Phase equilibria of systems containing oxygenated compounds: Polar or “pseudo-association” approach?

Journal Pre-proof Phase equilibria of systems containing oxygenated compounds: Polar or “pseudoassociation” approach? NguyenHuynh Dong, Siem T.K. Tran, Chau T.Q. Mai PII:

S0378-3812(19)30497-2

DOI:

https://doi.org/10.1016/j.fluid.2019.112435

Reference:

FLUID 112435

To appear in:

Fluid Phase Equilibria

Received Date: 4 September 2019 Revised Date:

13 December 2019

Accepted Date: 13 December 2019

Please cite this article as: N. Dong, S.T.K. Tran, C.T.Q. Mai, Phase equilibria of systems containing oxygenated compounds: Polar or “pseudo-association” approach?, Fluid Phase Equilibria (2020), doi: https://doi.org/10.1016/j.fluid.2019.112435. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Graphical abstract Manuscript title: “Phase equilibria of systems containing oxygenated compounds: polar or “pseudo-association” approach?”

370 350

Temperature (K)

330 310

asso+dipolar (kij=-0.022) Asso (kij=0.053) dipolar (kij=-0.05)

290 270 250 230 210 190 170 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-heptane)

1.0

Phase equilibria of systems containing oxygenated compounds: polar or “pseudoassociation” approach? Dong NguyenHuynh a,*, Siem T. K. Tran a, Chau T. Q. Mai b a)

PetroVietnam Manpower Training College, No 43 Road 30/4, Ward 9, Vung tau city, Viet Nam. b)

Department of Chemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

* Corresponding author e-mail: [email protected] or [email protected]

Abstract The modified group-contribution PC-SAFT (DOI: 10.1016/j.fluid.2016.09.020) has been extended in this work to model the fluid phase equilibria of strong polar systems. The importance of the association and the polar terms has been investigated using the PC-SAFT EoS by describing the vapor-liquid and liquid-liquid equilibira of several oxygenated compound’s mixtures. Oxygenated compounds were considered as polar or “pseudo-associative” or polar-associative molecules. The dipole moment parameter of oxygenated compounds was fixed to the experimental value, while its “pseudoassociation” energy parameter was estimated from the dimer association energy of acetone. The results obtained in this work suggest that: accounting for the polar interactions by applying the “pseudoassociation” approach could well reproduce the VLE but not able to correctly describe the LLE of their mixtures. Moreover, the addition of a dipolar term with the 1A association scheme to the PC-SAFT EoS has proven necessary to correctly describe the LLE/VLE of acetone containing mixtures.

1

Keywords mg-SAFT, prediction, ketones, methyl-acetate, oxygenated aromatics 1. Introduction Complex systems composed of polar (such as ketones, esters, oxygenated-aromatics), associating compounds (alcohols, water) and hydrocarbons are the main chemical families resultant of the pyrolysis or liquefaction of lignocellulose biomasses [1, 2]. During the process design and optimization, the chemical industry requires reliable and predictive thermodynamic models to calculate the liquid-liquid and vapor-liquid equilibria of the main components involved. Due to very complex intermolecular forces between these molecules (such as hydrogen bonding or multi-polar interactions), these mixtures exhibit highly non ideal phase behaviors. Moreover, the available experimental data for these systems are very limited, therefore, development of predictive thermodynamic model with strong theoretical basis and a wide range of applicability is necessary. In the last decades, in order to explicitly account for multi-polar interactions, several authors have incorporated a multipolar term into the SAFT-type EoS [2-5]. Some polar terms: Gross & Vrabec [6], Jog & Chapman [7] and Karakatsani & Economou [8] have been successfully applied to predict the phase equilibria of associative/ polar mixtures. Other attempts have been also proposed to account the effect of polar interactions via the “pseudo-association” approach, where the strong polar molecules are treated as self-associating compounds [9-14]. The later approach seems to satisfactory reproduce the VLE of several polar mixtures but the physical representation is not completely correct, because the molecules are not self-associative, moreover, this approach was not tested to model the LLE of polar mixtures. From a theoretical point of view, it is still a challenge for researchers to develop a thermodynamic approach to simultaneously and accurately describe the vapor-liquid and liquid-liquid equilibria of 2

mixtures composed of strong polar molecules [15, 16]. For the engineering purpose, it is desirable to have a single model with unique parameters set that is applicable over a wide range of thermodynamic conditions. In this direction, the PC-SAFT EoS is one of the most promising approach has been focused [10, 11, 16-21]. The main advantage of the SAFT-type EoS is capable to extensively account various intermolecular interactions including the hydrogen bonding or multipolar interactions [22-24]. To our best knowledge, only a few authors have simultaneously studied the vapor-liquid and liquid-liquid equilibria of oxygenated-aromatics containing mixtures and limited to mixtures of alkanes [12, 25-28]. The PC-SAFT parameters for the pure substances are commonly regressed to its vapor pressure and saturated liquid density. The parameterization is an important step in modeling the phase behavior of mixtures, particularly for associative and / or polar molecules since it might yield several equivalent parameter sets for pure component but provide very different prediction results on LLE/ VLE of their mixtures [29-31]. In this work, the performance of the PC-SAFT EoS was evaluated to model the phase equilibria of several oxygenated containing mixtures, by incorporating the polar term into the PCSAFT or applying the “pseudo-association” approach. New attempt was also made to extend the mgSAFT to phase equilibria of the mixtures composed of oxygenated molecules and in particular to model the LLE/VLE of mixtures involving acetone, ketones, methyl-acetate, acetophenone, phenyl-acetate or benzaldehyde with alkane or water. When possible, the model is compared to the similar model reported in the open literatures. 2. Theory 2.1. The modified group contribution PC-SAFT (mg-SAFT) mg-SAFT is a modification of group-contribution approach recently proposed to compute the PCSAFT EoS parameters for pure components [32]. mg-SAFT has been successfully applied to describe the phase equilibria of several pure component and their mixtures such as non-polar [33, 34], polar [3436] or associative [16, 29, 30, 37]. 3

In mg-SAFT, three PC-SAFT molecular parameters (dispersion energy, segment number and segment diameter) are calculated using the following relations [32]: n groups

ε=

σ=

∑

i =1

n groups

∑ i =1

ni

 ngroups n   ∏ εi i  − n groups α  i=1 

n iσ i

(1)

n groups

∑ ni

i =1

(2)

n groups

m = ∑ niR i i =1

(3)

In equation (1, 2, 3), ni is the number of groups i in the molecule made of ngroups different groups, α is the group’s dispersive energy correction factor ( α =0.223 K) [32]. Note that these equations are generally applied to compounds belonging to well defined chemical families with the exception of the first two members that should be treated specially. The original PC-SAFT EoS [38] is expressed as a sum of hard chain, dispersion, association and dipolar contributions to the residual Helmholtz energy [22, 39]: ares = ahc + adisp + aassoc + adipolar

(4)

For each non-associating species, the EoS requires three physical parameters (ε/k, m, σ). The EoS needs two additional parameters to characterize the pure associating molecule (association energy - εAiBj/k, association volume - κAiBj). In order to describe the dipolar substances, one more adjustable parameter was added (called the dipolar fraction (xp*m)) [22, 40] while the dipolar moment is often fixed to the experimental value. The expressions of PC-SAFT EoS and all related formulas of the dipolar term were detailed in the references [22]. The detailed expressions of adipolar may be found in Appendix A.

4

2.2. Binary dispersive interaction parameters (kij) PC-SAFT is applied to mixtures using the van der Waals one-fluid model [41] and modified Lorentz– Berthelot mixing rules that relate the potential parameters εij and σij between molecules, i and j [42-45].

ε ij = (1 − kij ) ε iiε jj

σ ij =

(5)

σ ii + σ jj 2

(6)

2.3. Cross-association parameters (wij) To extend the PC-SAFT EoS to the mixtures of two associating compounds, we applied the following combining rules to calculate the cross-association energy (εAiBj) and the cross-association volume (κAiBj) [2, 46]:

ε

AB ij

 ε iiAB + ε jjAB  = (1 − wij ) )    2  

κijAB = κiiAB .κ jjAB

(7)

(8)

2.4. Dipolar or “pseudo-association” approach? From the theoretical point of view, the understanding of what type of interaction forces (association or polar) predominate in strong polar molecules (such as acetone or aromatic ketones) is important, because it involves interactions between polar molecules which do not have clearly donor/ acceptor protons as it occurs in alcohol or amine or organic acid molecules [16, 29]. Because of its large dipole moment (2.88 D [47]), acetone molecule is inclined to interact with each other through short-range C-H…O=C hydrogen bonding interactions [48-50] and long-range dipoledipole interactions [51]. As a result, the self-associative nature of acetone has been the subject of 5

several investigations [52-59]. It can be noted that the nature of acetone dimers is not always subscribed to dipole-dipole interactions, it’s probably resulting from strong polar interactions of the molecule. Regarding the nature of the interactions between the two acetone molecules, Frurip et al. [49] concluded that there are only two of such interactions present, while Schindler et al. [52] used the Raman spectroscopy and Knözinger et al. [54] implemented the far-infrared spectra to study the selfassociative nature of acetone and shown that, the dipole-dipole forces are predominant with some evidence for a slight contribution of hydrogen bonding between methyl and ketone groups. They also concluded that the behavior of acetone on aggregation is exactly the same as that reported for acetonitrile [54]. On the other hand, Hermida-Ramon et al. [48] found that dimer formation is due to the origination of C=O…H-C hydrogen bonds. Moreover, Tamenori et al. [50] noted that the interaction probably is a combination of dipole-dipole and C=O…H-C hydrogen bonding interactions. Several spectroscopic investigations have demonstrated further evidence of such a dipolar association [50, 60]. E.g., according to Jalilian and Zahedi-Tabrizi [55, 56], acetone is self-associative in nature. The associative nature of acetone in its pure form and in its mixture with the non-polar cyclohexane has been investigated by 13C magnetic resonance [61] and UV-vis spectral methods [62]. Self-association of acetone was also found to be present in CCl4 and hexadecane solutions [51] or liquid krypton [63] and the dimers are assumed to be formed by dipole-dipole interactions. Other spectroscopic evidence for acetone self-association in the liquid and in the vapor phase was reported by Tiffon et al. [64] or Schindler et al. [52] or Frurip et al. [49]. These authors estimated the association enthalpy for acetone dimer formation to be around 1620 K. These experimental studies were also supported with Ab initio molecular orbital calculations, for that the dimer had a cyclic structure stabilized by C-H···O=C hydrogen bonds. Indeed, Ab initio molecular orbital calculations indicate that the most stable cyclic dimer is a cycle with two hydrogen bonds [49, 65]. The dimerization equilibrium persists in the vapor phase [65] and has been evidenced by analyzing the thermal conductivity of gaseous acetone and 6

second virial data, these data indicated also that the acetone dimers are as stable as water dimers [49]. From these studies, it was possible to conclude that in its pure form, acetone exists as molecular entities self-associated through C=O…H-C hydrogen bonds. To our best knowledge, most of authors have treated acetone as a dipolar compound [6, 17-19, 67-74]. Some others have modeled acetone as “pseudo-associative” molecule [9-14]. However, it’s hard to answer the question: is the “pseudo-association” approach applicable for other polar molecules? Acetone and methyl-acetate have very close boiling temperature but their molecular weight is relatively different, that’s probably due to the dipolar interaction forces between these molecules are quite different. We expected that, for strong polar molecules, the “pseudo-association” approach could be used to describe this polar interaction. In order to answer the above question, the importance of the association and dipolar terms of the PC-SAFT EoS in describing the LLE and VLE of acetone/ methylacetate/ acetophenone and n-alkanes mixtures has been investigated. For each case, the polar molecule is described by three parameter sets and the most suitable set will be used as reference to model all other similar molecules: 1) Dipolar set: the molecule is considered as dipolar, none self-associative. The dipole moment is reused from that reported experimentally. Only the dipolar fraction is fitted to LLE data of the key mixture (acetone + n-heptane, methyl-acetate + n-heptane and acetophenone + n-decane). 2) Association set: the compound is treated as non-polar but “pseudo-associative” molecule. The association energy is directly estimated from the dimer association enthalpy of acetone (1620 K), only the association volume is regressed (together with other pure compound parameters). 3) Dipolar + association set: The dipole moment and association energy parameters are fixed to experimental data. The dipolar fraction and association volume obtained from two previous parameter sets are reused. 7

3. Pure compound parameters In this work, new functional group for ketone series or PC-SAFT molecular parameters are determined by fitting the model to the corresponding vapor pressure and liquid density of pure compounds. The choice of pure compounds that is used in the regression database is dictated by the availability of experimental data [75]. The parameterization has been implemented using the experimental database in a range of 0.4Tc - 0.95Tc (Tc is critical temperature of each component) [34, 35]. The objective function is written as:

Fobj

1 = N P sat

N

P sat

∑ 1

sat Pcalsat − Pexp sat Pexp

1 + N ρ liq

N

ρ liq

∑ 1

liq liq ρcal − ρexp liq ρexp

(9)

NPsat and Nρliq are the number of the experimental vapor pressure and saturated liquid density data, respectively. Table 1 lists the regression sequence of different chemical series, the decomposition of molecules into groups is also detailed. 3.1. n-alkanes

The functional groups appearing in an n-alkane are (CH3), (CH2). All of these groups’ parameters were fully transferred from the previous work without any further regression [32]. 3.2. Ketones

Ketones molecules are composed of three kinds of chemical group: (CH3), (CH2) and (CO) [26]. The parameters of the first two groups have already known from alkanes [32]. The parameters of the (CO) group are determined by providing the optimal description of vapor pressure and liquid density of eleven ketones from 2-butanone to 5-nonanone (Tables 2 and 3). All other available data for heavier components will be used to test the prediction ability of the model.

8

The general chemical form of the ketones considered in this work is R1-CO-R2 (where the R1 and R2 are the alkyl-chain). In order to differentiate the ketone isomers (such as 2-hexanone and 3-hexanone), it is necessary to define the relative position of the (-CO-) group in the molecule [33]. If we call R1 is the number of chemical group in the left side of the (-CO-) group and R2 is the one that is in another side (defined in its IUPAC name), the chain length parameter (mi) of the (-CO-) group is estimated as following [36]:

mi = A * R1− B + C * R2− D

(10)

where A, B, C, D are adjustable parameters, being simultaneously regressed with two other group's parameters (ε, σ) from the vapor pressure and liquid density of ketone series. In PC-SAFT, we could consider ketones as chain molecules with or without the dipolar term. In order to test the transferability of the proposed empirical correlation (equation 10), this work decided to model ketones using two parameter sets: non-polar and polar. For the latter case, the dipole moment value of ketones was assumed to be unique and fixed to the average experimental data (µ = 2.7 D, Table 2) [47]. The dipolar fraction was assumed to be 0.5 for all ketones [16]. The average absolute deviations obtained on saturated liquid density and vapor pressure data are given in Table 3. Overall, a good agreement between the model and the experimental data was obtained (with an OAAD of 2.43%/2.76% on vapor pressure and 0.61%/0.85% on saturated liquid density for two version of mg-SAFT, without and with the polar term respectively). The mg-SAFT shows a slight improvement when compare to the results obtained previously with the GC-PPC-SAFT [26]. The highest deviation on vapor pressure was obtained for the case of 2-octanone (6%), this was already observed and noticed in previous works using PPC-SAFT [26] or PCK-SAFT [73].

9

3.3. Acetone, methyl-acetate, acetophenone

A large variety of oxygenated-aromatic molecules extracted from natural sources have revealed great potential application in biochemical, pharmaceutical, food and energy. In this section, some important oxygenated molecules such as acetone, methyl-acetate, acetophenone, phenylacetate, benzaldehyde, 4Phenylbutan-2-one will be studied. As observed and concluded in previous works, [2, 16, 27] these molecules are the first members in the chemical series. Due to the proximity of polar functional groups, the transferability of the mono-functional groups’ parameters to predict the thermodynamic properties of multi-functional molecules is not applicable. All of these components will be treated specifically, and considered as dipolar or associative or dipolar and associative molecules (see section 2.4). The modeling of polar compounds using the “pseudo-association” approach requires to assign the number of associative sites on the molecule, since the choice of association scheme have a significant impact on the phase equilibria of the mixtures [29, 39, 42]. As evidenced by different authors, acetone exists mostly as dimers and its behavior is very similar to that of carboxylic acids, therefore, once acetone is considered as associative molecule, the most (probably) suitable association scheme is 1A (corresponding to one polar segment). For oxygenatedaromatic molecules, there are two polar segments in the molecule: the first is on the oxygenated-group and the second is localized on the benzene ring. To simplify the approach, this work supposed that the 2B scheme could be assigned for the oxygenated-aromatic molecules.

PC-SAFT parameters for specific molecules are grouped in Table 4. Note that, the association energy of oxygenated molecules was fixed to the experimental value of acetone (1620 K), while the association volume of acetophenone was used to transfer for all other oxygenated-aromatic molecules without any further regression (Table 4). The average absolute deviation on vapor pressure and saturated liquid density for these molecules is reported in Table 5. As can be seen from the AAD given in this Table, good agreement with the experimental data is obtained for all considered molecules. These deviations are comparable to previous correlating results obtained on vapor pressure and liquid density of specific molecules [16, 29, 30, 37]. For the case of 4-Phenylbutan-2-one, to our best 10

knowledge, only the vapor pressure data are available (under the Antoine equation coefficients [76]). PC-SAFT molecular parameters for this molecule were obtained by fitting only to its vapor pressure data.

4. Results and discussions

The temperature range, number of data points and the average absolute deviation on vapor pressure and liquid density for several ketones are given in Table 3. These computation results have confirmed the ability of our empirical correlation (equation (10)) to distinguish different ketone isomers. In order to test and validate the new (CO) group’s parameters obtained in this work, other thermodynamic properties such as heat capacity (Cp), heat of vaporization (Hvap) of “regression-pool” molecules were also examined (over wide ranges of temperature). As it was reported in Table 6, mgSAFT could predict these properties with deviation lower than 5% for both version of mg-SAFT. 4.1. VLE prediction of heavy ketones

The extrapolation ability of the mg-SAFT is further tested in this section to predict the thermodynamic properties of other molecules that have not been included in the regression step. Based on Table 2, it is very easy to calculate the mg-SAFT molecular parameters for ketone molecules via the relations (1), (2) and (3). The only input that is required for the model is the number of the functional groups appearing in the molecule, the relative position number of the (CO) isomer group (R1 and R2 as defined in its IUPAC name). Heavy ketones

The assessment of the mg-SAFT’s capability in the prediction of the PVT properties of heavy ketones was implemented. Having PC-SAFT molecular parameters, the vapor pressure (Psat), liquid densities (ρliq), isobaric heat capacities (Cp) and heat of vaporization (Hvap) of heavy ketones up to 811

pentadecanone were predicted (Tables 3 and 6). The overall absolute average deviation for the predicted compounds remains essentially equivalent to that of the regressed components. The performance of the mg-SAFT in calculating the vapor pressure and isobaric heat capacities of selected ketones is illustrated in Figure 1. Single phase high pressure density

Having a reliable set of parameters, it is possible not only to extrapolate the values to other similar molecules but also to apply them to estimate the thermodynamic properties at other conditions of temperature and pressure. A comparison between the model’s computation results and the experimental data of high-pressure, high-temperature density shows a good agreement in almost of cases. This is demonstrated in Figures 2 and 3 where the predictions of mg-SAFT are compared with the available experimental data. For four considered components, our model provides good prediction results of high pressure liquid density for both version of mg-SAFT. The overall deviation for this property is lower than 3% over full range of temperature and pressure up-to 4000 bars. A slight increase in deviation was observed for pressure higher than 1000 bars. 4.2. VLE of ketone containing systems

As a final step to validate the (CO) group’s parameters, we examined the predictive capability of the model to describe vapor-liquid equilibrium of the mixtures containing ketone. As concluded in the previous works [22], the inclusion of the dipolar term usually results in lower the absolute-value of the required binary interaction parameter (kij). For all ketone containing mixtures considered in this section, a constant binary interaction parameter (kij=0.012) has been applied to compute the VLE curves [16]. Recalled that, in order to calculate the fluid phase behavior of the mixtures composed of ketone, only the number of different chemical groups that appears in the molecule is required as input parameters. 12

For 24 binary mixtures with 749 experimental data, mg-SAFT provides an OAAD on bubble pressure lower than 5%. The VLE of several ketone + alkane mixtures are displayed in Figures 4 and 5. As seen from these Figures, mg-SAFT demonstrated its ability to provide good VLE prediction results for all considered mixtures.

4.3. VLE and LLE of the mixtures composed of acetone, methyl-acetate, oxygenated-aromatic

Simultaneous describing of liquid-liquid and vapor-liquid equilibria of the mixtures composed of oxygenated-component + alkane or + water is often a difficult task for an equation of state. In this section, different parameter sets of oxygenated-component (section 2.4) are used to exam the importance of the association and/ or dipolar terms in representing the LLE of mixtures with n-alkanes. For all calculation in this section, temperature-independent binary interaction parameter (kij) is used which was fitted to LLE data and then reused to predict VLE data of the mixture (and attached in Figure correspondently). Acetone or methyl-acetate + n-alkane

Three parameter sets of acetone/ methyl-acetate have been tested against the LLE/ VLE data of acetone + n-heptane and methyl-acetate + n-heptane mixtures. From Figure 6, it is seen that, all of these parameter sets could reproduce the VLE data with a similar performance, however, only the “association-dipolar” parameter set could match all the LLE data points. For both cases, when applying the “pseudo-association” approach, the association parameter set shifts the LLE calculation curves to the high concentration of oxygenated-component and could not matching the LLE data. In the case of methyl-acetate + n-heptane system, as expected, since the dipole moment of methyl-acetate is moderate (1.68 D), the considering of methyl-acetate as dipolar molecule was sufficient to obtain a good representation of the LLE data of the mixture. A simultaneous accounting of the dipolar and pseudo13

association forces for methyl-acetate slightly improved the describing of LLE data of this mixture. In contrast to methyl-acetate, the considering of acetone as “dipolar molecule” or applying the “pseudoassociation” approach could not representing the LLE mixture’s data. Moreover, the “dipolarassociation” parameter set well reflects the physical behavior of acetone, where strong polar interactions (2.88 D) produce the molecular association force as experimentally detected. These results suggested that, accounting for dipolar interactions by applying the “pseudo-association” approach could well reproduce the VLE data but is not able to correctly represent the LLE of mixtures. This reflects the fact that acetone is a dimers-associative molecule but methyl-acetate is not, as observed experimentally [49, 65, 66]. The “dipolar-association” parameters is the most suitable set to describe the phase equilibrium of acetone containing mixtures, while this parameter set is the “best” set for methyl-acetate, however, for physical consistency, the dipolar parameter set should be selected. The liquid-liquid and liquid-vapor equilibria of acetone + n-alkane and methyl-acetate + n-alkane mixtures are illustrated in Figures 7, 8, 9. It is recognized that, these systems exhibit an azeotropic vapor-liquid equilibrium at higher temperature and a liquid-liquid equilibrium at lower temperature. A general correlation for kij value based on the carbon number of alkane was possible by fitting to data from n-pentane to n-tridecane and plotted in Figure 11. For methyl-acetate + alkane mixtures, a constant value of kij was possible to well describe their LLE/VLE data. In all cases, good agreement between the experimental data and the computed results from the mg-SAFT was achieved. The “dipolar-association” parameter set was also validated by calculating the phase equilibria of acetone + methanol and acetone + ethanol mixtures. From Figure 10, it could be confirmed that, the inclusion of the association and dipolar term allows correctly reproduce the VLE of these mixtures. Note that, the cross-association parameters of the mixture are directly calculated using the relations (7) and (8) by setting the correction factor wij equal zero.

14

For methyl-acetate + methanol and 2-butanone + ethanol mixtures, two options are possible to correlate the VLE data: (1) fitting the dispersive binary interaction parameter (kij) or (2) accounting one crossassociation link between two molecules as experimentally evidenced [77]. Since methyl-acetate and 2butanone are not self-associative molecules, we assumed to set the association parameters of 2butanone and methyl-acetate equal to that of ethanol and methanol, respectively. So that, only the wij parameter in equation (7) must be fitted. By applying these assumptions, it was found necessary to apply the “physical approach” which is accounting one cross-association link between two molecules while fitting on kij parameter is not able to correctly reproduce the VLE data for both cases (Figure 10). Oxygenated aromatic + n-alkane

Phase equilibria of mixtures composed of oxygenated-aromatic molecules are available only for some components and mainly the LLE data. In this section, two parameter sets of oxygenated-aromatic molecules are used to check the importance of association/ dipolar terms in representing the LLE of mixtures with n-alkanes. From Figure 11, it can be seen that, the “association + dipolar” parameter set are better than the “dipolar” parameter in matching the LLE data, particularly for benzaldehyde + nalkane mixtures. However, that was not the case for phenyl-acetate, for which the computation results are very similar between the “dipolar” and “association + dipolar” parameter sets. This was probably due to the moderate dipole moment of phenyl-acetate (1.72 D) compared to that of acetophenone, 4phenyl-butan-2-one or benzaldehyde (up to 3.21 D). These results lead us to a possible explanation that the “pseudo-association” approach is applicable only for strong polar molecules and not for moderate polar components – as observed for methyl-acetate in the previous section. Therefore, only the dipolar parameter set for phenyl-acetate was reported (Table 4). Aqueous systems

Accurate modeling of phase equilibria of water + oxygenated-component mixtures is a difficult and challenging task, because these systems show extremely non-ideal behavior [23, 24, 78]. For water15

containing mixtures, no adequate results could be achieved by applying a fully predictive approach (kij=0) [79]. The PC-SAFT molecular parameters for water were taken from the previous work without any further regression (water is considered as a non-polar and self-associative 4C type molecule, Table 4). In order to correlate the LLE/ VLE data of aqueous systems, several options were possible. To simplify the calculation, except for the acetone, the dipolar parameter set was used for all oxygenated molecules. It was found necessary to account one cross-association link between water and these oxygenated molecules. The two cross-association parameters of oxygenated-molecules were supposed to be directly taken from that of water, only the binary interaction parameter (kij) and/ or the crossassociation parameter (wij) were fitted to LLE or VLE data. VLE of acetone + water mixture was first modelled. By applying a single value of kij, PC-SAFT could well reproduce all considered isotherms from 293 K to 523 K. A very difficult cross-associating system is the 2-butanone + water mixture, because of its closed-loop LLE exhibition (Figure 12). Our model under-estimates the solubility of water in 2-butanone and significantly over-calculates the UCST of mixture. Although PC-SAFT with our molecular parameters was not able to match all LLE data of the closed-loop, our model could qualitatively reproduce the LLE shape behavior. The VLE of 2-butanone + water mixture was also satisfactory predicted using the same parameters set obtained from the fitting of LLE data. The LLE of water + acetophenone, water + phenylacetate, water + benzaldehyde and water + methylacetate mixtures is depicted in Figure 13. By applying the assumption described above, the PC-SAFT was able to qualitatively reproduce the phase equilibrium of these mixtures. For all of these considered mixtures, the solubility of both phases is well reproduced. The fitting value of kij and wij for each mixture was also attached in Figure.

16

4.4. Comparison with other similar approaches

To our best knowledge, only few authors have attempted to model the phase behavior of ketones, oxygenated-aromatic compounds and their mixtures in a systematic manner. In this section, the performance of mg-SAFT was compared to that obtained with different thermodynamic models. In all cases, a single temperature-independent kij is used. Figure 14 presents LLE/ VLE calculations of acetone + n-octane, phenyl-acetate + n-alkanes, benzaldehyde + n-dodecane and acetone + water mixtures. As seen from this Figure, mg-SAFT is superior to UNIFAC [12] or sPC-SAFT [11] or DISQUAC [80] in representing the fluid phase equilibria of considered mixtures. The performance of mg-SAFT and DISQUAC is very similar in describing of LLE of phenyl-acetate + n-alkane systems. Regarding to methyl-acetate + n-alkane mixtures, the calculation results obtained with our model is graphically comparable to that reported by Fernández et al [25] using the NRTL model.

5. Conclusions

In this work, we have extended the applicability of the mg-SAFT to model the phase behavior of some oxygenated-compounds and their mixtures. We have also evaluated the “pseudo-association” and “polar” approaches using the PC-SAFT EoS by describing the liquid-liquid and vapor-liquid equilibria of several oxygenated-component’s mixtures. Based on the results obtained in this work, some conclusions are drawn as the following: − By fixing the dipole moment of ketones to the average experimental data, new functional group

(CO) was determined by fitting the model to vapor pressure and liquid density of selected compounds. An empirical approach recently proposed to distinguish different isomer molecules has been successfully applied in this work to model ketones. 17

− VLE of several mixtures composed of ketone have been predicted by applying a unique binary

interaction parameter (kij=0.012). For all considered mixtures, the deviation on bubble pressure is lower than 5% compared to experimental data. − New “physical sound” parameterization approach for acetone, methyl-acetate and oxygenated-

aromatic compounds was proposed. The association energy of these molecules has been estimated based on the dimers association enthalpy of acetone. The including of the dipolar term with the 1A association scheme to the PC-SAFT EoS has proven necessary to qualitatively and quantitatively reproduce the LLE/ VLE of acetone + alkane mixtures. − For oxygenated-molecules, accounting for dipolar interactions by applying the “pseudo-

association” approach could reproduce the vapor-liquid equilibrium but not able to correctly reproduce the liquid-liquid equilibrium of their mixtures. For the moderate polar components, the polar approach is sufficient to correctly describe the phase equilibria of the mixtures, while the “dipolar + pseudo-association” approach could be applied to obtain satisfactory description of the phase behavior of mixture composed of strong polar molecules.

SYMBOLS

AAD = Average Absolute Deviation CPA= Cubic Plus Association DIPPR = Design Institute for Physical Property Data EoS = Equation of State GC-PPC-SAFT = Group contribution polar PC-SAFT IUPAC = International Union of Pure and Applied Chemistry LLE = Liquid-liquid equilibrium mg-SAFT = modified group-contribution PC-SAFT Npt = Number of data points OAAD = Overall Average Absolute Deviation 18

P = Pressure (bar) PC-SAFT = Perturbed-Chain Statistical Associating Fluid Theory PCK-SAFT = Polar Chen-Krewlewski Statistical Associating Fluid Theory T = Temperature (K) VLE = Vapor liquid equilibrium Subscripts c = critical liq = liquid sat = saturation exp = experimental calc = calculated

Appendix A. Dipolar contribution to SAFT equation of state [22, 40].

The dipolar contribution is written as a Padé approximant:

A dipolar

  1 = A2  1 − A 3  A 2

    

Where a2 and a3 are the second and the third order terms in the perturbation expression. The A2 term is:

A2 = −

µα2 µβ2 (6) 2 π Nρ µ µ x x x x m m ∑ α β pα pβ α β σ 3 Jαβ 3 kT αβ αβ

The A3 term is: 32  14π  A3 =   135  5 

1/2

Nρ2 ( kT ) 2

µα2 µ β2 µγ2 ∑ xα xβ xγ x x x mα mβ mγ (σ σ σ ) Kαβγ (222;333) αβγ αβ αγ βγ µ pα

µ pβ

µ pγ

In the equations above, ρ is the total number density of molecules, mα is the chain length of molecule α. σαβ is the arithmetic average of segments diameters σα and σβ. µα are the dipole moment of the polar 19

segments in the chain compound α. x µpα refer to the fractions of dipolar segment in the chain of component α and should not be confused with xα, the mole fraction of component α. J and K are integral over pair and triplet correlation functions; these integrals are a function of reduced density and temperature and have the empirical form as follows [81]. ln J (n ) = An ρ *2 ln T * + Bn ρ *2 +C n ρ * ln T * + Dn ρ * + E n ln T * + Fn

with T* =

kT εαα .εββ

and ρ * = Nmx ρσ x3 where mx and σx are mixture chain length and diameter.

Constant parameters A, B, C, D, E, F are fitted coefficients available in reference [82].

References

[1] E. Hendriks, G.M. Kontogeorgis, R. Dohrn, J.-C. de Hemptinne, I.G. Economou, L.F. Zilnik, V. Vesovic, Industrial requirements for thermodynamics and transport properties, Industrial & Engineering Chemistry Research, 49 (2010) 11131-11141.10.1021/ie101231b [2] D. NguyenHuynh, J.-C. de Hemptinne, R. Lugo, J.-P. Passarello, P. Tobaly, Simultaneous liquid– liquid and vapour–liquid equilibria predictions of selected oxygenated aromatic molecules in mixtures with alkanes, alcohols, water, using the polar GC-PC-SAFT, Chemical Engineering Research and Design, 92 (2014) 1912-1935.http://dx.doi.org/10.1016/j.cherd.2014.05.018 [3] S.P. Tan, H. Adidharma, M. Radosz, Recent Advances and Applications of Statistical Associating Fluid Theory, Industrial & Engineering Chemistry Research, 47 (2008) 80638082.http://dx.doi.org/10.1021/ie8008764 [4] J.T. Cripwell, Assessment of the capabilities of two polar sPC-SAFT terms through application to measured ketone-alkane phase equilibria data, (2014) [5] E. Sauer, M. Stavrou, J. Gross, Comparison between a Homo-and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State, Industrial & Engineering Chemistry Research, 53 (2014) 1485414864.http://dx.doi.org/10.1021/ie502203w [6] J. Gross, J. Vrabec, An Equation-of-State Contribution for Polar Components: Dipolar Molecules, AIChE Journal, 52 (2006) 1194-1204 [7] P.K. Jog, S.G. Sauer, J. Blaesing, W.G. Chapman, Application of Dipolar Chain Theory to the Phase Behavior of Polar Fluids and Mixtures, Ind. Eng. Chem. Res., 40 (2001) 4641-4648. [8] E.K. Karakatsani, I.G. Economou, Perturbed Chain-Statistical Associating Fluid Theory Extended to Dipolar and Quadrupolar Molecular Fluids, J. Phys. Chem. B, 110 (2006) 9252-9261 [9] E. Voutsas, C. Perakis, G. Pappa, D. Tassios, An Evaluation of the Performance of the Cubic-PlusAssociation Equation of State in Mixtures of Non-Polar, Polar and Associating Compounds: Towards a Single Model for Non-polymeric Systems, Fluid Phase Equilibria, 261 (2007) 343-350

20

[10] G.K. Folas, G.M. Kontogeorgis, M.L. Michelsen, E.H. Stenby, Application of the Cubic-PlusAssociation Equation of State to Mixtures with Polar Chemicals and High Pressures, Ind. Eng. Chem. Res., 45 (2006) 1516-1526 [11] N. Von Solms, M.L. Michelsen, G.M. Kontogeorgis, Applying Association Theories to Polar Fluids, Ind. Eng. Chem. Res., 43 (2004) 1803-1806 [12] M. Sadeqzadeh, V. Papaioannou, S. Dufal, C.S. Adjiman, G. Jackson, A. Galindo, The development of unlike induced association-site models to study the phase behaviour of aqueous mixtures comprising acetone, alkanes and alkyl carboxylic acids with the SAFT-γ Mie group contribution methodology, Fluid Phase Equilibria, 407 (2016) 39-57 [13] I. Tsivintzelis, G.M. Kontogeorgis, On the predictive capabilities of CPA for applications in the chemical industry: Multicomponent mixtures containing methyl-methacrylate, dimethyl-ether or acetic acid, Chemical Engineering Research and Design, 92 (2014) 29472969.http://dx.doi.org/10.1016/j.cherd.2014.03.011 [14] N. Von Solms, I.A. Kouskoumvekaki, M.L. Michelsen, G.M. Kontogeorgis, Capabilities, limitations and challenges of a simplified PC-SAFT equation of state, Fluid Phase Equilibria 241 (2006) 344-353 [15] E. Schäfer, G. Sadowski, S. Enders, Calculation of complex phase equilibria of DMF/alkane systems using the PCP-SAFT equation of state, Chemical Engineering Science, 115 (2014) 4957.http://dx.doi.org/10.1016/j.ces.2013.04.053 [16] D. NguyenHuynh, S.T.K. Tran, C. Mai, Predicting the phase behavior of alcohols, aromatic alcohols and their mixtures using the modified Group-Contribution PC-SAFT, Industrial & Engineering Chemistry Research, 58 (2019) 16963-16977.10.1021/acs.iecr.9b03198 [17] J.T. Cripwell, C.E. Schwarz, A.J. Burger, SAFT-VR-Mie with an incorporated polar term for accurate holistic prediction of the thermodynamic properties of polar components, Fluid Phase Equilibria, 455 (2018) 24-42.https://doi.org/10.1016/j.fluid.2017.09.027 [18] A. De Villiers, C. Schwarz, A. Burger, Extension of the CPA equation of state with dipolar theories to improve vapour–liquid-equilibria predictions, Fluid Phase Equilibria, 312 (2011) 66-78 [19] M. Kleiner, G. Sadowski, Modeling of Polar Systems Using PCP-SAFT: An Approach to Account for Induced-Association Interactions, J. Phys. Chem. C, 111 (2007) 1554415553.http://dx.doi.org/10.1021/jp072640v [20] F.A. Sánchez, Y. Ille, N. Dahmen, S. Pereda, GCA-EOS extension to mixtures of phenol ethers and derivatives with hydrocarbons and water, Fluid Phase Equilibria, 490 (2019) 1321.https://doi.org/10.1016/j.fluid.2019.02.017 [21] N. Haarmann, R. Siewert, A.A. Samarov, S.P. Verevkin, C. Held, G. Sadowski, Thermodynamic Properties of Systems Comprising Esters: Experimental Data and Modeling with PC-SAFT and SAFTγ Mie, Industrial & Engineering Chemistry Research, 58 (2019) 6841-6849.10.1021/acs.iecr.9b00714 [22] D. NguyenHuynh, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Application of GC-SAFT EOS to polar systems using a segment approach, Fluid Phase Equilibria, 264 (2008) 62– 75.http://dx.doi.org/10.1016/j.fluid.2007.10.019 [23] I. Polishuk, Y. Sidik, D. NguyenHuynh, Predicting phase behavior in aqueous systems without fitting binary parameters I: CP-PC-SAFT EOS, aromatic compounds, AIChE Journal, 63 (2017) 4124– 4135.http://dx.doi.org/10.1002/aic.15715 [24] I. Polishuk, H. Lubarsky, D. NguyenHuynh, Predicting Phase Behavior in Aqueous Systems without Fitting Binary Parameters II: Gases and Non-Aromatic Hydrocarbons, AIChE Journal, 63 (2017) 5064–5075.http://dx.doi.org/10.1002/aic.15815 [25] L. Fernández, E. Pérez, J. Ortega, J. Canosa, J. Wisniak, Multiproperty modeling for a set of binary systems. Evaluation of a model to correlate simultaneously several mixing properties of methyl

21

ethanoate + alkanes and new experimental data, Fluid Phase Equilibria, 341 (2013) 105123.http://dx.doi.org/10.1016/j.fluid.2012.12.027 [26] D. NguyenHuynh, J.P. Passarello, J.C. de Hemptinne, P. Tobaly, Extension of polar GC-SAFT to systems containing some oxygenated compounds: Application to ethers, aldehydes and ketones, Fluid Phase Equilibria, 307 (2011) 142-159.http://dx.doi.org/10.1016/j.fluid.2011.04.009 [27] D. NguyenHuynh, J.-P. Passarello, P. Tobaly, In Situ Determination of Phase Equilibria of Methyl Benzoate+ Alkane Mixtures Using an Infrared Absorption Method. Comparison with Polar GC-SAFT Predictions†, Journal of Chemical & Engineering Data, 54 (2009) 16851691.https://doi.org/10.1021/je800757j [28] C. Alonso Tristán, J.A. González, F. Hevia, I. García de la Fuente, J.C. Cobos, Liquid–Liquid Equilibria for Systems Containing 4-Phenylbutan-2-one or Benzyl Ethanoate and Selected Alkanes, Journal of Chemical & Engineering Data, 62 (2017) 988-994.10.1021/acs.jced.6b00803 [29] D. NguyenHuynh, C.T.Q. Mai, Application of the Modified Group Contribution PC-SAFT to Carboxylic Acids and Their Mixtures, Industrial & Engineering Chemistry Research, 58 (2019) 89238934.10.1021/acs.iecr.9b02052 [30] D. NguyenHuynh, T.T.X. Nguyen, Application of the modified group-contribution PC-SAFT to nitrile and their mixtures, Fluid Phase Equilibria, 450 (2017) 112125.https://doi.org/10.1016/j.fluid.2017.07.017 [31] D. NguyenHuynh, Correlation and prediction of liquid–liquid equilibria for alcohol/hydrocarbon mixtures using PC-SAFT equation of state at high pressure up to 150 MPa, Fluid Phase Equilibria, 425 (2016) 206-214.http://dx.doi.org/10.1016/j.fluid.2016.06.002 [32] D. NguyenHuynh, A modified group-contribution PC-SAFT equation of state for prediction of phase equilibria, Fluid Phase Equilibria, 430 (2016) 33-46.http://dx.doi.org/10.1016/j.fluid.2016.09.020 [33] D. NguyenHuynh, D. NguyenHuynh, Application of the modified Group-Contribution PerturbedChain SAFT to branched alkanes, n-olefins and their mixtures, Fluid Phase Equilibria, 434 (2017) 176192.http://dx.doi.org/10.1016/j.fluid.2016.12.006 [34] H. Lubarsky, I. Polishuk, D. NguyenHuynh, The group contribution method (GC) versus the critical point-based approach (CP): Predicting thermodynamic properties of weakly- and nonassociated oxygenated compounds by GC-PPC-SAFT and CP-PC-SAFT, The Journal of Supercritical Fluids, 110 (2016) 11-21.http://dx.doi.org/10.1016/j.supflu.2015.12.007 [35] H. Lubarsky, I. Polishuk, D. NguyenHuynh, Implementation of GC-PPC-SAFT and CP-PC-SAFT for predicting thermodynamic properties of mixtures of weakly- and non-associated oxygenated compounds, The Journal of Supercritical Fluids, 115 (2016) 6578.http://dx.doi.org/10.1016/j.supflu.2016.04.013 [36] T.T.X. Nguyen, D. NguyenHuynh, Predicting the phase equilibria of esters/alcohols mixtures and biodiesel density from its fatty acid composition using the modified group-contribution PC-SAFT, Fluid Phase Equilibria, 472 (2018) 128-146.https://doi.org/10.1016/j.fluid.2018.05.017 [37] D. NguyenHuynh, T.T. Nguyen, T.T.X. Nguyen, Prediction of vapor-liquid and liquid-liquid equilibria at high pressures of 2-alkoxyethanol mixtures using PC-SAFT EoS, Fluid Phase Equilibria, 434 (2017) 7-20.http://dx.doi.org/10.1016/j.fluid.2016.11.020 [38] J. Gross, G. Sadowski, Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules, Ind. Eng. Chem. Res., 40 (2001) 12441260.http://dx.doi.org/10.1021/ie0003887 [39] D. NguyenHuynh, A. Falaix, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Predicting VLE of heavy esters and their mixtures using GC-SAFT, Fluid Phase Equilibria, 264 (2008) 184200.http://dx.doi.org/10.1016/j.fluid.2007.11.013

22

[40] D. Nguyenhuynh, Modélisation thermodynamique de mélanges symétriques et asymétriques de composés polaires oxygénés et/ou aromatiques par GC-SAFT, PhD thesis, in: Institut Galileé, Universite Paris Nord, Villetaneuse, France, 2008 Page 59-105. [41] J. Gross, G. Sadowski, Application of the Perturbed-Chain SAFT Equation of State to Associating Systems, Ind. Eng. Chem. Res., 41 (2002) 5510-5515.http://dx.doi.org/10.1021/ie010954d [42] M. Mourah, D. NguyenHuynh, J.P. Passarello, J.C. de Hemptinne, P. Tobaly, Modeling LLE & VLE of methanol + n-alkane series using GC-PC-SAFT with a group contribution kij. , Fluid Phase Equilibria, 298 (2010) 154-168.http://dx.doi.org/10.1016/j.fluid.2010.07.013 [43] T.K.S. Tran, D. NguyenHuynh, N. Ferrando, J.P. Passarello, J.C. de Hemptinne, P. Tobaly, Modeling VLE of H2 + Hydrocarbon Mixtures Using a Group Contribution SAFT with a kij Correlation Method Based on London's Theory, Energy & Fuels, 23 (2009) 2658-2665.10.1021/ef801101z [44] D. NguyenHuynh, T.K.S. Tran, S. Tamouza, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Modeling phase equilibria of asymmetric mixtures using a Group Contribution SAFT (GC -SAFT) with a kij correlation method based on London's theory. Part 2: application to binary mixtures containing aromatic hydrocarbons, n-alkane, CO2, N2 and H2S., Ind. Eng. Chem. Res., 47 (2008) 88598868.http://dx.doi.org/10.1021/ie071644j [45] D. NguyenHuynh, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Modeling phase equilibria of asymmetric mixtures using a Group Contribution SAFT (GC -SAFT) with a kij correlation method based on London's theory. Part 1: application to CO2 + n-alkane, methane + n-alkane and ethane + nalkane systems., Ind. Eng. Chem. Res., 47 (2008) 8847-8858.http://dx.doi.org/10.1021/ie071643r [46] D. NguyenHuynh, J.P. Passarello, J.C. de Hemptinne, F. Volle, P. Tobaly, Simultaneous modeling of VLE, LLE and VLLE of CO2 and 1, 2, 3 and 4 alkanol containing mixtures using GC-PPC-SAFT EOS, The Journal of Supercritical Fluids, 95 (2014) 146157.http://dx.doi.org/10.1016/j.supflu.2014.07.022 [47] R. Rowley, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, (2010) Ref Type: Electronic Citation [48] J.M. Hermida-Ramón, M.A. Ríos, The Energy of Interaction between Two Acetone Molecules:  A Potential Function Constructed from ab Initio Data, The Journal of Physical Chemistry A, 102 (1998) 2594-2602.10.1021/jp973309m [49] D.J. Frurip, L.A. Curtiss, M. Blander, Characterization of molecular association in acetone vapor. Thermal conductivity measurements and molecular orbital calculations, The Journal of Physical Chemistry, 82 (1978) 2555-2561.10.1021/j100513a004 [50] Y. Tamenori, O. Takahashi, K. Yamashita, T. Yamaguchi, K. Okada, K. Tabayashi, T. Gejo, K. Honma, Hydrogen bonding in acetone clusters probed by near-edge x-ray absorption fine structure spectroscopy in the carbon and oxygen K-edge regions, The Journal of Chemical Physics, 131 (2009) 174311.10.1063/1.3257962 [51] T.F. Lin, S.D. Christian, H.E. Affsprung, Self-association and hydration of ketones in carbon tetrachloride, The Journal of Physical Chemistry, 71 (1967) 968-973.10.1021/j100863a031 [52] W. Schindler, P.T. Sharko, J. Jonas, Raman study of pressure effects on frequencies and isotropic line shapes in liquid acetone, The Journal of Chemical Physics, 76 (1982) 34933496.10.1063/1.443449 [53] B. Ancian, B. Tiffon, J.-E. Dubois, Molecular interactions and reorientational motion of neat acetone in the liquid state. 17O NMR chemical shifts and linewidths at variable temperature, Chemical Physics, 74 (1983) 171-177.https://doi.org/10.1016/0301-0104(83)80020-2 [54] E. Knözinger, R. Wittenbeck, Far-infrared spectra of strongly polar molecules in solid solution: Acetone and nitromethane, Journal of Molecular Spectroscopy, 105 (1984) 314323.https://doi.org/10.1016/0022-2852(84)90221-2

23

[55] M.R. Jalilian, Spectra and structure of binary azeotropes: IV. Acetone–cyclohexane, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 69 (2008) 812815.https://doi.org/10.1016/j.saa.2007.05.032 [56] M.R. Jalilian, M. Zahedi-Tabrizi, Spectra and structure of binary azeotropes V-acetone– cyclopentane, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 69 (2008) 278281.https://doi.org/10.1016/j.saa.2007.03.043 [57] T. Shikata, N. Yoshida, Dielectric Behavior of Some Small Ketones as Ideal Polar Molecules, The Journal of Physical Chemistry A, 116 (2012) 4735-4744.10.1021/jp301520f [58] F. Kollipost, A.V. Domanskaya, M.A. Suhm, Microscopic Roots of Alcohol–Ketone Demixing: Infrared Spectroscopy of Methanol–Acetone Clusters, The Journal of Physical Chemistry A, 119 (2015) 2225-2232.10.1021/jp503999b [59] S.K. Srivastava, A.K. Ojha, J. Koster, M.K. Shukla, J. Leszczynski, B.P. Asthana, W. Kiefer, Isotopic dilution, self-association, and Raman non-coincidence in the binary system (CH3)2C=O+(CD3)2C=O reinvestigated by polarized Raman measurement and ab initio calculations, Journal of Molecular Structure, 661-662 (2003) 11-21.https://doi.org/10.1016/j.molstruc.2003.07.004 [60] Y. Matsuda, K. Ohta, N. Mikami, A. Fujii, Infrared spectroscopy for acetone and its dimer based on photoionization detection with tunable coherent vacuum-ultraviolet light, Chemical Physics Letters, 471 (2009) 50-53.https://doi.org/10.1016/j.cplett.2009.02.026 [61] H. Saitô, Y. Tanaka, S. Nagata, K. Nukada, 13C Nuclear Magnetic Resonance Studies on Molecular Association. I. Self-association of Dipolar Molecules, Canadian Journal of Chemistry, 51 (1973) 2118-2123.10.1139/v73-318 [62] G. Arivazhagan, A. Elangovan, R. Shanmugam, R. Vijayalakshmi, P.P. Kannan, Spectroscopic studies, NBO analysis and dielectric studies on the behaviour of acetone molecules in non-polar solvent environment, Chemical Physics Letters, 627 (2015) 101106.https://doi.org/10.1016/j.cplett.2015.03.051 [63] L.I. De Beuckeleer, W.A. Herrebout, Self-Associating Behavior of Acetone in Liquid Krypton, The Journal of Physical Chemistry A, 120 (2016) 884-894.10.1021/acs.jpca.5b10405 [64] B. Tiffon, B. Ancian, J.-E. Dubois, Natural abundance 17O NMR as a tool for intermolecular interaction studies: acetone self-association, Chemical Physics Letters, 73 (1980) 8993.https://doi.org/10.1016/0009-2614(80)85209-2 [65] L.N. Anderson, A.P. Kudchadker, P.T. Eubank, Volumetric properties of gaseous acetone, Journal of Chemical & Engineering Data, 13 (1968) 321-327.10.1021/je60038a007 [66] R. Vines, The Thermal Conductivity of Organic Vapours: The Influence of Molecular Interaction, Australian Journal of Chemistry, 6 (1953) 1-26.https://doi.org/10.1071/CH9530001 [67] K. Albers, G. Sadowski, Reducing the amount of PCP-SAFT fitting parameters. 1. Non-polar and dipolar components, Fluid Phase Equilibria, 326 (2012) 2130.http://dx.doi.org/10.1016/j.fluid.2012.04.011 [68] E.K. Karakatsani, I.G. Economou, Phase equilibrium calculations for multi-component polar fluid mixtures with tPC-PSAFT, Fluid Phase Equilibria, 261 (2007) 265-271 [69] M. Kleiner, J. Gross, An Equation of State Contribution for Polar Components: Polarizable Dipoles, AIChE Journal, 52 (2006) 1951-1961 [70] E.K. Karakatsani, T. Spyriouni, I.G. Economou, Extended Statistical Associating Fluid Theory (SAFT) Equations of State for Dipolar Fluids, AIChE Journal, 51 (2005) 2328-2342 [71] A. Dominik, W.G. Chapman, M. Kleiner, G. Sadowski, Modeling of Polar Systems with the Perturbed-Chain SAFT Equation of State. Investigation of the Performance of Two Polar Terms, Ind. Eng. Chem. Res. , 44 (2005) 6928-6938.http://dx.doi.org/10.1021/ie050071c [72] F. Tumakaka, G. Sadowski, Application of the Perturbed-Chain SAFT equation of state to polar systems, Fluid Phase Equilibria 217 (2004) 233-239 24

[73] S.G. Sauer, W.G. Chapman, A Parametric Study of Dipolar Chain Theory with Applications to Ketone Mixtures, Ind. Eng. Chem. Res., 42 (2003) 5687-5696 [74] J.-G. Mi, J. Chen, G.-H. Gao, W.-Y. Fei, Equation of state extended from SAFT with improved results for polar fluids across the critical point, Fluid Phase Equilibria, 201 (2002) 295-307 [75] B.D. Smith, R. Srivastava, Thermodynamic Data for Pure Compounds: Hydrocarbons and Ketones, Elsevier Science Limited, 1986. [76] J. Dykyj, K.R. Hall, Vapor pressure and antoine constants for oxygen containing organic compounds, Springer, Berlin, 2000. [77] T.M. Letcher, B.C. Bricknell, Calorimetric Investigation of the Interactions of Some HydrogenBonded Systems at 298.15 K, J. Chem. Eng. Data, 41 (1996) 166-169 [78] D. NguyenHuynh, J.-C. de Hemptinne, R. Lugo, J.-P. Passarello, P. Tobaly, Modeling liquid– liquid and liquid–vapor equilibria of binary systems containing water with an alkane, an aromatic hydrocarbon, an alcohol or a gas (methane, ethane, CO2 or H2S), using group contribution polar perturbed-chain statistical associating fluid theory, Industrial & Engineering Chemistry Research, 50 (2011) 7467-7483.http://dx.doi.org/10.1021/ie102045g [79] D. NguyenHuynh, Accurate modeling of multiphase behavior of aqueous systems. I. Alkanes, alkenes, cycloalkanes, alcohols, aromatics, Fluid Phase Equilibria, 473 (2018) 201219.https://doi.org/10.1016/j.fluid.2018.06.019 [80] J.A. González, C. Alonso-Tristán, I.G. de la Fuente, J.C. Cobos, Liquid–liquid equilibria for benzaldehyde+n-alkane mixtures and characterization of benzaldehyde+ hydrocarbon systems in terms of DISQUAC, Fluid Phase Equilibria, 366 (2014) 61-68 [81] C.H. Twu, K.E. Gubbins, Thermodynamics of polyatomic fluid mixtures-II : Polar, quadrupolar and octopolar molecules, Chemical Engineering Science, 33 (1978) 879-887 [82] K.E. Gubbins, C.H. Twu, Thermodynamics of Polyatomic Fluid Mixtures-I Theory, Chemical Engineering Science, 33 (1978) 863-878 [83] R. Malhotra, W. Price, L. Woolf, Thermodynamic properties of pentan-3-one at temperatures from 278 K to 338 K and pressures from 0.1 MPa to 380 MPa, The Journal of Chemical Thermodynamics, 25 (1993) 361-366 [84] R. Malhotra, L.A. Woolf, Volumetric measurements of liquid pentan-2-one, hexan-2-one, and 4methylpentan-2-one at temperatures from 278.15 K to 338.13 K and pressures in the range from 0.1 MPa to 386 MPa, The Journal of Chemical Thermodynamics, 28 (1996) 14111421.https://doi.org/10.1006/jcht.1996.0124 [85] J.T. Cripwell, C.E. Schwarz, A.J. Burger, Vapor–Liquid Equilibria Measurements for the Nine nAlkane/Ketone Pairs Comprising 2-, 3-, and 4-Heptanone with n-Octane, n-Nonane, and n-Decane, Journal of Chemical & Engineering Data, 60 (2015) 602-611.10.1021/je500731x [86] H. Renon, J.M. Prausnitz, Ind. Eng. Chem. Proc. Des. Develop., 7 (1968) 220 [87] U. Messow, U. Doye, D. Kuchenbecker, Thermodynamic Investigation on the Systems Solvent n-Paraffin. IX. The Systems n-Butanol - Dodecane, n-Butanol - n-Hexadecane and Butanone - nOctadecane, Z. Phys. Chem. Leipzig, 259 (1978) 664-666 [88] V.C. Maripuri, G.A. Ratcliff, Isothermal Vapor-Liquid Equilibria in Binary Mixtures of Ketones and Alkanes, J. Appl. Chem. Biotechnol., 22 (1972) 899-903 [89] M. Rolla, P. Franzosini, R. Riccardi, L. Bottelli, Z. Naturforsch, A: Phys. Sci., 96 (1966) 601–603 [90] M. Rolla, P. Franzosini, R. Riccardi, L. Botelli, Binary Systems containing Hydrocarbons. Note I. Miscibility Gaps in the Methylacetate + Alkanes Systems, Z. Naturforsch. Sec. A, 21 (1966) 601-603 [91] J.R. Loehe, H.C.V. Ness, M.M. Abbott, Vapor–liquid equilibrium of ketone and n-alkane mixtures, Int. Data Ser., Sel. Data Mixtures, Ser. A, (1979) 45 [92] J. Acosta, A. Arce, J. Martinez-Ageitos, E.S. Rodil, A.;, Vapor-Liquid Equilibrium of the Ternary System Ethyl Acetate + Hexane + Acetone at 101.32 kPa, J. Chem. Eng. Data, 47 (2002) 849-854 25

[93] W. Rall, K. Schäfer, Thermodynamische Untersuchungen an flüssigen Mischsystemen von Aceton und n-Pentan sowie von Aceton und n-Hexan, Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie, 63 (1959) 1019-1024.10.1002/bbpc.19590630904 [94] H.C. Ku, C.H. Tu, Isobaric Vapor-Liquid Equilibria for Mixtures of Acetone, Ethanol, and 2,2,4Trimethylpentane at 101.3 kPa, Fluid Phase Equilibria, 231 (2005) 99-108 [95] Kl. Schäfer, W. Ball, F.C. Wirth-Lindemann, Thermodynamische Untersuchungen an dem System Aceton-n-Heptan und Aceton-n-Nonan, in: Zeitschrift für Physikalische Chemie, 1958, pp. 197. [96] H. Wolff, K. Bernstorff, Mischungslücken von Gemischen aus Aceton und n-Paraffinen und ihre Berechnung aus Aktivitätskoeffizienten, Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie, 62 (1958) 1093-1101.10.1002/bbpc.19580621008 [97] G. Spinolo, R. Riccardi, Liquid-liquid equilibria in propanone and n-alkane mixtures, Int. Data Ser. Sel. Data Mixtures Ser. A, 2 (1977) 91-94 [98] J. Edwards, J.I. Rodríguez, A. Soto, On Partial Miscibility: The Systems Acetone/2,2,4 trimethylpentane (Isooctane), and Acetone/n-Heptane, in: Zeitschrift für Naturforschung A, 1970, pp. 1998. [99] S.W. Campbell, R.A. Wilsak, G. Thodos, Isothermal Vapor-Liquid Equilibria Measurements for the n-Pentane - Acetone System at 372.7, 397.7, and 422.6 K, J. Chem. Eng. Data, 31 (1986) 424-430 [100] G. Kolasinska, M. Goral, J. Giza, Vapor-Liquid Equilibria and Excess Gibbs Free Energy in Binary Systems of Acetone with Aliphatic and Aromatic Hydrocarbons at 313.15 K, Z. Phys. Chem. Leipzig, 263 (1982) 151-160 [101] K. Schaefer, Isothermal Liquid-Vapor Equilibrium in 2-Propanone + Normal Alkane (C5, C6, C7, C9) Binary Mixtures, Int. Data Ser. Sel. Data Mixtures Ser. A, (1979) 41-44 [102] A.N. Marinichev, M.P. Susarev, A Study of Liquid-Vapor Equilibrium in the Acetone - Methanol and Acetone - Cyclohexane Systems at Temperatures of 35,45 and 55 degrees C and a Pressure of 760 mm Hg, J. Appl. Chem. USSR, 38 (1965) 371-375 [103] J.N. Rhim, S.S. Park, A Study on the Derivation of Isobaric Vapor-Liquid Equilibrium Data from Isothermal Vapor-Liquid Equilibrium Data for Ternary Systems, Hwahak Konghak, 13 (1975) 147-155 [104] G. Bredig, R. Bayer, II. Vapor Pressure of the Ternary System Methanol - Methyl Acetate - Ethyl Acetate, Z. Phys. Chem. Stoechiom. Verwandtschaftsl., 130 (1927) 15-28 [105] R. Garriga, F. Sanchez, P. Perez, M. Gracia, Vapor pressures at six temperatures between 278.15 K and 323.15 K and excess molar functions at T = 298.15 K of (butanone + methanol or ethanol), J. Chem. Thermodyn., 28 (1996) 567-576 [106] L.R. Hellwig, M. van Winkle, Vapor-Liquid Equilibria for Ethyl Alcohol Binary Systems, Ind. Eng. Chem., 45 (1953) 624-629 [107] J.A. González, C. Alonso-Tristán, I.G.d.l. Fuente, J.C. Cobos, Liquid–liquid equilibria for acetophenone + n-alkane mixtures and characterization of acetophenone systems using DISQUAC, Fluid Phase Equilibria, 391 (2015) 39-48.http://dx.doi.org/10.1016/j.fluid.2015.01.026 [108] J. Griswold, Phase-equilibria of the acetone-methanol-water system from 100℃ into the critical region, Chem. Eng. Progr., Symp. Syr., 48 (1952) 18-34 [109] E.P. Sokolova.;, A.G. Morachevskii.;, Thermodynamic properties of the system acetone–water, Vestn Lenin U. Fiz. Kh., 16 (1967) 110–115 [110] R.E. Treybal, O.J. Vondrak, Distribution of Ketones in Water-Hydrocarbon Systems, Industrial & Engineering Chemistry, 41 (1949) 1761-1763.10.1021/ie50476a056 [111] H.M. Moon, K. Ochi, K. Kojima, Vapor-Liquid Equilibria for the Ethyl Methyl Ketone + Water System with Limited Miscibility, Journal of Chemical & Engineering Data, 40 (1995) 468471.10.1021/je00018a025 [112] I. Siegelman, C. Sorum, Phase Equilibrium Relationships in the Binary System Methyl Ethyl Ketone–Water, Canadian Journal of Chemistry, 38 (1960) 2015-2023 26

[113] R.M. Stephenson, Mutual solubilities: water-ketones, water-ethers, and water-gasoline-alcohols, Journal of Chemical & Engineering Data, 37 (1992) 80-95.10.1021/je00005a024 [114] R. Stephenson, J. Stuart, Mutual binary solubilities: water-alcohols and water-esters, Journal of Chemical & Engineering Data, 31 (1986) 56-70.10.1021/je00043a019 [115] R.M. Stephenson, Mutual solubility of water and aldehydes, Journal of Chemical and Engineering data, 38 (1993) 630-633.10.1021/je00012a040 [116] J. Kendall, L.E. Harrison, Part II. Intermediate addition-compounds and chain reactions. Compound formation in ester-water systems, Transactions of the Faraday Society, 24 (1928) 588-596 [117] A. Skrzecz, Mutual solubility of water and n-alkyl acetates, in, Polish chemical society c/o polish acad sciences, inst physical chemistry, 1980, pp. 1101-1104.

27

Table caption Table 1. Decomposition of molecules into groups for the different chemical series. Table 2. Group contribution parameters for mg-SAFT. The dispersive energy group correction factor, α = 0.223 K. Note: (*) parameters reused from previous work [32, 33]. Table 3. Average absolute deviations (%AAD) for the liquid density (ρliq) and vapor pressure (Psat) of the ketones obtained using the mg-SAFT with and without the dipolar term. Experimental data are taken from reference [75]. Table 4. Oxygenated molecules parameters for PC-SAFT EoS. Bold and italic numbers are experimental data [47]. Table 5. Average absolute deviations (%AAD) for the liquid density (ρliq) and vapor pressure (Psat) of the oxygenated molecules obtained with the PC-SAFT EoS. Table 6. Average absolute deviations (%AAD) for the liquid density (ρliq), isobaric heat capacity (Cp), heat of vaporization (Hvap) and vapor pressure (Psat) of the ketones obtained using the mg-SAFT with and without the dipolar term. Experimental data are taken from DIPPR [47].

28

Table 1. Decomposition of molecules into groups for the different chemical series. (−CH2−)

(CH3−)

n-alkanes

n

2

ketones

n

2

Molecules/ sequence

(-CO)p

1

Note: (group)p is the isomer group, p is its isomer position within the molecule. Hashed cell: group parameters that are reused (transferred) from previous sequences. (CO) group: dipolar moment is fixed to experimental value, 2.7 D and dipolar fraction is fixed to 0.5. Table 2. Group contribution parameters for mg-SAFT. The dispersive energy group correction factor, α = 0.223 K. Note: (*) parameters reused from previous work [32, 33]. Chemical series

Group

ε/k (K)

σ (Å)

m

(-CH2-)

263.0678

3.9388

0.3862

A

B

C

D

µ (D)

xp*m

2.7

0.5

n-alkanes (*) Ketones R1-CO-R2

(CH3-)

192.5045

3.4965

0.7713

(CO)

405.4959

2.4320

mi = A.R1− B + C.R2− D

0.6208

0.3356

0.8589

0.5490

3.1935

−B 1

0.6852

0.1653

0.3487

2.1328

(CO)

416.7745

mi = A.R

−D 2

+ C .R

29

Table 3. Average absolute deviations (%AAD) for the liquid density (ρliq) and vapor pressure (Psat) of the ketones obtained using the mg-SAFT with and without the dipolar term. Experimental data are taken from reference [75].

Compound Correlation 2-butanone 2-pentanone 3-pentanone 2-hexanone 3-hexanone 2-heptanone 2-octanone 3-octanone 4-octanone 2-nonanone 5-nonanone Prediction 3-nonanone 4-nonanone 5-nonanone 2-undecanone 6-undecanone 2-tridecanone 8-pentadecanone

Vapor pressure, Psat AAD%

Liquid density, ρliq AAD%

T (K)

Npt

non-polar

polar

T (K)

Npt

non-polar

polar

272-536 282-544 340-544 299-427 299-407 274-452 389-446 323-440 --336-468 301-485

35 38 34 40 44 45 14 36 --35 41

2.30 1.94 1.27 0.94 0.40 1.04 6.92 2.39 --0.66 3.04

1.61 1.72 1.47 2.29 0.92 2.04 6.22 2.16 --1.15 3.61

195-319 233-353 273-347 283-332 297-324 290-428 253-433 293-360 297-321 298-437 283-356

17 18 13 16 12 35 42 21 9 37 17

0.34 0.40 0.89 0.41 0.50 0.30 0.41 0.99 1.98 0.15 2.12

1.07 0.28 0.29 0.51 0.55 0.94 0.98 0.34 1.09 1.32 1.22

265-645 247-637 267-637 298-538 298-531 335-541 443-600

39 40 38 44 44 39 25

4.10 4.39 3.57 1.15 8.10 1.23 8.34

3.51 2.16 3.32 1.13 5.72 1.82 3.63

265-645 247-637 267-637 293-432 293-358 303-433 312-351

39 40 38 26 13 25 7

2.56 4.60 3.43 0.08 2.71 2.10 3.46

1.27 3.34 2.56 1.35 1.32 2.89 1.67

30

Table 4. Oxygenated molecules parameters for PC-SAFT EoS. Bold and italic numbers are experimental data [47]. Compound

σ (Å)

m

259.49

3.5950

2.2945

239.59 249.17

3.4205 3.3265

2.6200 2.8136

322.55

4.3978

1.2603

302.73 233.56

3.7532 3.7016

1.9120 1.9913

329.82 364.18

3.9333 4.1681

2.4549 2.1052

Phenyl-acetate

262.24

3.4749

4-Phenylbutan-2-one

331.45 368.26

Acetophenone

Methyl-acetate

Acetone

ε/k (K)

εΑΒ/ κ, Κ 1620

κΑΒ 0.0005

1620

0.0005

1620 1620

0.005

µ (D))

xp*m

1.68

1.10

1.68

1.10

Note 1A schema 1A schema

2.88

0.75

0.005

1A schema 1A schema

2.88

0.75

3.21 3.21

0.70 0.70

4.2646

1.72

1.80

3.7946 4.0633

3.1594 2.6338

3.00 3.00

0.80 0.90

2B schema

315.16 324.45

3.8313 3.9110

3.0569 2.8998

1620

0.001

3.00 3.00

0.70 0.70

2B schema

Methanol (*)

193.82

3.1555

1.6538

2750

0.04613

2B schema

Ethanol (*) Water (**)

189.92 201.82

2.8913 2.8776

3.1139 1.1838

2222 1813

0.08388 0.07002

2B schema 4C schema

Benzaldehyde

1620

1620

0.001

0.001

2B schema

Pure component parameters are taken from (*) [31] and (**) [79].

31

Table 5. Average absolute deviations (%AAD) for the liquid density (ρliq) and vapor pressure (Psat) of the oxygenated molecules obtained with the PC-SAFT EoS.

Compound Methyl-acetate

Liquid density, ρliq (%)

Vapor pressure, Psat (%)

Npt

AAD%

T (K)

Npt

AAD%

186-506

30

5.66 2.15

186-506

30

1.23 0.92

1A schema/ polar polar

1.17

1A schema

3.75

1A schema/ polar

3.61

1A schema

2.02

polar

1.06

polar

1.49

2B schema

4.03 Acetone

204-508

30

4.11

183-503

30

4.59 2.6 Benzaldehyde

216-662

30

2.22

216-662

30

6.31 Phenyl-acetate

251-687

30

3.01

251-687

30

4-Phenylbutan-2-one

293-373

17

2.16

---

---

2.04

293-709

30

2.56 4.06

2B schema 293-709

30

Ref. data

[47]

[47]

[47] [47]

polar

2.68 Acetophenone

Note

T (K)

1.72

polar

1.88

2B schema

[76] [47]

32

Table 6. Average absolute deviations (%AAD) for the liquid density (ρliq), isobaric heat capacity (Cp), heat of vaporization (Hvap) and vapor pressure (Psat) of the ketones obtained using the mg-SAFT with and without the dipolar term. Experimental data are taken from DIPPR [47]. Liquid density, ρliq (AAD%) Compound T (K)

Vapor pressure, Psat (AAD%)

Heat capacity, Cp (AAD%)

Npt

nonpolar

polar

T (K)

Npt

nonpolar

polar

T (K)

Npt

nonpolar

polar

Heat of vaporization, Hvap (AAD%) T (K)

Npt

nonpolar

polar

Correlation 3-pentanone

240-560

40

2.18

1.78

240-560

40

4.38

6.81

240-374

17

0.65

9.85

240-560

40

6.55

7.39

2-hexanone

220-586

46

0.81

0.62

220-586

46

1.67

5.57

220-460

30

0.42

6.57

220-586

46

1.30

2.41

3-hexanone

220-582

46

2.01

1.30

220-582

46

1.51

6.29

220-460

30

0.66

5.99

220-582

46

5.84

6.83

2-heptanone

240-610

47

1.35

1.07

240-610

47

2.27

5.46

240-490

32

0.60

3.81

240-610

47

2.03

2.19

2-octanone

255-631

47

1.80

1.42

255-631

47

2.80

4.77

255-499

31

0.66

2.47

255-631

47

3.25

2.86

3-octanone

260-626

46

1.45

0.89

260-626

46

2.40

3.79

260-440

23

1.08

2.54

260-626

46

3.64

4.28

4-octanone

250-622

47

3.78

2.26

250-622

47

5.86

4.06

250-436

24

1.09

2.68

250-622

47

7.55

6.68

2-nonanone

270-652

48

1.10

1.26

270-652

48

3.52

4.41

270-510

30

0.80

1.78

270-652

48

4.31

4.03

5-nonanone

270-640

47

3.79

2.29

270-640

47

3.59

5.72

270-510

30

0.74

2.02

270-640

46

4.28

3.92

Prediction 3-heptanone

235-605

47

1.91

0.64

235-605

47

9.40

6.68

235-479

31

0.84

3.70

235-605

47

5.44

4.78

3-nonanone

270-648

48

2.73

1.10

270-648

48

3.85

2.33

270-460

24

2.30

2.44

270-648

48

8.22

8.40

4-heptanone

245-601

45

3.77

2.89

245-601

45

7.38

5.35

245-479

30

2.05

3.00

245-601

45

6.47

5.88

4-nonanone

250-642

49

5.01

3.08

250-642

49

4.33

2.05

250-460

27

2.20

2.88

250-642

49

3.96

6-undecanone

290-678

49

4.41

2.61

290-678

49

11.80

11.64

290-678

49

8.36

7.80

---

---

---

4.05 ---

X exp − X cal 1 The average absolute deviation of a property X is defined as: % AAD X = ∑ ; n is the n n X exp number of data points of property X, Xexp is the experimental value, and Xcal is the calculated value for the same property under the conditions.

33

Figure caption Figure 1. Vapor pressures and isobaric heat capacity of the ketones. The symbols represent the experimental data [47] while the solid lines correspond to the non-polar mg-SAFT description. Figure 2. Single phase densities of ketones. Symbols are experimental data [83, 84]. Solid lines are prediction results of non-polar mg-SAFT. Figure 3. Single phase densities of ketones. Symbols are experimental data [34] Solid lines are prediction results of polar mg-SAFT. Figure 4. VLE phase diagram of ketone + n-alkane mixtures. Symbols are experimental data [85-88]. Solid lines are mg-SAFT prediction results. Figure 5. VLE phase diagram of ketone + n-alkane mixtures at 1 bar condition. Symbols are experimental data [85-88]. Solid lines are mg-SAFT prediction results. Figure 6. Effects of the association and dipolar terms on LLE/VLE phase diagram of acetone + nheptane and methyl-acetate + n-heptane mixtures. Symbols are experimental data [89, 90]. Lines are mg-SAFT computation results using different parameter sets. Figure 7. VLE and LLE phase diagram of acetone + alkane mixtures. Symbols are experimental data taken from references [91-93] and [88, 94-98]. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term. Figure 8. VLE phase diagram of acetone + alkane mixtures. Symbols are experimental data taken from references [99-101]. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term. Figure 9. VLE and LLE phase diagram of methyl-acetate + alkane mixtures. Symbols are experimental data taken from references [89, 90] and [25]. Solid lines are mg-SAFT computation results by considering methyl-acetate is associative molecule type 1A with dipolar term. Figure 10. Effects of cross-association and dispersive binary interaction parameter kij on VLE phase diagram of acetone + methanol [102], acetone + ethanol [103], methyl-acetate + methanol [104] and 2butanone + ethanol [105, 106] mixtures. Symbols are experimental data. Lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term while 2butanone and methyl-acetate are dipolar, non-associative. Figure 11. LLE phase diagram of oxygenated aromatic containing mixtures (kij is linearly correlated versus the carbon number of n-alkane for PC-SAFT). Symbols are experimental data [28, 80, 107]. Figure 12. VLE/LLE phase diagram of water + acetone [108, 109], water + 2-butanone [80, 110-113]. Symbols are experimental data. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term while 2-butanone is dipolar molecule. Figure 13. LLE phase diagram of water + acetophenone [113], water + phenyl-acetate [114], water + benzaldehyde [115] and water + methyl-acetate mixtures [116, 117]. Symbols are experimental data. Solid lines are mg-SAFT computation results by considering oxygenated molecules are polar molecule. Figure 14. Comparison of LLE/ VLE calculation results of acetone + n-octane, phenylacetate + alkanes, benzaldehyde + n-dodecane and acetone + water, using sPC-SAFT [11], DISQUAC [80], UNIFAC [12] and this work.

34

2-pentanone 3-pentanone 2-hexanone 3-hexanone 3-octanone 2-nonanone mg-SAFT

1

0.1

450

2-butanone 2-hexanone 2-octanone mg-SAFT

400

3-pentanone 3-heptanone 5-nonanone

350

CP (J/mol-K)

Pressure (bar)

10

300 250 200

0.01

150 0.001 0.002

100 0.0025

0.003 1/T (K)

0.0035

0.004

150

300 T (K)

450

Figure 1. Vapor pressures and isobaric heat capacity of the ketones. The symbols represent the experimental data [47] while the solid lines correspond to the non-polar mg-SAFT description.

rsat exp 338.15 K mg-SAFT

1000 100

278.15 K 473.15 K

P (bar)

10 4,000 3,500

1

3,000

2-hexanone 2,000

1 1,500

2,500

0.1

0.1

2,000

1,000

1,500

0.01

0.01

1,000

500

500

0.001

0.001

0 650

0.0001 0

298.15 K 473.15 K

100

10

P (bar)

rsat exp 373.15 K mg-SAFT

1000

150

800

300

950

3-pentanone

450 600 750 density, ρ (g/l)

900

0 650

0.0001 0

150

800

300

950

450 600 750 density, ρ (g/l)

900

Figure 2. Single phase densities of ketones. Symbols are experimental data [83, 84]. Solid lines are prediction results of non-polar mg-SAFT.

35

rsat exp 373.15 K mg-SAFT

1000

293.15 K 473.15 K

100

273.15 K 473.15 K

100

10

10

2-octanone

1

2,000

0.1

1,500

P (bar)

P (bar)

rsat exp 373.15 K mg-SAFT

1000

2-nonanone 1

2,000

0.1

1,500

1,000

0.01

1,000

0.01 500

500

0.001

0.001 0

0 650

0.0001 0

150

800

300

950

450 600 750 density, ρ (g/l)

650

0.0001 900

0

150

800

300

950

450 600 750 density, ρ (g/l)

900

Figure 3. Single phase densities of ketones. Symbols are experimental data [34] Solid lines are prediction results of polar mg-SAFT. 1.1

0.4

Pressure (bar)

Pressure (bar)

0.35

0.9

0.7

0.3

0.25

0.2 338.15 K 333.15 K mg-SAFT

318.15 K 323.15 K mg-SAFT

0.15

0.5

0.1 0.0

0.2 0.4 0.6 0.8 2-butanone mole fraction (+n-hexane)

1.0

0.0

0.2 0.4 0.6 0.8 2-butanone mole fraction (+n-heptane)

1.0

36

0.7

1.2 313.15 K

353.15 K

338.15 K

0.6

Pressure (bar)

Pressure (bar)

333.15 K

1

mg-SAFT 0.5 0.4 0.3

mg-SAFT

0.8

0.6

0.4 0.2 0.2

0.1 0

0 0.2 0.4 0.6 0.8 2-butanone mole fraction (+n-octane)

1.0

0.0

1.2

1.2

1

1

Pressure (bar)

Pressure (bar)

0.0

0.8

0.6

0.4

0.2 0.4 0.6 0.8 1.0 2-butanone mole fraction (+n-dodecane)

4-heptanone + C6 (338.15 K) 3-pentanone + C6 (338.15 K) mg-SAFT

0.8

0.6

0.4 353.15 K 368.15 K 338.15 K mg-SAFT

0.2

0 0.0

0.2 0.4 0.6 0.8 3-pentanone mole fraction (+n-heptane)

0.2

0 1.0

0.0

0.2 0.4 0.6 0.8 n-hexane mole fraction (+ketone)

1.0

Figure 4. VLE phase diagram of ketone + n-alkane mixtures. Symbols are experimental data [85-88]. Solid lines are mg-SAFT prediction results.

37

415

+C9 +C10 +C8 mg-SAFT

410

Temperature (K)

Temperature (K)

405

+C9 +C10 +C8 mg-SAFT

395

385

395

380 375

365

365 0.0

420

1.0

0.0

0.2 0.4 0.6 0.8 n-alkane mole fraction (+3-heptanone)

1.5

+C9 +C10 +C8 mg-SAFT

400

390

1.0

343.15 K 353.15 K 333.15 K mg-SAFT

1.2

Pressure (bar)

410

Temperature (K)

0.2 0.4 0.6 0.8 n-alkane mole fraction (+2-heptanone)

0.9

0.6

380 0.3

370

360

0 0.0

0.2 0.4 0.6 0.8 n-alkane mole fraction (+4-heptanone)

1.0

0.0

0.2 0.4 0.6 0.8 5-nonanone mole fraction (+n-hexane)

1.0

Figure 5. VLE phase diagram of ketone + n-alkane mixtures at 1 bar condition. Symbols are experimental data [85-88]. Solid lines are mg-SAFT prediction results.

38

380

370 360

350

340

310

asso+dipolar (kij=-0.022) Asso (kij=0.053) dipolar (kij=-0.05)

290

Temperature (K)

Temperature (K)

330

270 250

320 asso+dipolar (kij=-0.008) Asso (kij=0.04) dipolar (kij=-0.011)

300 280 260

230 240

210

220

190

200

170 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-heptane)

0.0

1.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+n-heptane)

Figure 6. Effects of the association and dipolar terms on LLE/VLE phase diagram of acetone + nheptane and methyl-acetate + n-heptane mixtures. Symbols are experimental data [89, 90]. Lines are

350

350

330

330

310

310

290

290

LLE/ VLE

270

mg-SAFT (kij=-0.021)

Temperature (K)

Temperature (K)

mg-SAFT computation results using different parameter sets.

LLE/ VLE

270

mg-SAFT (kij=-0.02) 250 230

250 230

210

210

190

190

170

170 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-pentane)

1.0

0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-hexane)

1.0

39

420 420

Temperature (K)

Temperature (K)

370

320

270

220

370

320

270

220

LLE/ VLE mg-SAFT (kij=-0.024)

LLE/ VLE mg-SAFT (kij=-0.025)

170

170 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-nonane)

1.0

0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-decane)

1.0

380

520

360 470

340 LLE/ VLE mg-SAFT (kij=-0.028)

370

Temperature (K)

Temperature (K)

420

320

320 300

LLE/ VLE mg-SAFT (kij=-0.038)

280 260 240

270

220 220

200 180

170 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-tridecane)

1.0

0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+iso-octane)

1.0

Figure 7. VLE and LLE phase diagram of acetone + alkane mixtures. Symbols are experimental data taken from references [91-93] and [88, 94-98]. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term.

40

0.75

16

0.6

Temperature (K)

Pressure (bar)

20

12

8

0.45

+C8 (kij=-0.023)

0.3

+C9 (kij=-0.024) +C6 (kij=-0.021)

4

0.15 397.7 K

422.6 K

372.7 K

mg-SAFT (kij=0)

0

0 0.0

1.5

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-pentane)

0.0

1.0

1.8

mg-SAFT (kij=-0.022)

1.5

Pressure (bar)

Pressure (bar)

273.15 K 338.15 K

1

0.5

1.0

313.15 K 333.15 K 338.15 K mg-SAFT (kij=-0.025)

323.15 K 313.15 K

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-alkane)

1.2

0.9

0.6

0.3

0

0 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-heptane)

1.0

0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-decane)

1.0

Figure 8. VLE phase diagram of acetone + alkane mixtures. Symbols are experimental data taken from references [99-101]. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term.

41

360

340

340

320

Temperature (K)

LLE/ VLE

280

mg-SAFT (kij=0.008) 260 240

Temperature (K)

320 300

300 LLE/ VLE 280

mg-SAFT (kij=0.008)

260 240

220

220 200

200 0.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+n-pentane)

0.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+n-hexane)

380 400 360 340

300

LLE/ VLE

280

mg-SAFT (kij=0.008)

260

Temperature (K)

Temperature (K)

350 320

300

LLE/ VLE mg-SAFT (kij=0.008)

250

240 220 200

200 0.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+n-hepane)

0.0

0.2 0.4 0.6 0.8 Methyl-acetate mole fraction (+n-octane)

1.0

42

440

400 380 360

360

320 LLE/ VLE mg-SAFT (kij=0.008)

280

Temperature (K)

Temperature (K)

400

340 320 300

LLE/ VLE

280

mg-SAFT (kij=0.0)

260 240

240

220 200

200 0.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+n-nonane)

0.0

0.2 0.4 0.6 0.8 1.0 Methyl-acetate mole fraction (+iso-octane)

Figure 9. VLE and LLE phase diagram of methyl-acetate + alkane mixtures. Symbols are experimental data taken from references [89, 90] and [25]. Solid lines are mg-SAFT computation results by considering methyl-acetate is associative molecule type 1A with dipolar term.

43

1.2 19 17

Pressure (bar)

Pressure (bar)

1

0.8

0.6

0.4

400 K 425 K 375 K PC-SAFT (kij=-0.02)

15 13 11 9 7

318.15 328.15 308.15 with cross-link (kij=0) non cross-link (kij=0)

0.2

0 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+methanol)

5 3 1 0.0

1.0

1

0.2 0.4 0.6 0.8 Acetone mole fraction (+ethanol)

1.0

0.15 0.14

0.9

Pressure (bar)

Pressure (bar)

0.13 0.8 0.7 0.6

0.12 0.11 0.1 0.09

0.5 322.91 K 312.91 K 1 cross-link (wij=0.191, kij=0) non-cross (kij=-0.1)

0.4 0.3 0.0

298.15 K 328.15 K 1 cross-link (wij=0.285, kij=0) non-cross (kij=-0.05)

0.08 0.07 0.06

0.2 0.4 0.6 0.8 1.0 Methanol mole fraction (+n-methyl-acetate)

0.0

0.2 0.4 0.6 0.8 2-butanone mole fraction (+ethanol)

1.0

Figure 10. Effects of cross-association and dispersive binary interaction parameter kij on VLE phase diagram of acetone + methanol [102], acetone + ethanol [103], methyl-acetate + methanol [104] and 2butanone + ethanol [105, 106] mixtures. Symbols are experimental data. Lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term while 2butanone and methyl-acetate are dipolar, non-associative.

44

310

300 295

+C12 (kij=-0.029) +C14 (kij=-0.027) +C16 (kij=-0.025) +C10 (kij=-0.031) asso + dipolar dipolar

320 310

Temperature (K)

305

Temperature (K)

330

+C10 (kij=-0.016) +C12 (kij=-0.0155) +C14 (kij=-0.015) +C16 (kij=-0.0145) asso + dipolar dipolar

290 285 280 275

300 290 280

270 270

265 260

260 0.0

310

1.0

295

Binary interaction parameter (kij)

300

0.0

0.2 0.4 0.6 0.8 1.0 4-Phenylbutan-2-one mole fraction (+alkane)

0.03

+C10 (kij=-0.023) +C12 (kij=-0.021) +C14 (kij=-0.0208) +C16 (kij=-0.0195) asso + dipolar dipolar

305

Temperature (K)

0.2 0.4 0.6 0.8 Acetophennone mole fraction (+alkane)

290 285 280 275 270 265 260

Acetophenone 4-Phenylbutan-2-one Phenyl-acetate Methyl-acetate Acetone

0.02 0.01 0 -0.01 -0.02 -0.03 -0.04

0.0

0.2 0.4 0.6 0.8 Benzaldehyde mole fraction (+alkane)

1.0

4

8 12 Alkane carbon number

16

Figure 11. LLE phase diagram of oxygenated aromatic containing mixtures (kij is linearly correlated versus the carbon number of n-alkane for PC-SAFT). Symbols are experimental data [28, 80, 107].

45

70

490

523.15 K

60

mg-SAFT (kij=-0.049)

473.15 K 373.15 K

50

440

PC-SAFT (kij=-0.095)

Tempereture (K)

Pressure (bar)

MEK+W

423.15 K

40 30

390

340

20 290

10 0

240 0.0

0.2 0.4 0.6 0.8 Water mole fraction (+acetone)

1.0

0.0

0.2 0.4 0.6 0.8 2-butanone mole fraction (+water)

1.0

Figure 12. VLE/LLE phase diagram of water + acetone [108, 109], water + 2-butanone [80, 110-113]. Symbols are experimental data. Solid lines are mg-SAFT computation results by considering acetone is associative molecule type 1A with dipolar term while 2-butanone is dipolar molecule.

46

380

380 LLE

PC-SAFT (kij=0.013/wij=0.073)

LLE

PC-SAFT (kij=-0.009/wij=0.085)

370 360

350

Temperature (K)

Temperature (K)

360

340 330 320

340

320

300

310 280 300 290 0.0001

260 0.0001

0.001 0.01 0.1 Acetophenone mole fraction (+water)

390

0.001 0.01 0.1 Phenyl-acetate mole fraction (+water)

1

370 LLE

PC-SAFT (kij=0.02/ wij=0.128)

LLE

PC-SAFT (kij=-0.046/wij=-0.3)

360 350

Temperature (K)

Temperature (K)

370

350

330

310

340 330 320 310 300 290

290

280 270 0.0001

270 0.001 0.01 0.1 Benzaldehyde mole fraction (+water)

1

0.0

0.2 0.4 0.6 Methyl-acetate mole fraction (+water)

0.8

Figure 13. LLE phase diagram of water + acetophenone [113], water + phenyl-acetate [114], water + benzaldehyde [115] and water + methyl-acetate mixtures [116, 117]. Symbols are experimental data. Solid lines are mg-SAFT computation results by considering oxygenated molecules are polar molecule.

47

420

320

+C14 (kij=-0.006) +C16 (kij=-0.005) +C7 (kij=-0.0105) DISQUAC mg-SAFT (dipolar)

310 300

Temperature (K)

Temperature (K)

370

Acetone + C8 mg-SAFT (kij=-0.023) UNIFAC

320

270

290 280 270

220 260 170

250 0.0

0.2 0.4 0.6 0.8 Acetone mole fraction (+n-octane)

1.0

0.0

320

0.2 0.4 0.6 0.8 Phenyl-acetate mole fraction (+alkane)

1.0

35 +C12 mg-SAFT

310

Pressure (bar)

Pressure (bar)

DISQUAC 300

290

30

25

280 20 473.15 K

270

mg-SAFT sPC-SAFT

260

15 0.0

0.2 0.4 0.6 0.8 1.0 Benzaldehyde mole fraction (+n-dodecane)

0.0

0.2 0.4 0.6 0.8 Water mole fraction (+acetone)

1.0

Figure 14. Comparison of LLE/ VLE calculation results of acetone + n-octane, phenylacetate + alkanes, benzaldehyde + n-dodecane and acetone + water, using sPC-SAFT [11], DISQUAC [80], UNIFAC [12] and this work.

48

Conflicts of Interest Statement

Manuscript title: “Phase equilibria of systems containing oxygenated compounds: polar or “pseudo-association” approach?” The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Author names: 1. NguyenHuynh Dong, 2. Tran Thi Kim Siem, 3. Mai Thi Quynh Chau.

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