Modeling Viscosities of Pure Compounds and Their Binary Mixtures

Article pubs.acs.org/IECR

Modeling Viscosities of Pure Compounds and Their Binary Mixtures Using the Modified Yarranton−Satyro Correlation and Free Volume Theory Coupled with SAFT+Cubic EoS Ilya Polishuk* and Abraham Yitzhak Department of Chemical Engineering, Ariel University, 40700 Ariel, Israel S Supporting Information *

ABSTRACT: In the current study, two viscosity models, namely, the modified Yarranton−Satyro correlation (MYS) and the free volume theory (FVT) coupled with the SAFT+cubic EoS, have been implemented for correlation and prediction of data of about 20 pure compounds and their binary mixtures. A representative selection of nearly 4000 experimental points covering a large part of the available elevated pressure data has been considered. It has been demonstrated that MYS is characterized by superior predictive potential and exhibits higher overall accuracy. Nevertheless, this approach still does not completely address a fundamental problem of predicting viscosities in the entire PVT range without relying on experimental data.

I. INTRODUCTION The recent investigation on industrial requirements for thermodynamic and transport properties1 carried out by the pertinent Working Party of the European Federation of Chemical Engineering (EFCE) has emphasized a need for predicting phase equilibria, thermodynamic, and transport properties within a single modeling framework. This framework can be created by coupling the PVT equations of state (EoS) with the transport property models. Thus far, several studies2−6 have presented simple approaches coupling empirical density-based viscosity models with cubic EoS. However, the latter equations are characterized by limited accuracy in estimating densities at high pressures in comparison with the molecular-based approaches such as the statistical association fluid theory (SAFT) models.7,8 Therefore, various versions of SAFT seem to be a better alternative for developing advanced frameworks for simultaneous modeling of thermodynamic and transport properties.9−21 A major problem related to these frameworks is a need for fitting of the compound-dependent adjustable parameters, both for the SAFT equations and the viscosity models. While significant progress was achieved in generalizing various versions of SAFT,22−32 the problem of attaching predictive character to viscosity models in wide PVT range has not been satisfactorily solved. It should be pointed out that, unlike most thermodynamic properties of liquids, their viscosities can vary by orders of magnitude, which presents significant difficulty for predictions. Currently, the reliable predictive schemes for modeling liquid viscosities have been developed mostly for the n-alkane series. In this respect, two recent studies of Llovell et al.17,18 coupling the highly accurate free volume theory (FVT)33−44 with the soft-SAFT EoS45−47 present major interest. In particular, it has been found that, although all three FVT adjustable parameters of n-alkanes can be generalized just by the molecular weights,17 this approach might hardly be implemented for hydrofluorocarbons.18 In the previous study,21 an alternative model, namely, the modified Yarranton−Satyro correlation (MYS) coupled with the SAFT+cubic EoS,48 has been proposed. Although this © 2013 American Chemical Society

approach does not completely address an issue of predicting viscosities without relying on experimental data, it makes an initial step in this direction. In particular, it has been demonstrated that the same MYS parameters can be successfully implemented in the extended PVT range for predicting the viscosities of different groups of compounds, such as n-alkanes together with some heavy organic compounds, carbon dioxide jointly with some halocarbons, and certain families of ionic liquids. A purpose of the current study was comparing the accuracies and the predictive capabilities of FVT and MYS, while covering a large part of the available elevated pressure viscosity data. In order to avoid the possible diversities in estimating densities and their influence on modeling viscosities, both FVT and MYS have been coupled with the same PVT EoS, namely, SAFT+cubic, a model whose high accuracy in predicting volumetric data has been discussed previously.7,32,48−55 Both frameworks have been implemented for modeling data of a representative amount of various pure compounds and their mixtures at a wide range of pressures. For this purpose, the mixing rules for MYS have been developed. The details of the approaches under consideration are given below.

II. THEORY The details of the SAFT+cubic EoS have been discussed previously.7,32,48−55 For the non-associating compounds, this model has five parameters, namely, m, c, σ, ε/k, and a. The last three parameters are numerically solved at the pure compound critical point conditions. m and c are currently adjusted to the experimental vapor pressure and density data of particular compounds. The values of SAFT+cubic parameters of compounds considered in this study are listed in Table S1 (see the Supporting Information). Received: Revised: Accepted: Published: 959

September 13, 2013 November 6, 2013 November 7, 2013 November 8, 2013 dx.doi.org/10.1021/ie4030352 | Ind. Eng. Chem. Res. 2014, 53, 959−971

Industrial & Engineering Chemistry Research

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Figure 1. Viscosities of pure n-alkanes. Points: experimental data.61−70 Solid lines: MYS. Dashed lines: FVT.

In order to attach predictive character to the model, m and c can be generalized in various ways, such as the group contribution methods. However, these approaches might be complicated and sometimes inexact. An alternative method is the numerical solution of m and c at two arbitrary density points, the data that similarly to critical constants can be easily accessed in databases such as DIPPR for a large number of compounds.32 In this respect, it seems expedient to develop additional SAFT+cubic approaches based on other robust variations of SAFT, such as SAFT-VR56 or Liang et al.’s version of PC-SAFT.57,58 Having the same number of adjustable parameters, MYS and FVT represent two different approaches for modeling data. While MYS is empirical in nature, FVT has a theoretical basis. MYS is given as follows:21

η (mPa s) = 0.165 ⎛ ⎧ ⎜ ⎪ ⎜ ⎪ ⎜ ⎪ ⎜ ⎪ ⎜ ⎪ MW 4 ⎜ ⎪ c1 + ln 1 + v 4c2 ln × ⎜exp⎨ ⎧ ⎫ ⎜ ⎪ ⎧ ⎪ ⎪ c3P ⎪ ⎨ ⎬ 1.08 v exp ⎪ ⎜ ⎛ ∂P ⎞ ⎪ v ⎪ − ⎩ ⎝ ∂v ⎠T ⎭ ⎜ ⎪ exp⎪ ⎨ − ⎜ ⎪ ⎪ mNAv(σ*)3 ⎪ ⎜ ⎜ ⎪ ⎪ ⎝ ⎩ ⎩

{

⎞ ⎫ ⎟ ⎪ ⎟ ⎪ ⎟ ⎪ ⎟ ⎪ ⎟ T ⎪ ⎪ ⎟ 330 ⎬ − 1⎟ + η0 ⎫ ⎪ ⎟ ⎪ ⎪ ⎟ ⎪ ⎪ ⎟ 1⎬ − 1 ⎪ ⎟ ⎪ ⎪ ⎟ ⎪ ⎪ ⎟ ⎭ ⎭ ⎠

} { }

⎜

⎟

(1) 960

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Figure 2. Viscosities of pure 2,6,10,15,19,23-hexamethyltetracosane (squalane), bis(2-ethylhexyl) phthalate (DEHP), diisodecyl phthalate (DIDP), and 2-ethylhexyl benzoate (EHB). Points: experimental data.71−73 Solid lines: MYS. Dashed lines: FVT.

Figure 3. Viscosities of ionic liquids. Points: experimental data.74−77 Solid lines: MYS. Dashed lines: FVT. 961



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Here v is the molar volume (L/mol) yielded by the SAFT+cubic EoS, P is the pressure (bar), T is the temperature (K), and MW is the molecular weight (g/mol). The rationale behind the empirical structure of MYS was attaching specific functions to its adjustable parameters. In particular, c1 is responsible for estimating the viscosity data under ambient conditions. Its increase moves the calculated values up. c2 is the parameter responsible for the temperature dependence of viscosity. Its increase enhances the temperature dependence as well. c3 is the parameter responsible for the pressure dependence. Its raise makes the dependence weaker. Attaching eq 1 by σ supports its capability to predict viscosities of different compounds with the same values of c1− c3. However, implementing this model to asymmetric mixtures has required formulation of the specific MYS mixing rule for σ (yet distinct by asterisk): σ* =

3

∑i ∑j xixj(miimjj)1.2 σij 3 ∑i (ximii)2.4

(2)

Note that the binary parameter l12 is not applied to eq 2. For other MYS parameters, the simple mixing rule has been adopted: c=

∑ xici

(3)

i

where c = c1 − c3. The second viscosity model considered in this study, FVT, is given as follows: η (mPa s) = 105L V ρ

10RT fV exp[BfV 3/2 ] + η0 3MW

(4)

Here ρ is the density (g/L) yielded by the SAFT+cubic EoS and the units of R are (L bar)/(K mol). f V is the fraction of free volume, which for pure compounds is defined as the difference between the molecular molar volumes and the hard-core volumes: fV =

αρ 100

+

PMW ρ

(5)

RT

In eqs 4 and 5, α is the adjustable parameter related to the molecular barrier energy required for self-diffusion. LV is the adjustable parameter related to the molecular size. The adjustable parameter B characterizes an overlap of free volumes. Unfortunately, the molecular background does not provide quantitative information regarding the values of these parameters. Moreover, since they tend to compensate each other, their roles in fitting the pressure and temperature dependence of viscosity data cannot be clearly identified as in the case of c1 − c3. As a result, all of them should be evaluated simultaneously, which complicates the fitting procedure and hinders generalization. Nevertheless, Llovell et al.17 have provided an effective MW-based generalization scheme of the FVT parameters for n-alkanes. Considering the available elevated pressure data, this scheme has been slightly modified as follows: α = 1.02MW + 5

(6)

L V = −6.39 × 10−4MW + 0.918

(7)

−3

B = 0.0087 exp[−3.813 × 10 MW ]

Figure 4. Viscosities of pure methane, nitrogen, and carbon dioxide at the extreme pressures. Points: experimental data.78−80 Solid lines: MYS. Dashed lines: FVT.

particular mixtures. One of the mixing rules has been proposed by Baylaucq at al.:41,42 1 fv = x ∑i f i

(9)

v

LV =

∑ xiLVi i

B= (8)

1 x ∑i Bi

i

Numerous studies have developed different mixing rules for the FVT adjustable parameters. Each of them is advantageous for

(10)

(11)

These mixing rules substantially improves the results for methane(1)−toluene(2) and methane(1)−n-decane(2); however, 962



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Figure 5. Viscosities of pure benzene, toluene, 1-methylnaphtalene, and cis-Decaline. Points: experimental data.70,81−87 Solid lines: MYS. Dashed lines: FVT.

Table 1. Parameters of the Viscosity Models modified Yarranton−Satyro correlation compound

c1 (dimensionless)

c2 (L/g)4

n-hexane n-heptane n-octane n-decane n-dodecane n-tetradecane n-hexadecane squalane DIDP DEHP EHB CH4 N2 toluene isocetane benzene methylcyclohexane 1-methylnaphtalene cis-decaline carbon dioxide R134a hexafluorobenzene acetone TriEGDME ionic liquids

0.36

3.7 × 1012

0.27 0.34 0.35 0.41 0.43 0.43 0.43 0.47 0.59 0.59 0.59 0.41 0.40 0.43

1.0 9.0 1.0 1.0 1.0 1.0 1.0 1.0 2.5 2.5 2.5 2.5 2.5 3.7

× × × × × × × × × × × × × ×

1012 1012 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1012

c3 [bar−0.5(L/mol)

free volume theory α (J L mol−1 g−1)

LV (Å)

B (dimensionless)

0.0067

eq 6

eq 7

eq 8

0.0095 0.0099 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0080 0.0080 0.0080 0.0095 0.0060 0.0075

37.8049 17.7867 80.2527 140.598 80.5157 94.7970 106.894 115.636 20.1255 31.5768 51.4930 104.576 192.907 282.058

0.59080 0.56130 0.49155 0.74363 0.54816 0.73600 0.47863 0.74410 0.85780 0.79895 0.57504 0.51465 0.37504 0.00609

0.0090 0.0090 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0080 0.0080 0.0080 0.0035 0.0035 0.0047

963

−0.25

]



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Figure 6. Viscosities of pure methylcylohexane, 2,2,4,4,6,8,8-heptamethylnonane (isocetane), hexafluorobenzene, triethylene glycol dimethylether (TriEGDME), 1,1,1,2-tetrafluoroethane (R134a), and propan-2-one (acetone). Points: experimental data.81,86−91 Solid lines: MYS. Dashed lines: FVT.

then the results for mixtures of other compounds are significantly less accurate in comparison to the following mixing rules:36

α=

∑ xiαi i

LV =

∑ xiLVi i

B=

1 x ∑i Bi

i

However, we have found that, for the representative sample of binary systems considered in the current study, the best overall results are yielded by the arrangement of eqs 12−14. In eqs 1 and 4, η0 is the zero density viscosity, typically having a negligible small contribution to the viscosities of liquids. For both approaches under consideration, it has been obtained using Chung et al.’s correlation59 and implemented to mixtures according to the mixing rule of Wilke.60 All the calculations have been performed in the Mathematica 7 software, and the pertinent routines can be obtained from the corresponding author by request. Modeling of viscosities is discussed in the subsequent Results section. Additional properties are considered in the Supporting Information.

(12)

(13)

(14)

Llovell at al.18 have proposed to replace eq 14 by

B=

∑ xiBi i

III. RESULTS Having three adjustable parameters, both FVT and MYS are flexible enough to fit the viscosity data of most compounds in a

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Figure 7. Viscosities of binary mixtures of n-alkanes in the one-phase region. Points: experimental data.62,65 Solid lines: MYS. Dashed lines: FVT.

Figure 8. Viscosities of binary mixtures containing aromatic compounds in the one-phase region. Points: experimental data.81,86,87,92 Solid lines: MYS. Dashed lines: FVT. 965



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wide range of pressures and temperatures nearly precisely. Therefore, evaluation of extrapolative and predictive potentials of these models seems to be more important than comparison of their correlative accuracies. As indicated earlier, both models can be applied to the n-alkane series in a semipredictive manner (see Table 1). Figure 1 depicts the representative results including some recently published data63 that have not been considered previously.21 As seen, both models under consideration can be generally characterized by similar performance, which should be recognized as satisfactorily accurate (keeping in mind the experimental uncertainties and deviations between different data sources). While FVT is more accurate in estimating some data, such as the 298.27 K isotherm of n-dodecane,65 MYS is superior in the case of other data, such as the 273.15 K isotherm of ntetradecane.70 In the preceding study,21 it has been established that the extrapolative capability of the MYS parameters evaluated for nalkanes might be extended far beyond this series. In particular, it has been demonstrated that that triplet of parameters can yield reasonable predictions of the varying by orders of magnitude viscosity data of some heavy organic compounds such as bis(2-ethylhexyl) phthalate (DEHP), diisodecyl phthalate (DIDP), and 2-ethylhexyl benzoate (EHB). Figure 2 demonstrates that unfortunately it is not a case of FVT attached by eqs 6−8, that exhibit particularly poor predictions of the data under consideration. Similar results are obtained also in the case of ionic liquids (Figure 3). While MYS can accurately predict the viscosity data of two families ([PF6]− and [BF4]−) with the same triplet of the adjustable parameter, FVT fitted to the data of [C4min][PF6] yields inaccurate results for the related ionic liquids.

Figure 9. Viscosities of binary mixtures of methane, nitrogen, and carbon dioxide in the one-phase region. Points: experimental data.95,96 Solid lines: MYS. Dashed lines: FVT.

Figure 10. Viscosities of four asymmetric binary mixtures in the one-phase region. Points: experimental data.42,43,89,97 Solid lines: MYS. Dashed lines: FVT. 966


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2.041 3.470 2.946 1.330 3.036 0.369

1−5055 1−4551 1−5028 1−1957 1−5103 1−1000 1−1000 1−1000 1−1000 1−1000 1−1000 6.9−600 16.5−335.6 33.85−692.43 206.9−1393.2 200−1400 1−1400 1−1400

38 24 159 17 120 378 162 162 378 90 90 160 306 132 101 280 439 124

0 0 0 0 0 0 0 0 0 0 0 0 0 0 −0.075 −0.090 −0.025 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.005 0.010 0.015 0

0.336 0.369 0.838 0.532 0.273 0.345 0.293 0.285 0.136 0.571 0.538

7.542 6.541 12.34 8.224 7.955 6.414 15.08 6.479 3.845 16.64 5.004 5.598 9.490 17.10 13.01 5.151 13.09 8.519

5.893 6.571 14.83 47.93 8.328 8.959 6.978 2.200 2.846 15.71 19.23 11.42 31.29 22.00 11.37 16.96 23.69 7.134

Figure 4 depicts the predictions of viscosity data of nitrogen, methane, and carbon dioxide under the extreme pressure conditions. The adjustable parameters of both models have been fitted to the data at the much lower pressures.21 As seen, both models can be characterized by similar accuracy at the lower temperatures and MYS is superior at the higher ones. Figure 5 shows the results for four aromatic compounds for which the high pressure viscosity data are available in the literature,70,81−87 and Figure 6 depicts the rest of the compounds considered in the present study. Unfortunately, it seems impossible to describe all the aromatic compounds with the same set of MYS parameters. One of the possible reasons for this result is the varying configurations of different aromatic molecules. As indicated previously,21 the molecular geometry significantly influences the values of MYS parameters. Nevertheless, it can be seen (Table 1) that the standardized triplet still can be applied to some substances, such as benzene, methylcyclohexane, and 1-methylnaphtalene. At the same time, in the cases of toluene isocetane and cis-decaline, it was a need to correct one of the adjustable parameters, namely, c1. It should be pointed out that the paucity of the high pressure viscosity data currently hinders evaluation of the universality of MYS for particular classes of compounds. Anyways, it is evident that in this respect MYS is once again advanced in comparison to FVT. In particular, as seen, only one parameter of the latter model (B) can be kept constant for all six compounds under consideration. Remarkably, similar results are obtained for carbon dioxide, R134a, and hexafluorobenzene: on one hand a universal triplet of MYS parameters and just a common value of B on the other one. The prediction mixtures in the one phase region are partially presented in Figures 7−10. Table 2 lists the ranges of experimental data, the numbers of experimental points, and the absolute average deviations (AAD%). It should be pointed out that these records are usually closely inter-related. In particular, wider PVT ranges typically result in bigger AAD%. In addition, smaller numbers of experimental points increase the influence of experimental uncertainty. Therefore, the AAD% values themselves might not necessarily be considered as the data having categorical and doubtless importance. However, they become particularly informative while comparing different models. As seen (Figure 7), both MYS and FVT yield comparable results for mixtures of n-alkanes, which, considering the extension of the pressure range, can be recognized as satisfactorily accurate. Since the biggest number of experimental points is available for n-hexane(1)−n-hexadecane(2),62 the results for this system should be considered as the most representative ones. As seen, in this particular case, MYS is slightly more accurate than FVT. The accuracy of predicting mixtures containing aromatic compounds is much less stable (see Figure 8). In particular, for some mixtures, such as n-hexane(1)−toluene(2) and toluene(1)−1-methylnaphtalene(2), both models under consideration yield comparable results. At the same time, while FVT is clearly more accurate for n-heptane(1)−1-methylnaphtalene(2), MYS has doubtless superiority in the cases of benzene(1)− hexafluorobenzene(2), toluene(1)−isocetane(2), and benzene(1)−n-tetradecane(2). Implementation of the models under consideration to light gases and their mixtures at the relatively high temperatures and moderate pressures presents a considerable challenge, since the pertinent values of viscosities are very small. Consequently,

73 73 70 85 96 91 97 97 90 92 92 98 99 100 101 50 51, 102 93, 103 n-C8(1)−n-C12(2) n-C6(1)−n-C12(2) n-C6(1)−n-C16(2) benzene(1)−hexafluorobenzene(2) n-C6(1)−toluene(2) isocetane(1)−cis-decaline(2) n-C7(1)−n-1-methylnaphtalene(2) n-C7(1)−n-methylcyclohexane(2) methylcyclohexane(1)−cis-decaline(2) toluene(1)−1-methylnaphtalene(2) toluene(1)−isocetane(2) benzene(1)−n-C14(2) N2(1)−CH4(2) CH4(1)−CO2(2) CH4(1)−methylcyclohexane(2) CH4(1)−toluene(2) CH4(1)−n-C10(2) R134a(1)−TriEGDME(2)

298.2−373.17 298.1−373.16 298.09−373.24 323.31−373.09 298.23−373.35 293.15−353.15 303.15−343.15 303.15−343.15 293.15−353.15 298.15−363.15 298.15−363.15 313.2−393.2 100−300 323.25−473.75 323−423 293.15−373.15 293.15−393.15 293.15−373.15

reference system

Table 2. Prediction of Mixtures

T range (K)

P range (bar)

number of points

k12

l12

AAD% in predicting densities by SAFT+cubic

AAD% in predicting viscosities by MYS

AAD% in predicting viscosities by FVT


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four asymmetric binary systems, namely, methane(1)−methylcyclohexane(2), methane(1)−toluene(2), methane(1)−ndecane(2), and R134a(1)−TriEGDME(2), have been experimentally investigated at wide PTVx ranges and in representative number of experimental points. The binary adjustable parameters k12 and l12 for three systems have been fitted to the available phase equilibria data (see the Supporting Information). Unfortunately, this practice does not address another problem, namely, the imperfect predictions of densities, which are characteristic for many complex mixtures (see Table 2 and Figure S16 in the Supporting Information). Although in the case of SAFT+cubic these inaccuracies are usually relatively small, their possible impact on predicting viscosities cannot be neglected. The pertinent analysis can hardly be performed for MYS, since this approach cannot be disconnected from the EoS. Unlike that, in the case of FVT, the densities predicted by SAFT+cubic can be easily replaced by the experimental data. Surprisingly, these replacements usually achieve particularly small improvements; for example, in the case of methane(1)− n-decane(2), a system with one of the highest AAD% exhibited by FVT, the results are improved by less than 2%. It can thus be observed that MYS exhibits more stable overall accuracy of predictions. Similar results are obtained in the case of the challenging phase equilibria viscosity data (see Figure 11). Although FVT is superior for carbon dioxide(1)−n-decane(2), it exhibits significant inaccuracy in the case of carbon dioxide(1)−acetone(2).

IV. CONCLUSIONS In the current study, two viscosity models, namely, the modified Yarranton−Satyro correlation (MYS) and the free volume theory (FVT) coupled with the SAFT+cubic EoS, have been implemented for correlation and prediction of data of about 20 pure compounds and their binary mixtures. A representative selection of nearly 4000 experimental points in a wide PVT range has been considered. Both viscosity models have been attached by simple mixing rules for their adjustable parameters. While MYS is an empirical in nature approach, FVT has a solid theoretical background. Unfortunately, this background does not attach the latter model by advanced predictive potential. Only one of its three adjustable parameters can be kept constant while modeling families of similar compounds. Although the FVT adjustable parameters can be generalized as functions of molecular weights for n-alkanes, this approach can hardly be implemented for other families of compounds. In spite of its empirical nature, MYS exhibits superior predictive and extrapolative capacities. In particular, it can accurately describe large groups of compounds with the same values of adjustable parameters. In many cases, it requires just slight changes of one of its parameters. As seen, while this approach presents doubtless progress, it still does not completely address a fundamental problem of predicting viscosities in the entire PVT range without relying on experimental data. Although FVT has achieved better accuracy for certain binary mixtures, the overall advantage of MYS was still apparent. In particular, MYS has demonstrated a better stability of predictions of various systems with maximal AAD% < 20, which was not a case of FVT. Considering the results of other properties presented in the Supporting Information, it could be concluded that at the current stage of research the SAFT-based modeling framework has a nearly universal character and in most of the cases reasonable accuracy. However, its major drawback is lack of

Figure 11. Viscosities of saturated phases in three asymmetric binary mixtures. Points: experimental data.100−103 Solid lines: MYS. Dashed lines: FVT.

factors insignificant for liquids, such as the errors introduced by the generalized expression for η059 and its mixing rule,60 can substantially affect the results. Generally speaking, both FVT and MYS are supposed to perform better at the higher values of viscosities. In the case of light gases and their mixtures, these values appear at elevated pressures and/or very low temperatures. Reference 95 provides an opportunity to test the predictions for the binary mixtures of gases (nitrogen(1)− methane(2)) under cryogenic conditions. As seen (Figure 9), MYS yields nearly precise predictions below 200 K, which is not a case of FVT, which substantially overestimates these data. Unsurprisingly, both approaches are imperfect at the higher temperatures, where FVT still has slight superiority. Asymmetric mixtures often have signifiact practical value and typically present the biggest challenge for modeling. Thus far, 968



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(14) Goel, T.; Patra, C. N.; Mukherjee, T.; Chakravarty, C. Excess Entropy Scaling of Transport Properties of Lennard-Jones Chains. J. Chem. Phys. 129, 2008, 164904. (15) Galliero, G.; Boned, C.; Fernández, J. Scaling of the Viscosity of the Lennard-Jones Chain Fluid Model, Argon and Some Normal Alkanes. J. Chem. Phys. 2011, 134, 064505. (16) Novak, L. T. Fluid Viscosity-Residual Entropy Correlation. Int. J. Chem. React. Eng. 2011, 9, A107. (17) Llovell, F.; Marcos, R. M.; Vega, L. F. Free-Volume Theory Coupled with Soft-SAFT for Viscosity Calculations: Comparison with Molecular Simulation and Experimental data. J. Phys. Chem. B 2013, 117, 8159. (18) Llovell, F.; Marcos, R. M.; Vega, L. F. Transport Properties of Mixtures by the Soft-SAFT + Free-Volume Theory: Application to Mixtures of n-Alkanes and Hydrofluorocarbons. J. Phys. Chem. B 2013, 117, 5195. (19) Burgess, W. A.; Tapriyal, D.; Gamwo, I. K.; Morreale, B. D.; McHugh, M. A.; Enick, R. M. Viscosity Models Based on the Free Volume and Frictional Theories for Systems at Pressures to 276 MPa and Temperatures to 533 K. Ind. Eng. Chem. Res. 2012, 51, 16721. (20) Burgess, W. A.; Tapriyal, D.; Morreale, B. D.; Soong, Y.; Baled, H. O.; Enick, R. M.; Wu, Y.; Bamgbade, B. A.; McHugh, M. A. Volume-Translated Cubic EoS and PC-SAFT Density Models and a Free Volume-Based Viscosity Model for Hydrocarbons at Extreme Temperature and Pressure Conditions. Fluid Phase Equilib. 2013, 359, 38−44. (21) Polishuk, I. Modeling of Viscosities in Extended Pressure Range Using SAFT + Cubic EoS and Modified Yarranton−Satyro Correlation. Ind. Eng. Chem. Res. 2012, 51, 13527. (22) Tihic, A.; Kontogeorgis, G. M.; von Solms, N.; Michelsen, M. L.; Constantinou, L. A Predictive Group-Contribution Simplified PCSAFT Equation of State: Application to Polymer Systems. Ind. Eng. Chem. Res. 2008, 47, 5092. (23) Lymperiadis, A.; Adjiman, C. S.; Galindo, A.; Jackson, G. A; Galindo, A. A Generalisation of the SAFT- γ Group Contribution Method for Groups Comprising Multiple Spherical Segments. Fluid Phase Equilib. 2008, 274, 85. (24) Peng, Y.; Goff, K. D.; dos Ramos, M. C.; McCabe, C. Predicting the Phase Behavior of Polymer Systems with the GC-SAFT-VR Approach. Ind. Eng. Chem. Res. 2010, 49, 1378. (25) dos Ramos, M. C.; Haley, J. D.; Westwood, J. R.; McCabe, C. Extending the GC-SAFT-VR Approach to Associating Functional Groups: Alcohols, Aldehydes, Amines and Carboxylic Acids. Fluid Phase Equilib. 2011, 306, 97. (26) Tihic, A.; von Solms, N.; Michelsen, M. L.; Kontogeorgis, G. M.; Constantinou, L. Analysis and Applications of a Group Contribution sPC-SAFT Equation of State. Fluid Phase Equilib. 2009, 281, 60. (27) Tihic, A.; von Solms, N.; Michelsen, M. L.; Kontogeorgis, G. M.; Constantinou, L. Application of sPC-SAFT and Group Contribution sPC-SAFT to Polymer Systems: Capabilities and Limitations. Fluid Phase Equilib. 2009, 281, 70. (28) Rozmus, J.; de Hemptinne, J.-C.; Ferrando, N.; Mougin, P. Long Chain Multifunctional Molecules with GC-PPC-SAFT: Limits of Data and Model. Fluid Phase Equilib. 2012, 329, 79. (29) Nguyen, T.-B.; de Hemptinne, J.-C.; Creton, B.; Kontogeorgis, G. M. GC-PPC-SAFT Equation of State for VLE and LLE of Hydrocarbons and Oxygenated Compounds. Sensitivity Analysis. Ind. Eng. Chem. Res. 2013, 52, 7014. (30) Vijande, J.; Pineiro, M. M.; Legido, J. L.; Bessieres, D. GroupContribution Method for the Molecular Parameters of the PC-SAFT Equation of State Taking into Account the Proximity Effect. Application to Nonassociated Compounds. Ind. Eng. Chem. Res. 2010, 49, 5867. (31) Paduszynski, K.; Domanska, U. Heterosegmented PerturbedChain Statistical Associating Fluid Theory as a Robust and Accurate Tool for Modeling of Various Alkanes. 1. Pure Fluids. Ind. Eng. Chem. Res. 2012, 51, 12967.

predictivity. In particular, the pure compound parameters and the binary parameters of asymmetric mixtures have to be evaluated relying on experimental data. Consequently, further research should be focused on solving this fundamental problem.

■

ASSOCIATED CONTENT

* Supporting Information S

Figures S1−S9 depict modeling of some additional compounds whose thermodynamic property data are available in the literature. Figures S10−S15 present phase equilibria in some asymmetric binary systems considered in this study, and Figure S16, their densities. Table S1 lists the values of SAFT+cubic parameters of the compounds considered in this study. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +972-3-9066346. Fax: +972-3-9066323. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Hendriks, E.; Kontogeorgis, G. M.; Dohrn, R.; de Hemptinne, J.Ch; Economou, I. G.; Ž ilnik, L. F.; Vesovic, V. Industrial requirements for thermodynamics and transport properties. Ind. Eng. Chem. Res. 2010, 49, 11131. (2) Martins, R. J.; de M. Cardoso, M. J. E.; Barcia, O. E. A New Model for Calculating the Viscosity of Pure Liquids at High Pressures. Ind. Eng. Chem. Res. 2003, 42, 3824. (3) Yarranton, H. W.; Satyro, M. A. Expanded Fluid-Based Viscosity Correlation for Hydrocarbons. Ind. Eng. Chem. Res. 2009, 48, 3640. (4) Satyro, M. A.; Yarranton, H. W. Expanded Fluid-Based Viscosity Correlation for Hydrocarbons Using an Equation of State. Fluid Phase Equilib. 298, 2010, 1. (5) Motahhari, H.; Satyro, M. A.; Yarranton, H. W. Predicting the Viscosity of Asymmetric Hydrocarbon Mixtures with the Expanded Fluid Viscosity Correlation. Ind. Eng. Chem. Res. 2011, 50, 12831. (6) Motahhari, H.; Satyro, M. A.; Yarranton, H. W. Viscosity Prediction for Natural Gas Processing Applications. Fluid Phase Equilib. 322−323, 2012, 56. (7) Polishuk, I. Till Which Pressures the Fluid Phase EOS Models Might Stay Reliable? J. Supercrit. Fluids 2011, 58, 204. (8) Kontogeorgis, G. M. Association Theories for Complex Thermodynamics. Chem. Eng. Res. Des. 2013, 91, 1840−1858. (9) de Wijn, A. S.; Vesovic, V.; Jackson, G.; Trusler, J. P. M. A Kinetic Theory Description of the Viscosity of Dense Fluids Consisting of Chain Molecules. J. Chem. Phys. 128, 2008, 204901. (10) de Wijn, A. S.; Riesco, N.; Jackson, G.; Trusler, J. P. M.; Vesovic, V. Viscosity of Liquid Mixtures: The Vesovic-Wakeham Method for Chain Molecules. J. Chem. Phys. 136, 2012, 074514. (11) Tan, S. P.; Adidharma, H.; Towler, B. F.; Radosz, M. Friction Theory and Free-Volume Theory Coupled with Statistical Associating Fluid Theory for Estimating the Viscosity of Pure n-Alkanes. Ind. Eng. Chem. Res. 2005, 44, 8409. (12) Tan, S. P.; Adidharma, H.; Towler, B. F.; Radosz, M. Friction Theory Coupled with Statistical Associating Fluid Theory for Estimating the Viscosity of n-Alkane Mixtures. Ind. Eng. Chem. Res. 2006, 45, 2116. (13) Quiñones-Cisneros, S. E.; Zéberg-Mikkelsen, C. K.; Fernández, J.; García, J. General Friction Theory Viscosity Model for the PCSAFT Equation of State. AIChE J. 52, 2006, 1600. 969



Article

(32) Polishuk, I. Generalization of SAFT + Cubic Equation of State for Predicting and Correlating Thermodynamic Properties of Heavy Organic Substances. J. Supercrit. Fluids 2012, 67, 94. (33) Allal, A.; Moha-Ouchane, M.; Boned, C. A New Free Volume Model for Dynamic Viscosity and Density of Dense Fluids Versus Pressure and Temperature. Phys. Chem. Liq. 2001, 39, 1. (34) Allal, A.; Boned, C.; Baylaucq, A. Free-volume Viscosity Model for Fluids in the Dense and Gaseous States. Phys. Rev. E 2001, 64, 011203. (35) Zéberg-Mikkelsen, C. K.; Baylaucq, A.; Barrouhou, M.; Boned, C. The Effect of Stereoisomerism on Dynamic Viscosity: A Study of cis-Decalin and trans-Decalin versus Pressure and Temperature. Phys. Chem. Chem. Phys. 2003, 5, 1547. (36) Comuñas, M. J. P.; Baylaucq, A.; Plantier, F.; Boned, C.; Fernández, J. Influence of the Number of CH2-CH2-O Groups on the Viscosity of Polyethylene Glycol Dimethyl Ethers at High Pressure. Fluid Phase Equilib. 2004, 222−223, 331. (37) Reghem, P.; Baylaucq, A.; Comuñas, M. J. P.; Fernández, J.; Boned, C. Influence of the Molecular Structure on the Viscosity of some Alkoxyethanols. Fluid Phase Equilib. 2005, 236, 229. (38) Baylaucq, A.; Comuñas, M. J. P.; Boned, C.; Allal, A.; Fernández, J. High Pressure Viscosity and Density Modeling of Two Polyethers and Two Dialkyl Carbonates. Fluid Phase Equilib. 2002, 199, 249. (39) Boned, C.; Zéberg-Mikkelsen, C. K.; Baylaucq, A.; Daugé, P. High-Pressure Dynamic Viscosity and Density of Two Synthetic Hydrocarbon Mixtures Representative of some Heavy Petroleum Distillation Cuts. Fluid Phase Equilib. 2003, 212, 143. (40) Zéberg-Mikkelsen, C. K.; Watson, G.; Baylaucq, A.; Galliéro, G.; Boned, C. Comparative Experimental and Modeling Studies of the Viscosity Behavior of Ethanol + C7 Hydrocarbon Mixtures versus Pressure and Temperature. Fluid Phase Equilib. 2006, 245, 6. (41) Baylaucq, A.; Boned, C.; Canet, X.; Zéberg-Mikkelsen, C. K.; Quiñones-Cisneros, S. E.; Zhou, H. Dynamic Viscosity Modeling of Methane+n-Decane and Methane+Toluene Mixtures: Comparative study of some Representative Models. Petr. Sci. Technol. 2005, 23, 143. (42) Baylaucq, A.; Boned, C.; Canet, X.; Zéberg-Mikkelsen, C. K. High-Pressure (up to 140 MPa) Dynamic Viscosity of the Methane and Toluene System: Measurements and Comparative Study of Some Representative Models. Int. J. Thermophys. 2003, 24, 621. (43) Canet, X.; Baylaucq, A.; Boned, C. High-Pressure (up to 140 MPa) Dynamic Viscosity of the Methane+Decane System. Int. J. Thermophys. 2002, 23, 1469. (44) Monsalvo, M. A.; Baylaucq, A.; Reghem, P.; Quiñones-Cisneros, S. E.; Boned, C. Viscosity Measurements and Correlations of Binary Mixtures. 1,1,1,2-Tetrafluoroethane (HFC-134a) + Tetraethylene Glycol Dimethylether (TEGDME). Fluid Phase Equilib. 2005, 233, 1. (45) Blas, F. J.; Vega, L. F. Thermodynamic Behaviour of Homonuclear and Heteronuclear Lennard-Jones Chains with Association Sites from Simulation and Theory. Mol. Phys. 1997, 92, 135. (46) Llovell, F.; Pàmies, J. C.; Vega, L. F. Thermodynamic Properties of Lennard-Jones Chain Molecules: Renormalization-Group Corrections to a Modified Statistical Associating Fluid Theory. J. Chem. Phys. 2004, 121, 10715. (47) Llovell, F.; Vega, L. F. Global Fluid Phase Equilibria and Critical Phenomena of Selected Mixtures Using the Crossover Soft-SAFT Equation. J. Phys. Chem. B 2006, 110, 1350. (48) Polishuk, I. Hybridizing SAFT and Cubic EOS: What Can be Achieved? Ind. Eng. Chem. Res. 2011, 50, 4183. (49) Polishuk, I. Implementation of SAFT + Cubic, PC-SAFT and Soave-Benedict-Webb-Rubin Equations of State for Predicting Properties of Binary and Ternary Mixtures of CH4, CO2 and n-C16H34. Ind. Eng. Chem. Res. 2011, 50, 14175. (50) Polishuk, I. Semi-Theoretical vs. Entirely Empirical: Comparing SAFT + Cubic and Soave-Benedict-Webb-Rubin Equations of State. Ind. Eng. Chem. Res. 2011, 50, 11422. (51) Polishuk, I. Implementation of SAFT + Cubic and PC-SAFT for Comprehensive Description of Thermodynamic Properties of nOctane and its Mixtures. J. Supercrit. Fluids 2012, 62, 47.

(52) Polishuk, I.; Katz, M.; Levi, Y.; Lubarsky, H. Implementation of PC-SAFT and SAFT + Cubic for Modeling Thermodynamic Properties of Haloalkanes. I. 11 Halomethanes. Fluid Phase Equilib. 2012, 316, 66. (53) Polishuk, I.; Perel, A. Implementation of PC-SAFT and SAFT + Cubic for Modeling Thermodynamic Properties of Eight 1-Alkenes and their Mixtures. J. Chem. Thermodyn. 2012, 54, 155. (54) Polishuk, I.; Assor, E.; Cohen, N.; Potievsky, R. Implementation of PC-SAFT and SAFT + Cubic for Modeling Thermodynamic Properties of Haloalkanes. II. 7 Haloethanes and their Mixtures. Int. J. Refrig. 2013, 36, 980. (55) Polishuk, I. Implementation of PC-SAFT, GSAFT + Cubic and CPA for Modeling Thermophysical Properties of Selected 1-alkyl-3methylimidazolium Ionic Liquids in Wide Pressure Range. J. Phys. Chem. A 2013, 117, 2223. (56) 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. (57) Liang, X.; Maribo-Mogensen, B.; Thomsen, K.; Yan, W.; Kontogeorgis, G. M. Approach to Improve Speed of Sound Calculation within PC-SAFT Framework. Ind. Eng. Chem. Res. 2012, 51, 14903. (58) Polishuk, I.; Privat, R.; Jaubert, J.-N. A Novel Methodology for Analysis and Evaluation of SAFT-Type Equations of State. Ind. Eng. Chem. Res. 2013, 52, 13875. (59) Chung, T. H.; Ajlan, M.; Lee, L. L.; Starling, K. E. Generalized Multiparameter Correlation for Nonpolar and Polar Fluid Transport Properties. Ind. Eng. Chem. Res. 1988, 27, 671. (60) Wilke, C. R. A Viscosity Equation for Gas Mixtures. J. Chem. Phys. 1950, 18, 517. (61) Oliveira, C. M. B. P.; Wakeham, W. A. The Viscosity of Five Liquid Hydrocarbons at Pressures Up to 250 MPa. Int. J. Thermophys. 1992, 13, 773. (62) Dymond, J. H.; Young, K. J.; lsdale, J. D. Transport Properties of Nonelectrolyte Liquid Mixtures-II. Viscosity Coefficients for the nHexane + n-Hexadecane System at Temperatures from 25 to 100°C at Pressures Up to the Freezing Pressure or 500 MPa. Int. J. Thermophys. 1980, 1, 345. (63) Sagdeev, D. I.; Fomina, M. G.; Mukhamedzyanov, G. Kh.; Abdulagatov, I. M. Experimental Study of the Density and Viscosity of n-Heptane at Temperatures from 298 to 470 K and Pressure up to 245 MPa. Int. J. Thermophys. 2013, 34, 1. (64) Assael, M. J.; Oliveira, C. P.; Papadaki, M.; Wakeham, W. A. Vibrating-Wire Viscometers for Liquids at High Pressures. Int. J. Thermophys. 1992, 13, 593. (65) Dymond, J. H.; Robertson, J.; lsdale, J. D. Transport Properties of Nonelectrolyte Liquid Mixtures-III. Viscosity Coefficients for nOctane, n-Dodecane, and Equimolar Mixtures of n-Octane +nDodecane and n-Hexane + n-Dodecane from 25 to 100°C at Pressures Up to the Freezing Pressure or 500 MPa. Int. J. Thermophys. 1981, 2, 133. (66) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. Viscosity and Density of Five Hydrocarbon Liquids at Pressures up to 200 MPa and Temperatures up to 473 K. J. Chem. Eng. Data 2009, 54, 359. (67) Naake, L.-D.; Wiegand, G.; Franck, E. U. The Viscosity of nDecane to High Temperatures of 573 K and High Pressures of 300 MPa. Z. Phys. Chem. 2002, 216, 1295. (68) Krahn, U. G.; Luft, G. Viscosity of Several Liquid Hydrocarbons in the Temperature Range 298−453 K at Pressures up to 200 MPa. J. Chem. Eng. Data 1994, 39, 670. (69) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. The Viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa and Temperatures up to 473 K. Int. J. Thermophys. 2004, 25, 1339. (70) Ducoulombier, D.; Zhou, H.; Boned, C.; Peyrelasse, J.; SaintGuirons, H.; Xans, P. Pressure (1−1000 bar) and Temperature (20− 970



Article

100 °C) Dependence of the Viscosity of Liquid Hydrocarbons. J. Phys. Chem. 1986, 90, 1692. (71) Harris, K. R.; Bair, S. Temperature and Pressure Dependence of the Viscosity of Diisodecyl Phthalate at Temperatures between (0 and 100) °C and at Pressures to 1 GPa. J. Chem. Eng. Data 2007, 52, 272. (72) Harris, K. R. Temperature and Pressure Dependence of the Viscosities of 2-Ethylhexyl Benzoate, Bis(2-ethylhexyl) Phthalate, 2,6,10,15,19,23-Hexamethyltetracosane (Squalane), and Diisodecyl Phthalate. J. Chem. Eng. Data 2009, 54, 2729. (73) Peleties, F.; Trusler, J. P. M. Viscosity of Liquid Di-isodecyl Phthalate at Temperatures Between (274 and 373) K and at Pressures up to 140 MPa. J. Chem. Eng. Data 2011, 56, 2236. (74) Harris, K. R.; Kanakubo, M.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquid 1-Butyl-3methylimidazolium Tetrafluoroborate: Viscosity and Density Relationships in Ionic Liquids. J. Chem. Eng. Data 2007, 52, 2425. (75) Harris, K. R.; Kanakubo, M.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquids 1-Methyl-3octylimidazolium Hexafluorophosphate and 1-Methyl-3-octylimidazolium Tetrafluoroborate. J. Chem. Eng. Data 2006, 51, 1161. (76) Harris, K. R.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquid 1-Butyl-3methylimidazolium Hexafluorophosphate. J. Chem. Eng. Data 2005, 50, 1777. (77) Harris, K. R.; Kanakubo, M.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquids 1-Hexyl-3methylimidazolium Hexafluorophosphate and 1-Butyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide. J. Chem. Eng. Data 2007, 52, 1080. (78) Abramson, E. H.; West-Foyle, H. Viscosity of Nitrogen Measured to Pressures of 7 GPa and Temperatures of 573 K. Phys. Rev. E 2008, 77, 041202. (79) Abramson, E. H. Viscosity of Carbon Dioxide Measured to a Pressure of 8 GPa and Temperature of 673 K. Phys. Rev. E 2008, 80, 021201. (80) Abramson, E. H. Viscosity of Methane to 6 GPa and 673 K. Phys. Rev. E 2011, 84, 062201. (81) Dymond, J. H.; Robertson, J.; Isdale, J. D. Transport Properties of Nonelectrolyte Liquid Mixtures-IV. Viscosity Coefficients for Benzene, Perdeuterobenzene, Hexafluorobenzene, and an Equimolar Mixture of Benzene + Hexafluorobenzene from 25 to 100°C at Pressures up to the Freezing Pressure. Int. J. Thermophys. 1981, 2, 223. (82) Harris, K. R.; Malhotra, R.; Woolf, L. A. Temperature and Density Dependence of the Viscosity of Octane and Toluene. J. Chem. Eng. Data 1997, 42, 1254. (83) Harris, K. R. Temperature and Density Dependence of the Viscosity of Toluene. J. Chem. Eng. Data 2000, 45, 893. (84) Dymond, J. H.; Glen, N. F.; Isdale, J. D.; Pyda, M. The Viscosity of Liquid Toluene at Elevated Pressures. Int. J. Thermophys. 1995, 16, 877. (85) Barrouhou, M.; Zebérg-Mikkelsen, C. K.; Baylaucq, A.; Boned, C. High-Pressure Viscosity and Density Measurements for the Asymmetric Binary System cis-Decalin + 2,2,4,4,6,8,8-Heptamethylnonane. Int. J. Thermophys. 2003, 24, 93. (86) Zebérg-Mikkelsen, C. K.; Barrouhou, M.; Baylaucq, A.; Boned, C. Viscosity and Density Measurements of Binary Mixtures Composed of Methylcyclohexane + cis-Decalin Versus Temperature and Pressure. Int. J. Thermophys. 2003, 24, 361. (87) Barrouhou, M.; Zebérg-Mikkelsen, C. K.; Baylaucq, A.; Boned, C. High-Pressure Viscosity and Density Measurements for the Asymmetric Binary System cis-Decalin +2,2,4,4,6,8,8-Heptamethylnonane. Int. J. Thermophys. 2003, 24, 937. (88) Et-Tahir, A.; Boned, C.; Lagourette, B.; Xans, P. Determination of the Viscosity of Various Hydrocarbons and Mixtures of Hydrocarbons Versus Temperature and Pressure. Int. J. Thermophys. 1995, 16, 1309. (89) Monsalvo, M. A.; Baylaucq, A.; Quiñones-Cisneros, S. E.; Boned, C. High-pressure Viscosity Behavior of x 1,1,1,2-Tetrafluoroethane (HFC-134a) + (1−x) Triethylene Glycol Dimethylether

(TriEGDME) Mixtures: Measurements and Modeling. Fluid Phase Equilib. 2006, 247, 70; Corrigendum: 2007, 258, 95. (90) Laesecke, A.; Bair, S. High-Pressure Viscosity Measurements of 1,1,1,2-Tetrafluoroethane. Int. J. Thermophys. 2011, 32, 925. (91) Smith, D. S. Density and Viscosity Measurements of Acetone Water Solutions under High Pressure and Controlled Temperatures, 1972, Electronic Theses and Dissertations. Paper 1633. (92) Dymond, J. H.; Awan, M. A.; Glen, N. F.; Isdale, J. D. Transport Properties of Nonelectrolyte Liquid Mixtures. VIII. Viscosity Coefficients for Toluene and for Three Mixtures of Toluene + Hexane from 25 to 100° at Pressures up to 500 MPa. Int. J. Thermophys. 1991, 12, 275. (93) Baylaucq, A.; Boned, C.; Dauge, P.; Lagourette, B. Measurements of the Viscosity and Density of Three Hydrocarbons and the Three Associated Binary Mixtures Versus Pressure and Temperature. Int. J. Thermophys 1997, 18, 3. (94) Hernández-Galván, M. A.; García-Sánchez, F.; Macías-Salinas, R. Liquid Viscosities of Benzene, n-Tetradecane, and Benzene + nTetradecane from 313 to 393K and Pressures up to 60 MPa: Experiment and Modeling. Fluid Phase Equilib. 2007, 262, 51. (95) Diller, D. E. Measurements of the Viscosity of Compressed Gaseous and Liquid Nitrogen + Methane Mixtures. Int. J. Thermophys. 1982, 3, 237. (96) DeWitt, K. J.; Thodos, G. Viscosities of Binary Mixtures in the Dense Gaseous State: The Methane-Carbon Dioxide System. Can. J. Chem. Eng. 1966, 44, 148. (97) Tohidi, B.; Burgass, R. W.; Danesh, A.; Todd, A. C. Viscosity and Density of Methane + Methylcyclohexane from (323 to 423) K and Pressures to 140 MPa. J. Chem. Eng. Data 2001, 46, 385. (98) Audonnet, F.; Pádua, A. A. H. Viscosity and Density of Mixtures of Methane and n-Decane from 298 to 393 K and up to 75 MPa. Fluid Phase Equilib. 2004, 216, 235. (99) Comuñas, M. J. P.; Baylaucq, A.; Boned, C.; Fernández, J. Dynamic Viscosity for HFC-134a + Polyether Mixtures up to 373.15 K and 140 MPa at Low Polyether Concentration. Measurements and Modeling. Ind. Eng. Chem. Res. 2004, 43, 804. (100) Gozalpour, F.; Danesh, A.; Todd, A. C.; Tohidi, B. Viscosity, Density, Interfacial Tension and Compositional Data for Near Critical Mixtures of Methane + Butane and Methane + Decane Systems at 310.95 K. Fluid Phase Equilib. 2005, 233, 144. (101) Kariznovi, M.; Nourozieh, H.; Abedi, J. Phase Composition and Saturated Liquid Properties in Binary and Ternary Systems Containing Carbon Dioxide, n-Decane, and n-Tetradecane. J. Chem. Thermodyn. 2013, 57, 189. (102) Nourozieh, H.; Kariznovi, M.; Abedi, J. Measurement and Correlation of Saturated Liquid Properties and Gas Solubility for Decane, Tetradecane and their Binary Mixtures Saturated with Carbon Dioxide. Fluid Phase Equilib. 2013, 337, 246. (103) Sih, R.; Foster, N. R. Viscosity Measurements on Saturated Gas Expanded Liquid Systems  Acetone and Carbon Dioxide. J. Supercrit. Fluids 2008, 47, 233.

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