Comparison of the a Priori COSMO-RS Models and Group

Article pubs.acs.org/IECR

Comparison of the a Priori COSMO-RS Models and Group Contribution Methods: Original UNIFAC, Modified UNIFAC(Do), and Modified UNIFAC(Do) Consortium Zhimin Xue,† Tiancheng Mu,*,† and Jürgen Gmehling*,‡ †

Department of Chemistry, Renmin University of China, 100872, Beijing, China Department of Industrial Chemistry, Institute for Pure and Applied Chemistry, Carl von Ossietzky Universität Oldenburg, D-26111, Oldenburg, Germany

‡

S Supporting Information *

ABSTRACT: A comparison of the performances of the COSMO-SAC, COSMO-RS(Ol), original UNIFAC, modified UNIFAC(Do), and modified UNIFAC(Do) Consortium for activity coefficients at infinite dilution and binary VLE data is presented. The σ-profiles used in performing COSMO-SAC and COSMO-RS(Ol) calculations were taken from the published σprofile database VT 2005. The predicted results were compared with the experimental data stored in the Dortmund Data Bank and analyzed with respect to the types of components in the mixture. The results show that the UNIFAC models based on experimental data are superior to the a priori COSMO-RS models. have proved to be most reliable.10 Group contribution methods belong to the most important thermodynamic tools for the daily work of a chemical engineer and are therefore integrated in most of the available commercial process simulators (e.g., Aspen Plus, CHEMCAD, Pro/II, HYSIM, etc.). The range of applicability and the quality of the results of these group contribution methods mainly depend on the size of the parameter matrix and the quality of the group interaction parameters. Therefore, a continuous revision, extension, and further development of these predictive methods (especially modified UNIFAC(Do)) is carried out. For this purpose a company consortium11 was founded at the University of Oldenburg. The revised and extended group interaction parameter matrices of the consortium are only available to the sponsors of the project and not available via the different process simulators. The direction of the further developments is influenced by the sponsors, so the models become more and more attractive for the chemical industry. To obtain thorough information of these models, the predicted results with the parameters from the consortium are also presented. In the following part of this article, original UNIFAC is abbreviated as orig. UNIFAC, modified UNIFAC(Do) is abbreviated as mod. UNIFAC(Do), and modified UNIFAC(Do) using the Consortium parameters is abbreviated as mod. UNIFAC(Do) Consortium. A dielectric continuum solvation model 12,13 named COSMO-RS (COnductor-like Screening MOdel for Real Solvents)14−17 was proposed recently. Instead of the calculation of the interactions of structural groups in the mixture, the potential of a surface segment based on the shielding charge

1. INTRODUCTION The reliable knowledge of thermodynamic properties of multicomponent mixtures is of central importance in chemical engineering. Satisfactory experimental data are often not available for the desired temperature, pressure, and composition for the given design problem. It is therefore often necessary to predict the missing phase equilibria with the help of thermodynamic models. Today different predictive models are available. The group contribution concept1 is widely accepted and used for the estimation of thermophysical properties. In group contribution methods, a system is considered as a mixture of predefined independent functional groups and the activity coefficients of the compounds in the mixture are calculated using group interaction parameters. Once the group interaction parameters are available, the activity coefficients in mixtures composed of these structural groups can be calculated. The advantage of group contribution methods is that the number of functional groups is much smaller than the number of chemical compounds. The main limitation of group contribution methods is that they cannot account for isomer or proximity effects. Since the group interaction parameters between all groups in the mixture must be known, they are not applicable for mixtures containing new functional groups. In 1975, Fredenslund et al. combined the solution of groups concept with the UNIQUAC equation. The result was the group contribution method UNIFAC (Universal Quasichemical Functional Group Activity Coefficients).2,3 UNIFAC is one of the most successful group contribution models for the prediction of vapor−liquid equilibria (VLE). Gmehling et al. developed modified UNIFAC(Do)4−8 using group interaction parameters fitted simultaneously to a large amount of reliable experimental data (VLE, hE, γ∞, solid−liquid equilibria (SLE), etc.) stored in the Dortmund Data Bank (DDB).9 The predicted results using modified UNIFAC(Do) © 2012 American Chemical Society

Received: Revised: Accepted: Published: 11809

June 18, 2012 August 15, 2012 August 16, 2012 August 16, 2012 dx.doi.org/10.1021/ie301611w | Ind. Eng. Chem. Res. 2012, 51, 11809−11817

Industrial & Engineering Chemistry Research

Article

density of this segment and the other segments in the mixture is calculated in COSMO-RS. It is assumed that any segment can get in contact with every other segment. The calculation is based on the shielding charge density distribution of the surface elements of the molecules (σ-profiles). In the procedure of deriving the σ-profiles, information on the mutual positions of the segments with respect to each other is lost. While a few experimental data were used to fit the basic parameters, no additional experimental data are required in performing COSMO-RS calculations. It has been extended to predict various thermodynamic properties (VLE, LLE, SLE, etc.) and was also used for many complex systems (ionic liquids,18,19 polymers, surfactant micelles, biomembranes, etc.). The required COSMO calculation has been implemented in various quantum chemistry software packages (Gaussian,20,21 Turbomole,22 DMol3,23 GAMESS,24 etc.), and different versions of COSMO-RS were developed (COSMOtherm,25 COSMO-SAC,26,27 and COSMO-RS(Ol)28). The σ-profile calculations are very time-consuming, especially for large molecules. Until now, only one σ-profile data bank, VT 2005,29 calculated with DMol3 using BP/DNP (double numerical basis with polarization functions) with a total 1432 σ-profiles has been publicly accessible. GC-COSMO models were developed by Mu et al. to simplify the complex σ-profile calculations.30,31 Various comparisons of the predictive capability of the group contribution methods (orig. UNIFAC, mod. UNIFAC(Do), mod. UNIFAC(Ly)) and a priori models (COSMO-SAC, COSMO-RS(Ol)),32 have been carried out; however, complete and detailed information has not yet been published. In this work, a comprehensive comparison of the predicted activity coefficients at infinite dilution and VLE of binary systems with the experimental data stored in the DDB was carried out and the reliability of these models for the different classes of compounds is discussed. The comparisons are useful for engineers to get an idea about the quality of the calculations based on these models. The version of COSMO-RS proposed by Klamt and coworkers was implemented in the software package COSMOtherm. It is a commercial package and is not fully published in the open literature. Since the authors are not able to reproduce the calculation procedure, a comparison with this version is not included in this work. We can see from the paper that the mod. UNIFAC(Do) Consortium (the commercially available UNIFAC) shows only a little improvement compared to the mod. UNIFAC(Do) developed about 20 years ago. Actually, mainly the range of applicability of the mod. UNIFAC(Do) Consortium is larger than that of mod. UNIFAC(Do), since it contains more parameters and can be applied for more systems. In the paper, most of the comparisons are for the published mod. UNIFAC(Do) parameters by Gmehling et al. about 20 years ago and open published COSMO-RS parameters.

The combinatorial part accounts for the influence of the shape and size of the molecules and can be calculated from the information of the pure compounds (eq 2). ⎡ ⎛ V ⎞⎤ V ln γiC = 1 − Vi + ln(Vi ) − 5qi⎢1 − i + ln⎜ i ⎟⎥ ⎢⎣ Fi ⎝ Fi ⎠⎥⎦

where qi denotes the surface area and xi denotes the mole fraction, with qi Fi = ∑j qjxj (3) Vi =

ri ∑j rjxj

(4)

ri is the relative van der Waals volume. In the mod. UNIFAC(Do) model, eq 2 was modified to eq 5 using an empirically changed Vi′ (eq 6) to improve the prediction results for asymmetric systems. ⎡ ⎛ V ⎞⎤ V ln γiC = 1 − Vi′ + ln(Vi′) − 5qi⎢1 − i + ln⎜ i ⎟⎥ ⎢⎣ Fi ⎝ Fi ⎠⎥⎦ Vi′ =

(5)

ri 3/4 ∑j rj 3/4xj

(6)

ri and qi can be calculated from the van der Waals properties of the groups.33 Different combinatorial expressions are used in COSMO-SAC and COSMO-RS(Ol). The residual part takes into account the energetic interactions between the molecules. It can be obtained by using group activity coefficients of the groups in the mixture Γk and for the pure compounds Γ(i) k . ln γi R =

∑ νk(i)(ln Γk − ln Γ(ki))

(7)

k

The group activity coefficient Γk can be calculated using eq 8: ⎛ ln Γk = Q k ⎜⎜1 − ln(∑ ΘmΨmk) − ⎝ m

∑ m

ΘmΨmk ⎞ ⎟ ∑m ΘmΨmk ⎟⎠

(8)

where the surface fraction Θm is defined as follows:

Θm =

Q mX m ∑n Q nX n

(9)

The mole fraction Xm of group m is defined as Xm =

∑j νm(j)xj ∑j ∑n νn(j)xj

(10)

Temperature-dependent group interaction parameters were introduced in mod. UNIFAC(Do) to allow a better description of the real behavior in a wide temperature range. The temperature dependence of group interaction parameters in orig. UNIFAC is given by

2. THEORY AND MODEL The contributions to the activity coefficient (UNIFAC and COSMO-RS) are composed of two parts: the combinatorial part γCi and the residual part γRi . The activity coefficient γi is calculated using the following equation: ln γi = ln γiC + ln γi R

(2)

⎛ a ⎞ ψnm = exp⎜ − nm ⎟ ⎝ T ⎠

(11)

while in mod. UNIFAC(Do), the following temperature dependence is used:

(1) 11810

dx.doi.org/10.1021/ie301611w | Ind. Eng. Chem. Res. 2012, 51, 11809−11817

Industrial & Engineering Chemistry Research ⎛ a + b T + c T2 ⎞ nm nm ⎟ ψnm = exp⎜ − nm T ⎝ ⎠

Article

(12)

The residual part in COSMO-RS is calculated from the segment activity coefficients, which have to be computed via the solution of a self-consistent equation. The detailed procedure, equations, and parameters used for orig. UNIFAC, mod. UNIFAC(Do), COSMO-SAC, and COSMO-RS(Ol) are given in the literature.2−8,26−28 The σ-profiles used in COSMO calculations from different model chemistries have an impact on the COSMO-RS prediction results. In this paper, the σ-profiles from the VT 200529 data bank were used. COSMO-SAC using DMol3 BP/ DNP was abbreviated to SAC VT 2005, and COSMO-RS(Ol) using DMol3 BP/DNP was abbreviated to OL VT 2005.

Figure 1. Values of rmsd between experimental and calculated γ∞ based on COSMO-SAC and COSMO-RS(Ol) as well as orig. UNIFAC, mod. UNIFAC(Do), and mod. UNIFAC(Do) Consortium.

3. RESULTS AND DISCUSSION 3.1. Results for Activity Coefficients at Infinite Dilution. Activity coefficients at infinite dilution (γ∞) usually represent the highest deviation from ideal behavior. These values have great practical importance for the simulation of distillation processes, environmental protection, etc. Various techniques for the measurement of γ∞ are available, and more than 64 000 values have been published. Modified UNIFAC(Do) is commonly used to predict these data since also γ∞-data are used to simultaneously regress the group interaction parameters. COSMO-RS presents an alternative in case the required interaction parameters are not available.34 The γ∞-values of binary systems calculated using COSMOSAC, COSMO-RS(Ol), orig. UNIFAC, mod. UNIFAC(Do), and mod. UNIFAC(Do) Consortium are analyzed. To get a useful comparison of the different models, the nonreliable experimental data were excluded based on the following criterion. The published γ∞ data cover a range from 0.02 to 1010. However, the γ∞ data with very large values are often unreliable; e.g., the published γ∞-values of n-hexane in water vary between 2600 and 588 000. If data of different authors are available, sometimes poor quality codes can be assigned to poor data. For example, the γ∞-values measured by liquid−liquid chromatography usually are not in agreement with the results obtained by other techniques. For the comprehensive comparison, only systems were used which could be predicted by all models. Finally, 15 590 γ∞-values were used for the model comparison. 3.1.1. Overall Root-Mean-Square Deviations (rmsd), Relative Average Deviations (RAD), and Relative Deviations (RD) in γ∞. The root-mean-square deviations (rmsd) of the calculated results with respect to the experimental γ∞ data were calculated using eq 13. The results are shown in Figure 1. rmsd =

1 n

∞ ∞ 2 ) − ln γexp ∑ (ln γcalc n

RAD =

RD =

∞ ∞ ⎞ ⎛ |γcalc − γexp | 1⎜ ⎟ ∑ ∞ ⎜ ⎟ γexp n⎝ ⎠

∞ ∞⎞ ⎛ − γexp γcalc 1⎜ ⎟ ∑ ∞ ⎟ γexp n ⎜⎝ ⎠

(14)

(15)

RD provides the information for most of the calculated γ∞ data and shows a positive or negative deviation from the experimental data. The RAD and RD results calculated by eqs 14 and 15 are shown in Figure 2 and Table 1, separately. In all tables of this paper, the lowest deviations are printed in italics.

Figure 2. RAD between experimental and calculated γ∞ based on COSMO-RS(Ol) and COSMO-SAC as well as orig. UNIFAC, mod. UNIFAC(Do), and mod. UNIFAC(Do) Consortium. Calculated by eq 14.

From Figures 1 and 2 it can be seen that the rmsd and RAD of both COSMO-RS models are a factor of approximately 1.6 higher than for orig. UNIFAC and a factor of approximately 2.5 higher than for mod. UNIFAC. This means the results for the COSMO-RS models are less accurate than those for the group contribution method orig. UNIFAC and its modified versions. For most systems, mod. UNIFAC(Do) Consortium and mod. UNIFAC(Do) provide similar results. That is not surprising since for a large number of group combinations for the common database the group interaction parameters are identical. The great advantage of mod. UNIFAC(Do) Consortium is the fact that the parameter matrix is much larger, so mod. UNIFAC(Do) Consortium can be applied for many more systems. The RD values listed in Table 1 show that all models predict γ∞-values which are on average smaller than the experimental data.

(13)

∞ In eq 13, n is the number of data points and γ∞ calc and γexp are the calculated and experimental activity coefficients at infinite dilution. To allow a suitable comparison of these models, the relative average deviations (RAD) and relative deviations (RD) between experimental and calculated γ∞ for mixtures were calculated using eqs 14 and 15.

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Table 1. RD between Experimental and Calculated γ∞-Values Calculated by eq 15 model RD

SAC VT 2005 −0.232

OL VT 2005 −0.192

orig. UNIFAC −0.13

3.1.2. RAD and RD of γ∞ for Different Classes of Compounds. The RAD information and RD information of specific compound classes calculated using eqs 14 and 15 are presented in Tables S1−S4 in the Supporting Information. The mean relative average deviations (MRAD) calculated by eq 14 for those specific compounds are given in Table 2. Since mod.

2103 404 3420 1452 525 87 559

SAC VT 2005

OL VT 2005

orig. UNIFAC

mod. UNIFAC(Do) Consortium −0.042

data points). Modified UNIFAC(Do) provides again the best results. For saturated hydrocarbons in aromatic hydrocarbon systems (244 data points), the results show that COSMO-RS(Ol) and orig. UNIFAC underpredict the values of most of the systems. Modified UNIFAC(Do) is superior to the other models. The γ∞-values for ethers in hydrocarbons (125 data points) predicted by COSMO-SAC are higher than the predicted ones by COSMO-RS(Ol). The COSMO-RS model is slightly better than orig. UNIFAC, while mod. UNIFAC(Do) provides again the best results. For esters (HC, unconjugated in this paper; HC denotes components that contain only the further elements H and C) in hydrocarbons (206 data points), all models give the right trend of the nonideal behavior of these systems. COSMO-SAC and COSMO-RS(Ol) tend to overestimate the nonideal behavior while orig. UNIFAC tends to underestimate the nonideal behavior of these systems. Again mod. UNIFAC(Do) provides the best results. For hydrocarbon−ether systems (221 data points.), mod. UNIFAC(Do) provides best results, and orig. UNIFAC tends to underestimate the results. With increasing real behavior of these systems, all models tend to underestimate the results. COSMO-SAC and COSMO-RS(Ol) provide similar results in predicting γ∞-values of hydrocarbons in esters (HC, unconjugated) (158 data points), and they tend to underestimate the nonideality of these systems. Original UNIFAC and mod. UNIFAC(Do) provide similar results which are better than the results predicted using COSMO-SAC and COSMO-RS(Ol). In general, not only for alkanes and aromatics, but also for esters, ethers, and hydrocarbons, the smallest deviation is achieved using mod. UNIFAC. While orig. UNIFAC provides better results for hydrocarbons than the COSMO-RS models, for esters and ethers slightly better results are obtained for COSMO-RS models than for orig. UNIFAC. Polar−Nonpolar Systems. From the mean deviations obtained for polar−nonpolar systems, it can be seen that the predicted activity coefficients using the UNIFAC methods are superior when compared with the results of the COSMO-RS methods. In most cases, the predicted results of polar compounds in nonpolar compounds are less reliable than for nonpolar mixtures. The reason is that the interactions in these systems are more complex than in nonpolar mixtures, and reliable experimental data are more difficult to obtain. In the case of hydrocarbons in alcohols (1434 data points), COSMO-SAC, COSMO-RS(Ol), and orig. UNIFAC underestimate the results, while mod. UNIFAC(Do) provides the best results. In the case of hydrocarbons in ketones (412 data points), only in the case of ketones (HC, conjugated) (78 data points) mod. UNIFAC(Do) overestimates the nonideality of most of the systems. In other cases, all models tend to underestimate the γ∞-values. In the case of hydrocarbons in carboxylic acids (164 data points), COSMO-SAC and COSMO-RS(Ol) overestimate the nonideal behavior of most systems and COSMO-SAC is superior to COSMO-RS(Ol), while orig. UNIFAC and mod. UNIFAC(Do) underpredict the γ∞-values; the predicted results of the UNIFAC methods are similar. In the case of hydrocarbons in other nitro compounds

Table 2. MRAD γ% Values (eq 14) for Mixtures Composed of Different Compound Classes ndata

mod. UNIFAC(DO) −0.046

mod. UNIFAC(Do)

Nonpolar Systems: Alkanes and Aromatic Compounds 24.86 21.34 14.86 6.35 Nonpolar Systems: Esters and Ethers 14.49 15.62 19.86 10.44 Nonpolar Solutes in Polar Solvents 37.12 37.48 26.55 16.72 Polar Solutes in Nonpolar Solvents 57.87 46.88 29.68 20.14 Polar Solutes in Polar Solvents 131.22 232.56 72.09 30.48 Water as Solute 66.95 34.18 28.93 18.89 Systems with Halogenated Compounds 33.47 35.73 29.94 17.39

UNIFAC(Do) Consortium parameters often provide the same results as mod. UNIFAC(Do), the results based on the consortium parameters are presented in Table 4. Modified UNIFAC(Do) Consortium parameters improve most of the results which show large deviations from the experimental data. Nonpolar Systems. In nonpolar−nonpolar systems, especially n-alkane in n-alkane systems, the contribution of the residual part to γ∞ can be neglected. The contribution to γ∞ is mainly caused by the shape and size of the molecules (combinatorial part). Different expressions are used to calculate the combinatorial part of γ∞ in these models. To compare the reliabilities of these expressions, the γ∞-values of n-heptane in other n-alkanes were calculated and compared. Since most ethers and esters show only minor polarity, they were assigned to nonpolar compounds in this study. The results show that orig. UNIFAC underpredicts the values of the activity coefficients at infinite dilution. A comparison of COSMOSAC and COSMO-RS(Ol) shows that COSMO-RS(Ol) tends to overpredict the combinatorial part of γ∞. The equation used in mod. UNIFAC(Do) provides the best results, so it is strongly recommended to use the equation of mod. UNIFAC(Do) to calculate the combinatorial part. The predicted results (1195 data points) of saturated hydrocarbons in saturated hydrocarbons show that mod. UNIFAC(Do) provides the best results. Original UNIFAC usually underestimates the γ∞-values. The results for aromatic compounds in hydrocarbons (433 data points) predicted by the UNIFAC variants are distinctly better than the results of COSMO-SAC and COSMO-RS(Ol). COSMO-SAC and COSMO-RS(Ol) tend to overestimate the values. COSMO-RS(Ol) is superior to COSMO-SAC in predicting the γ∞-values of aromatic hydrocarbons in binary mixtures (71 11812



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Table 3. RAD γ% Values (eq 14) for Mixtures Composed of Different Compound Classes solutes

solvents

ndata

mod. UNIFAC(Do)

mod. UNIFAC(Do) Consortium

hydrocarbons (HC) hydrocarbons (HC) esters (HC, unconj) aldehydes (HC, conj) ketones (HC, unconj) ketones (HC, conj) ketones (HC, unconj) ketones (HC, unconj) alcohols (HC) ketones (HC, unconj) alcohols (HC) amines aldehydes (HC, unconj) ketones (HC, unconj) amines water water MRAD

aldehydes (HC, unconj) aldehydes (HC, conj) ketones (HC, unconj) hydrocarbons (HC) hydrocarbons (HC) hydrocarbons (HC) ethers (HC) esters (HC, unconj) fluorinated (HC) alcohols (HC) ketones (HC, unconj) alcohols (HC) alcohols (HC) water water amines esters (HC, unconj)

15 5 10 2 313 1 6 6 2 120 42 20 18 82 28 5 11 686

23.68 36.28 8.57 31.28 15.66 95.88 10.45 8.15 19.81 13.53 23.69 32.93 33.01 24.07 60.24 14.36 27.62 20.03

14.15 7.68 4.06 20.78 13.21 27.57 15.89 5.25 15.31 9.99 20.67 38.49 30.03 29.11 42.51 42.29 8.96 17.37

hydrogen bond can be formed. It causes inaccurate prediction of properties of aqueous systems. Association models can improve the results. The inadequate description of hydrogen bonding in COSMO-RS affects not only aqueous systems, but also other systems which can form hydrogen bonds, for example alcohols. In the case of more than one hydrogen bonding site (diols, triols, diamines, etc.), chains or association networks can be formed. Then the problems are even more serious. UNIFAC and mod. UNIFAC(Do) based on experimental data provide much better results than the a priori models COSMO-SAC and COSMO-RS(Ol) for aqueous systems, for example, for alcohols (including methanol, 1-alkanols, secondary alkanols, tertiary alkanols), ketones, and amines in water systems (274 data points). Modified UNIFAC(Do) improves a lot in comparison to UNIFAC, with some exceptions including diols and triols in water (20 data points) systems, etc. In most cases, COSMO-SAC is superior to COSMO-RS(Ol); the exceptions are esters and carboxylic acids in water. In the case of water as solute, orig. UNIFAC and mod. UNIFAC(Do) are superior to COSMO-SAC and COSMORS(Ol). Mostly COSMO-RS(Ol) provides better results than COSMO-SAC. In the case of water in carboxylic acids, and ester (HC, unconjugated) (10 data points) systems, orig. UNIFAC provides better results. In the case of water in ketones, mod. UNIFAC(Do) provides better results. In other cases, the predicted results of orig. UNIFAC and mod. UNIFAC(Do) provide similar results. In the case of water in esters (HC, unconjugated) (10 data points), COSMO-SAC provides very large deviations. Systems with Halogenated Compounds. For systems including halogenated compounds, commonly orig. UNIFAC and mod. UNIFAC(Do) perform better than the COSMO-RS models. The exception is observed for ethers in chlorinated compounds, where orig. UNIFAC shows surprisingly high deviations. 3.1.3. Results of mod. UNIFAC(Do) vs mod. UNIFAC(Do) Consortium. To give an idea about the improvement obtained with the mod. UNIFAC(Do) Consortium parameters, the results obtained by mod. UNIFAC(Do) Consortium are given and compared with the publicly available mod. UNIFAC(Do)

(169 data points), COSMO-SAC predicts slightly better results than COSMO-RS(Ol), but both of them underpredict the γ∞values. Original UNIFAC provides scattering data. Original UNIFAC and mod. UNIFAC(Do) provide a reliable description of aromatic hydrocarbons in alcohols (328 data points) and in ketones, while COSMO-SAC and COSMORS(Ol) underestimate the nonideality of these systems. In the case of alcohols in hydrocarbons (655 data points), mod. UNIFAC(Do) and COSMO-SAC provide better results. COSMO-RS(Ol) gives the largest deviations. For ketones in hydrocarbons (313 data points), in most cases, mod. UNIFAC(Do) gives better results in comparison to orig. UNIFAC; however, in some cases, orig. UNIFAC provides better results than mod. UNIFAC(Do). In the case of mixtures with halogenated compounds (375 data points), mod. UNIFAC(Do) provides the best results, while COSMO-SAC and COSMO-RS(Ol) underpredict the γ∞-values. Polar−Polar Systems. Also for polar systems the same conclusion can be drawn. Both UNIFAC methods provide better γ∞ results than COSMO-SAC and COSMO-RS (Ol), where the RAD for mod. UNIFAC are approximately a factor of 4 smaller than those for the COSMO-RS models. In the case of polar−polar systems, such as alcohols in alcohols, ketones in alcohols, etc., it is obvious that the UNIFAC models provide much better results than COSMORS. In the case of ketones and alcohols (120 data points), alcohols in nitro compounds, alcohols in amines, and aldehydes in alcohols, mod. UNIFAC(Do) provides better results than orig. UNIFAC. In the case of alcohols, amines in alcohols, and nitro compounds in ketones, orig. UNIFAC and mod. UNIFAC(Do) provide similar results. In the case of nitro compounds in alcohols, ketones in nitro compounds, and alcohols in carboxylic acids (33 data points), orig. UNIFAC provides better results in comparison to mod. UNIFAC(Do). Aqueous Systems. Aqueous systems are very important both in theory and in application. Water is a widely used, cheap, and environmentally benign solvent. Water forms hydrogen bonds and local structures; the interactions between water and other compounds are complex. In COSMO-RS, hydrogen bonding is treated in a rather simple way, which does not account for the fact that, between two donor−acceptor sites, only one 11813



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parameters. It should be mentioned that the number of systems which can be predicted by the mod. UNIFAC(Do) Consortium parameters are much larger than the number of predicted with the publicly available mod. UNIFAC(Do) parameters. The main task of the consortium is the introduction of new main groups (sulfides, disulfides, peroxides, mono- and dialkylated anilines, conjugated double bonds, ethylene oxide, etc.), the introduction of more flexible groups (e.g., cyclic amines, acetals, cyclic sulfides, aromatic ethers), and the extension of the parameter matrix of mod. UNIFAC(Do). Since most of the parameters for a common database are identical, only results for combinations with different parameters are given in Table 3. Table 3 shows that, for binary systems of hydrocarbons and aldehydes, esters (HC, unconjugated) and ketones (HC, unconjugated), alcohols and ketones (HC, unconjugated), amines in water, and water in esters (HC, unconjugated), mod. UNIFAC(Do) Consortium parameters provide much better results than the publicly available mod. UNIFAC(Do) parameters. However, for ketones (HC, unconjugated) in ethers or in water, water in amines, and amines in alcohols, mod. UNIFAC(Do) provides better results than mod. UNIFAC(Do) Consortium. However, for a few cases also the experimental database is very limited and questionable. 3.1.4. γ∞ for a Binary System as Function of Temperature. The temperature dependence of the activity coefficients can be calculated with the help of the Gibbs−Helmholtz equation (eq 16) using partial molar excess enthalpy data hiE: E ⎛ ∂ ln γi ⎞ hi = − ⎜ ⎟ ⎝ ∂T ⎠ P , x RT 2

(16)

Figure 4. (a) Experimental and predicted γ∞-values for (a) hexane in ethanol and (b) ethanol in hexane as a function of temperature.

In Figures 3 and 4 the γ∞-values for water in ethanol, hexane in ethanol, and ethanol in hexane as a function of temperature

better than those for mod. UNIFAC(Do). To be concise, we did not provide all these extensive results. 3.1.5. General Remarks on the Description of γ∞. Tables 2 and 3 and Tables S1−S4 in the Supporting Information indicate that better results for COSMO-RS are obtained when the solvents and the solutes are similar. The missing description of dispersive interactions and the inadequate consideration of hydrogen bonding interactions lead to errors of different magnitude in mixtures of dissimilar compounds. 3.2. Results for Binary Vapor−Liquid Equilibria. Additionally, a comparison of the predicted results for binary VLE with the experimental VLE data stored in DDB was performed with all the predictive models. To ensure the quality of the experimental data used for the comparison, the data were checked at first. The principle and the method to select reliable data were same as before.32 Finally, 1759 binary VLE data sets were used for the model comparison. The absolute average deviations (AAD) in the vapor phase composition, the RAD of the system pressure, the AAD of the system temperature, and the RAD of the activity coefficients were calculated using eqs 17, 18, 19, and 14. The results are listed in Table 4.

Figure 3. Experimental and predicted γ∞-values for ethanol in water as a function of temperature.

are shown. From the diagrams the scattering of the γ∞-values can be recognized. Furthermore, it can be seen that not only the absolute values but also the temperature dependence of the γ∞-values are much better predicted using mod. UNIFAC(Do). This means that also the excess enthalpies are described much better using mod. UNIFAC(Do) following the Gibbs− Helmholtz equation. The overall prediction results of excess enthalpies of mod. UNIFAC(Do) Consortium are slightly

Δyabs =

1 2

∑

ΔPrel (%) = 11814

2 ⎞ 1⎛ ⎜⎜∑ |y − y |⎟ k ,i k , i ,calc ⎟ n ⎝ i=1 ⎠

P − Pk ,calc 1⎛ ⎜⎜∑ k n⎝ Pk

⎞ ⎟⎟ ·100 ⎠

(17)

(18)



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Table 4. Deviations for All Models for the Complete Set of VLE Data Used for the Comparison RAD RAD AAD AAD

γa Pb yc Td

ndata

SAC VT 2005

OL VT 2005

orig. UNIFAC

mod. UNFAC(Do)

mod. UNIFAC(Do) Consortium

1759 904 1759 855

9.44 6.244 2.30 1.678

10.32 5.927 2.13 1.777

6.56 3.129 1.33 0.984

4.63 2.226 1.00 0.710

4.51 2.096 0.98 0.709

a

Relative average deviation in activity coefficients [RAD, %]. bRelative average deviation of system pressures [RAD, %]. cAbsolute average deviation of vapor phase composition times 100 [AAD, %]. dAbsolute average deviation of temperature [AAD, %].

ΔTabs =

1 n

(∑ |Tk − Tk ,calc|)

However, in the case of hydrocarbons with fluorinated compounds, UNIFAC and its modified versions provide much better results than the COSMO-RS versions. This is possibly due to the inadequate description of dispersive forces of the COSMO-RS models for fluorinated compounds. In the case of the hydrocarbon and chlorinated compound systems, all models provide similar results while UNIFAC and its modified version are slightly better than the COSMO-RS versions. In the case of the hydrocarbon with brominated (HC) compounds, the COSMO-RS models are superior to the UNIFAC versions, and orig. UNIFAC provides the worst results. Systems with Benzene. Table S9 in the Supporting Information shows that in the case of benzene with hydrocarbons, ethers, amines, or halogenated compounds again UNIFAC and its modified version are superior to the COSMO-RS versions, except for benzene−ether systems, where the average deviations in the case of orig. UNIFAC are a little larger than those for the other models. For systems of benzene with alcohols or ketones, the predicted results of the COSMO-RS versions are significantly worse than those for the UNIFAC versions. Aqueous Systems. For alcohol−water and ketone−water systems (Table S10 in the Supporting Information), the UNIFAC versions provide much better results than the COSMO-RS versions, while COSMO-RS(Ol) provides better results than COSMO-SAC. In the case of water−amine systems, COSMO-SAC and COSMO-RS(Ol) provide very poor results. Isothermal P−x data. Figures 5−7 show the experimental and predicted VLE data of the binary systems hexane + 1propanol at 323.15 K and perfluorohexane + hexane at 318.15 K. It can be seen that the COSMO-RS models in contrast to the UNIFAC models provide very large deviations. That is

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From Table 4, it can be concluded that in the comparison of COSMO-SAC with COSMO-RS(Ol) using the σ-profiles from VT 2005, COSMO-SAC provides better results in predicting the activity coefficients and temperature, while COSMORS(Ol) is more accurate in predicting the pressure and the vapor phase composition. The results of the group contribution methods are again distinctly better than those of the COSMORS methods. Modified UNIFAC(Do) is superior to orig. UNIFAC. Modified UNIFAC(Do) Consortium parameters provide the best results for VLE predictions. The results were analyzed separately for individual types of mixtures (Tables S5−S10 in the Supporting Information). This comparison provides detailed information for the different models. Nonpolar−Nonpolar Systems. In nonpolar mixtures (Table S5 in the Supporting Information), the intermolecular interactions are simple. They form nearly ideal systems, and all the models provide reliable results. Since for UNIFAC(Do) Consortium the parameters were not modified, the prediction results of both models are identical. For ethers, the parameters were modified, and the results (for hydrocarbons (HC) or aromatics (HC) with ethers) were slightly improved by the mod. UNIFAC(Do) parameters of the Consortium. Nonpolar−Polar Systems. For nonpolar−polar binary systems (Table S6 in the Supporting Information), such as hydrocarbon−alcohol, hydrocarbon−ketone, and hydrocarbon−amine, the average deviations are larger than those for nonpolar−nonpolar systems. The RAD of the activity coefficients range from 3 to 15%. In the case of hydrocarbons (HC) and alcohol or ketone systems, usually the predicted results of UNIFAC and its modified version provide much better results than the COSMO-RS versions. This can be attributed to the unreliable description of the hydrogen bonding contributions. For ether (HC) and alcohol (HC) systems, the predicted results of VLE by COSMO-RS(Ol) were significantly improved in comparison to COSMO-SAC; this can be ascribed to the “dual σ-profile” concept used in COSMO-RS(Ol). Polar−Polar Systems. For polar−polar systems (Table S7 in the Supporting Information), with similar components, for example, alcohol−alcohol systems or ketone−ketone systems, the predicted results of all models provide reliable results. The accuracy is similar to that for nonpolar−nonpolar systems. In the case of systems with dissimilar compounds such as of alcohol−ketone or alcohol−amine systems, UNIFAC and its modified version are much more reliable than the COSMO-RS versions. In most cases mod. UNIFAC(Do) Consortium provides the best results. Systems with Halogenated Compounds. For binary systems with a halogenated compound (Table S8 in the Supporting Information), all models provide reliable results.

Figure 5. Vapor−liquid equilibrium of the system hexane (1) + 1propanol (2) at 323.15 K. 11815



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provide better results than the UNIFAC based models. The quality of the results for the different classes of compounds and information about the superior results are given by italic and bold numbers in Tables S1−S10 in the Supporting Information. • The weaknesses of the COSMO-RS models are mainly caused by the inadequate description of hydrogen bonding (e.g., in polar systems) and dispersive effects (e.g., for fluorinated compounds). • For most types of mixtures, the differences between COSMO-SAC and COSMO-RS(Ol) are small. • Since most of the parameters of mod. UNIFAC(Do) and mod. UNIFAC(Do) Consortium are identical for the common database, similar results are obtained for this database. However, there is the great advantage of the mod. UNIFAC(Do) Consortium version that it can be applied for distinctly more systems. • Although there is the disadvantage that in the UNIFAC methods group interaction parameters are required, there is also the advantage that in contrast to the COSMO-RS models the different effects of hydrogen bonding, dispersive forces, etc. can be properly taken into account with the help of these group interaction parameters.

especially true for the system perfluorohexane + hexane. While nearly ideal behavior is predicted using the COSMO-RS models, azeotropic behavior occurs, which is predicted with the UNIFAC models. The very poor prediction is mainly caused by the poor consideration of dispersive interactions.28 Figures 6 and 7 give us a hint that one should be cautious to use the COSMO-RS models for systems which show strong real behavior.

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ASSOCIATED CONTENT

S Supporting Information *

RAD and RD γ% values (eqs 14 and 15) for mixtures composed of different compound classes are given in Tables S1−S4. Selected average deviations of vapor−liquid equilibria for mixtures composed of different compound classes are presented in Tables S5−S10. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 6. Vapor−liquid equilibrium data of the system perfluorohexane (1) + hexane (2) at 318.15 K.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (T.M.); gmehling@tech. chem.uni-oldenburg.de (J.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the National Natural Science Foundation of China (21173267), the State Key Laboratory of Heavy Oil Processing, the China University of Petroleum, the Basic Research Funds in Renmin University of China from the Central Government (12XNH097) and Deutsche Forschungsgemeinschaft SPP-1155 for financial support of the research project. We also thank DDBST GmbH for providing the latest version of the Dortmund Data Bank.

Figure 7. y−x diagram of the system perfluorohexane (1) + hexane (2) at 318.15 K.

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REFERENCES

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4. CONCLUSIONS A thorough examination of the performances of COSMO-SAC, COSMO-RS(Ol), orig. UNIFAC, mod. UNIFAC(Do), and mod. UNIFAC(Do) Consortium for the prediction of activity coefficients at infinite dilution and VLE of binary systems has been carried out, which leads to the following results: • Original UNIFAC and in particular its modified version provide better results than the COSMO-RS models investigated. However, in a few cases, the COSMO-RS models 11816



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Comparison of the a Priori COSMO-RS Models and Group

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