Thermodynamic Modeling of Refrigerants Using the Statistical

Department of Chemical Engineering, Tennessee Technological University, Box 5013,. Cookeville, Tennessee 38505. An ever increasing concern on the ...
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Ind. Eng. Chem. Res. 2005, 44, 4806-4814

Thermodynamic Modeling of Refrigerants Using the Statistical Associating Fluid Theory with Variable Range. 2. Applications to Binary Mixtures Saravanan Swaminathan and Donald P. Visco, Jr.* Department of Chemical Engineering, Tennessee Technological University, Box 5013, Cookeville, Tennessee 38505

An ever increasing concern on the stratospheric ozone depletion has led to a worldwide ban on fully halogenated chlorofluorocarbons (CFCs) and prompted a rigorous search for alternative refrigerants with a zero ozone-depletion potential (ODP) and a low global warming potential (GWP). Accurate thermodynamic information is required to develop an optimum alternative to replace an existing CFC pure fluid or mixture. In this work, statistical associating fluid theory with variable range (SAFT-VR) is used to correlate the vapor liquid equilibria (VLE) and the vapor-liquid-liquid equilibria (VLLE) for various refrigerant mixtures. An analysis on the pure component parameters for pentane was performed due to the existence of multiple parameter sets using SAFT-VR. The effects of the pure component parameters in mixture phase predictions were investigated. An optimized binary interaction parameter (kij) value was used to correlate the experimental data. It was found that the mixture phase predictions were sensitive to the adjusted kij value in such a way that fundamental changes in the phase diagram can occur with a small change in the kij value. Hence, an attempt was made to model new refrigerant mixture blends by transferring the kij value to similar mixtures. The good agreement of the predictions made using the transferred kij value and the experimental data aids in suggesting new alternative refrigerant blends. 1. Introduction Owing to the phase-out of commonly used chlorinated refrigerants such as CFCs (chlorofluorocarbons), CHCs (chlorinated hydrocarbons) before 2000 and HCFCs (hydrochlorofluorocarbons) by 2030 according to the Montreal Protocol and the Copenhagen Amendment, modeling of chlorine-free refrigerants and their mixtures has gained importance among thermodynamicists in government research labs, industry, and academia. The new generation refrigerants that were considered as suitable and viable substitutes were HFCs (hydrofluorocarbons), HFEs (hydrofluoroethers), HCs (hydrocarbons), etc. and their mixture blends. These alternative refrigerants are evaluated based on toxicity, insulating ability, flammability, physical stability, solubility, cost, ODP (ozone-depletion potential), and GWP (global warming potential).1 These new refrigerants and their mixtures are used as suitable replacements for CFCs and HCFCs as blowing agents, fire extinguishers, aerosol sprays, rocket propellants, etc. Oftentimes working with mixture blends is preferable to pure component fluids on account of energy saving and flexibility of operation.2 In order to select the optimal mixture composition for design and operation of a process, it is necessary to know several pieces of thermodynamic data, especially vapor-liquid equilibria (VLE). Thermodynamic modeling using computational methods has gained popularity owing to the inexpensive and expedient nature of this approach in comparison with traditional experiments. Hence, the best choice would be to collect a minimum amount of VLE data at * To whom correspondence should be addressed. Tel.: (931)372-3606. Fax: (931)372-6352. E-mail: [email protected].

selected temperatures and pressures and then use these data with a model to extrapolate phase behavior to other temperatures and pressures. The new generation of refrigerants and their mixtures exhibit complex phase behavior that necessitates the use of a robust and a molecular-based EOS (equation of state). The thermodynamic model chosen should also be able to capture the features of mixtures such as the presence of an azeotrope or an immiscibility gap, which are important to know for separation processes. Various combining and mixing rules are used for finding the interaction parameters for the mixture from the individual pure component parameters. To decrease the deviation of the predictions made by the model in comparison to the experimental data, a binary interaction parameter (kij) is used. Due to the linking of the parameters in the equations involved, the kij value becomes sensitive, and this value can sometimes determine the nature of the phase coexistence curve. The primary objective of this work is to predict/ correlate VLE, liquid-liquid equilibria (LLE), and vapor-liquid-liquid equilibria (VLLE) of refrigerant mixtures based on our previous work with pure components.3 The efforts made by earlier groups for modeling refrigerant mixtures are outlined in section 2. Section 3 discusses the SAFT-VR EOS used to model the refrigerant mixtures in this study. The combining and mixing rules that are used for finding the interaction parameters have also been provided. The approach used to model the mixtures and the SAFT-VR predictions/correlations have been illustrated in section 4. An analysis of the pure component parameters and transferring the binary interaction parameter is also detailed in this section. Conclusions are drawn in the final section.

10.1021/ie048862m CCC: $30.25 © 2005 American Chemical Society Published on Web 05/24/2005

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4807

2. Review of Models The efforts made by earlier researchers to model pure component and mixture phase behavior of these refrigerants has been provided in our companion paper.3 The more recent efforts made that have relevance to mixtures are discussed in this section. In the early 1980s, Patel and Teja4 developed a new cubic EOS for modeling polar compounds that captures the good features of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) EOS for nonpolar compounds with some modifications to account for the polar compounds.4 Numerous modifications have been proposed to the Patel-Teja EOS to increase its predictive nature for refrigerants and their mixtures.5 In the late 1980s, Iwai et al. extended the VDWEOS for modeling pure and refrigerant mixtures using the Huron-Vidal (HV) mixing rule.6 In the early 1990s, Barolo et al. contributed to extending the SRK EOS using a HV mixing rule to model refrigerant mixtures.7 In the late 1990s, Lemmon and Johnson developed a mixture model explicit in Helmholtz energy that is capable of predicting the VLE for refrigerant mixtures.9 In 1998, Elvassore et al. presented and validated a Group-Contribution EOS for predicting the VLE for HFC-alkane mixtures.10 Michelsen et al. analyzed the predictions of mixture phase properties based on a Wong-Sandler linear combination of the Vidal and Michelsen rules (LCVM) and first-order modified Huron-Vidal (MHV-1) mixing rules. They show that there is a severe mismatch in the predictions due to the temperature extrapolations over an extended range, leading to increasing differences between the equation of state and the underlying Gibbs excess model. More relevant to this work, in 1998 Galindo et al. modeled HFCs and their mixtures using a new version of SAFT known as the statistical associating fluid theory with variable range (SAFT-VR).11,12 The SAFT-VR EOS predicted that properties had excellent correlation with the experimental data for both the pure component HFCs and the HFC mixtures. Hence, SAFT-VR was used to model the mixtures that were chosen in this work, as it has already shown great success in modeling a wide variety of compounds.3 3. SAFT-VR EOS Six molecular-based parameters are used for correlating the pure component phase behavior using the SAFTVR model. A fixed number of off-centered square-well sites are placed on a sphere of diameter σ. The sites are placed at a distance (rd) from the center of the sphere and have a cutoff range (rc). These two parameters define the available association bonding volume. When two sites come closer to each other than the cutoff distance (rc), there is an attractive interaction (hb). The thermodynamics of the long-range attractive forces are described here by a second-order temperature expansion of the Helmholtz free energy for a square-well potential. The attractive square-well is characterized by a depth (mf) and a range (λ). The bonding volume (K) is calculated using rc* (rc/σ) and rd* (rd/σ ) 0.25). Implementation of SAFT-VR has been discussed in various works; we will explain here the important conditions used along with the model to correlate/predict mixture phase behaviors. The cross-interaction parameters for the mixtures are obtained using the MX1b mixing rule with Lorentz-Berthelot combining rules.12

The mixtures are modeled in two different cases: 2 site-2 site and 2 site-0 site, where “2 site” denotes the number of association sites available for bonding for the pure component, which is dependent on the dipole moment of the compound, and “0 site” represents the compound that has a negligible dipole moment and, hence, has no sites for association. To increase the correlative nature of SAFT-VR, a binary interaction parameter (kij) was introduced for the unlike squarewell energy parameter. While correlating the available experimental data, the kij value was adjusted to best match existing experimental data. For the systems that lack experimental data, the predictions were made using kij ) 1. The combining rules used here are presented below:

σ1 + σ2 2

(1)

hb hb hb 12 ) x1 2

(2)

mf mf mf 12 ) kijx1 2

(3)

σ12 )

K12 )

(

λ12 )

3

3

)

xK1 + xK2 2 λ1σ1 + λ2σ2 σ1 + σ2

3

(4)

(5)

where Ki is a function of rci*.11 4. Results Mixtures. The mixture phase equilibria were predicted as well as correlated at three different conditions, namely, isothermal, isobaric, and isoplethic (constant liquid or vapor mole fraction). Calculating VLE/LLE/ VLLE properties of refrigerant mixtures requires solving the mixture phase equilibrium constraint equations for the saturated volumes of the two phases that are in equilibrium. Using the phase rule for an isothermal/ isobaric/isoplethic calculation, the equations are solved using a root-finder algorithm.13 Different kinds of mixtures such as HFC/HC, HFE/HC, HFC/CFC, HFC/ HCFC, etc. have been used in this work. As the kij value is the only parameter we optimize in mixture phase behavior calculations, it is adjusted so as to correlate the SAFT-VR predictions for mixtures to the experimental data available in the literature. Then the kij is adjusted to best correlate the experimental data. If the predictions (kij ) 1) are in accordance with the experimental data, then the EOS has been successful in predicting the properties of that particular system at that particular state. The greater the value of kij varies from unity, the less successful the model is in going from pure component correlations to mixture predictions. The mixture parameters are obtained after applying the mixing rules to the pure component parameters. A number of binary mixtures under different conditions have been correlated using SAFT-VR based on the experimental data present. To test the robustness of SAFT-VR, predictions are compared with the available experimental data. Some predictions were made for systems that did not have any experimental data

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Table 1. Predictions/Correlations of Mixtures at Isobaric Conditionsa experimental system

pressure (bar)

Taz (K)

yaz

R245fa/hexane14 R245fa/isohexane14 R245fa/pentane14 R245fa/isopentane14 R245fa/cyclopentane14

1 1 1 1 1

287 287 282.3 280.1 284.8

0.913 0.927 0.651 0.581 0.705

a

predictions with kij ) 1 Taz (K)

yaz

none none 286.34 284.12 none

none none 0.779 0.561 none

correlations with kij kij

Taz (K)

yaz

xa

xb

%AAD

0.960 0.963 0.955 0.960 0.960

288.41 287.82 282.35 280.1 284.76

0.884 0.904 0.657 0.59 0.766

0.741 0.598 0.597

0.129 0.232 0.159

0.778

0.102

0.231 0.257 0.219 0.233 0.239

y denotes the mole fraction; subscript az denotes the azeotrope; xa and xb are the mole fractions of miscibility gap.

Figure 1. Mixture phase behavior of R245fa/cyclopentane. The empty circles are the experimental data,14 and the solid line is the correlation using SAFT-VR with kij ) 0.960. The dotted line is the prediction using kij ) 1. The filled circle denotes the experimental azeotrope.

available. The predictions made for all the systems discussed are tabulated in Tables 1-6. As we examined many mixtures, providing plots for each of them would greatly extend the printed length of the paper, hence plots for the predictions of only a few representative systems are provided in Figures 1-6. These predictions are compared to the experimental data that are available. After these results were analyzed, the binary interaction parameter was introduced. It is also of interest to study the importance of the binary interaction parameter in these predictions and correlations to have a better understanding about the sensitivity of the kij value. This aids in selecting a useful kij value for predicting the mixture phase behavior of systems that lack experimental data. While Figures 1-6 provide a qualitative picture of the correlations/predictions, to provide a quantitative measure of the deviation from experimental data, percentage absolute average deviation (% AAD) values have been given in all the tables for the mixtures. % AAD is defined as:

% AAD )

|

|

1 Qexp - Qbmod × 100 N Qexp

(6)

where Q denotes the physical property (temperature or pressure) depending on the conditions of the mixture and N is the number of experimental data points. % AAD is calculated using the pressures for the isothermal systems, temperatures for the isobaric systems, and pressures for the isoplethic systems. In Figure 1, the T-xy slices for the prediction and correlation of the R245fa/cyclopentane system at 1 bar with experimental data14 have been illustrated. The predictions indicate the presence of an azeotrope though

Figure 2. Mixture phase behavior of R23/R13. The empty circles are the experimental data,15 the dashed line is for kij ) 1.0, and the solid line is the correlation using SAFT-VR with kij ) 0.930. The filled circle denotes the experimental azeotrope.

it is predicted at a different temperature and composition relative to experiment. After adjusting the kij value, the new predictions not only show an azeotrope but also an immiscibility gap. It is to be noted that the immiscibility gap is not reported in the literature. This may be a shortcoming of the model or may be associated with the parameter set used. We are currently exploring this area more extensively.20 Table 1 provides other predictions/correlations performed also for the R245fa/pentane, R245fa/isopentane, R245fa/hexane, and R245fa/isohexane systems at isobaric conditions. All other mixtures in Table 1 exhibit similar behavior as R245fa/cyclopentane except R245fa/ isopentane predicts an azeotrope, as the experimental data suggests. Figure 2 shows the VLE for the R23/R13 system at 273.09, 255.32, 224.79, and 199.05 K for which experimental data15 are available in the literature. The dashed line shown only for 273.09 K provides the predictions using kij ) 1, and it shows that there is no azeotrope predicted. After adjusting the kij value it was observed that one kij value could correlate the Pxy data for the system over a range of temperatures. It is to be noted that no spurious features have occurred for R23 even though the value of λ was greater than 1.8.3 Table 2 provides other predictions/correlations performed for R152a/R12 and various other HFC/propane and HFC/ isobutane systems that have the presence of an azeotrope at isothermal conditions. The predictions for the R245fa/R134a system at 293.15, 303.15, and 313.15 K using SAFT-VR were compared with the available experimental data16 in Figure 3. The predictions were in very good agreement with experimental data. To have a consistent kij value for a mixture at all temperatures, the individual kij

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4809 Table 2. Mixture Phase Predictions and Correlations of Azeotropic Isothermal Systemsa experimental system R23/R1315

R152a/R1215 R125/propane26

R227ea/propane27,28

R32/propane31

R134a/isobutane30 R32/isobutane30 R152a/isobutane30

R125/isobutane33 R227ea/isobutane33 R245fa/isobutane16

a

temp (K)

Paz (bar)

yaz

273.09 255.32 224.79 199.05 273.15 273.15 283.15 293.15 303.15 313.15 278.15 293.16 303.15 308.15 313.14 333.15 278.1 294.8 303.2 313.2 303.2 323.2 301.8 321.8 303.2 313.2 323.2 333.2 293.15 303.15 313.15 323.15 293.15 303.15 313.15

27.6 17 6.22 2.15 3.63 8.34 10.98 14.14 17.52 23.05 5.89 8.93 11.53 13.02 14.64 22.66 12.21 19.06 23.42 29.61 8.82 14.35 19.39 30.78 7.69 9.98 12.78 16.09 12.11 6.59 8.46 10.82 3.37 4.57 5.95

0.652 0.605 0.516 0.552 0.264 0.802 0.769 0.772 0.766 0.779 0.178 0.189 0.181 0.196 0.201 0.205 0.663 0.679 0.683 0.702 0.746 0.757 0.906 0.934 0.791 0.806 0.82 0.839 0.976 0.601 0.611 0.616 0.204 0.226 0.264

predictions with kij ) 1 Paz (bar) none none none none none 7.81 9.74 13.42 16.57 21.57 6.01 9.19 11.92 13.47 14.98 21.89 11.68 18.45 22.79 28.56 None None None None 7.42 9.79 12.66 15.82 None 6.26 8.13 10.34 3.32 4.49 5.96

correlations with kij

yaz none none none none none 0.711 0.612 0.625 0.678 0.637 0.121 0.139 0.138 0.149 0.158 0.178 0.512 0.526 0.532 0.563 None None None None 0.705 0.722 0.745 0.769 None 0.539 0.546 0.561 0.132 0.142 0.149

kij 0.930 0.930 0.975

0.980

0.965 0.950 0.900 0.985 0.970 0.985 0.960

Paz (bar)

yaz

% AAD

27.67 17.11 6.3 2.15 3.4965 8.02 10.41 13.89 17.72 22.79 6.23 9.58 12.42 14.05 15.42 23.39 12.46 19.32 23.78 29.94 8.57 14.31 19.48 30.69 7.73 10.17 13.12 16.56 11.998 6.72 8.63 10.97 3.6 4.99 6.19

0.669 0.64 0.599 0.545 0.433 0.762 0.692 0.721 0.714 0.727 0.169 0.178 0.174 0.182 0.188 0.192 0.634 0.651 0.662 0.689 0.752 0.773 0.903 0.938 0.769 0.791 0.803 0.815 0.964 0.589 0.602 0.609 0.211 0.219 0.225

0.393 0.352 0.441 0.344 2.235 0.512 0.584 0.483 0.385 0.483 0.935 0.928 0.923 0.920 0.917 0.907 0.459 0.410 0.491 0.386 0.627 0.379 0.266 0.252 0.333 0.317 0.397 0.399 0.460 0.384 0.464 0.399 2.784 2.621 2.616

y denotes the mole fraction; subscript az denotes the azeotrope. Table 3. Mixture Phase Behavior of Zeotropic Isothermal Systems system R23/R1417

R245fa/R134a16 R152a/R11325

R113/R2325

Figure 3. Mixture phase behavior of R245fa/R134a. The empty circles are the experimental data,16 and the solid line is the correlation using SAFT-VR with kij ) 1.005.

values were averaged. The averaged kij value used for this system was 1.005, hence the predictions at kij ) 1 were not included in this plot. Table 3 provides other predictions/correlations performed for the R152a/R113, R113/R23, HFC/isobutane, and R22/R23 systems that do not have an azeotrope at isothermal conditions. SAFT-VR was also used to correlate the mixture phase behavior of the R245fa/isobutane system at 293.15, 303.15, and 313.15 K and which is illustrated in Figure 4. The predictions of SAFT-VR for Pxy as well as the azeotrope were not in good agreement with the experi-

R22/R2322

R23/isobutane29 R143a/isobutane29 R125/isobutane33 R23/R152a32 R23/R143a32

temp (K) 145.15 199.98 224.79 255.32 283.15 293.15 303.15 313.15 298.15 323.15 348.15 373.15 298.15 323.15 348.15 373.00 273.00 293.00 303.00 323.00 343.00 353.15 283.15 293.15 323.15 333.15 303.15 313.15 283.15 293.15 283.15 293.15

kij

0.950

1.005

0.920

0.850

0.983

0.955 1.035 0.970 0.995 1.005

% AAD 1.241 0.752 0.777 0.807 0.835 0.111 0.120 0.115 0.235 0.243 0.282 0.259 1.321 1.181 0.636 0.681 0.411 0.410 0.410 0.418 0.433 0.438 0.325 0.294 0.381 0.412 0.472 0.421 0.745 0.686 0.489 0.561

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Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 Table 4. Predictions/Correlations of Mixtures at Isoplethic Conditionsa predictions with kij system R125/R134a18 R125/R143a18

R32/R134a18 R143a/R134a18 Figure 4. Mixture phase behavior of R245fa/isobutane. The empty circles are the experimental data,16 and the solid line is the correlation using SAFT-VR with kij ) 0.960. The filled circle denotes the experimental azeotrope.

R152a/R11424

R152a/R2223 R32/R143a18

mole fraction 0.90 0.75 0.25 0.86 0.75 0.50 0.10 0.90 0.75 0.50 0.75 0.60 0.25 0.96 0.91 0.72 0.39 0.22 0.13 0.57 0.91 0.90 0.40 0.15

avg kij 1.007

1.030

1.006 1.030

0.947

1.040 1.010

Tc (K)

Pc (bar)

% AAD

387.5 366.4 358.9 352.8 354.7 356.2 356.2 389.6 391.5 392.5 389.2 363.8 371.5 403.2 405.8 406.5 419.6 423.5 394.5 401.9 405.3 383.2 363.8 360.6

54.50 50.09 48.06 45.50 46.96 46.86 47.10 91.70 83.70 72.50 55.52 41.16 52.23 60.08 59.89 55.20 48.50 46.80 68.02 65.95 63.44 90.44 62.88 53.35

0.406 0.481 0.443 0.571 0.995 0.684 0.561 0.703 0.406 0.531 0.571 0.651 0.634 0.406 0.430 0.393 0.470 0.419 0.366 0.315 0.263 0.211 0.461 0.423

a Subscript c denotes the critical value. Mole fraction denotes the mole fraction of the first component.

Figure 5. Mixture phase behavior of R23/R14. The empty circles are the experimental data,17 and the solid line is the correlation using SAFT-VR with kij ) 0.950.

mental data16 for all the temperatures mentioned above. After using an averaged kij value of 0.960 also, the correlations were good only for the predicting a part of the Px data and the azeotropic composition. Hence, here is an example where it is easier to model a polar/polar mixture (R245fa/R134a) with similar size interactions than a polar/nonpolar mixture (R245fa/isobutane). The VLE predictions for the R23/R14 system at 145.15, 199.98, 224.79, 255.32, and 283.15 K are illustrated in Figure 5 along with the experimental data17 available in the literature for comparison. The Pxy results are predicted at all the experimental conditions mentioned above. The averaged kij value was used to correlate the mixture properties presented in Figure 5. The correlations are in good agreement with the experimental data at lower temperatures (lower than the critical temperature of R14). It is seen that the critical pressure for the mixture at 255.32 and 283.15 K was not correlated accurately. This may be due to the fact that the pure component parameterization for R14 was preformed at subcritical conditions and, thus, extrapolation to higher temperatures for mixture predictions is problematic. The kij value for most of the systems provided in Table 4 have a greater deviation from unity relative to the mixture of R245fa/R134a. This can be due to the differences in the interactions between a HFC/CFC mixture relative to a HFC/HFC mixture. Also,

Figure 6. Mixture phase behavior of R32/134a. The empty circles are the experimental data,18 and the solid line is the correlation using SAFT-VR with an averaged kij ) 1.005.

the kij value of R22/R23 mixture is 0.983, R23/R13 mixture is 0.930, R23/R14 mixture is 0.950, and R113/ R23 mixture is 0.850. The reason that can be attributed to this change in the kij value may lie in the complexity of interactions between the components of the mixture or due to the different parameter sets. Figure 6 presents the isoplethic predictions of R32/ R134a at 0.9, 0.75, and 0.5 of R32 using SAFT-VR and the vapor pressure of the pure components. The temperature, pressure, and vapor fraction are solved, and the bubble point curve is predicted for a particular composition of R32 in the mixture. After optimizing the kij value so that the predictions are in good agreement with experimental data,18 the dew point curve is predicted. For the dew point curve, the vapor phase fraction is fixed, and the kij is fixed equal to the value obtained in the bubble point curve and the dew point values are predicted and plotted to obtain the critical point of that particular blend. The same procedure is applied to the

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4811 Table 5. Predictions Based on the Attempt to Transfer the kij Value for Some Mixtures† experimental system

pressure (bar)

Taz(K)

yaz

R245fa/isopentane14 R365mfc/isopentane21 R338mccq/isopentane HFE-245mc/isopentane HFE-347mcc/isopentane

1 1 1 1 1

280.1 no data no data no data no data

0.581 no data no data no data no data

†

prediction with kij ) 1 Taz(K) 284.12 299.23 296.83 none 293.60

predictions with kij

yaz

kij

0.561 0.174 0.333 none 0.297

0.960 0.960 0.960 0.960 0.960

Taz(K) 280.1 294.76 292.29 none 289.58

yaz 0.590 0.317 0.418 none 0.349

xa

xb

none none none none 0.605

none none none none 0.053

y denotes the mole fraction; subscript az denotes the azeotrope; xa and xb are the mole fractions of miscibility gap.

Figure 7. Mixture phase behavior of R125/134a. The empty circles are the experimental data,18 and the solid line is the correlation using SAFT-VR with an averaged kij ) 1.007.

other compositions of the blend and the critical points of all the compositions used are connected together to obtain the critical loci of the system to estimate information on the critical properties of this system. Figure 7 illustrates the isoplethic predictions of R125/ R134a at 0.9, 0.5, and 0.25 of R125 using SAFT-VR and the pure component vapor pressures. The temperature, pressure, and vapor fraction are solved, and the bubble point curve is plotted for a particular composition of R125 in the blend. After optimizing the kij value so that the predictions are in good agreement with experimental data,18 the dew point curve is predicted. The same procedure as described above is adopted to predict the dew point curve of all the compositions of the mixture. Table 4 provides other predictions/correlations performed for the R125/R143a, R143a/R134a, R152a/R114, R152a/R22, and R32/R143a systems at isoplethic conditions. Transferring the kij Value. After finding the kij value for all the above-mentioned systems in this work, an attempt was made to transfer the kij value of similar systems and predict their phase behavior. This is an important step toward predicting the mixture phase properties of new mixtures that do have any experimental data available. An understanding of transferring the kij values of a system to another can lead to the discovery of new mixtures that can be used as substitutes to the existing conventional refrigerants. After modeling the mixtures described in the previous sections, the kij value of the R245fa/isopentane system (source system) was chosen to be used for two additional HFC/isopentane mixtures and two HFE/isopentane mixtures. In this case, the hydrocarbon is fixed, and the HFCs and the HFEs chosen have the same number of carbon atoms or have one additional carbon atom in their molecular formula. Table 5 shows the predictions

Figure 8. Mixture phase behavior of R245fa/isopentane. The empty circles are the experimental data,14 and the solid line is the correlation using SAFT-VR with kij ) 0.960. The dotted line is the prediction using kij ) 1. The filled circle denotes the experimental azeotrope.

Figure 9. Mixture phase behavior of HFE245mc/isopentane. The solid line is the prediction using SAFT-VR with kij ) 0.960, and the dotted line is the predictions of SAFT-VR using kij ) 1.

(using the transferred kij ) 0.960) for R365mfc/isopentane, HFC338mccq/isopentane, HFE 245mc/isopentane, and HFE347mcc/isopentane. Figure 8 provides the predictions/correlations of R245fa/isopentane system at 1 bar that serves as the source system from where the kij values will be transferred. The predictions show the presence of an azeotrope, as is the case according to the experimental data, but at a slightly different temperature and composition. After a kij value of 0.960 was used to correlate the experimental data, the azeotrope was predicted at the right temperature and composition. Figures 9-11 illustrate the predictions and correlations of the two HFC/HC and the HFE/HC mixtures. It is seen from the figures that the kij value has a significant effect on the correlations. In Figure 11, the T-xy slices for the prediction and correlation of the R365mfc/isopentane system at 1 bar using a kij value of unity and the transferred kij value have been illustrated. The predictions show the presence of an azeotrope at a different temperature and concentration

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Figure 10. Mixture phase behavior of HFC338mccq/isopentane. The solid line is the prediction using SAFT-VR with kij ) 0.963, and the dotted line is the predictions of SAFT-VR using kij ) 1.

Figure 11. Mixture phase behavior of R365mfc/isopentane. The solid line is the prediction using SAFT-VR with kij ) 0.960, the dotted line is the predictions of SAFT-VR using kij ) 1, and the empty circle is the experimental data.21 Table 6. Alternate Mixture Blends for Conventional Refrigerants composition (%) refrigerant NBP (K) R141b

305.15

R21

282.05

alternative blends

liquid

vapor

R365mfc/isopentane HFE 245mc/isopentane HFE 245mc/isopentane

56.5 38.3 97.4

76.7 9.1 99.1

than the predictions using the transferred kij value. From Figure 11, it was found that the prediction (using the transferred kij value) was in accordance to the one experimental data point available for this system.21 This result provides some hope for the ability to use transferred kij parameters in SAFT-VR where experimental data are not available. Using these data, we can suggest alternatives to the non-zero ODP refrigerants such as R141b and R21. Table 6 gives the list of alternate refrigerants that can be considered instead of the abovementioned HCFCs. Analysis of Pure Component Parameters. Predicting/correlating the mixture properties using an EOS is predicated on specifying the parameters of the pure components. Pure component parameterization is done such that the parameters are physically meaningful. Proper relationships have been designed and explored extensively by researchers for the interaction parameters for the mixture, known as mixing rules. Eventually, a binary interaction parameter (kij) is used to fit to the available experimental data for the mixture. The kij value is known to be sensitive to temperature and substance in a complex way. A small change in its value

Figure 12. (a) Saturated liquid and vapor volumes of R125 using both the sets of parameters. Empty circles are the experimental data.34 Solid lines are the correlations from our companion paper.3 Dashed lines are the correlations using Galindo et al.’s parameters.16 (b) Vapor pressure curves for the pure component of R125 using both the sets of parameters. Empty circles are the experimental data.34 Solid lines are the correlations from our companion paper.3 Dashed lines are the correlations using Galindo et al.’s parameters.16

can lead to changing the phase diagram completely. Hence, this poses a problem when analyzing suitable alternate refrigerant system properties where no experimental data are available. In this brief investigation, we analyze the effect of the pure component parameters on the mixture phase predictions. Hence, we first analyze the pure component phase equilibrium correlations for R125 using two different sets of parameters for SAFT-VR, (i) existing set of parameters by Galindo et al.11,12 and (ii) parameters for R125 from our previous work.3 The pure component correlations using both the sets of parameters were illustrated in Figure 12a,b. It is seen that the pure component correlations using both the sets of parameters were in good agreement with the experimental data. Now to examine the effect these two parameter sets have on mixture phase predictions, we consider the R125/propane mixture at 293.15 K. We use two different sets of parameters given in Table 7 for R-125 and a published set of parameters for propane by Gil-Villegas et al.19 Using these sets of parameters, predictions for the mixture are made and presented in Figure 13. From the comparison of the predictions using two sets of parameters for R125, we find that there is a big difference in the mixture phase properties predicted using SAFT-VR for this system. The experimental data26 indicates that there is an azeotrope at 77.2% R125 and 14.14 bar at 293.15 K. Predictions (kij ) 1) using the Galindo et al.’s set of parameters11 indicate an azeotrope at 94.6% R125 and 12.23 bar, and the set of parameters from our previous work3 predicts an azeotrope at 61.9% R125 and 12.72 bar. The small

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4813 Table 7. Comparison of Parameters for R125a refrigerant

molecular formula

R125

CHF2CF3

parameter set

hb/kb (K)

mf/kb (K)

r c*

σ (Å)

m

λ

1*

1204.4841 724.8

116.3186 303.8

0.7307 0.669

4.2358 4.535

1.2355 1.35

1.8024 1.36

2+

a *Denotes the parameters from our companion paper,3 + denotes the parameters from Galindo et al.11 Mole fraction denotes the mole fraction of the first component.

Figure 13. Mixture phase behavior of R125/propane using both the sets of parameters for R125 and one set of parameters for propane. The solid line is the predictions from this work, and the dashed line is the predictions using Galindo et al.’s parameters11 for R125. The filled circle is the azeotrope from experimental data.26

difference on the pure component side of R125 is due to the slight difference in the pure component correlations using two different sets of parameters. It is clear that the difference in the predictions/ correlations and the experimental data are due to the mixture parameters, which in turn depend on the pure component parameters. At its core, the problem is 2-fold: (i) the existence of multiple minima and (ii) the different pure component parameterization procedures that have been followed. EOS that were widely used in the past tended to be perturbations of the van der Waals type; such EOS project a terrain in parameterization space that were, relatively, uncomplicated. Hence, the finding and utilization of the local minima was not a large impediment. However, when molecular-based EOS are used, parameterization space not only increases in dimension but becomes quite complicated owing to the complicated nature of the functions intrinsic to these EOS. Hence, one wonders whether finding all the local minima in the “acceptable range” for the parameter space could glean information on optimal “locations” of parameter sets. At any rate, it is clear that authors who publish parameters on molecular-based EOS should be quite specific about the important features of their parameterization (i.e., objective function, number of experimental data points etc.). Work is being done to explore the pure component parameterization methodology and the effect of multiple minima, standardization of the temperature range of the data sets, the objective function, etc. on the prediction of mixture phase properties.20 5. Conclusions The main objective of this work was to predict as well as correlate mixture phase properties of refrigerants using SAFT-VR. An ample amount of experimental data was utilized for the pure component parameterization using SAFT-VR of a wide variety of refrigerants such as HFCs, HCFCs, CFCs, PFCs (perfluorocarbons), etc.

in our companion paper.3 The mixture parameters are obtained after applying the mixing rules to the pure component parameters. SAFT-VR has not only been used to correlate the pure component phase behavior but also has been useful in predicting/correlating the mixture phase behavior of the systems used. The mixture blends that had experimental data available were used to find a binary interaction parameter (kij) that is used to correlate the mixture phase behavior. The kij value was obtained so that the predictions made using SAFT-VR have a low relative deviation with respect to the experimental data. This is important because many mixture blends lack experimental data for the model to correlate the VLE/LLE/VLLE properties. In this research, there was an attempt to transfer the kij value to mixtures with similar components. After transferring the kij value, the predictions using SAFTVR were compared to the existing experimental data. It was found that the predictions were in accordance to the experimental data. This led to suggesting alternate refrigerant mixture blends for the existing HCFC refrigerants. Finally, important issues about the pure component parameterization procedures and its effects on mixture phase predictions were discussed. Acknowledgment The authors acknowledge gratefully the Center for Manufacturing Research, Tennessee Tech University, for partially funding this research. The authors also thank Honeywell Inc. for partially sponsoring this research. Computational work on this project was performed at the Computer Aided Engineering Laboratory on the Tennessee Technological University campus. Literature Cited (1) Zipfel, L.; Barthelemy, P.; Dournel, P. The next generation blowing agents: from one single product to a product range. J. Cell Plast. 1999, 35, 345. (2) Kagawa, N.; Uematsu, M.; Watanabe, K. Theoretical analysis of heat pump cycle characteristics with pure refrigerants and binary refrigerant mixtures. 1. Cycle characteristics with pure refrigerants. Nippon Reito Kyokai Ronbunshu 1990, 7, 43. (3) Swaminathan, S.; Visco, D. P. Thermodynamic modeling of refrigerants using statistical associating fluid theory with variable range. 1. Pure components. Ind. Eng. Chem. Res. 2005, 44, 47984805. (4) Patel, N. C.; Teja, A. S. A new cubic equation of state for fluids and fluid mixtures. Chem. Eng. Sci. 1982, 37, 463. (5) Patel, N. C. Improvements of the Patel-Teja equation of state. Int. J. Thermophys. 1996, 17, 673. (6) Iwai, Y.; Margerum, M.; Lu, R.; Benjamin C. Y. A new threeparameter cubic equation of state for polar fluids and fluid mixtures. Fluid Phase Equilib. 1988, 42, 21. (7) Barolo, M.; Bertucco, A.; Scalabrin, G. Prediction of vaporliquid equilibria of refrigerant mixtures by a cubic group-contribution equation of state. Sci. Tech. Froid 1994, 501. (8) Morrison, J. D.; Barley, M. H.; Murphy, F. T.; Parker, I. B.; Wheelhouse, R. W. The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures. Int. J. Thermophys. 1995, 16, 1165. (9) Lemmon, E. W.; Jacobsen, R. T. A generalized model for the thermodynamic properties of mixtures. Int. J. Thermophys. 1999, 20, 825.

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Received for review November 24, 2004 Revised manuscript received April 1, 2005 Accepted April 25, 2005 IE048862M