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Fluid Phase Equilibria 416 (2016) 104e119

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Fluid Phase Equilibria

journal homepage: www.elsevier .com/locate/fluid

Application of the SAFT-g Mie group contribution equation of state tofluids of relevance to the oil and gas industry

Vasileios Papaioannou a, Filipe Calado b, Thomas Lafitte b, Simon Dufal a,Majid Sadeqzadeh a, George Jackson a, Claire S. Adjiman a, Amparo Galindo a, *

a Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, SW7 2AZ, United Kingdomb Process Systems Enterprise Ltd., 5th Floor East, 26-28 Hammersmith Grove, London, W6 7HA, United Kingdom

a r t i c l e i n f o

Article history:Received 14 October 2015Received in revised form20 December 2015Accepted 21 December 2015Available online 24 December 2015

Keywords:SAFT-VRSAFTGroup contribution methodsOil and gasFluid-phase behaviour

* Corresponding author.E-mail address: a.galindo@imperial.ac.uk (A. Galin

http://dx.doi.org/10.1016/j.fluid.2015.12.0410378-3812/© 2016 The Authors. Published by Elsevie

a b s t r a c t

The application of the SAFT-g Mie group contribution approach [Papaioannou et al., J. Chem. Phys., 140(2014) 054107] to the study of a range of systems of relevance to the oil and gas industry is presented. Inparticular we consider carbon dioxide, water, methanol, aromatics, alkanes, and their mixtures.Following a brief overview of the SAFT-g Mie equation of state, a systematic methodology for thedevelopment of like and unlike group parameters relevant to the systems of interest is presented. Thedetermination of groupegroup interactions entails a sequence of steps including: the selection ofrepresentative components and mixtures (in this instance carbon dioxide, water, methanol, aromatics,and alkanes); the definition of an appropriate set of groups to describe them; the collection of targetexperimental data used to estimate the groupegroup interactions; the determination of the groupegroup interaction parameters; and the assessment of the adequacy of the parameters and theoreticalapproach. The predictive capability of the SAFT-g Mie group contribution approach is illustrated for aselection of mixtures, including representative examples of the simultaneous description of vapoureliquid and liquideliquid equilibria, the densities of the coexisting phases, second derivative thermo-dynamic properties, and excess properties of mixing. Good quantitative agreement between the pre-dictions and experimental data is achieved, even in the case of challenging mixtures comprising carbondioxide and water, n-alkanes and water, and methanol and methane.© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Thermodynamic methodologies are applied extensively inbroad sectors of the chemical industry, alongside experimentalvalidation, for the prediction of the properties of highly complexfluids and fluid mixtures. A plethora of models are available, andnumerous reviews have been published on the industrial re-quirements for the development of high-fidelity methodologiesthat can be used for the accurate description of the properties of anever-increasing range of substances, relevant to the oil and gas,chemical and pharmaceutical industries. The oil and gas sector inparticular has long been a driver for the development of classes ofequations of state applicable to real systems, such as the Pen-geRobinson equation (PR) [1], the SoaveeRedlicheKwong equation(SRK) [2], the cubic-plus-association equation (CPA) [3], and the

do).

r B.V. This is an open access article

statistical associating fluid theory (SAFT) [4,5]. In recent years, therehas been increasing focus on predictive equations of state, such asthe predictive PR2SRK [6], predictive PengeRobinson PPR78 [7],and SAFT methods incorporating group-contribution concepts[8e13] with a view to deliver accurate predictions of properties foran ever-increasing range of systems.

Thermodynamic models are routinely employed in the designand optimization of separation and production processes, wherethe accuracy of the model can greatly impact the design of theprocess [14,15]. The systems typically encountered in the context ofthe oil and gas industry include mixtures of water, carbon dioxide,hydrocarbons (comprising aliphatic and aromatic components),and in some cases alcohols used as hydrate inhibitors [16]. Thesesystems are highly non-ideal and the accurate modelling of theirfluid-phase behaviour, which can include vapoureliquid and liq-uideliquid equilibria, is a challenging task.

Crude oil can contain thousands of different components, not allof which can be considered specifically, and the capability of

under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 105

thermodynamic approaches to treat multicomponent mixturespredictively is an important consideration in model developmentin this context. As a result, the suitability of a thermodynamicmethodology is judged in part based on its success in predicting thefluid-phase behaviour of multicomponent mixtures based on alimited set of binary interaction parameters. Another considerationis the modelling of the fluid-phase behaviour and properties ofmixtures in the vicinity of the critical region, especially in systemscomprising carbon dioxide, that has a critical point at near-ambienttemperature (Tcrit;CO2

¼ 304.13 K, Pcrit;CO2¼ 7.372 MPa [17]). While

considerable effort has been devoted to the prediction of the fluid-phase behaviour of binary and multi-component mixtures, severalaspects of the application of thermodynamic models to the oil andgas industry warrant more attention. As summarized by Konto-georgis and Folas [18] in their excellent book, these include theprediction of caloric properties (i.e., heats of mixing and heat ca-pacities) over a range of thermodynamic conditions and the pre-diction of a variety of properties that are important for fluid-flowcalculations from equations of state (e.g., densities, speed of sound,etc.).

A single thermodynamic modelling framework would ideallyprovide an accurate description of all of the relevant properties forthe systems of interest in the oil and gas sector over a broad rangeof conditions. In current industrial practice, however, cubic equa-tions of state (EoSs) such as the RedlicheKwong (RK) [19], the SRK[2], or the PR [1] equations are often used for the study of non-aqueous mixtures (e.g., mixtures of carbon dioxide and hydrocar-bons) while more sophisticated approaches that explicitly accountfor association (e.g., variants of the statistical associating fluidtheory (SAFT) [4,5,20,21], or the cubic-plus-association (CPA) EoS[3]) are applied for the study of more complex mixtures, includingaqueous solutions, and mixtures containing methanol and/or otheralcohols.

The application of thermodynamic methodologies to themodelling of systems of relevance to the oil and gas industry hasbeen the subject of numerous studies. The performance of the mostpopular modifications of the van der Waals EoS, the RK [19], SRK[2], and PR [1] variants, in the description of the phase behaviourand volumetric properties of mixtures of carbon dioxide with al-kanes has been extensively studied [22,23]. While these methodscan provide a very good description of the compositions andpressure of the fluid-phase equilibria of binary and multicompo-nent mixtures of hydrocarbons, carbon dioxide, and other gases,the volumetric properties of these systems are not described asaccurately; this can be addressed to some extent by employingvolume-translation methods [24]. Moreover, in order to achieve anaccurate representation of the properties of multi-componentmixtures, a considerable amount of experimental data is requiredfor the determination of the binary interaction parameters betweeneach of the binary pairs of components in a given mixture. In aneffort to overcome the reliance on experimental data, and with theaim of developing more predictive approaches, extensions of theclassical cubic EoSs have been developed. The predictive Pen-geRobinson (PPR78) [7] and the PR2SRK [6] EoSs are, perhaps, thebest known. In these approaches the unlike intermolecular binaryinteraction parameters are determined based on the differentchemical groups the molecules comprise. The PPR78 EoS has beenapplied to describe the fluid-phase behaviour of mixtures of carbondioxide and alkanes [25], as well as of aqueous solutions of hy-drocarbons and carbon dioxide [26], where the capability of theEOS was demonstrated in the description of the fluid-phasebehaviour and excess enthalpies of mixing (using temperature-dependent interaction parameters). These studies did not includethe prediction of the excess volume of mixing and other thermo-dynamic properties that relate to the compressibility of fluids, such

as the isothermal compressibility or the speed of sound [27].When the focus is the description of the fluid-phase behaviour

of systems with components that hydrogen bond or are stronglypolar, more sophisticated methods, such as the statistical associ-ating fluid theory (SAFT) [4,5] or the cubic-plus-association (CPA)EoS [3] are recommended. These thermodynamic approaches areparticularly suited for the description of fluid-phase behaviour inassociating systems, as they account explicitly for the presence ofdirectional interactions. Numerous examples have been reporteddemonstrating the capability of several variants of the SAFT andCPA EoSs to describe accurately the highly non-ideal phasebehaviour characteristic of associating systems such as aqueoussolutions of hydrocarbons, or mixtures of methanol with hydro-carbons [28e35]. In general, both approaches require pure-component parameters specific to each species and appropriatebinary interaction parameters need to be determined for thecharacterization of mixtures. This laborious process can be allevi-ated to some extent with the use of parameters for homologousseries [36,37] rather than single components, together with the useof predictive methods to estimate the binary interactions [38,39]. Inthe case of SAFT-variants reformulations within the context ofgroup contribution (GC) approaches [8e13] have gained promi-nence inmore recent years with the aim to combine the accuracy ofthese sophisticated thermodynamic approaches with the predic-tive capabilities inherent to the GC concept. Some of these meth-odologies can be used to describe the properties of purecomponents as well as mixtures within the same group-contribution framework, whereas other employ the group contri-bution concept to predict only binary interaction parameters be-tween unlike molecules [6,7,40]. Of particular note is also thegroup-contribution with association (GCA) EoS [41], which hasbeen applied to the study of the fluid-phase behaviour of a numberof associating systems, including aqueous solutions of hydrocar-bons [42]. In GC-based theories, the molecular properties thatdescribe a given compound are obtained, in accordance with thegroup-contribution principle, by appropriate summation of thecontributions of the chemical moieties that characterize the com-pound of interest, and binary interactions are determined based onthe corresponding functional groups. The parameters that describethe like and unlike group interactions are estimated by regressionto an extensive set of experimental data for common compounds,and once determined, are used to predict the thermodynamicproperties of compounds for which limited or no experimental dataare available. These versatile thermodynamic methods can be usedto describe accurately the fluid-phase behaviour of a wide-range ofchallenging systems, but the prediction of thermodynamic deriv-ative properties is not always accurate [43], even for simple hy-drocarbons. To achieve a more accurate representation, it has beenfound that the specific form of the molecular interactions, ascaptured by the intermolecular potential, is paramount, and thatthe Mie (generalized Lennard-Jones) potential can be used to pro-vide an much improved model [44,45]. The recent development ofa third-order perturbation expansion for the Mie potential withinthe SAFT-VR Mie EoS [43] provides an accurate simultaneous rep-resentation of the fluid-phase behaviour and the second-orderthermodynamic derivative properties for a variety of systems[43e47]. The perturbation theory has now been reformulated as agroup-contribution equation equation of state (SAFT-g Mie [13])and shows promise as a generic tool for the prediction of thermo-dynamic properties of a wide variety of systems based on groupparameters [48]. The aim of our current work is the development ofmodels for components of special interest to the oil and gas in-dustry within the framework of the SAFT-g Mie EoS. We considermixtures containing water, carbon dioxide, methanol, aromaticsand alkanes.

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119106

A brief outline of the SAFT-gMie group contribution approach ispresented next, highlighting the key features of the theory and theunderlying molecular model, followed by a discussion of the sys-tems of interest within the context of our current work, and anoverview of the methodology adopted to estimate the group pa-rameters for these systems. The performance of the theory in thedescription of the thermodynamic properties of selected mixturesis illustrated for a variety of property calculations and predictions,and comparisons are made with other benchmark thermodynamicapproaches.

2. Methodology

2.1. SAFT-g Mie models and theory

In the SAFT-g Mie [13] EoS a model of heteronuclear chains isemployed where different fused spherical segments are used torepresent the distinct chemical moieties of a given molecule. Anexample of the heterosegment molecular model employed withinthe theory is shown in Fig. 1 for the case of n-propylbenzene, wherethe constituentmethyl (CH3), methanediyl (CH2), aromatic methine(aCH) and aCCH2 chemical functional groups that characterize themolecule are highlighted.

Each compound i is defined by a set of values ni,k that denote thenumber of functional groups of type k in the compound. A givengroup k is characterized by one or more identical segments n�k and ashape factor Skwhich determines the extent towhich each segmentcontributes to the overall molecular properties. The Mie [49] pairpotential model employed for the description of segmentesegmentinteractions is a generalized form of the Lennard-Jones potential[50e54], with variable attractive and repulsive ranges. In the caseof interactions between segments of the same group-type k, theMie potential is written as

FMiekk ðrkkÞ ¼ C kkεkk

"�skkrkk

�lrkk

��skkrkk

�lakk#; (1)

where rkk is the centreecentre distance between the segments, skkis the diameter of the segments, εkk is the depth of the potential,and C kk is a constant, which is a function of the repulsive (lrkk) andattractive (lakk) exponents of the potential and is defined as

Fig. 1. Pictorial representation of the heterosegment molecular model employedwithin the SAFT-g Mie group contribution approach. The example shown correspondsto n-propylbenzene, where the methyl (CH3), methanediyl (CH2), aromatic methine(aCH) and aCCH2 chemical functional groups are highlighted in blue, red, green, andpurple respectively. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

C kk ¼lrkk

lrkk � lakk

lrkklakk

! lakk

lrkk

�lakk

; (2)

which ensures that the minimum of the potential is at �εkk.The group interactions are thus characterized by the diameter of

each segment skk, the potential well-depth εkk, and the repulsiveand attractive ranges of the interaction potential lrkk and lakk,respectively. Association between groups where appropriate istreated by the addition of square-well short-ranged bonding siteson the group segments, as commonly employed within SAFT-typeapproaches. Together with the number of different site typescharacterizing the association of a group NST,k, and the number ofsites of a given type nk,a which are typically chosen a priori, theenergy ε

HBkk;ab of the association interaction between sites of types a

and b, and the corresponding bonding volume Kkk,ab which de-scribes the geometric features of this association interaction arerequired for the complete description of interactions.

The interaction between unlike groups k and l is characterizedby an unlike segment diameter skl defined as

skl ¼skk þ sll

2; (3)

the unlike BarkereHenderson effective hard-sphere diameter as

dkl ¼dkk þ dll

2; (4)

the unlike dispersion energy obtained using a modified geometricmean that takes into account the size asymmetry of the groups as[39]

εkl ¼ffiffiffiffiffiffiffiffiffiffiffiffis3kks

3ll

qs3kl

ffiffiffiffiffiffiffiffiffiffiffiεkkεll

p; (5)

and the unlike repulsive and attractive exponents of the Mie po-tentials as

lkl ¼ 3þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðlkk � 3Þðlll � 3Þ

p: (6)

These combing rules are determined from a geometric mean ofthe van der Waals integrated energy of the respective Sutherlandpotentials [13,43]. The unlike association parameters are defined as

εHBkl;ab ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiεHBkk;aaε

HBll;bb

q; (7)

and

Kkl;ab ¼0@

ffiffiffiffiffiffiffiffiffiffiffiffiKkk;aa

3q

þffiffiffiffiffiffiffiffiffiffiffiKll;bb

3q

2

1A

3

: (8)

The values obtained through these combining rules are oftenrefined by regression to experimental data to capture more accu-rately the features of the specific interactions. In our current paper,as in other work with the SAFT-g Mie EoS, the unlike segment andhard-sphere diameters as well as the unlike attractive exponent arealways given by Equations (3), (4) and (6).

Once the models for the chemical functional groups character-izing the system have been established, the Helmholtz free energycan be determined following the expressions presented in previouswork [13,48], with the association contribution detailed inRef. [46,47]. Other thermodynamic properties can be obtained from

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 107

the free energy using the standard thermodynamic relations.

2.2. Systems of interest and definition of groups

The aim of the work presented in our current study is toinvestigate the suitability of the SAFT-g Mie GC approach to modelmixtures of components of relevance to the oil and gas industry.These include mixtures of carbon dioxide, water, methanol,methane, linear alkanes (ethane to n-decane), and aromatic hy-drocarbons (benzene, toluene, and alkylbenzenes). Of the com-pounds listed, carbon dioxide, water, methanol, and methane aremodelled as molecular groups, e.g., the CO2 group for carbon di-oxide, the CH3OH group formethanol, etc. For the linear alkanes theparameters readily available for the methyl (CH3) and methanediyl(CH2) groups from previous work [13,48] are employed. The aro-matic hydrocarbons are modelled by developing new aCH, aCCH2,and aCCH3 functional groups in our current work. Benzene ismodelled with six equivalent aCH groups, toluene as 5� aCH and1� aCCH3 groups, and the n-alkylbenzenes as 5� aCH, 1� aCCH2and the appropriate number of CH3 and CH2 groups of the alkylchain. The functional groups that are required to fully characterizethe mixtures of interest are summarized in Table 1, where thefunctional groups and the unlike interactions considered arehighlighted. (As shown in Table 1, not all of the unlike interactionsbetween the listed functional groups are required for the charac-terization of the mixtures of interest.) The values of some of theparameters have already been collected in an earlier paper [48];herewe provide details of the parameter-estimation procedure andperformance of the models.

2.3. Parameter estimation

Within the framework of the SAFT-g Mie GC approach allfunctional groups k (molecular or not) are characterized by thefollowing set of parameters: the number of spherical segments n�k,the shape factor Sk, the segment diameter skk, the dispersive energyεkk, and the repulsive and attractive ranges of the potential lrkk andlakk, respectively. For associating groups, such as the H2 O andCH3OH molecules considered here, additional parameters arerequired, namely, the energy ε

HBkkab and extent Kkkab of the associa-

tion interactions, the number of sites nk,a of each type a for eachgroup, together with the total number of site types NST,k. In practicen�k, NST,k, and nk,a are assigned fixed values based on the chemicalnature of each group or, in some cases, with a trial-and-errorapproach. Of the parameters that describe the unlike dispersioninteractions between functional groups, only the unlike dispersionenergy εkl, and in some cases the value of the unlike repulsiveexponent lrkl, are adjusted to reproduce the experimental purecomponent and mixture data more accurately. For the description

Table 1Summary of the SAFT-g Mie functional groups and unlike interactions required forthe modelling of the mixtures of interest in our current work. The stars indicate thelike and unlike parameters required for the modelling of the systems of interestdeveloped here, while the literature references indicate interactions developedpreviously [13,46,48].

CH3

CH3 [13] CH2

CH2 [13] [13] aCHaCH + + + aCCH3

aCCH3 e e + + aCCH2

aCCH2 + + + e + CH4

CH4 e e e e e + H2OH2O + + e e e + [46] CH3OHCH3OH + + e e e + + + CO2

CO2 + + e e e + + + +

of associating interactions between different functional groups thevalue of the unlike association energy ε

HBklab, and extent of associa-

tion Kklab are also treated as adjustable parameters. All other unlikeinteraction parameters are determined by means of appropriatecombining rules as discussed in Section 2.1 and in Refs. [13,48,46].

Either pure component data or mixture data are employed inthe characterization of group parameters. In the case of moleculargroups, such as H2O, CO2, CH4, and CH3OH, the model parametersare estimated from the pure-component vapoureliquid equilib-rium (VLE) data for each substance. Vapour-pressure Pvap, andsaturated-liquid density rsat data are typically employed. Additionalexperimental single-phase liquid densities, or even second-orderthermodynamic derivative properties, such as the speed of soundor heat capacities, can sometimes be useful in order to improve thephysical significance of the molecular parameters; single-phasedata are not used in our current work. The objective functionused in the estimation of molecular group parameters is of thefollowing form:

minU

fobj ¼ wP

XNPvap

m¼1

"PexpvapðTmÞ � Pcalcvap ðTm;UÞ

PexpvapðTmÞ

#2

þwr

XNrsat

n¼1

"rexpsat ðTnÞ � rcalcsat ðTn;UÞ

rexpsat ðTnÞ

#2; (9)

whereU represents the vector of estimated parameters, andwP andwr are weighting factors that can be adjusted according to thedesired level of accuracy for each property; in our current workequal weights wP¼wr ¼ 1 are employed. The summations inEquation (9) are over the number of experimental points NPvap forthe vapour pressure, and Nrsat for the saturated-liquid densityconsidered in the parameter estimation. The minimizations areperformed using the numerical solvers provided by the commercialsoftware package gPROMS© [55].

In the case of other (non-molecular) groups the determinationof the parameters describing the groups of interest is carried outusing experimental data for several molecules comprising thecorresponding groups, such as benzene and the n-alkylbenzenesfor the determination of the aCH and aCCH2 group parameters. Inorder to enhance the physical significance of the parameters ob-tained, mixture data (fluid-phase equilibria or excess properties ofmixing) can also be included in the estimation procedure; in ourcurrent work some excess enthalpy and volumetric data areincluded, leading to the following objective function:

minU

fobj ¼ wP

XNC

i¼1

XNPvap

m¼1

24Pexpvap;iðTmÞ � Pcalcvap;iðTm;UÞ

Pexpvap;iðTmÞ

352

þwr

XNC

i¼1

XNrsat

n¼1

"rexpsat;iðTnÞ � rcalcsat;iðTn;UÞ

rexpsat;iðTnÞ

#2

þwh

XNhE

j¼1

"hE;exp

�Tj; Pj; xj

�� hE;calc�Tj; Pj; xj;U

�hE;exp

�Tj; Pj; xj

�#2

þwvE

XNvE

j¼1

"vE;exp

�Tj; Pj; xj

�� vE;calc�Tj; Pj; xj;U

�vE;exp

�Tj; Pj; xj

�#2

;

(10)

where the first two sums are over the NC pure components iincluded in the estimation, while the last two terms run over thenumber NhE of experimental excess enthalpy points, and NvE ofexcess volume data points considered; the weights are taken as

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119108

equal with wP ¼ wr ¼ wh ¼ wv ¼ 1. The n-alkylbenzenes alsocomprise the CH3 and CH2 groups, which have been characterizedin previous work [13]; the estimation of groupegroup parametersusing these data provides additional values for the unlike in-teractions between the aCH-CH3, aCH-CH2, aCCH2-CH3 and aCCH2-CH2 groups. This is a unique characteristic of heterosegment SAFTapproaches that greatly enhances their predictive capability, as hasbeen demonstrated for the case of the n-alkanes with the SAFT-gMie GC approach [13,48], as well as with other approaches[9e11,56,57]. Our new parameters hence enable the description ofmixtures of benzene, n-alkylbenzenes and alkanes without furtherparameter estimation.

In the case of mixtures involving molecular groups experi-mental binary mixture data needs to be considered to estimate theunlike interaction parameters. Herewe use fluid-phase equilibriumdata and the corresponding objective function is given by

minU

fobj ¼wx

Nx

XNx

m¼1

hxexpðTm; PmÞ � xcalcðTm; Pm;UÞ

i2

þwy

Ny

XNy

n¼1

hyexpðTn; PnÞ � ycalcðTn; Pn;UÞ

i2; (11)

and expresses the sum of the square of the residuals between theexperimental (exp) and calculated (calc) values of the liquid x(T,P)and vapour y(T,P) compositions of a given mixture at specifiedvalues of the pressure and temperature over all experimentalpoints (Nx for the liquid and Ny for the vapour phase). The desiredlevel of accuracy in each of the phases can be tuned by adjusting theweighting factors for the liquid wx or the vapour wy phases. As theobjective function of equation (11) is expressed in terms of molefractions, which are constrained to be between zero and one, theuse of an absolute error is considered more appropriate. In ourwork the calculation of the fluid-phase behaviour is undertaken bymeans of a reliable P-T algorithm [58] and a multi-start gradient-based algorithm is used for parameter estimation.

The metric used in our work to quantify the quality of thetheoretical description of the experimental data in the case of purecompounds is the percentage average absolute deviation (%AAD),defined for a given property R as

%AAD R ¼ 1NR

XNR

i¼1

�����Rexp:i � Rcalc:i

Rexp:i

������ 100; (12)

where NR is the number of data points of property R, and Rcalc:i andRexp:i are the calculated and experimental values for the sameproperty, respectively, at the conditions of the ith experimentalpoint. For the case of binary mixtures absolute errors in composi-tion are reported, defined as

Dz ¼ 1Nz

XNz

i¼1

���zexp:i � zcalc:i

���� 100; (13)

where Nz is the number of data points, and zcalc:i and zexp:i are thecalculated and experimental values for the composition, respec-tively, at the conditions of the ith experimental point.

All SAFT-g Mie group parameters used in our current work arereported in Tables 2e4. Some of these parameters have been re-ported previously [13,46,48] and this is indicated in the tables. Inaddition, further details related to the development of the param-eters that were not provided in earlier work is now given forcompleteness together with the description of the development ofnew parameters carried out in our current work.

3. Results and discussion

We consider now the characterization of each of the SAFT-gMiegroupegroup interactions needed to treat the fluids of interest. Wepresent first the development of the proposed group parametersfrom pure component data and their adequacy, followed by thestudy of binary mixtures and the estimation of unlike interactionparameters; the predictive capability of the SAFT-g Mie GCapproach in describing ternary mixtures is then investigated.

3.1. Pure components

The parameters characterising themolecular groups of methane(CH4), carbon dioxide (CO2), water (H2O), and methanol (CH3OH),and the functional groups for the modelling of the family of n-alkylbenzenes (aCH and aCCH2) and toluene (aCCH3), are devel-oped based on pure-component vapoureliquid equilibrium (VLE)experimental data only (i.e., no single-phase data are used). Thetemperature range of the data included in the estimation of groupparameters is from 30 to 90% of the experimental critical temper-ature for each compound.

Methane is modelled by means of the molecular group CH4,consisting of a single spherical segment (i.e., with the shape factorfixed to one) and the attractive Mie potential exponent is fixed tothe London value of 6. The remaining parameters are estimatedusing pure methane vapour pressure and saturated-liquid densitydata [59]. The resulting model provides a very good description ofthe VLE of methane, as illustrated in Fig. 2.

Carbon dioxide is modelled by means of the molecular groupCO2, formed from two fused Mie segments. An unlike inducedassociation-site of type H is also included in order to model thephase behaviour of carbon dioxide þ water mixtures, cf. Section3.2; this site is inactive in the absence of water [60], i.e.,εHBCO2CO2 ;HH

¼ 0. This type of association scheme for aqueous mix-tures of CO2 has been proposed previously and employed in otherwork [61e63]). The CO2-CO2 interaction group parameters areestimated using pure carbon dioxide vapour pressure andsaturated-liquid density data [59]. The description of the VLE ofpure carbon dioxide obtained with the estimated parameters isexcellent, as can be seen from Fig. 2. As has been shown in previouswork [13,46,48,60], one of the strengths of the SAFT-gMie (and theunderlying SAFT-VR Mie [43]) approach is the accuracy of thepredictions of single-phase and secondederivative properties(density, heat capacity, speed of sound) from parameters estimatedusing VLE data. The SAFT-g Mie predictions for the single-phasedensity and the isobaric heat capacity of carbon dioxide are pro-vided in Fig. 3 and compared to corresponding experimental data;the excellent agreement of the predictions with the measured datais apparent.

The H2O molecular group used to model water comprises asingle Mie segment with four association sites (two sites of type eand two sites of type H). The parameters were presented inRef. [46], andwere determined using experimental vapour pressureand saturated-liquid density data [59]. The description of the VLEobtained with this model is illustrated in Fig. 4.

Methanol is modelled with the CH3OH molecular groupcomprising two fused Mie segments and three association sites(two sites of type e and one site of type H). The parameters areestimated using experimental methanol VLE data [59], as before.The phase behaviour of methanol as described by the SAFT-g Mieapproach [13] and experimental data are shown in Fig. 4.

The aromatic aCH, aCCH2, and aCCH3 groups used to modelbenzene, toluene, and the n-alkylbenzenes are represented assingleMie segments. The parameters describing the aCH and aCCH2groups as well as the aCH-aCCH2, aCH-CH3, aCH-CH2, aCCH2-CH3,

Table 2Like group parameters for use within the SAFT-g Mie group-contribution approach: n�k , Sk, and skk are the number of segments constituting group k, the shape factor, and thesegment diameter of group k, respectively; lrkk and lakk are the repulsive and attractive exponents, and εkk is the dispersion energy of the Mie potential characterizing theinteraction between two k groups, and kB is the Boltzmann constant;NST,k represents the number of association site types on group k, with nk,H and nk,e denoting the number ofassociation sites of type H and e respectively.

k Group k n�k Sk lrkk lakk skk/Å (εkk/kB)/K NST,k nk,H nk,e Ref.

1 CH3 1 0.57255 15.050 6.0000 4.0773 256.77 e e e [13]2 CH2 1 0.22932 19.871 6.0000 4.8801 473.39 e e e [13]3 aCH 1 0.32184 14.756 6.0000 4.0578 371.53 e e e [48]4 aCCH3 1 0.31655 23.627 6.0000 5.4874 651.41 e e e current work5 aCCH2 1 0.20859 8.5433 6.0000 5.2648 591.56 e e e [48]6 CH4 1 1.0000 12.504 6.0000 3.7370 152.58 e e e current work7 H2O 1 1.0000 17.020 6.0000 3.0063 266.68 2 2 2 [46]8 CH3OH 2 0.83517 19.235 6.0000 3.2462 307.69 2 1 2 [48]9 CO2 2 0.84680 26.408 5.0550 3.0500 207.89 1 1 0 current work

Table 3Group dispersion interaction energies εkl and repulsive exponents lrkl for use withinthe SAFT-gMie group-contribution approach. In all cases the unlike group diametersskl and dkl as well as the unlike attractive exponents of the Mie potential lakl areobtained from the combining rules defined in Equations (3), (4) and (6), respectively.CR indicates that the unlike repulsive exponents lrkl are obtained from Equation (6).

k l Group k Group l (εkl/kB)/K lrkl Ref.

1 1 CH3 CH3 256.77 15.050 [13]1 2 CH3 CH2 350.77 CR [13]1 3 CH3 aCH 305.81 CR [48]1 5 CH3 aCCH2 396.91 CR [48]1 7 CH3 H2O 274.80 CR [48]1 8 CH3 CH3OH 275.76 15.537 [48]1 9 CH3 CO2 205.70 CR current work2 2 CH2 CH2 473.39 19.871 [13]2 3 CH2 aCH 415.64 CR [48]2 5 CH2 aCCH2 454.16 CR [48]2 7 CH2 H2O 284.53 CR [48]2 8 CH2 CH3OH 341.41 17.050 [48]2 9 CH2 CO2 276.45 CR current work3 3 aCH aCH 371.53 14.756 [48]3 4 aCH aCCH3 471.23 CR current work3 5 aCH aCCH2 416.69 CR [48]4 4 aCCH3 aCCH3 654.41 23.627 current work5 5 aCCH2 aCCH2 591.56 8.5433 [48]6 6 CH4 CH4 152.58 12.504 current work6 7 CH4 H2O 175.41 CR current work6 8 CH4 CH3OH 233.21 CR current work6 9 CH4 CO2 144.72 11.950 current work7 7 H2O H2O 266.68 17.050 [46]7 8 H2O CH3OH 278.45 CR [48]7 9 H2O CO2 226.38 CR current work8 8 CH3OH CH3OH 307.69 19.235 [48]8 9 CH3OH CO2 157.83 8.3462 current work9 9 CO2 CO2 207.89 26.408 current work

Table 4Group association energies εHBkl;ab and bonding volume parameters Kkl,ab for use within the SAFT-g Mie group-contribution approach. For groups with two site types, the in-teractions are symmetrical, e.g., εHBkl;ab ¼ ε

HBkl;ba . Other interactions not reported here are set to zero, e.g., εHBCO2CO2 ;HH

¼ 0.

k l Group k Site a of group k Group l Site b of group l (εHBkl;ab=kB)/K Kkl,ab/Å3

7 7 H2O H H2O e 1985.4 101.697 8 H2O H CH3OH e 1993.5 104.117 8 H2O e CH3OH H 1993.5 104.117 9 H2O e CO2 H 1398.1 91.4198 8 CH3OH H CH3OH e 2062.1 106.57

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 109

and aCCH2-CH2 unlike group interactions are estimated usingexperimental VLE data for pure benzene, and alkylbenzenes fromn-ethylbenzene to n-decylbenzene [64e84], as well as excess en-thalpies for the benzene þ n-propylbenzene binary mixture atambient conditions (T ¼ 298.15 K, P ¼ 1 atm) [85]. The aCCH3 like

parameters and the aCH-aCCH3 unlike group interaction are esti-mated using vapour pressure and saturated-liquid density data [59]of pure toluene, as well as excess enthalpies and volumes for thetoluene þ benzene binary mixture at ambient conditions(T¼ 298.15 K, P¼ 1 atm) [86,87]. Themodels obtained, summarizedin Tables 2e4, are found to provide a good representation of thevapour pressures and saturated-liquid densities of the pure com-ponents, as can be seen from the values of the %AADs presented inTable 5.

3.2. Binary mixtures

In this section the characterization of the remaining unlikegroup interaction parameters involving at least one moleculargroup is discussed and the performance of the SAFT-g Mieapproach in describing the properties of binary mixtures contain-ing the compounds of interest is investigated. We first considermixtures containing alkanes of different chain length and one othercomponent chosen from carbon dioxide, methanol, and water,illustrating the increasing non-ideality of the fluid-phase behaviourexhibited by these systems as one of the components becomesprogressively more polar. Mixtures not containing alkanes, namely,water þ carbon dioxide and water þ methanol, are thenconsidered.

An accurate description of the properties of mixtures containingn-alkanes and carbon dioxide is important in the oil and gas in-dustry as methane and alkanes are prevalent components of crudeoil and natural gas, while carbon dioxide is ubiquitous, either asnaturally occurring in reservoir fluids or injected in the context ofenhanced oil recovery or carbon storage. It is also of interest to notethat the type of fluid-phase behaviour exhibited by binary mixtures

of carbon dioxide and n-alkanes changes with the chain length ofthe alkane [88,89].

As mentioned previously, methane is represented as a singleMie sphere and carbon dioxide as two fused Mie segments in theSAFT-g Mie approach. Methane and carbon dioxide are both

100

150

200

250

300

350

0 5 10 15 20 25 30

a)

T/K

ρsat / mol dm−3

0.1

1

10

100 150 200 250 300 350

b)

P vap

/MPa

T / KFig. 2. Vapoureliquid equilibria of pure methane and carbon dioxide. The symbolsrepresent the experimental data [59] for methane (squares) and carbon dioxide (cir-cles) and the continuous curves the description with the SAFT-g Mie approach [13]: (a)saturated densities, and (b) vapour pressures. The filled symbols correspond to theexperimental critical points.

200

300

400

500

600

700

800

0 5 10 15 20 25 30

a)

T/K

ρ / mol dm−3

50

100

200

300

200 300 400 500 600 700 800

b)

c P/J

mol−1

K−1

T / KFig. 3. Single-phase properties of pure carbon dioxide. The symbols represent theexperimental data [59] at pressures of P ¼ 10 MPa (squares), P ¼ 20 MPa (circles),P ¼ 30 MPa (triangles), P ¼ 40 MPa (crosses), and P ¼ 50 MPa (diamonds), and thecontinuous curves the predictions with the SAFT-g Mie approach [13]: (a) single-phasedensities, (b) isobaric heat capacities.

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119110

modelled with molecular groups so that is not possible to deter-mine their unlike interactions using pure component data; insteadthese are estimated using the fluid-phase equilibria experimentaldata for the carbon dioxide þ methane mixture. The unlikedispersion energy εkl, and repulsive Mie exponent lrkl are deter-mined using isothermal VLE data at 240 and 270 K [90]. Theresulting interaction parameter values are presented in Table 3. InFig. 5(a) the SAFT-g Mie description of the phase behaviour iscompared to the experimental data for the temperatures consid-ered in the parameter estimation [90] and for two other isotherms[91] that are obtained predicively. The fluid-phase behaviour ob-tained using the PPR78 equation of state [25] is also included in thefigure for comparison. The PPR78 model is considered one of themost accurate predictive cubic EoSs, often used in modelling thesesubstances within the oil and gas industry. The comparison withthe SAFT-g Mie EoS presented in Fig. 5 provides a validation of theaccuracy of our group-contribution methododology.

The n-alkanes are modelled in SAFT-g Mie with the appropriatenumber of CH3 and CH2 groups, so that the complete series ofcarbon dioxide þ n-alkane binary mixtures can be treated from thedetermination of just two unlike interactions between theCH3eCO2 and CH2eCO2 groups. In our current work only the unlikedispersion energies εkl are estimated. Experimental VLE data forcarbon dioxide þ n-decane at 344.23 and 377.59 K [92], as well ascarbon dioxide þ n-pentane at 344.15 and 377.59 K [93] are used tocharacterize the unlike dispersion energies. The resulting

interaction-parameter values are displayed in Table 3. Once thegroup parameters have been determined the fluid-phase behaviourof different carbon dioxide þ n-alkane mixtures can be predicted,as illustrated in Fig. 5(b) and (c) for carbon dioxide mixtures con-taining n-propane and n-decane, respectively. In the figures thepredictions of the SAFT-g Mie approach are compared withexperimental data [92,94] and with calculations carried out usingthe PPR78 EoS [25]. The very good descriptions obtained withSAFT-g Mie underline the transferability of the SAFT-g Mie modelsto conditions (in the case of n-decane) and compounds (in the caseof n-propane) removed from the parameter estimation procedure.

The versatility of the SAFT-g Mie approach is further illustratedin Fig. 6 where the excess properties of mixing of two binarymixtures predicted with the SAFT-gMie EoS are compared with thecorresponding experimental data [95,96]. The excess enthalpy ofmixing for carbon dioxide þ n-pentane at different temperaturesand pressures is presented in Fig. 6(a) and the excess volume ofmixing of carbon dioxideþ n-hexane at different temperatures andpressures in Fig. 6(b). The effect of a change in temperature orpressure is captured well with the approach, leading to a near-quantitative description of the excess properties considered.

Methanol is widely used in the oil and gas industry as a ther-modynamic inhibitor to prevent the formation of clathrate hydrates[16]. As such, an accurate description of the properties of its mix-tures with alkanes and water is essential. The fluid-phase behav-iour of methane þ methanol [98,99] is of type III based on theclassification of van Konynenburg and Scott [100], with entensive

200

300

400

500

600

700

0 10 20 30 40 50 60

a)T

/K

ρsat / mol dm−3

10−6

10−4

10−2

100

102

200 300 400 500 600 700

b)

P vap

/MPa

T / KFig. 4. Vapoureliquid equilibria of pure methanol and water. The symbols representthe experimental data [59] for methanol (circles) and water (squares) and thecontinuous curves the description with the SAFT-g Mie approach [13]: (a) saturateddensities, (b) vapour pressures. The filled symbols correspond to the experimentalcritical points.

Table 5Percentage average absolute deviations (%AAD) for the vapour pressures Pvap(T) and the saturated-liquid densities rsat(T) obtained with the SAFT-g Mie group-contributionapproach [13] (where n is the number of data points) for the pure components of interest in our current work.

Compound T range/K n %AAD Ref. T range/K n %AAD Ref.

Pvap(T) rsat(T)

Methane 95e190 20 0.70 [59] 95e190 20 2.16 [59]Carbon dioxide 220e300 17 0.07 [59] 220e300 17 0.41 [59]Benzene 280e540 53 2.52 [59] 280e540 53 1.04 [59]Toluene 220e530 32 0.55 [59] 220e530 32 0.35 [59]Water 280e640 37 1.15 [59] 280e640 37 1.95 [59]Methanol 180e510 34 0.43 [59] 180e510 34 0.72 [59]n-Ethylbenzene 424e555 29 1.10 [65] 183e490 38 0.49 [70,82]n-Propylbenzene 283e433 25 1.77 [69,79] 223e543 20 0.43 [68,75,84]n-Butylbenzene 313e523 43 0.99 [73,76,81,82] 223e583 22 0.44 [66,68,75,78,81,82]n-Pentylbenzene 293e477 18 2.63 [72,79,83] 233e633 14 1.46 [74,75]n-Hexylbenzene 264e463 27 1.57 [77] 253e613 53 0.37 [71,75]n-Heptylbenzene 309e513 20 5.30 [72,83] 281e368 11 0.25 [72,74]n-Octylbenzene 293e463 25 5.24 [64,73] 243e648 12 1.00 [75]n-Nonylbenzene 332e466 29 3.30 [64,77,80] 282e368 9 0.14 [72]n-Decylbenzene 343e571 25 1.82 [67,73,83] 273e678 11 1.35 [75]

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 111

regions of liquideliquid demixing. Mixtures of the longer alkaneswith methanol present different types of fluid-phase behaviour.The binary mixture of ethane þ methanol also exhibits type IIIbehaviour, while n-propane þ methanol and mixtures involvinglonger n-alkanes and methanol exhibit type II behaviour [99].

A treatment of the entire series of methanol þ alkane binary

mixtures from methane to long alkanes requires the determi-nation of the CH4eCH3OH unlike interaction for the case of themethane þ methanol mixture, as well as those of theCH3eCH3OH and CH2eCH3OH unlike interactions for the othern-alkane þ methanol mixtures. The CH4eCH3OH unlike interac-tion parameters (unlike dispersion energy εkl, and repulsiveexponent lrkl) are estimated using experimental phase-equilib-rium data at 290 and 330 K [101], and the corresponding valuesare reported in Table 3. Once the parameters have been deter-mined, they are validated with predictions of two additionalisotherms at 273.15 and 310 K. The results are compared toexperimental data [101] in Fig. 7. The SAFT-g Mie approachprovides an excellent description of the composition of the twophases, as evidenced in Fig. 7(b) and (c). A particular feature ofthis system is the trend of solubility of methane in themethanol-rich phase: at pressures below 30 MPa the solubilitydecreases with increasing temperature, whereas at higher pres-sures the opposite is observed. This feature is captured very wellwith the SAFT-g Mie EoS, as is apparent from the figure.

The CH3-CH3OH and CH2-CH3OH unlike interaction parameters(unlike dispersion energy εkl and repulsive exponent lrkl) are esti-mated using experimental n-hexane þ methanol isobaric phaseequilibrium data at 0.101 MPa [102,103]. The values of the groupparameters are presented in Table 3. These parameters are thenused to predict the fluid-phase behaviour of the mixtures ofmethanol with two shorter n-alkanes (ethane and n-butane). Acomparison of the SAFT-g Mie description with the experimentaldata for these mixtures as well as the predictions for n-hexane þ methanol [102e105] is made in Fig. 8. The descriptionprovided by SAFT-gMie in the case of n-hexane þmethanol is verygood, both for the VLE and LLE regions. The predictive capabilitiesof the approach are confirmed by the quality of the predictions inthe case of the ethane þ methanol and n-butane þ methanol sys-tems, with the VLE, LLE, and three-phase VLLE well described.

Mixtures of alkaneswithwater are notoriously difficult tomodeldue to the extreme liquideliquid demixing (type III phase behav-

iour) encountered in these systems, with solubilities that differ byorders of magnitude between the two coexisting phases. In order tomodel the methane þ water system, the CH4-H2O unlike interac-tion needs to be determined. The unlike dispersion energy εkl be-tween the two molecular groups is estimated using experimentalphase equilibrium data at 423.15 and 473.15 K [106]; the value of

0

2

4

6

8

10

0.0 0.2 0.4 0.6 0.8 1.0

a)

P/M

Pa

xCO2

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0

b)

P/M

Pa

xCO2

0

5

10

15

20

0.0 0.2 0.4 0.6 0.8 1.0

c)

P/M

Pa

xCO2

Fig. 5. Isothermal pressure-mole fraction (P-x) vapoureliquid equilibria of selectedbinary mixtures of carbon dioxide þ n-alkanes. The symbols represent the experi-mental data, the continuous curves the description with the SAFT-g Mie approach [13]and the dashed curves the description with the PPR78 equation of state [25]: (a) phasediagram of carbon dioxide þ methane at temperatures of T ¼ 230 K [91] (squares),T ¼ 240 K [90] (circles), T ¼ 270 K [91] (triangles), and T ¼ 293 K [97] (diamonds);(b) fluid-phase diagram of carbon dioxide þ n-propane [94] at temperatures ofT ¼ 253.15 K (squares), T ¼ 273.15 K (circles), T ¼ 293.15 K (triangles), and T ¼ 313.15 K(diamonds); (c) phase diagram of carbon dioxide þ n-decane [92] at temperatures ofT ¼ 310.93 K (squares), T ¼ 444.26 K (circles), and T ¼ 510.93 K (triangles).

0

1

2

3

4

5

0.0 0.2 0.4 0.6 0.8 1.0

a)

hE/k

J mol−1

xCO2

−120

−100

−80

−60

−40

−20

0

0.0 0.2 0.4 0.6 0.8 1.0

b)

vE/c

m3 m

ol−1

xCO2

Fig. 6. Isothermal-isobaric excess properties of mixing for carbon dioxide þ n-alkanebinary mixtures. The symbols represent the experimental data and the continuouscurves the predictions with the SAFT-gMie approach [13]: (a) excess molar enthalpy ofmixing for carbon dioxide þ n-pentane [95] at temperatures and pressures ofT ¼ 470.15 KeP ¼ 7.58 MPa (squares), T ¼ 470.15 KeP ¼ 12.45 MPa (circles), andT ¼ 573.15 KeP ¼ 7.58 MPa (diamonds); (b) excess molar volume of mixing for carbondioxide þ n-hexane [96] at temperatures and pressures of T ¼ 308.15 KeP ¼ 7.5 MPa(squares), T ¼ 308.15 KeP ¼ 10.5 MPa (circles), and T ¼ 313.15 KeP ¼ 7.5 MPa(diamonds).

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119112

the parameter is reported in Table 3. This parameter is then used topredict the phase equilibrium at other temperatures. The SAFT-gMie predictions are compared to experimental data [106] in Fig. 9.SAFT-g Mie provides a good description of the experimental data,with both phases described accurately over a range of tempera-tures, although the minimum of solubility of methane in the water-

rich phase around 340 K is not captured.The modelling of other n-alkane þ water mixtures requires the

determination of the CH3eH2O and CH2eH2O unlike group in-teractions; the dispersion energies εkl are reported in Table 3. Thesevalues are estimated using experimental isobaric (P ¼ 1 atm) n-heptane þwater phase equilibrium data [108,109], and can then beused to predict the isothermal phase equilibria of three other n-alkane þ water mixtures. The predictions for n-butane þ water, n-hexane þ water, and n-decane þ water are compared with exper-imental data [110e115] in Fig.10. As can be seen from the figure, theSAFT-g Mie predictions provide a good overall description of boththe VLE and LLE of the three systems considered. The ability todescribe the higher (LLE) and lower (VLE) pressure regimes of themixtures is a stringent test of the model. The SAFT-g Mie group-contribution method is shown to provide a very accurate predic-tion in both regimes; a similarly encouraging result was presentedearly on with the SAFT-g square-well methodology [56].

As for the alkane þ water systems, the carbon dioxide þ waterbinary mixture also exhibits type III fluid-phase behaviour char-acterized by extensive regions of liquideliquid immiscibility. Asmentioned earlier, CO2 is modelled here including one associationsite that is inactive except in the presence of water where it in-teracts with the two e sites of water. Previous work using theWertheim association theory concluded that such an association

0

5

10

15

20

25

30

35

40

45

0.0 0.2 0.4 0.6 0.8 1.0

a)P

/MPa

xCH4

0

5

10

15

20

25

30

35

40

45

0.00 0.05 0.10 0.15 0.20 0.25

b)

P/M

Pa

xCH4

0

5

10

15

20

25

30

35

40

45

0.90 0.92 0.94 0.96 0.98 1.00

c)

P/M

Pa

xCH4

Fig. 7. Isothermal pressure-mole fraction (P-x) vapoureliquid and liquideliquidequilibria of methanol þ methane. The symbols represent the experimental data [101]at temperatures of T ¼ 273.15 K (squares), T ¼ 290 K (circles), T ¼ 310 K (triangles), andT ¼ 330 K (diamonds), while the continuous curves represent the description with theSAFT-g Mie approach [13]: (a) global fluid-phase diagram, (b) methanol-rich phase,and (c) methane-rich phase.

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0

a)

P/M

Pa

xCH3OH

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

b)

P/M

Pa

xCH3OH

260

280

300

320

340

0.0 0.2 0.4 0.6 0.8 1.0

c)

T/K

xCH3OH

Fig. 8. Vapoureliquid and liquideliquid equilibria of selected binary mixtures ofmethanol þ n-alkanes. The symbols represent the experimental data and the contin-uous curves the description with the SAFT-g Mie approach [13]: (a) isothermalpressure-mole fraction (P-x) phase diagram of methanol þ ethane [104] at a temper-ature of T ¼ 298.15 K, the triangles represent vapoureliquid equilibrium data, and thediamonds liquideliquid equilibrium data; (b) isothermal pressure-mole fraction (P-x)phase diagram of methanol þ n-butane [105] at temperatures of T ¼ 323.15 K (circles),and T ¼ 373.15 K (squares); (c) isobaric temperature-mole fraction (T-x) phase diagramof methanol þ n-hexane at a pressure of P ¼ 0.101 MPa, the circles representvapoureliquid equilibrium data [102], and the squares liquideliquid equilibrium data[103].

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 113

scheme was the most suited to describe the fluid-phase behaviourof water þ carbon dioxide [61e63]. The determination of theCO2eH2O unlike interaction hence involves three unlike parame-ters: the unlike dispersion energy (εCO2H2O), the unlike associationenergy (εHBCO2H2O;He

), and the unlike association bonding volume(KCO2H2O;He). These parameters are estimated using experimentalphase equilibrium data at 323.2 K [116] and are presented in Tables3 and 4. Once these parameters have been determined they areused to predict other isotherms. The results of the SAFT-g Miepredictions are compared with experimental data, as well as with

the description obtained using the CPA EoS [3,117] in Fig. 11. Weprovide a comparison with results obtained with the CPA EoS hereinstead of the PPR78 as the CPA EoS accounts for the association inthe mixture and hence provides a better point of comparison toassess the quality of our SAFT-g Mie methodology. It can be seen inthe figure that SAFT-g Mie provides an excellent description of the

0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8 1.0

a)

P/M

Pa

xCH4

0

20

40

60

80

100

0.000 0.005 0.010 0.015 0.020

b)

P/M

Pa

xCH4

0

20

40

60

80

100

0.90 0.92 0.94 0.96 0.98 1.00

c)

P/M

Pa

xCH4

Fig. 9. Isothermal pressure-mole fraction (P-x) vapoureliquid and liquideliquidequilibria of water þ methane. The symbols represent the experimental data at tem-peratures of T ¼ 310.93 K [107] (squares), T ¼ 344.26 K [107] (circles), T ¼ 377.59 K[107] (triangles), T ¼ 423.15 K [106] (diamonds), and T ¼ 473.15 K [106] (crosses), whilethe continuous curves represent the description with the SAFT-g Mie approach [13]:(a) entire composition range, (b) water-rich phase, and (c) methane-rich phase.

Fig. 10. Isothermal pressure-mole fraction (P-x) vapoureliquid and liquideliquidequilibria of n-alkanes þ water. The symbols represent the experimental data, whilethe continuous curves represent the predictions with the SAFT-g Mie approach [13].The dashed line corresponds to the three-phase (vapoureliquid-liquid) equilibriumpressure. (a) n-butane þ water [110e112] at a temperature of T ¼ 377.59 K,(b) n-hexane þ water [113e115] at a temperature of T ¼ 473.15 K, and (c) n-decane þ water [113,114] at a temperature of T ¼ 498.15 K.

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119114

compositions of both the water-rich and carbon dioxide-rich pha-ses of this challenging mixture, including the minimum of solubi-lity of water in the carbon dioxide-rich phase characteristic of non-azeotropic type III phase behaviour with gasegas immiscibility ofthe second kind [100], which is discussed in more detail bydos Ramos et al. [118,119]. This minimum in solubility is difficult tocapture accurately as it requires a good description of the locus ofthe three-phase line as well as good agreement with the high-pressure solubilities.

The Henry's law coefficients and excess enthalpies of mixing for

the carbon dioxide þ water system are also predicted with theSAFT-g Mie approach and are compared with experimental data[120e137] in Fig. 12. It can be seen that a very good description ofthe experimental data is obtained in a fully predictive manner.

The water þ methanol binary mixture exhibits type I phasebehaviour in the classification of van Konynenburg and Scott [100]:only VLE is observed for this mixture. The determination of the CH3OHeH2O unlike interaction requires the adjustment of the unlikedispersion energy εkl, the unlike association energy ε

HBkl;ab, and the

0

5

10

15

20

0.0 0.2 0.4 0.6 0.8 1.0

a)P

/MPa

xCO2

0

5

10

15

20

0.00 0.01 0.02 0.03 0.04 0.05

b)

P/M

Pa

xCO2

0

5

10

15

20

0.980 0.985 0.990 0.995 1.000

c)

P/M

Pa

xCO2

Fig. 11. Isothermal pressure-mole fraction (P-x) vapoureliquid and liquideliquidequilibria of water þ carbon dioxide. The symbols represent the experimental data[116] at temperatures of T ¼ 323.2 K (squares), T ¼ 333.2 K (circles), and T ¼ 353.1 K(triangles), while the continuous curves represent the description with the SAFT-g Mieapproach [13], and the dashed curves the description with the CPA equation of state[3,117]: (a) entire composition range, (b) water-rich phase, and (c) carbon-dioxide-richphase.

Fig. 12. (a) Henry's law coefficients for water þ carbon dioxide; the symbols representthe experimental data [120e136], and the continuous curve the prediction of theSAFT-g Mie approach [13]; (b) Isothermal-isobaric excess molar enthalpy of mixing forwater þ carbon dioxide. The symbols represent the experimental data [137] at atemperature of T ¼ 523.15 K and pressures of P ¼ 10.4 MPa (squares), P ¼ 12.4 MPa(circles), and P ¼ 15 MPa (diamonds); the continuous and dashed curves represent thepredictions of the SAFT-g Mie approach [13] for the one- and two-phase regions,respectively.

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 115

unlike association bonding volume Kkl,ab. A symmetrical associationscheme is used: ε

HBCH3OH�H2O;He

¼ εHBCH3OH�H2O;eH

andKCH3OH�H2O;He ¼ KCH3OH�H2O;eH . These parameters are estimatedusing experimental VLE data at 0.101 MPa [138], and the resultingparameters are then transferred to the prediction of the isothermalVLE at four temperatures. The results of these predictions arecompared with experimental data in Fig. 13, where the excellentquality of the description provided by SAFT-g Mie is apparent.

In addition to the graphical comparisons provided, a summaryof the absolute error in the composition for the phase equilibria of

the binary mixtures examined in this section is provided in Table 6.The small values of these errors confirm the accuracy and predic-tive capability of the SAFT-g Mie group-contribution methodology.

3.3. Ternary mixtures

Although ternary mixtures are more complex than binarymixtures and thus a step towards the description of the real fluidsencountered in the oil and gas industry that can contain largenumbers of components, they are simple enough that experimentaldata on well-characterized systems are available. As all of thenecessary group interactions have been determined from purecomponents and binary mixtures, ternary mixtures can now betreated without any further parameter estimation, providing afurther test of the predictive capabilities of the methodology. Toillustrate the performance of the SAFT-gMie approach in describingternary mixtures two systems are chosen: methanol þ n-propane þ carbon dioxide; and water þ methanol þ n-hexane.

Three sets of conditions are considered for the methanol þ n-propane þ carbon dioxide ternary mixture: T ¼ 313.1 K, P ¼ 1.21MPa; T ¼ 343.1 K, P ¼ 1.21 MPa; and T ¼ 343.1 K, P ¼ 2.7 MPa. Atthese conditions the methanol þ carbon dioxide binary mixtureexhibits a wide fluidefluid immiscibility gap. For both tempera-tures at the lower pressure the methanol þ n-propane binary

0

10

20

30

40

50

60

70

80

90

0.0 0.2 0.4 0.6 0.8 1.0

P/k

Pa

xCH3OH

Fig. 13. Isothermal pressure-mole fraction (P-x) vapoureliquid equilibria ofmethanol þ water. The symbols represent the experimental data at temperatures ofT ¼ 298.14 K [139] (squares), T ¼ 308.15 K [140] (circles), T ¼ 323.15 K [141] (triangles),and T ¼ 333.15 K [141] (diamonds), while the continuous curves represent the pre-dictions with the SAFT-g Mie approach [13].

Table 6Absolute errors in composition (defined in Eq. (13)) for the binary systems presentedin Figs. 5 to 12.

System Dx Dy

Methane þ Carbon dioxide 1.11 0.47Propane þ Carbon dioxide 3.20 1.50n-Decane þ Carbon dioxide 2.00 0.76Methane þ Methanol 0.23 0.56Ethane þ Methanol 0.08 0.17n-Butane þ Methanol 0.16 0.03n-Hexane þ Methanol 1.00 0.45Methane þ Water 4.14 2.41n-Butane þ Water 7.45 2.10n-Hexane þ Water 5.21 2.58n-Decane þ Water 0.03 0.33Carbon Dioxide þ Water 3.02 1.38Methanol þ Water 3.44 1.70

xCH3OH xC3H8

xCO2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

a)

xH2O xCH3OH

xC6H14

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

b)

Fig. 14. Isothermal-isobaric fluid-phase equilibrium of ternary mixtures. The symbolsrepresent the experimental data and the continuous curves the predictions of theSAFT-g Mie approach [13]: (a) Propane þ carbon dioxide þ methanol [142] at tem-peratures and pressures of T ¼ 313.1 K, P ¼ 1.21 MPa (circles), T ¼ 343.1 K, P ¼ 1.21 MPa(squares), and T ¼ 343.1 K, P ¼ 2.7 MPa (diamonds); (b) Water þ n-hexane þ methanolat a temperature of T ¼ 318.15 K and a pressure of P ¼ 0.101 MPa [144], the dash dottedlines and the dashed lines represent the experimental and predicted tie lines,respectively .

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119116

mixture exhibits vapoureliquid phase equilibria while carbon di-oxide and n-propane are fully miscible. As a result, for both tem-peratures at the lower pressure considered, the fluid-phasebehaviour of the ternary mixture is characterized by a two-phaseregion, with the phase boundaries extending from themethanol þ carbon dioxide binary mixture to themethanol þ n-propane mixture VLE boundary. At the higher tem-perature and pressure considered, methanol and propane aremiscible [142], while the carbon dioxide þ propane mixture ex-hibits a small vapoureliquid region close to pure propane (althoughno experimental data are available, the pressure is slightly abovethe vapour pressure of propane and a simple extrapolation of thedata of Reamer et al. [143] leads to a phase split at these condi-tions). The phase behaviour of the ternary mixture, while stillcharacterized by a two-phase region, reflects the change in thephase behaviour of the constituent binary mixtures, with the phaseboundaries now extending from the methanol þ carbon dioxidebinary mixture phase boundaries to those of the carbondioxide þ propane binary mixture. The experimental data [142] forthis system are compared with the SAFT-g Mie predictions inFig. 14(a). It can be seen from the figure that the SAFT-g Mie pre-dictions are in good agreement with the data and capture thischange in phase behaviour very well.

The second ternary mixture considered in our current work is

waterþmethanolþ n-hexane at T¼ 318.15 K and P¼ 0.101MPa. Asmentioned in the previous section the water þ n-hexane binarymixture exhibits extensive liquideliquid immiscibility under theseconditions, while methanol is fully miscible with both water andn-hexane at these conditions. This leads to the appearance of abroad two-phase region in the ternary phase diagram with meth-anol partitioning between a water-rich phase and a n-hexane-richphase, a feature common to ternary mixtures containing water, analkane and a small polar molecule. The comparison between theexperimental data [144] and the SAFT-g Mie predictions providedin Fig. 14(b) highlights the fidelity of the approach in reproducingthe experimental phase envelope and tie-lines. The quality of thepredicted calculations is better appreciated studying the corre-sponding K values for the two ternary systems; these are presentedin Fig. 15. For the methanolþ propane þ carbon dioxide system theK value of propane is calculated as

0.01

0.1

1

10

0.01 0.1 1 10

KSA

FT

Kexp

Fig. 15. Experimental (exp) versus calculated (SAFT) K values for the ternary mixturespropane þ carbon dioxide þ methanol (squares) and water þ n-hexane þ methanol(circles).

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 117

KC3H8¼ yC3H8

xC3H8

; (14)

and a comparison of the experimental and calculated values for agiven composition of propane in the gas phase yC3H8

is provided. Forthe water þmethanol þ n-hexane mixture the K value of methanolis calculated as

KCH3OH ¼ xWRCH3OH

xHRCH3OH

; (15)

where the superscripts WR and HR indicate the water-rich and n-hexane-rich phases, respectively. A comparison of the experimentaland calculated values for a given value of xHRCH3OH

is given in thefigure. It is apparent that, with the exception of a small number ofpoints (corresponding to the higher temperature and pressurestates for the propane þ carbon dioxide þ methanol system and tothe region of very low methanol content for the water þ n-hexane þ methanol system) the calculated values are in goodagreement with the experimental data.

4. Conclusion

The application of the SAFT-g Mie group-contribution approach[13] to selected mixtures with components relevant to the oil andgas industry is shown to provide an excellent description of theproperties for the systems of interest. Pure-component coexistenceproperties are reproduced well with our method, and single-phasedensities and secondederivative properties are predicted withexcellent accuracy. Several of the compounds considered here havebeen modelled using molecular groups due to their small size.Others have been described with representative chemical func-tional groups, making it possible to make use of the advantageconferred to SAFT-gMie by its heterosegment nature, which allowsone to obtain unlike group interactions from pure-component dataalone. The capability of SAFT-g Mie to give exceptional predictionsof the fluid-phase behaviour of binary mixtures of families ofcompounds based on interactions developed using data for only afew of the members of the family is demonstrated on an extensiveset of mixtures and highlights the versatility of the group-contribution methodology. The predictive capability of the SAFT-gMie approach also extends to the treatment of mixtures at differentconditions and for other properties. The use of association sites

within the underlying SAFT base of the approach enables a highquality treatment of hydrogen-bonding and polar fluids, such aswater, carbon dioxide, methanol, and mixtures containing thesespecies. The SAFT-gMie approach provides good descriptions of theVLE and LLE for the systems of interest, including challengingphenomena such as the solubility minimum of water in the carbon-dioxide-rich phase and the crossing point of the isotherms of themethane solubility in the methanol-rich phase. Furthermore, sec-ondederivative properties and excess properties of mixing are alsodescribed well, making SAFT-g Mie a promising generic platformfor thermodynamic modelling in the oil and gas industry. In ourcurrent work new groups, including CO2, CH3OH, aCH, aCCH2, andaCCH3, and groupegroup interactions have been characterized. Asthe table of available interactions continues to expand, anincreasingly large number of mixtures becomes accessible. Infuture work we will continue testing the performance of themethod on an increasing set of systems. The intermolecular pa-rameters obtained with the SAFT-g Mie methodology can also beused directly with molecular dynamics simulation to provide aroute to structural, interfacial and dynamical properties that are notdirectly accessible from the equation of state enhancing the pre-dictive capabilities of the methodology [145e150].

Acknowledgements

The authors would like to acknowledge financial support fromTOTAL S.A, the Technology Strategy Board (TSB) of the UnitedKingdom (project CADSEP-101326), the Engineering and PhysicalSciences Research Council (EPSRC) of the UK (grants GR/N35991,EP/E016340 and EP/J014958). We thank Laurent Avaul�ee, PierreDuchet-Suchaux, and Charles Yacono for useful discussion andinput. V.P. acknowledges the award of a PhD studentship and aDoctoral Prize Fellowship 2013 from the EPSRC. C.S.A. is thankful tothe EPSRC for the award of a Leadership Fellowship (EP/J003840/1).The authors acknowledge additional funding from the JointResearch Equipment Initiative (JREI) (GR/M94426), and the RoyalSociety-Wolfson Foundation. refurbishment scheme.

Data underlying this article can be accessed on Zenodo athttps://zenodo.org/record/44391, and used under the CreativeCommons Attribution licence.

References

[1] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59.[2] G. Soave, Chem. Eng. Sci. 27 (1972) 1197.[3] G.M. Kontogeorgis, E. Voutsas, I.V. Yakoumis, D.P. Tassios, Ind. Eng. Chem.

Res. 35 (1996) 4310.[4] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Fluid Phase Equilib. 52

(1989) 31.[5] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res. 29

(1990) 1709.[6] J.-N. Jaubert, R. Privat, Fluid Phase Equilib. 295 (2010) 26.[7] J.N. Jaubert, F. Mutelet, Fluid Phase Equilib. 224 (2004) 285.[8] S. Tamouza, J.P. Passarello, P. Tobaly, J.C. de Hemptinne, Fluid Phase Equilib.

222e223 (2004) 67.[9] A. Lymperiadis, C.S. Adjiman, A. Galindo, G. Jackson, J. Chem. Phys. 127

(2007) 234903.[10] A. Lymperiadis, C.S. Adjiman, G. Jackson, A. Galindo, Fluid Phase Equilib. 274

(2008) 85.[11] Y. Peng, K.D. Goff, M.C. dos Ramos, C. McCabe, Fluid Phase Equilib. 277 (2009)

131.[12] K. Paduszy�nski, U. Doma�nska, Ind. Eng. Chem. Res. 51 (2012) 12967.[13] V. Papaioannou, T. Lafitte, C. Avenda~no, C.S. Adjiman, G. Jackson, E.A. Müller,

A. Galindo, J. Chem. Phys. 140 (054107) (2014).[14] W.B. Whiting, J. Chem. Eng. Data 41 (1996) 935.[15] R. Dohrn, O. Pfohl, Fluid Phase Equilib. 194e197 (2002) 15.[16] E.D. Sloan, C.A. Koh, Clathrate Hydrates of Natural Gases, third ed., CRC Press,

Boca Raton, 2008.[17] J.V. Sengers, J.M.H. Levelt Sengers, Ann. Rev. Phys. Chem. 37 (1986) 189.[18] G.M. Kontogeorgis, G.K. Folas, Thermodynamic Models for Industrial Appli-

cations. From Classical and Advanced Mixing Rules to Association Theories,

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119118

Wiley, UK, 2010.[19] O. Redlich, E.L. Derr, G.J. Pierotti, J. Am. Chem. Soc. 81 (1959) 2283.[20] G. Jackson, W.G. Chapman, K.E. Gubbins, Mol. Phys. 65 (1988) 1.[21] W.G. Chapman, G. Jackson, K.E. Gubbins, Mol. Phys. 65 (1988) 1057.[22] A. Danesh, D.-H. Xu, A. Todd, Fluid Phase Equilib. 63 (1991) 259.[23] H. Li, J. Yan, Appl. Energy 86 (2009) 826.[24] A. Peneloux, E. Rauzy, R. Freze, Fluid Phase Equilib. 8 (1982) 7.[25] S. Vitu, R. Privat, J.N. Jaubert, F. Mutelet, J. Supercrit. Fluids 45 (2008) 1.[26] J.-W. Qian, R. Privat, J.-N. Jaubert, Ind. Eng. Chem. Res. 52 (2013) 16457.[27] T.S. Khasanshin, A.P. Shchamialiou, O.G. Poddubskij, Int. J. Thermophys. 24

(2003) 1277.[28] A. Galindo, P.J. Whitehead, G. Jackson, A.N. Burgess, J. Phys. Chem. 100 (1996)

6781.[29] G.M. Kontogeorgis, I.V. Yakoumis, H. Meijer, E. Hendriks, T. Moorwood, Fluid

Phase Equilib. 158e160 (1999) 201.[30] E.C. Voutsas, G.C. Boulougouris, I.G. Economou, D.P. Tassios, Ind. Eng. Chem.

Res. 39 (2000) 797.[31] B.H. Patel, P. Paricaud, A. Galindo, G.C. Maitland, Ind. Eng. Chem. Res. 42

(2003) 3809.[32] X.S. Li, P. Englezos, Fluid Phase Equilib. 224 (2004) 111.[33] L.F. Vega, F. Llovell, F.J. Blas, J. Phys. Chem. B 113 (2009) 7621.[34] J.M. Miguez, M.C. dos Ramos, M.M. Pi~neiro, F.J. Blas, J. Phys. Chem. B 115

(2011) 9604.[35] S.Z.S. Al Ghafri, E. Forte, G.C. Maitland, J.J. Rodriguez-Henriquez,

J.P.M. Trusler, J. Phys. Chem. B 118 (2014) 14461.[36] C. McCabe, G. Jackson, Phys. Chem. Chem. Phys. 1 (1999) 2057.[37] P. Paricaud, A. Galindo, G. Jackson, Ind. Eng. Chem. Res. 43 (2004) 6871.[38] G.H. Hudson, J.C. McCoubrey, Trans. Faraday Soc. 56 (1960) 761.[39] A.J. Haslam, A. Galindo, G. Jackson, Fluid Phase Equilib. 266 (2008) 105.[40] M. Hajiw, A. Chapoy, C. Coquelet, Can. J. Chem. Eng. 93 (2015) 432.[41] H.P. Gros, S. Bottini, E.A. Brignole, Fluid Phase Equilib. 116 (1996) 537.[42] T.M. Soria, F.A. S�anchez, S. Pereda, S.B. Bottini, Fluid Phase Equilib. 296 (2010)

116.[43] T. Lafitte, A. Apostolakou, C. Avenda~no, A. Galindo, C.S. Adjiman, E.A. Müller,

G. Jackson, J. Chem. Phys. 139 (2013) 154504.[44] T. Lafitte, D. Bessieres, M.M. Pi~neiro, J.L. Daridon, J. Chem. Phys. 124 (2006),

024509.[45] T. Lafitte, M.M. Pi~neiro, J.L. Daridon, D. Bessieres, J. Phys. Chem. B 111 (2007)

3447.[46] S. Dufal, T. Lafitte, A.J. Haslam, A. Galindo, G.N.I. Clark, C. Vega, G. Jackson,

Mol. Phys. 113 (2015) 948.[47] S. Dufal, T. Lafitte, A. Galindo, G. Jackson, A.J. Haslam, AIChE J. 61 (2015) 2891.[48] S. Dufal, V. Papaioannou, M. Sadeqzadeh, T. Pogiatzis, A. Chremos,

C.S. Adjiman, G. Jackson, A. Galindo, J. Chem. Eng. Data 59 (2014) 3272.[49] G. Mie, Ann. Phys. 316 (1903) 657.[50] E.A. Grüneisen, Z. Elektrochem, Angew. Phys. Chem. 17 (1911) 737.[51] E.A. Grüneisen, Ann. Phys. 344 (1912) 257.[52] J.E. Jones, Proc. Roy. Soc. Lond. A 106 (1924) 441.[53] J.E. Jones, Proc. Roy. Soc. Lond. A 106 (1924) 463.[54] J.E. Lennard-Jones, Proc. Phys. Soc. 43 (1931) 461.[55] PSE Ltd, gPROMS V. 3.4.0, 2011. http://www.psenterprise.com/.[56] V. Papaioannou, C.S. Adjiman, G. Jackson, A. Galindo, Fluid Phase Equilib. 306

(2011) 82.[57] M.C. dos Ramos, J.D. Haley, J.R. Westwood, C. McCabe, Fluid Phase Equilib.

306 (2011) 97.[58] F.E. Pereira, G. Jackson, A. Galindo, C.S. Adjiman, Fluid Phase Equilib. 299

(2010) 1.[59] E.P.J. Linstrom, W.G. Mallard, NIST Chemistry WebBook, NIST Standard

Reference Database Number 69, National Institutes of Standards and Tech-nology WebBook, Gaithersburg MD, 2013, 20899.

[60] M. Sadeqzadeh, V. Papaioannou, S. Dufal, C.S. Adjiman, G. Jackson, A. Galindo,Fluid Phase Equilib. 407 (2016) 39.

[61] G.M. Kontogeorgis, M.L. Michelsen, G.K. Folas, S. Derawi, N. von Solms,E.H. Stenby, Ind. Eng. Chem. Res. 45 (2006) 4869.

[62] R. Sun, J. Dubessy, Geochim. Cosmochim. Acta 74 (2010) 1982.[63] I. Tsivintzelis, G.M. Kontogeorgis, M.L. Michelsen, E.H. Stenby, Fluid Phase

Equilib. 306 (2011) 38.[64] N. Allemand, J. Jose, J.C. Merlin, Thermochim. Acta 105 (1986) 79.[65] D. Ambrose, J. Chem. Thermodyn. 19 (1987) 1007.[66] C.A. Buehler, T.S. Gardner, M.L. Clemens, J. Org. Chem. 2 (1937) 167.[67] D.L. Camin, A.D. Forziati, F.D. Rossini, J. Phys. Chem. 58 (1954) 440.[68] E.B. Evans, J. Inst. Pet. Technol. 24 (1938) 537.[69] A.F. Forziati, W.R. Norris, F.D. Rossini, J. Res. Natl. Bur. Stand 43 (1949) 555.[70] J.L. Hales, R. Townsend, J. Chem. Thermodyn. 4 (1972) 763.[71] E.C. Ihmels, Viscosity Measurements with a Ubbelohde-viscosimeter and

Density Measurements with a Resonance Frequency Transducer Prototype,Diplomarbeit, 1998 (cited in DETHERM).

[72] T.Y. Ju, G. Shen, C.E. Wood, J. Inst. Pet. 26 (1940) 514.[73] H. Kasehgari, I. Mokbel, C. Viton, J. Jose, Fluid Phase Equilib. 87 (1993) 133.[74] T. Kimura, T. Matsushita, T. Kamiyama, J. Solut. Chem. 33 (2004) 875.[75] G. Liessmann, W. Schmidt, S. Reiffarth, Data Compilation of the Saechsische

Olefinwerke Boehlen Germany, 1995 (cited in DETHERM).[76] J. Linek, V. Fried, J. Pick, Collect. Czech. Chem. Commun. 30 (1965) 1358.[77] I. Mokbel, E. Rauzy, J.P. Meille, J. Jose, Fluid Phase Equilib. 147 (1998) 271.[78] J. Ortega, G. Bolat, E. Marrero, Phys. Chem. Liq. 45 (2007) 251.

[79] V. Ruzicka, M. Zabransky, K. Ruzicka, V. Majer, Thermochim. Acta 245 (1994)121.

[80] P.M. Sherblom, P.M. Gschwend, R.P. Eganhouse, J. Chem. Eng. Data 37 (1992)394.

[81] W.V. Steele, R.D. Chirico, S.E. Knipmeyer, A. Nguyen, J. Chem. Eng. Data 47(2002) 648.

[82] N.B. Vargaftik, Handbook of Thermophysical Properties of Gases and Fluids,1972. Nauka, Moscow.

[83] S.P. Verevkin, J. Chem. Thermodyn. 38 (2006) 1111.[84] Z.W. Yu, X.H. He, R. Zhou, Y. Liu, X.D. Sun, Fluid Phase Equilib. 164 (1999)

209.[85] D. Jain, N. Dhar, Fluid Phase Equilib. 47 (1989) 89.[86] K. Hsu, H. Clever, J. Chem. Thermodyn. 7 (1975) 435.[87] S. Murakami, V. Lam, G. Benson, J. Chem. Thermodyn. 1 (1969) 397.[88] M.M. Miller, K.D. Luks, Fluid Phase Equilib. 44 (1989) 295.[89] G.M. Schneider, J. Supercrit. Fluids 13 (1998) 5.[90] T.A. Al-Sahhaf, A.J. Kidnay, E.D. Sloan, Ind. Eng. Chem. Fundam. 22 (1983)

372.[91] M.S.W. Wei, T.S. Brown, A.J. Kidnay, E.D. Sloan, J. Chem. Eng. Data 40 (1995)

726.[92] H.H. Reamer, B.H. Sage, J. Chem. Eng. Data 8 (1963) 508.[93] G. Besserer, D. Robinson, J. Chem. Eng. Data 18 (1973) 416.[94] J.H. Kim, M.S. Kim, Fluid Phase Equilib. 238 (2005) 13.[95] J.J. Christensen, P.W. Faux, D. Cordray, R.M. Izatt, J. Chem. Thermodyn. 18

(1986) 1053.[96] W.K. Tolley, R.M. Izatt, J.L. Oscarson, Thermochim. Acta 181 (1991) 127.[97] B. Bian, Ph.D. Thesis, University of Nanjing, Nanjing (1992).[98] E. Brunner, J. Chem. Thermodyn. 17 (1985) 871.[99] I. H€olscher, G. Schneider, J. Ott, Fluid Phase Equilib. 27 (1986) 153.

[100] P.H. van Konynenburg, R.L. Scott, Philos. Trans. R. Soc. A 298 (1980) 495.[101] J.H. Hong, P.V. Malone, M.D. Jett, R. Kobayashi, Fluid Phase Equilib. 38 (1987)

83.[102] J.D. Raal, R.K. Code, D.A. Best, J. Chem. Eng. Data 17 (1972) 211.[103] G. Hradetzky, H.J. Bittrich, Int. Data Ser. Sel. Data Mix. Ser. A (1986) 216e218.[104] K. Ishihara, H. Tanaka, M. Kato, Fluid Phase Equilib. 144 (1998) 131.[105] A.D. Leu, C.J. Chen, D.B. Robinson, AIChE Symp. Ser. 85 (1989) 11.[106] R.G. Sultanov, V.G. Skripka, A.Y. Namiot, Deposited Doc, VINITI 4386-72,

1972, p. 1 (cited in DETHERM).[107] R.H. Olds, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 34 (1942) 1223.[108] J. Polak, B.C.-Y. Lu, Can. J. Chem. 51 (1973) 4018.[109] M. Freire, L. Gomes, L. Santos, I. Marrucho, J. Coutinho, J. Phys. Chem. B 110

(2006) 22923.[110] H.H. Reamer, R.H. Olds, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 36 (1944) 381.[111] H.H. Reamer, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 44 (1952) 609.[112] W. Brooks, G. Gibbs, J. McKetta, Petro. Refin. 30 (1951) 118.[113] A.Y. Namiot, V.G. Skripka, G.Y. Lotter, Deposited Doc, VINITI 1213-76, 1976,

p. 1 (cited in DETHERM).[114] R.G. Sultanov, V.G. Skripka, Deposited Doc, VINITI 4386-72, 1972, p. 1 (cited

in DETHERM).[115] R.G. Sultanov, V.G. Skripka, Deposited Doc, VINITI 2347-73, 1973, p. 1 (cited

in DETHERM).[116] A. Bamberger, G. Sieder, G. Maurer, J. Supercrit. Fluids 17 (2000) 97.[117] Infochem Computer Services Ltd, Multiflash V. 4.3, 2013. http://www.kbcat.

com/.[118] M.C. dos Ramos, F.J. Blas, A. Galindo, Fluid Phase Equilib. 261 (2007a) 359.[119] M.C. dos Ramos, F.J. Blas, A. Galindo, J. Phys. Chem. C 111 (2007b) 15924.[120] M. Postigo, M. Katz, J. Solut. Chem. 16 (1987) 1015.[121] D. Hagewiesche, S. Ashour, O. Sandall, J. Chem. Eng. Data 40 (1995) 627.[122] L. Lizano, M. Lopez, F. Royo, J. Urieta, J. Solut. Chem. 19 (1990) 721.[123] E. Wilhelm, R. Battino, R. Wilcock, Chem. Rev. 77 (1977) 219.[124] J. Tokunaga, J. Chem. Eng. Data 20 (1975) 41.[125] J. Foussard, P. Reilhac, F. Cammas, H. Debellefontaine, High. Temp. High.

Press. 30 (1998) 43.[126] W. Su, D. Wong, M. Li, J. Chem. Eng. Data 54 (2009) 1951.[127] G. Schulze, J. Prausnitz, Ind. Eng. Chem. Fundam. 2 (1981) 175.[128] D. Zheng, T. Guo, H. Knapp, Fluid Phase Equilib. 129 (1997) 197.[129] M. Malegaonkar, P. Dholabhai, P. Bishnoi, Can. J. Chem. Eng. 75 (1997) 1090.[130] A. Dhima, J. de Hemptinne, J. Jose, Ind. Eng. Chem. Res. 38 (1999) 3144.[131] G. Anderson, J. Chem. Eng. Data 47 (2002) 219.[132] J. Kiepe, S. Horstmann, K. Fischer, J. Gmehling, Ind. Eng. Chem. Res. 41 (2002)

4393.[133] I. Dalmolin, E. Skovroinski, A. Biasi, M. Corazza, C. Dariva, J. Oliveira, Fluid

Phase Equilib. 245 (2006) 193.[134] C. Dell’Era, P. Uusi-Kyyny, J. Pokki, M. Pakkanen, V. Alopaeus, Fluid Phase

Equilib. 293 (2010) 101.[135] A. Ellis, R. Golding, Am. J. Sci. 261 (1963) 47.[136] R. Crovetto, R. Wood, Fluid Phase Equilib. 74 (1992) 271.[137] X. Chen, S. Gillespie, J. Oscarson, R. Izatt, J. Solut. Chem. 21 (1992) 825.[138] V. Olevskii, I. Golub’ev, Tr Gos, Nauchno. Issled. Proektn. Inst. Azotn. Promst.

Prod. Org. Sin. 4 (1954) 36.[139] Z.S. Koner, R.C. Phutela, D.V. Fenby, Aust. J. Chem. 33 (1980) 9.[140] M.L. McGlashan, A.G. Williamson, J. Chem. Eng. Data 21 (1976) 196.[141] K. Kurihara, T. Minoura, K. Takeda, K. Kojima, J. Chem. Eng. Data 40 (1995)

679.[142] F. Galivel-Solastiouk, S. Laugier, D. Richon, Fluid Phase Equilib. 28 (1986) 73.

V. Papaioannou et al. / Fluid Phase Equilibria 416 (2016) 104e119 119

[143] H.H. Reamer, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 43 (1951) 2515.[144] J. Liu, Z. Qin, J. Wang, J. Chem. Eng. Data 47 (2002) 1243.[145] C. Avenda~no, T. Lafitte, A. Galindo, C.S. Adjiman, G. Jackson, E.A. Müller,

J. Phys. Chem. B 115 (2011) 11154.[146] C. Avenda~no, T. Lafitte, C.S. Adjiman, A. Galindo, E.A. Müller, G. Jackson,

J. Phys. Chem. B 117 (2013) 2717.[147] T. Lafitte, C. Avenda~no, V. Papaioannou, A. Galindo, C.S. Adjiman, G. Jackson,

E.A. Müller, Mol. Phys. 110 (2012) 1189.[148] O. Lobanova, C. Avenda~no, T. Lafitte, E.A. Müller, G. Jackson, Mol. Phys. 113

(2015) 1228.[149] S. Rahman, O. Lobanova, C. Braga, V. Raptis, E. A. Müller, G. Jackson, and A.

Galindo, J. Phys. Chem. B, in preparation.[150] O. Lobanova, A. Mejía, G. Jackson, E.A. Müller, J. Chem. Thermodyn. 93 (2016)

320.