Estimation of Mixture Properties from First- and Second-Order Group

In the second-order UNIFAC model (Fluid Phase Equilib. ... problems such as the design of molecule/solvents, group-contribution-based methods are ...
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3260

Ind. Eng. Chem. Res. 2002, 41, 3260-3273

Estimation of Mixture Properties from First- and Second-Order Group Contributions with the UNIFAC Model Jeong Won Kang, Jens Abildskov, and Rafiqul Gani* CAPEC, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

Jose´ Cobas Center of Pharmaceutical Chemistry, POB 16042, Havana, Cuba

A new UNIFAC (extended model), to be called KT-UNIFAC, is proposed for estimation of mixture properties (activity coefficients and excess enthalpies) for vapor-liquid equilibrium from group contributions. Estimation is performed at two levels: the basic level uses contributions from first-order simple groups, while the second level uses a small set of second-order groups having the first-order groups as building blocks. The role of the second-order groups is to consider, to some extent, the proximity effects and to distinguish among isomers. In the second-order UNIFAC model (Fluid Phase Equilib. 1999, 158, 349), the excess Gibbs function is calculated as a sum of a first-order combinatorial contribution, a first-order residual contribution, and a secondorder residual contribution. The sets of first- and second-order groups have been revised and extended. The performance of this KT-UNIFAC model has been tested through correlation and prediction of vapor-liquid equilibria, infinite dilution activity coefficients, and excess enthalpies covering data involving 4413 binary mixtures and 27 ternary systems. Compared with some of the currently used versions of UNIFAC, the KT-UNIFAC model makes significant improvements in accuracy while providing a much wider range of applicability. Introduction In the production of a chemical product, many essential process steps such as extraction, adsorption, distillation, leaching, and absorption involve phase contacting. Accordingly, an understanding of any one of them is based in part on phase-equilibrium data. Typically, in large-scale chemical plants, a major part of the total cost is related to the investment for the separation steps in the process where energy costs for distillation (if present) account for a major part of the operating cost. Incentives to improve process efficiency may require examination of numerous alternative arrangements of process steps. Such efforts require quick evaluation of phase equilibria under different conditions of temperature, pressure, and/or composition. Therefore, it is more practical to predict data when screening among alternatives. However, as Xin and Whiting1 and Clark et al.2 have pointed out, it is necessary to be aware of the sensitivity and uncertainty of process design to physical properties estimation. Group-contribution-based property estimation methods are very suitable for such preliminary screening purposes if they are able to provide quick estimates with acceptable uncertainties at low computational costs. In reverse property prediction problems such as the design of molecule/solvents, group-contribution-based methods are ideally suited because they offer a means of generating molecular structures with desired properties as well as a predictive method for estimation of properties. The best-known and most successful of group-contribution-based methods for prediction of liquid-phase activity coefficients for mixtures is the UNIFAC model,3 to be referred to in this paper as the original UNIFAC model. It has already been used successfully in many * Corresponding author. Telephone: (45) 45252882. Fax: (45) 45932906. E-mail: [email protected].

areas, for example, (1) for calculating vapor-liquid equilibria (VLE),3 (2) for calculating liquid-liquid equilibria,4 (3) for calculating solid-liquid equilibria,5 (4) for determining activities in polymer solutions,6 (5) for determining vapor pressures of pure components,7 (6) for determining flash points of solvent mixtures,8 (7) for determining solubilities of gases,9 and (8) for estimation of excess enthalpy (HE).10 The original UNIFAC model, however, had some deficiencies. For example, the original UNIFAC model does not yield quantitatively acceptable predictions of the excess enthalpy and extrapolations to temperatures beyond 425 K should be avoided.11 Independently, two similar modifications of the original UNIFAC model have been developed.12,13 Such modifications enable quantitative, simultaneous correlation of VLE and HE data, which again ensures a good temperature dependence of the activity coefficients in most cases up to 550-600 K. Recent papers by Gmehling et al.14,15 contain details of 78 new and/or revised pairs of group interaction parameters for modified UNIFAC (Dortmund) covering a large temperature range. Despite the many successful applications of the original UNIFAC model and/or its modified forms, some deficiencies still remain. For example, the uncertainty of predictions is quite high for many complex mixtures while the current groups set is generally unable to distinguish among isomers because of the oversimplification of the molecular structure based on the solutionof-groups approach.11 To overcome these limitations, some attempts have been reported in the literature. Wu and Sandler16,17 have suggested an approach which is based on quantummechanical calculations of charge distribution on groups in isolated molecules and which identifies the situations where a given group is likely to change its interaction parameters. In such cases, the definition of new groups

10.1021/ie010861w CCC: $22.00 © 2002 American Chemical Society Published on Web 06/01/2002

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3261

for UNIFAC is proposed. Abildskov et al.18,19 have investigated the addition of second-order terms to the UNIFAC model where estimation is performed at two levels: a basic (first-order) level that uses contributions from first-order simple groups and a higher (secondorder) level that uses a small set of second-order groups. These second-order groups use the first-order groups as building blocks and permit the second-order UNIFAC model, in a limited manner, to account for proximity effects and to distinguish among isomers. For the second-order UNIFAC model to make a significant impact, there is a need for enhancing the group-contribution approach with a larger set of firstorder functional groups permitting a more detailed representation of chemical structures. For example, the absence of suitable groups to allow the differentiation between aromatic and nonaromatic substituents and, within aromatics, the isomer distinction restricts considerably the accuracy and range of applicability of much of the existing group-contribution methods, as pointed out by Marrero and Gani20 for estimation of pure-component properties. It was decided, therefore, in this paper to focus on developing an extension of the second-order UNIFAC model of Abildskov et al.18 in order to provide more accurate and reliable mixture property estimations for a considerably wider range of chemical substances than that covered by current models. This extended UNIFAC model will permit firstorder as well as second-order mixture property estimations and will be called KT-UNIFAC.

The second-order groups permit a better description of polyfunctional compounds and differentiation among isomers. At the higher (second-order) level, contrary to the case of first-order groups, the entire molecule does not need to be described. Second-order groups are intended to describe only molecular fragments that could not be described well enough by first-order groups, and thereby yielded a poor performance in the estimation at the first level. Second-order groups can be allowed to overlap each other. That is, a specific atom of the molecule may be included in more than one group, contrary to the case of first-order groups. It should be noted, however, that there can be mixtures where none of the mixture compounds need second-order groups. Proposed Model The KT-UNIFAC model treats activity coefficients as composed of three additive parts, a combinatorial part to account for molecular size and shape differences, a residual part to account for molecular interactions, and a second-order residual part to account for second-order effects on molecular interactions.

ln γi ) ln γCi + ln γRi + wR2 ln γR2 i

with wR2 ) 0 for the KT-UNIFAC first-order model and wR2 ) 1 for the KT-UNIFAC second-order model. The combinatorial and residual terms are the same as those for the method known also as linear UNIFAC.21

Theoretical Background In the KT-UNIFAC model, the molecular structure of a compound is considered to be a collection of two types of groups: first-order groups and second-order groups. The first-order groups are intended to describe a wide variety of organic compounds, while the role of the second is to provide more structural information about molecular fragments of compounds whose description is insufficient through the first-order groups. Thus, the estimation is performed at two successive levels. The first level provides an initial approximation that is improved at the second level. The ultimate objective of this multilevel scheme of estimation is to enhance the accuracy, reliability, and the range of application for mixtures properties. Marrero and Gani20 have recently proposed a comprehensive set of first- and second-order groups and a corresponding set of rules for assignment of groups to represent molecular structures. To maintain consistency between the group-contribution-based models for purecomponent properties and mixture properties, it was decided in this work to use the same set of first- and second-order groups as Marrero and Gani,20 who only estimated pure-component properties. The set of firstorder groups from Marrero and Gani20 allow the representation of a wide variety of chemical classes, including aromatic and aliphatic hydrocarbons, alcohols, phenols, ketones, aldehydes, acids, esters, ethers, amines, anilines, and many other different classes of organic compounds. The first-order groups describe the entire molecule and capture partially the proximity effects and differences among isomers. For this reason, the first level of estimation is intended to deal with simple and monofunctional compounds while further refinements required for mixtures involving more complex compounds are provided through second-order groups.

(1)

C C + ln γi,SG ln γCi ) ln γi,FH

(2)

C ) 1 - Ji + ln Ji ln γi,FH

(3)

(

Ji Ji Z C ) - qi 1 - + ln ln γi,SG 2 Li Li

)

(4)

where,

Li )

qi

ri

, Ji )

j

xjqj ∑ NC

xjrj ∑ NC

And the residual term is NMG

ln γRi ) qi(1 - ln Li) -

(5)

j

∑k

(

ski ηk

)

ski

- Gki ln

ηk

(6)

where NMG

Gki )

∑ νmiQm, m∈k

NC

ϑk )

∑i xiGki,

NMG

ski )

Gmiτmk, ∑ m NC

ηk )

∑i xiski

(7)

τmk ) exp(-∆umk/T)

(8)

∆umk ) amk,1 + amk,2(T - T0)

(9)

The second-order residual part is derived from perturbations with respect to structural and energetic parameters by expanding the excess Gibbs energy as a Taylor

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Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002

series around a state of zero correction:18

gR2 )

( ) GE

RT

R2

( ) T,n

∑j m∈j ∑ n*m ∑

∂∆umn

∂δumn,j

δumn,j +

[( ) ∂gR

NSOG NSG NSG

)

(

∂∆umn ∂g

R

∂∆unm

( )

δu*mn,j

)

T,n,Q,v,∆u*mn

T,n,Q,v,∆u*nm

∂∆unm

∂δunm,j

]

δunm,j (10)

δu*nm,j

In eq 10, the sum over j is a sum over all second-order groups identified in the mixture, the sum over m is a sum over all first-order groups in the mixture other than n, and m′ is a particular first-order group (type m) which is part of a second-order group j and has its interactions modified:18

∀ k*m: (∆umk :) ∆umk + δum′k,j; ∆ukm :) ∆ukm + δukm′,j) (11) Only the two lower-case deltas in gR2 (δumn,j and δunm,j) depend on second-order information.18 Thus, the term to be added to the natural logarithm of the first-order activity coefficient is

[ ( ) (

NSOG NSG NSG

ln γR2 i )

∑j m∈j ∑ n*m ∑

Gm′iGni

τmn sni

+

δum′n,j RT

δunm′,j RT

τmn

(Gm′iϑn - ϑm′Vni)

τnm

(Gniϑm′ - ϑnVm′i)

NC

∑i xiGki;

Vmi ) ϑm

smi ηm

-

)]

(12)

∑k Gmiτmk

(13)

GniGm′i

Gki ) νkiQk; ϑk )

ηm

-

ηn

τnm smi

NC

ηk )

∑i xiski; NSG

- Gmi; ski )

This approach, if unrestricted, introduces too many additional parameters. Therefore, to make the KTUNIFAC model more realistic, two simple rules that allow a reduction of the model parameters are employed: (1) Second-order effects do not cause two groups to start interacting if they did not do that in the first-order model. For example, first-order group CH in secondorder group (CH3)2CH does not interact with first-order group CH3 in solution, because CH and CH3 do not interact in the first-order UNIFAC model. (2) Second-order effects on interactions apply uniformly to the first-order main groups UNIFAC. Unlike the first-order UNIFAC model where the interaction parameters involve two main groups, the second-order interaction parameters involve the interaction between a main group and another main group that is contained by a second-order group (e.g. main group CH2 in secondorder group (CH3)2CH). The list of first-order groups, along with sample assignments, group occurrences, volume parameters (R), and surface area parameters (Q) is presented in Table

1. Compared to the first-order groups of Marrero and Gani,20 this table includes a subset of special molecular groups, since such groups are only needed for estimation of mixture properties with the UNIFAC models. These special molecular groups represent compounds such as methanol, water, dimethyl sulfoxide, and others. The group volume and group surface parameters have been determined from atomic and molecular structure data on the basis of the work of Bondi (see ref 3). The list of second-order groups is given in Table 2 together with sample assignments along with occurrences for each group. Parameter Optimization The KT-UNIFAC model parameters were determined by fitting a database involving 4413 binary measurement series (59 878 values) for vapor-liquid equilibria, infinite dilution activity coefficients (γ∞), and excess enthalpies in the temperature range from 273 to 373 K. The parameter estimations of this work are primarily based on isothermal data. Isothermal data are clearly preferable, because one need not specify the vapor pressure or its dependence upon temperature.23 Some isobaric data were also used in order to improve the temperature dependency of the parameters and to obtain parameters for systems with limited experimental VLE data. To enhance the range of application, we include γ∞ values for strongly nonideal systems (e.g. water-alkanes, water with higher ethers), although some authors22 exclude them, since the values published by different sources are contradictory. The complete VLE data sets were checked for thermodynamic consistency using the test of Van Ness et al.23 in the version suggested by Fredenslund et al.3 For other incomplete VLE data and HE data, a flexible Legendre polynomial was used to fit the data and check for goodness of fit. In this work, first-order parameters have been estimated before second-order parameters. Second-order parameters are in this way based on first-order parameters held constant. For the choice of an objective function, we have taken into account the following conditions: (1) Different types of data exist (VLE, HE, γ∞). Furthermore, the experimental uncertainties and the quality of the data differ. (2) It is difficult to distinguish between important and less important data. Sometimes lots of data exist for one system, which distort the objective function. (3) As the objective function normally uses sums of quadratic deviations, it can happen that a few data points that are reproduced badly form the largest part of the function, possibly because of inappropriate changes in the independent variables. In these cases, the numerical method usually tries to vary the related parameters in order to decrease the deviations with respect to these points. As a side effect, the results of well-described data points can deteriorate significantly, because they have only a marginal influence on the objective function. Hence, to put a reasonable weight on the measured quantities according to their experimental accuracy, the following objective function was used: N

S)

(∆P)2

∑ i)1 0.01

+

(∆HE)2 0.1

+

(∆γ∞)2 0.05

(14)

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3263 Table 1. First-Order Main Groups and Their Subgroups along with R and Q Values and Sample Assignments (Bold Face ) New Groups) no.

main group

subgroup

example Hydrocarbon Chains n-hexane (2) n-hexane (4) 2-methylpentane (1) 2,2-dimethylbutane (1)

1 2 3 4

CH2

5 6 7 8 9 10 11 12

CdC

13 14

CtC

CHtC... CtC...

15 16 17 18 19 20 21 22 23 24 25 26

ACH

ACH... AC(link) AC(cond) ACCH3... ACCH2... ACCH... ACC... ACCHdCH2 ACCHdCH... ACCdCH2... ACC#CH... ACCt-C...

CdCdC

ACCH2

ACCdC ACCtC

Hydrocarbon ChainssDouble Bond CH2dCH... 1-hexene (1) CHdCH... 2-hexene (1) 2-methyl-1-butene (1) CH2)C... CHdC... 2-methyl-2-butene (1) CdC... 2,3-dimethyl-2-butene (1) CH2)CdCH 1,2-butadiene (1) CH2dCdC... 3-methyl-1,2-butadiene (1) CHdCdCH... 2,3-pentadiene (1) Hydrocarbon ChainssTriple Bond 1-pentyne (1) 3-nonyne (1) Aromatic Cabon Chains benzene (6) biphenyl (2) naphthalene (2) toluene (1) ethylbenzene (1) cumene (1) tert-butylbenzene (1) styrene (1) 1-propenylbenzene (1) r-methylstyrene (1) phenylacetylene (1) 1-phenyl-1-propyne (1) Cyclic Carbon Chains cyclododecane (12) butylcyclohexane (1) 1,1-dimethylcyclopentane (1) β-pinene (1) methylene cyclohexane (1) 1,8-m-menthadiene (1) dichlorohexafluorocyclopentene (1)

Ri

0.8480 0.5400 0.2280 0.0000

0.9011 0.6744 0.4469 0.2195

1.1760 0.8670 0.9880 0.6760 0.4850 1.4200 2.7480 0.8640

1.3454 1.1167 1.1173 0.8886 0.6605 1.5405 1.4838 1.7732

1.0880 0.7840

1.2920 1.0613

0.4000 0.1200 0.0840 0.9680 0.6600 0.3480 0.0840 1.2960 1.6080 1.1080 1.2080 0.9040

0.5313 0.3652 0.3125 1.2663 1.0396 0.8121 0.5847 1.7106 1.9394 1.4825 1.6572 1.4265

0.5400 0.2280 0.0000 0.8670 0.9880 0.6760 0.4850

0.6744 0.4469 0.2195 1.1167 1.1173 0.8886 0.6605

1.2000 1.4320 1.4000 0.6800 2.2480

1.0000 1.4311 0.9200 0.8952 2.4088

1.9040 1.5920 1.5920

2.1226 1.8952 1.8952

27 28 29 30 31 32 33

CdC(cyc)

CH2,cy... CH,cy... C,cy... CHdCH,cy CH2dC,cy CHdC,cy... CdC,cy...

34 35 36 37 38

OH CH3OH H2O ACOH DOH

OH... CH3OH... H2O..... AC-OH... (CH2OH)2

39 40 41

OCCOH

C2H5O2... C2H4O2-1 C2H4O2-2

42 43 44 45 46 47

CH2CO

ACCO CdO (cyc)

CH3CO... CH2CO... CHCO... CCO... ACCO... CdO,cy...

Ketones 2-butanone (1) 3-pentanone (1) 2,4-dimethyl-3-pentanone (1) 3-hydroxy-3-methyl-2-butanone (1) acetophenone (1) cyclopentanone (1)

1.4880 1.1800 0.8680 0.6400 0.7240 0.0840

1.6724 1.4457 1.2182 0.9908 1.1365 0.3652

48 49 50

CHO ACCHO FURFURAL

CHO... ACCHO... FURFURAL

Aldehydes 1-hexanal (1) benzaldehyde (1) furfural (1)

0.9480 1.0680 2.4840

0.9980 1.3632 3.1680

51 52 53 54 55 56 57 58

CCOO

CH3COO... CH2OO... CHCOO...C CCOO... HCOO... ACCOO... ACOOC... COO...

Esters butyl acetate (1) methyl butyrate (1) ethyl acetoacetate (1) ethyl 2,2-dimethylpropionate (1) propyl formate (1) methyl benzoate (1) ethyl phenyl acetate (1) ethyl acrylate (1)

1.7280 1.4200 1.1080 0.8800 1.1880 1.0000 1.0000 1.2000

1.9031 1.6764 1.4489 1.2215 1.2420 1.3672 1.3672 1.3800

CH3O... CH2O... CHO... CO... CH2O,f... O,cy... ACO...

Ethers methyl butyl ether (1) ethyl isobutyl ether (1) ethyl sec-buty ether(1) di-tert-butyl ether (1) tetrahydrofuran (1) furan (1) diphenyl ether (1)

1.0880 0.7800 0.4680 0.2400 1.1000 0.2400 0.3600

1.1450 0.9183 0.6908 0.9183 0.9183 0.2439 0.6091

59 60 61 62 63 64 65

CH2(cyc)

CH3... CH2... CH... C...

Qi

HCOO ACCOO ACOOC COO CH2O

O (cyc) ACO

Alcohol, Water 2-propanol (1) methanol (1) water (1) phenol (1) ethylene glycol (1) Oxygenated Alcohols 2-ethoxyethanol (1) 2-ethoxy-1-propanol (1) 1-methoxy-2-propanol (1)

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Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002

Table 1. (Continued) no. 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

main group CNH2

NH2 (C)2NH (C)3N pyridine ACNH2 AN N (cyc)

subgroup CH3NH2... CH2NH2... CHNH2... CNH2... NH2... CH3NH... CH2NH... CHNH... CH3N... CH2N... C5H5N... C5H4N... C5H3N... ACNH2... ACNH... ACN..... AN... NH,cy... N,cy...

85 86 87 88 89 90 91 92 93

CCN

94 95 96 97

COOH ACCOOH OCOCO

COOH... HCOOH... ACCOOH... OCOCO...

98

OCOO

OCOO

CCN ACCN ACRY CN CN (cyc)

99 100 101 102 103 104 105 106 107 108 109 110

CCL

111 112 113 114 115 116 117 118 119

CF2

CCl2 CCl3 CCl4 Cl-(CdC) ACCl Cl

ACF F

CH3CN... CH2CN... CCN... CCN... AC-CN... CH2dCHCN CN... CHdNcyc... CdNcyc...

CH2Cl... CHCl... CCl... CH2Cl2... CHCl2... CC12... CHCl3... CCl3... CCl4... Cl(CdC)... ACCl... Cl... CHF3... CF3... CHF2... CF2... CH2F... CHF... CF... ACF... F...

120 121 122 123 124 125 126 127

CClF

CCl3F... CCl2F... HCCl2F... HCClF CClF2... HCClF2... CClF3... CCl2F2...

128 129

I ACl

I... ACl...

example

Qi

Ri

1.5440 1.2360 0.9240 0.6960 0.6960 1.2440 0.9360 0.6240 0.4000 0.6320 2.1130 1.8330 1.5530 0.0920 0.8160 0.5160 0.2120 0.3960 0.0920

1.5959 1.3692 1.1417 0.9275 0.6948 1.4337 1.2070 0.9795 1.1865 0.9597 2.9993 2.8332 2.6670 0.3428 1.0600 0.8978 0.506 0.5326 0.2854

benzothiazole (1) 3-methylpyrazole (1)

1.7240 1.4160 1.1040 0.8760 0.9960 2.0520 0.8760 0.5240 0.3360

18701 1.6434 1.4160 1.1885 1.3342 2.3144 0.9690 0.8438 0.6157

Acids acetic acid (1) formic acid benzoic acid (1) acetic anhydride (1)

1.2240 1.5320 1.3440 1.5200

1.3013 1.5280 1.6664 1.7864

Carbonates dimethyl carbonate (1)

1.1200

1.2591

chlorobenzene (1) ethyl chloroacetate (1)

1.2640 0.9520 0.7240 1.9880 1.6840 1.4480 2.4100 2.1840 2.9100 0.7240 0.8440 0.7240

1.4654 1.2380 1.0106 2.2564 2.0606 1.8016 2.8700 2.6401 3.3900 0.7910 1.1562 0.7910

Fluorine Groups fluoroform perfluorohexane (2) 1,1,2-trifluoroethane (1) perfluorohexane (4) fluoroethane (1) 2-fluropropane (1) 2-fluoro-2-mehylpropane (1) hexafluorobenzene (6) fluoroethene (1)

1.5480 1.3800 1.1080 0.9200 0.9800 0.6680 0.4600 0.5240 0.4400

1.5781 1.4060 1.2011 1.0105 1.0514 0.8240 0.6150 0.6948 0.3771

2.6440 1.9160 2.1160 1.4160 1.6480 1.8280 2.1000 2.3760

3.0356 2.2287 2.4060 1.6493 1.8174 1.9670 2.1721 2.6243

0.9920 0.9720

1.2640 1.3619

Amine methylamine (1) ethylamine (1) isopropylamine (1) tert-butylamine (1) cyclohexylamine (1) dimethylamine (1) diethylamine (1) diisopropylamine (1) methyldiethylamine (1) triethylamine (1) pyridine (1) 2-methylpyridine 2,3-dimethylpyridine (1) aniline (1) n-ethylanilinene (1) n,n-dimethylaniline (1) pyridine (1) piperidine (1) n-methylpiperidine (1) Nitrile acetonitrile (1) propionitrile (1) isobutyronitrile (1) 2,2-dimethylpropionitrile (1) benzonitrile (1) acrylonitrile (1)

Chlorine Groups 1-chlorobutane (1) 2-chloropropane (1) 2-chloro-2-methylpropane (1) dichlormethane (1) 1,1-dichloroethane (1) 2,2-dichloropropane (1) chloroform (1) 1,1,1-trichloroethane (1) tetrachloromethane (1)

Chloro Fluoro Groups trichloromethane (1) tetrachloro-1,2-difluoroethane (2) diclorofluoromethane (1) 1-chloro-1,2,2,2-tetrafluoroethane (1) 1,2-dichlorotetrafluoroethane (2) trichlorofluoromethane (1) chlorofluoromethane (1) dichlorodifluoromethane (1) Iodine Groups iodoethane (1) iodobenzene (1)

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3265 Table 1. (Continued) no.

main group

130 131

Br ACBr

Br... ACBr...

132 133 134 135 136 137

CNO2

CH3NO2... CH2NO2... CH2NO2... CNO2... ACNO2... NO2... CH3SH... CH2SH... CHSH... CSH... CH3S CH2S... CHS... CS... CS2... C4H4S... C4H3S... C4H2S... ACSH... ACS... SH...

138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

ACNO2 NO2 CH3SH

CH2S

CS2 THIOPHEN

ACSH SH DMSO SO SO2 SO3 SO4 ACSO ACSO2 DMF

CONCH2

CONCO ACCONH ACNHCO

NCO UREA

ACNCON

EPOXY

subgroup

CH3SOCH3 SO... SO2... O(SO)O... O(SO2)... SO4... ACSO... ACSO2...

example

Qi

Ri

0.8320 1.1240

0.9492 1.6599

Nitro Groups nitromethane (1) 1-nitropropane (1) 2-nitropropane (1) 2-methyl-2-nitropropane (1) nitrobenzene (1) nitrocyclohexane (1)

1.8680 1.5600 1.2480 1.0200 1.1040 1.4200

2.0086 1.7818 1.5544 1.3270 1.4199 1.1074

Sulfide Groups methanethiol (1) ethanethiol (1) 2-propanethiol (1) 2-methyl-2-propanethiol (1) dimethyl sulfide (1) diethyl sulfide (1) diisopropylsulfide (1) di-tert-butyl sulfide (1) carbon disulfide (1) thiophene (1) 2-methylthiophene (1) 2,3-dimethylthiophene (1) benzenethiol (1) phenyl methyl sulfide (1) cyclohexanethiol (1)

1.6760 1.3680 0.2280 0.0000 1.3680 1.0600 0.7480 0.5200 1.6500 2.1400 1.8600 1.580 0.5200 0.1200 1.0400

1.8770 1.6510 1.4232 1.1958 1.6130 1.3863 1.1589 0.9314 2.0570 2.8569 2.6908 2.5247 0.7119 1.3415 1.0771

Sulfur Oxide Groups dimethyl sulfoxide (1) diethyl sulfoxide (1) dimethyl sulfone (1) dimethyl sulfite (1) dimethyl sulfonate (1) dimethyl sulfate (1) phenyl methyl sulfoxide (1) diphenyl sulfone (1)

2.4720 0.7760 1.0400 1.2560 1.2800 1.5200 0.8960 1.1600

2.8266 1.0244 1.3382 1.5122 1.5821 1.8260 1.3896 1.7034

Bromine Groups bromoethane (1) bromobenzene (1)

DMF... CON(Me)2 CONMeCH2 HCON2CH2 CON2CH2... CONHCH3... HCONHCH2 CONHCH2... CONH2 CONHCO... CONCO... ACCONH2... ACCONH... ACNHCOH... ACNHCOH... ACNHCO... Ac-NCO... NCO

Amides diethylformamide (1) n,n-dimethylacetamide (1) n,n-methylethylacetamide (1) diethylformamide (1) n,n-diethylacetamide (1) methylacetamide (1) n-methylformamide (1) n-methylformamide (1) acrylamide (1) diacetamide (1) methyldiacetamide (1) benzamide (1) n-methylbenzamide (1) n-phenylformamide (1) n-methyl-n-phenylmethanamide (1) n-(2-methylphenyl)acetamide (1) phenyl isocyanate (1) methyl isocyante (1)

2.7360 2.4280 2.1200 2.1200 1.8120 1.8640 1.8840 1.5760 1.3360 1.3440 1.6760 1.3720 1.4560 1.1560 1.4640 1.1600 1.1560 0.732

3.0856 2.8589 2.6322 2.6322 2.4054 2.2050 2.2050 1.9782 1.4661 1.5307 2.0751 1.8279 1.8312 1.6691 1.8958 1.6486 1.6691 1.0567

UREA... NH2CONH... NH2CON... UREA NHCON... NCON... ACNHCON2 ACNHCON1

Urea urea (1) methylurea (1) n,n-dimethylurea (1) n,n′-dimethylurea (1) trimethylurea (1) tetramethylurea (1) phenylurea (1) n,n′-diphenylurea

2.0320 1.7320 1.4280 1.4320 1.1280 0.8240 1.8520 1.5520

2.1608 1.9987 1.7515 1.8365 1.5893 1.3421 2.3639 2.2017

CH2OCH2... CH2OCH... CH2OC... CHOCH... CHOC... COC...

Epoxides ethylene oxide (1) 1,2-propylene oxide (1) 1,2-epoxy-2-methylpropane (1) 2,3-epoxybutane (1) 2,3-epoxy-2-methylbutane (1) 2,3-epoxy-2,3-dimethylbutane (1)

1.3200 1.0080 0.7800 0.6960 0.4680 0.2400

1.5926 1.3652 1.1378 1.1378 0.9103 0.6829

3266

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002

Table 1. (Continued) no.

main group

193 194

ONO ONO2

ONO... ONO2...

195 196

NMP MORFOLIN

NMP... MORFOLIN

197 198 199 200 201 202 203

SiH2

SiH3... SiH2 SiH... Si... SiH2O... SiHO... SiO...

SiO

subgroup

example Nitrates butyl nitrite (1) n-butyl nitrate (1) Molecular Groups N-methylpyrolidone morfoline (1) Silicone methylsilane (1) diethylsilane (1) heptamethyltrisiloxane (1) hexamethyldisiloxane (1) 1,3-dimethyldisiloxane (1) 1,1,3,3-tetramethyldisiloxane (1) octamethylcyclotetrasiloxane (1)

For systems not needing association terms, the equilibrium pressure was calculated as follows:

Pcalc )

∑

xiγiPsat i (POY); Ki,calc )

yi γiPsat i (POY) ) xi Pcalc (15)

where POY is the Poynting correction. For systems needing an association term, chemical equilibria were solved and bubble-dew point calculations were performed with association constants. The optimization algorithm used for the data fitting was the LevenbergMarquardt technique. Figure 1 shows a matrix of the available first-order interaction parameters. The corresponding values (amk,1 and amk,2) for these interaction parameters are presented in the Supporting Information, which also shows the second-order parameters δum′k,j and δukm′,j given in terms of interaction of second-order group j and firstorder group mk. Table 3 presents for each property the average absolute error and the average relative error for the first- and second-order estimations. Correlation results for the original UNIFAC model24 and the modified UNIFAC-Lyngby model,24 to be called modified UNIFAC hereafter, are also included. It is worth mentioning that it would not have been a fair comparison between these methods if we had not used a common set of data. The statistics given in Table 4 for the second-order estimations include only those data points where the mixture compound(s) needed secondorder group assignments. Table 4 gives an impression of the broad spectrum of data which were available for the parameter estimation step where different compound (type) combinations, different types of data, and the average relative error for the first and second estimations are highlighted. Since the parameters for other versions of UNIFAC, such as Modified UNIFAC,14,15 were not available, comparisons with versions of UNIFAC not originating from Denmark have not been possible. Model Analysis and Prediction Table 5 presents results for binary and ternary data using the original UNIFAC,24 modified UNIFAC,21 and KT-UNIFAC. The basis for this comparison is provided by 213 binary data sets (5133 data points) and 27 ternary data sets (531 data points), not used for correlation. The binary data for VLE and γ∞ have been tested. Only isobaric VLE were available for ternary data, which did not have the addition of second-

Qi

Ri

1.4200 1.6600

11.1074 1.3514

3.2000

3.9810 3.4740

1.2630 1.0060 0.7490 0.4100 1.0620 0.7640 0.4660

1.6035 1.4443 1.2853 1.0470 1.4838 1.3030 1.1044

order effects. Whenever necessary, vapor pressures were estimated through the DIPPR correlations,25 based on the equation

(

Psat i ) exp Ai +

)

Bi + Ci ln T + DiTEi T

(16)

where A, B, C, D, and E are adjustable constants. In this paper, the comparison has been limited to the number of systems which could be calculated with the original UNIFAC and modified UNIFAC methods. From the results shown in Tables 3-5, it can be concluded that the KT-UNIFAC model gives the best results. When compared with the original UNIFAC, a clear improvement can be observed. Also when comparison is made with modified UNIFAC, better results are predicted for all the mentioned quantities. The consistency of the ternary system data has not been checked, and the data were either accepted or rejected on the basis of whether or not the vapor pressures calculated with eq 16 were in reasonable agreement with known experimental values. This means that the experimental error has a considerable influence on the calculated deviations. Because of this reason, the comparisons with ternary VLE systems should not be considered as conclusive. Comparisons of improvements in the predictions of VLE are shown in Figures 2-8. Figure 2 shows results for mixtures of cyclic and aliphatic compounds. These systems usually give large errors with the original UNIFAC and modified UNIFAC models, because for the cyclic compounds the same main group as that for aliphatic substances is used. To overcome this limitation, the KT-UNIFAC model introduces new first-order main groups (CH2 (cyc), CdCcyc, NHcyc, Ncyc, CdNcyc, Ocyc, COcyc, Scyc, and SO2 (cyc)). A new main group aromatic ether (ACO) and epoxy have also been added. This main group allows better representations of aromatic ether- and epoxy-type substances, as shown in Figures 3 and 4. The performance of the KT-UNIFAC model was also found to be good for binary mixtures with associating compounds, as shown in Figures 5 and 6. The experimental data lie on the calculated curves for the new method; thus, the azeotropic points are also well described. In most cases, deviations of the secondorder model are less than the deviation of the first-order model, the original UNIFAC and the modified UNIFAC, as shown in Figures 7 and 8. There are cases in which the correction is not large, but improvements in estimation were generally observed.

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3267 Table 2. Second-Order Groups and Sample Assignments no.

class

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

structural alkanes

structral alkenes monofunctional

acry

benzyl

nonfused aromatics

nonfused pyridines

alicyclic subst

second-order group

description

example

(CH3)2CH (CH3)3C CH(CH3)CH(CH3) CH(CH3)C(CH3)2 C(CH3)2C(CH3)2 CHndCHmsCHpdCHk CH3sCHmdCHn CH2sCHmsCHn CHsCHmdCHn CHCHO CH3COCH2 CH3COCH CHCOOH CH3COOCH CHOH COH CHmdCHnsCI CHmdCHnsF CHmdCHnsBr CHmdCHn-1 CHndCHmsCOO CHmdCHnsCHO CHmdCHnsCN CHmdCsCN CHmdCHnsCOOH CHndCHmsCOOH CHndCHmsCONHp CHmsOsCHndCHp ACsCHnsCI ACsCHnsF ACsCHnsBr ACsCHnsI ACsCHnsNHm ACsCHnsOsCHm ACsCHnsOH ACsCHnsCN ACsCHnsCHO ACsCHnsSH ACsCHnsCOOH ACsCHnsCOsCHm ACsCHnsSsCHm ACsCHnsOOCH ACsCHnsNO2 ACsCHnsCONH2 ACsCHnsCOO ACsCHnsOOC ACsSOnsOH ARs1s2 ARsls3 ARsls4 ARsls2s3 ARsls2s4 ARs1s3s5 ARsls2s3s4 ARsls2s3s5 ARsls2s4s5 Pyri-s2 Pyri-s3 Pyri-s4 Pyri-s2s3 Pyri-s2s4 Pyri-s2sS Pyri-s2s6 Pyri-s3s4 Pyri-s3sS Pyri-s2s3s6 CHcycsCH3 CHcycsCH2 CHcycsCH CHcycsC CcycsCH3 CcycsCH2 (CHndC)cycsCH3 (CHndC)cycsCH2 CHcycs(CHdCHn) CHcycs(CdCHn) CHcycsCI CHcycsF CHcycsBr (CHndC)cycsCI CHcycsOH CcycsOH

(CH3)2CH (CH3)3C CH(CH3)CH(CH3) CH(CH3)C(CH3)2 C(CH3)2C(CH3)2 CHndCHmsCHpdCHk (k,m,n,p in 0-2) CH3sCHmdCHn (m,n in 0-2) CH2sCHmdCHn (m,n in 0-2) CHsCHmdCHn or CsCHmdCHn (m,n in 0-2) CHCHO or CCHO CH3COCH2 CH3COCH or CH3COC CHCOOH or CCOOH CH3COOCH or CH3COOC CHOH COH CHmdCHnsCI CHmdCHnsF (m,n in 0-2) CHmdCHnsBr (m,n in 0-2) CHmdCHnsl (m,n in 0-2) CHndCHmsCOO (n,m in 0-2), acrylate CHmdCHnsCHO (m,n in 0-2) CHmdCHnsCN (m,n in 0-2), acrylonitrile CHmtCsCN (m in 0-1) CHmdCHnsCOOH (m,n in 0-2), acrylic acid CHntCsCOOH (n in 0-1) CHndCHmsCONHp (m,n,p in 0-2) CHmsOsCHndCHp (m,n,p in 0-2) ACsCHnsCI (n in 1-2) ACsCHnsF (n in 1-2) ACsCHnsBr (n in 1-2) ACsCHnsI (n in 1-2) ACsCHnsNHm (n in 1-2, m in 0-2) ACsCHnsOsCHm (m,n in 1-2) ACsCHnsOH (n in 1-2) ACsCHnsCN (n in 1-2) ACsCHnsCHO (n in 1-2) ACsCHnsSH (n in 1-2) ACsCHnsCOOH (n in 1-2) ACsCHnsCOsCHm (n,m in 1-2) ACsCHnsSsCHm (n,m in 1-2) ACsCHnsOsCHO (n in 1-2) ACsCHnsNO2 (n in 1-2) ACsCHnsCONH2 (n in 1-2) ACsCHnsCOO (n in 1-2) ACsCHnsOOC (n in 1-2) ACsSOnsOH (n in 1-2) ARsls2 ARsls3 ARsls4 ARsls2s3 ARsls2s4 ARsls3s5 ARsls2s3s4 ARsls2s3s5 ARsls2s4s5 Pyri-s2 Pyri-s3 Pyi-s4 Pyri-s2s3 Pyri-s2s4 Pyri-s2s5 Pyri-s2s6 Pyri-s3s4 Pyri-s3sS Pyri-s2s3s6 CHcycsCH3 CHcycsCH2 CHcycsCH CHcycsC CcycsCH3 CcycsCH2 (CHndC)cycsCH3 (n in 0-1) (CHndC)cycsCH2 (n in 0-1) CHcycs(CHdCHn) (n in 1-2) CHcycs CHcycsCI CHcycsF CHcycsBr (CHndC)cycsCI (n in 0-1) CHcycsOH CcycsOH

2-methylpentane (1) 2,2,4,4-tetramethylpentane (2) 2,3,4-trimethylpentane (2) 2,2,3,4,4-pentamethylpentane (2) 2,2,3,3,4,4-hexamethylpentane (2) 1,3-butadiene (1) 2-methyl-2-butene (3) 1,4-pentadiene (2) 3-methyl-l-butene (1) methylbutyraldehyde (1) 2-pentanone (1) 3-methyl-2-pentanone (1) 2-methyl butanoic acid (1) isopropyl acetate (1) 2-butanol (1) 2-methyl-2-butanol (1) vinyl chloride (1) 1-fluoro-l-propene (1) 1-bromo-l-propene (1) 1-iodo-l-propene (1) ethyl acrylate (1) propenaldehyde (1) acrylonitrile (1) propiolonitrile (1) acrylic acid (1) propiolic acid (1) acrylamide (1) ethyl vinyl ether (1) benzyl chloride (1) benzyl fluoride (1) benzyl bromide (1) benzyl iodide benzylamine (1) benzyl ethyl ether (1) benzyl alcohol (1) phenyl acetonitrile (1) phenyl acetaldehyde (1) benzyl mercaptan (1) phenyl acetic acid (1) 1,3-diphenyl-2-propanone (1) dibenzyl sulfide (1) benzyl formate (1) phenyl nitromethane (1) phenyl ethanamide (1) methyl phenyl acetate (1) benzyl acetate (1) benzenesulfonic acid (1) 1,2-dimethylbenzene (1) 1,3-dimethylbenzene (1) 1,4-dimethylbenzene (1) 1,2,3-trimethylbenzene (1) 1,2,4-trimethylbenzene (1) 1,3,5-trimethylbenzene (1) 1,2,3,4-tetramethylbenzene (1) 1,2,3,5-tetramethylbenzene (1) 1,2,4,5-tetramethylbenzene (1) 2-methylpyridine (1) 3-methylpyridine (1) 4-methylpyridine (1) 2,3-dimethylpyridine (1) 2,4-dimethylpyridine (1) 2,5-dimethylpyridine (2) 2,6-dimethylpyridine (1) 3,4-dimethylpyridine (1) 3,5-dimethylpyridine (1) 2,3,5-trimethylpyridine (1) methylcyclopentane (1) ethylcyclopentane (1) isopropylcydohexane (1) tert-butylcyclohexane (1) 1,1-dimethylcyclopentane (2) 1-methyl-1-ethylcyclopentane (1) 1-methylcyclopentene (1) 1-ethylcyclopentene vinylcyclopentane (1) limonene (1) chlorocyclopentane (1) fluorocyclohexane (1) bromocyclohexane (1) 2-chlorofuran (1) cyclopentanol (1) 1-methylcyclohexanol (1)

3268

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002

Table 2. (Continued) no. 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122

class alicyclic subst

polyfunctional subst

second-order group

description

example

CHcycsCOO CHcycsOOC CHcycsOOCH CHcycsNH2 CHcycsCN (CHndC)cycsCN CHcycsCOOH CHcycsNO2 CHcycsSH CHcycsSCHcycsCHO (CHndC)cycsCHO >NsCH2 (cyc) >NsCH3 (cyc) (CH3)2CH (subst in aromatic) (CH3)3C (subst in aromatic) CF3 (aromatic subst) COCH2COO CHm(OH)CHn(OH) CHm(OH)CHn(NHp) CHm(NH2)CHn(NH2) CHm(NHn)sCOOH CNsCHnsCOO HOOCsCHnsCOOH HOOCsCHnsCHmsCOOH HOsCHnsCOOH NHnsCHnsCHmsCOOH CHnsOsCHnsCOOH HSsCHnsCOOH HSsCHnsCHmsCOOH CH3sCOsCHnsOH CNsCHnsOH OHsCHnsCOOsCHm H2NCOsCHnsCHmsCONH2 NCsCHnsCHmsCN HSsCHnsCHmsSH COOsCHnsCHmsOOC OOCsCHmsCHmsCOO OHsCHnsCHmsCN CHm(NH)CHn(NH2)

CHcycsCOO CHcycsOOC CHcycsOOCH CHcycsNH2 CHcycsCN (CHndC)cycsCN CHcycsCOOH CHcycsNO2 CHcycsSH CHcycsSCHcycsCHO (CHndC)cycsCHO >NsCH2- (cyc) >NsCH3 (cyc) (CH3)2CH (subst in aromatic) (CH3)3C (subst in aromatic) CF3 (aromatic subst) COCH2O or COCHCOO or COCCOO CHm(OH)CHn(OH) (m,n in 0-2) CHm(OH)CHn(NHp) (m,n,p in 0-2) CHm(NH2)CHn(NH2) (m,n in 0-2) CHm(NHn)sCOOH (m,n in 0-2) CNsCHnsCOO (n in 1-2) HOOCsCHnsCOOH (n in 1-2) HOOCsCHnsCHmsCOOH (m,n in 1-2) HOsCHnsCOOH (n in 1-2) NHnsCHnsCHmsCOOH CH3sOsCHnsCOOH (n in 1-2) HSsCHnsCOOH HSsCHnsCHmsCOOH (m,n in 1-2) CH3sCOsCHnsOH (n in 0-2) CNsCHnsOH (n in 1-2) OHsCHnsCOOsCHm (m,n in 1-2) H2NCOsCHnsCHmsCONH2 (m,n in 1-2) NCsCHnsCHmsCN (m,n in 1-2) HSsCHnsCHmsSH COOsCHnsCHmsOOC OOCsCHmsCHmsCOO (m,n in 1-2) OHsCHnsCHmsCN (m,n in 1-2) CHm(NH)CHn(NH2) (m,n in 1-2)

ethyl cyclobutyrate (1) cyclohexyl acetate (1) cyclohexyl formate (1) cyclohexylamine (1) cyanocyclopentane (1) 3-cyanofuran (1) cyclopropanecarboxylic acid (1) nitrocyclohexane (1) cyclohexyl mercaptan (1) cannot assign UNIFAC group cyclohexanecarboxaldehyde (1) furfural (1) N-ethylpyrrole (1) N-methylpyrrole (1) cumene (1) tert-butylbenzene (1) perfluorotoluene (1) ethyl acetoacetate (1) 1,2,3-propanetriol (2) 1-amino-2-butanol (1) 1,2-propanediamine (1) 2-aminohexanoic acid (1) ethyl cyanoacetate (1) malonic acid (1) succinic acid (1) 2-hydroisobutyric acid alanine (1) methoxyacetic acid 2-mercaptopropionic acid (1) 3-mercaptoproionic acid (1) acetol (1) lactonitrile (1) ethyl lactate (1) butanediamide (1) succinonitrile (1) 1,2-ethanedithiol (1) ethylene glycol diacetate (1) dimethylsuccinate (1) hydroacrylonitrile (1) diethylenetriamine (1)

Table 3. Prediction Results: Deviation between Experimental and Estimated Dataa new method UNIFAC

modified UNIFAC

first order

second order

property

AAE

ARE (%)

AAE

ARE (%)

AAE

ARE (%)

AAE

ARE (%)

P y1 HE γinf

3.50 0.0153 388.82 89.53

3.47 3.64 192.03 39.41

4.09 0.0147 476.62 68.07

3.89 3.60 1167.50 58.81

1.95 0.0129 137.94 134.96

2.69 3.04 20.33 25.78

1.78 0.0112 115.79 124.97

1.99 2.79 20.20 25.11

Xest - Xexp 1 1 |Xest - Xexp| and ARE ) | | × 100%, where N is the number of data points, Xest is the estimated N N Xexp value of the property X, and Xexp is the experimental value of the property X. a

AAE )

∑

∑

Figures 9-12 show results in the form of HE-x diagrams for several systems. The results indicate that the excess enthalpy is more difficult to represent with a group-contribution method than VLE. It is evident that the KT-UNIFAC model gives better predictions for VLE as well as excess enthalpy than the original UNIFAC and the modified UNIFAC. Significant improvements are observed by introducing the new firstorder group CH2 (cyc) and the new second-order group ARs1s2. Accurate predictions of excess enthalpy are important in several chemical engineering applications such as distillation or heat exchanger design. The difficulties in the representation of complex systems, with respect to both VLE and HE, are not surprising. They are to be expected, because a simple groupcontribution model such as original UNIFAC and modified UNIFAC is not able to account for proximity effects, that is, the influence on a group from nearby groups on the same molecule. These effects can influence the

properties of a functional group significantly, especially when conjugation effects or intramolecular hydrogen bonds are present. Figure 13 compares the performance of the KT-UNIFAC model with experimental data and the original UNIFAC and modified UNIFAC models. As can be seen, the KT-UNIFAC model is also able to handle isobaric systems. Conclusions The KT-UNIFAC model allows better predictions of the phase behavior of nonelectrolyte systems than the other UNIFAC versions tested in this work. In addition, it guarantees a wide range of applicability. This was possible by using extended sets of first- and second-order groups and a second-order residual part, which is derived from perturbations with respect to structural and energetic parameters. The role of these larger sets of functional groups is to permit a more detailed

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3269 Table 4. Prediction Results: Average Relative Error for Chemical Families new method mixture alkane + alkene alkane + aromatics alkane + alcohols alkane + ketones alkane + aldehyde alkane + ether alkane + ester alkane + amine alkane + halogenated alkane + pyridine alkene + alkene alkene + aromatics alkene + alcohol alkene + ketone alkene + aldehyde alkene + ether alkene + ester aromatic + alcohol aromatic + ketone aromatic + ether aromatic + ester aromatics + amines aromatics + pyridine water + alcohol

property P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf P HE γinf

UNIFAC

modified UNIFAC

first order

second order

ARE (%)

ARE (%)

ARE (%)

ARE (%)

2.41 18.88 5.87 1.57 60.65 8.25 4.18 31.09 16.41 2.86 35.74 7.90 3.45

3.51 377.73 6.59 1.81 357.28 51.67 3.64 25.33 15.21 1.78 9.95 7.06 1.63

2.43 5.77 5.47 1.13 3.87 4.45 3.69 21.29 16.51 2.52 6.00 11.03 1.60

0.94 3.67 7.27 0.60 4.44 3.62 2.32 18.85 20.37 2.09 8.08 18.39 0.37

3.45

3.82

1.36

0.92

13.06 5.59

13.56 2.18

14.13 1.39

11.18 1.02

5.10 4.72

6.56 3.85

13.62 4.41

4.24 1.16

4.75

3.19

2.43

0.79

6.49 72.16

3.03 38.49

3.44 10.14

1.03 15.53

2.41 18.88 5.87 8.01

3.51 377.73 6.59 8.47

2.43 5.77 5.47 1.42

0.94 3.67 7.27 1.36

15.01 4.16

22.89 4.15

16.21 2.51

3.26 2.19

12.71 2.87

19.00 3.27

11.79 3.19

11.47 0.60

3.69

4.02

1.16

4.19 168.63

1.55 1010.80

1.12 2.41

3.54 113.52

7.59

3.41

1.86

1.70

11.50 4.32 46.82 19.21 1.99 7996.70 13.10 0.94

6.88 3.37 65.73 10.66 1.94 60640.00 28.00 1.36

50.20 2.35 17.86 13.56 1.62 57.36 9.90 3.26

5.29 1.97 13.20 7.06 2.15 85.66 8.27 3.96

3.33 0.93

4.18 0.35

12.70 1.66

5.80 0.62

15.47 3.26 131.36

86.88 3.86 153.96

13.63 3.82 24.22

0.01 3.51 7.22

0.77 28.03

1.15 68.50

0.65 3.43

0.29 3.39

5.34 186.47 413.10

7.90 506.26 610.12

3.04 63.87 186.19

4.05 55.58 161.69

3270

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002

Table 4. (Continued) new method mixture water + ketone alcohol + ketone alcohol + ethers alcohol + amines alcohol + pyridines ketone + ethers ketone + amines ketone + pyridines

UNIFAC

modified UNIFAC

first order

second order

property

ARE (%)

ARE (%)

ARE (%)

ARE (%)

P HE γinf P HE γinf P γinf P HE P HE γinf P HE γinf P HE P HE γinf

4.08 96.40 24.02 4.97 56.13 10.10 1.55 80.19 2.41 81.10 3.74 50.97

5.81 71.11 31.39 4.59 38.77 9.90 1.02 80.61 6.10 66.88 7.88 59.76

8.25 54.63 56.20 2.93 11.84 11.02 3.44 42.59 4.07 62.05 3.52 39.33

4.15 90.17 38.87 2.36 11.67 10.00 3.55 68.25 1.34 50.81 2.36 33.75

2.14 44.09 40.74 0.99 41.54 0.25

2.09 48.01 25.68 1.91 18.98 2.07

5.77 19.79 78.26 0.98 1.76 0.91

1.57 17.56 44.87 0.87 1.33 0.24

Figure 1. Present status of the new UNIFAC extension parameter tables. Table 5. Prediction Results: Deviation between Experimental and Estimated Data new method UNIFAC property

AAE

P y1 HE γinf P (ternary)

8.09 0.0210 425.66 60.01 35.74

ARE (%) 6.98 4.08 250.14 37.60 8.68

modified UNIFAC AAE 8.23 0.0201 367.99 53.20 31.25

ARE (%) 7.06 4.01 180.16 40.20 8.76

first order AAE 7.22 0.0196 200.30 127.80 28.75

ARE (%) 5.68 3.98 87.60 58.00 7.94

second order AAE 6.97 0.0184 186.17 118.60 -

ARE (%) 5.42 3.58 72.54 60.76 -

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3271

Figure 2. Experimental and predicted results for VLE (water + 1,4-dioxane at 308.15 K).

Figure 5. Experimental and predicted results for VLE (1-butanol + acetic acid at 308.15 K).

Figure 3. Experimental and predicted results for VLE (hexane + methoxybenzene at 333.25 K).

Figure 6. Experimental and predicted results for VLE (water + acetic acid at 353.15 K).

Figure 4. Experimental and predicted results for VLE (1,2epoxybutane + n-heptane at 313.15 K).

Figure 7. Experimental and predicted results for VLE (heptane + 2-methyl isobutyl ketone at 348.15 K).

representation of chemical structures, to partially account for proximity effects, and to distinguish among isomers. These advantages should allow a more reliable synthesis and design of separation processes, design/ selection of solvents for extractive distillation or extraction, calculation of chemical equilibria, design of formulations, and so on. When additional experimental phase-equilibrium data and especially excess enthalpy data are available, some of the new group interaction parameters may need to be revised and the KT-UNIFAC model parameter matrix may need to be further extended.

Supporting Information Available: Tables of first- and second-order interaction parameters. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature amk,1, amk,2 ) adjustable parameters in eq 9 GE ) excess Gibbs free energy Ji ) defined by eq 5 Ki ) K-factor for component i Li ) defined by eq 5 nk ) total number of groups k in the mixture

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Figure 8. Experimental and predicted results for VLE (heptane + 2-methyl-2-butanol at 328.15 K).

Figure 11. Experimental and predicted results for excess enthalpy (benzene + 2-propanol at 308.15 K).

Figure 9. Experimental and predicted results for excess enthalpy (methanol + acetone at 323.15 K).

Figure 12. Experimental and predicted results for excess enthalpy (hexane + tert-butyl alcohol 303.15 K).

Figure 10. Experimental and predicted results for excess enthalpy (benzene + 1,2,3,4-tetrahydronaphthalene at 298.15 K).

Figure 13. Experimental and predicted results for isobaric VLE (hexane + 2-propanol at 380 mmHg).

P ) pressure Psat ) vapor pressure Qk ) surface area parameter, for group k R ) gas constant ri ) molecular volume parameter, for component i Rk ) volume parameter, for group k S ) sum of quadratic deviations T ) temperature T0 ) temperature, reference xi ) mole fraction of component i in the liquid phase yi ) mole fraction of component i in the vapor phase z ) lattice coordination number

Greek Symbols ∆γE ) difference between observed and estimated values for the infinite dilution activity coefficient ∆HE ) difference between observed and estimated values for the excess enthalpy ∆P ) difference between observed and estimated values for the pressure ∆umn ) interaction parameter for the m-k interaction δum′n,j ) perturbation of ∆umn due to m’s appearance in j δumn′,j ) perturbation of ∆umn due to n’s appearance in j

Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3273 γi ) activity coefficient for molecule i γCi ) activity coefficient, combinatorial part γRi ) activity coefficient, first-order residual part γR2 i ) activity coefficient, second-order residual part Γk ) residual group activity coefficient for group k Γik ) residual group activity coefficient for group k, in pure component i νki ) number of groups k present in molecule i τmk ) local composition weighting factors ϑi ) modified volume fraction of component i in the mixture Indexes calc ) calculated quantity C ) combinatorial part R ) residual part, first order R2 ) residual part, second order E ) excess quantity

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Received for review October 17, 2001 Revised manuscript received April 24, 2002 Accepted April 29, 2002 IE010861W