for recall at a later time. A user-
`defined set of preferences is loaded upon program startup.
`
`The pure fluid or mixture of interest is specified with commands in the Substance menu.
`Most of the refrigerant mixtures of current commercial interest (those having an ASHRAE
`R400 or R500-series designation) are predefined. In addition, new mixtures can be specified
`and saved by combining up to five pure components.
`
`2
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`Page 4 of 40
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`

`
`The Calculate menu initiates the calculations that generate a property table. Each property
`selected for display is shown in a separate column of the table. Two types of tables are
`provided. The first type provides properties at saturation or with a property (such as
`temperature or pressure) held constant with another selected property varying over a
`specified range. The second type allows the user to select the independent variables. Values
`of the independent variables may then be entered with the keyboard, read from a file, or
`pasted from another application.
`
`The Plot menu provides high-quality x-y plots of any variables appearing in a table. In
`addition, temperature-entropy, pressure-enthalpy, temperature-composition and pressure-
`composition diagrams may be generated automatically. Controls are provided to modify the
`plot size, axis scaling, plot symbols, line type, legend, and other plot features.
`
`Each table or plot appears in a separate window and can be accessed, resized, or retitled with
`commands in the Window menu. The number of windows is limited only by available
`memory.
`
`A complete online-help system can be accessed through the Help menu.
`
`A status line at the bottom of the screen displays the currently specified mixture, composition, and
`reference state. Clicking on the status line will call up a screen for each of the components providing
`documentation for fluid constants, the source of the models, and their range of applicability.
`
`The database calculates seventeen thermodynamic and transport properties, including surface
`tensions of pure fluids and mixtures. Commercialized blends, such as R407C and R410A, are predefined
`in the interface and are listed in Table 2.
`
`Modeling of Transport Properties with Extended Corresponding States
`
`We have developed a new model for the thermal conductivity of refrigerants based on the extended
`corresponding states (ECS) concept. The principle of corresponding states stems from the observation
`that the properties of many fluids are similar when scaled according by their respective critical
`temperature and density. Extended corresponding states models modify this scaling by additional “shape
`factors” to improve the representation of data. ECS methods have often been used to represent both the
`thermodynamic and transport properties of a fluid, especially fluids with limited data. Recently, high-
`accuracy equations of state have been developed for many of the refrigerants of industrial interest. But,
`the situation for the transport properties of viscosity and thermal conductivity lags the thermodynamic
`properties—accurate, wide-ranging, fluid-specific correlations are available for only a few refrigerants.
`There is a need for a method which can predict the transport properties in the absence of data yet also
`take advantage of whatever experimental data might be available to improve upon the purely predictive
`scheme.
`
`The method we present starts with the ECS model of Huber et al. (1992). We combine this
`predictive model with the best available thermodynamic equations of state. Furthermore, when thermal
`conductivity data are available, we use those data to fit a new “thermal conductivity shape factor” and/or
`a term in the traditional correlation for the dilute-gas portion of the thermal conductivity. Use of these
`additional factors results in significantly improved agreement between the ECS predictions and
`experimental data. The method has been applied to 11 halocarbon refrigerants and ammonia. The
`average absolute deviations between the calculated and experimental thermal conductivity values are 4%
`or less for 10 of the 12 fluids studied. This new model is analogous to our parallel work on viscosity
`
`3
`
`Page 5 of 40
`
`

`
`(Klein et al. 1997). It accomplishes more than what was set out in the original task statement in that all
`available data (not just data at saturation) can be used in fitting the shape factors.
`
`Details of this model are presented in Appendix C. This Appendix forms the basis of a paper
`which will be submitted for publication in the International Journal of Refrigeration.
`
`References
`Huber, M.L. and Ely, J.F. (1994). A predictive extended corresponding states model for pure and mixed
`refrigerants including an equation of state for R134a. Int. J. Refrigeration 17: 18-31.
`Klein, S.A., McLinden, M.O. and Laesecke, A. (1997). An improved extended corresponding states
`method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20: 208-
`217.
`
`Lemmon, E.W. (1996). A generalized model for the prediction of the thermodynamic properties of
`mixtures including vapor-liquid equilibrium. Ph.D. thesis, University of Idaho, Moscow, ID.
`
`Lemmon, E.W. and Jacobsen, R.T. (1997). Thermodynamic properties of mixtures of refrigerants R-32,
`R-125, R-134a, and R-152a. Conference Preprint, 13th Symposium on Thermophysical Properties,
`Boulder, Colorado, June 22-27, submitted for publication in Int. J. Thermophysics.
`
`Tillner-Roth, R. (1993). Die thermodynamischen Eigenschaften von R 152a, R 134a und ihren
`Gemischen—Messungen und Fundamentalgleichungen. Ph.D. thesis, Universität Hannover.
`
`Tillner-Roth, R. and Baehr, H.D. (1994). An international standard formulation of the thermodynamic
`properties of 1,1,1,2-tetrafluoroethane (HFC-134a) covering temperatures from 170 K to 455 K at
`pressures up to 70 MPa. J. Phys. Chem. Ref. Data 23: 657-729.
`Younglove, B.A. and McLinden, M.O. (1994). An international standard equation-of-state formulation of
`the thermodynamic properties of refrigerant 123 (2,2-dichloro-1,1,1-trifluoroethane). J. Phys.
`Chem. Ref. Data 23: 731-779.
`
`4
`
`Page 6 of 40
`
`

`
`Table 1. Fluids in the REFPROP Database
`
`Short Name
`
`CAS number
`
`Full Chemical Name
`
`ammonia
`butane
`carbon dioxide
`ethane
`isobutane
`propane
`propylene
`R11
`R12
`R13
`R14
`R22
`R23
`R32
`R41
`R113
`R114
`R115
`R116
`R123
`R124
`R125
`R134
`R134a
`R141b
`R142b
`R143a
`R152a
`RC318
`R227ea
`R236ea
`R236fa
`R245ca
`R245fa
`
`7664-41-7
`106-97-8
`124-38-9
`74-84-0
`75-28-5
`74-98-6
`115-07-1
`75-69-4
`75-71-8
`75-72-9
`75-73-0
`75-45-6
`75-46-7
`75-10-5
`593-53-3
`76-13-1
`76-14-2
`76-15-3
`76-16-4
`306-83-2
`2837-89-0
`354-33-6
`359-35-3
`811-97-2
`1717-00-6
`75-68-3
`420-46-2
`75-37-6
`115-25-3
`431-89-0
`431-63-0
`690-39-1
`679-86-7
`460-73-11
`
`ammonia
`butane
`carbon dioxide
`ethane
`2–methylpropane
`propane
`propene
`trichlorofluoromethane
`dichlorodifluoromethane
`chlorotrifluoromethane
`tetrafluoromethane
`chlorodifluoromethane
`trifluoromethane
`difluoromethane
`fluoromethane
`1,1,2–trichloro–1,2,2–trifluoroethane
`1,2–dichloro–1,1,2,2–tetrafluoroethane
`chloropentafluoroethane
`hexafluoroethane
`1,1–dichloro–2,2,2–trifluoroethane
`1–chloro–1,2,2,2–tetrafluoroethane
`pentafluoroethane
`1,1,2,2–tetrafluoroethane
`1,1,1,2–tetrafluoroethane
`1,1–dichloro–1–fluoroethane
`1–chloro–1,1–difluoroethane
`1,1,1–trifluoroethane
`1,1-difluoroethane
`octafluorocyclobutane
`1,1,1,2,3,3,3–heptafluoropropane
`1,1,1,2,3,3–hexafluoropropane
`1,1,1,3,3,3–hexafluoropropane
`1,1,2,2,3–pentafluoropropane
`1,1,1,3,3–pentafluoropropane
`
`5
`
`Page 7 of 40
`
`

`
`Table 2. Predefined Mixtures in the REFPROP Database
`
`ASHRAE
`Designation
`
`Components
`
`Composition
`(mass percentages)
`
`R401A
`R401B
`R401C
`R402A
`R402B
`R404A
`R405A
`R406A
`R407A
`R407B
`R407C
`R407D
`R407E
`R408A
`R409A
`R409B
`R410A
`R410B
`R411A
`R411B
`R414B
`R500
`R501
`R502
`R503
`R504
`R507A
`R508A
`R508B
`
`R22/152a/124
`R22/152a/124
`R22/152a/124
`R125/290/22
`R125/290/22
`R125/143a/134a
`R22/152a/142b/C318
`R22/600a/142b
`R32/125/134a
`R32/125/134a
`R32/125/134a
`R32/125/134a
`R32/125/134a
`R125/143a/22
`R22/124/142b
`R22/124/142b
`R32/125
`R32/125
`R1270/22/152a
`R1270/22/152a
`R22/124/600a/142b
`R12/152a
`R22/12
`R22/115
`R23/13
`R32/115
`R125/143a
`R23/116
`R23/116
`
`53/13/34
`61/11/28
`33/15/52
`60/2/38
`38/2/60
`44/52/4
`45/7/5.5/42.5
`55/4/41
`20/40/40
`10/70/20
`23/25/52
`15/15/70
`25/15/60
`7/46/47
`60/25/15
`65/25/10
`50/50
`45/55
`1.5/87.5/11.0
`3/94/3
`50/39/1.5/9.5
`73.8/26.2
`75/25
`48.8/51.2
`40.1/59.9
`48.2/51.8
`50/50
`39/61
`46/54
`
`6
`
`Page 8 of 40
`
`

`
`APPENDIX A
`
`Task Statement
`
`Development of REFPROP
`
`The REFPROP database program is widely used in the refrigeration industry for the calculation of
`refrigerant properties. This program had its origins as a tool for investigating refrigerant mixtures at a
`time when property data on mixtures (and even many pure fluids) were extremely limited. Given the data
`situation in the early 1980’s, the program was based on the Carnahan-Starling-DeSantis (CSD) equation
`of state—a model which does a reasonable job of calculating near-saturation properties with limited input
`data. Over the years, we have added the extended corresponding states (ECS) model and modified
`Bennedict-Webb-Rubin (MBWR) equations of state for selected pure fluids. Even so, the database has
`not always kept up with the demands of industry—with the commercialization of refrigerant blends,
`accuracy demands for mixtures have increased; also, fluids such as R32 and R125 are used much closer
`to the critical point than traditional refrigerants. In addition, the user interface to REFPROP is not the
`most modern.
`
`We propose both a major upgrade of the capabilities of REFPROP and a complete rewrite of the
`code. We would retain the MBWR and ECS models and add at least two new models for the
`thermodynamic properties: the so-called “fundamental” equation of state for pure fluids and a Helmholtz
`energy model for mixtures. The University of Idaho and at least two groups in Germany have produced
`high-quality fits of several fluids using the fundamental equation of state; including this model would
`allow us to use their equations for fluids, such as R22, for which we do not have MBWR equations.
`
`The mixture Helmholtz model is under development at NIST (in cooperation with the University of
`Hannover, Germany) and at the University of Idaho (under contract to NIST). This model shares many
`concepts with the ECS model, but it applies mixing rules to the Helmholtz free energy of each of the
`mixture components rather than referencing properties to a single pure reference fluid as is the case with
`the ECS model. It thus starts with high-accuracy properties for each of the mixture components (mixture
`properties can be no better than the constituent pure components) and reduces exactly to the pure
`components at the limits of composition. It is simpler (and should thus be faster) than the ECS model.
`The mixture Helmholtz model was shown to be clearly superior to both ECS and cubic equations of state
`in a preliminary comparison of mixture models conducted by IEA Annex 18. Although further
`development work is needed to incorporate additional fluids and mixtures into this scheme, it is the most
`promising model currently available and should satisfy the accuracy demands of the refrigeration
`industry.
`
`The ECS model is still the best comprehensive model available for the transport properties of
`mixtures and would be retained. We would also add high-accuracy transport correlations for selected
`pure fluids as available in the literature. A model for surface tension would be added.
`
`We would also add a modern graphical user interface (GUI) which would allow easier access to
`options, multiple calculation windows, plotting capabilities, and easy cut-and-paste data transfer to
`spreadsheets. Of equal significance for users of the core subroutines, we would completely restructure
`and rewrite the code to make it modular, more understandable, and more robust. Fluid-specific
`coefficients would be stored in data files (rather than compiled Fortran block data routines) making it
`much easier to update fluids or add new fluids.
`
`A-1
`
`Page 9 of 40
`
`

`
`Modeling of pure-fluid transport properties
`
`We use several different approaches to model pure-fluid transport properties. For fluids with
`extensive data, we develop fluid-specific surfaces for the viscosity and thermal conductivity as functions
`of temperature and density. For fluids with limited data, we use variations of the extended corresponding
`states (ECS) model. The ECS model uses a “transport shape factor” in addition to the two shape factors
`for the thermodynamic properties together with viscosity and thermal conductivity surfaces for a
`reference fluid (R134a in the case of refrigerants). This transport shape factor is based on saturated
`liquid viscosities, if available; in the absence of data, it is based on a generalized correlation involving
`the acentric factor.
`
`Each of these approaches could be improved. Some of the more important pure fluids warrant
`fluid-specific surfaces. In particular, the surface for R134a, which serves as the reference surface in the
`ECS model is in need of an update—considerable new data have become available since the present
`surface was fitted in 1992. The ECS approach based on saturated liquid viscosities works well, but needs
`to be updated with recent experimental data and refit to the new R134a reference surface. This approach
`is somewhat limited in that it cannot make use of data away from saturation. For some fluids, single-
`phase data are available, which, while not sufficient for a fluid-specific surface, would be valuable in
`fitting a fluid. At present, we must discard these data because the current implementation of the ECS
`model is not able to make use of them. The generalized ECS approach needs further development; again,
`recently available data will allow an improvement of this approach.
`
`As a first phase in this area, we propose to fit high-accuracy viscosity and thermal conductivity
`surfaces for R134a, for pure-fluid uses and as a reference fluid for the ECS model. We will compile all
`available data for the common HFC and HCFC refrigerants, and use these data to update the ECS model
`based on saturation data.
`
`A-2
`
`Page 10 of 40
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`

`
`APPENDIX B
`
`A Predictive Model for Refrigerant Mixtures
`
`Eric W. Lemmon
`
`Physical and Chemical Properties Division
`National Institute of Standards and Technology
`Boulder, Colorado 80303 USA
`
`Version 6 of the REFPROP database implements a new model for the thermodynamic properties of
`mixtures. This model applies mixing rules to the Helmholtz free energy of each of the mixture
`components. It starts with high–accuracy properties for each of the mixture components (mixture
`properties can be no better than the constituent pure components) and reduces exactly to the pure
`components at the limits of composition. This mixture Helmholtz model makes use of a generalized
`mixing function which is applicable to entire classes of fluids. This generalized function is modified by a
`multiplier, Fpq, and reducing parameters kT and kV for particular mixtures. This approach allows a highly
`accurate representation of mixtures with extensive data. This Appendix describes a predictive scheme
`for the kT parameter in the mixture Helmholtz model based on the fundamental molecular parameters
`dipole moment, acentric factor, and critical parameters. The kT parameter is the most important of the
`three and has the closest parallels with the mixing parameters in other mixture models.
`
`Mixture data for a total of 75 binary pairs have been collected for use in this modeling task. About
`three–fourths of the binary pairs contain an HCFC and/or CFC and, so, will not be applicable for use in
`refrigeration equipment. Nevertheless, the HCFC and CFC-containing mixtures have provided a wider
`range of molecular parameters which has proven useful for developing the predictive model. (For
`example, the HFCs are highly polar while the hydrocarbons are nonpolar; the CFCs and HCFCs provide
`intermediate values of dipole moment.) These data have been evaluated, and while their quality varies
`widely, they provide a sufficient database of VLE data.
`
`The model takes the form of correlation for the ζ12 parameter. The ζ12 parameter is equivalent to the
`more familiar kT parameter, with the conversion between them given by:
`
`kT = 1+ 2
`
`ζ12
`T1crit + T2
`
`
`
`crit
`
`(1)
`
`A wide variety of fluid parameters were examined in developing the predictive method; these included
`the dipole moment, molecular volume, acentric factor, critical temperature, critical pressure, critical
`density, triple point temperature, and the normal boiling point temperature. Of these, only the critical
`temperature Tcrit, critical pressure Pcrit, and acentric factor ω were used in the final scheme to calculate
`ζ12. The dipole moment µ was used to determine the order of the inputs to the scheme. ζ12 is given by
`
`B-1
`
`Page 11 of 40
`
`

`
`ζ
`
`12
`
`
`= T2
`
`
`T1
`
`crit
`
`crit
`
`
`
`
` 40.4 − 25.03exp 0.69315
`
`
`
`
`
`
`critω
`T1crit P2
`
`critω
`
`T2crit P1
`
`2
`
`1
`
`
`
`
`
`
`
` ,
`
`(3)
`
`where fluid “1” is the one with the smaller value of the dipole moment. In the special case where the
`dipole moments of the two fluids are identical, fluid “1” is the fluid with the larger value of:
`
`T crit
`Pcritω .
`The value of ζ12 ranges between –100 and +20. A value of zero for ζ12 corresponds to ideal mixing. In
`most cases, the predictive scheme predicts ζ12 within ± 20. Even for one of the worst cases, the
`propylene/R115 mixture, using the predicted ζ12 value of –18 instead of the experimental value of –41
`increases the average absolute deviation in bubble–point pressure only from 1.5% to 4.5%. For most of
`the other systems, deviations using the predicted value will be much less. The values of ζ12 calculated
`from experimental data and those predicted by Equation 3 are given in Table B-1.
`
`(4)
`
`A method for predicting the other parameters, Fpq and kV, is still unavailable due to lack of experimental
`data. The ζ12 parameter is the most important of the three and even this one parameter captures the most
`essential features of mixture behavior, including the azeotropic behavior that exists in some of the fluid
`pairs. With this parameter alone, vapor–liquid equilibria for nearly all systems can be calculated with
`acceptable uncertainty. The largest influence of the Fpq and ξ12 parameters is in the calculation of
`densities. When only the ζ12 parameter is used, densities are generally calculated within 1% of
`experimental measurements.
`
`Of course, one of the major results of this task is the fitting of experimentally based values of ζ12, and
`these should be used when available. But in the case of two mixtures, R23/134a and CO2/R12, the
`experimental data were of questionable accuracy, and we feel that using the predicted value will give
`more reliable results for the mixture properties. Likewise, the new mixture prediction scheme does not
`replace the values of Fpq, ζ12, and ξ12 determined in previous work for binary mixtures with extensive
`data, including mixtures of R32, R125, R134a, R152a, and R143a; mixtures of propane with R32, R125,
`and R134a; and the mixture CO2/R41.
`
`B-2
`
`Page 12 of 40
`
`

`
`Table B-1. Values of ζ12 evaluated from experimental data and calculated from Equation 3.
`
`Mixture
`
`Propane/R32
`Propane/R22
`Propane/R115
`Propane/R125
`Propane/R134a
`Propylene/R12
`Propylene/R13
`Propylene/R22
`Propylene/R23
`Propylene/R114
`Propylene/R115
`Propylene/R116
`Propylene/R134a
`Propylene/R142b
`Propylene/R152a
`CO2/R12†
`CO2/R22
`CO2/R23
`CO2/R32
`CO2/R41
`CO2/R142b
`R11/12
`R11/13
`R11/22
`R11/23
`R12/13
`R12/22
`R12/23
`R12/32
`R12/113
`R12/114
`R12/134a
`R12/142b
`R12/143a
`R12/152a
`R13/14
`R13/23
`R13/113
`R14/23
`R21/114
`R22/23
`R22/32
`R22/113
`
`ζ12—fit to
`experimental data
`
`ζ12—calculated with
`predictive model
`
`–102.34
` –43.44
` –41.19
` –74.31
` –73.73
` –8.75
` –31.18
` –15.86
` –62.15
` –21.87
` –41.09
` –79.47
` –46.98
` –8.04
` –37.88
` –37.06
` –0.62
` –12.26
` –3.12
` 1.79
` –15.84
` –0.53
` –7.87
` –26.89
` –67.26
` –13.44
` –22.32
` –55.24
` –71.97
` 20.16
` –2.04
` –45.30
` –22.24
` –34.22
` –44.30
` –9.08
` –40.35
` 12.71
` –32.70
` –34.61
` –10.68
` –5.05
` –27.29
`
` –106.11
` –41.14
` –19.15
` –45.99
` –62.26
` –12.91
` –16.13
` –39.14
` –72.84
` –14.85
` –18.06
` –23.10
` –59.26
` –26.17
` –48.83
` 10.63
` 4.59
` –2.64
` –5.02
` 0.04
` 8.51
` –10.58
` –13.11
` –31.62
` –58.90
` –12.61
` –31.44
` –58.52
` –80.66
` –8.48
` –11.18
` –47.78
` –20.66
` –26.35
` –39.32
` –2.99
` –51.35
` –4.03
` –36.63
` –18.67
` –21.80
` –30.19
` –30.89
`
`________________
`† The experimental data for this system are questionable, and the calculated value of ζ12 is recommended in preference to the
`experimental value.
`
`B-3
`
`Page 13 of 40
`
`

`
`Table B-1 (continued).
`
`Mixture
`
`R22/114
`R22/115
`R22/124
`R22/125
`R22/134a
`R22/142b
`R22/152a
`R23/113
`R23/114
`R23/116
`R23/134a†
`R32/115
`R32/125
`R32/134a
`R32/143a
`R32/152a
`R113/114
`R113/142b
`R113/152a
`R114/115
`R114/152a
`R116/134a
`R123/134a
`R124/134a
`R124/142b
`R124/152a
`R125/134a
`R125/143a
`R134a/142b
`R134a/143a
`R134a/152a
`R142b/152a
`
`ζ12—fit to
`experimental data
`
`ζ12—calculated with
`predictive model
`
` –25.51
` –40.47
` –18.64
` –16.52
` –6.89
` 0.23
` 6.36
` –63.32
` –57.97
` –51.22
` 40.90
` –83.98
` –14.54
` –6.14
` –17.00
` –2.64
` 0.24
` –17.64
` –52.63
` –2.15
` –40.56
` –42.80
` –21.73
` –9.93
` –1.46
` –4.78
` –2.00
` 3.06
` –11.07
` 1.52
` 0.87
` –13.37
`
` –27.71
` –24.02
` –6.24
` –11.76
` –16.86
` –3.93
` –13.02
` –57.56
` –51.62
` –37.04
` –5.22
` –62.65
` –26.74
` –2.69
` 1.76
` –0.47
` –7.19
` –20.74
` –38.52
` –6.76
` –34.68
` –29.59
` –27.74
` –21.84
` –7.12
` –17.43
` –14.30
` –5.71
` 0.23
` –3.04
` –6.76
` –21.15
`
`________________
`† The experimental data for this system are questionable, and the calculated value of ζ12 is recommended in preference to the
`experimental value.
`
`B-4
`
`Page 14 of 40
`
`

`
`APPENDIX C
`
`An Extended Corresponding States Model for the
`Thermal Conductivity of Refrigerants1
`
`Mark O. McLinden
`Sanford A. Klein2
`
`Physical and Chemical Properties Division
`National Institute of Standards and Technology
`Boulder, Colorado 80303 USA
`
`ABSTRACT
`
`The extended corresponding states (ECS) model of Huber et al. (Fluid Phase Equilibria, 1992, 80,
`249–261) for calculating the thermal conductivity of a refrigerant is modified by the introduction of a
`thermal conductivity shape factor which is determined from experimental data. An additional empirical
`correction to the traditional Eucken correlation for the dilute-gas conductivity was found to be necessary,
`especially for highly polar fluids. Use of these additional factors results in significantly improved
`agreement between the ECS predictions and experimental data. The method has been applied to 11
`halocarbon refrigerants and ammonia. The average absolute deviations between the calculated and
`experimental thermal conductivity values are 4% or less for 10 of the 12 fluids studied.
`
`KEYWORDS
`refrigerant; thermal conductivity; model; calculation; corresponding states
`
`1Contribution of the National Institute of Standards and Technology, not subject to copyright in the
`United States.
`
`2Permanent address: Solar Energy Laboratory, University of Wisco