simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equation...

Chemical Engineering Science 56 (2001) 6485–6510www.elsevier.com/locate/ces

Simultaneous prediction of the critical and sub-critical phase behaviorin mixtures using equation of state I. Carbon dioxide-alkanols

Ilya Polishuka ;∗, Jaime Wisniaka, Hugo SegurabaDepartment of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel

bDepartment of Chemical Engineering, Universidad de Concepci*on, Concepci*on, Chile

Received 18 January 2001; received in revised form 15 July 2001; accepted 26 July 2001

Abstract

The present study is a step towards solving the problem of predicting the properties of a mixture in the entire PTx range, withoutresource to experimental data. Vapor–liquid phase equilibria and liquid–liquid equilibria are shown to be closely related. A novelsemi-predictive approach (SPA) is introduced. It involves estimation of the binary adjustable parameters for a certain member ofa homologous series using the Quantitative Global Phase Diagram method, and their implementation for predicting the data ofother homologs. This approach has been combined with the equations of state (EOSs) of Peng–Robinson, Trebble–Bishnoi–Salim,and a four-parameter EOS (C4EOS), as described by Polishuk et al. (Chem. Eng. Sci. 55 (2000) 5705) for predicting data ofcarbon dioxide-alkanols. It is demonstrated that di8erent isomeric con9gurations of alkanols do not a8ect the reliability of SPA.The predicted results exhibit the behavior characteristic for many series of alkanols, however, they are not accurate for carbondioxide–methanol because of weak chemical interactions present in this system. C4EOS is more reliable predicting the topologyof phase behavior, the critical, and the bubble-point lines. However, it is less exact for predicting the gas phase composition. Theavailable experimental and theoretical results for carbon dioxide–alkanols are reviewed. The predictions of SPA usually exhibit asigni9cant advantage over other methods that do not predict but correlate the data. ? 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Phase equilibria; Supercritical ;uid; Carbon dioxide; Alkanols; Parameter identi9cation; Equation of state

1. Introduction

Process design in the high-pressure range has becomean important problem in modern industry. For man-madeprocesses like synthesis of diamonds or explosive weld-ing and plating, the technologies may require pressuresup to 106 bar (Prausnitz, Lichtenthaler, & de Azevedo,1999). Pressures around several hundreds bars are usedfor the synthesis of products like acetic acid, ammonia,and methanol. High pressures are also required for the in-dustrial applications of supercritical ;uids, which recentlyhave become useful for a wide variety of processes likeseparation of non-volatile mixtures (such as extraction ofnatural-;avor and dyeing materials, co8ee deca8eination,etc.), supercritical ;uid chromatography, hydrothermal

∗ Corresponding author. Tel.: +972-7-6461479; fax: +972-7-6472916.E-mail addresses: [email protected] (I. Polishuk),

[email protected] (J. Wisniak).

crystal growing, hydrothermal destruction of hazardouswaste, and polymer processing (Levelt Sengers, 2000).Thermodynamic properties of chemical compounds andtheir mixtures, especially phase equilibrium data, are thebasic information required in process design. However,adequate thermodynamic data have been measured foronly a few thousand compounds, while with the recentdevelopments of modern organic chemistry, some phar-maceutical laboratories are able to synthesize every yeararound 100 000 new compounds, which can produce al-most in9nite number of mixtures (Deiters, Hloucha, &Leonhard, 1999).Measurement of phase equilibria is a very time-

consuming procedure and requires expensive equip-ment, therefore, the data measured are usually re-stricted to single concentration points and to narrowtemperature ranges. In addition, it should be realizedthat the quality of the available experimental data issometimes doubtful. An evidence of this observation canbe the fact that di8erent data sets measured for the same

0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved.PII: S 0009-2509(01)00307-4

6486 I. Polishuk et al. / Chemical Engineering Science 56 (2001) 6485–6510

systems sometimes exhibit mutual deviations that arelarger than the reported experimental uncertainties.At the same time, the purity of the chemicals used

for phase equilibria measurements is usually better thanthe one used in industry. Impurities present in indus-trial reagents may exert signi9cant in;uence on the phaseequilibrium data.Hence, it seems important to reexamine the expediency

of the a precise local 9t of experimental laboratory datausing thermodynamic models, which neglect the predic-tive ability in many cases. For these purposes modernprocess design requires models capable of:

(1) Predicting the equilibria properties without prelimi-nary use of experimental data;

(2) yielding accurate results in both the sub-critical andcritical regions.

Simultaneous ful9llment of these requirements is a verydiGcult and challenging task for equations of state. Al-though vdW-like EOSs are unable to describe the density;uctuations in the critical region (Sengers & Levelt Sen-gers, 1986), it has been demonstrated that a proper selec-tion of the empirical functionalities will enable them topredict even very complicated critical lines with a highdegree of accuracy (Polishuk, Wisniak, & Segura, 1999a;Polishuk, Wisniak, Segura, Yelash, & Kraska, 2000b;Polishuk, Wisniak, & Segura, 2000a). However, these re-sults still have not provided an answer to the two abovebasic requirements for thermodynamic models.In the present study, we take a 9rst step towards solv-

ing these problems. It should be realized that phase be-havior in real ;uids is in;uenced by many factors, whichthermodynamic models are not always capable of takinginto account. For this reason even the most theoreticallybased equations will include crude approximations aboutthe molecular picture. Thus, at present, it does not seempossible to get a reasonable prediction of the proper-ties of real ;uids without using empirical functionalities,such as binary adjustable parameters. However, investi-gating the regularity of the appropriate values of theseparameters for di8erent systems may assist in develop-ing methods for predicting phase equilibria data withoutresource to experiment (see also Trebble & Sigmund,1990).Analysis of our previous results indicates that it is pos-

sible to describe the critical lines of di8erent binary sys-tems that belong to the same homologous series by cubicEOSs using similar values of the adjustable parameters(Polishuk et al., 1999a). This conclusion suggests exam-ining the possibility of adopting the parameters that havebeen optimized for a certain member in a homologousseries, for predicting the phase equilibria for other mem-bers. This approach can be de9ned as semi-predictive(SPA).It should be pointed out that although the original vdW

EOS was developed on the basis of the mean 9eld the-

ory, later engineering equations, such as that of Peng andRobinson (1976) (PR), are mostly empirical in nature.For these reasons, it is not always easy to explain theirpredictions on the basis of pure theory. For example, it isevident that semi-empirical cubic EOSs do not describefactors like polarity, molecular shape, chain length, hy-drogen bonds, and association. Nevertheless, these EOSsare able to correlate the consequences of all these fac-tors, while considering them as a “black box”. At thesame time, it should be remembered that several interac-tions (like association) are dependent on both tempera-ture and pressure (Fulton, Yee, & Smith, 1993) and varyfrom system to system in the homologous series (Nickel& Schneider, 1989). This fact may create diGculties forall semi-empirical models and, especially, for the SPA.Hence, we believe that the most severe test for the ap-proach lies in its implementation for mixtures of po-lar compounds where strong associative interactions arepresent.In the present study, we have initiated the imple-

mention of the SPA for predicting phase equilibria insystems of carbon dioxide and alkanols, up to and in-cluding the hexanols. These systems are of interest inapplications like solvent pairs in supercritical extraction,separation of alkanols from the solutions in which theyare synthesized, production of alkanols from syngas,the supercritical drying of aerogels (Jennings, Gude, &Teja, 1993), production of plasticizers, lubricant addi-tives, liquid crystals, pesticides, surfactants, ;avorings,dyes, medicines, and others (Elvers, Hawkins, & Schulz,1991).Recently, Gregorowicz and Chylinski (1998) have

demonstrated that the logarithm of the solubility ofn-alkanols in supercritical carbon dioxide at 313 K and60 bar exhibits a linear dependency on the carbon num-ber. Similar relationships have been previously describedby Peters, de Swaan Arons, Harvey, and Levelt Sen-gers (1989) for series like methane–paraGns and carbondioxide–paraGns. However, it should be realized thatType III behaviour (according to classi9cation of vanKonynenburg & Scott, 1980), which the series carbondioxide–n-alkanols begins to exhibit from n-hexanol on(Raeissi, Gauter, & Peters, 1998), restricts the validityof the approach of Gregorowicz and Chylinski (1998)to the near vicinity of the critical point of pure carbondioxide. In addition, it is probable that their approachwill not provide an accurate prediction for the solubilityof di8erent isomers. These facts emphasize a need fordevelopment of more general approaches like the SPAproposed here.The only way to test the validity of our approach is to

compare its predictive ability using a complete set of theexperimental data, in the entire PTx range. Therefore, wehave collected most of the available phase equilibria datafor the systems under consideration and compared themwith the ones predicted by SPA.

I. Polishuk et al. / Chemical Engineering Science 56 (2001) 6485–6510 6487

Following our previous study (Polishuk et al., 2000a),we have examined three EOSs:

(a) PR, as the most conventional 2-parameter cubic EOS;(b) modi9cation of the Trebble and Bishnoi (1987) EOS,

proposed by Salim and Trebble (1991) (TBS) asthe most accurate semi-empirical EOS for pure com-pounds;

(c) The simplest cubic four-parameter equation(C4EOS), using parameters calculated with ourapproach (Polishuk et al., 2000a).

The description of these models is given below.

2. Theory

The theory and development of cubic EOSs have beendiscussed elsewhere (Prausnitz et al., 1999; Orbey & San-dler, 1998, etc.), therefore we restrict ourselves to giv-ing a short description of the models used in the presentstudy.The Peng–Robinson EOS (Peng & Robinson, 1976) is

P=RT

Vm − b − a�V 2m + 2Vm − b2 ; (1)

where a and b are the cohesion term and the covolume,respectively. Their values can be determined from thecondition of a horizontal in;ection of the critical isothermat the critical point

a=0:45724R2T 2c =Pc; b=0:07780RTc=Pc; (2)

where � is a temperature functionality that has been de-veloped and generalized by Soave (1972) to 9t the vaporpressures of pure compounds as follows:

�=[1 +m(1− T 0:5r )]2; (3)

where for the PR EOS

m=0:37464 + 1:54226!− 0:26992!2: (4)

This temperature functionality is capable of accurate rep-resentation of non-polar short-chain compounds, but forpolar and long-chain compounds it may deviate from theexperimental data. Flexible multiparameter temperaturefunctionalities have been developed so far to improve the9t of the vapor pressure in the entire temperature rangeand for all kinds of compounds. However, these are com-plicated functionalities that may cause an erroneous pre-diction of di8erent thermodynamic properties. In addi-tion, experimental data for many compounds (includingalkanols) are scarce and it is not always possible to evalu-ate their accuracy (Ambrose & Walton, 1989). For thesereasons, nowadays it does not seem expedient to use amultiparameter temperature functionality. The problems

related with the application of Eq. (3) to mixtures willbe discussed below.A second equation examined here is the TBS EOS,

given by

P=RT

Vm − b − a�V 2m + (b+ c)Vm − (bc+ d2)

: (5)

Here, we have used the generalized version of TBSEOS and its parameters have been calculated as sug-gested by Salim and Trebble (1991). The advantage ofthis EOS over some other multiparameter semi-empiricalequations is that it yields a horizontal in;ection of thecritical isotherm at the critical point. In addition, it is par-ticularly accurate for describing pure compounds. How-ever, the ability of TBS to describe mixtures may be af-fected by the complicated empirical expressions for itsparameters.A method for de9ning the parameters in a C4EOS has

been proposed in a previous publication (Polishuk et al.,2000a). Examination of the values of the covolume thatyielded an accurate representation of the liquid densitiesled to the conclusion that its value should be near to thatof the liquid molar volume of the compound at low tem-peratures. It was also suggested that experimental val-ues be used for the critical compressibility. Besides thetwo conditions for a horizontal in;ection of the criticalisotherm at the critical point, this approach de9nes thevalues of the C4EOS parameters (which are not adjustedbut calculated). The proposed approach allows examina-tion of di8erent repulsive and attractive terms to developa proper expression of the C4EOS. Nevertheless, in thepresent study we continue to use the following simplestexpression:

P=RT

Vm − b − a�(Vm + c)(Vm + d)

; (6)

where

b=Vm; liq: phase at the triple point; expt (7)

Eq. (6) does not consider molecular shapes. Probably,this is the reason why it becomes less accurate in describ-ing the liquid densities of pure compounds with increas-ing chain length. Therefore, when the di8erence betweentriple and critical molar volumes exceeds 0:2 dm3=mol,the following expression has been used for C4EOS:

b=Vm; liq: phase at 298:15 K and 1 atm; expt : (8)

In this work, we have adopted Soave’s form of thetemperature functionality (Eq. (3)). The values of thecorresponding parameters appear in Table 1. The dataof the pure compounds have been taken from Daubert,Danner, Sibul, and Stebbins (1989–1999), except for3-hexanol, which is absent in the above data bank. Thecritical temperature and pressure of this compound havebeen obtained from Quadri, Khalar, Kudchadker, andPatni (1991), the critical molar volume from Anselmeand Teja (1988), and the liquid molar volume at 298:15 K


Table 1Values of parameters in C4EOS

Compound a b c d m

Carbon dioxide 5.03515 0.03728 −0:03413 0.13204 0.25276Methanol 13.4844 0.03583 −0:03201 0.24024 0.45546Ethanol 17.2170 0.05151 −0:04503 0.29056 0.63000n-Propanol 22.5651 0.06525 −0:05565 0.35625 0.639602-Propanol 21.3411 0.06823 −0:05887 0.35379 0.68662n-Butanol 28.0767 0.08322 −0:06989 0.40698 0.677982-Butanol 26.4364 0.07956 −0:06641 0.40548 0.671112-Methyl-2-propanol 25.4797 0.09474 −0:08385 0.41296 0.673891-Pentanol 34.6622 0.10854 −0:09461 0.47988 0.703402-Pentanol 29.5063 0.10945 −0:09249 0.40382 0.954013-Pentanol 30.6564 0.10802 −0:09201 0.42418 0.740232-Methyl-1-butanol 32.0119 0.10826 −0:09236 0.43385 0.744502-Methyl-2-butanol 30.5454 0.10959 −0:09428 0.44135 0.560583-Methyl-1-butanol 32.5114 0.10925 −0:09395 0.44334 0.712713-Methyl-2-butanol 30.1195 0.10831 −0:09153 0.41358 0.724091-Hexanol 42.1132 0.12520 −0:10748 0.55669 0.748802-Hexanol 38.9275 0.12607 −0:10862 0.52819 0.683773-Hexanol 38.6255 0.12516 −0:10692 0.52465 0.700002-Methyl-1-pentanol 41.0492 0.12459 −0:10760 0.54878 0.600003-Methyl-3-pentanol 34.8100 0.12412 −0:10252 0.44623 0.74000

and 1 atm from Aucejo, Cruz Burguet, Munoz, and San-chotello (1996).Extension of the EOS to mixtures is usually accom-

plished by specifying mixing rules for the equation pa-rameters, according to the van derWaals one-;uid theory.With this approach the mixture is treated as a pseudo-pure;uid. In the present study, we have used the classical vander Waals mixing rules

a�= x2a11�11 + 2(1− k12) (1− x)(a11�11a22�22)0:5

+ (1− x)2a22�22; (9)

b= x2b11 + 2(1− l12)(1− x)(b11 + b22)=2+ (1− x)2b22; (10)

c= xc11 + (1− x)c22; (11)

d= xd11 + (1− x)d22: (12)

It should be realized that combination of Eqs. (9) and (3)leads to the following expression:√�ii= |1 +mi(1−

√Tr; i)|: (13)

As the temperature increases, the term 1+mi(1−√Tr; i)

becomes negative and leads to a situation were the tem-perature derivative of Eq. (13) does not exist. Althoughthis pitfall usually takes place at very high temperature,it is important to outline this disadvantage of Eq. (3).In Eqs. (9) and (10) k12 and l12 are binary adjustable

parameters. As indicated before, proper values of theseparameters are an important factor for determining theaccuracy of semi-empirical EOS models. Unfortunately,

in many cases these parameters have not been evaluatedproperly, limiting the correlating ability of classical mix-ing rules. Fit of a single binary parameter (k12) whilekeeping a zero value for the other will usually lead toinaccurate results. However, simultaneous optimizationof two adjustable parameters is a non-trivial procedure. Itis usually based on de9ning objective functions that min-imize the average deviation from the experimental data.However, in many cases this practice leads to signi9cantmaximal deviations, particularly near the critical points.Thus far, Polishuk et al. (2000b) have proposed a new

application of the Global Phase Diagram (GPD) (whichdescribes phase behavior in the k12–l12 plane, klGPD) forunderstanding and generalizing the regularity establishedby binary parameters. In particular, it has been demon-strated that increasing the value of k12 decreases the co-hesion term of EOS and leads to a transition from TypeV to Type III phase behavior (according to classi9cationof van Konynenburg & Scott, 1980). At the same time,for some values of l12, this transition occurs through theregion of Types I=II. (For additional details about the in-;uence of parameter k12 on the predicted phase equilibriasee Polishuk, Wisniak, & Segura, 1999b.)Usually, the shape of the klGPD is qualitatively the

same for di8erent binary systems and EOSs. Fig. 1ademonstrates the in;uence of increasing values of k12on the sub-critical VLE of the system carbon dioxide–methanol at 394:2 K, calculated using the PR EOS. It isseen that for k12 = − 0:23 the shape of the bubble-pointcurve approaches a horizontal in;ection, pointing to theneighboring presence of a region of limited liquid–liquidimmiscibility (Type V). On the other hand, for k12 = 0:23the VLE boundaries approach a vertical in;ection,


Fig. 1. In;uence of binary adjustable parameters on phase boundariespredicted by PR EOS for carbon dioxide–methanol at 394:2 K. Solidlines—calculated data;�—data of Leu, Chung, and Robinson (1991).

resulting in absolute liquid–liquid immiscibility (TypeIII). For increasing values of k12 the bubble-point curvechanges its in;ection continuously from horizontal tovertical. Therefore, even if liquid–liquid immiscibilitydoes not appear in the phase diagram, its potential neigh-borhood continues to in;uence the bubble-point curve.Fig. 1b represents the in;uence of l12 on the phase

boundaries and con9rms what can be learned from theklGPD: increasing the value of l12 leads to results op-posite to those of increasing k12. Clearly, increasing l12

induces negative values for the excess covolume of mix-ture. Moreover, since the volume of a liquid phase tendsasymptotically to the covolume as the pressure increases,the predicted excess volume will become negative as l12increases. Using the relation between the excess Gibbsenergy and the excess volume (Smith, van Ness, & Ab-bott, 1996)

dGemT; X =Vem dP (14)

we can conclude that, as the pressure increases, the de-viations of the excess volumes exert a stronger in;uenceon the excess Gibbs energy. The derivatives of Ge de9nethe shape of the critical locus, hence the importance ofl12 for predicting high-pressure phase equilibria becomesclear.These facts suggest that a proper optimization of both

parameters may allow an acceptable degree of ;exibil-ity, even for classical mixing rules (as demonstrated inFig. 1c). Although the combination k12 = 0:1 and l12 = 0yields good results in the sub-critical region, it fails to de-scribe the near-critical phase boundaries because it doesnot predict the correct coordinates of the critical point.Similar results have been reported elsewhere for di8er-ent systems (particularly for carbon dioxide–alkanols byLee & Chen, 1994 and Jennings et al., 1993). Anyhow, acombination of two non-zero adjustable parameters suchas k12 = 0:05 and l12 = − 0:105, yields PTx coordinatesof the critical point that are more accurate. In addition, itappears that the latter combination of binary adjustableparameters yields accurate results simultaneously in thecritical and sub-critical regions.We can then summarize and say that the calculated

sub-critical VLE boundaries are strongly in;uenced bytwo factors:

(1) the position of the vapor–liquid critical point, and(2) the distance from the liquid–liquid critical lines.

That is, phase boundaries and critical lines are just twosides of one coin. For this reason, good practice can-not allow neglecting the critical lines in phase equilibriacalculations, as commonly done. We will now test theseconclusions by applying the SPA to mixtures of carbondioxide and alkanols.

3. Results

According to the above discussion, proper optimizationof the binary adjustable parameters requires both vapor–liquid and liquid–liquid data in the entire PTx range.The system carbon dioxide–2-butanol is the only carbondioxide–alkanol system for which detailed data (includ-ing VLE in the entire temperature range, critical points,and upper critical end point, UCEP) have been reported(Stevens, van Roermund, Jager, de Loos, & de SwaanArons, 1997a). For this reason we have used this system


Table 2Values of binary adjustable parameters implemented in the presentstudy

EOS k12 l12C4EOS 0.082 −0:042TBS 0.054 −0:053PR 0.030 −0:105

for optimizing the adjustable binary parameters. Thesehave been calculated using the klGPD method to obtainthe experimental value of the vapor–liquid critical pres-sure maximum (CPM) simultaneously with the temper-ature of UCEP. The experimental temperature of UCEPand CPM have been traced by paths in klGPD and theirintersection has given the values of the adjustable param-eters listed in Table 2. According to the SPA, these valueshave been used for predicting the phase behaviour of allcarbon dioxide–alkanols systems. First, we will analyzethe ability of SPA to predict the data of other isomers ofbutanol, then that of heavier alkanols and 9nally, that oflight members in the homologous series.

3.1. Carbon dioxide–2-butanol

Fig. 2 represents the results for this system. It can beseen that both the C4EOS and TBS EOS predict the crit-ical lines accurately and that above 400 K the PR EOSslightly overestimates the critical pressures (this resulthas been already discussed in detail by Polishuk et al.,2000a). It is also seen that the method yields relativelyaccurate results in the sub-critical region and, therefore,allows representing the VLE in the entire PTx range.The C4EOS is very accurate at high temperatures, but itunderestimates the data close to the critical temperatureof carbon dioxide. The TBS EOS is more accurate at lowtemperatures and less accurate above 350 K. Thus whilethe C4EOS is more accurate when there is an excess of2-butanol, the TBS EOS does a better job for isoplethswith higher CO2 content. In addition, both the TBS andPR EOS are more accurate in predicting the dew-pointdata. The PR EOS is slightly less accurate than the TBSand C4EOS in describing the isopleths and the vapor–liquid critical curve, but it still does not deviate signi9-cantly from the experimental data in the entirePTx range.

Fig. 2. System carbon dioxide–2-butanol. Solid lines—calculated vapor pressure lines, isopleths and dew-point curves; dotted lines—calculatedcritical lines. Experimental data of Stevens et al. (1997a): ©—experimental critical data; �—experimental UCEP; x—experimental vaporpressure data; •—x=0:1015; �—x=0:2069; ©—x=0:2998; �—x=0:3992; +—x=0:4998; —x=0:6072; 4—x=0:6982. Experimentaldata of Stevens et al. (1997b): ⊗—dew points at 313:2 K; ⊕—dew points at 333:2 K.


These results contradict Stevens’ et al. (1997a) con-clusion that the PR EOS with classical mixing rules willyield accurate results for the system carbon dioxide–2-butanol only if separate sets of k12 and l12 are adoptedfor each isotherm (thus removing the predictive characterof the model). An even better correlation ability has beendemonstrated by Stevens, Shen, de Loos, and de SwaanArons (1997b) for the mixing rules of Wong and Sandler(1992) using separate sets of three adjustable parametersper isotherm.The k12 and l12 values calculated by Stevens et al.

(1997a) are signi9cantly di8erent from those given inTable 2 for the PR EOS. This di8erence does not seemto be due to the temperature functionality of Stryjek andVera (1986) but more to the use of a di8erent 9ttingtechnique, (Stevens et al., 1997a, performed their 9ttingneglecting the liquid–liquid data).The importance of liquid–liquid critical data for pre-

dicting VLE in systems of Type II is not immediatelyevident. Figs. 2c and d compare the results for the PREOS using the binary adjustable parameters given in Ta-ble 2 and k12 = 0:04; l12 =−0:12. Although the values ofthe adjustable parameters taken from Table 2 yield moreaccurate results for liquid–liquid critical lines, they areslightly less accurate for the vapor–liquid critical line.Although the di8erence between both sets of parametersis not large, the second set is substantially less accuratefor the sub-critical VLE. These facts can be explained asfollows: an overestimation of the temperature for the ab-solute liquid–liquid immiscibility results in bubble-pointcurves that approach a more vertical in;ection in the P–xprojection and, consequently, in an overestimation of theexperimental pressures (Fig. 2d). The opposite result isobtained when the temperature of the liquid–liquid crit-ical line is underestimated. A similar behavior has beendetected for the other EOSs considered in this work.Therefore, it appears that an accurate prediction of

the bubble-point curves in the system carbon dioxide–2-butanol requires a proper representation of the liquid–liquid critical curve. The general validity of this observa-tion will be also tested for other carbon dioxide–alkanolsystems.

3.2. Carbon dioxide–n-butanol and–2-methyl-2-propanol

Unfortunately, the overall results for carbon dioxide–2-butanol cannot be extended to other isomers of butanolbecause the relevant experimental data are scarce. Whilefor the system carbon dioxide–n-butanol only the criticalpoints have been reported in the entire temperature range(Gurdial, Foster, Yun, & Tilly, 1993; Ziegler, Chester,Innis, Page, & Dorsey, 1995; Yeo, Park, Kim, & Kim,2000), for carbon dioxide–2-methyl-2-propanol the dataavailable is restricted to several isotherms only (Kim,

Yoon, & Lee, 1994; Heo, Shin, Park, Joung, Kim, & Yoo,2001). In what follows, we examine the ability of SPA topredict these data by direct use of the binary adjustableparameters listed in Table 2.The pertinent results for carbon dioxide–n-butanol are

presented in Fig. 3. It is seen that all the sets of experi-mental critical data are in excellent agreement in the P–T projection. However, the P–x projection shows a sig-ni9cant disagreement between the data of Gurdial et al.(1993) and those of Yeo et al. (2000). Jennings et al.(1993) claim that the data of Gurdial et al. (1993) do notseem to represent correctly the composition dependenceof the critical behavior; the critical compositions shouldbe richer in alkanol than the ones reported by Gurdial etal. (1993). It seems, therefore, reasonable to assume thatthe data of Yeo et al. (2000) are more accurate.Fig. 3 indicates that the system carbon dioxide–

n-butanol exhibits Type II behavior (according to theclassi9cation of van Konynenburg & Scott, 1980),

Fig. 3. Critical line of the system carbon dioxide–n-butanol. Thinsolid lines—vapor pressure lines; —critical points of pure com-pounds; thick black solid lines—data calculated by C4EOS; dot-ted line—data calculated by TBS EOS; gray solid line—data calcu-lated by PR EOS; x—calculated UCEPs; ⊕—experimental data ofGurdial et al. (1993); �—experimental data of Yeo et al. (2000);•—experimental data of Ziegler et al. (1995); �—experimentalUCEP of Lam, Jangkamolkulchai, and Luks (1990b).


nevertheless, King et al. (1983) have reported that at313:15 K the system presents limited liquid–liquid im-miscibility, that is, Type IV behavior. This result doesnot agree with that reported by Raeissi et al. (1998) whofound that limited liquid–liquid immiscibility starts ap-pearing from the carbon dioxide–n-pentanol system on.In addition, the results of King et al. (1983) have notbeen con9rmed by Ishihara et al. (1996) who performedtheir measurements at the same temperature. Therefore,the data of King et al. (1983) are judged to be inaccurate.The system carbon dioxide–n-butanol is diGcult not

only for experimental measurement but also for predic-tion. Prihodko, Victorov, Smirnova, and de Loos (1995)have predicted a false limited liquid–liquid immiscibil-ity for this system, using a Hole Lattice QuasichemicalGroup-Contribution Model (HM). Semi-empirical cubicEOSs appear to be less reliable than this theoreticallybased model, but they all predict the correct behaviorof Type II when using the SPA. Fig. 3 also shows thatboth the C4EOS and TBS EOS yield a quantitativelyaccurate prediction of the vapor–liquid critical line. ThePR EOS also predicts correctly the pressure of CPM, al-though it overestimates its temperature. Therefore, the PREOS slightly overpredicts the data points at high temper-atures and underestimates them at lower ones. In a previ-ous study (Polishuk et al., 2000a), we have concluded thatthe C4EOS has a clear advantage over those of TBS andPR in predicting global phase behavior, and yields a moreaccurate relation between VLE and LLE. The present re-sults for the system carbon dioxide–n-butanol con9rmthis assertion and that C4EOS is more accurate than boththe TBS and PR EOS in predicting the UCEP. In addi-tion, the critical compositions are predicted more accu-rately by the C4EOS and TBS EOS than by the PR EOS.Fig. 4 presents the results predicted by SPA for the

system carbon dioxide–2-methyl-2-propanol. It can beseen that although the predicted data do not deviate sig-ni9cantly from the experimental points, evaluation oftheir accuracy is diGcult due to the substantial deviationpresent among the available data sets. Although Heo etal. (2001) have measured additional isotherms, their dataexhibits scattering and thus, do not seem reliable. For thisreason we have included the results of Heo et al. (2001)in present study only when they can be compared withthe data from other sources.Kim et al. (1994) have correlated their data using a

modi9ed Huron–Vidal type mixing rules with di8erentvalues of adjustable parameters for each isotherm, andHeo et al. (2001) have implemented a multiparameterHM-type equation. Predictive ability of both approachesshould be recognized as doubtful.

3.3. Carbon dioxide–n-pentanol

Raeissi et al. (1998) have investigated the phase be-havior in quasi-binary mixtures of carbon dioxide and

Fig. 4. VLE of carbon dioxide–2-methyl-2-propanol. Dottedlines—calculated critical lines, solid lines—calculated VLE at323.15 and 343:15 K. Experimental VLE data of Kim et al.(1994): ©—323:2 K, —343:2 K. Experimental VLE data of Heoet al. (2001): •—323:15 K, �—343:15 K.

n-alkanols and found that the system carbon dioxide–n-pentanol exhibits a very narrow part of the limitedliquid–liquid immiscibility, which have been missed byother investigators (Lam, Jangkamolkulchai, & Luks,1990b; Gurdial et al., 1993). Therefore, the phase equi-libria of this system belong to Type IV, which is tran-sitional between Type II (carbon dioxide–n-butanol and


Table 3Critical end points of the system carbon dioxide–n-pentanol

UCEP (L=L− V ) LCEP UCEP (L− L=V )T (K) P (bar) T (K) P (bar) T (K) P (bar)

Expt.a 273.60 34.24 — — — —Expt.b 273.45 34.13 316.02 87.52 317.06 89.50C4EOS 296.20 51.76 331.8396 108.1142 331.8400 108.1151TBS EOS 268.79 27.50 — — — —PR EOS 273.99 28.96 — — — —

aData of Lam et al. (1990b).bData of Raeissi et al. (1997).

the previous homologs) and Type III (carbon dioxide–n-hexanol and the following homologs). Thus, calcula-tion of the phase equilibria of this system measures theability of thermodynamic models to predict global phasebehavior and, therefore, o8ers a severe test for them.Both the PR and TBS EOSs predict the wrong behav-

ior of Type II for the system carbon dioxide–n-pentanol,but C4EOS yields qualitatively correct results using SPA.This fact con9rms our previous observation (Polishuk etal., 2000a) that C4EOS is capable of a more accurateprediction of the balance between the VLE and LLE.However, as shown in Table 3, C4EOS overestimatesthe temperatures and pressures of the critical end points.This result can be explained by a rapid increase of thetemperature and pressure of the lower-temperature UCEPwhen approaching the double critical end point (DCEP),as demonstrated by Raeissi et al. (1998) also for exper-imental quasi-binary data. Probably, C4EOS predicts aphase behavior that is closer to the DCEP than in the realsystem carbon dioxide–n-pentanol. In spite of this, boththe PR and TBS EOSs yield an accurate prediction ofthe low-temperature UCEP, which is not very sensitiveto the value of carbon number far away from the DCEP(Raeissi et al., 1998). Hence, it seems that the experi-mental data are closer to DCEP than the ones predictedby the PR and TBS EOS.The two sets of sub-critical VLE experimental data

available (Jennings, Chang, Bazaan, & Teja, 1992; Staby& Mollerup, 1993) seem to be in acceptable agreement(Fig. 5). In addition, analysis of the available data allowsestimating the approximate positions of the vapor–liquidcritical points in the P–x projection. It can be seen thatthe PR EOS overpredicts the critical compositions andunderestimates the critical pressures. The TBS EOS pre-dicts relatively accurate results for critical compositions,however, it also underestimates the critical pressures.The C4EOS accurately predicts the critical pressures butunderestimates the compositions. Obviously, the accu-racy of the predicted critical data exerts a strong in;uenceon the sub-critical VLE. Therefore, the PR EOS is sig-ni9cantly less accurate than the TB EOS and C4EOS inpredicting the VLE. While the TBS EOS is more accu-

rate at low pressures, but underestimates the data in thenear-critical region, C4EOS yields good results near thecritical points but slightly overestimates the experimen-tal data far away from the critical region, probably dueto an overprediction of the low-temperature UCEP.Consideration of the predictive nature of SPA and the

complexity of the transitional phase behavior exhibited bythis asymmetric binary system, indicates that the presentresults of C4EOS are quite accurate. This conclusion canbe reached by comparing the present results with thoseof Prihodko et al. (1995), which have implemented the-oretically based models, such as the HM and the As-sociated Perturbed Anisotropic Chain Theory (APACT).In addition, Jennings et al. (1993) have calculated theVLE of carbon dioxide–n-pentanol using Patel and Teja’sEOS (1982) and the Statistical Associating Fluid Theory(SAFT, Huang & Radosz, 1991). Jennings et al. (1993)have 9tted k12 and kept a zero value for l12. Obviously,this method of estimating the binary adjustable parame-ters have not yielded accurate results in the entire PTxrange.

3.4. Carbon dioxide–isomers of pentanol

The available experimental data for these systems areat 313:2 K. Lee and Lee (1998) have measured the VLEof carbon dioxide with 2-pentanol; Lee, Mun and Lee(1999a) with 3-pentanol; Lee, Mun and Lee (1999b)with 2-methyl-1-butanol and 2-methyl-2-butanol; andLee, Mun and Lee (2000) with 3-methyl-1-butanol and3-methyl-2-butanol. In addition, Heo et al. (2001) havealso reported the VLE of the systems carbon dioxide–2-methyl-2-butanol, and Chrisohoou, Schaber, and Bolz(1995) those of carbon dioxide–3-methyl-1-butanol.Fig. 6 presents a comparison among these data sets andthe results predicted by SPA.It can be seen that the disagreement among the di8er-

ent sets of experimental data exceeds the reported exper-imental errors. This fact demonstrates that the concept ofexperimental accuracy sometimes can be relative. Nev-ertheless, Lee et al. (1999a, b, 2000) have performed an


Fig. 5. VLE of carbon dioxide–n-pentanol. Dotted lines—calculatedcritical lines; +—calculated critical end points; solid lines—calculatedVLE at 314.6, 325.9, 337.4, 343.2 and 373:2 K; ⊕—experimental crit-ical data of Gurdial et al. (1993). Experimental VLE data of Staby andMollerup (1993): —313:2 K, •—343:2 K, ©—373:2 K. Experi-mental VLE data of Jennings et al. (1992):�—314:6 K, 4—325:9 K,�—337:4 K.

exact 9t of the experimental data using di8erent modi9edHuron–Vidal type mixing rules. The reported values ofthe adjustable parameters signi9cantly di8er from systemto system, which makes impossible their generalization.Hence, the approach tested by Lee et al. (1999a, b, 2000)sacri9ces the predictive ability for the exactness of thelocal 9t.

Fig. 6 demonstrates that SPA o8ers an alternative tothe above approach. It is seen that the results predictedby C4EOS outside of critical region are always very ex-act, independent of the molecular shape of the pentanolisomer. On the other hand, the results of the PR andTBS EOS are sometimes less reliable. For example, theTBS EOS underestimates the data of the system car-bon dioxide–2-pentanol and the PR EOS slightly over-predicts the low-pressure experimental points in mixturesof 2-methyl-1-butanol and 3-methyl-1-butanol. AlthoughC4EOS is more accurate than both the PR and TBSEOS near the critical points, it still underestimates thenear-critical data. Nevertheless, Fig. 6 demonstrates thereliability of SPA for predicting VLE in systems underconsideration, regardless of their isomeric con9guration.

3.5. Carbon dioxide–n-hexanol

Scheidgen (1997) has reported detailed critical data forthe system carbon dioxide–n-hexanol and concluded thatit exhibits Type IIIm behavior (Fig. 7). Again, both thePR and TBS EOS fail to predict the topology of phasebehavior while C4EOS yields qualitatively correct resultsusing SPA. Once more, C4EOS overpredicts the temper-ature of the liquid–liquid critical curve and UCEP. ThePR and TBS EOS underestimate the liquid–liquid immis-cibility of the system. While the TBS EOS predicts thesame Type IV behaviour detected for the previous ho-molog (carbon dioxide–n-pentanol), the PR EOS contin-ues to predict Type II. Obviously, the low-temperatureVLE predicted by both the PR and TBS EOS is wrong.Figs. 7 and 8 also compare the liquid–liquid–vapor

(LLV) data predicted by the EOSs using SPA, with theexperimental data of Lam et al. (1990b). While both thePR and TBS EOSs do not predict the presence of LLVaround the critical temperature of carbon dioxide, C4EOSdemonstrates good agreement with the experimental datain the P–T projection. C4EOS has also a clear advantagein predicting the low temperature LLV, the pressure ofwhich is underestimated by the two other EOSs. The factthat the TBS and PR EOSs predict the wrong topology ofphase behavior prevents them from describing the phe-nomena related with LLV in the system carbon dioxide–n-hexanol. In spite of this, C4EOS yields a qualitativelycorrect description of the compositions, molar volumes,and densities of the two liquid phases (see Fig. 8). In par-ticular, C4EOS is able to predict the fact that as the tem-perature increases, the properties of the two liquid phasesapproach each other, up to a certain temperature. After-wards, the di8erence between the properties begins toincrease again. Nevertheless, C4EOS is unable to de-scribe the experimental data quantitatively. In particular,Fig. 7 demonstrates that the predicted liquid–liquid criti-cal pressure minimum is very close to the LLV line. Thisresult indicates that C4EOS overestimates the vicinity


Fig. 6. VLE of carbon dioxide and isomers of pentanol at 313:2 K. Thick black solid lines—data calculated by C4EOS; dotted line—datacalculated by TBS; gray solid line—data calculated by PR; —experimental data of Heo et al. (2001); ©—experimental data of Chrisohoouet al. (1995); •—experimental data of Lee and Lee (1998), Lee et al., (1999a, b, 2000).

of carbon dioxide–n-hexanol to DCEP, which stronglya8ects the accuracy of the calculated results. In addi-tion, although C4EOS yields a relatively accurate pre-diction of the molar volume and composition of the car-bon dioxide-rich liquid phase at low temperatures, it is

much less reliable in predicting the properties of then-hexanol-rich phase. Prihodko et al. (1995) have demon-strated that instead of HM, the APACT EOS is able to pre-dict LLV of the system carbon dioxide–n-hexanol quali-tatively.


Fig. 7. Critical lines of carbon dioxide–n-hexanol and carbondioxide–2-hexanol. Dotted lines—calculated liquid–liquid critical lineof carbon dioxide–2-hexanol; thick solid lines—calculated criticallines of carbon dioxide–n-hexanol; gray solid line—calculated LLVline of carbon dioxide–n-hexanol; thin solid lines—calculated vaporpressure line of carbon dioxide; �—calculated critical end points;—critical point of pure carbon dioxide; ⊗—experimental UCEP

of Lam et al., (1990); •—experimental LLV points of carbondioxide–n-hexanol Data (Lam et al., 1990); 4—experimental criti-cal points of carbon dioxide–2-hexanol (Alwani & Schneider, 1976);©—experimental critical points of carbon dioxide–n-hexanol (Schei-dgen, 1997).

Another important phenomena related to LLE isbarotropy, which involves an inversion of the densitiesof the phases in equilibrium (see Schneider, Scheidgen,& Klante, 2000). Quinones-Cisneros (1997) has demon-

Fig. 8. LLV of the system carbon dioxide and n-hexanol. Thickblack solid lines—data calculated by C4EOS; dotted line—data cal-culated by TBS EOS; gray solid line—data calculated by PR EOS;©—critical end point predicted by C4EOS; •—critical end pointspredicted by TBS EOS; •—critical end point predicted by PR EOS;�—experimental data on L1, the n-hexanol reach liquid phase (Lamet al., 1990); 4—experimental data on L2, the carbon dioxide reachliquid phase (Lam et al., 1990).

strated that the topological condition necessary for theintersection between the barotropic and the LLV linesis a Type III behavior. Fig. 8 demonstrates that C4EOSis able to predict this remarkable e8ect, although it over-estimates the temperature of the barotropic point. Again,


Fig. 9. VLE of the systems carbon dioxide–n-hexanol and 3-hexanol.Black solid lines—data calculated by C4EOS, dotted line—data cal-culated by TBS EOS; gray solid line—data calculated by PR EOS.Experimental data of Nickel and Schneider (1989): �—401:8 K. Ex-perimental VLE data of Friedrich and Schneider (1989): —397:3 K,•—362:8 K, �—323:4 K.

the relation between this result and the overpredictionof the vicinity to the DCEP is clearly seen in Fig. 8.This fact demonstrates, once more, the importance of aquantitative description of the global phase behavior forpredicting di8erent phenomena using EOS.Nickel and Schneider (1989) have measured dew-

and bubble-point data of the system carbon dioxide–n-hexanol using the near-infrared spectroscopic analyt-ical method. Fig. 9a compares their experimental datawith those predicted at 401:8 K. It should be pointed outthat the data of Nickel and Schneider (1989) are givennot in molar but in volumetric units. Thus, predictionof these data o8ers a severe test for EOSs, because itrequires an accurate representation of the densities in theentire pressure range.It is well known that two-parameter equations like that

of PR yield a constant value of the critical compress-ibility, a fact that makes impossible the accurate predic-tion of the critical densities for particular compounds. Onthe other hand, three- and four-parameter EOSs allow an

exact representation of these data, although this abilityhas been usually sacri9ced for better prediction of otherproperties. Schmidt and Wenzel (1980) have suggestedadopting the speci9c EOS’s values of the critical com-pressibility (di8erent from the experimental). This ideahas been also implemented by the TBS EOS. However,the in;uence of the above manipulation on the ability ofEOS to predict VLE in mixtures has not been consideredso far. Thus, binary experimental data given in volumet-ric units o8er a possibility to examine this in;uence.Although Nickel and Schneider (1989) did not report

critical data, their results allow an approximate estima-tion of the mass concentration of n-hexanol near the crit-ical point. As can be seen (Fig. 9a), the predicted criticalmass concentrations re;ect the ability of the EOSs to rep-resent the critical density of pure compounds. In partic-ular, the result predicted by C4EOS, which implementsexperimental values of critical compressibility for purecompounds, seems to be quite accurate. The TBS EOS,which divides the critical density of pure compounds by1.064, yields a slight underestimation of the mass con-centration of n-hexanol at the critical point. The PR EOS,which underestimates the critical densities of pure com-pounds more signi9cantly, results in a considerable un-derestimation of the critical mass concentration data.As already pointed out, the location of the critical point

exerts a strong in;uence on the shape of the phase bound-aries. Thus, Fig. 9 demonstrates that the underestimationof the mass concentration of alkanol at the critical pointshifts the data predicted by the PR EOS to lower values.By chance, this result may improve the accuracy of thePR EOS for predicting the vapor phase. However, it willstrongly a8ect the prediction of the liquid phase. This re-sult indicates that representation of critical compressibil-ity in pure compounds may be important for the abilityof the EOS to predict VLE in mixtures.In addition, as already discussed (Polishuk et al.,

2000a), the way in which EOSs represent the proper-ties of pure compounds exerts an strong in;uence onthe balance between VLE and LLE in binary systems,i.e., on the global phase behavior of the predicted data.For example, keeping the same form of the EOS whileincreasing the values of the pure compounds covolumes,enlarges the region of liquid–liquid immiscibility onklGPD. Probably, the approach for estimating the valuesof pure compound parameters in C4EOS is responsiblefor the clear advantage of this equation over PR andTBS in predicting the topology of the binary systemsunder consideration. In addition, and as discussed above,liquid–liquid data in;uence the vapor–liquid ones. Inparticular, increasing the temperature of liquid–liquidcritical curve causes a rising of the bubble-point linesand of the vapor–liquid critical pressures. However,Fig. 7 demonstrated that although C4EOS overpredictsthe liquid–liquid data, it only slightly overestimates thevapor–liquid part of critical curve. On the other hand,


the PR and TBS EOS underestimate both kind of data.Thus, Fig. 9a demonstrates the clear advantages ofC4EOS in predicting VLE of carbon dioxide–n-hexanol.This result can be compared with other studies that haveimplemented theoretically based models, such as SAFT(Huang & Radosz, 1991), HM and APACT (Prihodkoet al., 1995) for prediction, and correlation of Nickel andSchneider’s (1989) data. The results represented by bothstudies seem to be considerable less accurate than thepresent ones. They leave the impression that the abovemodels probably do not yield vapor–liquid critical pointat 401:8 K, i.e., they predict an absolute liquid–liquidimmiscibility at this temperature.

3.6. Carbon dioxide–isomers of hexanol

The fact that the above conclusions are also valid forthe available data on mixtures of carbon dioxide and dif-ferent isomers of hexanol, regardless of their isomericcon9guration, can be used as evidence for their general-ity.Thus far, Fig. 7 demonstrated that similarly to the case

of n-hexanol, C4EOS overpredicts the temperature of theliquid–liquid critical curve of carbon dioxide–2-hexanol,making it less accurate than the TBS EOS. Althoughthe PR EOS gives an accurate prediction of the liquid–liquid data at low pressures, it exhibits signi9cant devia-tions above 300 bar. Regrettably, Alwani and Schneider(1976) have not reported VLE data for carbon dioxide–2-hexanol, although VLE is the only data reported formixtures of other carbon dioxide–hexanols.Fig. 9b compares the experimental (Friedrich &

Schneider, 1989) and the predicted results for systemcarbon dioxide–3-hexanol. Regrettably, available data onvapor pressures of 3-hexanol does not allow estimatingthe value of acentric factor for this compound. In addi-tion, due to the complicated structure of this molecule,it does not seems expedient to apply correlations forestimating the value of acentric factor in the present case.These facts make the implementation of the PR and TBSEOS for predicting VLE in the system carbon dioxide–3-hexanol diGcult. For this reason Fig. 9b reports onlythe results of C4EOS. Again, these are in good agreementwith experimental data, thus demonstrating the reliabilityof the predictions yielded by C4EOS using SPA.Friedrich and Schneider (1989) have also reported

VLE for the system carbon dioxide–3-methyl-3-pentanol(see Fig. 10). Although this is a branched alkanol, theresults predicted for its mixtures with carbon dioxideexhibit the same regularity as those for n-hexanol. Oncemore, it is seen that the predicted mass concentrations of3-methyl-3-pentanol re;ect the ability of EOSs to pre-dict the critical density of the pure compounds. WhileC4EOS again yields an accurate prediction of the exper-imental data, the PR and TBS EOS underestimate the

Fig. 10. VLE of the system carbon dioxide and 3-methyl-3-pentanol.Solid lines—calculated VLE at 323.4, 362.8 and 381:6 K. Experi-mental VLE data of Friedrich and Schneider (1989): —381:6 K,•—362:8 K, �—323:4 K.

critical pressures and critical concentrations of alkanol,making their predictions inaccurate.Finally, Fig. 11 compares the experimental data (Lee

& Chen, 1994; Weng, Chen, & Lee, 1994) with the pre-dicted ones for mixtures of carbon dioxide with anotherbranched alkanol, 2-methyl-1-pentanol. It can be seenthat in general, the predicted results exhibit similar reg-ularities as the previous cases discussed so far. C4EOS


Fig. 11. VLE of the system carbon dioxide and 2-methyl-1-pentanol.Solid lines—calculated VLE at 348.15, 403.15 and 453:15 K. Exper-imental VLE data of Lee and Chen (1994) and Weng et al. (1994):�—348:15 K, —403:15 K, 4—453:15 K.

yields relatively accurate predictions for the bubble-pointlines but underestimates the compositions of the criticalpoints at high temperatures. This result strongly a8ectsthe dew-point predictions. While the TBS EOS is slightlyless exact than C4EOS in predicting the critical pres-sures, it does predict the dew-point data more accuratelythan C4EOS. C4EOS and the TBS EOS have a similarpredictive ability in the entire temperature range, but theresults of the PR EOS are less reliable. Fig. 11 indicates

that the experimental critical pressure at 403:15 K is sup-posed to be higher than at 453:15 K. Nevertheless, the PREOS predicts the opposite. This result can be explainedby an overestimation of the temperature of CPM, a char-acteristic feature of this equation. The PR EOS fails todescribe VLE in the entire pressure range at 348.15 and403:15 K. Hence the surprisingly accurate results yieldedby PR EOS at 453:15 K seem just accidental.Another conclusion is that the present predictions for

the system carbon dioxide–2-methyl-1-pentanol are moreaccurate than the correlative results reported by Wenget al. (1994). Once again, this fact demonstrates the reli-ability of SPA.

3.7. Carbon dioxide–2-propanol

No LLE data are available for this system and VLE dataare available only up to 394 K. In addition, there is noagreement between the reported data sets (see Bamberger& Maurer, 2000; Galicia-Luna & Ortega-RodrWXguez,2000). Therefore, we have selected the sets of dataof Radosz (1986), Bamberger and Maurer (2000) andthe high-temperature experimental results of Kwak andByun (1999), which do not exhibit signi9cant mutualdeviations, and not the data from other sources (althoughsometimes they show better agreement with our compu-tations). The results are represented in Figs. 12 and 13.Fig. 12 shows again that using the SPA both the C4EOS

and TBS EOS yield an accurate prediction of the criti-cal line in the P–T projection. Once again the PR EOSslightly overestimates the critical pressures at high tem-peratures and the C4EOS overestimates the alkanol con-tent of the vapor phase (Fig. 13). The two other EOSalso overestimate the data but their results agree betterwith experiment. The C4EOS has a slight advantage inpredicting the bubble-point isotherms.The deviations among the di8erent sets of experimen-

tal data make the proper evaluation of the accuracy ofthe predicted data diGcult. Nevertheless, it is seen thatthe SPA (which does not use the data for the given sys-tem) gives very good results. Considering the accurateprediction of the critical points in the entire temperatureregion, we can assume that this approach will also be re-liable for the unmeasured high-temperature VLE. Again,these results emphasize the advantage of the SPA overthe other procedures; all of them have correlated the VLEof carbon dioxide–2-propanol using available experimen-tal data. Huang and Radosz (1991) have implementedan EOS based on the statistical associating ;uid theory(SAFT). Although the SAFT model does consider as-sociation e8ects (and, therefore, would seem more suit-able for this system than semi-empirical cubic EOSs), ityielded accurate results at 394 K only in the low-pressurerange. Previously Radosz (1986) has demonstrated that acubic EOS and classical mixing rules with two adjustable


Fig. 12. Critical lines of carbon dioxide–alkanols in P–T projection. Thin solid lines—vapor pressure lines; —critical points of pure compounds;thick black solid lines—data calculated by C4EOS; dotted line—data calculated by TBS EOS; gray solid line—data calculated by PR EOS;x—calculated UCEPs; —experimental UCEP of Lam et al. (1990b); �—experimental data of Yeo et al. (2000); •—experimental data ofZiegler et al. (1995); ⊕—experimental data of Gurdial et al. (1993); —experimental data of Kwak and Byun (1999); +—experimental dataof Mendoza de la Cruz and Galicia-Luna (1999) and Galicia-Luna and Ortega-RodrWXguez (2000); �—experimental data of Brunner (1985) andBrunner, HYultenschmidt, and SchlichthYarle (1987); ⊗—experimental data of Lue, Chung, and Robinson (1991).

parameters give a better agreement to the experimentaldata. Kwak and Byun (1999) have recently improvedthe ability of SAFT model to correlate the VLE of car-bon dioxide–2-propanol using two adjustable parameters,nevertheless their results are still less accurate than thoseshown in Figs. 12 and 13.It is unfortunate that in several publications (for exam-

ple, Kao, Pozo de FernWandez, & Paulaitis, 1993), VLEdata of the system carbon dioxide–2-propanol have beencorrelated using composition-dependent combining rules.This procedure may lead to the inconsistency known asthe ‘syndrome of Michelsen and Kistenmacher (1990).In addition, Bamberger and Maurer (2000) and Weng etal. (1994) have used the mixing rules of Panagiotopou-los and Reid (1986) that Schwartzentruber and Renon(1991) had previously shown to be inconsistent. Imple-mentation of the above mixing rules violates the basicrequirement given to the thermodynamic model, i.e., apredictive ability.

3.8. Carbon dioxide–n-propanol

The results for this system appear in Figs. 12 and 14.Again, there is no agreement between the di8erent sourcesof experimental data (Jennings et al., 1993). Recently,Mendoza de la Cruz and Galicia-Luna (1999) have mea-sured the VLE of this system using very pure chemicalsand a modern apparatus having very low experimentaluncertainties. Their data are probably the most accurate.The data reported by Suzuki et al. (1990) are in accept-able agreement with those of Mendoza de la Cruz andGalicia-Luna (1999). For this reason both data sets havebeen selected for comparison with those obtained usingthe SPA. The data from other sources have not been in-cluded in the present study, although (again) sometimesthey show better agreement with our predictions.As seen in Fig. 12, once again the SPA yields an ac-

curate prediction of the vapor–liquid critical locus of thesystem in the P–T projection. However, this time the


Fig. 13. VLE of carbon dioxide–2-propanol. Dotted lines—calculatedcritical lines; solid lines—calculated VLE at 317, 335, 354, 373.15and 394 K; ⊕—experimental critical data of Gurdial et al. (1993);—experimental critical data of Kwak and Byun (1999). Experimen-

tal VLE data of Radosz (1986): •—317 K, 4—335 K, •—354 K,�—394 K. Experimental VLE data of Kwak and Byun (1999):+—333:15 K, �—373:15 K, —393:15 K. Experimental VLE dataof Bamberger and Maurer (2000): ©—313:7 K, —333:7 K.

UCEP temperature is signi9cantly overestimated. This re-sult can be explained using the fact that the liquid–liquidcritical lines are more sensitive to the values of the binaryadjustable parameters than the vapor–liquid ones. Thissensitivity seems to be the most serious obstacle for thegeneralization of the SPA because an inexact estimation

Fig. 14. VLE of carbon dioxide–n-propanol. Dotted lines—calculatedcritical lines; solid lines—calculated VLE at 313.4, 322.36, 334.61and 352:83 K; ⊕—experimental critical data of Gurdial et al.(1993); ⊗—experimental critical data of Mendoza de la Cruzand Galicia-Luna (1999). Experimental VLE data of Mendoza dela Cruz and Galicia-Luna (1999): �—322:36 K, —334:61 K,•—352:83 K. Experimental VLE data of Suzuki et al. (1990):©—313:4 K, 4—333:4 K.

of the liquid–liquid critical line may lead to inaccurateresults for the predicted bubble-point curves (see discus-sion above).Consequently, Fig. 14 represents less accurate results.

However, in agreement with previous conclusions (Pol-ishuk et al., 2000a), again the C4EOS yields a more


exact prediction of the UCEP, and this leads to a betterprediction of the bubble-point curves. The C4EOS yieldsaccurate predictions, except in the near-critical region.The TBS EOS is more accurate near the critical range (afact that may be explained by a slightly better predictionof the vapor–liquid critical line, see Fig. 14). The TBSEOS overestimates the bubble-points outside the criticalregion, which can probably be explained by an inaccu-rate prediction of UCEP. The PR EOS does not yieldaccurate results for the bubble-point data, however, it isaccurate in predicting the dew-point curves. The C4EOSis, as usual, the less accurate EOS for the dew-point data.

3.9. Carbon dioxide–ethanol

This system is very important industrially and manypapers have reported experimental VLE data aroundthe critical temperature of carbon dioxide. The avail-able data have been reviewed by Jennings et al., 1993;Chang, Day, Ko and Chiu, 1997; and Galicia-Luna andOrtega-RodrWXguez, 2000. There are signi9cant deviationsamong the data from di8erent sources. The measure-ments of Mendoza de la Cruz and Galicia-Luna (1999)and Galicia-Luna and Ortega-RodrWXguez (2000) seemthe most reliable and, in addition, they cover a widertemperature range. We have used them to compare withthe prediction of the SPA (Figs. 12 and 15).Although the vapor–liquid critical data of carbon

dioxide–ethanol predicted by C4EOS and TBS is stillvery accurate (giving it a distinct advantage over theSPA) prediction of the liquid–liquid data is inaccurate.Lam et al. (1990b) have provided experimental evidencethat the system carbon dioxide–ethanol does not exhibitliquid–liquid immiscibility, nevertheless, the SPA yieldsa false low temperature liquid–liquid split. The TBSEOS predicts that the UCEP temperature is even abovethe critical temperature of pure carbon dioxide. Theseresults can be explained by a decrease in the accuracyof estimating the UCEPs for systems of carbon dioxidewith alcohols lighter than 2-butanol. Again, the abilityto predict global phase behavior can be related to the ac-curacy of the results for bubble-point curves. Signi9cantoverestimation of UCEP of the system carbon dioxide–ethanol (which is supposed to be below solidi9cation),causes a serious overprediction of the bubble-point pres-sures near the critical temperature of carbon dioxide.Yet, the results for the bubble-points are less accuratethan in the previous cases. The C4EOS is, as usual, thebest predictor of global phase behavior and, as a con-sequence, of the bubble-point curves. Both the C4EOSand TBS EOS give inaccurate results at low tempera-tures, nevertheless, they are still quite exact at 373 and391:96 K (far away from the false LLE). The PR EOS isagain the less accurate EOS for predicting bubble-pointdata, and the C4EOS for predicting the dew point ones.

Fig. 15. VLE of carbon dioxide–ethanol. Dotted lines—calculatedcritical lines; solid lines—calculated VLE at 312.82, 333.82,348.4, 373 and 391:96 K; ⊕—experimental critical data of Gur-dial et al. (1993); ⊗—experimental critical data of Galicia-Luna and Ortega-RodrWXguez (2000). Experimental VLE dataof Galicia-Luna and Ortega-RodrWXguez (2000): ©—312.82,4—333:82 K, —348:4 K, •—373 K. Experimental VLE data ofMendoza de la Cruz and Galicia-Luna (1999): �—391:96 K.

However, when considering the predictive character ofthe SPA, the predicted VLE results for the system car-bon dioxide–ethanol are still reliable, especially in thehigh-temperature region. Hence, this approach can prob-ably be used for estimation of unmeasured VLE dataabove 391:96 K.


It is not easy to make a fair comparison between theresults of the SPA with the computation results of otherstudies. Most of them use experimental data, and, inaddition, they perform a local 9t of numerous isothermsthat do not consider the whole P–T–x range. Inotama,Nakabayashi and Saito (1996) have predicted inaccurateresults for the VLE of the system carbon dioxide–ethanolat 333:4 K, using a local composition model based onLennard–Jones potential. These approaches show howdiGcult it is to model this system. Prihodko et al.(1995) have shown that the hole lattice quasichemicalgroup-contribution model yields a precise prediction ofthe VLE at this temperature. Semi-empirical cubic EOShave also been used for 9tting the experimental data ofthe system carbon dioxide–ethanol. Chang et al. (1997)have implemented the equation of Patel and Teja (1982)with inconsistent non-quadratic mixing rules and thePR EOS with consistent classical mixing rules. In bothcases separate sets of two binary adjustable parametershave been used for each isotherm in the narrow temper-ature range of 291.15–313:14 K, a practice that cannotbe de9ned as predictive. Similar correlation capabilitieshave been observed for both consistent and inconsistentmodels. Tanaka and Kato (1995) have demonstratedthat cubic EOS and classical mixing rules with two ad-justable parameters give an accurate 9t of the 314:5 Kisotherm. Chrisohoou et al. (1995) have also obtainedgood results near this temperature using a cubic EOSand Huron–Vidal type mixing rules with three adjustableparameters. However, implementation of this model forpredicting data at higher temperatures has resulted ina signi9cant overestimation of the critical point. Pfohl,Pagel and Brunner (1999) have recently demonstratedthe advantages of simple thermodynamic models for cor-relating several carbon dioxide mixtures, including theone with ethanol at 373:15 K.

3.10. Carbon dioxide–methanol

The system carbon dioxide–methanol, besides its prac-tical importance, is also useful for the present study be-cause accurate VLE data and critical points are availableover the entire temperature range (Brunner, 1985a; Brun-ner et al., 1987; Lue et al., 1991). The complex chemicalnature of methanol mixtures o8ers a severe test for ther-modynamic models (Perschel & Wenzel, 1984); manyof them fail to predict correctly the behavior of this sys-tem (Orbey & Sandler, 1998). While experimental re-sults suggest that this system behaves like Type I, somemodels predict false liquid–liquid split at low tempera-tures. The models considered in the present study alsoyield this incorrect result (see Fig. 16). Both C4EOSand the PR EOS predict the correct continuous shape ofthe vapor–liquid critical locus. Still, the C4EOS yieldsthe correct prediction of CPM and (taking into account

Fig. 16. VLE of carbon dioxide–methanol. Dotted lines—calculatedcritical lines; solid lines—calculated VLE at 352.6, 373.15, 394.2,423.15 and 473:15 K; x—calculated UCEPs; ⊕—experimental criti-cal data of Gurdial et al. (1993); �—experimental critical data ofBrunner et al. (1987); ⊗—experimental data of Lue et al. (1991).Experimental VLE data of Brunner et al. (1987): —373:15 K,4—423:15 K, ©—473:15 K. Experimental VLE data of Lue et al.(1991): •—352:6 K, �—394:2 K.

the deviations among the di8erent data sets) quite accu-rate results for the critical points in both the P–x andP–T projections. Prediction of critical data with the PREOS is considerably less accurate. The TBS EOS, whichhas shown the worst global phase behavior in the pre-vious cases, predicts qualitatively the wrong Type III


behavior. Present results for the SPA are quite accuratewhen considering its predictive character and comparisonwith the results of others who have correlated the criticaldata of the system carbon dioxide–methanol. Kolar andKojima (1996) have used the Predictive-Soave–Redlich–Kwong (PSRK) group contribution EOS of Holderbaumand Gmeling (1991) and found that it yields a criticalcurve interrupted by false limited liquid–liquid split (be-havior of Type IV). Optimization of the EOS parametershave led to a continuous vapor–liquid critical curve thatis, however, less accurate than the one predicted here bythe C4EOS. Similar results have been obtained byNeicheland Frank (1995) using a theoretically based hard-sphereEOS. Neichel and Franck have found that use of valuesof the binary adjustable parameters similar to those ap-plied to other systems of methanol and small molecules,does not lead to an uninterrupted connection between thetwo critical points.Appearance of a false LLE in the predicted data results

in inaccurate 9ndings for sub-critical VLE, which againincludes overestimation of the bubble-point pressures atlow temperatures. Once again, the C4EOS is the bestdescriptor of the bubble-point curves and the worst oneof the dew-point curves. It is remarkable that predictionsof the dew points by the PR EOS are very accurate, asusual.Orbey and Sandler (1998) have suggested solving the

problem of false liquid–liquid split using the Huron–Vidal type mixing rules that combine Gibbs energy mod-els with EOS. They have 9tted the adjustable parametersfor the carbon dioxide–methanol system to data at 394 Kto predict the behavior at 273 and 477 K. However, theirapproach overestimates the critical point at 477 K, lead-ing to an incorrect shape of the vapor–liquid critical lo-cus. Kurihara and Kojima (1995) have obtained similarresults when extrapolating the 9t of an excess Gibbsenergy mixing rule from 273 K to higher temperatures.Their results demonstrate that an increase in temperatureleads to a substantial increase of the deviation betweenthe experimental and calculated data near the criticalpoints.The prediction of a false LLE should not be explained

using classical mixing rules but from the fact that thevalues of the binary adjustable parameters listed inTable 2 are inadequate for the system carbon dioxide–methanol. Inspection of the klGPDs calculated from dif-ferent models reveals that the parameters of this systemcan originate regions of Type II with very low temper-ature of UCEP and, sometimes, even Type I regions.Therefore, it is always possible to select values of theadjustable parameters that will yield the correct phasebehavior for this system. Several papers have reportedthat using classical mixing rules in the low-temperatureregion may produce accurate results for the systemcarbon dioxide–methanol. For example, Weber, Zeckand Knapp (1984) have implemented the PR EOS and

classical mixing rules with a temperature-dependentk12 for the successful correlation of data at 233:15–298:15 K. Similar results have been obtained by Changand Rousseau (1985) at 228:15 − 313:15 K and byChang et al. (1997) between 291.15 and 313:14 K.Although, all of them have used classical mixingrules, they have not predicted a false liquid–liquidsplit. At the same time, in addition to the results ofKolar and Kojima (1996), false LLE for carbon dioxide–methanol has been predicted by Keshtkar, Jalali, andMoshfeghian (1997), using the UNIQUAC-based PSRKEOS. A similar inaccuracy is clearly present in theresults of Yang, Chen, Yan and Guo (1997) that ex-tended the mixing rules of Wong and Sandler (1992)for the three-parameter EOS of Patel and Teja (1982).Hence, the selection of proper values for the binary ad-justable parameters can be as important as the selectionof the proper mixing rules.

4. Analysis

An unexpected observation of the present study is thatvapor–liquid critical curves are easier to predict thansub-critical VLE. This result may be explained by the de-pendence of VLE not only on vapor–liquid critical data,but also on other factors like LLE. Although the SPA isvery successful in predicting vapor–liquid critical curves,it is not always reliable for predicting the UCEPs of car-bon dioxide–alkanols mixtures, resulting in an inexactprediction of the VLE behavior. This result emphasizesthe importance of the possible ability of thermodynamicmodels to predict global phase behavior in real systems.We have already related the accuracy of EOSs for pre-dicting this behavior (using classical mixing rules) withtheir ability to describe the liquid molar volume of purecompounds (Polishuk et al., 2000a). The more accu-rate prediction of the UCEPs and bubble-point lines ofC4EOS over that of the TBS and PR EOSs seems to bedue to its better representation of the molar volumes in theliquid phase. On other hand, the inadequate prediction ofdew point data by the C4EOS can be related to the inac-curate prediction of the vapor density of pure compounds(Polishuk et al., 2000a). The advantage of C4EOSfor predicting the global phase behavior is especiallysigni9cant for implementing the SPA, nevertheless,it is still unable to yield accurate results for all themembers in the carbon dioxide–alkanols homologousseries.The carbon dioxide–alkanols homologous series is par-

ticularly diGcult to predict because of its unusual globalbehavior. In another series such as ethane–n-alkanols,the range of the liquid–liquid immiscibility shrinks ingoing from n-octanol toward n-butanol, where it reachesits minimum (Brunner, 1985b; Lam et al., 1990a).


However, an additional decrease of the alkanol carbonnumber causes a rapid increase of the liquid–liquidimmiscibility range up to the system ethane–methanol(which exhibits Type III behavior). The same regular-ity has also been reported for the homologous seriesof xenon–n-alkanols (Gricus, Luks, & Patton, 1995)and ethylene–n-alkanols (Peters, 1994). Similarly,methane and carbon dioxide are more miscible withethanol than with methanol (Brunner, 1985a; Brunner& HYultenschmidt, 1990; Tonner, Wainwright, & Trimm,1983). These facts validate the assumption that theseseries also exhibit a regular behavior, similar to thatof the series xenon–n-alkanols, ethane–n-alkanols, andethylene–n-alkanols.Inspection of the data available for several homolo-

gous series indicates that the global phase behavior in realsystems is strongly in;uenced by inter-molecular interac-tions. Peters (1994) has concluded that the liquid–liquidimmiscibility of ethylene with light alkanols is probablycaused by the high-degree of alcohol aggregation. As-sociated molecules of alcohol do not exhibit strong in-teractions with the molecules of the second compoundand may lead to a phase split. Since n-carboxylic acidsusually do not form aggregates higher than dimers, theseries of ethylene–n-carboxylic acids does not exhibitliquid–liquid immiscibility at low carbon numbers (Pe-ters, 1994).However, it seems that aggregation is not the only fac-

tor that a8ects the global phase behavior of homologousseries. Carbon dioxide–methanol and ethane–methanolcan be characterized by similar average aggregationnumbers (Fulton et al., 1993), nevertheless their phasebehaviour is very di8erent. Fulton et al. (1993) havedemonstrated that the quadrupole of carbon dioxide cre-ates strong interactions with the dipole moment of thehydroxyl group o8setting the expected trend of higheraggregation of this alcohol. This interaction can be char-acterized as chemical because it leads to formation ofa carbon dioxide–methanol adduct; the salts of which(methyl carbonates) are commercially important com-pounds (Hemmaplardh & King, 1972). Probably, theweak chemical interaction between carbon dioxide andmethanol causes their mutual solubility. However, withhigher n-alkanol carbon numbers the concentration ofhydroxyl groups in the solute decreases to the pointwhere they become less dominant than the increasinghydrocarbon portion. Therefore, systems of carbon diox-ide and heavier alkanols exhibit ordinary global phasebehavior.It seems that an accurate prediction of the unusual in-

teractions between carbon dioxide and methanol is analmost impossible task for semi-empirical EOSs. Any-how, it is remarkable that the SPA predicts a similarregularity in global phase behavior for the series carbondioxide–alkanols, as that, measured so far, for the se-ries with non-polar compounds such as ethane, ethylene,

xenon, etc. Figs. 3, 7, 12, and Table 3 show that in goingfrom n-hexanol to n-propanol results in a decrease of thepredicted temperature of UCEP. However, the predictedtemperature of UCEP begins to increase with a furtherdecrease in the alkanols carbon-number.We can summarize these results and establish that the

SPA yields good predictions from the viewpoint of cu-bic EOS that do not include inter-molecular directionalforces.In addition, the present results point to another

problem that can probably be related to the associa-tion of alkanols: underestimation of the experimentalVLE data at low temperatures. According to Fultonet al. (1993), aggregates of alkanol molecules decom-pose at high temperatures. Therefore, by optimizingthe binary adjustable parameters to 9t the value ofCPM (which is located at high temperature), we have“tuned” the model for representing the data relatedto the low value of the average aggregation num-ber. However, at a lower temperature, the strongeraggregation probably raises the experimental phaseboundaries to higher pressure. It seems that this fac-tor leads to an underestimation of the low-temperatureVLE data using the present approach. The appropri-ateness of this assumption can judged by the factthat the predicted low-temperature data are more ac-curate for branched alkanols than for chained ones(see Fig. 6). This is probably because, according toFulton et al. (1993), in CO2 solutions the close prox-imity of the CH3 and OH groups of branched alka-nols sterically hinders their aggregation numbers abovetwo.Thus, it seems reasonable that the local 9t of the

low temperature VLE results in an overestimation ofhigh-temperature data (see Chrisohoou et al., 1995;Kurihara & Kojima, 1995). It must be emphasized thataccurate representation of the temperature- and pressuredependency of aggregation is a very diGcult task forthermodynamic models. It is not always treated properlyeven by a theoretically based equation such as SAFT(Huang & Radosz, 1991). This is probably the reasonfor the overestimation of high-temperature data for thissystem reported by Huang and Radosz (1991). AlthoughKwak and Byun (1999) have improved the results ofthe SAFT EOS at high temperatures using two valuesof adjustable parameters, they have a8ected the perfor-mance of the model at low temperatures. These factsdemonstrate that although the proposed SPA is very sim-ple and has a doubtful theoretical basis, it still o8ers analternative, even for quite complex models.

5. Conclusions

Analysis of the publications dealing with phase equi-libria prediction shows that attention is usually paid to


the development of novel thermodynamic models, butthe problem of their proper implementation is sometimesneglected. This practice may lead to wrong conclusionsabout the characteristic features of the models and em-phasizes the need to develop a methodology for their ap-propriate implementation.In the present study, we have proposed to use theQuan-

titative Global Phase Diagrammethod (klGPD) for esti-mating the values of the adjustable parameters. The mainadvantage of this method is the possibility to deal notonly with the local 9t of numerous data points, but alsowith the complete picture of phase behavior of a real sys-tem. Implementation of the klGPD method allows detect-ing a fundamental regularity that has not been discussedbefore: the strong relation between the predicted VLEand LLE.In addition, implementation of the klGPD method for

estimating the value of the adjustable parameters for thesystem carbon dioxide–2-butanol has demonstrated thatclassical mixing rules are also capable of yielding accu-rate results for both the vapor–liquid and liquid–liquidcritical curves. This allows the simultaneous and accu-rate representation of the critical and sub-critical data fora given system in the entire PTx range.Analysis of the predictive ability of EOSs has led us to

introduce a novel predictive method, i.e., the SPA. Thisapproach involves estimation of the adjustable parametersfor a certain initial member of the homologous seriesof binary systems using the klGPD method, and theirimplementation for predicting the critical and sub-criticalphase equilibria data of other homologs.In the present study the SPA has been applied to the

three cubic equations C4EOS, PR and TBS EOS, forpredicting the phase equilibria in the series of carbondioxide–alkanols up to and including the hexanols. It hasbeen proven that SPA yields accurate predictions of theavailable experimental data, regardless of the isomericcon9guration of the homologs under consideration. Inparticular, the results of the present study allow drawingthe following conclusions:

(1) When using SPA, C4EOS is capable of predict-ing the vapor–liquid critical curves more accurately thanthe PR and TBS EOSs. In addition, C4EOS has a clearadvantage in predicting the topology of phase behavior.It is the only EOS which yields qualitatively correct re-sults for the transitional members of the carbon dioxide–n-alkanol homologous series, i.e., Type IV for n-pentanoland Type IIIm for n-hexanol homologs. The importanceof accurately estimated global phase behavior is demon-strated by the fact that C4EOS is capable of predicting thedensity inversion of two liquid phases along the LLV lo-cus of carbon dioxide–n-hexanol, while the PR and TBSEOSs are unable to do so.(2) If the liquid–liquid immiscibility is overestimated

then the bubble-point lines are overpredicted. The C4EOS

yields the most accurate results for global phase behav-ior and hence, it predicts the bubble-point data moreaccurately than the TBS and PR EOS. Notwithstand-ing, C4EOS is less accurate in predicting the compo-sitions of the vapor phase. These results can probablybe related with the ability of EOSs to describe purecompounds.(3) The SPA used with cubic EOSs predicts a global

phase behavior that characterizes the majority of theinvestigated homologous series of alkanols and lightcompounds, namely, a decrease of the liquid–liquid im-miscibility from methanol up to propanol and its furtherincrease after butanol. Carbon dioxide exhibits completemiscibility with ethanol and methanol probably becauseof weak chemical interactions that take place betweenthe quadrupole of carbon dioxide and the dipole momentof the hydroxyl group. For this reason the SPA is un-able to yield accurate results for these systems. C4EOSand the PR EOS predict the correct uninterrupted shapeof the vapor–liquid critical line of carbon dioxide–methanol, but the TBS EOS predicts wrongly Type IIIbehavior.(4) All three EOSs slightly underestimate the low

temperature vapor–liquid critical data. This result canprobably be explained by the inability of cubic EOSs todescribe the increasing aggregation of alkanol moleculesat low temperatures, which increases the experimen-tal critical pressures. However, the results reported inother papers demonstrate that theoretically based modelsthat consider inter-molecular association are also un-able to treat this problem, and yield even less accurateresults.We can summarize and say that in spite of several

disadvantages, the results predicted by the SPA willusually result in a signi9cant improvement over those ofother models that do not predict but correlate the data.In addition, it should be remarked that these predictionshave been obtained using the simplest EOSs and mix-ing rules. Possibly, even better results may be obtainedwhen applying the semi-predicitve approach to moreadvanced thermodynamic models. Anyhow, the pro-posed approach may warrant a fair comparison betweenthem.

Notation

a attraction parameterb covolumec; d attraction density dependence parameters in

Eqs. (5) and (6)Cm mass concentration of the heavier compoundGe excess Gibbs energym substance-dependent adjustable parameter in

Eq. (3)P pressure


R universal gas constantT temperaturex mole fraction of the lighter compound in the

liquid phasey mole fraction of the lighter compound in the

vapor phaseV volume

Greek letters

� temperature dependence of the attractionparameter

� density

Subscripts

c critical statem molar property

Abbreviations

APACT Associated Perturbed Anisotropic ChainTheory

C4EOS Four-parameter equation of stateCPM critical pressure maximumDCEP double critical end pointEOS equation of stateHM Hole Lattice Quasichemical Group-

Contribution ModelLCEP lower critical end pointLLE liquid–liquid equilibriaLLV liquid–liquid–vapor equilibriaPR Peng–Robinson equationPSRK Predictive-Soave–Redlich–Kwong Group

Contribution EOSSAFT Statistical Associating Fluid Theory EOSSPA semi-predictive approachTBS Trebble–Bishnoi–Salim equationUCEP upper critical end pointvdW van der Waals’ equationVLE vapor–liquid equilibria

Acknowledgements

This work was 9nanced by the Israel Science Founda-tion, Grant Number 340=00.

References

Alwani, Z., & Schneider, G. M. (1976). Fluid mixtures at highpressure. Phase separation and critical phenomena in binarymixtures of polar component with supercritical carbon dioxide,ethane and ethene up to 1000bar. Berichte der Bunsen-Gesellschaftf;ur Physikalische Chemie, 80, 1310–1315.

Ambrose, D., & Walton, J. (1989). Vapor pressures up to their criticaltemperatures of normal alkanes and 1-alkanols. Pure and AppliedChemistry, 61, 1395–1403.

Anselme, M., & Teja, A. S. (1988). Critical temperatures and densitiesof isomeric alkanols with six to ten carbon atoms. Fluid PhaseEquilibria, 40, 127–134.

Aucejo, A., Cruz Burguet, M., Munoz, R., & Sanchotello, M. (1996).Densities, viscosities, and refractive indices of some binary liquidsystems of methanol+isomers of hexanol at 298:15 K. Journal ofChemical and Engineering Data, 41, 508–510.

Bamberger, A., & Maurer, G. (2000). High-pressure (vapor–liquid) equilibria in (carbon dioxide+acetone or 2-propanol) attemperatures from 293 to 333 K. The Journal of ChemicalThermodynamics, 32, 685–700.

Brunner, E. (1985a). Fluid mixtures at high pressures I. Phaseseparation and critical phenomena of 10 binary mixtures of (agas+methanol). The Journal of Chemical Thermodynamics, 17,671–679.

Brunner, E. (1985b). Fluid mixtures at high pressures II. Phaseseparation and critical phenomena of (ethane+ n-alkanol) and of(ethene+methanol) and (propane+methanol). The Journal ofChemical Thermodynamics, 17, 871–885.

Brunner, E., & HYultenschmidt, W. (1990). Fluid mixtures at highpressures VIII. Isothermal phase equilibria in binary mixtures:(ethanol+hydrogen or methane or ethane). The Journal ofChemical Thermodynamics, 22, 73–84.

Brunner, E., HYultenschmidt, W., & SchlichthYarle, G. (1987). Fluidmixtures at high pressures IV. Isothermal phase equilibria inbinary mixtures consisting of (methanol+ hydrogen or nitrogen ormethane or carbon monoxide or carbon dioxide). The Journal ofChemical Thermodynamics, 19, 273–291.

Chang, T., & Rousseau, R. W. (1985). Solubilities of carbon dioxidein methanol and methanol–water at high pressures: experimentaldata and modeling. Fluid Phase Equilibria, 23, 243–258.

Chang, C. J., Day, C.-Y., Ko, C.-M., & Chiu, K.-L. (1997). Densitiesand P-x-y diagrams for carbon dioxide dissolution in methanol,ethanol, and acetone mixtures. Fluid Phase Equilibria, 131, 243–258.

Chrisohoou, A., Schaber, K., & Bolz, U. (1995). Phase equilibria forenzyme-catalyzed reactions in supercritical carbon dioxide. FluidPhase Equilibria, 108, 1–14.

Daubert, T. E., Danner, R. P., Sibul, H. M., & Stebbins, C. C. (1989).Physical and thermodynamic properties of pure chemicals Datacompilations. Bristol, PA: Taylor & Francis.

Deiters, U. K., Hloucha, M., & Leonhard, K. (1999). Experiments?- no thank you! In T. Letcher (Ed.), Chemical thermodynamics,A chemistry for the 21st century Monograph (p. 187). Oxford:Blackwell Science.

Elvers, B., Hawkins, S., & Schulz, G. (1991). Ullman’s encyclopediaof industrial chemistry. Weinheim: VCH Verlagsgesellschaft.

Friedrich, J., & Schneider, G. M. (1989). Near-infraredspectroscopic investigations on phase behaviour and associationof 1-octadecanol, 3-hexanol, and 3-methyl-3-pentanol in carbondioxide and chlorotri;uoromethane. The Journal of ChemicalThermodynamics, 21, 307–319.

Fulton, J. L., Yee, G. G., & Smith, R. D. (1993). Hydrogenbonding of simple alcohols in supercritical ;uids. Supercritical@uid engineering science, Fundamentals and Applications(p. 175). Washington: American Chemical Society.

Galicia-Luna, L. A., & Ortega-RodrWXguez, A. (2000). New apparatusfor the fast determination of high-pressure vapor–liquid equilibriaof mixtures and of accurate critical pressures. Journal of Chemicaland Engineering Data, 45, 265–271.

Gricus, T. A., Luks, K. D., & Patton, C. L. (1995). Liquid–liquid–vapor phase equilibrium behavior of certain binaryxenon+n-alkanol mixtures. Fluid Phase Equilibria, 108, 219–229.


Gregorowicz, J., & Chylinski, K. (1998). On the solubility ofchain alcohols in supercritical carbon dioxide. Polish Journal ofChemistry, 72, 877–885.

Gurdial, G. S., Foster, N. R., Yun, S. L. J., & Tilly, K. D. (1993).Phase behavior of supercritical ;uid-entrainer systems. In E. Kiran,J. F. Brennecke (Eds.), Supercritical @uid engineering science,fundamentals and applications (p. 34). Washington: AmericanChemical Society.

Hemmaplardh, B., & King Jr., A. D. (1972). Solubility of methanolin compressed nitrogen, argon, methane, ethylene, ethane, carbondioxide, and nitrous oxide. Evidence for association of carbondioxide with methanol in the gas phase. The Journal of PhysicalChemistry, 76, 2170–2175.

Heo, J.-H., Shin, H.-Y., Park, J.-U., Joung, S. N., Kim, S. Y., &Yoo, K.-P. (2001). Vapor–liquid equilibria for binary mixtures ofCO2 with 2-methyl-2-propanol, 2-methyl-2-butanol, octanoic acid,and decanoic acid at temperatures from 313.15 to 353:15 K andpressures from 3 to 24 MPa. Journal of Chemical and EngineeringData, 46, 355–358.

Holderbaum, T., & Gmeling, J. (1991). PSRK: A group contributionequation of state based on UNIFAC. Fluid Phase Equilibria, 70,251–265.

Huang, S. H., & Radosz, M. (1991). Equation of state for small,large, polydisperse and associating molecules: extension to ;uidmixtures. Industrial and Engineering Chemistry Research, 30,1994–2005.

Inotama, H., Nakabayashi, N., & Saito, S. (1996). Phase equilibriumcalculation with a local composition model based on Lennard–Jones potential. Fluid Phase Equilibria, 125, 13–20.

Ishihara, I., Tsukajima, A., Tanaka, H., Kato, M., Sako, T., Sato,M., & Hakuta, T. (1996). Vapor–liquid equilibrium for carbondioxide+1-butanol at high pressure. Journal of Chemical andEngineering Data, 41, 324–325.

Jennings, D. W., Chang, F., Bazaan, V., & Teja, A. S. (1992).Vapor–liquid equilibria for carbon dioxide +1-pentanol. Journalof Chemical and Engineering Data, 37, 337–338.

Jennings, D. W., Gude, M. T., & Teja, A. S. (1993). High-pressurevapor–liquid equilibria in carbon dioxide and 1-alkanol mixtures.In E. Kiran J. F. Brennecke (Eds.), Supercritical @uid engineeringscience, fundamentals and applications (p. 10). Washington:American Chemical Society.

Kao, C. C.-P., Pozo de Fern]andez, M. E., & Paulaitis, M. E.(1993). Equation-of-state analysis of phase behavior forwater-surfactant-supercritical ;uid mixtures. In E. Kiran J.F. Brennecke (Eds.), Supercritical @uid engineering science,fundamentals and applications (p. 74). Washington: AmericanChemical Society.

Keshtkar, A., Jalali, F., & Moshfeghian, M. (1997). Evaluationof vapor–liquid equilibrium of CO2 binary systems usingUNIQUAC-based Huron–Vidal mixing rules. Fluid PhaseEquilibria, 140, 107–128.

Kim, J.-S., Yoon, J.-H., & Lee, H. (1994). High-pressure phaseequilibria for carbon dioxide–2-methyl-2-propanol and carbondioxide–2-methyl-2-propanol–water: Measurement and prediction.Fluid Phase Equilibria, 101, 237–245.

King, M. B., Alderson, D. A., Fallah, F. H., Kassim, D. M.,Kassim, K. M., Sheldom, J. R., & Mahmud, R. S. (1983).Some vapor=liquid and vapor=solid equilibrium measurementsof relevance for supercritical extraction operations, and theircorrelations. In M. E. Paulitis J. M. L. Penninger, R. D. Gray,P. Davidson (Eds.), Chemical engineering at supercritical @uidconditions (p. 31). Ann Arbor: Ann Arbor Science.

Kolar, P., & Kojima, K. (1996). Prediction of critical points inmulticomponent systems using the PSRK group contributionequation of state. Fluid Phase Equilibria, 118, 175–200.

Kurihara, K., & Kojima, K. (1995). An implicit type EOS-GE(VP)

model employing vapor pressure standard state I. Prediction of

high pressure vapor–liquid equilibria based on low temperaturedata. Fluid Phase Equilibria, 113, 27–43.

Kwak, C., & Byun, H. C. (1999). Carbon dioxide–isopropyl alcoholsystem: High pressure phase behavior and application with SAFTequation of state. Journal of Korean Industrial and EngineeringChemistry, 10, 324–329 (in Korean).

Lam, D. H., Jangkamolkulchai, A., & Luks, K. D. (1990a). Liquid–liquid–vapor phase equilibrium behavior of certain binary ethane+n-alkanol mixtures. Fluid Phase Equilibria, 59, 263–277.

Lam, D. H., Jangkamolkulchai, A., & Luks, K. D. (1990b).Liquid–liquid–vapor phase equilibrium behavior of certain binarycarbon dioxide +n-alkanol mixtures. Fluid Phase Equilibria, 60,131–141.

Lee, M.-J., & Chen, J.-T. (1994). Vapor–liquid equilibrium forcarbon dioxide=alcohol systems. Fluid Phase Equilibria, 92,215–231.

Lee, H.-S., & Lee, H. (1998). High-pressure phase equilibria for thecarbon dioxide–2-pentanol and carbon dioxide–water–2-pentanolsystems. Fluid Phase Equilibria, 150–151, 695–701.

Lee, H.-S., Mun, S. Y., & Lee, H. (1999a). High-pressure phaseequilibria for the carbon dioxide–3-pentanol and carbon dioxide–3-pentanol–water systems. Journal of Chemical and EngineeringData, 44, 524–527.

Lee, H. -S., Mun, S. Y., & Lee, H. (1999b). High-pressurephase equilibria for the carbon dioxide–2-methyl-1-butanol, carbondioxide–2-methyl-2-butanol, carbon dioxide–2-methyl-1-butanol–water, carbon dioxide–2-methyl-2-butanol–water systems. FluidPhase Equilibria, 157, 81–91.

Lee, H.-S., Mun, S. Y., & Lee, H. (2000). High-pressurephase equilibria of binary and ternary mixtures containingmethyl-substituted butanols. Fluid Phase Equilibria, 167, 131–144.

Levelt Sengers, J. M. H. (2000). Supercritical ;uids: their propertiesand applications. In E. Kiran, P. G. Debenedetti, C. J. Peters (Eds.),Supercritical @uids. Fundamentals and applications, NATOScience Series E, Vol. 366 (p. 1). Dordrecht: Kluwer AcademicPublishers.

Lue, A.-D., Chung, S. Y.-K., & Robinson, D. B. (1991). Theequilibrium phase properties of (carbon dioxide + methanol). TheJournal of Chemical Thermodynamics, 23, 979–985.

Mendoza de la Cruz, J. L., & Galicia-Luna, L. A. (1999).High-pressure vapor–liquid equilibria for the carbon dioxide +ethanol and carbon dioxide + propan-1-ol systems at temperaturesfrom 322.36 to 391:96 K. The International Electronic Journalof Physico-Chemical Data, 5, 157–164.

Michelsen, M. I., & Kistenmacher, H. (1990). Oncomposition-dependent interaction parameters. Fluid PhaseEquilibria, 58, 229–230.

Neichel, M., & Frank, U. E. (1995). Critical curves and phaseequilibria of binary methanol-systems for high pressures andtemperatures. Zeitschrift f;ur Naturforschung, 50 a, 439–444.

Nickel, D., & Schneider, G. M. (1989). Near-infrared spectroscopicinvestigations on phase behaviour and association of 1-hexanol and1-decanol in carbon dioxide, chlorotri;uoromethane, and sulfurhexa;uoride. The Journal of Chemical Thermodynamics, 21,293–305.

Orbey, H., & Sandler, S. I. (1998). Modeling vapor–liquid equilibria.Cubic equations of state and their mixing rules. Cambridge:Cambridge University Press.

Panagiotopoulos, A. Z., & Reid, R. C. (1986). New mixing rules forcubic equations of state for highly polar, asymmetric systems. In K.C. Chao, R. L. Robinson (Eds.). Equations of state: Theories andapplications (p. 571). Washington: American Chemical Society.

Patel, N. C., & Teja, A. S. (1982). A new cubic equation of statefor ;uids and ;uid mixtures. Chemical Engineering Science, 37,463–473.


Peng, D. Y., & Robinson, D. B. (1976). A new two-constant equationof state. Industrial and Engineering Chemistry Fundamentals, 15,59–64.

Perschel, W., & Wenzel, H. (1984). Equation-of-state predictionsof phase equilibria at elevated pressures in mixtures containingmethanol. Berichte der Bunsen-Gesellschaft f;ur PhysikalischeChemie, 88, 807–812.

Peters, C. J. (1994). Multiphase equilibria in the near-critical solvents.In E. Kiran, J. M. H. Levelt Sengers (Eds.), Supercritical@uids. Fundamentals and applications, NATO Science Series E,Vol. 273 (p. 117). Dordrecht Kluwer Academic Publishers.

Peters, C. J., de Swaan Arons, J., Harvey, A. H., & Levelt Sengers,J. M. H. (1989). On the relationship between the carbon numberof n-paraGns and their solubility in supercritical solvents. FluidPhase Equilibria, 52, 389–396.

Pfohl, O., Pagel, A., & Brunner, G. (1999). Phase equilibria insystems containing—o-cresol, p-cresol, carbon dioxide and ethanolat 323.15–473:15 K and 10–35 MPa. Fluid Phase Equilibria, 157,53–79.

Polishuk, I., Wisniak, J., & Segura, H. (1999a). Prediction ofthe critical locus in binary mixtures using equation of state I.Cubic equations of state, classical mixing rules, mixtures ofmethane-alkanes. Fluid Phase Equilibria, 164, 13–47.

Polishuk, I., Wisniak, J., & Segura, H. (1999b). Transitional behaviorof phase diagrams predicted by the Redlich–Kwong equation ofstate and classical mixing rules. Physical Chemistry ChemicalPhysics, 1, 4245–4250.

Polishuk, I., Wisniak, J., & Segura, H. (2000a). A novel approachfor de9ning parameters in a four-parameter EOS. ChemicalEngineering Science, 55, 5705–5720.

Polishuk, I., Wisniak, J., Segura, H., Yelash, L. V., & Kraska, T.(2000b). Prediction of the critical locus in binary mixtures usingequation of state II. Investigation of van der Waals-type andCarnahan–Starling-type equations of state. Fluid Phase Equilibria,172, 1–26.

Prausnitz, J. M., Lichtenthaler, R. N., & de Azevedo, E. G. (1999).Molecular thermodynamics of @uid phase equilibria (3rd ed.).New Jersey: Prentice-Hall.

Prihodko, I. V., Victorov, A. I., Smirnova, N. A., & de Loos, Th. W.(1995). Phase equilibria modeling by the quasilattice equation ofstate for binary and ternary systems composed of carbon dioxide,water and some organic components. Fluid Phase Equilibria, 110,17–30.

Quadri, S. K., Khilar, K. C., Kudchadker, A. P., & Patni, M. J. (1991).Measurement of the critical temperatures and critical pressures ofsome thermally stable or mildly unstable alkanols. The Journalof Chemical Thermodynamics, 23, 67–76.

Quinones-Cisneros, S. E. (1997). Phase and critical behavior in typeIII phase diagrams. Fluid Phase Equilibria, 134, 103–112.

Radosz, M. (1986). Vapor–liquid equilibrium for 2-propanol andcarbon dioxide. Journal of Chemical and Engineering Data, 31,43–45.

Raeissi, S., Gauter, K., & Peters, C. J. (1998). Fluid multiphasebehavior in quasi-binary mixtures of carbon dioxide and certain1-alkanols. Fluid Phase Equilibria, 147, 239–249.

Salim, P. H., & Trebble, M. A. (1991). A modi9ed Trebble–Bishnoiequation of state: Thermodynamic consistency revisited. FluidPhase Equilibria, 65, 59–71.

Scheidgen, A. (1997). Fluid phase equilibria in binary and ternarymixtures of carbon dioxide with low-volatile organic substancesup to 100 MPa. Ph. D. dissertation. Ruhr-UniversitYat Bochum,Bochum (in German).

Schneider, G. M., Scheidgen, A. L., & Klante, D. (2000).Complex phase equilibrium phenomena in ;uid mixtures up to2 GPa—cosolvency, holes, windows, closed loops, high-pressureimmiscibility, barotropy, and related e8ects. Industrial andEngineering Chemistry Research, 39, 4470–4475.

Schmidt, G., & Wenzel, H. (1980). A modi9ed van der Waals typeequation of state. Chemical Engineering Science, 35, 1503–1512.

Schwartzentruber, J., & Renon, H. (1991). Equations of state: howto reconcile ;exible mixing rules, the virial coeGcient constraintand the “Michelsen–Kistenmacher syndrome” for multicomponentsystems. Fluid Phase Equilibria, 67, 99–110.

Sengers, J. V., & Levelt Sengers, J. M. H. (1986). Thermodynamicbehavior of ;uids near the critical point. Annual Review ofPhysical Chemistry, 37, 189–222.

Smith, J. M., van Ness, H. C., & Abbott, M. M. (1996). Introductionto chemical engineering thermodynamics (5th ed.). New York:McGraw-Hill.

Soave, G. (1972). Equilibrium constants from a modi9ed Redlich–Kwong equation of state. Chemical Engineering Science, 27,1197–1203.

Staby, A., & Mollerup, J. (1993). Measurement of mutual solubilitiesof 1-pentanol and supercritical carbon dioxide. The Journal ofSupercritical Fluids, 6, 15–19.

Stevens, R. M. M., van Roermund, J. C., Jager, M. D., de Loos, Th.W., & de Swaan Arons, J. (1997a). High-pressure vapor–liquidequilibria in the systems carbon dioxide+2-butanol, +2-butylacetate, +vinyl acetate and calculations with three EOS methods.Fluid Phase Equilibria, 138, 159–178.

Stevens, R. M. M., Shen, X. M., de Loos, Th. W., & de SwaanArons, J. (1997b). A new apparatus to measure the vapor–liquidequilibria of low-volatility compounds with near-critical carbondioxide. Experimental and modeling results for carbon dioxide+n-butanol, +2-butanol, +2-butyl acetate, +vinyl acetate systems.The Journal of Supercritical Fluids, 11, 1–14.

Stryjek, R., & Vera, J. H. (1986). PRSV: An improved Peng–Robinson equation of state for pure compounds and mixtures.Canadian Journal of Chemical Engineering, 64, 323–333.

Suzuki, K., Sue, H., Itou, M., Smith, R. L., Inomata, H., Arai, K.,& Saito, S. (1990). Isothermal vapor–liquid equilibrium data forbinary systems at high pressures: carbon dioxide–methanol, carbondioxide–ethanol, carbon dioxide–1-propanol, methane–ethanol,methane–1-propanol, ethane–ethanol, and ethane–1-propanolsystems. Journal of Chemical and Engineering Data, 35,63–66.

Tanaka, H., & Kato, M. (1995). Vapor–liquid equilibrium propertiesof carbon dioxide + ethanol mixture at high pressures. Journalof Chemical Engineering of Japan, 28, 263–266.

Tonner, S. P., Wainwright, M. S., & Trimm, D. L. (1983). Solubilityof carbon monoxide in alcohols. Journal of Chemical andEngineering Data, 28, 59–61.

Trebble, M. A., & Bishnoi, P. R. (1987). Development of a newfour-parameter cubic equation of state. Fluid Phase Equilibria,35, 1–18.

Trebble, M. A., & Sigmund, P. M. (1990). A generalized correlationfor the prediction of phase behavior in supercritical systems. TheCanadian Journal of Chemical Engineering, 68, 1033–1039.

van Konynenburg, P. H., & Scott, R. L. (1980). Critical lines andphase equilibria in binary van der Waals mixtures. PhilosophicalTransactions of the Royal Society of London, 298, 495–540.

Weber, W., Zeck, S., & Knapp, H. (1984). Gas solubilities in liquidsolvents at high pressures: Apparatus and results for binary andternary systems of N2, CO2 and CH3OH. Fluid Phase Equilibria,18, 253–278.

Weng, W.-L., Chen, J.-T., & Lee, M.-J. (1994). High-pressurevapor–liquid equilibria for mixtures containing a supercritical;uid. Industrial and Engineering Chemistry Research, 33,1955–1961.

Wong, D. S. H., & Sandler, S. I. (1992). Theoretically correct newmixing rules for cubic equations of state. A.I.Ch.E. Journal, 38,671–680.

Yang, T., Chen, G.-J., Yan, W., & Gou, T.-M. (1997). Extension ofthe Wong–Sandler mixing rule to the three-parameter Patel–Teja


equation of state: Application up to near-critical region. ChemicalEngineering Journal, 67, 27–36.

Yeo, S.-D., Park, S.-J., Kim, J.-W., & Kim, J.-C. (2000). CriticalProperties of carbondioxide + methanol, + ethanol, + 1-propanol,and + 1-butanol. Journal of Chemical and Engineering Data, 45,932–935.

Ziegler, J. W., Chester, T. L., Innis, D. P., Page, S. H.,& Dorsey, J. G. (1995). Supercritical ;uid ;ow injection methodfor mapping liquid–vapor critical loci of binary mixtures containingCO2. In E. K. H. Hutchenson, N.R. Foster (Eds.), Innovations insupercritical @uids. science and technology (p. 93). Washington:American Chemical Society.

simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equation...

Documents