duanyuanyuan322669-200809-30

Fluid Phase Equilibria 238 (2005) 229–238

Prediction of the second cross virial coefficients ofnonpolar binary mixtures

Long Meng, Yuan-Yuan Duan∗Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, PR China

Received 29 June 2005; received in revised form 6 October 2005; accepted 10 October 2005

Abstract

The binary interaction parameter,kij, of 268 nonpolar mixtures were determined from the database of second cross virial coefficients containing1728 experimental data points by fitting the second cross virial coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L.Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for bothn-alkane/n-alkane binariesand fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979)143–162] with the quantity of binary compounds enlarged using Dymond’s latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, VirialCoefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Bornstein, 2002]. Correlationswere also developed for inorganic/n-alkane binaries using newkij values. The predictions do not need any thermodynamic property parametersbesides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.©

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2005 Elsevier B.V. All rights reserved.

eywords: Second cross virial coefficients; Mixtures; Binary interaction parameters;n-Alkane

. Introduction

The thermodynamic properties of gas mixtures may be read-ly calculated from a knowledge of the mixing virial coefficientsnd their dependence on temperature. The virial equation oftate, truncated after the second virial coefficient, is a usefulxpression for calculating the gaseous properties for reducedensities less than 0.5. For binary mixtures, the importance of

he second cross virial coefficient,Bij, can be easily understoodrom Eqs.(1) and(2),

= 1 + Bm1

ν(1)

m =∑

i

∑j

xixjBij (2)

hereZ is the compressibility factor,ν the volume, andBii andjj are the second virial coefficients of the pure componentsi and

, which can be calculated from correlations for pure fluids.Bm isermed the mixing virial coefficient.Bij is usually predicted with

∗ Corresponding author. Tel.: +86 10 6279 6318; fax: +86 10 6277 0209.E-mail address: [email protected] (Y.-Y. Duan).

the help of mixing rules and the binary interaction paramkij. The parameterkij arises from the assumptions used to dethe equation of state (EoS) mixing rules and also corrects fodeviation between the EoS prediction and experimental da

Much new, high-quality experimental data for the seccross virial coefficientBij has been published since the 198with most of it recently collected by Dymond et al.[3]. Thisdata with a new correlation for the second virial coefficieof pure fluids[1] can be used to update the binary interacparameter,kij. In recent years, optimum values ofkij have beereported by Chueh and Prausnitz[4] and Hiza and Duncan[5],with extensions to the collection ofkij presented by Morrisoand McLinden[6], Tsonopoulos[2] and Kis and Orbey[7].Recently, Abusleme and Vera[8] and Plyasunov et al.[9] pub-lished somekij’s of strongly polar mixtures. Several empiricorrelations forkij have also been presented in the literature.and Firoozabadi[10], Nishiumi et al.[11], and Gao et al.[12]proposed correlations for hydrocarbon binary mixtures andrelations for mixtures containing carbon dioxide were repoby Coutinho et al.[13], Kato et al.[14], Nishiumi et al.[11],Darridon[15], Bartle et al.[16] and Kordas et al.[17]. How-ever, there are so many of them that it is impossible to dall the references here. Lately, the group contribution me

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230 L. Meng, Y.-Y. Duan / Fluid Phase Equilibria 238 (2005) 229–238

[18,19]has also been used to predictkij. Many researchers havefound that it is extremely difficult to correlatekij with respectto substance types or other characteristics. In some references,the authors assumedkij to be a temperature dependent parameterto obtain better results[20–23]. However, for many substances,the assumption thatkij is independent of temperature, density,and composition still gives good approximations for predictingBij within the experimental uncertainties and is certainly moreconvenient.

Meng et al.[1] presented a modified corresponding-state cor-relation that compares well with experimental data for the secondvirial coefficient for most nonpolar pure compounds, since thepredictions have been corrected for most physical adsorptioneffects. Detailed comparisons with the well-known Tsonopouloscorrelation[1] showed that the model is somewhat better thanTsonopoulos correlation for nonpolar compounds. This paperwill extend the correlation to binary mixtures. The correlationfor nonpolar fluids is:

BPc

RTc= f (0)(Tr) + ωf (1)(Tr) (3)

f (0) = 0.13356− 0.30252

Tr− 0.15668

T 2r

− 0.00724

Tr3 − 0.00022

Tr8

(4)

f

wpt nEr gm

T

P

ω

w

u uso inhee ientd peri-m ctiop thes

2

enr s,

they are the preferred binary types for analysis to test new ideas.Among these references, the relationship proposed by Chueh andPrausnitz[24] using critical volumes as the correlating parame-ters is most commonly used

kij = 1 − 8(νciνcj)1/2

(νci1/3 + νcj

1/3)3(9)

This correlation was developed from London’s theory of dis-persion forces, which makes it a theoretically based correlation.This correlation gives satisfactory results for all paraffin/paraffinmixtures. More generally, this equation has been applied byTarakad and Danner[25] to systems in which both specieswere hydrocarbons. Fender and Halsey[26] also proposed ageometric–arithmetic mean correlation with critical tempera-tures as correlating parameters using the expression:

kij = 1 − 2(TciTcj)1/2

Tci + Tcj(10)

This correlation was developed for Ar/Kr mixtures; however, itcan also be used for some inorganic binaries and hydrocarbonbinaries. Later, Tsonopoulos[2] proposed a quite different cor-relation with carbon numbers as correlating parameters, whichgives better results for methane/hydrocarbon binaries. More-over, he suggested a general form for hydrocarbon binariesusing

k

w ,T eterm

b eenc data,w rsuf

llyi datap entalu eep esentc dictsh -s rs ofc ofk rveda

ev rela-t eC al-u achg s-i onentj s

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(1) = 0.17404− 0.15581

Tr+ 0.38183

Tr2 − 0.44044

Tr3 − 0.00541

Tr8

(5)

hereTr(=T/Tc) is the reduced temperature,Pc andTc the criticalressure and critical temperature,R = 8.314472 J mol−1 K−1 is

he universal gas constant, andω is the acentric factor. Wheqs.(3)–(5) are used to calculateBij, Pc, Tc, andω should be

eplaced byPcij, Tcij, andωij, which are defined by the followinixing rules,

cij = (TciTcj)1/2(1 − kij) (6)

cij = 4Tcij(Pciνci/Tci + Pcjνcj/Tcj)

(νci1/3 + νcj

1/3)3(7)

ij = ωi + ωj

2(8)

hereνci andνcj are the critical volumes of componentsi andj.As mentioned in many references, the values ofkij obtained

sing different methods can be different. The inappropriatef these results may mislead observations concerning thent law forkij. Therefore, only the second cross virial coefficata for 268 nonpolar binary mixtures containing 1728 exental data points were used to evaluate the binary interaarameterkij in this work to improve the representation ofecond virial coefficients for binary mixtures.

. n-Alkane/n-alkane binaries

The values ofkij for n-alkane/n-alkane binaries have beeported in many references[2,4,11]. As the classical binarie

er-

n

ij = m[ln(ncj − nci + 1)]2 (11)

here nci is the carbon number of componenti. Howeversonopoulos did not give a method to calculate the param, which makes Eq.(11)of limited use.In this work, the optimum values ofkij for n-alkane/n-alkane

inaries were recalculated by minimizing the deviations betwalculated and experimental second cross virial coefficientith the results listed inTable 1. All the property parametesed for fitting in this study, namely,Pc, Tc, νc andω were taken

rom the DIPPR® 801 database[27].To obtain reliable values ofkij, the data quality was carefu

nvestigated and doubtful data points were rejected. Eachoint was weighted by the author’s recommended experimncertainty. Also, somekij’s were slightly adjusted within thxperimental data uncertainties. Mostkij’s in Table 1are lessositive than those of Tsonopoulos’ work, because the prorrelation for pure compounds at low temperatures preigher values than Tsonopoulos correlation[28], which is senitive tokij. Surprisingly, when the sum of the carbon numbeomponentsi andj was used as thex-coordinate and the valueij as they-coordinate, an interesting distribution was obses shown inFig. 1.

Fig. 1shows that each group in C1–C8 has the trend that thalues ofkij increase with increasing carbon numbers. Thisionship is abstractly illustrated inFig. 2, where Cij denotes th

i/Cj binary (Cii = 0 and Cij = Cji). The trends show that the ves ofkij(j ≥ i) increase with increasing carbon number for eroup having the same componenti and decrease with increa

ng carbon number for each group having the same comp. A similar distribution can also be found forkij when plotted a

L. Meng, Y.-Y. Duan / Fluid Phase Equilibria 238 (2005) 229–238 231

Table 1Optimum values ofkij for n-alkane/n-alkane, fluorocarbon/fluorocarbon, N2/n-alkane, CO2/n-alkane binaries and their deviations

i j No. of points kij RMSD in Bij (cm3 mol−1)

Present worka Present workb Tsonopoulosc Chueh and Prausnitzc Fender and Halseyc

CH4 C2H6 55 0.0054 3.1 3.1 3.9 3.1 6.4C3H8 26 0.0181 6.0 5.9 4.7 4.1 9.5C4H10 36 0.0205 6.5 6.4 9.8 6.6 15.1C5H12 19 0.0301 13.0 13.1 22.9 17.6 29.7C6H14 14 0.0419 8.9 8.9 21.1 14.0 28.7C7H16 12 0.0476 17.6 18.0 45.8 33.8 55.4C8H18 6 0.0658 3.7 3.6 35.6 22.5 43.6C9H20 3 0.0713T 31.0 32.3 88.2 66.2 97.0C10H22 4 0.1497T 48.3 46.7 18.5 28.7 17.4C12H26 4 0.1413 16.8 14.6 17.3 4.54 12.6C16H34 5 0.2058 38.5 35.5 29.7 38.5 40.0C20H42 4 0.1817 40.7 45.2 32.7 11.7 12.0C30H62 2 0.3371T 29.6 35.6 59.5 101.6 139.8

C2H6 C3H8 27 0.00002 3.7 3.6 2.9 3.7 3.8C4H10 11 0.0018 9.1 9.0 10.2 10.8 11.0C5H12 8 0.0110 15.6 15.5 17.5 17.8 17.2C6H14 7 0.0217 5.3 5.1 11.5 12.0 8.8C8H18 2 0.0452 1.4 3.3 9.8 10.7 1.6C16H34 3 0.1339T 26.4 19.2 45.9 23.3 106.0C20H42 4 0.1839 14.5 13.5 12.3 50.2 150.3C30H62 2 0.3141T 23.7 53.4 38.5 203.4 376.0

C3H8 C4H10 9 −0.0001 8.1 8.2 – 6.1 6.1C5H12 4 0.0064 3.3 3.2 – 1.9 2.8C6H14 7 0.0114 5.8 5.8 – 5.8 5.2C7H16 3 0.0134 11.8 12.0 – 17.7 11.5C8H18 3 0.0254 3.0 3.1 – 10.4 4.5

C4H10 C5H12 4 0.0002 4.6 4.6 – 3.7 4.3C6H14 8 0.0070 11.8 11.6 – 16.9 19.4C8H18 3 0.0136 5.9 6.9 – 11.8 5.1

C5H12 C6H14 7 0.0007 10.8 10.8 – 9.4 10.1C7H16 3 0.0039 2.1 2.0 – 2.4 3.5C8H18 2 0.0067 2.4 3.0 – 5.4 3.9

C6H14 C8H18 2 0.0032 1.8 1.8 – 2.8 5.6

C7H16 C8H18 2 0.0006 1.6 1.6 – 3.9 5.2

CF4 C2F6 2 0.0232 7.3 7.5 – 9.5 9.9C3F8 2 0.0368 10.0 9.2 – 5.6 5.0C4F10 2 0.0471 9.6 8.3 – 6.0 6.9C5F12 2 0.0744 0.7 3.0 – 5.6 18.5C6F14 2 0.0969 8.5 10.7 – 12.2 33.4

C2F6 C3F8 2 0.0255 10.1 9.4 – 16.7 16.8C4F10 2 0.0318 7.8 8.3 – 17.8 21.1C5F12 2 0.0443 11.4 14.0 – 21.9 32.5C6F14 2 0.0632 6.3 10.6 – 30.8 54.6

C4F10 C5F12 1 0.0160 1.6 3.6 – 34.0 37.5C6F14 1 0.0304 0.7 9.2 – 47.7 57.5

N2 CH4 28 0.0346 2.8 – 3.3 4.5 3.1C2H6 10 0.0502 0.8 – 1.8 6.2 4.4C3H8 18 0.0354 8.1 – 6.9 5.3 17.3C4H10 17 0.0642 6.9 – 7.0 8.1 18.8C5H12 17 0.1147 7.6 – 7.1 17.2 15.3C6H14 26 0.1167 8.6 – 9.6 15.6 25.5C7H16 15 0.1353 11.0 – 11.9 21.7 28.1C8H18 6 0.1418 5.6 – 10.8 17.6 31.1C9H20 4 0.1548 10.2 – 19.9 21.6 44.2C10H22 7 0.1593 9.0 – 17.8 17.9 33.9C12H26 4 0.1755 1.9 – 19.4 16.1 30.5

CO2 CH4 31 0.0399 2.2 – – 8.2 3.9



Table 1 (Continued )

i j No. of points kij RMSD in Bij (cm3 mol−1)

Present worka Present workb Tsonopoulosc Chueh and Prausnitzc Fender and Halseyc

C2H6 26 0.0847 3.1 – – 26.4 29.1C3H8 15 0.1097 11.2 – – 42.7 50.9C4H10 6 0.1433 19.4 – – 67.7 85.4C5H12 8 0.1749T 44.8 – – 116.3 144.5C6H14 2 0.2742 51.2 – – 157.6 198.2C7H16 2 0.2620 33.4 – – 163.4 220.9C8H18 1 0.2505 5.7 – – 128.8 189.7C9H20 1 0.2629 1.6 – – 143.9 223.1C10H22 2 0.2259T 63.1 – – 123.2 238.2

Superscript T denotes strong temperature dependence.a kij was calculated with the values ofm listed inTable 2.b By Eqs.(12)and(13) for n-alkane/n-alkane binaries and by Eq.(14)with m = 0.01747 for fluorocarbon/fluorocarbon binaries.c With Tsonopoulos correlation for pure fluids[28].

Fig. 1. Distribution ofkij’s for n-alkane/n-alkane binaries: (�) C1 group; (�)C2 group; (�) C3 group; (�) C4 group; (�) C5 group; (�) C6 group; (�) C7

group; (�) C8 group.

Fig. 2. Abstract distribution ofkij values as a function of the carbon numbersum of componentsi andj.

a function of various thermodynamic properties of the two com-ponents such asTciTcj, ωiωj, νciνcj, andωi +ωj on the abscissa,where the subscriptsi andj are transposable.

In addition, the slope of the curve for each group decreasesas the series number of the group increase. As a result, heav-ier n-alkane/n-alkane binaries probably havekij values closerto zero. This behavior makes it possible to correlate all then-alkane/n-alkane binaries using only one equation if thekij valuesof each group can be correlated with just one fitting coefficient.Such a correlation can be compared with the Chueh and Praus-nitz correlation for alln-alkane/n-alkane binaries. Therefore, thecorrelation developed here follows the approach suggested byTsonopoulos,

kij = m[ln(ncj − nci + 1)]7/2 (12)

wherem is a variable coefficient defined for eachn-alkane group.Although the relationship between (ncj + nci) andkij’s is clearlyshown inFig. 2, using (ncj − nci) instead of (ncj + nci) as thecorrelating parameter does not affect the correlation results. Eq.(12)implies that (ncj ≥ nci) and whenncj = nci,kij is equal to zero.Since thesekij results were somewhat different from Tsonopou-los, the exponent of the bracketed quantity was changed to 7/2 toget better results. The values ofm were listed inTable 2. Finally,the trends ofm for n-alkane/n-alkane binaries can be correlatedby

m

wr sn ngcte

alcu-l ofT att ta causet um


= 0.00678

1 + 0.336nci(13)

herenci is the carbon number of componenti(j ≥ i). This cor-elation is shown inFig. 3, which shows thatm decreases aci increases, with a limiting value of zero for an infinitely lohain. The optimizedkij’s for the CH4 group and the C2H6 groupogether with Eqs.(12) and (13) are plotted inFig. 4 as twoxamples to show the present correlation results.

The resulting deviations between experimental and catedBij for n-alkane/n-alkane binaries, along with the worksonopoulos, are given inTable 1. First, it should be noted th

he RMSD values in the column marked a inTable 1are nolways be smaller than those in the column marked b, be

he values ofm used in the column a is not to give the minim


Table 2Values ofm for nonpolar binaries

Componenti (nci) Componentj (ncj) m

n-Alkane/n-alkane binariesC1 0.00496C2 0.00436C3 0.0334C4 n-Alkane 0.00273C5 0.00244C6 0.00227C7 0.00209

Fluorocarbon/fluorocarbon binariesCF4 0.01855C2F6 Fluorocarbon 0.01583C4F10 0.01536

Inorganic/n-alkane binariesN2 n-Alkane 0.04311CO2 n-Alkane 0.07475

Fig. 3. Parameterm as a function ofnci for n-alkane/n-alkane binaries: (�)values ofm as listed inTable 2and (—) Eq.(13).

Fig. 4. Optimumkij values for CH4 and C2H6 groups: (�) optimum values ofCH4 group; (©) optimum values of C2H6 group; (—) Eqs.(12) and(13) withnci = 1; (- - -) Eqs.(12)and(13)with nci = 2.

RMSD for each kind of substances, but for overall substances inthis group. Although larger RMSD for some substances in thecolumn marked a, but the overall RMSD of this group is def-initely smaller than that in the column marked b. Comparisonof the present result with the Tsonopoulos model with the twowell-known correlations forkij, Eqs.(9) and(10), shows thatthe present model has a smaller overall RMSD of 13 cm3 mol−1

compared to 24 cm3 mol−1 for Eq. (9) and 43 cm3 mol−1 forEq. (10). Note that the present work has a 35.6 cm3 mol−1

RMSD for the methane/squalane binary, while Eqs.(9) and(10) have much worse results, 101.6 cm3 mol−1 for Eq.(9) and139.8 cm3 mol−1 for Eq.(10). Such case was also found for theethane/squalane binary with an RMSD of 53.4 cm3 mol−1 forthis work and a much larger 203.4 cm3 mol−1 RMSD for Eq.(9)and 376.0 cm3 mol−1 RMSD for Eq.(10). Therefore, the presentcorrelation is quite successful for long chainn-alkane binarieswith carbon numbers up to 30. The present prediction results forthe second virial cross coefficient forn-alkane/n-alkane binariesall show that Eqs.(12) and(13) are superior to the well-knowncorrelations, Eqs.(9)and(10), even though both give good repre-sentations of the experimental data for shortn-alkane binaries.Furthermore, the present work only used carbon numbers asthe correlating parameters, which is obviously more convenientthan the Chueh and Prausnitz[24] and Fender and Halsey[26]correlations. In addition, as shown in column c ofTable 1, evenwith comparisons between Eqs.(12)and(13)and the correlationg rbonb llg

3

s n-s g thed opti-mflTo arlyw oughv aviorm

u etterfi

k

w edi thee ar-b ev t wasm ea w-e l


iven only for methane/hydrocarbon and ethane/hydrocainaries proposed by Tsonopoulos[2], the present work stiives better results for these two groups.

. Fluorocarbon/ fluorocarbon binaries

As mentioned in the previous section,Fig. 2strongly impliesome regularity for then-alkane/n-alkane binaries. The relatiohip can also be investigated for other species by examininata for fluorocarbon/fluorocarbon binaries. The resultingized kij’s are listed inTable 1. The distribution ofkij’s for

uorocarbon/fluorocarbon binaries is similar to that inFig. 1.he slight difference is that the optimizedkij’s for each groupf fluorocarbon/fluorocarbon binaries possibly increase lineith increasing carbon numbers, although there are not enalues to provide assured evidence at present. This behore or less supports the case ofn-alkane/n-alkane binaries.Although a similar method can be used to describe thekij val-

es for fluorocarbon/fluorocarbon binaries, a substantially bt of the data is suggested,

ij = m(ncj − nci), (ncj ≥ nci) (14)

here the values ofm for each fluorocarbon group are listn Table 2. The predictions show good agreement withxperimental data, with an overall RMSD for the fluorocon/fluorocarbon binaries of 8.1 cm3 mol−1. However, sincery few data are available for these binaries, no attempade to correlatem. As new experimentalBij data becom

vailable, the correlation form should be established. Hover, for now, a rough estimated value ofm is 0.01747 for al


Fig. 5. Optimum values ofkij for fluorocarbon/fluorocarbon binaries: (�) opti-mum values and (—) Eq.(14)with m = 0.01747.

the fluorocarbon/fluorocarbon binaries which gives an overallRMSD of 9.2 cm3 mol−1, less than 20.2 cm3 mol−1 by Eq.(9)and 29.6 cm3 mol−1 by Eq.(10). The RMSDs from experimen-tal data are listed inTable 1with the representation ofkij shownin Fig. 5.

4. Inorganic/n-alkane binaries

For inorganic/n-alkane binaries,Table 1also presents opti-mum kij values for N2/n-alkane and CO2/n-alkane binaries.When Eq.(12)was used for the correlation, the exponent shouldbe changed to 3/2 to gain better results.

kij = m[ln(ncj + 1)]3/2 (15)

As compared with Eq.(12), Eq. (15) implies thatnci is equalto zero for the inorganic component. The values ofm arelisted in Table 2. The comparisons with the Tsonopoulos cor-relation for N2/n-alkane binaries as listed inTable 1 showthat the present work gives a better representation ofBij thanTsonopoulos correlation. The total RMSD for the present workis 7.3 cm3 mol−1 versus 9.4 cm3 mol−1 for Tsonopoulos. How-ever, the total RMSD using Eq.(9) is 13.6 cm3 mol−1 and up to21.5 cm3 mol−1 using Eq.(10). As for the CO2/n-alkane bina-ries, the total RMSD of present work is 19.6 cm3 mol−1 versus61.4 cm3 mol−1 using Eq.(9) and up to 83.0 cm3 mol−1 usingE -t endedt

Cw itht epi m 5t s foC undi re.Ac df ca

Fig. 6. Optimumkij values for N2/n-alkane and CO2/n-alkane binaries: (�)optimum values of N2/n-alkane binaries, (©) optimum values of CO2/n-alkanebinaries, (—) Eq.(15)with m = 0.04311, and (- - -) Eq.(15)with m = 0.07475.

bon number increases, such behavior observed in the presentwork, which was induced by only optimizing the second crossvirial coefficient, was not taken into account for correlatingkij’s,until morekij’s are reported to establish the true trend.

5. Other nonpolar binaries

Thekij’s of 202 nonpolar binary systems are listed inTable 3to update and enlarge thekij database. Substances with smalldipole moments (according to the DIPPR® 801 database[27])were not discussed in this work. Some nonpolar binaries showstrong temperature dependent characteristics. The optimumkij’smust be careful used because some were obtained from just twoor three experimental data points, which leads to less reliabilityof the optimum values. Further work is needed to update theresults inTable 3. Those mixtures could not be easily correlatedinto reasonable groupings. However, when all 268 optimumkij’sare plotted together inFig. 7with (TciTcj)1/2 as thex-coordinate,some additional interesting information is obtained. Almost all

Fv


q.(10). Since the RMSDs of Eqs.(9)and(10)from experimenal data are too large, these two equations can not be exto the binaries ofn-alkane with CO2 or N2.

Fig. 6 presents all the optimumkij’s for N2/n-alkane andO2/n-alkane binaries along with the relationship in Eq.(15),hich shows that Eq.(15)gives a satisfactory fit of the data w

he corresponding values ofm. However, the figure shows a stn the values ofkij when the carbon number increases froo 6, and thenkij deceases as the carbon number increaseO2/n-alkane binaries. A similar unusual behavior was fo

n the case of Ar/n-alkane binaries, which is not shown helthough many authors have mentioned, thekij’s of CO2/long-hain hydrocarbon binaries (most of theirkij’s were obtainerom VLE data) may decrease as the heavy hydrocarbon’s

r

r-ig. 7. Distribution of optimumkij values for nonpolar binaries: (�) optimumalues and (—) Eq.(16).


Table 3Optimum values ofkij for nonpolar binaries

Componentj kij Componentj kij

Argon+Carbon dioxide 0.0675 Benzene 0.1496Sulfur hetrafluoride 0.0420 1,1-Dimethylcyclopentane 0.1614Krypton −0.0015 cis-1,3-Dimethylcyclopentane 0.1604Nitrogen 0.0082 trans-1,2-Dimethylcyclopentane 0.1629Oxygen 0.0265 trans-1,3-Dimethylcyclopentane 0.1628Xenon 0.0528 Heptane 0.1338T

Tetrachloromethane 0.1443 2,2-Dimethylpentane 0.1892Tetrafluoromethane 0.0396 2,3-Dimethylpentane 0.1788Methane 0.0000 2,4-Dimethylpentane 0.1844Hexafluoroethane 0.0730 2-Methylhexane 0.1776Ethane 0.0556 3,3-Dimethylpentane 0.1876Propane 0.0607 3-Methylhexane 0.1748Octafluorocyclobutane 0.0535 2,2,3-Trimethylbutane 0.1937Butane 0.0392 1,4-Dimethylbenzene 0.0576Cyclopentane 0.1411 Octane 0.1219Pentane 0.1384 2,2,4-Trimethylpentane 0.1796T

2,2-Dimethylpropane 0.0817 1,3,5-Trimethylbenzene 0.0621Cyclohexane 0.1510 Nonane 0.1177Methylcyclopentane 0.1446 Naphthalene 0.2344T

Hexane 0.1357 1-Methyl-4-propylbenzene 0.08482,2-Dimethylbutane 0.1352T 1,4-Diethylbenzene 0.09172,3-Dimethylbutane 0.1924 1,2,4,5-Tetramethylbenzene 0.06932-Methylpentane 0.1403 Anthracene 0.23303-Methylpentane 0.1962T

Krypton+Xenon 0.0155 Methane −0.0115Sulfur hetrafluoride 0.0792 Hexafluoroethane 0.0780Carbon dioxide 0.0699 Ethane 0.0269T

Tetrafluoromethane 0.0588 Octafluorocyclobutane 0.0543

Xenon+Carbon dioxide 0.0921 Hexafluoroethane 0.1043Sulfur hetrafluoride 0.0826 Ethene 0.0200Nitrogen 0.0736 Ethane 0.0070Tetrafluoromethane 0.1018 Octafluorocyclobutane 0.0759Methane 0.0082

Tetrachloromethane+Carbon dioxide 0.2115T Ethene 0.0769T

Nitrogen 0.1735 Benzene −0.0186Methane 0.0944 Cyclohexane −0.0082

Tetrafluoromethane+Carbon dioxide 0.0737 Ethane 0.1061Sulfur hetrafluoride 0.0125 Butane 0.1081Nitrogen 0.0060 Pentane 0.0691Oxygen 0.0380 Hexane 0.1117Methane 0.0829

Hexafluoroethane+Methane 0.1042 Butane 0.1073Ethane 0.1138T Pentane 0.1114

Octafluoropropane+Propane 0.0919

Decafluorobutane+Methane 0.1009 Butane 0.0726Ethane 0.1008 Hexane 0.0959

Dodecafluoropentane+Methane 0.1424 Pentane 0.1040

Tetradecafluorohexane+Methane 0.2949 Hexane 0.0909Pentane 0.1004





Methane+Oxygen 0.0470 2-Methylpentane 0.0201T

Sulfur hetrafluoride 0.0745 2,2-Dimethylbutane 0.1014T

Ethene 0.0397 2,2,5-Trimethylhexane 0.1914Octafluorocyclobutane 0.0714 Naphthalene 0.1467T

2,2-Dimethylpropane 0.0619 Bicyclohexyl 0.2197T

Benzene 0.0725 Phenanthrene 0.1605Cyclohexane 0.1150T Anthracene 0.1839

Ethene+Nitrogen −0.0408T Bicyclohexyl 0.1455Carbon dioxide 0.0192 Phenanthrene 0.1406Ethane 0.0108 Anthracene 0.1509Benzene 0.1110 Hexadecane 0.1573Naphthalene 0.0838

Ethane+Naphthalene 0.1150 Anthracene 0.1587Bicyclohexyl 0.1087

Benzene+Pentane 0.0499 Heptane 0.0105Cyclohexane 0.0147 Octane 0.0302Hexane 0.0088

Cyclohexane+Hexane 0.0072

Carbon dioxide+Sulfur hetrafluoride 0.0989 2,2-Dimethylpentane 0.2867Nitrogen 0.0199 2,3-Dimethylpentane 0.2715Oxygen 0.0473 2,4-Dimethylpentane 0.29141,3-Butadiene 0.1955 3,3-Dimethylpentane 0.2877Cyclopentane 0.2544 3-Ethylpentane 0.2475Benzene 0.0469T 2,2,3-Trimethylbutane 0.3142Cyclohexane 0.1797T 1,4-Dimethylbenzene 0.1602Methylcyclopentane 0.2554 2,2,4-Trimethylpentane 0.23712-Methylpentane 0.2967 1,3,5-Trimethylbenzene 0.16183-Methylpentane 0.2930 Naphthalene 0.1905T

2,2-Dimethylbutane 0.3407 1-Methyl-4-propylbenzene 0.20752,3-Dimethylbutane 0.2977 1,2,4,5-Tetramethylbenzene 0.16552-Methylhexane 0.2680 Anthracene 0.23253-Methylhexane 0.2628 Phenanthrene 0.2185

Sulfur hetrafluoride+Nitrogen 0.0008 Pentane 0.1146Oxygen 0.0434

Nitrogen+Boron trifluoride 0.0086 2-Methylhexane 0.1301Oxygen −0.0075 3-Methylhexane 0.1411T

Cyclopentane 0.1475 3-Ethylpentane 0.1087(E)-2-Pentene 0.0912 2,2-Dimethylpentane 0.0479T

2,2-Dimethylpropane 0.1159 2,3-Dimethylpentane 0.1394T

Benzene 0.1070 2,4-Dimethylpentane 0.1360Cyclohexane 0.1221 3,3-Dimethylpentane 0.1327Methylcyclopentane 0.0876 2,2,3-Trimethylbutane 0.1598T

(E)-2-Hexene 0.1034T 2,2-Dimethylhexane 0.0878(E)-3-Hexene 0.0999T 2,2,4-Trimethylpentane 0.2392T

2-Methylpentane 0.1188T 2,2,3,3-Tetramethylbutane 0.14573-Methylpentane 0.1309T 2,2,5-Trimethylhexane 0.23262,2-Dimethylbutane 0.1546T Naphthalene 0.18912,3-Dimethylbutane 0.1288

Oxygen+Pentane 0.0232 2-Methylhexane 0.1024Cyclopentane 0.0121 3-Methylhexane 0.0906Benzene 0.1486T 3-Ethylpentane 0.1025Cyclohexane 0.0667 2,3-Dimethylpentane 0.1140





2-Methylpentane 0.0827 2,4-Dimethylpentane 0.10983-Methylpentane 0.0672 3,3-Dimethylpentane 0.11912,2-Dimethylbutane 0.0937 2,2,3-Trimethylbutane 0.12282,3-Dimethylbutane 0.0840 Naphthalene 0.2480Hexane 0.0766 Anthracene 0.2369Heptane 0.0976

Superscript T denotes strong temperature dependence.

of the optimumkij’s are located in the hatched area and thehatched area shape is consistent with that ofFig. 2. The impor-tance of the hatched area is that it gives a rough range forkij’s forunknown nonpolar binaries. The upper limit ofkij’s is roughlygiven by

kij = −0.17553+ 0.00135(TciTcj)1/2 (16)

while the lower limit is zero for all the nonpolar binaries. Thepredicting values of Eq.(10) are exactly located in this boundarea above about 150 K.

However, it is hard to say whetherkij will tend to decreasewith increasing molecular size as with the second cross virialcoefficients, although such trends have already been found insome cases using VLE data[13,17,29], because the experimentalsecond cross virial coefficient data for heavy molecules are stilltoo scarce to draw any conclusions. Another reason is that thepresent regression method to find the optimumkij’s is based onfitting just the second cross virial coefficient data while mostother references also used VLE data.

6. Conclusions

The optimumkij’s for 268 nonpolar binary systems are pre-sented using the correlation for pure compounds proposed byMeng et al.[1]. Optimum kij’s were determined by regress-in ibu-tw . Thm ithc less usna ent tu avea -r relat

LBfk

R

nZ

R universal gas constantR = 8.314472 J mol−1 K−1

T temperatureP pressureν molar volume

Greek lettersω acentric factor

Subscriptsc critical property (not includingnci, ncj)r reduced propertyi, j property of componenti, jij characteristic property used in the calculation of the

second cross virial coefficientm mixture property

Acknowledgements

This work was supported by The National Natural Sci-ence Foundation of China (No. 50225622) and FANEDD (No.200336).

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