Vapor−Liquid Equilibria Predictions for Alternative ... - ACS Publications

Ind. Eng. Chem. Res. 2008, 47, 7501–7508

7501

CORRELATIONS Vapor-Liquid Equilibria Predictions for Alternative Working Fluids at Low and Moderate Pressures Shu-Xin Hou,† Yuan-Yuan Duan,*,† and Xiao-Dong Wang‡ Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua UniVersity, Beijing 100084, China, Department of Thermal Engineering, School of Mechanical Engineering, UniVersity of Science and Technology Beijing, Beijing 100083, China

Alternative working fluid mixtures containing hydrofluoroethers, hydrofluorocarbons, alkanes, alcohols, ketones, and esters widely used as process fluids generally exhibit azeotropes, high nonideality, and association effects. In this work, the vapor-liquid equilibria for these mixtures are predicted using a combination of the Soave-Redlich-Kwong equation of state, zero reference pressure GE-EoS mixing rules, and the UNIFAC group contribution model. A new functional group assignment strategy was developed, and the model interaction parameters between groups were obtained from selected binary vapor-liquid equilibria data to give fairly good agreement between the calculated results and the experimental data. The method is also extended to ternary systems for VLE representations in a totally predictive manner with only the molecular structures, the critical parameters, and the acentric factors of the pure components needed. 1. Introduction Acoording to the Montreal Protocol and its amendments,1,2 chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) are among the restricted and prohibited compounds. Besides hydrofluorocarbons (HFCs), the so-called third generation alternatives, hydrofluoroethers (HFEs), have been identified as environmentally friendly substitutes because of their zero ozone-depletion potential (ODP), low global warming potential (GWP), short atmospheric lifetimes, and very low toxicity.3,4 Mixtures composed of these compounds are generally being used for the cleaning of electronic and magnetic devices, foaming, dry etching, and low-temperature refrigeration. The thermodynamic properties such as vapor-liquid equilibria (VLE) are essential in screening promising alternative working fluids. Recently, extensive experimental studies have been conducted to measure vapor-liquid equilibria data for the new generation of alternative mixtures, mostly HFE-related mixtures such as HFEs + HFEs binaries, HFCs + HFEs binaries, alkanes + HFEs binaries, and alcohols + HFEs binaries.5-8 VLE experiments are very time-consuming and expensive, especially with ternary and multicomponent mixtures, so predictive models are needed to describe the vapor-liquid equilibria properties. Therefore, numerous methods have been developed to enhance the predictive capability of vapor-liquid equilibria models so that they can be used without relying on experimental data. One way is to develop correlations for the binary interaction parameters in the VLE models for different families of mixtures. For example, Lee and Sun9 developed such correlations for binaries containing HCFCs, HFCs, and dimethyl ether when the Patel-Teja equation of states (EoS) and van der Waals one-fluid mixing rules is used for the VLE representation. Morrison and McLinden10 gave correlations for the binary interaction parameter during the selection of azeotropic refrigerants using the CarnahanStarling-de Santis EoS and van der Waal one-fluid mixing * To whom correspondence should be addressed. Tel: 86-1062796318. Fax: 86-10-62770209. E-mail: [email protected]. † Tsinghua University. ‡ University of Science and Technology Beijing.

rules. Swaminathan and Visco11 used statistical associating fluid theory with variable range (SAFT-VR) to correlate the vapor liquid equilibria (VLE) for several kinds of refrigerant mixtures following their work on pure fluids.12 They found that the mixture phase predictions were sensitive to the adjusted kij value that fundamental changes in the phase diagram can occur with a small change in kij. Hence, an attempt was made to model new refrigerant mixture blends by only transferring the kij value to similar mixtures with four systems as examples. Group contribution methods,13-17 which obtain interaction parameters between functional groups from analysis of phase equilibria data of systems containing the same functional groups, are valuable tools for predicting the properties of systems lacking experimental data. Such methods not only provide a powerful and systematic approach for characterizing the properties of existing systems but can also be used to preselect and design new systems with desired properties. The widely used group contribution method in its most recent modifications, such as UNIFAC,18 Modified UNIFAC (Dortmund),19 and PSRK,20 do not include all the group assignments and interaction parameters for the new generation of working fluids. Therefore, heterogeneous models21-25 using group contribution solution models to account for the liquid phase nonideality (γ-φ approach) and homogeneous models26-28 using various equation of states (EoS) combined with the group contribution solution models to represent both phases (φ-φ approach) have been used to describe vapor-liquid equilibria for targeted refrigerant mixtures. More experimental VLE data for various kinds of HFEs containing systems are available in recent publications, so previous developed models, group assignments and interaction parameters may not applicable or adequate for the newly developed alternative mixtures. In our previous work,29 the Soave-Redlich-Kwong equation of state (SRK EoS)30 was combined with the UNIFAC model13 to predict the VLE for several categories of HFCs related binary and ternary mixtures.

10.1021/ie800133b CCC: $40.75  2008 American Chemical Society Published on Web 08/27/2008

7502 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 1. Thermophysical Parameters for Pure Compounds ViL (dm3/mol) bi (dm3/mol)

compd

code

formula

Tc (K)

pc (MPa)

ω

pentafluorodimethylether 1,1,1-trifluorodimethylether octafluoromethylethylether heptafluoropropyl methyl ether 1,1,1,2,3,3-hexafluoro-3(2,2,2-trifluoroethoxy)propane 1,1,1,2,3,3-hexafluoro-3(2,2,2-trifluoroethoxy)propane 1,1,1,3,3,3-hexafluoro-2methoxypropane 1,1,2,2-tetrafluoro-1(2,2,2-trifluoroethoxy)ethane perfluoroisopropyl methyl ether pentafluoroethane 1,1,1,2-tetrafluoroethane 1,1,1-trifluoroethane 1,1-difluoroethane fluoroethane methanol ethanol 1-propanol 2-propanol 2-methyl-2-propanol 2-butanone ethyl acetate pentane heptane

HFE125 HFE143a HFE218 HFE347mcc HFE449mec-f

CF3OCHF2 CF3OCH3 CF3OCF2CF3 CF3CF2CF2OCH3 CF3CHFCF2OCH2CF3

353.24 378.02 356.85 437.70 475.74

3.326 3.588 2.315 2.481 2.233

0.293420 0.280558 0.354772 0.403744 0.542492

0.0987 0.0977 0.1462 0.1666 0.2019

0.0765 0.0756 0.1110 0.1271 0.1535

1.290 1.287 1.317 1.311 1.315

HFE356mf-f

CF3CH2OCH2CF3

476.31

2.783

0.492731

0.1604

0.1233

1.301 37,a 24b

HFE356mmz

CH3OCH(CF3)2

459.58

2.699

0.463206

0.1599

0.1227

1.303 38,a 24b

HFE347pc-f

CHF2CF2OCH2CF3

463.89

2.713

0.501777

0.1605

0.1232

1.303 37,a 24b

HFE347mmy HFC125 HFC134a HFC143a HFC152a HFC161

(CF3)2CFOCH3 CHF2CF3 CH2FCF3 CH3CF3 CH3CHF2 CH3CH2F CH3OH CH3CH2OH CH3CH2 CH2OH (CH3)2CHOH (CH3)3COH CH3COCH2 CH2 CH3COOCH2 CH2 CH3(CH2)3CH3 CH3(CH2)5CH3

433.30 339.17 374.21 345.86 386.41 375.31 512.50 514.00 536.80 508.30 506.20 535.50 523.30 469.70 540.20

2.553 3.6177 4.0593 3.761 4.5168 5.028 8.084 6.137 5.169 4.764 3.972 4.150 3.880 3.370 2.740

0.388530 0.3052 0.32684 0.2615 0.27521 0.219987 0.565831 0.643558 0.620432 0.666873 0.615203 0.323369 0.366409 0.251506 0.349469

0.1601 0.0793 0.0741 0.0721 0.0653 0.0589 0.0427 0.0627 0.0821 0.0831 0.1033 0.0976 0.1063 0.1183 0.1633

0.1223 0.0675 0.0665 0.0662 0.0616 0.0538 0.0457 0.060 0.0748 0.0769 0.0918 0.0930 0.0972 0.1004 0.1420

1.309 1.174 1.115 1.088 1.060 1.095 0.934 1.045 1.098 1.081 1.125 1.049 1.094 1.178 1.150

ui

ref 33,a 33,a 34,a 36,a 37,a

36,a 31,a 31,a 31,a 31,a 32,a 32,a 32,a 32,a 32,a 32,a 32,a 32,a 32,a 32,a

33b 33b 35b 25b 24b

24b 31b 31b 31b 31b 32b 32b 32b 32b 32b 32b 32b 32b 32b 32b

a Denotes references providing the experimental critical properties of the compounds. b Denotes references providing the saturated vapor pressure data used for the parameter estimations.

The purpose of this work is to further extend our group contribution method for the description of vapor-liquid equilibria of alternative working fluids containing HFEs, HFCs, alkanes, alcohols, ketones, and esters. Those mixtures exhibit azeotropes, high nonideality, and association effects, which were rarely or not at all included in previous studies. 2. Model Development and Evaluation Most of the binary mixtures used in this study were measured at low pressures, with several related ternary systems measured at high pressures. Moreover, these working fluids are usually used at moderate to high pressures in practical applications. As in the study of HFCs related systems by Hou et al.,29 the Soave-Redlich-Kwong equation of state (SRK EoS)30 is used here with the zero reference GE-EoS mixing rules and the UNIFAC group contribution model to represent the vapor-liquid equilibria for the systems considered in this work. The SRK EoS has the form a(T) RT p) V - b V(V + b)

(1)

where p is the pressure, R is the ideal gas constant, T is the temperature. and a and b are the energy and covolume parameters for the equation of state expressed as a(T) ) (0.42748R2T2c ⁄ pc)R(T)

(2)

b ) 0.08664RTc/pc

(3)

with R(T) ) [1 + (0.480 + 1.574ω - 0.1767ω2)(1 - Tr0.5)]2 (4) where Tc and pc denote the critical temperature and pressure for the pure compounds, ω is the acentric factor and Tr ) T/Tc is the reduced temperature. The critical properties and acentric factors for the compounds given in Table 1 used in this work were taken from REFPROP 7.131 and the DIPPR,32 except for those for the HFEs, for which the critical properties were directly

taken from the reported experimental results and the acentric factors were evaluated from related vapor pressure data based on the definitions. The molar excess free energy at zero pressure from the two parameter cubic equation of state can be given by39

( ) GE RT

) EoS

bi

∑ x ln b i

+ q(R) -

m

i

∑ x q(R ) i

i

(5)

i

with R ) a/bRT, which constitutes the basis for extending the SRK EoS to represent the vapor-liquid equilibria of mixtures. In this work, the approximation for q(R) is linear in R with a linear combining rule for the covolume parameter, b, to form the following mixing rules

[

am ) bm

GE0 RT + C C bm )

i

i

∑∑xx

i j

i

( )

∑ x ln j

bm + bi

bi + bj 2

ai

∑x b i

i

i

]

(6)

(7)

where C is a constant that needs to be determined to provide a better representation of the systems involved in this study. According to our previous work,29 the constant can be obtained through an analysis of ui, the ratio of the liquid molar volume at the normal boiling point to the covolume parameter from eq 3, as shown in Table 1, where the liquid molar volume, ViL, for the HFEs was calculated from the SRK EoS, with the other liquid molar volumes taken from REFPROP 7.131 or DIPPR.32 Taking the overestimation of the liquid volume by the SRK EoS into account,40 the average value of u ) 1.10 seems reasonable for all the pure compounds considered. G0E is the excess molar Gibbs function expressed by a low pressure solution model, which in this work is the group contribution model UNIFAC, given as a sum of a combinatorial and a residual part ln γi ) ln γCi + ln γRi

(8)

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7503 Table 2. Group Assignments for New Alternative Working Fluids main groups

subgroups

Rk

Qk

alkane

CH3 CH2 CH CHF CH2F CHF2 CH2F2 CF3CHF CHF3 CF3 CF2 CF3CH2 CF3OCHF2 CF3OCF3 CF3OCF2 CF3OCH3 CF2OCH3 CF2OCH2 CFOCH3 CH2OCH2 CH3OCH CH3OH CH2OH CHOH COH CH3CO CH3COO

0.9011 0.6744 0.4469 0.8240 1.0514 1.2011 1.4285 2.2300 1.5781 1.4060 1.0105 2.0804 2.8180 3.0229 2.6274 2.5180 2.1225 1.8958 1.7270 1.5927 1.5919 1.4311 1.2044 0.9769 0.7495 1.6724 1.9031

0.848 0.540 0.228 0.668 0.980 1.108 1.420 2.048 1.548 1.380 0.920 1.920 2.704 2.976 2.516 2.444 1.984 1.676 1.524 1.320 1.316 1.432 1.124 0.812 0.584 1.488 1.728

CHF

CHF3

CF3OCHF2 CF3OCF3 CF3OCH3

CH3OCH3 CH3OH

CH3CO CH3COO

where the combinatorial part provides the contribution due to differences in molecular size and shape through the expressions using the van der Waals volumes, Rk, and the surface areas, Qk, calculated based on the methods given by Bondi,41 as listed in Table 2. The residual part is obtained using the temperature independent interaction parameters of the original UNIFAC

( )

amn (9) T where amn and anm are the interaction parameters between different groups that need to be evaluated. Other temperaturedependent interaction parameters were considered, but with little success for the systems considered in this work. ψmn ) exp -

3. Group Assignment and Interaction Parameter Optimization Group assignments are essential in the development of the group contribution method to employ its predictive abilities, since a functional group is assumed to have identical properties independent of the entire molecules. The principles based on ab initio calculations42 as summarized previously,29 can be useful for classifying functional groups. However, the problem is still quite complex when it comes to alternative working fluid related compounds, because of the existence of strongly polarizing atoms, such as F and O. Therefore, new group assignments strategy was developed for the new refrigerants,29 which proved to be quite effective and suitable for several types of refrigerant mixtures. The newly developed group assignments strategy29 is further validated here for HFC + HFE mixtures, as will be discussed in the next section. For the HFEs considered in this work, although there are no quantum mechanical calculational results for the charge distribution, the electronic charge distributions for ethers, alcohols, esters, and aldehydes42 suggest that the etheric group O has a rather negative charge in a molecule which strongly influences the other segments or groups through intermolecular interactions. In their description of the PVT behavior of HFEs using the group contribution PC-SAFT EoS,

Vijande et al.43 followed the approach proposed by Carballo et al.44 to characterize the functional groups, which is a method based on Bader’s theory of atoms in molecules.45,46 Vijande et al.43 assumed that the etheric group O modifies the properties of the methyl (CH3), methylene (CH2), perfluoromethyl (CF3), and perfluoromethylene (CF2) groups bonded directly to the etheric group and that a distinction is needed between those groups and others in the β position. Such a strategy resulted in an undesirable increase in the number of functional groups, especially when too many HFEs and their constituent segments were involved. In this work, to minimize the influence of the etheric group O on other segments or groups and to fully utilize the predictive ability of the group contribution model, the etheric group O and its two neighboring groups were combined together to form new functional groups, which were then assigned to four main groups. All the HFEs were then characterized by these four main groups and those shared with the HFCs. The alcohols were described by two main groups in the commonly applied UNIFAC models to distinguish methanol from the other alcohols. Wu and Sandler47 showed that the VLE of alcohol related mixtures could be predicted with the same CHnOH main group and a reevaluation of the group volumes and surface areas, based on ab initio calculation results. Gonza´lez et al.48 gave a group definition criterion based on quantum mechanical calculations to characterize the functional groups in 1-alkanol and tested it with the NittaChao group contribution model49 for 1-alkanol + n-alkane mixtures. They pointed out that the hydroxyl functional group changed the properties of neighboring segments, so that a distinction was needed between the affected and unaffected groups. In this work, to reduce the number of the main groups and to make the model more predictive, the group assignment strategy used only one main group by combining the hydroxyl group with its neighboring segments. The alkanes, ketones, and esters involved in the binary systems were grouped as is commonly done in the UNIFAC13 and Mod. UNIFAC models.14,15 The group assignments for all compounds are listed in Table 2. The vapor-liquid equilibria were modeled using interaction parameters evaluated from carefully selected data sets. The VLE data for the mixtures were tested for thermodynamic consistency before used in the parameter generalization. Because most of the binary data were measured at low pressures and given in isobaric form, the experimental VLE data were examined using the points test of Fredenslund et al.50 and the area test of Herington,51 as also used in the DECHMA data series. The points test procedure gives more valuable and useful information than the area test about the quality of a set of VLE data. Nevertheless, the area test is still useful since the ln (γ1/γ2) data can be accurately fitted and at the same time, the lnγ1 and lnγ2 curves can be depicted in the same figure, which can serve as an additional test as discussed by Wisniak et al.52 The consistency of each data set was judged based on the generally adopted consistency test criteria, as detailed by Jackson and Wilsak53 and Wisniak et al.52 Altogether, as shown in Table 3, five systems with their original data sets did not passed the thermodynamic consistency tests. After removal of data points with large y-residuals detected by the points test in these five data sets, the remaining data points in these systems were found to be thermodynamically consistent when being rechecked. Because VLE data for these systems are scarce, these data sets were used in the parameter estimation after deleting the poor data points. No experimental vapor phase compositions were

7504 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 3. VLE Database and Calculated Results from the Group Contribution Model systems

N

T (K)

∆Ta

∆yb

data sources

HFE125+HFC161 HFE125+HFC152a HFE125+HFC143a HFE125+HFC134a HFE125+HFC125 HFE143a+HFC125 HFE143a+HFC134a HFE143a+HFE218 HFE125+HFE143a HFE218+HFC152a HFE347pc-f+pentanec HFE347mmy+heptane HFE347mcc+1-propanol HFE449mec-f+1-propanolc HFE347mcc+2-butanone HFE449mec-f+2-butanone HFE347mcc+ethyl acetate HFE449mec-f+ethyl acetate HFE449mec-f+methanol HFE449mec-f+ethanol HFE449mec-f+2-propanol HFE347pc-f+ethanol HFE347pc-f+1-propanolc HFE347pc-f +2-butanone HFE347pc-f+ethyl acetate HFE356mf-f+methanol HFE356mf-f+ethanol HFE356mf-f+1-propanolc HFE356mf-f+2-propanol HFE356mf-f +2-butanone HFE356mf-f+ethyl acetate HFE356mmz+methanol HFE356mmz+ethanol HFE356mmz+2-propanolc HFE356mf-f+2-methyl-2-propanol

47 45 48 59 46 21 24 110 47 38 15 31 31 21 23 36 24 37 26 25 22 21 13 19 21 24 29 18 22 26 14 33 32 26 25

209.85-239.05 212.75-245.75 208.75-235.15 214.85-244.15 211.45-234.65 279.989-349.984 279.989-349.984 208.25-246.85 219.80-246.70 217.20-239.00 304.16-329.37 302.49-371.49 307.25-370.40 343.72-370.40 307.31-352.93 345.03-354.86 307.31-350.20 345.03-353.05 330.67-345.52 337.89-351.45 341.24-355.39 326.68-351.35 329.25-370.29 329.37-352.72 329.37-350.23 326.32-337.60 331.92-351.45 336.22-370.32 334.17-355.45 337.00-352.78 337.00-350.26 318.36-337.66 322.21-351.49 323.44-355.42 335.42-355.62

1.20 1.37 0.79 0.87 0.68 0.81 0.43 0.36 0.80 0.39 1.45 1.71 0.22 0.30 0.16 0.17 0.09 0.12 0.23 0.52 0.37 0.43 0.44 0.15 0.08 0.47 0.69 0.37 0.55 0.13 0.09 0.40 0.38 0.23 0.88

n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 0.022 0.012 0.008 0.009 0.003 0.002 0.002 0.002 0.011 0.009 0.005 0.007 0.005 0.004 0.002 0.022 0.009 0.006 0.012 0.004 0.003 0.014 0.004 0.007 0.009

54 54 54 54 54 5 5 34 6 6 55 56 7 7 7 7 7 7 57 57 57 58 58 58 58 8 8 8 8 8 8 59 59 59 55

a ∆T ) 1/N ∑iN) 1 |(Ticalcd - Tiexp)|. b ∆y ) 1/N ∑iN) 1 |yicalcd - yiexp |, where N denotes the number of data points. c Denotes systems for which not all of the original experimental data points were used in the parameter estimations based on thermodynamic consistency tests.

Table 4. Interaction Parameters amn and anm (K) between the Main Groups Listed in Table 2 alkane alkane CHF CHF3 CF3OCHF2 CF3OCHF2 CF3OCH3 CH3OCH3 CH3OH CH3CO CH3COO a

0 50.17 108.23 207.70 340.09 -109.05 -16.04 -29.59 26.76a 114.80a

CHF 480.72 0 896.52 293.22 630.19 311.80 n.a. 62.11 -75.76 -18.90

CHF3 198.36 2509.83 0 207.78 -98.97 -112.18 834.13 20.29 n.a. n.a.

CF3OCHF2

CF3OCF3

-215.29 -121.97 -64.12 0 n.a. -145.89 n.a. n.a. n.a. n.a.

-116.65 29.28 1229.48 n.a. 0 67.48 n.a. n.a. n.a. n.a.

CF3OCH3

CH3OCH3

236.78 -68.82 1730.16 153.51 80.46 0 n.a. 92.57 333.23 331.92

-45.88 n.a. -32.77 n.a. n.a. n.a. 0 n.a. -268.17 -195.59

CH3OH 211.94 382.51 767.12 n.a. n.a. 2200.38 n.a. 0 35.69 15.84

CH3CO a

476.40 -206.89 n.a. n.a. n.a. 338.13 1184.06 17.83 0 n.a.

CH3COO 232.10a -208.20 n.a. n.a. n.a. 173.09 586.51 28.83 n.a. 0

Interaction parameters taken from the original UNIFAC.13 n.a. denotes parameters not available or not used in this work.

available for several of the HFCs related binaries, so it was impossible to test their thermodynamic consistency. For these data sets, a comparison of bubble pressure and bubble temperature calculation results was performed to check the data quality. Table 3 lists the VLE data of 35 systems with more than 1000 data points that were used in the parameter estimation. The original VLE data collected in this study can be obtained upon request. Because most of the binary data sets were given in isobaric form, the group interaction parameters amn and anm were determined using the objective function N

OF )

∑(

calcd 2 Texp i - Ti

)

(10)

i)1

where Tiexp and Ticalcd are the experimental and calculated temperatures and N is the number of data points. Because the

data sets used in parameter optimization were evaluated for thermodynamic consistency and carefully selected, the form of the objective function has little influence on the parameter optimization. The parameter optimization procedure was performed using both the Levenberg-Marquardt algorithm60 and the Simplex algorithm,61 to ensure that the optimum interactions parameters were obtained. The optimized interaction parameters are listed in Table 4. 4. Results and Discussion 4.1. Alkanes + HFEs, HFEs + HFEs, and HFCs + HFEs Systems. Mixtures composed of alkanes, hydrofluoroethers (HFEs), and hydrofluorocarbons (HFCs) are considered to be promising refrigerants, foaming agents, and propellants. Several such mixtures are in commercial use with a number of published vapor-liquid equilibria data sets for these systems.

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7505

Figure 1. VLE correlation results for the HFE347mmy(1) + heptane(2) system using the group contribution model. 0, Experimental data at 101.3 kPa from Tochigi et al.56

Figure 3. VLE correlation results for the HFE449mec-f(1) + 2-propanol(2) system using the group contribution model. 0, Experimental data at 101.3 kPa from Hiaki et al.57

Figure 2. VLE correlation results for the HFE356mf-f(1) + methanol(2) system using the group contribution model. 0, Experimental data at 101.3 kPa from Hiaki and Nanao.8

Figure 4. VLE correlation results for the HFE347pc-f(1) + ethyl acetate(2) system using the group contribution model. 0, Experimental data at 101.3 kPa from Hiaki et al.58

The systems in this class that were used for the parameter estimation are summarized in Table 3. The interaction parameters between the main groups Alkane, CHF, and CHF3 were previously determined from HFC-related systems.29 As demonstrated in Table 3, the average temperature deviation was 0.91 K for all the data sets, indicating that the previous group assignments for the HFCs and the group assignments for the HFEs in this work are reasonable and acceptable. The VLE prediction result for the HFE347mmy + heptane system is illustrated in Figure 1. 4.2. Alcohols + HFEs Systems. Mixtures of HFEs with organic solvents, such as alcohols, are useful mixtures to replace CFCs and HCFCs as cleaning solvents and blowing agents. Systems of alcohols and HFEs may form H bonds; thus, exhibiting association effects and strong positive deviations from Raoult’s law.62 Experimental VLE data for 15 alcohols + HFEs systems found in the literature served to further validate the group assignments strategy developed here. As listed in Table 3, the average deviations of the temperature and vapor phase composition were 0.43 K and 0.009, respectively. Thus, with the group divisions given in the previous section, both methanol and other alcohol related systems can be described accurately. The HFE356mf-f + methanol and HFE449mec-f + 2-propanol binary systems are shown in Figures 2 and 3. Both systems show excellent agreement between the predicted and the experimental results despite the strong deviations from Raoult’s law and the formation of azeotropic points.

4.3. 2-Butanone + HFEs and Ethyl Acetate + HFEs Systems. 2-Butanone and ethyl acetate are among other organic solvents frequently mixed with HFEs for use as alternative working fluids. The VLE predictions for eight such binary systems are listed in Table 3. The interaction parameters between the CH3 and CH3CO main groups and between the CH3 and CH3COO main groups were taken from the original UNIFAC parameters.13 The other needed interaction parameters between the main groups listed in Table 4 were optimized in this work. The results show that the model yields good reproduction of the experimental data with example shown in Figure 4. 4.4. Ternary Systems. Ternary and multicomponent mixtures have long been considered as potential alternative working fluids. Ternary mixtures account for a large part of the potential refrigerants listed by the EPA63 and ASHRAE Handbook Fundamentals.64 VLE calculations for ternary systems with interaction parameters estimated from binary data further tested the predictive ability of the group contribution model. Table 5 lists thirteen ternary systems containing HFEs and HFCs along with their temperature and pressure variations. VLE predictions for the thirteen mixtures require all the interaction parameters between the HFCs and HFCs. The group contribution model developed by Kleiber22 can be used to model interactions between HFCs. However, the available parameters can not describe all of the HFCs, and the predicted results from Kleiber’s model do not seem to perform better than merely assuming that the binary interaction parameters kij in the classical mixing rules are equal to zero. A thorough

7506 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 5. VLE Prediction Results for Ternary Systems systems

N

T(K)

p(kPa)

∆T(K)

∆p(%)

data sources

HFE125+HFC134a+HFC161 HFE125+HFE143a+HFC161 HFE218+HFE143a+HFC161 HFE125+HFC143a+HFC161 HFE125+HFC143a+HFC152a HFE125+HFC143a+HFC134a HFE125+HFC32+HFC161 HFE125+HFC32+HFC152a HFE125+HFC32+HFC134a HFE125+HFE143a+HFC143a HFE218+HFC134a+HFC161 HFE218+HFE143a+HFC152a HFE143a+HFC143a+HFC134a

12 9 23 13 11 12 12 28 26 12 189 30 14

216.2-240.6 218.9-240.8 211.0-238.1 211.95-232.95 221.05-235.95 213.45-35.65 210.75-229.65 214.65-362.65 215.05-353.95 220.75-236.75 215.15-350.55 215.75-240.25 212.85-237.55

27.3-98.1 32.3-97.9 26.9-99.5 34.3-98.9 48.4-98.9 31.9-99.1 37.6-100.3 40.4-4682.0 41.3-3675.8 46.1-98.8 37.6-3214.0 28.0-99.5 26.7-93.6

0.19 0.11 0.41 0.22 0.16 1.06 0.33 0.59 0.80 1.74 0.90 0.59 0.60

1.00 0.57 2.07 1.19 0.82 5.39 1.84 1.81 2.90 9.04 4.42 2.98 3.08

6 6 6 65 65 65 65 65 65 65 65 66 66

a ∆T ) 1/N ∑i N) 1 |(Ticalcd - Tiexp)|, represents the average temperature deviations calculated with the group contribution model through the bubble pressure calculations. b ∆p ) 1/N ∑i N) 1 |(picalcd - piexp)/piexp | × 100, represents the average absolute deviations of pressure calculated with the group contribution model through the bubble temperature calculations.

investigation showed that using kij ) 0 in the SRK EoS with the classical mixing rules model resulted in VLE predictions for HFC + HFC binaries that were comparable and in most cases better than those from Kleiber’s group contribution model. Although new evaluations of the model interaction parameters will somewhat improve the VLE prediction results, we decided not to follow such a procedure. One problem with ternary systems having two HFCs is how to describe such systems in a uniform and consistent model. To make the model fully predictive, the VLE data for HFCs + HFCs binary systems were generated using the SRK EoS and the classical mixing rules with the binary interaction parameters kij ) 0. These data were then used to obtain the group interaction parameters between the groups for HFCs based on the present group assignments strategy. The obtained parameters were then incorporated with the interaction parameters listed in Table 4 to predict the VLE for the corresponding ternary systems. The interaction parameters in Table 4 between the main group Alkane, CHF, CHF3 were redetermined because the Rk and Qk values for the HFC related groups were recalculated in the present work. As shown in Table 5, the average temperature deviations calculated using the group contribution model through the bubble pressure calculations is 0.59 K, wherea the average absolute deviations of pressure calculated using the group contribution model through the bubble temperature calculations is 2.85% for the thirteen ternaries. Because no experimental vapor phase compositions are available, comparisons with calculated results are not possible at present. Two ternary systems, HFE218 + HFE143a + HFC152a and HFE125+HFC32 +HFC134a, are shown in Figures 5 and 6, respectively, with the flash calculation results. For the HFE218 + HFE143a + HFC152a ternary system, the temperature was set to 239.95 K and the pressure to 99.1 kPa, while for the HFE125+HFC32 +HFC134a ternary system, the temperature was 328.35 K and the pressure was 2.2309 MPa. The results show that although the interaction parameters were mostly obtained from low pressure binary systems, the ternary mixtures at much high pressures are still well-represented. 5. Conclusions A group contribution model based on the cubic equation of states was extended to predict vapor-liquid equilibria for new alternative working fluids containing hydrofluoroethers, hydrofluorocarbons, alkanes, alcohols, ketones, and esters. A new group assignment strategy consistent with our previous

Figure 5. VLE prediction results for the ternary system HFE218(1) + HFE143a(2) + HFC152a(3) system at 239.95 K and 99.1 kPa using the group contribution model. 0, Experimental bubble point from Kul.66

Figure 6. VLE prediction results for the ternary system HFE125(1) + HFC32(2) + HFC134a(3) system at 328.35 K and 2.2309 MPa using the group contribution model. 0, Experimental bubble point from Kul et al.65

models was developed for these systems. Optimized interaction parameters between the ten main groups were obtained from selected binary VLE data sets. The applicability and predictive ability of the present method was further confirmed by VLE calculations for thirteen ternary systems. The results indicate that this group contribution method is suitable for predicting vapor-liquid equilibria of new working fluid mixtures and can be used for preselecting mixtures for

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7507

experimental studies, screening promising alternatives, determining optimal compositions and evaluating efficiencies for industrial applications. Acknowledgment This work was supported by the National Natural Science Foundation of China (50636020). Nomenclature a ) EoS energy parameter amn, anm ) interaction parameters between groups b ) covolume parameter am, bm ) EoS parameters for mixtures C ) constant in the zero pressure mixing rules c1, c2, c3 ) coefficients of R(T) function f ) fugacity GE ) excess Gibbs function kij ) binary interaction parameter in the classical mixing rules N ) number of data points p ) pressure q(R) ) approximation function R ) universal gas constant T ) temperature U ) packing fraction V ) volume in molar units x ) molar fraction in the liquid phase y ) molar fraction in the vapor phase AbbreViations CFC(s) ) chlorofluorocarbon(s) HCFC(s) ) hydrochlorofluorocarbon(s) EoS ) equation of state HFC(s) ) hydrofluorocarbon(s) HFE(s) ) hydrofluoroether(s) SRK ) Soave-Redlich-Kwong EoS VLE ) vapor-liquid equilibria Greek letters ∆ ) deviation R ) a/(bRT) R(T) ) EOS temperature dependent function Subscripts c ) critical point i, j ) components i and j and data point i m ) mixture r ) reduced property 0 ) zero pressure reference state Superscripts calcd ) calculated value E ) excess property exp ) experimental value L ) liquid phase

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ReceiVed for reView January 24, 2008 ReVised manuscript receiVed June 26, 2008 Accepted July 15, 2008 IE800133B