2620
Ind. Eng. Chem. Res. 1996,34, 2520-2525
Equation of State Modeling of Refrigerant Mixtures Hasan Orbey* and Stanley I. Sander? Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
The vapor-liquid equilibrium behavior of several conventional (hydrofluorocarbon (HFC) and hydrochlorofluorocarbon CHFC)) and proposed (HCFC alcohol or fluorinated alcohol) binary refrigerant mixtures are studied using a cubic equation of state, three recently developed multiparameter mixing and combining rules, and the conventional one-parameter van der Waals mixing rule. Of particular interest was determining how well these mixing models could correlate experimental data at a single temperature, and then how accurately each could predict phase behavior at other temperatures with temperature-independent parameters. The results indicate that for some of the new refrigerant mixtures only the excess free energy-based equation of state mixing rules can provide acceptable correlations, and also reasonable predictions over a range of temperatures. While all the models considered performed well for conventional refrigerant mixtures, only the excess free energy based-models consistently led to accurate predictions over wide ranges of temperature; the other models result in less accurate predictions and, in some cases, false liquid-liquid phase splitting.
+
Introduction The ozone-depletingproperties of chlorofluorocarbons (CFCs) led the international community t o restrict the use of such chemicals, and an international protocol in Montreal in 1989 required ,their phase out by 1995. These fluids were primarily used as refrigerants, but are also important as blowing agents in polymer foam manufacture and cleaning solvents in electronic circuit manufacture. In many cases, such as refrigeration applications (which is the most important area of use of CFCs), it is necessary to develop alternative fluids with thermodynamic properties that are similar to the CFCs they are to replace so that existing equipment can be used with a minimum of modification. For this purpose first hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) and their mixtures were suggested, though now fluorinated alcohols and their mixtures with HFCs and HCFCs and other fluids are also being considered (Sauermann et al., 1993; Laugier et al., 1994; Nowaczyk and Steimle, 1992). Thus the list of possible choices for new refrigerant mixtures to replace the CFCs is very large and growing. To develop an optimum alternative to replace an existing CFC pure fluid or mixture requires accurate thermodynamic information (especially vapor-liquid equilibrium behavior) of not only the old refrigerant, but also of the possible replacements. To obtain detailed experimental data for all promising substitutes is expensive and timeconsuming. Ideally, a predictive model such as UNIFAC would be useful in such cases, at least to screen possible candidate mixtures for their suitability in a specific application. However, recent attempts (Kleiber, 1994) indicate that current UNIFAC group definitions and interaction parameters for such fluids are either nonexistent or do not lead to accurate predictions. At present, the best choice for the design engineer is to collect a minimum amount of data at selected temperatures and pressures, and then to use these data with a model to extrapolate phase behavior t o other temperatures and pressures. Data for the CFCs are
* Author
to whom correspondence should be addressed. E-mail:
[email protected]. ' E-mail:
[email protected].
relatively easy to correlate with cubic equations of state using the conventional one-parameter van der Waals mixing rule. Also, a t least in narrow ranges of temperature, their phase behavior is predictable with only one temperature-independent binary interaction parameter (Abu-eisha, 1991; Moshfegian et al., 1992; Gow, 1993). However, with a growing number of new refrigerant mixtures, including alcohol-containing mixtures (Laugier et al., 19941, and the increased ranges of temperature and pressure of interest, this approach is no longer adequate for extrapolating vapor-liquid equilibrium (VLE) information. In this work, we compare the performance of several recently developed multiparameter mixing rules for a cubic equation of state t o predict the VLE behavior of some CFC, HCFC, and fluorinated alcohol binary mixtures.
Modeling of Refrigerant Mixtures The vapor-liquid equilibrium modeling of refrigerant mixtures can be done using either activity coefficient (the so-called gamma-phi) models or equations of state (EOS). Usually EOS modeling is preferable because in refrigeration design not only is VLE important, but so are other thermodynamic properties (such as density and enthalpy) and these can also be obtained from the same EOS model. In order to accurately correlate and/or predict VLE with equations of state, it is necessary to have an EOS that can represent pure component saturation pressures correctly. In recent years several such equations have been suggested (Sandler et al., 1993). Here we use a modification of the Peng-Robinson equation of state by Stryjek and Vera (1986a1, the PRSV equation:
p=-- R T V-b
a V2-2bV-b2
with a(T>= (0.457235(R2T,2/P,))a(T> (2a)
b = 0.077796(RTJPc)
0888-588519512634-2520$09.00/0 0 1995 American Chemical Society
(2b)
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2521 Table 1. Equation of State Parameters for Pure Compounds compound
1.1.2-trichlorotrifluoroethane(R113) 1~2~dichlorotetrafluoroethane (Rll4) hexafluoroethane (R116) l , l ,l,2-tetrafluoroethane (R134a) tetrafluoromethane (R14) chlorodifluoromethane (R22) trifluoromethane (R23) ethanol 2,2,2-trifluoroethanol
K~
= K~
= 0.378893
~~
~~
+ ~ (-1Tr)o'512
(34
+ q(1- T,0.5)(0.7- T,)
(3b)
a(T)= [l K
Tc (K) 487.30 418.90 293.00 374.26 227.60 369.20 299.06 513.92 499.29
Pc (bar) 34.10 32.70 30.18 40.68 37.40 49.80 48.41 61.48 48.70
+ 1.48971530 - 0 . 1 7 1 3 1 8 4 8 ~+~ 0.01965540~ (34
where w is the acentric factor, and the parameter ~1 is specific for each compound used to accurately fit its low temperature saturation pressures. The pure component parameters of the PRSV equation for the substances considered in this work are reported in Table 1. The K I parameter of the PRSV equation was fit to the saturation pressure of the pure compound in the temperature range of interest in this work. Various investigators have tested cubic equations of state with the van der Waals one-fluid mixing rules (1PVDW) for CFC mixtures (Abu-eisha, 1991; Moshfegian et al., 1992; Gow,1993). These mixing rules are
a, = b,
liJ
K1
0.2560 0.2417 0.2485 0.3261 0.1778 0.1998 0.264 0.6444 0.6343
0.0147 -0.1091 0.0000 0.0000 0.0366 -0.1010 -0.0497 -0.0337 0.1209
[Si; + $1
-
In eqs 5 , C is an equation of state-dependent constant that is In ( 4 2 - 11/42 for the PRSV equation used here, R is the gas constant, T is absolute temperature, and A," is the excess Helmholtz free energy of mixing at infinite pressure which, in this work, is represented by the NRTL expression:
Also, in eq 5 , we have used
b, = s i b i i
In eqs 4 am and 6 , are EOS mixture parameters, x is the mole fraction, the indices indicate components, and 6~ is the temperature-independent binary interaction parameter. The general conclusion to be drawn from those earlier investigations is that, in narrow ranges of temperature, a good representation of the VLE behavior of CFC mixtures is achievable with the one-parameter van der Waals mixing rule (1PVDW). Here we test the temperature extrapolation capabilities of the lPVDW and three recently introduced multiparameter mixing rules for some conventional and possible new refrigerant mixtures over broad ranges of temperature. The mixing rules considered here are the three-parameter mixing rule of Wong and Sandler (1992) which we refer to as 3PWS, a two-parameter empirical mixing rule introduced by Stryjek and Vera (198613) and various other investigators (Adachi and Sugie, 1986; Panagiotopoulos and Reid, 1986) and then developed into a multiparameter form by Schwartzentruber and Renon (1989) referred to here as SPSV, and a new form of a two-parameter modified Huron-Vidal (2PMHV)mixing rule (Sandler and Orbey, 1995). Each of these models is briefly described below. The Wong-Sandler mixing rule is
(b--1
(bi -
a
R T ij
=
&)+ (b, - &)(1 2
(7)
The model parameters in the 3PWS case are Ai, Aji in eq 6 and liij in eq 7; we have fixed the value of ~j at 0.35 in eq 6 (except for the R14 R23 binary at 145 K for which a = 0.40 was used to improve the correlation). In the two-parameter 2PSV model of Stryjek and Vera (1986b)the mixing rule is the same as in van der Waals mixing rule, as given in eq 41, except that the following combining rule is used:
+
ac = &(I
- ximy - xjmji>
(8)
where mij and mji are temperature-independent binary interaction parameters. This mixing rule is identical to that of Panagiotopoulos and Reid (1986)and of Adachi and Sugie (1986) for binary systems, and reduces to the van der Waals mixing rule if the numerical values of the two binary interaction parameters, mij and mji , are the same. The multiparameter mixing rule proposed by Schwartzentruber and Renon (1989) also reduces to this form for binary systems. However, the multicomponent form of the four mixing rules differ. Unlike the Wong-Sandler mixing rule presented above, the mixing rules in this group violate the theoretical requirement of producing a second virial coefficient that is quadratic in composition (Sandler et al., 19931, and suffer from dilution effects and the Michelsen-Kistenmacher syn-
2522 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Table 2. Model Parameters
T (K) of fit
system R134a R116 R14 + R23 R14 R23 R114 ethanol R114 TFEb R22 + TFE R113 ethanol
+
275 283 145 363 373 373 393
+ + + +
a
dl2 (1PVDW) 0.0928 0.1288 0.0905 0.0926 0.1513 0.0768 0.1350
m121mz1 (2PSV) 0.086010.1254 0.166210.0913 0.109710.0783 0.175510.0120 0.205610.0910 0.086810.0666 0.178310.0863
1751790 5471196 5831310 15071731 14971795 620158 11911983
0.13211531824 0.2011542195 019291437 0.103130621699 0.200120271475 0.23316581-36 0.0741159611303
*
A, are in cal/mol. 2,2,2-Trifluoroethanol.
drome (1990). Many refrigerant systems are twocomponent mixtures, for which these last two problems are unimportant. Because of the simplicity, and in some cases effectiveness,we have considered this mixing rule here. The 2PMHV (Sandler and Orbey, 1995) mixing rule is a slightly modified version of models proposed by Dah1 and Michelsen (1990) and others (Tochigi et al., 1994) that has been shown to be better for extrapolation in temperature. In this mixing rule the b term is obtained from eq 4b) and the a term from
As in the 3PWS mixing rule, we have used the NRTL equation (eq 6) to represent excess free energy of mixing. Thus the parameters to be fitted in this model are the Ag and Aji of the NRTL equation, again with ai = 0.35 (except for R14 R23 binary at 145 K for which a = 0.4). This mixing rule can used as a three-parameter model either by varying a, or by introducing a binary parameter in the combining rule
+
b,
l/(bibj)(l- ZJ;
i*j
(10)
However, trials with these three-parameter versions did not lead to significant improvements in VLE correlations or predictions, so that only the results for the twoparameter model are considered here. It should be noted that this mixing rule also violates the boundary condition of a quadratic composition dependence of second virial coefficient.
Results In this work, as explained earlier, we are concerned with the temperature extrapolability of the models; thus we selected binary refrigerant mixtures for which VLE data were available covering a range of temperatures. We then fit the model parameters to data at one temperature and investigated the VLE predictions with those parameters at other temperatures. In each case isothermal bubble point calculations were performed and parameter optimization was done using only total pressure data with a simplex routine. The model parameters found in this work are given in Table 2. The results for the three models mentioned above and the simple van der Waals mixing rule are presented below. There are large amounts of binary VLE data in the literature with CFC refrigerants, but less for HFC and HCFC refrigerant mixtures, and data for mixtures with alcohols and/or fluorinated alcohols are just beginning t o appear. Also, in many cases the temperature interval of the data is narrow. With many of the CFC systems
2.0
r
0.0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
MOLE FRACTION R134a
Figure 1. Experimental data for the R134a-Rl16 binary system at 251 ( 0 )and 275 K (VI, and correlations: solid line is the 3PWS model; long-dashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the lPVDW model.
for which data were available in only narrow temperature ranges we found that the one-parameter van der Waals mixing rule (1PVDW) can provide reasonable predictions of VLE behavior, as has been observed previously. However, there are exceptions: one example is the R134a R116 mixture (Kleiber, 1994) shown in Figure 1. For this case data reported a t 275 K were fit to obtain parameters using all four models, and the behavior at 250 K was then predicted. In this case all three multiparameter models can fit the 275 K isotherm data successfully, and the predictions at the lower temperature were good. In contrast, the lPVDW model cannot be made to correlate the data at 275 K accurately, and the predictions at 250 K are the least accurate. The data of Piacentini and Stein (1967)were used for the R14 + R23 mixture, as this data set covers the broadest range of temperature. When we fit all the models to the experimental data at 283 K and then predict the VLE behavior at 225 K (Figure 2), we see that the 3PWS model (solid line) and 2PMHV model (long-dashed line) lead to more accurate predictions than do the BPSV (dotted line) and lPVDW (shortdashed line) models. The difference between the mixing rules is more pronounced when these same parameters are used to predict the phase behavior for the 145 K isotherm (Figure 3). In this case the lPVDW and BPSV models are inaccurate to the extent of predicting a liquid-liquid phase split that is not seen in the experimental data. The excess free energy-based models (3PWS and PPMHV), on the other hand, produce much more accurate predictions. It is also of interest to correlate the experimental data on the 145 K isotherm with all four models and then predict the phase behavior at higher temperatures. The
+
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2523
14
500 12
m
I
a
400
m
a
I
w
W
9
300
9
8
W
6
v) v)
v) v)
w
a P
200
10
4 100
2 0
0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
MOLE FRACTION R14
MOLE FRACTION R14
Figure 2. Predictions for the R14-R23 binary system compared with experimental data a t 225 K (MI: solid line is the correlation of the 3PWS model; long-dashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the l P M W model. All model parameters were obtained using data a t 283 K. 1
8
~
"
'
~
"
'
"
"
'
"
'
'
b
Figure 4. Experimental data for the R14-R23 binary system at 145 K (O), and correlations: solid line is the 3PWS model; long dashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the lFV'DW model.
'
500
16 14
.-m
a W
9 v) v)
w
E
.-m
a w 5
12 10
400
300
v) v)
u
8
E
6
200
4
100
2 0
0.9
0.0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .O
MOLE FRACTION R14
Figure 3. Predictions for the R14-R23 binary system compared with experimental data at 145 K (0):solid line is the correlation of the 3PWS model; long-dashed line is the PPMHV model; dotted line is the BPSV model; short-dashed line is the lPVDW model. All model parameters were obtained using data at 283 K.
best correlation, as is shown in Figure 4, is obtained with the 3PWS model which does not lead to a false liquid-liquid split; all other models predict varying degrees of false liquid phase splitting. In Figure 5 the phase behavior predictions for the R14 R23 mixture using the different models with parameters fit t o the 145 K isotherm are shown. In this case the best representation is obtained using the 3PWS model. More pronounced differences between the predictive capabilities of the models were seen in the study of CFC/ HCFC alcohol or CFC/HCFC fluorinated alcohol binary mixtures. Typically VLE predictions for alcoholcontaining mixtures with cubic equations of state lead to false liquid-liquid phase splits that are not found experimentally (Schwartzentruber et al., 1989; Englezos et al., 1989, Vonka et al., 1993). The representation of the R114 ethanol (Laugier et al., 1994) system by various methods is shown in Figure 6. The model parameters have been fit to the VLE data at 363 K, and the behavior along the 383 K isotherm is predicted. In
+
+
+
+
U.1
U.Z
U.3
U.4
U.3
U.b
U.f
U.6
U.Y
1.U
MOLE FRACTION R14
Figure 5. Experimental data for the R114-R23 binary system at 225 K (B)compared with predictions: solid line is the 3PWS model; long-dashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the lPVDW model. All model parameters were obtained using data at 145 K.
this case also the 3PWS model is superior for correlation of the 363 K data and in predicting the 383 K data. The BPSV model correlates the pressure well at 363 K but gives a false liquid-liquid split, and is less accurate in predicting the 383 K behavior. The 2PMHv model results in pressures lower than those found experimentally in both correlation at 363 K and prediction at 383 K. The worst performance is from the lPVDW model, which gives an exaggerated false liquid split at 363 K and poor predictions for the 383 K isotherm. Model behavior similar t o that discussed above is found for the R114 + 2,2,2 trifluoroethanol (TFE) mixture (Laugier et al., 1994) in Figure 7. Here all model parameters were fit to data on the 373 K isotherm, and predictions were made for the other isotherms (348,323, and 298 K). The best performance is obtained with the excess free energy-based 3PWS and 2PMHV models, although they also predict a small false liquid split a t 298 K. The BPSV model correlates the data for the 373 K isotherm well, but does not lead t o accurate predictions for the other isotherms, producing
2524 Ind. Eng. Chem. Res., Vol. 34, No. 7,1995 2.0 1.a 1.6 1.4
m
!i1.2 1 .o
0.8 0.6 0.4 0.2
0.01 " " " " " " " ' I " 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .O '
I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .O
MOLE FRACTION R114
Figure 6. Experimental data for the R114-ethanol binary system at 363 ( 0 )and 383 K (A)data compared with predictions: solid line is the 3PWS model; longdashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the l P M W model. All model parameters were obtained using data at 383 K.
MOLE FRACTION R22
Figure 8. Experimental data for the R22-2,2,2-trifluoroethanol binary system at 298 K (e),323 (B), 348 (A),and 373 K ( 0 ) compared with predictions: solid line is the 3PWS model; longdashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the lPVDW model. All model parameters were obtained using data a t 373 K. 0.9
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MOLE FRACTION R l l 4
Figure 7. Experimental data for the R114-2,2,2-trifluoroethanol binary system at 298 K (e),323 (B), 348 (A), and 373 K ( 0 ) compared with predictions: solid line is the 3PWS model; longdashed line is 2PMHV model; dotted line is the BPSV model; shortdashed line is the lPVDW model. All model parameters were obtained using data a t 373 K.
false liquid splits in all three. The worst performance is again obtained with the lPVDW model, which correlates the 373 K isotherm data less successfully than the other models and predicts exaggerated false liquid splits a t the lower temperatures. The VLE data for the R22 + TFE binary mixture (Laugier et al., 1994) is reasonably well represented by all models when model parameters are fit to 393 K data and VLE at 348,323, and 298 K are predicted. The best correlations, however, are obtained with the 3PWS and 2PSV models, while the 2PMHv and lPVDW models underpredict the observed pressure as shown in Figure 8. The last example considered here is the binary system of R113 ethanol. The results are presented in Figure 9. In this case the VLE data for the 393 K isotherm were fit, and the behavior of the 373 K isotherm was predicted. While the lPVDW model gives a rather poor correlation, all of the multiparameter models correlated
+
1
0.2 0.0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MOLE FRACTION R113
Figure 9. Experimental data for the R113-ethanol binary system a t 387 K (A)and 393 K ( 0 )compared with predictions: solid line is the 3PWS modeb long-dashed line is the 2PMHV model; dotted line is the 2PSV model; short-dashed line is the 1PVDW model. All model parameters were obtained using data at 393 K.
the available data quite well. In predicting the phase behavior on the lower temperature isotherm, however, only the excess free energy-based mixing models (3PWS and 2PMHV) were successful. The lFVDW model again exhibited a false liquid split and the BPSV model predictions deviated significantly from the experimental data with an indication of false liquid-liquid splits a t lower temperatures.
Conclusions Mixtures of halogenated compounds (either paraffin or alcohol based) have been used, and will continue to
be used as refrigerants, as solvents, and in other applications. The traditional approach t o modeling the vapor-liquid phase behavior of these systems has been to use cubic equations of state with the simple oneparameter van der Waals mixing rule. Now the design engineer is being forced to consider unconventional
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2626 mixtures of these compounds over a range of temperatures and pressures. Since present techniques do not accurately predict the VLE behavior of such systems in the absence of experimental data, the engineer must rely on a few data points collected in a restricted temperature range t o predict the behavior of these mixtures at other temperatures, pressures, and concentration ranges. In this work we have shown that the use of the traditional approach based on the van der Waals mixing rule is not suitable, and indeed may be seriously misleading, for the prediction of the phase behavior of new refrigerant mixtures. Consequently, new, multipameter mixing rules should be used. Three recently proposed multiparameter mixing rules have been compared here using experimental data for some conventional and proposed refrigerant mixtures. The results indicate that among these mixing rules the one proposed by Wong and Sandler (1992) is the most accurate. It is the only model that consistently resulted in qualitatively and quantitatively accurate predictions for all the cases investigated here. The other excess free energy-based model, the modified Huron-Vidal approach, also exhibited qualitatively correct behavior, but was not as accurate in temperature extrapolations. The Stryjek and Vera (1986b) and related models were satisfactory over small temperature ranges, but sometimes resulted in false liquid-liquid splits, and produced inaccurate predictions over wide ranges of temperature. These latter models, in contrast to excess free energy-based models, do not have built-in temperature dependence. Consequently, for better predictions their parameters may have to be made temperature dependent. In this case one would have to develop methods to evaluate those temperature-dependent parameters without relying on VLE data over wide temperature ranges since this would defeat the goal of temperature extrapolation of phase behavior using these models. One alternative would be to simultaneously fit VLE along one isotherm and excess enthalpy data, if such data were available. Such work is currently in progress. One might argue that since the 3PWS model contains three parameters, on that basis alone it should be expected to be superior to the other models considered here. However, an attempt to improve the correlative and predictive capabilities of the 2PMHV model by adding a third parameter, as described in the text, did not lead to significant improvements. On the basis of the results presented here, we suggest the use of the 3PWS mixing rule with a cubic equation of state for correlation and extrapolation of the vapor-liquid equilibria of refrigerant mixtures, and especially for the newer mixtures now under consideration. Indeed, when a very limited amount of experimental data are available for a system, the 3PWS model used here can be fit to these data, and then used for extrapolation to higher and lower temperatures.
Acknowledgment This research was supported, in part, by Grant DOEFG02-85ER13436 from the U.S. Department of Energy and Grant CTS-9123434fkom the U.S. National Science Foundation, both t o the University of Delaware.
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Adachi, Y.; Sugie, H. A New Mixing Rule-Modified Conventional Mixing Rule. Fluid Phase Equilib. 1986,23, 103-118. Dahl, S.; Michelsen, M. L. High Pressure Vapor-Liquid Equilibrium with a UNIFAC-based Equation of State. AIChE J . 1990, 36, 1829-1836. Englezos, P.; Kalogerakis, N.; Bishnoi, P. R. Estimation of Binary Interaction Parameters for Equations of State Subject to Liquid Phase Stability Requirements. Fluid Phase Equilib. 1989,53, 81-88. Gow, A. S. A Modified Clausius Equation of State for Calculation of Multicomponent Refrigerant Vapor-Liquid Equilibria. Fluid Phase Equilib. 1993, 90, 219-249. Kleiber, M. Vapor-Liquid Equilibria of Binary Refrigerant Mixtures Containing Propylene or R134a. Fluid Phase Equilib. 1994,92, 149-194. Laugier, S.; Richon, D.; Renon, H. Chlorofluorocarbon-Alcohol Mixtures: Bubble Pressures and Saturated Molar Volumes (Experimental Data and Modeling). Chem. Eng. Sci. 1994,49, 2135-2144. Michelsen, M. L.; Kistenmacher, H. On Composition Dependent Interaction Coefficients. Fluid Phase Equilib. 1990, 58, 229230. Moshfeghian, M.; Shairat, A.; Maddox, R. N. Prediction of Refrigerant Thermodynamic Properties by Equations of State: VaporLiquid Equilibrium Behavior of Binary Mixtures. Fluid Phase Equilib. 1992, 80, 33-44. Nowaczyk, U.; Steimle, F. Thermophysical Properties of New Working Fluid Systems for Absorption Processes. Znt J . Refrig. 1992,15, 10-15. Panagiotopoulos, A. Z.; Reid, R. C. New Mixing Rules for Cubic Equations of State for Highly Polar Asymmetric Mixtures. ACS Symp. Ser. 1986,300,571-582. Piacentin, A.; Stein, F. P. An Experimental and Correlative Study of the Vapor-Liquid Equilibria of the TetrafluoromethaneTrifluoromethane System. AICHE Symp. Ser. 1967,63 (Sl), 2835. Sauermann, P.; Holzapfel, K.; Oprzynski, J.; Nixdorf, J.; Kohler, F. Thermodynamic Properties of Saturated and Compressed Liquid 2,2,2-Trifluoroethanol, Fluid Phase Equilib. 1993, 84, 165-182. Sandler, S. I.; Orbey, H. On the Combination of Equation of State and Excess Free Energy Models. Fluid Phase Equilib. 1995, in press. Sandler, S. I.; Orbey, H.; Lee, B. I. Equations of State. In Chapter 2 in Modeling for Thermodynamic and Phase Equilibrium Calculations; S. I. Sandler, Ed.; Marcel Dekker: New York, 1993; Chapter 2. Schwartzentruber, J.; Renon, H. Extension of UNIFAC to High Pressures and Temperatures by the Use of a Cubic Equation of State. Znd. Eng. Chem. Res. 1989,28,1049-1055. Schwartzentruber, J.; Galivel-Solastiouk, F.; Renon, H. Representation of the Vapor-Liquid Equilibrium of the Ternary System Carbon Dioxide-Propane-Methanol and its Binaries with a Cubic Equation of State. Fluid Phase Equilib. 1987, 38, 217226 Stryjek, R.; Vera, J. H. PRSV: An Improved Peng-Robinson Equation of State for Pure Compounds and Mixtures. Can. J . Chem. Eng. 1986a, 64,323-333. Stryjek, R.: Vera, J. H. PRSV2: A Cubic Equation of State for Accurate Vapor-Liquid Equilibria Calculations. Can. J . Chem. Eng. 1986b, 64,820-826. Tochigi, K.; Kolar, P.; Izumi, T.; Kojima, K. A Note on a Modified Huron-Vidal Mixing Rule Consistent with the Second Virial Coefficient Condition. Fluid Phase Equilib. 1994,96,215-221. Wong, D. S. H.; Sandler, S. I. A Theoretically Correct Mixing Rule for Cubic Equations of State. MChE J . 1992, 38, 671- 680. Vonka, P.; Dittrich, P.; Lovland, J. Comparison of Many Different Mixing Rules in a Cubic Equation of State for 1-Alkanol Plus n-Alkane Mixtures. Fluid Phase Equilib. 1993, 88, 63-78. Received for review December 14, 1994 Accepted April 27, 1995 @
IE940737V
@Abstractpublished in Advance A C S Abstracts, J u n e 15, 1995.
