Ind. Eng. Chem. Res. 1998, 37, 3105-3111
3105
Group-Contribution Equation of State for the Prediction of Vapor-Liquid Equilibria of Mixtures Containing Hydrofluorocarbons and Alkanes Nicola Elvassore,* Massimiliano Barolo, and Alberto Bertucco Istituto di Impianti Chimici, Universita` di Padova, via Marzolo 9, I-35131 Padova PD, Italy
This work is aimed to present and validate a thermodynamic model that enables the prediction of vapor-liquid equilibria of refrigerant mixtures of alkanes and hydrofluorocarbons, in the temperature and pressure ranges of interest for refrigeration cycles and heat pump applications. A modified Redlich-Kwong-Soave equation of state is used with Huron-Vidal mixing rules and a modified UNIFAC group-contribution approach for calculating the component infinitepressure activity coefficients. A new classification of functional groups is suggested, and the values of interaction parameters between groups are provided. These parameters are regressed from selected binary vapor-liquid equilibrium data. A good regression is obtained for all group pairs, with a maximum root-mean-square deviation on relative pressure residuals of 1.86%. The proposed method is totally predictive since only the structure, critical constants, and vapor pressure of pure components are needed in order to calculate thermodynamic properties of refrigerant mixtures. Results for a number of binary and ternary mixtures are reported and compared to available experimental data. Introduction As a consequence of the regulations of the Montreal Protocol in 1986, currently there is a need to replace phased out chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) with compounds having no effects on the depletion of the ozone layer, but exhibiting also a minimum global-warming potential. Pure hydrofluorocarbons (HFCs) and their mixtures seem to be the best alternatives, since they are nonflammable and nontoxic. Also, mixtures between alkanes (HCs) and HFCs are an interesting possibility to study. Technical reasons play in favor of using mixtures rather than pure fluids, since only in a few cases pure HFCs can ensure as high performances as those provided by chlorinated and chlorofluorinated compounds. The selection among different potential alternatives is a task that calls for high investment costs. In particular, it is too expensive to measure directly the thermodynamic properties of all possible mixtures. Therefore, it would be desirable to make a first screening by means of a tool able to predict the mixture behavior with reasonable accuracy. The aim of this work is to develop a predictive method for the calculation of vapor-liquid equilibria (VLE) of refrigerant mixtures containing HFCs and HCs. It is known that classical group-contributions GE-based models are not suitable to this purpose, as they can be applied successfully at low-pressure only, while pressures in refrigerant cycles may be as high as 40 bar. Moreover, the group divisions available even in their most recent versions (for instance, UNIFAC, according to Hansen et al., 1991 or to Gmehling et al., 1993) are not sufficient to represent all the compounds of interest for refrigeration applications (Kleiber, 1995). On the * To whom correspondence should be addressed. Phone: +390 49 8275473. Fax: +390 49 8275461. E-mail: nelvas@ polochi.cheg.unipd.it.
other hand, cubic equations of state (EOSs) with classical mixing rules show limited predictivity; at best, they can be used for correlation of experimental data (Gow, 1993), but they are not flexible enough to represent polar systems. In this respect, Morrison and McLinden (1993) suggested that binary interaction parameters should depend on composition to represent VLE binary data accurately. A first predictive method based on an EOS was proposed by Fransson et al. (1993), according to the group-contribution approach previously developed by Abdoul et al. (1991). Kleiber (1995), on the basis of a γ-φ approach, and following the suggestion of Wu and Sandler (1991), presented some simple rules that can be used to build up an optimized UNIFAC group assignment, but it is not clear how these rules can be extended to new refrigerants, such as propane derivatives. A predictive GE-EOS model was proposed by Barolo et al. (1995), who applied a Redlich-KwongSoave (RKS) EOS with Huron-Vidal mixing rules, and derived the interaction parameters from infinite-dilution activity coefficients data. However, only a preliminary group table was supplied in that paper, mostly related to CFC and HCFC systems. In the last two years, more VLE data involving HFCs have been made available in the open literature, so that it is now possible to extend, reliably modify, and thoroughly validate our previous approach. Thus, the presently proposed method is intended as an ad hoc model for refrigerant mixtures; it has been developed with the aim of being as accurate as possible to reproduce the data available so far. The Model Equation of State. The method is based on a RKS EOS (Soave, 1972) including a volume-shift (Peneloux et al., 1982):
S0888-5885(97)00867-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/28/1998
3106 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
P)
a RT v + c - b (v + c)(v + c + b)
(1)
where P, T, and v are the pressure, temperature, and molar volume and R is the universal gas constant. With symbols a, b, and c, the attractive, repulsive, and volume-shift parameters are indicated, respectively. It is useful to rewrite eq 1 in terms of the compressibility factor Z ) Pv/RT and in dimensionless parameters:
When dealing with mixtures, eq 2 still holds, but mixing rules must be set to evaluate mixture parameters. In our case, the Huron-Vidal mixing rules at infinite pressure were selected (Huron and Vidal, 1979). Accordingly, we have
A
)
B
(BA - 1 - B) -
(Z + C)3 - (Z + C)2 + B(Z + C)
A 2 B ) 0 (2) B
(
∑i zi B
aP R2T2
(3)
B)
bP RT
(4)
C)
cP RT
(5)
We note that parameter A in eq 2 appears only as the ratio A/B, which is independent of pressure; in the following we will refer to this ratio, rather than to A. Moreover, even though parameter C does not affect VLE calculations (Peneloux et al., 1982), it has been included in the model in order to better calculate the system volumetric properties, thus improving the estimation of the excess-free energy at infinite pressure (see next section). For pure components, parameters A/B, B, and C can be evaluated by
A Ωa R(T) ) B Ωb TR
PR C ) Ωc TR
(8)
where TR and PR are the reduced temperature and pressure, respectively. The constants Ωa and Ωb are only related to the cubic EOS (Ωa ) 0.427 48 and Ωb ) 0.086 640 for the RKS EOS), while Ωc is also a function of the component. In summary, to apply the proposed RKS EOS, the following pure component data are needed: 1. The ratio TC/PC. If unknown, it can be estimated by a group-contribution method, such as the one proposed by Soave et al. (1995). 2. The vapor pressure at the temperature of interest, from which the value of R(T)/TR can be biunivocally determined (Soave, 1986). For components above their critical temperature, an extrapolation of the function R(T) has to be done (Soave et al., 1993). 3. One liquid density at some T and P and the vapor pressure at the same temperature, to estimate the Ωc value; usual conditions are T ) 20 °C and P ) 1 atm, except for light components, for which the boiling temperature at P ) 1 atm is taken as the reference state.
)
(9)
∑i ziBi
(10)
C)
∑i ziCi
(11)
) ln γ∞i ) ln γ∞,R i
∑k vk,i(ln Γk - ln Γk,i)
(12)
where Γk and Γk,i are the activity coefficients of group k in the mixture of all components and in a mixture containing groups belonging to component i only, respectively; vk,i is the number of groups k in molecule i. They have been calculated by the following expression:
[
∑ m
ln Γk ) Rk 1 - ln( (7)
ln(2)
i
where i is the component index, γ∞ is the activity coefficient at the infinite pressure reference state, and z is the mole fraction in the phase considered. Finally, to render the model predictive, a functionalgroup approach must be used, such as UNIFAC. Modified UNIFAC. With respect to a previous version of this group-contribution RKS EOS, developed by Soave et al. (1994) and applied to refrigerants in a previous work (Barolo et al., 1995), the excess Gibbs energy expression has been slightly modified, so as to improve the model performances. According to this revised version of UNIFAC, we have
(6)
PR B ) Ωb TR
-
ln γ∞i
B)
where
A)
Ai
ΘmΨm,k) -
ΘmΨk,m
]
∑ m ∑n ΘnΨn,m
(13)
where group parameters Θm and Rk are given by
Θm )
R hm NF
(14)
∑ Rh n
n)1
with NC
R hn )
ziR h n,i ∑ i)1
(15)
NG(n)
∑ vk,iRk
(16)
Rk ) CF(b - c)k
(17)
R h n,i )
k)1
In eqs 14-17 NF, NC, and NG(n) are the numbers of main groups, components, and groups within main group n, respectively; (b - c)k is the group “true co-volume”, either calculated from critical parameters
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3107 Table 1. Pure Component Database for Regression; References Are Referring to Critical Constants and to the Vapor Pressure Equations and Parameters
a
component
chemical formula
Tc [K]
Pc [bar]
reference
R13 R22 R134a R290 R600a R600 R236fa R143a R152a R32 R218 R125 R116 nC5 nC6
CClF3 CHClF2 CF3CH2F CH3CH2CH3 CH3CH(CH3)2 CH3(CH2)2CH3 CF3CH2CF3 CH3CF3 CHF2CH3 CH2F2 CF3CF2CF3 CF3CHF2 CF3CF3 CH3(CH2)3CH3 CH3(CH2)4CH3
301.88 369.33 374.21 369.82 408.13 425.16 398.07 345.88 386.44 351.36 345.03 339.165 293.0 469.7 507.3
38.77 49.9 40.56 42.50 36.48 37.97 32.0 37.697 45.2 57.931 26.75 36.199 30.6 33.69 30.12
Reid et al. (1988) Reid et al. (1988) McLinden (1990) Reid et al. (1988) Reid et al. (1988) Reid et al. (1988) Reid et al. (1988)a Giuliani et al. (1995) McLinden (1990) Weber and Silva (1994) Leu and Robinson (1992) Ye et al. (1995) Reid et al. (1988) TRC tables (1980) TRC tables (1980)
For R236fa the vapor pressure equation and parameters were taken from Bobbo et al. (1997).
Table 2. Binary VLE Database and Regression Results for the Systems Considered ∆y
(∆P/P)% system
reference
Np
T [K]
P [bar]
rmsa
biasa
rmsa
biasa
R13-R600a R13-R600 R22-nC6 R134a-R290 R134a-R600a R152a-nC5 R32-R134a R134a-R236fa R134a-R125 R32-R125 R143a-R134a R22-R152a R218-R22 R143a-R125
Weber (1989) Weber (1989) Xu et al. (1991) Kleiber (1994) Bobbo et al. (1997) Fransson et al. (1992) Higashi (1995a) Bobbo et al. (1997) Nagel and Bier (1995) Higashi (1995b) Kubota and Matsumoto (1993) Stro¨m and Gre´n (1993) Leu and Robinson (1992) Nagel and Bier (1996)
35 50 28 31 38 39 15 19 20 22 41 46 26 6
310-400 310-400 363-400 255-298 293-303 303-384 293-313 283-303 206-323 283-313 278-333 301-327 323-338 243-323
5.4-38.3 4.3-45.5 20.1-44.9 2.6-6.6 2.0-7.8 3.0-29.1 5.6-24.7 1.6-7.8 0.1-22.1 9.9-24.7 4.1-28.7 8.71-1.8 16.5-27.1 2.1-23.8
1.332 1.907 1.112 1.308 1.880 2.228 1.003 1.262 1.693 1.013 0.797 0.968 1.863 0.025
0.831 0.842 -0.227 -0.725 -1.524 0.384 -0.020 -0.011 -0.766 0.626 0.007 0.030 -0.288 0.000
0.008 0.010 0.005 0.007 0.010 0.012 0.010 0.013 0.011 0.006 0.006 0.010 0.023 0.001
0.003 0.006 -0.001 0.002 0.005 -0.010 0.004 0.008 0.004 0.001 -0.002 0.007 -0.003 0.000
a
The rms is defined by eq 19; the bias is the arithmetic mean of residuals.
and density data or predicted by a group-contribution method (Soave et al., 1995), and CF a suitable damping factor. Equations 12 and 13 are formally similar to the residual part of original UNIFAC, except that here the volume parameters Rk, calculated as per eq 17, are replacing the surface parameters Qk. Although this is an empirical assumption not justified theoretically, we believe that the rigorousness of the method can be slightly sacrificed in order to achieve a better fit of available data. By introducing CF the model contains one additional parameter. However, we have verified that for all groups the same value of CF can be used, and that CF ) 0.08 mol/cm3 appears to be the best compromise in order to minimize the residuals of VLE calculations involving all group pairs (Benso, 1994; Elvassore, 1995). The temperature dependence of the model is embedded in the factors Ψm,k:
Ψm,k ) exp(τm,k) τm,k ) -
am,k bm,k - 2 T T
(18a) (18b)
where am,k and bm,k are the group interaction parameters. They can be either symmetrical or asymmetrical. We will show that for the systems under investigation a temperature function like eq 18b can be used to correlate temperature effects over wide temperature ranges.
Parameter Determination Regression Database. To be able to evaluate the interaction parameters, a database of both pure components and mixtures was first built. As for the purecomponent parameters, critical temperatures, critical pressures, and the vapor pressure equations were collected for each component. These data are summarized in Table 1 along with the relevant references. We have noticed that the goodness of regression results depends quite markedly on the calculated component vapor pressure Pvap. Therefore, care was taken in order to collect reliable expressions and parameters for the evaluation of Pvap. As for mixtures, only binary VLE data were included in the regression database, which is updated to mid1997. A total amount of 65 systems (more than 1000 binary data points) were screened for thermodynamic consistency with the method proposed by Bertucco et al. (1997). Data sets were discarded if they either were CFC-containing, or lacked vapor-phase compositions, or thermodynamically inconsistent. Eventually, the data sets belonging to the 14 binaries reported in Table 2 were considered for regression. The pressure range of the experimental data points was 0.1-45 bar, the temperature range was 205-400 K. Particular attention was drawn in order to include only HFC-containing systems, as they are interesting candidates for substitution of banned and almost-banned refrigerants. In this respect, we have discarded as many banned refrigerants as possible from data reduction. However, since experimental data on new refrigerants are not abounding at
3108 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Table 3. Assignment of Main Groups and Groupsa main groups alkane
CH3Fa CH2Fa
CHFaClb
CFaClb
groups
(b - c) [cm3/mol]
-CH3 -CH2 -CH -C CH3F -CH3 CH2F2 -CH2F -CH2-CH2-CF3 CHF3 -CHF2 -CHF>CHCHClF2* CF4 -CF3 -CF2>CF>C< CClF3*
20.88 15.93 10.25 5.12 27.21 5.12 32.10 29.08 15.93 47.21 36.43 30.01 23.40 10.25 47.03 37.59 31.28 24.88 18.27 5.12 52.88
a Groups labeled with (*) were included for regression purposes only.
the moment, it was necessary to include also some banned systems in the regression database. Group Assignment. Group assignment is a crucial point for a correct development of the proposed method. It was already shown (see, for example, Barolo et al., 1995) that the current versions of UNIFAC (Hansen et al., 1991; Gmehling et al., 1993) are not suitable for calculating VLE of refrigerant mixtures. Therefore, ad hoc group divisions are usually proposed for the treatment of these systems. Two opposite requirements need to be fulfilled in this case. From one hand, the number of groups should be large enough to allow a comprehensive and precise representation of all possible group interactions. On the other hand, the number of groups should be small for reducing both the number of interaction parameters that needs to be regressed and the number of systems that must be included in the regression database. Barolo et al. (1995) noted that groups containing chlorine and fluorine atoms behave similarly as far as VLE calculations are concerned. Therefore, they proposed to categorize the refrigerant compounds into two main groups, each of them including molecular segments with a different number of hydrogen atoms. However, only a limited number of components were considered there. A different group division was presented by Kleiber (1995), who provided a thorough analysis of previously proposed group assignments. Following Wu and Sandler (1991), Kleiber improved these assignments by taking the molecular segments proximity effects into account. As a result, he proposed an 11-main-group table. Since the available experimental VLE data on alternative refrigerants are not so abundant in the literature as to justify the creation of a relatively large number of groups, an improvement of Barolo et al. (1995) group division has been considered in this work. The group assignment proposed here is illustrated in Table 3, together with segment true co-volume values, which were calculated by Elvassore (1995). Actually, this table borrows results from both Barolo et al. (1995) and Kleiber (1995). Fluorine- and chlorine-containing segments are again categorized according to the number
Table 4. Summary of Data Reduction Results: the Value of Objective Function ×102, eq 19, Is Reported for Each Main Group Pair alkane CH3Fa CH2Fa CHFaClb CFaClb
alkane
CH3Fa
CH2Fa
CHFaClb
CFaClb
x 1.80 1.25 1.11 1.32
x 1.25 0.96 0.24
x 0.85 0.20
x 1.86
x
of hydrogen atoms of the segment, but proximity effects on alkane groups are taken into account. Namely, an alkane group bound to a fluorinated carbon is affected by fluorine electronegativity, as pointed out by Wu and Sandler (1991); therefore, CH3, CH2, and CH may belong to two different main groups. In summary, the number of groups is maintained low in order to provide reliable group contributions on the basis of the selection of experimental data presently available. However, the overall accuracy of the method is improved due to a better understanding of the molecular structure. As previously indicated, due to the lack of experimental data concerning alternative refrigerants, subgroups CHClF2 (R22) and CClF3 (R13) had to be included in the database for regression purposes. Regression Procedure. A nonlinear fit of the experimental data was performed by adjusting the interaction parameters am,k and bm,k so as to minimize the following objective function:
obf ) where
i )
x
(
Np
(i)2 ∑ i)1 Np
)
Pcalc - Pexp Pexp
(19)
(20)
and Np is the number of experimental data points. Symmetrical parameters (am,k ) ak,m and bm,k ) bk,m) were used unless a significant improvement in the minimization was obtained by considering asymmetrical ones. Results and Discussion In Table 2, columns 6-9, the regression results for each system are shown; in general, a good correlation was obtained in all cases. The minimization results are summarized in Table 4, while the regressed values of interaction parameters are given in Table 5. It is remarkable that the worst fitting result is as low as 1.86% (relative percent deviation on pressure). Some examples are presented in the following figures, and a few predictive calculations are also considered. The first system examined is an azeotropic, binary one (R134a/R600a). In Figure 1, the VLE calculated by our model is compared to available experimental data at two different temperatures. The proposed approach yields a good reproduction of the data; in particular, the azeotropic points are reproduced satisfactorily. It can also be noted that the VLEs of the system are captured well at both temperatures, thus suggesting that the
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3109 Table 5. Values of Interaction Parameters: am,k [K] (Upper Values) and bm,k [K2] (Lower Values) alkane alkane CH3Fa CH2Fa CHFaClb CFaClb a
-41.25 35 085.2 -460.52 152 607.4 49.25 -10 548.9 -25.02 13 607.2
CH3Fa -41.25 35 085.2 -201.10 57 769.4 -51.10 -1344.6 -205.70 -190 224.7
CH2Fa
CHFaClb
CFaClb
271.43 -30 773.4 -201.10 57 769.4
49.25 -10 548.9 -51.10 -1344.6 -225.02 13 068.1
-25.02 13 607.2 -453.49 51 296.4 -248.21 81 540.0 46.78 -587.9
815.58 -104 282.5 -248.21 81 540.0
46.78 -587.9
With m, k the row and column are indicated, respectively.
Figure 1. System R134a/R600a. Comparison between calculated bubble (s) and dew (- - -) lines and experimental data (symbols) at two temperatures. Experimental data from Bobbo et al. (1997).
Figure 2. System R134a/R236fa. Comparison between calculated bubble (s) and dew (- - -) lines and experimental data (symbols) at two temperatures. Experimental data from Bobbo et al. (1997).
temperature dependence of model parameters is described correctly by eq 18b. The system R134a/R236fa is considered in Figure 2. Again, the proposed model allows a good reproduction of the available experimental data. A full VLE prediction is reported in Figure 3. In this case, none of the groups used for the definition of R12 and R23 were included in the regression database. Pure-component properties are summarized in Table 6. From Figure 3 it can be seen that model predictions are satisfactory up the maximum system pressure (i.e., 19 bar). It is confirmed that Cl and F atoms can be treated in the same way, as long as group interactions are concerned. For the system R236fa/R600a the model predictions are worse, as can be seen from Figure 4. Actually, the calculation of the azeotropic point composition is satisfactory, but the model fails in providing an accurate prediction of the system bubble pressures.
Figure 3. System R12/R23. Comparison between calculated bubble (s) and dew (- - -) lines and experimental data (symbols) at two temperatures. Experimental data from the databank of Maczynsky and Niedziela (1990).
VLE calculations of ternary systems are a further test on the predictivity of the model, since no ternary data were used for parameter evaluation. We present here results for three systems. The first one (Figure 5) is R143a/R125/R134a in a quite wide range of temperatures and pressures. This system was chosen in order to check the temperature dependence of the model parameters. The symbols represent the experimental compositions of vapor and liquid at equilibrium for different pressure-temperature pairs. A flash calculation was performed at the equilibrium pressure and temperature of each data set; the corresponding bubble curves and dew curves have been reported in Figure 5. It can be noted that the model calculations match the experimental points satisfactorily. A similar approach was used for the representation of system R134a/R125/R32 (Figure 6). In this case, only one equilibrium temperature is considered (T ) 303.3 K), and the pressure range is narrower. The points indicated by arrows represent the composition of two commercial refrigerant mixtures (namely, R407b and R407a). Again, the model does a good job in reproducing the experimental data. Note that some calculated tie lines have been drawn at two pressures in order to be able to judge the estimated values of the equilibrium ratios. The estimations are good. Finally, a fully predictive ternary calculation is presented in Figure 7. None of the binaries involved were included in the regression database; pure-component properties are summarized in Table 6. In this case, three bubble point compositions of R113/R114/propane solutions at different equilibrium pressures and temperatures were taken from the literature. Flash calculations were performed at experimental T and P val-
3110 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Table 6. Database of Pure Components Not Included in the Regression: References Are Referring to Critical Constants and to Vapor Pressure Equations and Parameters component
chemical formula
Tc [K]
Pc [bar]
reference
(b - c) [cm3/mol]
R113 R114 R12 R23
CCl2FCClF2 CClF2CClF2 CCl2F2 CHF3
487.3 418.6 384.95 299.3
34.1 33.0 41.29 48.6
Reid et al. (1988) Reid et al. (1988) Reid et al. (1988) Reid et al. (1988)
93.16 83.78 62.55 36.43
Figure 4. System R236fa/R600a. Comparison between calculated bubble (s) and dew (- - -) lines and experimental data (symbols). Experimental data from Bobbo et al. (1997).
Figure 5. System R143a/R125/R134a. Comparison between calculated bubble and dew lines and experimental data: (a) dew point (O) and bubble point (b) at T ) 343.29 K and P ) 26.11 bar; (b) dew point (0) and bubble point (9) at T ) 303.16 K and P ) 10.04 bar; (c) dew point (]) and bubble point ([) at T ) 263.99 K and P ) 2.97 bar; (d) dew point (4) and bubble point (2) at T ) 223.33 K and P ) 0.50 bar. The bubble and dew lines have been calculated at each (P, T) pair. Experimental data from Nagel and Bier (1996).
ues: even though a lack of data precludes a thorough analysis, it can be noted that the model predictions are indeed satisfactory. Conclusions A thermodynamic model enabling the prediction of vapor-liquid equilibria of refrigerant mixtures of alkanes and hydrofluorocarbons was developed. A group-contribution cubic equation of state was devised, with a modified UNIFAC model and a new classification of groups, that is a compromise between the number of functional groups and the amount of experimental data presently available. The values of interaction parameters between four main group pairs were regressed from selected binary vapor-liquid equilibrium data. The worst fitting result was as low as 1.86% (relative percent deviation on pressure). The predictivity of the proposed method was satisfactory for most binary systems, and it was confirmed by
Figure 6. System R134a/R125/R32. Comparison between calculated bubble and dew lines and experimental data at T ) 303.3 K: (a) dew point (4) and bubble point (2) at P ) 15.07 bar; (b) dew point (O) and bubble point (b) at P ) 14.42 bar; (c) dew point (0) bubble point (9) at P ) 13.26 bar. The bubble and dew lines have been calculated at each (P, T) pair. Experimental data from Nagel and Bier (1995).
Figure 7. System R113/R114/propane. Comparison between calculated bubble and dew lines and experimental data: (a) bubble point (2) at P ) 21.23 bar, T ) 403.1 K; (b) bubble point (b) at P ) 20.24 bar, T ) 383.2 K; (c) bubble point (9) at P ) 18.31 bar, T ) 363.2 K. The bubble and dew lines have been calculated at each (P, T) pair. Experimental data from Chareton et al. (1992).
the calculation of VLE of several ternary systems. It appears that the model is suitable for predicting the vapor-liquid equilibria of HFCs and HCs mixtures, and it can be applied as a tool for preliminary screening of alternative refrigerant mixtures. Acknowledgment We are grateful to Dr. Ing. Giorgio Soave for helpful discussions. This work was partially supported by the Italian Ministero dell’Universita` e della Ricerca Scientifica e Tecnologica (ex-40%). Literature Cited Abdoul, W.; Rauzy, E.; Pe´neloux, A. Group-Contribution Equation of State for Correlating and Predicting Thermodynamic Properties of Weakly Polar and Non-Associating Mixtures. Binary and Multicomponent Systems. Fluid Phase Equilib. 1991, 68, 47.
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3111 Barolo, M.; Bertucco, A.; Scalabrin, G. A Method for the Prediction of Vapor-Liquid Equilibria of Refrigerant Mixtures at Low and Moderate Pressure Int. J. Refrig. 1995, 18, 550. Benso, V. Prediction of VLE of Gaseous Mixtures and of Polar Compounds by a Cubic EOS (in Italian). M.S. Thesis in Chemical Engineering, Istituto di Impianti Chimici, Universita` di Padova, Italy, 1994. Bertucco, A.; Barolo, M.; Elvassore, N. Thermodynamic Consistency of Vapor-Liquid Equilibrium Data at High Pressure. AIChE J. 1997, 43, 547. Bobbo, S.; Strijek R.; Elvassore, N.; Bertucco, A. A Ricirculation Apparatus for Vapor-Liquid Equilibrium Measurements on Multicomponent Mixtures of Alternative Refrigerants. Presented at the 13th Symposium of Thermophysical Properties, Boulder, CO, June 22-27, 1997. Chareton, A.; Valtz, S.; Rinchon, D.; Renon, H. Bubble Pressure and Saturated Liquid Molar Volumes of the Propane R113 R114 Ternary System and of the Three Corresponding Binaries. Int. J. Refrig. 1992, 15, 186. Elvassore, N. A Cubic EOS for the Prediction of VLE of Refrigerant Mixtures (in Italian). M.S. Thesis in Chemical Engineering, Istituto di Impianti Chimici, Universita` di Padova, Italy, 1995. Fransson, E.; Barreau, A.; Vidal, J. Vapor-Liquid Equilibrium in Binary Systems of n-Pentane + Chlorodifluoromethane or + 1, 1,-Difluoroethane. J. Chem. Eng. Data 1992, 37, 521. Fransson, E.; Vamling, L.; Vidal, J. The Abdoul-Rauzy-Peneloux Group Contribution Equation of State Extended to CFCcontaining Mixtures. Chem. Eng. Sci. 1993, 48, 1753. Giuliani, G.; Kumar, S.; Zazzini, P.; Polonara, F. Vapor Pressure and Gas-Phase PVT Datat and Correlation for 1,1,1-Trifluoroethane (R143a). J. Chem. Eng. Data 1995, 40, 903. Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model: 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 179. Gow, A. S. A Modified Clausius Equation of State for Calculation of Multicomponent Refrigerant Vapor-Liquid Equilibria. Fluid Phase Equilib. 1993, 90, 219. Hansen, H.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contributions. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2352. Higashi, Y. Vapor-Liquid Equilibrium, Coexistence Curve, and Critical Locus for Binary HFC-32/HFC-134a Mixture. Int. J. Thermophys. 1995a, 16, 1175. Higashi, Y. Vapor-Liquid Equilibrium, Coexistence Curve and Critical Locus for Binary R32/R125 Mixture. 19th Int. Congress Ref. 1995b, IVa, 297. Huron, M. J.; Vidal J. New Mixing Rules in Simple Equations of State for Representing Vapour-Liquid Equilibria of Strongly Non-Ideal Mixtures. Fluid Phase Equilib. 1979, 3, 255. Kleiber, M. Vapor-Liquid Equilibria of Binary Refrigerant Mixtures Containing Propylene or R134a. Fluid Phase Equilib. 1994, 92, 149. Kleiber, M. An Extension to the UNIFAC Group Assignment for Prediction of Vapor-Liquid Equilibria of Mixtures Containing Refrigerants. Fluid Phase Equilib. 1995, 107, 161. Kubota, H.; Matsumoto, T. High-Pressure Vapor-Liquid Equilibria for the System HFC134a+HFC143a J. Chem. Eng. Jpn. 1993, 26, 320. Leu, A.; Robinson, D. B. High-Pressure Vapor-Liquid Equilibria Phase Properties of the Octafluoropropane (K-218)-Chlorodifluoromethane (Freon-22) Binary System. J. Chem. Eng. Data 1992, 37, 7.
Maczynsky, A.; Niedziela, J. TRC Data Base for Chemistry and Engineering Floppy Book on Vapour-Liquid Equilibrium Data; Polish Academy of Sciences, Poland, 1990. McLinden, M. O. Thermodynamic Properties of CFC Alternatives: A Survey of the Avaiable Data. Int. J. Refrig. 1990, 13, 149. Morrison, G.; McLinden, M. O. Azeotropy in Refrigerant Mixtures. Int. J. Refrig. 1993, 16, 129. Nagel, M.; Bier, K. Vapor-Liquid Equilibrium of Ternary Mixtures of the Refrigerants R32, R125 and R134a. Int. J. Refrig. 1995, 18, 534. Nagel, M.; Bier, K. Vapor-Liquid Equilibrium of Ternary Mixtures of the Refrigerants R125, R143a and R134a. Int. J. Refrig. 1996, 19, 264. Peneloux, A.; Rauzy, E.; Freze, R. A Consistent Correction for Redlich-Kwong-Soave Volumes. Fluid Phase Equilib. 1982, 8, 7. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1988. Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972, 27, 1197. Soave, G. Direct calculation of Pure Compound Vapour Pressures Through Cubic Equations of State. Fluid Phase Equilib. 1986, 31, 203. Soave, G.; Bertucco, A.; Barolo, M. The Estimation of HighPressure Fugacity Coefficient of Pure Gaseous Fluids by a Modified SRK Equation of State. Fluid Phase Equilib. 1993, 91, 87. Soave, G.; Bertucco, A.; Vecchiato, L. Equation of State Group Contributions from Infinite-Dilution Activity Coefficients. Ind. Eng. Chem. Res. 1994, 33, 975. Soave, G.; Bertucco, A.; Sponchiado, M. Avoiding the Use of Critical Constants in Cubic Equations of State. AIChE J. 1995, 41, 1964. Stro¨m, K.; Gre´n, U. B. A Study of Vapor-Liquid Equilibria for the Binary Mixtures HFC22/CFC114, HCFC22/HCFC142b and HFC22/HFC152a. Can. J. Chem. Eng. 1993, 71, 940. TRC Thermodynamic Tables; Thermodynamics Research Center: Texas A&M University, 1980. Weber, L. A. Vapor-Liquid Equilibrium in Binary Systems of Chlorotrifluoromethane with n-Butane and Isobutane. J. Chem. Eng. Data 1989, 34, 452. Weber, L. A.; Silva, A. M. L. Measurements of the Vapor Pressures of Difluoromethane, 1-Chloro-1,2,2,2-Tetrafluoroethane, and Pentafluoroethane. J. Chem. Eng. Data 1994, 39, 808. Wu, H.; Sandler, S., I.. Use of ab Initio Quantum Mechanics Calculations in Group Contribution Methods. 1. Theory and the Basis for Group Identifications. Ind. Eng. Chem. Res. 1991, 30, 881. Xu, N. P.; Yao, J. M.; Wang, Y. R.; Shi, J.; Lu, B. C. Y. VaporLiquid-Equilibria of 5 Binary-Systems Containing R-22. Fluid Phase Equilib. 1991, 69, 261. Ye, F.; Haruki, S.; Watanabe, K. Gas-Phase PVT Properties and Vapor Pressures of Pentafluoroethane (HFC-125) Determined According to the Burnett Methodology. J. Chem. Eng. Data 1995, 40, 148.
Received for review November 13, 1997 Revised manuscript received March 12, 1998 Accepted March 13, 1998 IE970867E
