Thermodynamic Modeling of Refrigerants Using the Statistical

May 24, 2005 - Department of Chemical Engineering, Tennessee Technological University, Box 5013, ... 1974, two chemists from the University of Califor...
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Ind. Eng. Chem. Res. 2005, 44, 4798-4805

Thermodynamic Modeling of Refrigerants Using the Statistical Associating Fluid Theory with Variable Range. 1. Pure Components Saravanan Swaminathan and Donald P. Visco, Jr.* Department of Chemical Engineering, Tennessee Technological University, Box 5013, Cookeville, Tennessee 38505

The statistical associating fluid theory for potentials of variable attractive range (SAFT-VR) has been used for the phase equilibrium calculations of 49 pure refrigerants divided into eight classes: hydrofluorocarbons (HFCs), hydrochlorofluorocarbons (HCFCs), chlorofluorocarbons (CFCs), chlorinated hydrocarbons (CHCs), perfluorocarbons (PFCs), hydrofluoroethers (HFEs), C1-C6 hydrocarbons (HCs), and fluoroiodides (HIs). The optimized values of the pure component parameters for the model are obtained by fitting to the available experimental data such as the vapor pressure and saturated phase densities of each of the pure components. The correlations using the model were in good agreement with experimental data for most of the substances. In our companion paper, these parameters are used with standard combining rules to predict and correlate mixture phase properties based on the pure components discussed in this work. 1. Introduction Refrigerators in the late 19th and the 20th centuries used the toxic gases, ammonia (NH3), methyl chloride (CH3Cl), and sulfur dioxide (SO2) as refrigerants. After a series of fatal accidents in the 1920s when methyl chloride leaked out of refrigerators, a search for a less toxic replacement begun as a collaborative effort of three American corporationssFrigidaire, General Motors, and Du Pont. Thomas Midgley, Jr., of General Motors synthesized the first chlorofluorocarbon (CFC-12, dichlorodifluoromethane) in 1928 as a safe chemical for refrigerators used in large commercial applications.1 In 1974, two chemists from the University of California showed that the CFCs could be a major source of inorganic chlorine in the stratosphere, which could become active chlorine (due to their photolytic decomposition by ultraviolet radiation) and destroy the ozone in the stratosphere.1 In 1987, 27 nations signed the “Montreal Protocol To Reduce Substances That Deplete the Ozone Layer” 2 an environmental treaty that ensured 50% reduction in the production of CFCs having high ozone depletion potential (ODP) and global warming potential (GWP). The London Amendment to the Protocol in 1990 and the Copenhagen Amendment in 1992 stopped the production of CFCs by January 1, 1996.2 In response to the Montreal Protocol, the industry developed two classes of halocarbon substitutessthe hydrochlorofluorocarbons (HCFCs) and the hydrofluorocarbons (HFCs). However, HCFCs still contain chlorine and that makes it possible for them to destroy ozone. The Copenhagen Amendment calls for their production to be eliminated by the year 2030.3 The chlorine-free compounds are considered one of the best substitutes for reducing stratospheric ozone loss. Hence HFCs, hydrofluoroethers (HFEs), fluoroiodo compounds (FI), hydrocarbons (HCs), etc. are being considered. These new generation refrigerants are evaluated based on a number of factors including toxicity, insulating * To whom correspondence should be addressed. Tel.: (931)372-3606. Fax: (931)372-6352. E-mail: [email protected].

ability, flammability, physical stability, solubility, cost, ODP, GWP, compatibility, chemical stability, performance, and permeability.4 The HFCs have gained importance as an effective substitute for the CFCs (first generation refrigerants) and the HCFCs (second generation refrigerants) in some applications. These next generation blowing agents (such as R245fa, R365mfc) are also well-accepted by the polyurethane foam industries (thermal conductivity similar to that of R141b, reduction in total equivalent warming impact (TEWI), and hence global warming) and are in full commercial production.5 HFEs are being considered as new generation refrigerants and blowing agents, although they are still in the evaluation phase. Thermodynamic modeling using computational methods has gained popularity owing to the inexpensive and expedient nature of this approach in comparison with traditional experiments. Modeling of the phase behavior using complex molecular-based equations of state (EOS) is more complicated and computationally expensive than cubic EOS. Complex thermodynamic modeling has been a key tool for understanding the phase behavior of a wide variety of systems when there is very limited experimental data available. For example, thermodynamic modeling helps in the development of new hightemperature processes, in examining the phase stability of the mixtures at various temperatures, and in predicting the properties of a toxic, hazardous, or an expensive compound over a broad range of temperatures and pressures.6 Additionally, owing to the molecular complexity of the non-ozone-depleting substances being developed (i.e., HFCs and HFC mixtures), complex thermodynamics models are required. This paper is organized as follows. Section 2 provides an insight to the different EOS that were used for modeling refrigerants. The specifications of the model used in this work, SAFT-VR, are provided in section 3. Section 4 discusses the approach and the SAFT-VR correlations for the 49 compounds considered in this work. Conclusions are drawn in the final section.

10.1021/ie048863e CCC: $30.25 © 2005 American Chemical Society Published on Web 05/24/2005

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2. Review of Models Modeling of HFCs effectively started in the late 1960s7 and has been a burgeoning field from that time. In the mid-1970s, EOS were formulated specifically for fluorocarbons, and they were used for a wide range of refrigerants.8 The next attempt to model fluorocarbon mixtures was made by Fukuzato et al.9 as they modified the Benedict-Webb-Rubin EOS (BWR EOS) and predicted the vapor liquid equilibrium of these substances. In the late 1980s, Kadhem et al.10 modified the SoaveRedlich-Kwong EOS to model CFCs, HFCs, and fluorocarbons. In the early 1990s, Nishiumi et al.11 extended the BWR EOS with five polar parameters and modeled fluorocarbons, chloroform, and carbon tetrachloride. An EOS that was developed in the late 1980s and has gained considerable popularity in both the academic and industrial communities is the Statistical Associating Fluid Theory (SAFT). Chapman, Gubbins, Jackson, and Radosz at Cornell University and Exxon Research12,13 developed SAFT based on the thermodynamic perturbation theory of Wertheim.14-17 SAFT was parameterized for a wide range of fluids including organic compounds, light and heavy polymers, water, etc. It was shown to correlate accurately multicomponent phase equilibria at low and high pressures.18,19 Numerous modifications and improvements to SAFT were proposed and are being used for various compounds.20 Therefore, it is not surprising to find several versions of SAFT with similar underlying concepts, such as SAFT hard-sphere (SAFTHS),21 SAFT Lennard-Jones (SAFT-LJ),51 soft-SAFT,52 perturbed-chain SAFT (PC-SAFT),53 polar SAFT,54 SAFT with variable range (SAFT-VR),22,23 and SAFT with variable range for electrolytes (SAFT-VRE)55 in the literature. In 1997, Galindo et al.24 used the SAFT-HS model, one of the versions of the SAFT, to model pure HFCs, water, and hydrogen fluoride and their mixtures. In 1998, Galindo et al.25 modeled HFCs and their mixtures using a new version of SAFT known as the Statistical Associating Fluid Theory with variable range (SAFTVR). The SAFT-VR model predictions had excellent agreement with the experimental data for both pure component HFCs and HFC mixtures.25 SAFT-VR also was used for modeling a wide variety of systems such as xenon/alkanes,26 long-chain n-alkanes,27 alkane mixtures,28 perfluoroalkane/alkane mixtures,29 absorption of short-chain hydrocarbons in polymers,30 etc. Hence, SAFT-VR was used to model the pure components and mixtures that were chosen in this work because it has already shown great success in modeling a wide variety of compounds. In this work, the robustness of SAFTVR is demonstrated in modeling several classes of refrigerants. 3. SAFT-VR Equation of State Since SAFT-VR and its details have been reported in various works previously,22-29 we will explain here the salient features specific to our applications. In the SAFT-VR approach, the fluids are modeled as chains of tangentially-bonded hard, equal-sized spheres interacting with attractive potentials of variable range. The variable range potential models the van der Waals longrange forces including dispersion as well as permanent induced polar forces. Short-ranged attractive sites mediate the molecular association, and they also model the short-ranges polar anisotropic effects.

Figure 1. Model depicting the off-center square-well sites.

A fixed number of sites of off-center square-wells 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 refrigerants having more than one carbon atom are modeled with multiple fused hard spheres to describe the nonspherical shape of these molecules. As shown in Figure 1, two different types of sites are colored white and black; bonding is allowed only between the white and the black sites. These two different attractive sites account for the anisotropy of the dipolar interactions. The two sites allow the molecules to form ring aggregates48 as well as chain aggregates, although the former is not used here. The noninteger value for the number of segments in a chain (m) models its anisotropy. This parameter is fitted to give the best agreement with the experimental data, although it is important to retain a physically reasonable molecular shape to model the aspect ratio of the chain. The sites are normally placed at a distance of rd/σ ) 0.25 from the center of the sphere so that, once rc is determined, the bonding volume is known.8 The flexibility of SAFT-VR is exhibited by modeling the pure component phase behavior of HFCs, CFCs, HCFCs, hydrocarbons (C1-C6), and a few other refrigerants. Hydrocarbons and the other compounds that have zero dipole moment have no association to be included in the model. Hence, while modeling these compounds, one does not include the association contribution; thereby, these substances do not have parameters rc* and hb. For refrigerants having a nonzero dipole moment, irrespective of their molecular structure, we have assumed that they have two sites of association. This approach is consistent with other researchers who model strong polarity via association.8 4. Approach and Results Approach. Theoretical phase diagrams for eight classes of pure refrigerants (namely, PFCs, CFCs, CHCs, HCFCs, HFCs, HFEs, HCs, and hydroiodides (HIs)) are obtained using the SAFT-VR model with a square-well potential. The number of parameters varies based on the type of interactions of the individual components. To determine the pure component parameters of SAFT-VR for the compounds involved in this work and to predict/correlate the VLE properties, there

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Table 1. Pure Component Parameters of HFCs refrigerant

molecular formula

HB/kb (K)

MF/kb (K)

HFC23 HFC32 HFC125 HFC134a HFC143a HFC152a HFC245 HFC227eaa HFC236ea HFC236fa HFC245fa HFC365mfc HFC338mccqb

CHF3 CH2F2 CHF2CF3 CH2FCF3 CF3CH3 CHF2CH3 CH3CF2CF3 CF3CHFCF3 CF3CHFCHF2 CF3CH2CF3 CF3CH2CHF2 CF3CH2CF2CH3 CF3CF2CF2CH2F

972.8689 883.4331 1204.4841 1288.1694 1280.0048 1347.3108 1604.0523 1204.2474 1776.1013

100.2682 164.2553 116.3186 136.7538 99.4039 120.0388 117.9799 164.0270 146.3472 135.2120 146.5357 202.3236 161.9243

1894.1320 2106.6870 1684.7308

r c* 0.7164 0.6731 0.7307 0.6877 0.7584 0.7420 0.7099 0.7496 0.7531 0.6761 0.5827 0.6522

σ (Å)

m

λ

OBJ

N

exptl data source

3.7736 3.2098 4.2358 3.9920 4.1079 3.8583 4.7965 4.6216 4.6513 3.1123 4.8750 4.6180 4.7935

1.1237 1.6078 1.2355 1.4053 1.2054 1.3573 1.0743 1.7526 1.1609 3.6092 1.0400 1.4488 1.3467

1.9004 1.6942 1.8024 1.8110 1.8635 1.8426 1.8346 1.5770 1.6579 1.6935 1.8155 1.7545 1.8301

1.669E-02 1.249E-02 1.225E-03 6.260E-03 1.560E-02 2.935E-02 2.032E-02 3.820E-05 7.947E-03 3.572E-03 1.628E-03 3.895E-03 8.500E-06

13 15 19 25 21 26 21 42 32 41 46 9 26

32 32 32 32 32 32 32 33, 34 35 36, 37 38 39 40

a Compound was parameterized using experimental vapor pressure and saturated liquid volume data only. b Compound was parameterized using experimental vapor pressure data only.

is a need to enforce the phase equilibrium constraints for the liquid and vapor pure component phases. The equations are nonlinear in nature and, hence, require the use of a method that finds the roots of a system of nonlinear equations. The Newton-Raphson (NR) method, which is a fixed-point iterative method, was used here to find the roots of the series of coupled, nonlinear equations that result. The parameters for each pure component are obtained by fitting vapor pressure, saturated liquid, and vapor volumes based on the availability of experimental data. We use VLE data during parameterization because we desire to use these parameter sets for mixture phase predictions and in finding important mixture phase features such as azeotropes and miscibility gaps. The Simplex method31 was used to minimize the objective function, shown in eq 1. This function is appropriately weighted to enhance the predictions of vapor pressure and liquid volume. The degree of weighting made is dependent on the properties that we are trying to correlate accurately. Correlating the saturated liquid volume via equations of state has been a challenge for thermodynamic modelers; hence the higher weightage to the least squares part of the saturated liquid volumes. Vapor pressure correlation is also important in mixture calculations; hence we weight its least squares as well. The objective function (OBJ) is given as

OBJ )

(

1 N

[ ( N

5

∑ i)1

Pexp i

) (

Vliqexp - Vliqmodel i i Vliqexp i

)

Pexp - Pmodel i i 2

N

+

∑ i)1

2

N

∑ i)1

+ 50

)]

Vvapexp - Vvapmodel i i Vvapexp i

2

(1)

where N is the number of experimental points and coefficients for the least squares are the weightage given for the pure components. This methodology is a local minimization scheme and is consistent with previous work.21-30 The EOS parameters are supposed to describe the interactions and size of the molecule. The parameters HB, MF, rc*, and λ describe the interactions and their range while σ and m describe the size of the molecules. In total, 49 pure components of eight different classes have been studied. Results. The VLE correlations of the pure components for the various classes of refrigerants are presented in this section. The optimized parameters for the

pure components that were used for the correlations for all the compounds studied are tabulated in Tables 1-5. Table 1 provides the pure component parameters for the HFCs studied. The normalized objective function value provides a measure of the extent to which the SAFTVR model can correlate the pure component phase properties. Due to the scarcity of experimental data for new refrigerants such as HFC227ea where saturated vapor volumes were not available, the parameterization was performed based on the vapor pressure and saturated liquid volumes alone. Figure 2a shows the vapor pressure curves for all the HFCs listed in Table 1. Figure 2b shows the saturated liquid volume curves for the compounds in Table 1. The saturated liquid volume and vapor pressure correlations made using SAFT-VR are compared with the experimental data. The saturated vapor volume correlations with experimental data are not provided, as it is comparatively easier to correlate vapor volumes than liquid volumes and vapor pressure. It is seen from Figure 2a,b that the correlations are in good agreement with the available experimental data. The most noticeable difference is visible in the T-V (temperaturevolume) plots near the critical point. The difference could be accounted for by using a crossover function as done in SAFT-VRX,49 but in this work we are not interested in increasing the number of parameters of a model at the expense of improved critical region performance. On the basis of some approximations used in the development of SAFT-VR, the range for the squarewell potential (λ) is limited to values between 1.1 and 1.8. Table 1 shows parameters for some compounds that lie slightly outside the upper limit and yet correlate the pure component phase behavior well. We will comment on this in our companion paper.50 Table 2 provides the pure component parameters for the model for six CFCs. The pure component properties of CFCs were also correlated to show that SAFT-VR could be used to model the phase behavior of CFCs. The saturated liquid volume and the vapor pressures were correlated and plotted in Figure 3a,b to compare with the experimental data that are available. It was found that the predictions were in good agreement with the experimental data. Though CFCs are phased-out and are mostly not in use, the pure component phase behavior of these compounds were chosen to be correlated using SAFT-VR to demonstrate the versatility of the model. Table 3 provides the pure component model parameters for all the hydrocarbons that have been studied.

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Figure 2. (a) Vapor pressure curves for HFCs. The symbols are experimental data (O, R23; 0, R32; 4, R125; 3, R134a; , R143a; ), R152a; ], R245; *, R245fa; +, R365mfc; ∞, HFC338mccq; :, R227ea; /, R236ea; †, R236fa), and the solid lines represent the model. (b) Saturated liquid volume curves for HFCs. The symbols are experimental data (O, R23; 0, R32; 4, R125; 3, R134a; , R143a; ), R152a; ], R245; *, R245fa; +, R365mfc; ∞, HFC338mccq; :, R227ea; /, R236ea; †, R236fa), and the solid lines represent the model.

Since these compounds have negligible or zero dipole moments, the association contribution of SAFT-VR are “turned off”. Hence, these compounds have only four parameters in the model.

Figure 3. (a) Vapor pressure curves for CFCs. The symbols are experimental data (+, R11; O, R12; 0, R13; :, R113; ], R114; 4, R115), and the solid lines represent the model. (b) Saturated liquid volume curves for CFCs. The symbols represent the experimental data (+, R11; O, R12; 0, R13; :, R113; ], R114; 4, R115), and the solid lines represent the model.

Figure 4a,b show the vapor pressure and the saturated liquid density curves for hydrocarbons. Hydrocarbons are viable refrigerants due to their inexpensive nature, zero ODP, and low GWP. Pentanes are also used in the polyurethane industry as blowing agents at certain pressures and temperatures, although their flammability is always an issue. The correlations of

Table 2. Pure Component Parameters for CFCs refrigerant

molecular formula

HB/kb (K)

MF/kb (K)

rc*

σ (Å)

m

λ

OBJ

N

exptl data source

R11 R12 R13 R113 R114 R115

CCl3F CCl2F2 CClF3 CCl2FCClF2 CClF2CClF2 CClF2CF3

1488.4978 1059.3853 622.7778 1589.8039 1403.1424 1253.3747

166.0726 176.3249 263.7340 171.1703 216.5494 130.0400

0.7862 0.7103 0.6551 0.7392 0.7035 0.7251

4.5401 4.5135 4.5117 4.8090 5.1051 4.8028

1.1990 1.1083 1.0347 1.3208 1.0949 1.1028

1.7435 1.7255 1.4263 1.7835 1.6033 1.7643

9.751E-02 1.350E-02 6.159E-03 4.210E-03 3.766E-02 7.356E-03

19 22 21 26 24 16

32 32 32 32 32 32

Table 3. SAFT-VR Model Parameters for Hydrocarbons refrigerant

molecular formula

MF/kb (K)

σ (Å)

m

λ

OBJ

N

exptl data source

R50 acetylene R170 R1150 R1270 R290 R600 R600a pentane isopentane cyclopentane hexane isohexane

CH4 C2H2 C2H6 C2H4 C3H6 C3H8 C4H10 C4H10 C5H12 C5H12 C5H10 C6H14 C6H14

109.4245 252.5500 136.2276 140.8215 142.2193 172.2703 427.6538 171.6701 186.1341 197.5895 190.8847 191.3876 157.5497

3.2066 3.3714 3.1894 3.1681 4.4123 3.4300 4.7256 3.5232 3.5583 3.7044 3.4305 3.6317 3.4968

1.3568 1.5039 1.9533 1.8220 1.0152 2.1728 1.3109 2.4942 2.8795 2.5773 2.6607 3.1504 3.3541

1.6101 1.4030 1.6635 1.6159 1.8172 1.6153 1.3319 1.6407 1.6466 1.6275 1.6949 1.6591 1.7419

1.687E-02 7.500E-02 3.513E-02 3.045E-02 4.302E-02 7.324E-03 6.094E-02 3.408E-02 2.932E-02 1.445E-02 2.622E-02 2.161E-02 1.727E-02

20 15 20 20 25 24 23 29 42 35 39 42 23

32 32 32 32 32 32 32 32 41 41 41 41 41

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Table 4. Pure Component Parameters for HCFCs refrigerant

molecular formula

HB/kb (K)

MF/kb (K)

r c*

σ (Å)

m

λ

OBJ

N

exptl data source

R21 R22 R123 R124 R141b R142b HCFC225caa HCFC225cba

CHCl2F CHClF2 CHCl2CF3 CHClFCF3 CCl2FCH3 CClF2CH3 CHCl2CF2CF3 CHClFCF2CClF2

1175.6846 891.7308 1614.2383 1559.6866 1222.5997 1470.7513 1680.2662 1803.3695

240.1404 131.6616 126.9291 108.8705 175.4317 117.6485 228.9136 159.9992

0.8173 0.7769 0.7870 0.7739 0.8006 0.7743 0.6342 0.8169

4.5324 3.5608 4.2615 4.3406 4.1539 4.5988 4.9262 5.0673

1.0107 1.6388 1.5113 1.2498 1.5915 1.0130 1.3862 1.1756

1.5544 1.7706 1.8284 1.8207 1.7255 1.8702 1.6911 1.6938

9.180E-02 5.673E-03 8.139E-03 2.900E-02 1.348E-03 2.168E-02 4.487E-03 2.152E-03

19 22 18 18 19 22 13 13

32 32 23 32 55 32 42 42

a

Compounds were parameterized using experimental vapor pressure and saturated vapor volume data only.

Figure 4. (a) Vapor pressure curves for hydrocarbons. The symbols are the experimental data points (, R50; ×, acetylene; /, R170; +, R1150; x, R290; × inside a square, R1270; ), R600; ∞, R600a; :, pentane; ], isopentane; 4, cyclopentane; 0, hexane; O, isohexane), and the solid lines are the model predictions. (b) Saturated liquid volume curves for hydrocarbons. The symbols are the experimental data points (, R50; ×, acetylene; /, R170; +, R1150; x, R290; × inside a square, R1270; ), R600; ∞, R600a; :, pentane; ], isopentane; 4, cyclopentane; 0, hexane; O, isohexane), and the solid lines are the model predictions.

saturated liquid volume and vapor pressures of the hydrocarbons (C1-C6) were plotted along with the experimental data for comparison. They were found to be in good agreement with the experimental data. Other groups working on the parameterization of pure components using SAFT-VR have provided different sets of parameters for hydrocarbons.22 Galindo et al.25 also report parameters for three HFCs (R32, R125, and R134a) that are different from the set of parameters that are provided in Table 1. All the parameter sets have good agreement with the experimental data for the pure component. The reason for the same compound having multiple parameter sets might lie in a host of reasons including: using a different objective function, using

Figure 5. (a) Vapor pressure curves for HCFCs. The symbols are the experimental data (+, R21; ∞, R22; :, R123; ], R124; 4, R141b; 0, R142b; O, R225ca; ×, R225cb), and the solid lines are the model correlations. (b) Saturated liquid volume curves for HCFCs. The symbols are the experimental data (+, R21; ∞, R22; :, R123; ], R124, 4, R141b; 0, R142b; O, R225ca; ×, R225cb), and the solid lines are the model correlations.

different number of experimental data points for optimization, using different ranges of temperature, etc., which can lead to a change in the parameter space. Having multiple sets of parameters for the pure components can pose a problem when one has to choose “a parameter set” for mixture phase predictions. The effect of multiple sets of parameters for a compound on mixture phase predictions is discussed in more detail in our following paper.50 SAFT-VR was also used to parameterize the secondgeneration refrigerants in order to correlate the saturated liquid, vapor volume, and vapor pressure. Table 4 provides the pure component model parameters of this class of refrigerants that were a temporary replacement for CFCs. Figure 5a,b provide the vapor pressure and the saturated liquid volume curves for the HCFCs that were studied in this work. The correlations were compared to the experimental data that are available for

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4803 Table 5. SAFT-VR Pure Component Parameters for the CHCs, PFCs, HFEs, and FI molecular formula

refrigerant

HB/kb (K)

MF/kb (K)

0.7718 0.7289

exptl data source

σ (Å)

m

λ

OBJ

N

5.0076 4.0288 4.0046

1.0379 1.5393 1.0446

1.7448 1.8641 1.5920

2.330E-02 1.832E-02 3.700E-02

29 15 43

32 32 32

HFEs 0.5300 2.7746 0.8150 4.5269

4.9011 1.8959

1.8572 1.4680

3.568E-01 1.375E-01

25 20

43, 44 43, 44

0.7209

6.2755

1.5545

1.7788

2.000E-06

44

45

3.9915 3.2444 4.5736

1.0661 3.7263 1.5650

1.6876 1.6887 1.3162

3.253E-02 2.986E-02 4.104E-05

13 20 16

32 32 46, 47

rc* CHCs

R10 R20 R40

CCl4 CHCl3 CH3Cl

1433.1316 886.5489

242.5245 163.4429 254.5389

R245mc R347mcc

CF3CF2OCH3 CF3CF2CF2OCH3

2004.2268 1466.0097

92.0179 222.3136

FIa

CF3I

1556.6506

84.4212

PFCs R14 C318 Sifren 46a a

CF4 C4F8 C3F8

110.1190 129.5800 411.3450

Compound was parameterized using experimental vapor pressure data only.

the individual compounds, and it was found that they were in good agreement. HCFCs 225ca and 225cb do not have any saturated vapor densities reported in the literature; hence only their liquid densities and vapor pressures were used for their pure component parameterizations. Note that, like the HFCs in Table 1, Table 4 also shows parameters for some compounds that have a value for λ that lies just outside the upper limit and yet correlate the pure component phase behavior well. Table 5 provides the pure component parameters for four classes of refrigerants such as perfluorocarbons, hydrofluoroethers, fluoroiodides, and chlorinated hydrocarbons that are characterized as refrigerants. Figure 6a,b illustrates the vapor pressure and saturated liquid density curves for the pure components discussed in Table 5. In Table 5 and Figure 5a,b we work with a large variety of compounds such as chlorinated hydrocarbons, cyclic compounds, ethers, and fluoroiodides. Two HFEs that were used in this study are HFE245mc and HFE347mcc. Liquid volume and vapor pressure data were only available for these compounds; hence, these were only used for their parameterizations. The predictions made using SAFTVR were plotted against the experimental data in Figure 6a,b for comparison. It is observed from the figures that the correlations were in good agreement to the experimental data that were available. The overall results obtained from our 49 compounds show that SAFT-VR predicts not only the vapor pressure but also the saturated liquid volumes well. The vapor pressure and the saturated liquid volume curves show that weighting given to these properties in the objective function aids in their correlation. The representative curves provided here demonstrate the ability of SAFT-VR to model a wide variety of compounds. Figures 2-6 provide a very good description of the phase behavior of the compounds discussed in this study, although the theory overpredicts the critical temperature and, therefore, the critical pressure. This is a common feature to all EOS, as the phase coexistence curve tends to flatten out at the critical point in comparison to the parabolic nature of the curve at lower pressures or temperatures. 5. Conclusions The main objective of this work was to correlate the pure component properties of refrigerants using SAFTVR and to use the parameters obtained in our companion paper for mixture predictions. A wide variety of

refrigerants such as HFCs, HCFCs, CFCs, PFCs, etc. were chosen to be parameterized using SAFT-VR, and their predictions are compared with the experimental data available. An ample amount of experimental data was utilized for the pure component parameterization. In our companion paper,50 these results will be used in the prediction and correlation of mixture phase properties based on the pure components discussed in this work. The pure component parameters will be used with appropriate mixing rules to obtain the interaction parameters for the mixtures. Prediction of mixture

Figure 6. (a) Vapor pressure curves for all the pure components in Table 5. The symbols are the experimental data points (+, R10; O, R20; 0, R40; 4, HFE245mc; ×, HFE347mcc; ], R14; /, C318), and the solid lines are the model correlations. (b) Saturated liquid density curves for the compounds in Table 5. The symbols are the experimental data points (+, R10; O, R20; 0, R40; 4, HFE245mc; ×, HFE347mcc; ], R14; /, C318), and the solid lines are the model correlations.

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phase features such as azeotropes, miscibility gaps, etc. are vital for the design of a process. This method of predicting mixture properties gains substantial significance due to the scarce availability of VLE/LLE/VLLE experimental data. In the correlation of mixture phase properties, we use a binary interaction parameter (kij value), which reduces the relative deviation from experimental data. In the following work, we look to transfer the kij value to similar mixtures where no experimental data exist in order to suggest alternate refrigerant mixture blends for the existing refrigerants. 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) Midgley, T.; Henne, A. Organic fluorides as refrigerants. Ind. Eng. Chem, 1930, 22, 542. (2) The Montreal Protocol on Substances that Deplete the Ozone Layer. Ozone Secretariat, United Nations Environment Program: 2000. (3) Creazzo, J. A.; Hammel, H S.; Cicalo, K J.; Schindler P. ZeroODP Blowing Agents for Polyurethane Foams. Presented at the Polyurethane World Congress, 1993. (4) 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. (5) U.S. EPA website; http://www.epa.gov/ebtpages/air.html. (6) Decaire, B. R.; Pham, H. T.; Richard, R. G.; Shankland, I. R. Blowing agents: the next generation. J. Cell. Plast. 1994, 30, 1. (7) Siebert, E. D. Equation of state of mixtures of nonspherical molecules. Diss. Abstr. Int. B 1970, 30, 5000. (8) Kondo, H.; Watanabe, K.; Tanishita, I. Equations of state of several fluorocarbon refrigerants. Formulation of the equations of state. Bull. JSME 1974, 17, 783. (9) Fukuzato, R.; Tomisaka, Y.; Arai, K.; Saito, S. The prediction of binary vapor-liquid equilibrium for fluorocarbon mixtures by use of a modified BWR equation of state. J. Chem. Eng. Jpn. 1983, 16, 147. (10) Kadhem, Q. M. A.; Al-Sahhaf, T. A.; Hamam, S. E. M. Parameters of the modified Soave-Redlich-Kwong equation of state for some chlorofluorocarbons, hydrofluorocarbons and fluorocarbons. J. Fluorine Chem. 1989, 43, 87. (11) Nishumi, H.; Kura, S.; Yokoyama, T. Extended BWR equation of state for fluorocarbons, chloroform and carbon tetrachloride. Fluid Phase Equilib. 1991, 69, 141. (12) Jackson, G.; Chapman, W. G.; Gubbins, K. E. Phase equilibria of associating fluids: Spherical molecules with multiple bonding sites. Mol. Phys. 1988, 65, 1. (13) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New reference equation of state for associating fluids. Ind. Eng. Chem. Res. 1990, 29, 1709. (14) Wertheim, M. S. Fluids with highly directional attractive forces. I. Statistical thermodynamics. J. Stat. Phys. 1984, 35, 19. (15) Wertheim, M. S. Fluids with highly directional attractive forces. II. Thermodynamic directional attractive forces. J. Stat. Phys. 1984, 35, 35. (16) Wertheim, M. S. Fluids with highly directional attractive forces. III. Multiple attraction sites. J. Stat. Phys. 1986, 42, 459. (17) Wertheim, M. S. Fluids with highly directional attractive forces. IV. Equilibrium polymerization. J. Stat. Phys. 1986, 42, 477. (18) Huang, S. H.; Radosz, M. Equation of state for small, large, polydisperse and associating molecules. Ind. Eng. Chem. Res. 1990, 29, 2284.

(19) Huang, S. H.; Radosz, M. Equation of State for small, large, polydisperse and associating molecules: Extension to fluid mixtures. Ind. Eng. Chem. Res. 1991, 30, 1994. (20) Economou, I. G. Statistical associating fluid theory: A successful model for the calculation of thermodynamic and phase equilibrium properties of complex fluid mixtures. Ind. Eng. Chem. Res. 2002, 41, 953. (21) Galindo, A.; Whitehead, P. J.; Jackson, G.; Burgess, A. N. Predicting the high-pressure phase equilibria of water +n-alkanes using a simplified SAFT approach. J. Phys. Chem. 1996, 100, 6781. (22) Gil-Villegas, A.; Galindo, A,; Whitehead, P. J.; Mills, S. J.; Jackson, G. Statistical associating fluid theory for chain molecules with attractive potentials of variable range. J. Chem. Phys. 1997, 106, 4168. (23) Galindo, A.; Davies, L. A.; Gil-Villegas, A.; Jackson, G. The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range. Mol. Phys. 1998, 93, 241. (24) Galindo, A.; Whitehead, P. J.; Jackson, G. Predicting the phase equilibria of mixtures of hydrogen fluoride with water, difluoroethane (R-32) and 1,1,1,2-tetrafluoroethane (HFC-134a) using a simplified SAFT approach. J. Phys. Chem. B 1997, 101, 2082. (25) Galindo, A.; Whitehead, P. J.; Jackson, G.; Burgess, A. N. Prediction of phase equilibria of refrigerant mixtures of difluoroethane (HFC-32), 1,1,1,2-tetrafluoroethane (HFC-134a) and pentafluoroethane (HFC-125) using SAFT-VR. J. Phys. Chem. B 1998, 102, 7632. (26) Eduardo, J. M.; Filipe L.; Martin, F. G.; Jorge, C.; Calado, G.; McCabe, C.; Jackson, G. Thermodynamics of liquid mixtures of xenon with alkanes: (xenon + n-butane) and (xenon + isobutane). J. Phys. Chem. B 2000, 104, 1322. (27) McCabe, C.; Jackson, G. SAFT-VR modeling of the phase equilibrium of long chain n-alkanes. Phys. Chem. Chem. Phys. 1999, 1, 2057. (28) McCabe, C.; Gil-Villegas, A.; Jackson, G. Predicting the high-pressure phase equilibria of methane + n-hexane using the SAFT-VR approach. J. Phys. Chem. B 1998, 102, 4183. (29) McCabe, C.; Galindo, A.; Gil-Villegas, A.; Jackson, G. Predicting the high-pressure phase equilibria of binary mixtures of perfluoro-n-alkanes + n-alkanes using the SAFT-VR approach. J. Phys. Chem. B 1998, 102, 8060. (30) McCabe, C.; Galindo, A.; Garcia-Lisbona, M. N.; Jackson, G. Examining the adsorption (vapor-liquid equilibria) of shortchain hydrocarbons in low-density polyethylene with the SAFTVR approach. Ind. Eng. Chem. Res. 2001, 40, 3835. (31) Reklaitis, G. V.; Ravindran, A.; Ragsdell, K. M. Engineering OptimizationsMethods and Applications; Wiley-Interscience: New York, 1983. (32) Perry, R. H.; Green, D. W.; Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill: New York, 1997. (33) Shi, L.; Duan, Y. Y.; Zhu, M.; Han, L.; Lei, X. Vapor pressure of 1,1,1,2,3,3,3-heptafluoropropane. Fluid Phase Equilib. 1999, 163, 109. (34) Patek, J.; Klomfar, J.; Prazak, J.; Sifner, O. The (P,F,T) behavior of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) measured with a Burnett apparatus. J. Chem. Thermodyn. 1998, 30, 1159. (35) Laesecke, A.; Defibaugh, D. R. Viscosity of 1,1,1,2,3,3hexafluoropropane and 1,1,1,3,3,3-hexafluoropropane at saturated liquid conditions from 262 to 353 K. J. Chem. Eng. Data 1996, 41, 59. (36) Defibaugh, D. R.; Gillis, K. A.; Moldover, M. R.; Schmidt, J. W.; Weber, L. A. Thermodynamic properties of CF3-CHF-CHF2, 1,1,1,2,3,3-hexafluoropropane. Fluid Phase Equilib. 1996, 122, 131. (37) Nicola, G. D.; Giuliani, G.; Polonara, F.; Stryjek, R. Saturated pressure and P-V-T measurements for 1,1,1,3,3,3hexafluoropropane (R-236fa). J. Chem. Eng. Data 1999, 44, 696. (38) Sotani, T.; Kubota, H. Vapor pressures and PVT properties of 1,1,1,3,3-pentafluoropropane (HFC-245fa). Fluid Phase Equilib. 1999, 161, 325. (39) Marrucho, I. M.; Oliviera, N. S.; Dohrn, R. Vapor-phase thermal conductivity, vapor pressure and liquid density of R365mfc. J. Chem. Eng. Data 2002, 47, 554.

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4805 (40) Defibaugh, D. R.; Carrillo-Nava, E.; Hurly, J. J.; Moldover, M. R.; Schmidt, J. W.; Weber, L. A. Thermodynamic properties of HFC-338mccq, CF3CF2CF2CH2F. J. Chem. Eng. Data 1997, 42, 488. (41) Smith, D B.; Srivatsava, R. Thermodynamics of Pure Compounds. A. Hydrocarbons and Ketones; Elsevier Science Publishing Company: Amsterdam, 1986. (42) Widiatmo, J. V.; Maezawa, Y.; Sato, H.; Watanabe, K. Liquid densities and vapor pressure of HCFC 225ca and HCFC 225cb. Fluid Phase Equilib. 1992, 80, 227. (43) Tamai, R.; Urata, S.; Sekiya, A.; Takeyasu, H.; Sato, H. HFE’s as New Generation Blowing Agents. Presented at Polyurethanes Expo, 2001. (44) Ohta, H.; Morimoto, Y.; Widiatmo, J. V.; Watanabe, K. Liquid phase thermodynamic properties of new refrigerants, pentafluoroethyl methyl ether and heptafluoropropyl methyl ether. Presented at the 14th Symposium on Thermodynamic Properties, Boulder, CO, June 25-30, 2000. (45) Duan, Y. Y.; Zhu, M.; Han, L. Experimental vapor pressure data and a vapor pressure equation for trifluoroiodomethane (CF3I). Fluid Phase Equilib. 1996, 121, 227. (46) Bobbo, S.; Fedele, L.; Scattolini, M.; Camporese, R. Compressed liquid densities, saturated liquid densities and vapor pressures of hexafluoro-1,3-butadiene (C4F6). J. Chem. Eng. Data 2002, 47, 179. (47) ASHRAE Handbook Fundamentals 2001; American Society of Heating, Refrigerating, and Air-Conditioning Engineers: Atlanta, 2001. (48) Galindo, A.; Burton, S. J.; Jackson, G.; Visco, D. P.; Kofke, D. A. Improved models for the phase behavior of hydrogen fluoride: Chain and ring aggregates in the SAFT approach and the AEOS model. Mol. Phys. 2002, 100, 2241.

(49) McCabe, C.; Kiselev, S. B. Application of crossover theory to the SAFT-VR equation of state: SAFT-VRX for pure fluids. Ind. Eng. Chem. Res. 2004, 43, 2839. (50) Swaminathan, S.; Visco, D. P. Thermodynamic modeling of refrigerants using statistical associating fluid theory with variable range. 2. Applications to binary mixtures. Ind. Eng. Chem. Res. 2005, 44, 4806-4814. (51) Muller, E. A.; Gubbins, K. E. An equation of state for water from a simplified intermolecular potential. Ind. Eng. Chem. Res. 1995, 34, 3662. (52) Blas, F. J.; Vega, L. F. Prediction of binary and ternary diagrams using statistical associating fluid theory (SAFT) equation of state. Ind. Eng. Chem. Res. 1998, 37, 660. (53) Gross, J.; Sadowski, G. Perturbed chain-SAFT: An equation of state based on perturbed theory of chain molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (54) Jog, P. K.; Sauer, S. G.; Blaesing, J.; Chapman, W. G. Application of dipolar chain theory to the phase behavior of polar fluids and mixtures. Ind. Eng. Chem. Res. 2001, 40, 4641. (55) Galindo, A.; Gil-Villegas, A.; Jackson, G.; Burgess, A. N. SAFT-VRE: Phase behavior of electrolyte solutions with the statistical associating fluid theory for potentials of variable range. J. Phys. Chem. B. 1999, 103, 10272.

Received for review November 24, 2004 Revised manuscript received April 1, 2005 Accepted April 13, 2005 IE048863E