improved prediction of water properties and phase

Improved Prediction of Water Properties and Phase Equilibria with aModified Cubic Plus Association Equation of StateAndre M. Palma,† Antonio J. Queimada,*,‡ and Joao A. P. Coutinho†

†CICECO, Chemistry Department, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal‡KBC Advanced Technologies Limited (A Yokogawa Company), 42-50 Hersham Road, Walton-on-Thames, Surrey KT12 1RZ,United Kingdom

*S Supporting Information

ABSTRACT: One of the major challenges of an equation of state lies in thedescription of water and aqueous systems. Its abundance and uniqueproperties turn water into one of the most important molecules in theindustry. However, because of these peculiar characteristics, its modeling is farmore complex than for any other common solvent. In this work, a modifiedcubic plus association (CPA) model, which includes the correct description ofthe pure component critical temperature and critical pressure, is expanded towater and its systems. A brief analysis of the predicted water purity propertiesis conducted, comparing those to a previous version of the model. Results for agroup of binary systems, including liquid−liquid equilibria with alkanes andalcohols, highlighting their minima in aqueous solubility, and gas solubility in water/water solubility in gas, are also presented.Finally, ternary and multicomponent systems of water + hydrocarbons and water + polar compound + hydrocarbons are alsomodeled and discussed.

1. INTRODUCTION

The importance of water both in the industry and in the dailylives of the world population is undeniable, and its uniqueproperties are an asset used in diverse ways in almost everyprocess.The correct description of pure water and its mixtures using

an equation of state is both a necessity and a challenge. Duringthe last decades, the development of association modelsbrought a significant improvement to the accuracy of thesesystems. Some of the most well-known association models arebased on perturbation theory, in most cases on Wertheim’sfirst-order thermodynamic perturbation theory (TPT1) forassociating fluids.1 Cubic plus association (CPA)2 is one suchmodels and combines the simplicity of a cubic equation of statewith the theoretical background and accuracy expected from anassociation model.This equation of state (EoS) is able to describe accurately

binary vapor−liquid equilibrium (VLE), liquid−liquid equili-brium (LLE), and solid−liquid equilibrium (SLE) for mixturesof water, alkanols, and alkanes with very reasonable results alsofor the vapor−liquid−liquid equilibrium (VLLE) of ternarysystems containing water an alkanol and an alkane.1 CPA hasbeen shown, in many cases, to outperform more complexmodels in the description of these type of systems. Recently,Kontogeorgis and co-workers3−9 presented various worksshowing the capacities of CPA in describing water + hydrateinhibitor + petroleum fluid with very satisfactory results.The above-mentioned hydrate formation/inhibition is one of

the better known CPA applications, and these systems have

been one of the main driving forces for the widespread of CPA,promoting its use on commercial and in-house software.The ease of integration in process software and the simplicity

of CPA are two of the main advantages of this model. Theversion studied here uses a mechanism to force the correctdescription of the pure component critical temperatures andpressures while keeping the other features intact.10,11

In this work, a modified CPA model10,11 was applied to thedescription of binary and multicomponent systems containingwater while still preserving the accuracy of the pure waterproperties. For the latter, this study analyses the description ofnot only vapor pressure and liquid density, the most usedproperties in the parametrization of CPA, but also theestimation of derivative properties such as liquid Cp and heatof vaporization. A diverse group of mixtures is then analyzedwith a focus on the description of water + alkanes and water +alcohols/hydrate inhibitors (MEG and methanol) while alsostudying petroleum related fluids and their equilibria with waterand these polar compounds.As will be demonstrated, this new version of the model can

reasonably describe, for the first time for CPA, the minimum inthe water solubility of hydrocarbons while also matching thepure components critical temperature and pressure and betterrepresenting second derivative properties such as liquid heatcapacity and enthalpy of vaporization.

Received: August 25, 2017Revised: October 24, 2017Accepted: November 29, 2017Published: November 29, 2017

Article

pubs.acs.org/IECRCite This: Ind. Eng. Chem. Res. 2017, 56, 15163−15176

© 2017 American Chemical Society 15163 DOI: 10.1021/acs.iecr.7b03522Ind. Eng. Chem. Res. 2017, 56, 15163−15176

pubs.acs.org/IECR

http://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.iecr.7b03522

http://dx.doi.org/10.1021/acs.iecr.7b03522

2. MODELThe modified version of CPA used here is based on the original(simplified) CPA model,12 to which a different α function andoptimization process were introduced.The α function is a modified Mathias−Copeman function,13

which can use up to five parameters:

= + ′ × + ′ × + ′ × + ′ ×

+ ′ ×

a T a T c T c T c T c

T c

( ) (1

)0 1

22

33

44

55

2

(1)

with ′ = −T T(1 )r and Tr = T/Tc.This version of CPA uses some restrictions in the pure

component parametrization process. The a0 and co-volume (b)are forced to describe the critical temperature and criticalpressure. In this manner, these two parameters are obtainedfrom the critical data, increasing the predictive capacity of themodel:

=P T V P( , )CPA cexp

ccalc

cexp

(2)

∂∂

==

=

⎜ ⎟⎛⎝

⎞⎠

Pv

0T T T

v vc

calc (3)

∂∂

==

=

⎛⎝⎜

⎞⎠⎟

Pv

0T T T

v v

2

2c

calc (4)

It is also important to note that the molar volume is notoptimized directly, being instead obtained from a single densitypoint by a Peneloux type volume shift:14

= −v v ct 0 vs (5)

where cvs is a temperature independent volume shift. Jaubert etal.15 have shown that using this type of volume shift does notinfluence the results for vapor pressure, heat of vaporization,and heat capacities.During the parametrization, the α function parameters are

generated directly by fitting to the vapor pressure curve.Introducing a change on the associative parameters leads to anautomatic recalculation of the cubic term parameters. Theassociative parameters were fitted to the liquid heat capacityand vapor pressure data. As said above, the liquid density wasnot used in the main parametrization.To optimize the binary interaction parameter (kij) values,

three different equations were applied depending on the type ofequilibria and experimental data:

∑=−⎛

⎝⎜⎜

⎞⎠⎟⎟T T

TOF

i

npbubexp

bubcalc

bubexp

2

(6)

∑=−⎛

⎝⎜⎜

⎞⎠⎟⎟P P

POF

i

npbubexp

bubcalc

bubexp

2

(7)

∑ ∑=−⎛

⎝⎜⎜

⎞⎠⎟⎟

x x

xOF

k i

i k i k

i k

npo np,exp

,calc

,exp

2

(8)

where npo is the number of phases to optimize.For mixtures with more than one associative compound,

combining rules are applied to calculate the cross-associative

parameters. The CR-2 combining rules16 were appliedwhenever necessary:

β β β=ij i j(9)

ε ε ε= +( )2

iji j

(10)

This version of CPA uses a heteronuclear approach forassociation, thus association schemes are introduced for eachgroup instead of a general scheme for the entire molecule. Theassociation scheme applied here for the hydroxyl group is the2B scheme as discussed in our previous works,10,11 while forwater the selected scheme was 4C. This scheme is consideredbetter than the 3B scheme for application on equations of stateand is also suggested as the preferential scheme by a group ofmolecular simulation results.17

3. RESULTS AND DISCUSSION3.1. Pure Water Results. Our experience with the version

of the CPA model11 described above has shown that the

selection of the associative parameters needs to be carried withcare, especially for smaller and stronger associative compoundssuch as water and methanol. For methanol, we found thathigher values for the associative parameters could be employed,improving the description of saturated pressures but decreasingthe quality of LLE and derivative properties. The same holdstrue for water. Thus, the set presented here takes into accountnot only the description of pure water properties but also theneed to correctly describe mixtures.It is important to note that for nonassociative compounds,

the model is simply SRK with the fitting of vapor pressure to adifferent α function and a constant volume shift fitted to asingle density point. For associative compounds, from theexperience of this and previous works, the fitting of associativeparameters should be addressed by looking (or including in theparametrization) some derivative properties or binary data. Forthe set presented in this work, the association parameters werefitted to Cp. Even then, more than one set was able to describethe pure properties accurately. Thus, as between VLE and LLE,the latter is harder to model, the set of parameters presentingthe best description of the LLE for n-hexane + water wereselected.The description of the remaining water properties is rather

accurate. A comparison between the results for this set andthose using s-CPA with the set from Kontogeorgis et al.12 ispresented in Table 1 and Figures 1 and 2. A summary of the

Table 1. Water CPA Parameters and Comparison betweenthe Set Obtained in This Work and the One fromKontogeorgis et al.12 Trange [260−450 K]

Industrial & Engineering Chemistry Research Article

DOI: 10.1021/acs.iecr.7b03522Ind. Eng. Chem. Res. 2017, 56, 15163−15176

15164


calculated and experimental critical properties is reported inTable 2. Water critical constants (Tc, Pc, Vc) and temperature-dependent correlations for vapor pressure, liquid density, Cp,and ideal gas heat capacities were obtained from the Infodata

database in the commercial software Multiflash.18 The vaporpressure curve applied was:

= + − − + −

− − − −

⎡⎣⎤⎦

P P T T

T T T

Ln ln ( 7.798(1 ) 1.540(1 )

2.896(1 ) 1.038(1 ) )/c r r

3/2

r3

r6

r

As can be observed in Table 1, the water association energy(ε) used in the new set is higher than that used for the s-CPA.This will have a very relevant impact in the description ofsystems containing water as discussed below. The remainingpure associative compound parameters applied in this work arepresented in our previous works.10,11 The parameters for thenonassociating compounds are presented as SupportingInformation.In Figure 1, it can be seen that changing the usual reference

reduced temperature for the volume shift has a significantimpact on the density results, particularly at lower temper-atures. This change leads to a correct description of the heat ofvaporization close to the critical point and an overall bettertrend with temperature for this property.As discussed in some previous works, the use of an

unconstrained, highly flexible α function can introduce someinconsistencies. However, for some specific compounds, likewater, where the simple nature of CPA, and similar EoS, areunable to capture the trends of many of its unique properties,the introduction of constrictions might lead to an even worsethermophysical description. In Figure 3, the α function used inthis work for water is plotted between reduced temperatures of0.4 and 1 and is compared to the water set of s-CPA.12

Figure 1. Results for the description of water saturated liquid density and heat of vaporization using the two sets of parameters and differenttemperatures to fit the volume shift.

Figure 2. Results for the description of water heat capacity using the two parameter sets. Cv data values are from Abdulagatov et al.,19 while thevalues for Cp were taken from the Infodata database in MULTIFLASH.18

Table 2. Experimental Critical Data and Results with theTwo Parameter Sets

data this work s-CPA12

Tc (K) 647.3 647.3 656.6Pc (MPa) 22.12 22.12 23.73Vc (m

3·kmol−1) 0.056 0.069 0.035

Figure 3. Alpha functions analyzed in this work between Tr 0.4 and 1.



15165

http://pubs.acs.org/doi/suppl/10.1021/acs.iecr.7b03522/suppl_file/ie7b03522_si_001.pdf



As can be seen, this α function does not decrease in thewhole range of temperatures, continuously increasing in thefitted temperature range. It is important to note that the Cp wasused in the parametrization of this set and that Cv presents aseemingly correct physical behavior for the range of temper-atures in analysis, as observed in Figure 2.One important topic to address at this point is that from the

experimental data available for liquid Cp and Cv, the value of

these properties seems to almost cross each other between

273.15 and 300 K, as can be observed in the work of Chen.20

Knowing that

− = −∂ ∂∂ ∂

C C TP TP V

( / )( / )

V

Tp v

2

(11)

Figure 4. Description of the results for water + n-alkane (C6 to C10, except C9) with both sets. Full lines are results from this work ((a) kij = 0.180;(b) kij = 0.150; (c) kij = 0.120; (d) kij = 0.065), dashed lines are results using s-CPA33,34 ((a) kij = 0.044; (d) kij = −0.069).

Figure 5. Description of the results for water + n-alkane (C4 and C5) with both sets. Full lines are results from this work ((left) kij = 0.240, (right) kij= 0.210), and dashed lines are results using s-CPA33−35 ((left) kij = 0.085, (right) kij = 0.065).



15166


For Cp to have the exact same value of Cv above 0 K, eitherthe first derivative of pressure in relation to volume at constanttemperature is infinite or else the first derivative of pressurewith relation to temperature at constant volume is zero. Thesecond hypothesis is the one of interest. It is thus important toknow how this happens with CPA:

α∂∂

=−

−+

∂∂

⎜ ⎟⎛⎝

⎞⎠

PT

Rb V V b TV

1( )V

cubic

(12)

In this term (cubic contribution to the derivative), the firstterm is always positive, while the second is positive only if the αfunction monotonically decreases with temperature.The contribution for pressure from the association term is

τ=P RT hassociation (13)

where:

τ =∂∂

−⎛⎝⎜

⎞⎠⎟V

Vg

V1

2ln

1(14)

∑= −h m X(1 )i

i i

allsites

(15)

with mi being the mole number of sites of type i.The derivative for this term is then:

∑τ τ∂∂

= −∂∂

⎜ ⎟⎛⎝

⎞⎠

PT

R h R T mXTV i

ii

association allsites

(16)

h is always positive, as well as ∑ ∂∂mi i

XT

allsites i . The ln g decreases

with increasing volume, in this way its derivative is negativeabove 278 K, when considering saturation or atmosphericconditions. Taking this into account, the first term of thederivative (concerning association) is negative while the secondterm is positive above this temperature, the opposite being truebelow. In the case of the Soave α function, one association termneeds to compensate both the remaining association term and

Figure 6. kij correlations applied in this work for the systems of polarcompounds + petroleum fluids.

Figure 7. Results for water (1) + aromatic hydrocarbon (benzene (2), toluene (3), ethylbenzene (4), m-xylene (5), o-xylene (6) p-xylene (7)). Fulllines are the results from this work (k12 = 0.170, β12 = 0.0095; k13 = 0.145, β13 = 0.0090; k14 = 0.120, β14 = 0.0060; k15 = 0.102, β15 = 0.0050; k16 =0.119, β16 = 0.0080 ; k17 = 0.111, β17 = 0.0070), dashed lines are those obtained using s-CPA.33



15167


the cubic terms for the total derivative to be zero. With the αfunction and water parameter set proposed in this work,between 273 and 300 K the second term of the cubiccontribution is negative and liquid densities are not used

directly in the parametrization. Thus, allowing ∂∂( )P

Tto be close

to zero while retaining a correct description of vapor pressuresand its derivatives.

Considering ∂∂( )P

Table to be zero, or close, leads to an over

reliance on ∂∂( )P

Vfor the description of saturation pressures, and

thus, despite presenting a better physical behavior, the values ofthe volume are far from correct when using a volume shiftanchored to a temperature far from this region. Through thiscompensation of errors, it is possible to increase the accuracy ofpredictions for pure properties of water and some LLE whilekeeping a correct description of VLE.It will also be important to analyze the Pitfalls of Soave type

α functions presented by Segura et al.21 and the guidelines byDeiters22 when looking at properties and phase equilibria wherethe associative compounds are near or at the critical point.3.2. Modeling Mixtures Containing Water. 3.2.1. Binary

Mixtures with Alkanes (C4 to C10). As was referred before, thevalue of the association energy is higher with the proposed setof parameters, which in turn introduces a heavier weight intothe temperature dependence of the associative contribution.This change, as well as the α function and the volume shift,depending on the kind of system and conditions, introduceimportant improvements on the results, leading however to lessaccuracy for a few other systems. A noteworthy example of this

is the description of water + n-alkane and water + n-alkanolsystems, where the increase in the association energy of waterenables a better estimation of the minima in the solubility of n-alkanes in water and a better description of the solubility trendfor the alkanols. The better trend for these systems isassociated, in some cases, with higher deviations at lowtemperatures. Figures 4 and 5 present the results for water +alkane between C4 and C10. Experimental data for thesesystems was taken from Tsonopoulos et al.,23 Marche et al.,24

Heidman et al.,25 Jou et al.,26 Pereda et al.,27 Economou et al.,28

Schatzberg,29 Noda et al.,30 and Goral and co-workers31 andcalculated with the expressions from Tsonopoulos.32

As in the previous works with this version of CPA,11 thebinary interaction parameters are larger than those of s-CPA.Figures 5 and 6 present the results for the remaining systemsused in this analysis. It is important to note that theimprovements in the description of the aqueous phase alsointroduce a change in the trend for the solubility in thehydrocarbon phase. Thus, if only the hydrocarbon phase wasoptimized, in some particular cases (mixture with decane)higher deviations would be observed for the aqueous phasethan in s-CPA. However, it is important to note that a relevantvariability in the experimental data is verified (noticeable whenlooking at the mixtures with hexane and octane). Two figuresare presented in Supporting Information concerning thisbehavior, including the worst case, the mixture with decane.Before addressing a different class of compounds, it is

important to evaluate if there is any trend for the binaryinteraction parameters of water + n-alkanes, as previouslyobserved with s-CPA by Oliveira et al.33 Using the results forthe studied systems, it is possible to observe a good correlation

Figure 8.Water + 1-butanol, multiphasic results at 1 atm (a) and LLE for a larger range of temperatures (b) with the modified CPA (kij = 0.032) ands-CPA (kij = −0.065) and LLE for water + 1-octanol (c,d). Using the CR-2 combining rules.



15168



for the binary interaction parameters, as can be observed fromFigure 6.Later in this paper, the results for some multicomponent

systems will be analyzed, using water, methanol/MEG, andpetroleum fractions. Thus, it is of importance to know how thebinary interaction parameters of these two other compounds(MEG and methanol) behave for systems with alkanes. Theresults for methanol are presented in Supporting Information,while those for MEG are from a previous article.10 A trend isalso obtained for these systems.Equations 17−19 present the correlations used between the

associative compounds (water, MEG,10 and methanol) and thehydrocarbon molecular weight. Figure 6 shows the descriptionof the fitting of the kij’s through these equations.

= − +k 0.133ln(MW) 0.701iMEG (17)

= − +k 0.195ln(MW) 1.042iH O2 (18)

= − × + ×− −k 2.89 10 MW 6.10 10imethanol4 2

(19)

3.2.2. Binary Mixtures with Aromatic Hydrocarbons. Usingthe approach of Folas et al.34 for the description of aromatics

(ε = εij2

assoc

; βij = fitted), it is possible to describe also the

solubility of aromatics with this version of CPA. Figure 7presents the results for water + benzene, water + toluene, water+ ethylbenzene, and water + o/m/p-xylene. Experimentalresults for these systems were taken from Goral et al.,36 Millerand Hawthorne,37 Jou and Mather,38 Shen et al.,39 and Pryorand Jentoft.40

As in the case of alkanes, the version of CPA applied in thiswork presents a more accurate trend for the solubility ofaromatics in the water phase. The results for this group ofcompounds are in general accurate.

3.2.3. Binary Mixtures with Alkanols. The improvement onthe description of the solubility minima might be in part due tothis version of CPA containing more accurate pure componentinformation (more accurate Cp, corrected Tc, and Pc), however,the higher value for the association energy, and different αfunction, should be the main reason for this enhanced behavior.A similar effect is observed in systems containing water and n-alkanols. However, in this case, the improvement on thequalitative description of the systems does not ensure anincrease in their overall accuracy, as the influence on theaqueous phase is less accurate in this case. Figure 8 presents theresults for the systems water + 1-butanol and water + 1-octanol.Experimental data are from Goral et al.,41 Lohmann et al.,42

Hessel et al.,43 and Dallos and Liszi.44

For heavier alcohols, where the association contributionbecomes smaller, this is less noteworthy. Also, the currentversion of the model is using the same association parametersfor every OH− group in whatever alcohols,10,11 which mightaffect more the LLE results of smaller chain alcoholsThe VLE of water with four light chain alcohols (methanol,

ethanol, 1-propanol, and 2-propanol) were also analyzed. Forthe mixtures with methanol and ethanol, temperatureindependent binary interaction parameters (kij = −0.045 andkij = −0.004 respectively) were applied, while for the mixtureswith 1-propanol and 2-propanol there was a need to apply atemperature dependency in these parameters (water + 1-

Figure 9. Results for water + ethanol at three different pressures (a), water + 1-propanol at 10 bar (b), water + methanol at four different pressures(c), and water + 2-propanol at 1 atm (d).



15169



propanol [kij = −2.93 × 10−4T + 0.125], water + 2-propanol [kij= −4.05 × 10−4T + 0.122]). A table presenting the deviationsfor these systems is presented as Supporting Information.Figure 9 presents these binary systems using data from Voutsaset al.,45 Vercher et al.,46 Soujanya et al.,47 and Bermejo et al.48

Since our previous work,10 we observed that the vaporpressure curve used in the parametrization of ethanol presentedrelevant deviations below 300 K. This was now corrected,leading to new α function parameters and volume shift (theother parameters remaining the same). This does not affectdetrimentally the previous results for ethanol, and a comparisonof the two sets is presented in Supporting Information.

These results are very accurate and able to describe the VLEof these compounds in a wide range of conditions.Figure 10 presents the results for water + ethylene glycol

(using a 2 × 2B association scheme)10 at two differenttemperatures (kij = −0.025), as well as the prediction (kij = 0)of the VLE for water + 1,3-propanediol and the correlation (kij= −0.030) for the VLE of water + glycerol. Experimental dataare from Kamihama et al.,49 Sanz et al.,50 Oliveira et al.,51 andSoujanya et al.47

The ternary system containing these compounds was alsostudied, yielding 1.20% of absolute average deviation on thebubble temperatures and 4.15% on the dew temperatures whencompared to the results of Sanz et al.50 A table with theseresults is also presented in the Supporting Information.

3.2.4. Solubility of Water in Gas/Gas in Water. Descriptionof the solubility for binary systems containing lighter alkanesand water, despite being possible with a temperatureindependent binary interaction parameter, usually requires atemperature dependency for an accurate description of bothphases. Figures 11 and 12 present the results for gas solubilityof the three lighter alkanes with water. Experimental data valuesare from Kiepe et al.,52 Rigby and Prausnitz,53 Lekvam et al.,54

Mohammadi et al.,55 Coan and King,56 Chapoy et al.,57 andKobayashi et al.58

The results for the system water + methane shows the modelto be able to accurately describe the solubility of water in thegaseous phase while presenting good results in the liquid phase.For higher temperatures, the pressure dependencies start topresent deviations. Similar results are obtained for the systemscontaining ethane and propane.Aqueous mixtures containing nitrogen and carbon dioxide

were also studied, while considering these compounds asnonassociative. For the former, the results are accurate in bothphases, using a temperature dependent kij (kij = 3.30 × 10−3T−0.6), while for the latter the solubility in water is welldescribed (kij = 7.20 × 10−4T −0.07). These results arepresented in Figure 13. Experimental data was obtained fromRigby and Prausnitz,53 King et al.,59 and Hou et al.60

3.3.1. Multicomponent Mixtures. Having established theability of our new version of CPA to describe with accuracybinary systems with water and a range of different compounds,we turned our attention to the evaluation of its ability todescribe more complex mixtures. For a start, two ternarysystems were studied: MEG + water + methane and MEG +water + ethanol. The results for the VLLE of the first system arepresented in Figure 14, while for the second the %AAD of thebubble temperature is 0.19 and for the dew temperatures is0.71. The results for this second system when compared to thedata of Kamihama et al.61 are presented as SupportingInformation. More results at different conditions for themixture presented in Figure 14 are presented in the SupportingInformation.As discussed in our previous work10 this version of CPA is

able to describe multicomponent systems containing ethyleneglycol. These mixtures have been analyzed by Kontogeorgis andco-workers,3−9 using s-CPA, with good results. Two of thesesystems have not been previously studied using this version ofthe model, and the results of these fluids when mixed withMEG are presented as Supporting Information.It is important to note that the parameters used for the

interactions between water/methanol and methane/ethane/propane are those previously fitted in this work. For many ofthese systems, a temperature dependency was needed on the kij

Figure 10. Results for water + ethylene glycol at two differenttemperatures (a), water + 1,3-propanediol at 30 kPa (b), and for water+ glycerol at three different pressures (c).



15170










to correctly describe the phase equilibria. The binaryinteraction parameters between associative compounds arethose obtained for their binary VLE description.Figures 15 and 16 present the results for some of the systems

of water + MEG + oil-based fluid studied by Kontogeorgis andco-workers3−9 using the version of CPA proposed here. In theSupporting Information, a table is presented comparing theaverage deviations of the two CPA versions for these systems.The condensate description considered the real components upto five carbons. From six carbons up to nine carbons, fourmolecular lumps were considered (C6, C7, C8, C9), where allcompounds in the mixture with that carbon number wereconsidered. Heavier molecules with 10 or more carbons wereconsidered in a single lump (C10+) with averaged properties.

Accurate results were also obtained for the polar compoundsin the hydrocarbon phase in most systems, but a higherdecrease on the accuracy was verified for the heaviest system(light oil) than with s-CPA.Applying the same approach, the description of the gas

condensate studied by Pedersen et al.64 was also tested. Theseresults are presented in Figure 17 as well as those from Yan etal. using s-CPA.65 The results obtained for these system are, ingeneral, comparable to those of s-CPA.Concerning results with water + methanol + HC, the mixture

2 presented by Pedersen et al.66 and a synthetic mixture fromRossihol67 were analyzed. These results were compared tothose of Yan et al.65 in Tables A6 and A7 presented asSupporting Information. It is noteworthy that the resultsobtained with the two CPA versions diverge on the accuracy for

Figure 11. Mutual solubility for methane + water (a,b; kij = 1.48 × 10−3T −0.093) and for ethane + water (c,d; kij = 9.95 × 10−4T).

Figure 12. Mutual solubility for propane + water with kij = 8.90 × 10−4T −0.01.



15171





the methanol fraction in the hydrocarbon phase. The s-CPApresents significant deviations for this fraction in the syntheticmixture, while the version applied in this work provides a gooddescription of the experimental data. The opposite is verifiedwith the data from Pedersen et al.,66, while the maincomponent in the condensate being the same as in thequaternary mixture (methane, and in similar proportions). Thisshould in part be due to the use of different combining rules, as

the ratio water:methanol is rather different in these systems andthe use of different approaches for the binary interactionparameters calculation between the two versions.

4. CONCLUSIONS

A new version of CPA was evaluated here for the description ofwater containing mixtures. While its description of density forsmall, highly associative compounds, with a volume shiftapplied at 0.7 Tc, presents somewhat higher deviations, thetrend with temperature is more accurate than that obtainedwith s-CPA. Moreover, if a lower Tr is used to fit the volumeshift, it is possible to obtain reasonable results for densitybetween 0.45 and 0.85 Tr. The modifications applied in thisversion also lead to a better description of liquid Cp and correctvalues for Tc and Pc. This also enables the correct trend for thedescription of the heat of vaporization as well as a better trendwith temperature for Cv. It is also important to note that for thecompounds with hydroxyl groups studied in this work, it waspossible to consider the association energy as constant.The parameters for water in this version also lead to a higher

temperature dependency on the association term; this in turn,leads to a different behavior than previous versions on thesolubility of alkanes/alkanols in water. The solubility of thesecond compound, in many of these systems, now presents atrend closer to what is experimentally observed.Accurate results are obtained for the description of the vapor

liquid equilibria with alkanols and the solubility of gases inwater/water in gases. It is important to remember that a singlecombining rule for the association parameters was applied,while some of the results from s-CPA have used differentcombining rules.In the case of multicomponent systems, seven petroleum

fluids were studied, using correlations for the interactionparameters between water/MEG and the petroleum com-pounds/fractions. These results are in most cases accurate witha decrease in accuracy for heavier fluids, which is to be expecteddue to the large extrapolations used in these cases. The resultsfor multicomponent systems are comparable to those of s-CPAwhile in general improving the results of binary LLE equilibriaand pure properties.This version of CPA is thus able to describe a relevant group

of properties for a complex molecule like water whilepresenting very promising results for VLE and LLE and anaccurate representation of multicomponent systems.

Figure 13. Results for the solubility of N2 in water (a), water in N2(b), and CO2 in water (c).

Figure 14. Results for the solubility of methane in water + MEG at298.15 K. Full lines: modified CPA results. Dashed lines: s-CPAresults. Data from Folas et al.62 and Burgass et al.63



15172


■ ASSOCIATED CONTENT

*S Supporting Information

The Supporting Information is available free of charge on the

ACS Publications website at DOI: 10.1021/acs.iecr.7b03522.

Pure component parameters as well as other VLE, LLE,and gas solubility results for systems containing water,hydrocarbons, and alcohols (including methanol and/orMEG); discussion on fitting interaction parameters usingonly hydrocarbon phase data (PDF)

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected]. Phone: +44 207 234 8505.

ORCID

Andre M. Palma: 0000-0002-5580-6883Antonio J. Queimada: 0000-0001-8699-9094Joao A. P. Coutinho: 0000-0002-3841-743X

Notes

The authors declare no competing financial interest.

Figure 15. Results for the system cond-1 + water + MEG at 323 K (a), cond-2 + water + MEG at 303 K (b), cond-3 + water + MEG at 323 K (c),and for the system light-oil-1 + water + MEG at 303 K (d). Data from Riaz et al.3,4,7 and Frost et al.6

Figure 16. Results for the system light-oil-2 + water + MEG at 323 K (left) and fluid-1 + water + MEG at 323 K (right). Data from Riaz et al.4 andFrost et al.9



15173

http://pubs.acs.org

http://pubs.acs.org/doi/abs/10.1021/acs.iecr.7b03522


mailto:[email protected]

mailto:+44 207 234 8505

http://orcid.org/0000-0002-5580-6883

http://orcid.org/0000-0001-8699-9094

http://orcid.org/0000-0002-3841-743X


■ ACKNOWLEDGMENTS

This work was funded by KBC Advanced Technologies Limited(a Yokogawa Company) under project “Extension of the CPAModel for Polyfunctional Associating Mixtures”. Andre M.Palma acknowledges KBC for his Ph.D. grant. Tony Moorwoodis acknowledged for mentoring this project and providinghelpful insights. Mariana Belo Oliveira is acknowledge for herhelpful insight in the first stages of this work. This work wasdeveloped within the scope of the project CICECO-AveiroInstitute of Materials, POCI-01-0145-FEDER-007679 (FCTref. UID/CTM/50011/2013), financed by national fundsthrough the FCT/MEC and when appropriate cofinanced byFEDER under the PT2020 Partnership Agreement.

■ NOMENCLATURE

a = energy parameter of CPAac = value of the energy parameter at the critical pointb = co-volumec1 − c5 (cx) = alpha function parametersCp = Isobaric heat capacitycvs = volume shiftkij = binary interaction parameter for the cubic energy termP = vapor pressureT = temperaturev0, vt = volume before and after translation, respectivelyx = mole fraction

Greek Symbolsβ = association volumeε = association energyρ = molar density

Sub and Superscriptscn = carbon numberexp, calc = experimental, calculatedi, j = pure component indexesnp = number of pointsnpo = number of phases to optimize

Abbreviations%AAD = percentage of average absolute deviationCPA = cubic plus associations-CPA = simplified CPAEoS = equation of stateHC = hydrocarbonMEG = monoethylene glycols-CPA = simplified cubic plus association

■ REFERENCES(1) Kontogeorgis, G. M.; Folas, G. K. Thermodynamic Models forIndustrial Applications; John Wiley & Sons, Ltd: Chichester, UK, 2010.(2) Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D.P. An Equation of State for Associating Fluids. Ind. Eng. Chem. Res.1996, 35 (11), 4310−4318.(3) Riaz, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Haugum,T.; Christensen, K. O.; Lokken, T. V.; Solbraa, E. Measurement ofLiquid-Liquid Equilibria for Condensate plus Glycol and Condensateplus Glycol plus Water Systems. J. Chem. Eng. Data 2011, 56 (12),4342−4351.(4) Riaz, M.; Yussuf, M. A.; Frost, M.; Kontogeorgis, G. M.; Stenby,E. H.; Yan, W.; Solbraa, E. Distribution of gas hydrate inhibitormonoethylene glycol in condensate and water systems: experimentalmeasurement and thermodynamic modeling using the cubic-plus-association equation of state. Energy Fuels 2014, 28 (5), 3530−3538.

Figure 17. Results for the water solubility in the hydrocarbon phase at 100 MPa (a) and 473.15 K (b) and for the methane solubility in the aqueousphase at 100 MPa (c) and 473.15 K (d) (left).



15174


(5) Frost, M.; Kontogeorgis, G. M.; von Solms, N.; Solbraa, E.Modeling of phase equilibrium of North Sea oils with water and MEG.Fluid Phase Equilib. 2016, 424, 79−89.(6) Frost, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yussuf, M. A.;Haugum, T.; Christensen, K. O.; Solbraa, E.; Løkken, T. V. Liquid-liquid equilibria for reservoir fluids+monoethylene glycol and reservoirfluids+monoethylene glycol+water: Experimental measurements andmodeling using the CPA EoS. Fluid Phase Equilib. 2013, 340, 1−6.(7) Riaz, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Haugum,T.; Christensen, K. O.; Solbraa, E.; Løkken, T. V. Mutual solubility ofMEG, water and reservoir fluid: Experimental measurements andmodeling using the CPA equation of state. Fluid Phase Equilib. 2011,300 (1−2), 172−181.(8) Riaz, M.; Yussuf, M. A.; Kontogeorgis, G. M.; Stenby, E. H.; Yan,W.; Solbraa, E. Distribution of MEG and methanol in well-definedhydrocarbon and water systems: Experimental measurement andmodeling using the CPA EoS. Fluid Phase Equilib. 2013, 337, 298−310.(9) Frost, M.; Kontogeorgis, G. M.; von Solms, N.; Haugum, T.;Solbraa, E. Phase equilibrium of North Sea oils with polar chemicals:Experiments and CPA modeling. Fluid Phase Equilib. 2016, 424, 122−136.(10) Palma, A. M.; Oliveira, M. B.; Queimada, A. J.; Coutinho, J. A. P.Evaluating Cubic Plus Association Equation of State PredictiveCapacities: A Study on the Transferability of the Hydroxyl GroupAssociative Parameters. Ind. Eng. Chem. Res. 2017, 56 (24), 7086−7099.(11) Palma, A. M.; Oliveira, M. B.; Queimada, A. J.; Coutinho, J. A. P.Re-evaluating the CPA EoS for improving critical points and derivativeproperties description. Fluid Phase Equilib. 2017, 436, 85−97.(12) Kontogeorgis, G. M.; Yakoumis, I. V.; Meijer, H.; Hendriks, E.;Moorwood, T. Multicomponent phase equilibrium calculations forwater−methanol−alkane mixtures. Fluid Phase Equilib. 1999, 158-160,201−209.(13) Mathias, P. M.; Copeman, T. W. Extension of the Peng-Robinson equation of state to complex mixtures: Evaluation of thevarious forms of the local composition concept. Fluid Phase Equilib.1983, 13, 91−108.(14) Peneloux, A.; Rauzy, E.; Freze, R. A consistent correction forRedlich-Kwong-Soave volumes. Fluid Phase Equilib. 1982, 8 (1), 7−23.(15) Jaubert, J.-N.; Privat, R.; Le Guennec, Y.; Coniglio, L. Note onthe properties altered by application of a Peneloux−type volumetranslation to an equation of state. Fluid Phase Equilib. 2016, 419, 88−95.(16) Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. Prediction ofphase equilibria in water/alcohol/alkane systems. Fluid Phase Equilib.1999, 158−160, 151−163.(17) Kontogeorgis, G. M.; Michelsen, M. L.; Folas, G. K.; Derawi, S.;Von Solms, N.; Stenby, E. H. Ten Years with the CPA (Cubic-Plus-Association) equation of state. Part 1. Pure compounds and self-associating systems. Ind. Eng. Chem. Res. 2006, 45 (14), 4855−4868.(18) MULTIFLASH, version 4.4; KBC Process Technology, London,United Kingdom, 2014.(19) Abdulagatov, I. M.; Dvoryanchikov, V. I.; Kamalov, A. N.Measurements of the heat capacities at constant volume of H2O and(H2O+KNO3). J. Chem. Thermodyn. 1997, 29 (12), 1387−1407.(20) Chen, C. T. A. High-pressure specific heat capacities of purewater and seawater. J. Chem. Eng. Data 1987, 32 (4), 469−472.(21) Segura, H.; Kraska, T.; Mejía, A.; Wisniak, J.; Polishuk, I.Unnoticed Pitfalls of Soave-Type Alpha Functions in Cubic Equationsof State. Ind. Eng. Chem. Res. 2003, 42, 5662−5673.(22) Deiters, U. K.; De Reuck, K. M. Guidelines for publication ofequations of state - I. Pure fluids. Chem. Eng. J. 1998, 69, 69−81.(23) Tsonopoulos, C.; Wilson, G. M. High-temperature mutualsolubilities of hydrocarbons and water. Part I: Benzene, cyclohexaneand n-hexane. AIChE J. 1983, 29 (6), 990−999.(24) Marche, C.; Ferronato, C.; Jose, J. Solubilities of n -Alkanes (C 6to C 8) in Water from 30 to 180 °C. J. Chem. Eng. Data 2003, 48 (4),967−971.

(25) Heidman, J. L.; Tsonopoulos, C.; Brady, C. J.; Wilson, G. M.High- Temperature Mutual Solubilities of Hydrocarbons and Water.AIChE J. 1985, 31, 376−384.(26) Jou, F.; Mather, A. E. Vapor−Liquid−Liquid Locus of theSystem Pentane + Water. J. Chem. Eng. Data 2000, 45 (5), 728−729.(27) Pereda, S.; Awan, J. A.; Mohammadi, A. H.; Valtz, A.; Coquelet,C.; Brignole, E. A.; Richon, D. Solubility of hydrocarbons in water:Experimental measurements and modeling using a group contributionwith association equation of state (GCA-EoS). Fluid Phase Equilib.2009, 275 (1), 52−59.(28) Economou, I. G.; Heidman, J. L.; Tsonopoulos, C.; Wilson, G.M. Mutual solubilities of hydrocarbons and water: III. 1-hexene; 1-octene; C10-C12 hydrocarbons. AIChE J. 1997, 43 (2), 535−546.(29) Schatzberg, P. Solubilities of Water in Several normal alkanesfrom C7 to C16. J. Phys. Chem. 1963, 67, 776−779.(30) Noda, K.; Sato, K.; Nagatsuka, K.; Ishida, K. Ternary Liquid-Liquid Equilibria for the systems of Aqueous Methanol Solutions AndPropane or n-Butane. J. Chem. Eng. Jpn. 1975, 8 (6), 492−493.(31) Maczyn ski, A.; Wisniewska-Gocłowska, B.; Goral, M. Recom-mended Liquid−Liquid Equilibrium Data. Part 1. Binary Alkane−Water Systems. J. Phys. Chem. Ref. Data 2004, 33 (2), 549−577.(32) Tsonopoulos, C. Thermodynamic analysis of the mutualsolubilities of normal alkanes and water. Fluid Phase Equilib. 1999,156 (1−2), 21−33.(33) Oliveira, M. B.; Coutinho, J. A. P.; Queimada, A. J. Mutualsolubilities of hydrocarbons and water with the CPA EoS. Fluid PhaseEquilib. 2007, 258 (1), 58−66.(34) Folas, G. K.; Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E.H. Application of the cubic-plus-association (CPA) equation of stateto complex mixtures with aromatic hydrocarbons. Ind. Eng. Chem. Res.2006, 45 (4), 1527−1538.(35) Folas, G. K.; Gabrielsen, J.; Michelsen, M. L.; Stenby, E. H.;Kontogeorgis, G. M. Application of the Cubic-Plus-Association (CPA)Equation of State to Cross-Associating Systems. Ind. Eng. Chem. Res.2005, 44 (1), 3823−3833.(36) Goral, M.; Wisniewska-Gocłowska, B.; Maczyn ski, A. Recom-mended liquid-liquid equilibrium data. Part 3. Alkylbenzene-watersystems. J. Phys. Chem. Ref. Data 2004, 33 (4), 1159−1188.(37) Miller, D. J.; Hawthorne, S. B. Solubility of Liquid Organics ofEnvironmental Interest in Subcritical (Hot/Liquid) Water from 298 to473 K. J. Chem. Eng. Data 2000, 45, 78−81.(38) Jou, F.; Mather, A. E. Liquid - Liquid Equilibria for BinaryMixtures of Water + Benzene, Water + Toluene, and Water + p-Xylene from 273 to 458 K. J. Chem. Eng. Data 2003, 48, 750−752.(39) Shen, Z.; Wang, Q.; Shen, B.; Chen, C.; Xiong, Z. Liquid-LiquidEquilibrium for Ternary Systems Water + Acetic Acid + m-Xylene andWater + Acetic Acid + o-Xylene at (303.2 to 343.2) K. J. Chem. Eng.Data 2015, 60 (9), 2567−2574.(40) Pryor, W. A.; Jentoft, R. E. Solubility of m- and p-Xylene inWater and in Aqueous Ammonia from O° to 300° C. J. Chem. Eng.Data 1961, 6 (1), 36−37.(41) Goral, M.; Wisniewska-Gocłowska, B.; Maczyn ski, A. Recom-mended liquid-liquid equilibrium data. Part 4. 1-alkanol-water systems.J. Phys. Chem. Ref. Data 2006, 35 (3), 1391−1414.(42) Lohmann, J.; Joh, R.; Gmehling, J. Solid−Liquid Equilibria ofViscous Binary Mixtures with Alcohols. J. Chem. Eng. Data 1997, 42(6), 1170−1175.(43) Hessel, D.; Geiseler, G. Pressure dependence of theheteroazeotropic system n-butanol + water. Z. Phys. Chem. 1965,229O, 199−209.(44) Dallos, A.; Liszi, J. (Liquid + liquid) equilibria of (octan-1-ol +water) at temperatures from 288.15 to 323.15 K. J. Chem. Thermodyn.1995, 27 (4), 447−448.(45) Voutsas, E. C.; Pamouktsis, C.; Argyris, D.; Pappa, G. D.Measurements and thermodynamic modeling of the ethanol-watersystem with emphasis to the azeotropic region. Fluid Phase Equilib.2011, 308 (1−2), 135−141.



15175


(46) Vercher, E.; Rojo, F. J.; Martínez-Andreu, A. Isobaric vapor-liquid equilibria for 1-propanol + water + calcium nitrate. J. Chem. Eng.Data 1999, 44 (6), 1216−1221.(47) Soujanya, J.; Satyavathi, B.; Vittal Prasad, T. E. Experimental(vapour + liquid) equilibrium data of (methanol + water), (water +glycerol) and (methanol + glycerol) systems at atmospheric and sub-atmospheric pressures. J. Chem. Thermodyn. 2010, 42 (5), 621−624.(48) Bermejo, M. D.; Martín, A.; Florusse, L. J.; Peters, C. J.; Cocero,M. J. Bubble points of the systems isopropanol−water, isopropanol−water−sodium acetate and isopropanol−water−sodium oleate at highpressure. Fluid Phase Equilib. 2006, 244 (1), 78−85.(49) Kamihama, N.; Matsuda, H.; Kurihara, K.; Tochigi, K.; Oba, S.Isobaric Vapor−Liquid Equilibria for Ethanol + Water + EthyleneGlycol and Its Constituent Three Binary Systems. J. Chem. Eng. Data2012, 57 (2), 339−344.(50) Sanz, M. T.; Blanco, B.; Beltran, S.; Cabezas, J. L.; Coca, J.Vapor Liquid Equilibria of Binary and Ternary Systems with Water,1,3-Propanediol, and Glycerol. J. Chem. Eng. Data 2001, 46, 635−639.(51) Oliveira, M. B.; Teles, A. R. R.; Queimada, A. J.; Coutinho, J. A.P. Phase equilibria of glycerol containing systems and their descriptionwith the Cubic-Plus-Association (CPA) Equation of State. Fluid PhaseEquilib. 2009, 280 (1−2), 22−29.(52) Kiepe, J.; Horstmann, S.; Fischer, K.; Gmehling, J. ExperimentalDetermination and Prediction of Gas Solubility Data for Methane +Water Solutions Containing Different Monovalent Electrolytes. Ind.Eng. Chem. Res. 2003, 42 (21), 5392−5398.(53) Rigby, M.; Prausnitz, J. M. Solubility of water in compressednitrogen, argon, and methane. J. Phys. Chem. 1968, 72 (1), 330−334.(54) Lekvam, K.; Bishnoi, P. R. Dissolution of methane in water atlow temperatures and intermediate pressures. Fluid Phase Equilib.1997, 131 (1−2), 297−309.(55) Mohammadi, A. H.; Chapoy, A.; Tohidi, B.; Richon, D.Measurements and Thermodynamic Modeling of Vapor−LiquidEquilibria in Ethane−Water Systems from 274.26 to 343.08 K. Ind.Eng. Chem. Res. 2004, 43 (17), 5418−5424.(56) King, A. D.; Coan, C. R. Solubility of water in compressedcarbon dioxide, nitrous oxide, and ethane. Evidence for hydration ofcarbon dioxide and nitrous oxide in the gas phase. J. Am. Chem. Soc.1971, 93 (8), 1857−1862.(57) Chapoy, A.; Mokraoui, S.; Valtz, A.; Richon, D.; Mohammadi, A.H.; Tohidi, B. Solubility measurement and modeling for the systempropane-water from 277.62 to 368.16 K. Fluid Phase Equilib. 2004, 226(1−2), 213−220.(58) Kobayashi, R.; Katz, D. Vapor-Liquid Equilibria For BinaryHydrocarbon-Water Systems. Ind. Eng. Chem. 1953, 45 (2), 440−446.(59) King, M. B.; Mubarak, A.; Kim, J. D.; Bott, T. R. The mutualsolubilities of water with supercritical and liquid carbon dioxides. J.Supercrit. Fluids 1992, 5 (4), 296−302.(60) Hou, S.-X.; Maitland, G. C.; Trusler, J. P. M. Measurement andmodeling of the phase behavior of the (carbon dioxide+water) mixtureat temperatures from 298.15K to 448.15K. J. Supercrit. Fluids 2013, 73,87−96.(61) Kamihama, N.; Matsuda, H.; Kurihara, K.; Tochigi, K.; Oba, S.Isobaric Vapor−Liquid Equilibria for Ethanol + Water + EthyleneGlycol and Its Constituent Three Binary Systems. J. Chem. Eng. Data2012, 57 (2), 339−344.(62) Folas, G. K.; Berg, O. J.; Solbraa, E.; Fredheim, A. O.;Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E. H. High-pressurevapor−liquid equilibria of systems containing ethylene glycol, waterand methane. Fluid Phase Equilib. 2007, 251 (1), 52−58.(63) Burgass, R.; Reid, A.; Chapoy, A.; Tohidi, B. GlycolsPartitioning at High Pressures. In GPA Conference, San Antonio, April9−12, 2017; Gas Processors Association: Tulsa, OK, 2017.(64) Pedersen, K. S.; Milter, J.; Rasmussen, C. P. Mutual solubility ofwater and a reservoir fluid at high temperatures and pressures. FluidPhase Equilib. 2001, 189, 85−97.(65) Yan, W.; Kontogeorgis, G. M.; Stenby, E. H. Application of theCPA equation of state to reservoir fluids in presence of water and polarchemicals. Fluid Phase Equilib. 2009, 276 (1), 75−85.

(66) Pedersen, K. S.; Michelsen, M. L.; Fredheim, A. O. Phaseequilibrium calculations for unprocessed well streams containinghydrate inhibitors. Fluid Phase Equilib. 1996, 126 (1), 13−28.(67) Rossihol, N. Equilibres de phases a basse temperature demelanges d’hydrocarbures legers, demethanol et d’eau: mesure etmodelisation, Ph.D. Thesis, Universite Lyon I Claude Bernard, Lyon,1995.



15176


improved prediction of water properties and phase

Documents