Fluid Phase Equilibria 234 (2005) 136143

Generalized binary interaction parametentaixid

ck Zaersity ola 724,ational

May 20

Abstract

Generaliz ns ofalkanol + carbon dioxide mixtures, were obtained. Ten mixtures containing sub and supercritical carbon dioxide and one n-alkanol (frommethanol to decanol) were considered in the study. The PengRobinson equation of state has been used and the WongSandler mixing rules,that include a model for the excess Gibbs free energy gE, have been incorporated into the equation of state constants. In the WongSandlermixing rules the van Laar model for gE has been used. The experimental data were obtained from literature sources and the adjustableparameters wphase. It is savailable in 2005 Else

Keywords: E

1. Introdu

Supercrusually reqthe producsuch as limalgae, or cAlthough wof naturalmolecularof these mbiomoleculthe extractcarbon dioxsyngas [7].

CorresponE-mail ad

0378-3812/$doi:10.1016/jere found by minimizing the errors between predicted and experimental data of pressure and solute concentration in the gashown that the proposed generalized correlations have predictive capabilities with accuracy similar to the best correlating toolsthe literature.vier B.V. All rights reserved.

quations of state; PengRobinson; Supercritical fluids; WongSandler mixing rules

ction

itical extraction processes of natural productsuire a cosolvent, a substance that serves to releaset of interest from the matrix of source materialsonene from lemon peels, astaxantine from microaffeine from coffee grains, just to name some.ater is the preferred cosolvent for the extraction

products, sometimes n-alkanols of low and highweight are needed [13]. For example, the studyixtures is of special interest in the extraction ofes with supercritical carbon dioxide [4,5], inion of n-alkanols from aqueous solutions withide [6], and in the production of n-alkanols from

ding author.dress: citchile@entelchile.net (J.O. Valderrama).

To analyze the feasibility of supercritical extractionprocesses, to design new processes or to analyze andsimulate existing processes using carbon dioxide as thesupercritical solvent, phase equilibrium properties in car-bon dioxide + n-alkanols at high pressures are required.These properties must be either experimentally obtainedor semi empirically correlated. Several sets of data havebeen presented in the literature for this type of mix-tures and some correlating methods have been used[79].

One of the most common methods used for the correla-tion and prediction of phase equilibrium in mixtures is theuse of equations of state (EoS). Common and industriallyimportant EoS are the cubic equations derived from van derWaals equation of state (VdW). Among the many cubic EoSof VdW type nowadays available, the model proposed byPeng and Robinson [10] is widely used because of its sim-plicity and flexibility [11]. The PengRobinson EoS can be

see front matter 2005 Elsevier B.V. All rights reserved..fluid.2005.05.020mixing rules for mixtures coand carbon dio

Jose O. Valderrama a,b,, Jaa Faculty of Engineering, Mechanical Engineering Department, Univ

b Centro de Informacion Tecnologica, Casilc Faculty of Engineering, Chemical Engineering Department, N

Received 28 August 2004; received in revised form 23

ed correlations for mixing rule interaction parameters as functiors in the WongSandlerning n-alkanolsevaleta b,c

f La Serena, Casilla 554, La Serena, ChileLa Serena, ChileEngineering University, Lima, Peru

05; accepted 26 May 2005

the reduced temperature and a polar parameter in n-

J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143 137

written in a general form as follows:

P = RTV b

ac(TR) (1)

In this esubstance.are determi(TR) is a fof the acen

ac = 0.457b = 0.077(TR) = [1F = 0.376

For mixdependent,rules, as de

Duringto mixturesmixing ruleinto the forcproperties.the use of arules give aing the lastapplicabilitresentationmixtures. Tinclude theing rules, tand the useon EoS gi[11].

Anotherdevelop motion of an E(or activitybeen used flink betweeis done at ithe link bemodel is doPengRobidler mixingGibbs freeThe studying CO2 wpentanol, 11-decanol.

2. Equatio

The PWongSan

Table 1Models for the Gibbs free energy and the activity coefficients for the vanLaar model used with the WongSandler mixing rule

aar

Ni

xi

binary m(A12/Rx1(A12/

datag ruleN

i

1a

RT

)

bm

[

thesex) is catAEs Gibor (be van

ded inmpiriary mitablees theadjusminedant testudieture uodels

nt mixble 1.engRg rul

, modr.

pplications

n gas + liquid binary systems containing sub and super-al carbon dioxide with an n-alkanol, were selected for(CO2+: methanol, ethanol, 1-propanol, 1-butanol, 1-

nol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol andanol). The experimental data were taken from the litera-

Table 2 shows the basic properties of the fluid substancesV (V + b)+ b(V b)quation, ac and b are parameters specific for eachThese parameters ac and b for pure substancesned using the critical properties, Tc and Pc. Also,unction of the reduced temperature TR =T/Tc andtric factor , as follows:

235(R2T 2c /Pc)796(RTc/Pc)+ F (1 T 0.5R )]

2

46+ 1.54226 0.269922(2)

tures, the parametersa andb are also concentrationdependency expressed through defined mixing

scribed later here.the period 19701980, most applications of EoSconsidered the use of the classical van der Waalss. An interaction parameter has been introducede parameter a to improve predictions of mixtureIt has been recognized, however, that even withn interaction parameter the classical VdW mixingccurate results for simple fluid mixtures only. Dur-25 years, efforts have been put on extending they of cubic equations of state to obtain accurate rep-of phase equilibria in many industrially importanthe different approaches presented in the literature,use of multiple interaction parameters in the mix-

he introduction of the local-composition concept,of non-quadratic mixing rules. A recent review

ves more details on these different approaches

attractive way, which has been proposed tore accurate mixing rules, has been the combina-oS with a model for the excess Gibbs free energycoefficient model). Two main approaches have

or applying these models. In the first approach, then the EoS and the excess Gibbs free energy modelnfinite pressure [12,13]. In the second approach,tween the EoS and the excess Gibbs free energyne at low or zero pressure [14]. In this work, thenson EoS in combination with the Wong and San-

rules including different models for the excessenergy are applied to CO2/n-alkanols mixtures.considers data for ten binary mixtures, includ-ith methanol, ethanol, 1-propanol, 1-butanol, 1--hexanol, 1-heptanol, 1-octanol, 1-nonanol and

ns of state and mixing rules used

engRobinson equation of state with thedler mixing rules has been used to correlate

Van L

gE

RT=

For agE

RT=

VLEmixin

bm =

(b

am =

InAE(ing thexces

rule fTh

inclutwo ea binadjusbesidthreedeterconstturesliterathe mponein Tathe Pmixinrulespape

3. A

Tecriticstudypenta1-decture.NjxjAij

1xi

[1

xi

NjxjAij

xi

NjxjAij+(1xi)xi

NjxjAij

]2

ixtureT )x1x2A21)+x2

for CO2/n-alkanol mixtures. The WongSandlers can be summarized as follows [14]:Ni xixj

(b a

RT

)ijN

i xixi

biRTi A

E(x)RT

ij= 1

2[bi + bj]

aiaj

RT(1 kij)N

i xiai

bi+ A

E(x)

](3)

equations, = 0.34657 for the PR equation, andalculated using an appropriate model and assum-(x) AE0 (x) GE0 (x) = being GE0 (x) = gE, the

bs free energy at low pressure [15]. The combininga/RT)ij includes one adjustable parameter kij.

Laar model for the excess Gibbs free energy gEthe WongSandler was used. This model contains

cal parameters for a binary mixture. Therefore, forxture the WongSandler mixing rule includes onebinary interaction parameter k12 for (b a/RT)ij,two parameters included in the gE model. These

table parameters for each of the models have beenusing experimental phase equilibrium data at

mperature, available in the literature for the mix-d. The van Laar model has been presented in thesing different expressions for the parameters of. The expressions used in this work for multicom-tures and those for binary mixtures are presentedIn summary, the thermodynamic model includeobinson equation of state, the WongSandler

e, and the van Laar model for gE in the mixingel designated as PR/WS/VL in the rest of the

138 J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143

Table 2Properties of the pure substances included in the mixtures studied

Substance Tc (K) Pc (bar) vc (L/mol) zc (Debye) CO2 .22362Methanol .56583Ethanol .643561-Propanol .620431-Butanol .589461-Pentanol .573141-Hexanol .576361-Heptanol .567021-Octanol .582911-Nonanol .599691-Decanol .62192

The data are f

involved inture, Pc isis the acentor, is tdefined bythe criticalcarbon dioxDIPPR dattal vaporliincluding tTable 3, dawere consiand the pre

Bubble pformed usiters (A12,Ation of thedesigned corithm [18] awas defineexperiment

F =Ni=1

P

Once the irules for thLaar modeequilibriumtion in termreduced po

pij = p0 +

Here, pij rmixing ruleA21 and k12p1 were fou

ure of

m0 +

m1 +

m2 +

olar pdipo

lvin a

2.83T

paramre prelationd in thbeen cant terures cose of df polaeter as thlate thures.

esults304.2 73.83 0.094 0512.5 80.84 0.117 0514.0 61.37 0.168 0536.8 51.69 0.218 0563.1 44.14 0.274 0588.1 38.97 0.326 0610.3 34.17 0.387 0632.6 30.58 0.435 0652.5 27.77 0.497 0670.7 25.28 0.572 0687.3 23.15 0.649 0

rom the DIPPR database [17].

the study. In Table 2, Tc is the critical tempera-the critical pressure, vc is the critical volume, tric factor, zc is the critical compressibility fac-he dipole moment and is a polar parameterNishiumi [16], a function of the dipole moment,temperature and the critical volume. The data foride and all the n-alkanols were obtained from the

abase [17]. Table 3 gives details on the experimen-quid equilibrium data for the ten mixtures studiedhe literature source for each data set. As seen inta for 41 isotherms with a total of 416 data pointsdered. The temperature ranges from 291 to 453 Kssure from 0.5 to 19.8 MPa.ressure calculations for binary mixtures were per-

ng the PR/WS/VL model. The adjustable parame-21 and k12) the model are determined by optimiza-objective function given by Eq. (4). The programnsiders the use of the LevenbergMarquardt algo-s the optimization method. The objective functiond as the relative error between calculated andal values of the pressure:

expi PcalciP

expi

(4)

nteraction parameter kij included in the mixinge force constant a and the parameters of the van

perat

p0 =

p1 =

p2 =

The pof thein Ke

=

Theand acorre

sentealsorelevmixtthe uties oparamwithcorre

mixt

4. Rl (A12 and A21) were calculated from vaporliquiddata, they were correlated to a good approxima-s of the reduced temperature (TR =T/Tc) and the

lar parameter of the n-alkanol, as follows:

p1 + p22 (5)

epresents any of the parameters involved in thes and in the excess Gibbs free energy model (A12,for PR/WS/VL). The terms designated as p0 andnd to have linear dependency of the reduced tem-

Resultsare presentusing the gthe constanabsolute deing the presgas phase (

The devare lower thof mixturesented in th0.274 0 0.00000.224 1.700 0.13640.241 1.691 0.09370.252 1.679 0.06820.258 1.661 0.05060.26 1.700 0.04270.261 1.649 0.03260.253 1.739 0.03110.254 1.649 0.02370.259 1.610 0.01910.263 1.619 0.0166

the n-alkanol, as follows:n0TRn1TRn2TR

(6)

arameterwas defined by Nishiumi [16], in termsle moment in Debye, the critical temperature Tcnd the critical volume vc in L/mol, as follows:

2

cvc(7)

eters mi and ni are constant for a CO2/n-alkanolsented in Table 4. It should be mentioned that others were also attempted, following information pre-e literature. The acentric factor, for instance, hasonsidered, but we have found that is a morem for correlating the model parameters for thesentaining polar fluids. Nishiumi [16] has discussedifferent parameters to generalize different proper-r fluids and obtained good results using the defined

. Therefore, the perturbation-type expression (5),e perturbation parameter, has a reasonable basis toe model parameters for carbon dioxide/n-alkanol

and discussionof the application of the different mixing rulesed in Table 5. All these calculations were doneeneralized parameters described by Eq. (6) withts defined in Table 4. The results are shown as theviations given by the different models for predict-sure (P) (%) and the solute concentration in they2) (%).iations in the gas phase concentration of the solutean those reported in the literature for similar type

s, as presented in Table 6. The calculations pre-e literature were done using other similar models,

J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143 139

Table 3Experimental data for the systems considered in this study

System CO2+ N T (K) Range P (MPa) Range (x2 103) Range (y2 103) ReferenceMethanol

Ethanol

1-Propanol

1-Butanol

1-Pentanol

1-Hexanol

1-Heptanol

1-Octanol

1-Nonanol

1-Decanol

In the table, tamplified by 1

Table 4Coefficients f(6) and (7)pij mok12 0.4680A12 1.59A21 12.9pij =

(m0 +17 313 18 6887715 320 19 3288016 330 111 3482117 336 111 3379318 343 112 24760

10 313 18 2687313 333 111 20817

6 315 68 3438459 325 69 337758 337 611 272704

17 345 112 30800

8 315 37 14456010 327 39 15756210 337 39 145448

8 315 58 2836959 325 58 285805

10 337 612 301781

5 333 712 3938868 326 611 2837189 337 612 2837185 333 712 3938864 344 1214 6538625 414 1419 500792

12 427 419 130748

12 398 720 3058566 403 820 3018187 432 220 35772

8 375 415 2176245 412 1621 6208705 412 1621 620870

6 313 716 4928147 328 417 240862

12 348 119 20486914 403 119 25563412 453 120 231595

9 308 28 16261110 318 310 16565215 328 310 179758

13 348 119 5079513 403 119 3974513 453 119 35661

he temperature and pressure values have been rounded to the closest integer. In th03.

or the generalized correlations for the parameters pij in Eqs.

no m1 n1 m2 n2

0.1730 20.51 11.39 74.08 36.764 1.072 21.37 1.116 26.073 81.517 8.308 340.1 193.5 1402.2 754.3n0TR

)+(m1 + n1TR

) +

(m2 + n2TR

)2.

but compatreatment iscan be welcalculationage absolutfor the solual. [8] modof state ofdeviationsconcentratisystems coconcentrati12.035.0 [9]8599 [21]

114142140194200228

1940 [7]92959.016.0 [1]13362265

127193 [21]5.08.0 [22]7.016.012.016.0

1960 [1]3424659481

8.6104.7 [23]1.738.3 [1]2.525.58.6104.7

38.6111 [23]58.8188.973.1192.6

13.4113.2 [3]19.2138.274.9199

2.29.8 [3]16107

16.1106.8

0.380.3 [9]0.380.30.667.15.526.9

21.652.7

09 [8]015026

0.1629.8 [9,24]1.813.58.729.4

e table, x2 and y2 refer to the concentration of the solute

rison are still valid because the thermodynamicthe same, so the improvements found in this study

l observed. Elizalde-Sols [3] did similar type ofs for the system CO2/1-hexanol and found aver-e deviations of 4.3% for the pressure and of 108%te concentration in the gas phase. Chiehming et

eled the system CO2/1-nonanol using the equationPatel and Teja [19], and found average absoluteof 1.1% for the pressure and of 127% for the soluteon in the gas phase. For all this cases and for thensidered in this study, deviations in the solventon in the gas phase is below 1%. However, con-

140 J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143

Table 5Deviations in the correlated values for the pressure and the solute concentration in the gas phase

TR T (K) System CO2+ |P| (%) |y2| (%)0.611 0.136 313.1 Methanol 2.6 11.30.625 0.136 320.2 4.4 25.60.644 0.136 330.0 3.2 14.60.655 0.136 335.7 2.1 15.00.669 0.136 342.8 2.3 11.1

0.610 0.094 313.4 Ethanol 2.6 7.20.612 0.094 314.5 1.5 10.90.633 0.094 325.2 0.7 12.60.649 0.094 333.4 1.5 10.60.656 0.094 337.2 0.7 12.60.671 0.094 344.8 1.5 12.7

0.587 0.068 315.0 1-Propanol 3.2 16.10.608 0.068 326.6 3.8 15.40.628 0.068 337.2 3.4 12.0

0.559 0.051 314.8 1-Butanol 2.9 9.30.578 0.051 325.3 4.4 26.60.599 0.051 337.2 3.2 7.5

0.535 0.043 314.6 1-Pentanol 2.7 37.10.554 0.043 325.9 5.5 20.10.566 0.043 333.1 5.3 51.30.574 0.043 337.4 2.0 13.10.584 0.043 343.7 8.8 34.90.704 0.043 414.2 3.0 13.50.726 0.043 426.9 5.9 8.6

0.652 0.033 397.8 1-Hexanol 6.9 19.50.661 0.033 403.4 4.1 21.70.709 0.033 432.5 11.4 22.7

0.592 0.031 374.6 1-Heptanol 11.2 79.90.651 0.031 412.0 5.8 32.60.682 0.031 431.5 9.8 77.5

0.480 0.024 313.2 1-Octanol 2.0 18.70.503 0.024 328.2 2.9 32.10.534 0.024 348.2 4.3 36.20.618 0.024 403.2 7.0 18.20.694 0.024 453.2 11.5 15.3

0.459 0.019 308.1 1-Nonanol 3.4 58.80.474 0.019 318.1 2.4 55.50.489 0.019 328.2 3.1 57.4

0.507 0.017 348.2 1-Decanol 3.6 33.20.587 0.017 403.2 7.7 32.10.659 0.017 453.2 7.8 8.9

Average 4.4 25.1

Deviations for the solvent concentration in the gas phase (CO2 in the mixtures studied) are below 2% for all cases, so details are not shown.

Table 6Deviations in the correlated values for the pressure and the solute concentration in the gas phase presented in the literature for some cases studied in this work

System CO2+ T (K) This work PR/WS/VL Literature|P| (%) |y2| (%) |P| (%) |y2| (%) Model Reference

Methanol 313 2.6 11.3 1.9 24.3 PR/VDW [8]1-Pentanol 333 5.3 51.3 0.1 44.5 PT/VDW [23]

343 8.8 34.9 1.9 81.8 PT/VDW

1-Hexanol 397 6.9 19.5 4.3 108.2 PR/WS/NRTL [3]1-Octanol 453 11.5 15.3 10.4 127.7 PT/VDW [9]1-Nonanol 308 3.4 58.8 1.1 126.8 PR/VDW [8]

J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143 141

Fig. 1. Predicmodel PR/WS

sidering thinterested iaccuracy osolute concerature, usiat least a mgiven mode

The deva little higobservationliterature instudied inas deviatiodecrease [1

One shofor those cphase is vede solute m102, thisthe higher

To bettefor the parated phase equilibrium diagram for selected CO2/n-alkanol mixtures using the gen/VL.

at in supercritical fluid extraction one is usuallyn the solute being extracted, a severe test of thef a model must be the correct correlation of theentration in the gas phase. As shown in the lit-ng the solvent concentration in the gas phase isisleading way of analyzing the capabilities of al [20].iations for the pressure found in this work areher than those presented in the literature. This

agrees with information already reported in thedicating that, for complex systems such as thosethis work, deviations for the pressure increasens for the solute concentration in the gas phase1,20].uld notice that the highest deviations are found

ases in which the solute concentration in the gasry low. Table 3 shows that while for most systems

ole fraction in the gas phase is of the order ofconcentration is of the order of 104 to 103 forn-alkanols (heptanol to decanol).r show the capabilities of the proposed correlationsmeters of the PR/WS/VL model, graphical results

for four syFig. 1. As slated valuesoverestimathe highertion can beAll these rthe modelrepresenteddicting VLin several e

5. Conclu

1. The concan be oied.

2. Solutedicted udeviatiopresenteeralized correlations for the mixing rules parameters for the

stems but for different temperatures are shown ineen in the figure, good agreement between calcu-and experimental data is found. Pressure is a little

ted for the system CO2/1-octanol at 403.15 K inpressure range (over 100 bar). The same observa-done for CO2/methanol for pressures over 60 bar.esults show that the generalized correlations forparameters (A12, A21 and k12 for van Laar), allby pij in Eq. (5) have good capabilities for pre-

E properties in CO2/n-alkanol mixtures of interestngineering processes.

sions

centration of the solvent (CO2) in the gas phasebtained with good accuracy with the model stud-

(n-alkanol) concentration in the gas phase pre-sing the proposed generalized parameters givens similar and lower than other correlating modelsd in the literature.

142 J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143

3. The proposed generalized correlation given by Eq. (5) hasa predictive character, since one needs only pure compo-nent properties for then-alkanol to predict the pressure andthe gasalkanol

4. The genhave sherties inenginee

List of symAE, AE0 HAij, Aji, A12ai, bi Eoaij, bij Eo

iam, bm EoF paGEo Gkij, k12 bim,m0,m1,

paN nun, n0, n1, n

papij inp0, p1 adP prPc crR idT teTc crTR reV vovc cr

xi, xj mph

yi, yj mph

AbbreviatioEoS eqPR PePT PaVDW vaVL vaWS W

Greek lette de co

te di ac

N

Acknowledgments

The authors thank the support of the National Commis-for Sc), thr0402Sere

rch grn (CI

ort.

rence

.W. JeO2-eth

1991) 3. Arta

-undecaon diox85.. Elizaernandioxide +hase E.T. Sch

n supercluid Ph.M. Woioxide4.. de lainaryarbon d. Suzuaito, Ist highethane

ropanol.C. Chihe detelkanols23237.L. We

ibria foes. 33.Y. Pen

nd. Eng.O. Valhem. R.J. Hu

or repreions, Fl.S. Wo

quation. Dahl,ith a82918. Orbequationress, U. Nishi

hree popn. 13solute concentration in binary carbon dioxide/n-mixtures.eralized correlations for the model parameters

own good capabilities for predicting VLE prop-CO2/n-alkanol mixtures of interest in several

ring processes.

bolselmholtz free energy at infinite and zero pressure, A21 parameters in the van Laar modelS parameters for pure componentsS interaction coefficients between components

and j in a mixtureS parameters for mixturesrameter in the function of the PR EoSibbs free energy at zero pressurenary interaction parameter in an EoSm2 parameter in the correlation for the interactionrameter pijmber of points in a data set

2 parameter in the correlation for the interactionrameter pijteraction parameterjustable parameters in pij (Eq. (3))essureitical pressureeal gas constantmperatureitical temperatureduced temperature (TR =T/Tc)lumeitical volumeole fraction of components i and j in the liquidaseole fraction of components i and j in the vaporase

nsuation of statengRobinson EoStelTeja EoSn der Waalsn LaarongSandler mixing rule

rsviationnstant in the WongSandler mixing rulemperature function in an EoSpole momententric factorishiumis polar parameter (Eq. (7))

sionChileand 1of Laresea

matiosupp

Refe

[1] DC(

[2] M1b9

[3] OHdP

[4] SiF

[5] Jd3

[6] MBc

[7] KSa

m

p[8] J

ta

2[9] W

lR

[10] DI

[11] JC

[12] Mft

[13] De

[14] Sw

1[15] H

EP

[16] HtJientific and Technological Research (CONICYT-ough the research grants FONDECYT 100003185, the Direction of Research of the Universityna, Chile for permanent support through severalants and of the Center for Technological Infor-T, La Serena, Chile), for computer and library

s

nnings, R.J. Lee, A.S. Teja, Vaporliquid equilibria in theanol and CO2-1-butanol systems, J. Chem. Eng. Data 36 (3)03307.l, V. Pauchon, J. Munoz, J. Jose, Solubilities of 1-nonanol,nol, 1-tridecanol, and 1-pentadecanol in supercritical car-ide at T= 323.15 K, J. Chem. Eng. Data 43 (1998) 983

lde-Solis, L.A. Galicia-Luna, S.I. Sandler, J.G. Sampayo-ez, Vaporliquid equilibria and critical points for the carbon1-hexanol and carbon dioxide + 1-heptanol systems, Fluid

quil. 200 (2002) 161172.aeffer, L. Zalkow, A.S. Teja, Solubility of monocrotalineritical carbon dioxide and carbon dioxide-ethanol mixtures,ase Equil. 43 (1988) 4556.ng, K.P. Johnston, Solubilization of biomolecules in carbonbased supercritical fluids, Biotechnol. Prog. 2 (1986) 29

Ossa, E.V. Brandani, G. Del Re, G. Di Giacomo, E. Ferri,and ternary phase behavior of the system water-ethanol-ioxide, Fluid Phase Equil. 56 (1990) 325361.ki, H. Sue, M. Itou, R.L. Smith, H. Inomata, K. Arai, S.othermal vaporliquid equilibrium data for binary systemspressures: CO2-methanol, CO2-ethanol, CO2-1-propanol,

-ethanol, methane-1-propanol, ethane-ethanol, and ethane-1-systems, J. Chem. Data 35 (1990) 6366.

ehming, C. Kou-Lung, D. Chang-Yih, A new apparatus forrmination of P-x-y and Henrys constants in high pressurewith critical carbon dioxide, J. Supercrit. Fluids 12 (1998).ng, J.T. Chen, M.J. Lee, High-pressure vaporliquid equi-

r mixtures containing a supercritical fluid, Ind. Eng. Chem.(8) (1994) 19951961.g, D.B. Robinson, A new two-constant equation of state,. Chem. Fundam. 15 (1) (1976) 5964.

derrama, The state of the cubic equations of state, Ind. Eng.es. 42 (7) (2003) 16031618.

ron, J. Vidal, New mixing rules in simple equations of statesenting vaporliquid equilibria of strongly non-ideal solu-

uid Phase Equil. 3 (1979) 255271.ng, S.I. Sandler, A theoretically correct mixing rule for cubics of state, AIChE J. 38 (1992) 671680.

M.L. Michelsen, High-pressure vaporliquid equilibriumUNIFAC-based equation of state, AIChE J. 36 (1990)36.y, S.I. Sandler, Modeling vaporliquid equilibria, in: Cubics of State and Their Mixing Rules, Cambridge UniversitySA, 1998.umi, An improved generalized BWR equation of state withlar parameters applicable to polar substances, J. Chem. Eng.(1980) 178183.

J.O. Valderrama, J. Zavaleta / Fluid Phase Equilibria 234 (2005) 136143 143

[17] T.E. Daubert, R.D. Danner, H.M. Sibul, C.C. Stebbins, Physical andthermodynamic properties of pure chemical, in: Data Compilations,Taylor and Francis, Washington, DC, USA, 1996.

[18] M. Reilly, Computer Programs for Chemical Engineering Education,vol. 2, Sterling Swift, TX, USA, 1972, pp. 276295.

[19] N.C. Patel, A.S. Teja, A new cubic equation of state for fluids andfluid mixtures, Chem. Eng. Sci. 37 (1982) 463473.

[20] J.O. Valderrama, V.H. Alvarez, Vaporliquid equilibrium in mixturescontaining supercritical CO2 using a new modified Kwak-Mansoorimixing rule, AIChE J. 50 (2) (2004) 480488.

[21] S.N. Joung, C.W. Yoo, H.Y. Shin, S.Y. Kim, K.P. Yoo, C.S.Lee, Measurements and correlation of high-pressure VLE of

binary CO2-alcohol systems (methanol, ethanol, 2-methoxyethanoland 2-ethoxyethanol, Fluid Phase Equil. 185 (12) (2001) 219230.

[22] V. Vandana, A.S. Teja, Vaporliquid equilibria in the carbon diox-ide + 1-propanol system, J. Chem. Eng. Data 40 (1995) 459461.

[23] G. Silva-Oliver, L.A. Galicia-Luna, S.I. Sandler, Vaporliquid equi-libria and critical points for the carbon dioxide + 1-pentanol andcarbon dioxide + 2-pentanol systems at temperatures from 332 to432 K, Fluid Phase Equil. 200 (2002) 161172.

[24] M.-J. Lee, J.T. Chen, Vaporliquid equilibrium for CO2/alkanol sys-tems, Fluid Phase Equil. 92 (1994) 2152317.

Generalized binary interaction parameters in the Wong-Sandler mixing rules for mixtures containing n-alkanols and carbon dioxideIntroductionEquations of state and mixing rules usedApplicationsResults and discussionConclusionsAcknowledgmentsReferences