Bertucco, A.

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Lawrence Berkeley National LaboratoryRecent WorkTitleA Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria of Mixtures Containing a Refrigerant and a Lubricant OilPermalinkhttps://escholarship.org/uc/item/8x749340JournalFluid Phase Equilibria, 158-60ISSN0378-3812AuthorBertucco, A.Publication Date1998-08-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaLBNL-42224 Preprint ERNEST DRLANDCJ LAWRENCE BERKELEY NATICJNAL LABCJRATDRY A Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria of Mixtures Containing a Refrigerant and a Lubricant Oil A. Bertucco, N. Elvassore, M. Fermeglia, and John M. Prausnitz Chemical Sciences Division August 1998 Submitted to Fluid Phase Equilibria - .... .. •• ,~ " .L ' < / , .. -~ . r-0" Q) , O"lll 0 , "'1'< Ill r+l 0 "'1 :::0 '< Ill -tl ("') 0 "C '< ,.... Cl z ,.... I "" N N N "" DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal 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. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. LBNL-42224 A Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria of Mixtures Containing a Refrigerant and a Lubricant Oil A. Bertucco1, N. Elvassore1 , M. Fermeglia2 and John M. Prausnitz Department of Chemical Engineering University of California and Chemical Sciences Division Lawrence Berkeley National Laboratory University of California Berkeley, CA 94720, U.S.A. August 1998 This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract Number DE-AC03-76SF00098. 11stituto di Impianti Chimici, Universita di Padova, 35131 Padova, Italy 2 DICAMP, Universita di Trieste, 34100 Trieste, Italy Abstract A modification of the Perturbed-Hard-Sphere-Chain equation of state is used to describe vapor-liquid (VLE) and liquid-liquid equilibria (LLE) of mixtures containing new-generation refrigerants and a lubricant oil. For refrigerants, pure-component parameters are obtained from thermodynamic data. For the oil, they are predicted by a group-contribution method, and the calculation is checked on liquid density values of polyol-ester lubricants. Extension to mixtures is performed by using conventional one-fluid mixing rules with binary interaction parameters regressed from vapor-liquid equilibrium experimental data. VLE calculations are reported for mixtures containing a refrigerant and a polyol-ester lubricant over wide temperature and concentration ranges. The thermodynamic condition for LLE is checked. If two liquid phases are present, LLE is calculated and compared with experimental measurements. Introduction and Scope In engineering practice there is a strong current need for a molecular thermodynamic model suitable to represent both volumetric and equilibrium properties of new refrigerants. In most cases these new refrigerants are mixtures of hydro-fluorocarbons and hydrocarbons. Mixtures are required because no pure fluid alternatives exist that can provide as high performance as those attained by refrigerants to be phased out because of environmental laws. In a refrigeration cycle mutual solubility may occur between refrigerant and lubricant oil. This solubility can reduce dramatically the efficiency of a refrigeration plant. Lubricant oils modify the equilibrium pressure and the refrigerant composition, and may induce an undesired liquid-liquid phase split. Therefore, the thermo-physical properties of mixtures of new refrigerants and lubricant oils are essential for proper design and operation of new refrigeration systems. The phase equilibria of such mixtures has been addressed in the open literature only recently. Among others, a Flory-Huggins type model has been proposed by Thomas and Pham [1], who concentrated on the R134a-Polyalkylene Glycol system. These authors correlated vapor-liquid equilibria (VLE) by introducing a temperature and composition dependence in the Flory parameter; Martz et al (2] compared the performance of sever~l excess Gibbs energy (GE) models for VLE calculation of systems containing Polyol Ester oil (POE). However, the best model for representing such systems is an equation of state (EOS). An EOS suitable to this purpose should be able to: - describe both volumetric and equilibrium properties of pure components and mixtures; - take into account the effect of long-chain molecules and; - represent simultaneously VLE and liquid-liquid equilibria (LLE). The poor volumetric behavior of cubic equations of state and their inherent difficulties for describing both long-chain molecules and LLE is well known as discussed in a previous paper [3] where models based on perturbation theories were shown to be more reliable due to their theoretical basis. In this work the Modified Perturbed-Hard-Sphere-Chain equation of state (MPHSC EOS) proposed by Song et al. [4] is used to establish oil-refrigerant equilibria. This equation has been tested by Fermeglia et al. [5] on a large database of hydro-chloro-fluorocarbons, hydrocarbons and their mixtures, with reference to both volumetric and equilibrium properties. 2 To apply the MPHSC EOS to mixtures containing lubricant oils, a method for the calculation of pure oil parameters is required. For refrigerants, parameter values are obtained from experimental data. For oils, however, PVT data are available only at atmospheric pressure. Extension to mixtures are discussed here; binary interaction parameters (kij) are introduced to describe VLE and LLE of mixtures containing new-generation refrigerants and a lubricant oil. The correlation presented in this work may be useful for improved design of new refrigeration systems. Model According to the MPHSC EOS, the Chiew [6] expression for hard-sphere chains is taken as the reference term, while the perturbation is described by the van der Waals attractive form: (1) where P is the pressme, T the absolute temperature, p= NIV the number density, N the ( number of molecules, V the volume of the system, k the Boltzmann's constant, d the hard-sphere diameter and g(d+) the pair radial distribution function of hard spheres at contact. Three segment-based parameters appear in Eq. (1): r is the number of segments per molecule, a reflects attractive forces between two non-bonded segments and b is the segment Van der Waals co-volume. Eq. 1 shows that the repulsive term accounts for chain connectivity. Expressions for a and b are obtained by applying the method of Song and Mason [7]: 3 2tr 3 a(T) = -u &Fa(kTl e) 3 (2) 2tr 3 b(T) = -u Fb(kT I&) 3 (3) where & is the depth of the minimwn in the pair potential and u j!) the separation distance between segment centers at this minimwn. Fa and Fb are universal function of the reduced temperature kTI &; they are determined from thermodynamic properties of-argon and methane over large ranges of temperature and density and are expressed by empirical equations, given by Song et al. [4]. For Argon and methane, r=l. The MPHSC EOS for simple fluids contains two parameters: CY and &!k. For molecular fluids and chainlike molecules, a third parameter (r) is needed. It is convenient to redefine these parameters through a characteristic volwne, V*, a characteristic surface area, A* and a characteristic «cohesive» energy, E* per mole of molecules: V* = (n I 6)rcr 3 N A (4) A*= nrcr 2 N A (5) (6) where NA and Rg are Avogadro's and the universal gas constants. -Pure component parameters are molecular quantities that reflect the size, shape and interaction energy dfthe molecule. For refrigerants, expressions for V* and A* are given as a function of the Bondi volwne .and surface area based on thermodynamic data as given in [5], while E* is specific to reproduce the vapor pressure at the temperature of interest. 4 Since experimental data are insufficient for determining the EOS parameters for the oil~ a group-contribution method was developed based on vapor-pressure and liquid-density data for a large number of ordinary molecular-weight compounds containing the functional groups needed to represent the oil [8]. This method is used to establish lubricant-oil parameters. Extension of the MPHSC EOS to mixtures is obtained by applying mixing rules to the EOS parameters, leading to the following equation [9]: where xi = Ni / N is the number fraction of molecules of species i, ri the number of segments for the i-th component and giJ ( d;) the ij pair radial distribution function of hard-sphere mixtures at contact. The exact statistical mechanic expression for g11 ( d;) is given by Boublik [10] and Mansoori et al. [11]. The molecular-weight range of typical lubricant oils 1s not so high to allow the assumption of an infinite number of segments, as it 1s for high-molecular weight polymers [4]. For each pair of components, two parameters aiJ and biJ are needed: they are obtained by extensions of equations (2) and (3): a!f = (2tr/3 )ate!JFa (kT/ & !f) bu =(2tr/3)atFb(kT/e!f) where Fa and Fh are the same universal function as those in Eqs. (2) and (3). The combining rule for a is defined without any interaction parameter: 5 (8) (9) cru+crii () .. =----=--1) 2 (10) A binary interaction parameter, ky·, is introduced in the combining rule for the energetic parameter s: (11) Values for kif's are regressed from experimental binary vapor-liquid equilibrium data. Calculation methods Equations (1) through (11) utilize a pressure-explicit EOS. For phase equilibrium calculations, we want the Helmholtz energy because we can then obtain all relevant thermodynamic properties by simple partial differentiation Equations for the chemical potential and thermodynamic subroutine details are reported elsewhere [5]. Table 1 Pure component parameters. 1POE of reference [14], 2POE of references [15-17]. Substance Molecular A* V* E* weight (10"9 cm2/mol) (cm3/mol) (bar cm3/mol) R134a 102.031 6.781 41.40 45085 R125 120.022 7.936 39.99 51191 R32 52.054 4.787 24.69 41816 696 73.80 458.95 483920 612 64.77 398.83 425258 For LLE, a Gibbs tangent plane stability test has been implemented, according to the method proposed by Michelsen [ 12,13]. This test distinguishes between stable and 6 1.10 ,...----------------------~--------, .J)' E (J 1:: 1.05 ~ ~ 1.00 1/) 1: Q) c 0.95 f f f f t t 0.90 +-------,-------.-----r-----.----.---y------,-----,----,-----1 250 260 270 280 290 300 310 320 330 340 350 T [K] Figure 1 Density of POE: experimental (14] and calculated results. The bar corresponds to 0. 75% experimental error. 14.0 12.0 10.0 ~ 8.0 T=303 K cu ..c ....... fl. 6.0 4.0 2.0 -T=323 K 0.0 0 0.2 0.4 0.6 0.8 1 X Figure 2 VLE calculation for the system R134a-POE. Data from (16]. x =molar fraction of refrigerant 7 14 12 10 'i:" 8 cu .c ...... a.. 6 4 2 0 0 0.2 0.4 0.6 0.8 1 X Figure 3 VLE calculation for the system R125-POE. Data from [15]. x =molar fraction of refrigerant. 21 18 15 'i:' 12 cu ..c ...... 0... 9 6 3 0 0 0.2 0.4 0.6 0.8 1 . X Figure 4 VLE calculation for the system R32-POE. Data from [17]. x =molar fraction of refrigerant. 8 350 330 ~ 310 ..... 1-290 270 250 0,2 0,3 0,4 0,5 0,6 w kij =0.07 0,7 0,8 0,9 1 Figure 5 Parametric LLE curves for the system R32-POE. Continuous line P=20 bar and dashed line P=5 bar. w =weight fraction of refrigerant. 320 .---------------------------------------------~ 310 • 300 • ~' 290 ..... • ..... 280 • 270 260 I 250+----,-,--~----~----~--------~----.---~ 0.2 0.3 0.4 0.5 0.6 w 0.7 0.8 0.9 1 Figure 6 LLE calculation for the system R32-POE. Data from [17]. w =weight fraction of refrigerant 9 unstable regions of the liquid phase and provides an initial estimate for the LLE flash calculation robust enough to avoid undesirable trivial solutions. Results Table 1 shows pure-component parameters for refrigerants and lubricant oils as needed for VLE and LLE calculations. Table 2 Summary ofVLE calculation results. *denotes temperature where k!i was filled. System T(K) kij LJ.P/P% * 0.0391 . 0.83 323.15 R134a-POE 303.15 0.0391 0.95 283.15 0.0391 0.49 263.15 0.0391 3.76 * 0.0202 1.41 293.15 R125-POE 283.15 0.0202 1.62 273.15 0.0202 2.85 263.15 ·0.0202 4.07 R32-POE 303.15 0.0695 3.00 * 0.0695 1.61 293.15 273.15 0.0695 1.48 243.15 0.0695 12.40 For refrigerants, Fermeglia et al. [5] have shown that these parameters provide equilibrium and volumetric properties with a precision comparable to the experimental error. The parameter values presented in Table 1 are updated by fitting to new experimental data [18, 19]. To check the reliability of the group-contribution approach 10 developed by Elvassore et al. [8] for lubricant oils, Figure 1 shows the liquid density of a POE as a function of temperature. The prediction is satisfactory. The error is larger at .lower temperature; probably because the energetic parameter is taken to be independent -of temperature. In Table 2 and Figures 2, 3 and 4, VLE calculations are reported for mixtures containing a refrigerant and a POE lubricant over wide temperature and concentration ranges. A single interaction parameter ky is able to reproduce very well all data for a single system. For the system R32-POE, the thermodynamic condition for LLE is checked. First, the occurrence of two liquid phases is detected as a function of temperature, pressure and ky value, as shown in Figure 5. Then, the LLE curve is compared to experimental measurements in Figure 6. It is remarkable that, by using the value of ky regressed in VLE calculations, satisfactory agreement is obtained. The good results obtained suggest that the physical significance of the EOS and of the parameters give a good phenomenological representation of phase behavior for the systems of interest here. Conclusions Calculations for prediction of phase equilibria are presented for mixtures containing hydro-fluoro-carbons and lubricant oils. Calculations are based on a modified Perturbed-Hard-Sphere-Chain equation of state. Calculation of pure-oil parameters was performed by a predictive group-contribution method. With these values, the oil density could be predicted satisfactorily. The ability of the proposed equation of state for calculating VLE and LLE of binary systems was shown; for all cases considered, a single value of the only binary 11 interaction parameter was able to reproduce with good accuracy the experimental data in a relatively wide temperature range. To confirm these promising results, the model needs to be checked with a larger data base of phase-equilibrium data for the mixtures of interest. Acknowledgement A. Bertucco. N. Elvassorc and M. Fcnncglia gratefully acknowledge the partial financial support of the Italian MURST (ex-40% and ex-60%). J.M. Prausnitz acknowledges the support of the Office of Energy Research, Office of Basic Energy Sciences, Chemical Science Division of the U.S. Department of Energy. References [I] R.H.P Thomas and H.T. Pham, ASHRAE Trans., 98 (1992) 783 [2] W. L. Martz, C. M. Buron and A. J. Jacobi, Int. Jl. Refrig., 19 (1996) 25 [3] M. Fermeglia, A. Bertucco, A. and D. Patrizio, Chern. Engng. Sci., 52 (1997) 1517 [4] Y. Song, T. Hino, S.M. Lambert and J.M. Prausnitz, Fluid Phase Equilibria, 117 (1996) 69 [5] M. Fermeglia, A. Bertucco and S. Bruni, submitted for publication in Chern. Engng. Sci. (1997) [6] Y.C. Chiew, Mol. Phys., 70 (1990) 129 [7] Y. Song and E.A. Mason, J. Chern. Phys., 12 (1991) 7840 [8] N. Elvassore, A. Bertucco, M. Fermeglia, in preparation (1998) [9] Y. Song, S.M. Lambert and J.M. Prausnitz, Chern. Engng. Sci., 47 (1994) 2765 [10]T.J. Boublik, Chern. Phys., 53 (1970) 471 [11]G.A. Mansoori, N.F. Carnahan, K.E. Starling and T.W. Leland, J. Chern. Phys., 54 (1971) 1523 12 [12]M.L. Michelsen, Fluid Phase Equilibria, 9 (1982) 1 [13]M.L. Michelsen, Fluid Phase Equilibria, 9 (1982) 21 [14]W. Martz, C. M. Burton and A.M. Jacobi, ASRHAE Trans. Res., 102 (1996) 367 and private communication [15] Y. Takaishi, M. Izumi and K. Oguchi, Proc. Int. Conference "CFCs, The day After", Padova, Italy, 3 (1994) 99 [16]Y. Takaishi and K. Oguchi, Proc. IIR Conference, Gent, Belgium, Comm Bl/2, (1993) 141 [17] Y. Takaishi and K. Oguchi, Proc. 19th Int. Congress of Refrigeration, The Hague, The Netherlands, Comm. B I (1995) 568c [18]D. R. Defibauugh, G. Morrison and L. A. Weber, J. Chern. Eng. Data, 39 (1994) 333 [19]H. A. Duarte-Garza, C. E. Stouffer, K. R. Hall, J. C. Hostle, K. N. Marsh and B. E. Gammon, J. Chern. Eng. Data, 42 (1997) 745 13 @J£1~1¥-:nt ~ [hl.i.b!A;J#III~iliJ#IC @Jj;J:fii#IY%? ~ ~ ®D3 ~ 0 l?\,.;;t3,.Y3\'?o ~~ 

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A Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria of Mixtures Containing a Refrigerant and a Lubricant Oil

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A Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria of Mixtures Containing a Refrigerant and a Lubricant Oil

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