7632 J. Phys. Chem. B 1998, 102, 7632-7639 Prediction of Phase Equilibria for Refrigerant Mixtures of Difluoromethane (HFC-32), 1,1,1,2-Tetrafluoroethane (HFC-134a), and Pentafluoroethane (HFC-125a) Using SAFT-VR Amparo Galindo,† Alejandro Gil-Villegas,‡ Paul J. Whitehead, and George Jackson*,† Department of Chemistry, UniVersity of Sheffield, Sheffield S3 7HF, U.K. Andrew N. Burgess Research and Technology, ICI Chemicals and Polymers, PO Box 8, The Heath, Runcorn, Cheshire WA7 4QD, U.K. ReceiVed: January 29, 1998; In Final Form: July 1, 1998 The statistical associating fluid theory for chain molecules with attractive potentials of variable range (SAFT- VR) is used to model the phase equilibria for three binary mixtures formed by difluoromethane (HFC-32), 1,1,1,2-tetrafluoroethane (HFC-134a), and pentafluoroethane (HFC-125a). Molecules are represented as chains of spherical segments with short-ranged attractive sites. The intermolecular van der Waals forces are modeled with variable-range square-wells. The optimized values of the parameters of the model are obtained by fitting to experimental data for the vapor pressures and saturated liquid densities of each of the pure components. These parameters are the number and diameters of the spherical segments and the strengths and ranges of the potentials describing the site-site and segment-segment interactions. Using the values of the pure-component parameters and standard combining rules, the phase equilibrium of the mixtures is described very accurately. SAFT-VR improves the predictive power of mean-field versions of SAFT. Introduction The HFCs do not contain chlorine atoms, have a zero ozone depletion potential, and have lifetimes of the order of 10 times Chlorofluorocarbons (CFCs) are stable, nontoxic compounds, shorter than those of the CFCs. The thermodynamical properties 1 first used as refrigerants in 1930, when they replaced the toxic of pure HFCs have been extensively measured over the past 10 fluids that were used as coolants in refrigeration systems years and are well-known; it now seems likely that blends of (CH3Cl, SO2,NH3,CH2CH2, and hydrocarbons). They have a new refrigerants rather than pure substances will replace the very good refrigerating performance, and their nontoxic nature common CFCs; e.g., mixtures of HFC-32 (difluoromethane), encouraged widespread industrial applications, being used as HFC134a (1,1,1,2-tetrafluoroethane), HFC-125 (pentafluoroet- foam-blowing agents for polystyrene and polyurethane, solvents, hane), and HFC-152a (1,1-difluoroethane) are used in air and cleaning agents over the following 50 years. Their stability, conditioning systems. The number of mixtures of HFCs however, causes them to reach the stratosphere where they potentially viable as replacements for the old CFCs is, however, eventually decompose under solar ultraviolet radiation releasing very extensive. Equilibrium experimental data is available for chlorine radicals that react with ozone molecules (O3) to yield a small number of mixtures and only over limited ranges of 2 molecular oxygen O2. Molina and Rowland were the first to temperature and pressure. Further, the synthesis of the replace- suggest a connection between the CFCs in the stratosphere and ment refrigerants requires separation processes involving mul- the depletion of the ozone layer, a hypothesis that was confirmed ticomponent mixtures of these compounds and various other in the late 70s and early 80s. A detailed account on the role of components. It becomes then of crucial importance to develop chlorine in stratospheric chemistry can be found in a recent paper reliable theoretical models to predict the phase equilibria and by Molina.3 other thermodynamical properties of such mixtures. The Montreal Protocol of 1987 provided the first international Several equations of state (EOSs) have already been used in agreement limiting the production of CFCs worldwide. It the prediction and correlation of experimental data of refrigerant initially called only for a 50% reduction in the manufacture of systems. In a recent paper Gow4 reviews the achievements of CFCs by the year 2000. The London and Copenhagen amend- two- and three-parameter cubic EOSs in the description of such ments of 1990 and 1992 strengthened the ban to ask for a mixtures. He uses a three-parameter cubic equation with a phaseout of production by the end of 1995. CFCs are now being temperature-dependent attractive term to correlate binary vapor- replaced by hydrochlorofluorocarbons (HCFCs) and hydrofluo- liquid equilibrium data and extends it to predict the phase rocarbons (HFCs); the presence of the hydrogen atoms allows equilibria of a ternary refrigerant mixture. Good agreement with water-soluble compounds to be formed, which are removed from experimental data is found, although only one isotherm of the the atmosphere by rainfall. ternary mixture is studied. Obey and Sandler5 have examined several refrigerant mixtures with a cubic EOS and a number of † Current address: Department of Chemical Engineering and Chemical mixing rules taking special interest in the predicting capabilities Technology, Imperial College of Science Technology and Medicine, of their approach for extended ranges of temperature. University of London, Prince Consort Road, London SW7 2BY. ‡ Current address: Instituto de Fı´sica, Universidad de Guanajuato, Leo´n Cubic EOSs coupled with group contribution methods have 37150, Mexico. also been extensively used to study the phase equilibria of binary S1089-5647(98)00943-2 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/09/1998 Phase Equilibria for Refrigerant Mixtures J. Phys. Chem. B, Vol. 102, No. 39, 1998 7633 mixtures. The fundamental assumption of the group contribu- tion methods is that the properties of a molecular group are the same in every molecule and have no influence on other segments. On the basis of this idea the thermodynamic properties of new substances are predicted with a database of the interaction parameters of the “groups” involved. The interaction parameters for the different “groups” are obtained by comparisons with experimental data. It should be noted, however, that the assumption of a new molecular group with no influence on other segments of a molecule is rarely true. Barolo et al.6 used the Soave-Redlich-Kwong EOS with a group contribution method derived from UNIFAC to study mixtures of refrigerants and proposed a list of groups and subgroups for CFCs, HCFCs, HFCs, and FCs. Similarly, Kleiber7 has extended the UNIFAC group assignment with the UNIQUAC equation to deal with replacement refrigerants; 10 Figure 1. Models for (a) HFC-32, (b) HFC-134a and HFC-R125. A new groups were described. number of off-center square-well sites are placed on a sphere of diameter 8 σi. The sites are placed at a distance rd from the centre of the sphere Blindenbach et al. used the perturbed anisotropic chain theory and have a cut-off range r . The two different types of sites are 9,10 c (PACT) developed by Vimalchand and Donohue, in order colored white and grey; only white-grey bonding is allowed. The white to model the thermodynamic properties of pure CFCs and and grey sites interact with a hydrogen-bonding energy hb when the - - HCFCs, and the vapor liquid equilibria of their mixtures, site site distance is less than rc. HFC-32 is modeled with a single including mixtures with hydrocarbons. PACT is an EOS that hard sphere (m ) 1 ) and HFC-134a and HFC-125 are modeled with ) ) takes into account dispersion, polar, and induced polar interac- two overlapping hard spheres (m 1.4 and m 1.35, respectively). Long-range dispersion interactions are modelled via a high-temperature tions. On the basis of pure component parameters, very good perturbation expansion for a site-site square-well potential of depth agreement with experimental data was found and better predic- and range λ. tive results than the ones obtained with cubic equations of state. 11 Economou et al. have measured the properties of the mixture that is in very good agreement with experimental data for + HFC-22 (chlorodifluoro ethane) HFC-134a up to the critical strongly associated systems such as the mixtures containing region and have compared their data with PACT, obtaining very hydrogen fluoride. SAFT-VR introduces a more accurate good agreement. The statistical associating fluid theory (SAFT) description of the thermodynamics due to attractive van der also takes into account the anisotropies of the fluid, both due Waals forces by using a second-order perturbation theory. With to molecular shape and to directional forces. In the SAFT this approach is possible to describe mixtures of refrigerants in approach the free energy can be written as separate contribu- a more accurate way than the simplified SAFT-HS approach, tions, describing the effects of molecular shape, dispersion as we will show in this paper. forces, and molecular association. In the original SAFT approach,12,13 the molecules are modeled as chains of Lennard- Jones segments, with embedded short-range sites to describe 2. Models and Theory association. In its many versions, the SAFT approach has been used to examine a wide range of fluids, from linear small alkanes It is useful to illustrate the models used in the description of - to polymeric fluids (see refs 14 16 and references therein). An these molecules with the SAFT-VR approach and then give a extended version of the SAFT equation, which accounts for short reminder of the specific equations involved in each of explicit contributions to the free energy due to dipolar interac- the mixtures. The comparison with experimental data is 17 tions (based on previous work of Mu¨ller and Gubbins and presented in the following section. 18 the well-known Pade´ approximation due to Stell et al. ), was 2.1. Models. We model our molecules as hard-spherical 19,20 recently used by Kraska and Gubbins to study the phase cores formed from tangentially bonded segments of diameter σ equilibria of mixtures of alcohols.