Simple three parameter equations for correlating liquid phase compositions in subcritical and...

Accepted Manuscript

Title: Simple Three Parameter Equations for CorrelatingLiquid Phase Compositions in Subcritical and SupercriticalSystems

Author: Ram C. Narayan Giridhar Madras

PII: S0896-8446(14)00243-5DOI: http://dx.doi.org/doi:10.1016/j.supflu.2014.08.010Reference: SUPFLU 3055

To appear in: J. of Supercritical Fluids

Received date: 22-5-2014Revised date: 1-8-2014Accepted date: 3-8-2014

Please cite this article as: R.C. Narayan, G. Madras, Simple ThreeParameter Equations for Correlating Liquid Phase Compositions in Subcriticaland Supercritical Systems, The Journal of Supercritical Fluids (2014),http://dx.doi.org/10.1016/j.supflu.2014.08.010

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http://dx.doi.org/doi:10.1016/j.supflu.2014.08.010

http://dx.doi.org/10.1016/j.supflu.2014.08.010

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Highlights • Two Chrastil type expressions to correlate liquid phase data within AARD of 5%

• Model requires only three tunable parameters

• Potential to be used for testing self-consistency of experimental data

• Applicability of the expressions over a wide range of temperatures and pressures

• Applicability over a wide range of liquid solutes like alcohols, esters and ionic liquids.

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Graphical abstract

3.0 3.5 4.0 4.5 5.0 5.5 6.0

36

37

38

ln X

Gas

- B

ln T

ln ρ0.04 0.06 0.08 0.10 0.12

16.0

16.5

17.0

ln X

Gas

- B ln

T

lnρ/P

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Simple Three Parameter Equations for Correlating Liquid Phase

Compositions in Subcritical and Supercritical Systems

Ram C Narayan and Giridhar Madras*

Department of Chemical Engineering,

Indian Institute of Science, Bangalore 560012, India

Abstract

Two Chrastil type expressions have been developed to model the solubility of

supercritical fluids/ gases in liquids. The three parameter expressions proposed correlates

the solubility as a function of temperature, pressure and density. The equation can also be

used to check the self consistency of the experimental data of liquid phase compositions

for supercritical fluid-liquid equilibria. Fifty three different binary systems (carbon-

dioxide + liquid) with around 2700 data points encompassing a wide range of compounds

like esters, alcohols, carboxylic acids and ionic liquids were successfully modeled for a

wide range of temperatures and pressures. Besides the test for self-consistency, based on

the data at one temperature, the model can be used to predict the solubility of

supercritical fluids in liquids at different temperatures.

Keywords: Supercritical solubility; Henry’s law; Binary system; Mendez-Teja model

* Corresponding author. Tel. +91 80 22932321; Fax: +91 80 23600683 Email: [email protected] (G.Madras)

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1. Introduction

The understanding of phase equilibria is very important in order to capitalize on the

unique characteristics of supercritical fluids for its various applications in chemical

engineering and biotechnology [1]. Two approaches are used in modeling solubility data

of supercritical systems: the equation of state method and the empirical/semi-empirical

method. The former method is theoretically robust but requires pure component

properties and appropriate mixing rules. The empirical/semi-empirical methods do not

require additional solute properties and is thus more convenient to apply. These models

relate solubility directly to operation parameters like pressure and temperature (and thus

density) [2, 3].

In supercritical fluid-solid equilibria, the solubility of supercritical fluid in the

solid phase is almost negligible. In case of supercritical/vapor- liquid systems, both

phases need to be modeled to obtain a complete picture of the equilibria, as both solute

liquid and vapor/ supercritical phase are soluble in each other. This could also be more

relevant in case of processing solid compounds in supercritical fluids at temperatures

close to the melting point of the solid solutes and their mixtures [4, 5]. The supercritical

fluid dissolved in the liquid can have a pronounced effect on the composition of the vapor

phase. The higher the solubility of liquid in the vapor phase, the higher is the

corresponding solubility of vapor phase/SCF in the liquid phase [6]. There are several

models to correlate the vapor phase data in case of solids and liquids empirically or semi-

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empirically [7-12]. A wide range of liquid compounds such as lipids and ionic liquids are

processed using supercritical fluids [13-15]. However, to the best of our knowledge,

empirical/semi-empirical models correlating liquid phase data are scarce [16-18]. One of

the earliest approaches to describe the solubility of gases in liquid is the Henry’s law,

which postulates a linear dependence of mole fraction of solute gas in liquid to the partial

pressure of the liquid. Theoretically, this law assumes infinite dilution for solute gas and

low partial pressures in vapor/gas phase. Thus, it is popularly used in environmental

applications for estimating pollutant solubility or volatility [19, 20]. To overcome the

shortcoming relating to the applicability at low pressures, the Krichevsky-Kasarnovsky

equation [21] was developed to calculate the Henry’s law constant for wide pressure

ranges for extremely low solvent vapor pressures. However, in supercritical fluid-liquid

systems, the solubility of the vapor phase in liquid cannot be considered dilute and thus

these equations are not directly applicable.

In a recent pioneering work [16, 17], the liquid phase compositions were

correlated directly with the density of supercritical fluid with a simple Chrastil type

expression developed empirically from Henry’s law. The objective of this work was to

extend the equation developed by these authors to accommodate for the dependence of

solubility on temperature. The equation can be used to determine the self-consistency of

the experimental data of the solubilities of supercritical fluids in liquids at various

temperatures.

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2. Theoretical Background

Chrastil equation was one of the first models proposed to correlate solubility of

solutes in a supercritical fluid. It related the solubility of the solute to the density and

temperature as [7]

'ln ln 'aS bT

κ ρ= + + (1)

S (kg.m-3) is the solubility of liquid/solid solute in the supercritical fluid and ρ (kg.m-3) is

the density of the supercritical fluid and T (K) is the temperature of system. This is a

simple correlation for modeling vapor phase experimental data. As discussed earlier, in

case of supercritical fluid-liquid systems, there are very few empirical or semi-empirical

models to correlate liquid phase data, i.e. to express liquid phase compositions as a

function of operating conditions, like pressure and temperature.

At very low pressures, the gas behaves ideally; hence, Henry’s law follows. The

following equation can be written

GasHGas PkX = (2)

XGas is the solubility of the supercritical fluid/ vapor in liquid, PGas (MPa) is the

partial pressure of the solute gas in the vapor phase. kH is the inverse of the classical

Henry’s law constant. This notation is used as liquid phase compositions need to be

correlated. Eq. (2) can be rewritten as follows:

VGasGas YHX ρ'= (3)

H’ is the temperature dependent constant ( RTkH H=' ), YGas is the mole-fraction

of the gas/supercritical fluid in the vapor phase of the system and Vρ is the density of the

vapor phase and. As vapor phase solubility of liquids in supercritical fluids/gases is less

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than a few mole percent, the vapor phase can be considered pure i.e. YGas ≈ 1 and Vρ ≈ ρ ,

where ρ is the density of the supercritical fluid/ gas, the following equation is obtained:

ln ln ln H'GasX A ρ= + (4)

In the above expression, A is a constant. The above Eq. (4) was derived by Fornari et al.

[16]. Eq. (4) is valid only at a particular temperature. This work therefore attempts to

extend the correlation to all temperatures.

The Henry’s law constant kH is related to the temperature, by the van’t Hoff equation [22]

given by

2

lnRT

HdT

kd disH Δ−= (5a)

disHΔ is the heat of dissolution (J mol-1), which is the difference between heat of

vaporization and excess heat of solution and R is the universal gas constant (J mol-1K-1).

For a wide temperature range, the heat of dissolution can be assumed to be a function of

temperature. Considering linear dependence of heat of dissolution with temperature, with

e (J mol-1) and f (J mol-1 K-1) as parameters, Eq. 5(a) would be modified to

2

ln (e )Hd k fTdT RT

− += (5b)

Integration of the above equation and using RTkH H=' , H’ can be correlated with

temperature to yield the following expression:

ln ' ln CH B T DT

= + + (6)

In Eq. (6), eCR

= , 1 fBR

⎛ ⎞= −⎜ ⎟⎝ ⎠

and ln R constantN = + .Substituting the above

expression in Eq. (4), the following equations are obtained

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ln ln lnGasCX A B T DT

ρ= + + + (7a)

ln *ln ( *) *ln *GasCX A B T D

P Tρ

= + + + (7b)

for smaller and higher molecular weight compounds respectively, where A,B,C and D

are temperature independent adjustable parameters. In Eq. 7(a), ln ρ is replaced by

lnPρ to account for the negative deviation from Henry’s Law (for higher molecular

weight compounds) [16] to obtain Eq. 7(b) with temperature independent adjustable

parameters A*, B*, C* and D*.

3. Results and Discussion

Liquid phase compositions of various binary mixtures of carbon dioxide + liquid

were collected from published literature. A wide range of solutes, ranging from alcohols,

ketones, hydrocarbons, esters, carboxylic acid, water and ionic liquids was considered.

Both sub and supercritical conditions were included in the dataset. Fatty acid esters and

alcohols with various chain lengths were selected due to their relevance in lipid

processing and biodiesel/biolubricant production. In more recent investigations,

supercritical fluids were used to extract solid/liquid solutes from ionic liquids post

reaction or extraction. Thus liquid phase data of binary systems (carbon dioxide + ionic

liquid) containing ionic liquids with different cation chain length (ethyl, butyl, octyl and

dimethyl) and anion functionality (hexafluorophosphatyl (PF6), trifluorosulphonyl(TF3N)

and tetrafluoroborate(BF4)) were considered. Hydrocarbon systems, including short and

long chain hydrocarbons and aromatic compounds were included due to their significance

in petroleum processing.

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The density of carbon-dioxide was calculated using the twenty-seven parameter equation

of state [23]. Multiple linear regression was then carried out using POLYMATH 5.1®.

The value of AARD (%) was calculated to quantify the deviation of the predicted from

experimental data. It is expressed as:

1

ˆ1(%) 100N Gas Gas

i Gas

X XAARD x

N X=

⎛ ⎞−⎜ ⎟=⎜ ⎟⎝ ⎠∑ (8)

where GasX and GasX̂ are the solubility of supercritical fluid in liquid determined

experimentally and predicted by the model and N is the number of data points. For

smaller molecular weight compounds, around 800 data points were collected from a

broad temperature range from 277 K to 477 K and pressures in the range 0.1 MPa to 19.2

MPa. As discussed earlier, ln ρ is replaced by lnPρ term to account for the negative

deviation prevalent in higher molecular weight compounds from Henry’s law. More

binary systems were considered for this case due to the increased importance of higher

molecular weight compounds in supercritical processes. The database consisted of 1800

liquid phase composition data points in the temperature range 297 K to 473 K and in the

pressure range of 0.5 MPa to 97 MPa.

For smaller molecular weight components like short chain alkanes, alcohols etc,

Eq. (7a) was used to correlate the data. For higher molecular weight compounds like fatty

acid esters, higher alcohols, higher hydrocarbons, water and ionic fluids, Eq. (7b) was

used to correlate data. In most cases, the coefficient of 1/T was statistically insignificant

and this term could thus be omitted (C = C* =0) in Eq. (7a) and Eq. (7b), leading to an

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expression with lower number of parameters. Hence the final expressions for correlating

the solubility of supercritical fluid/vapor in liquid are:

ln ln lnGasX A B T Dρ= + + (9a)

lnln ( *) *ln *GasX A B T DPρ

= + + (9b)

Eq. (9a) and Eq. (9b) were used to model the liquid solubility for the low and high

molecular weight compounds, respectively. As an example, the statistical analysis of the

multiple linear regression for carbon-dioxide + methyl oleate system is shown in Table 1.

High F value and very low p values suggest statistically significant parameter values.

In the case of smaller molecular weight compounds, the regression coefficients

were found to be greater than 0.97 for all the compounds considered. The values of

parameters ‘A’ and ‘B’ and ‘D’ are shown in Table 2, with standard error (S.E) of the

estimated parameters obtained by multiple linear regression, which was related to the

residual sum of squares error (RSS) given by ( )2

Gas Gasˆ

NRSS X X= −∑ .The average

deviation obtained using this model was around 5.6 % with AARD (%) varying from

1.7% to 13%. From Table 2, it can be observed that ‘A’ values are positive and ‘B’

values are negative. Thus, at constant temperature, the solubility of carbon dioxide in the

liquid exponentially increases with density. This is consistent with the observations made

by Fornari et al. [16]. The ‘B’ values are negative for all the compounds analyzed, which

implies an increase in temperature at constant density conditions results in lower

solubility of the gas/supercritical fluid in the liquid of interest. This can be seen in the

plots wherein the variation of ln XGas is plotted against ln ρ, where the value of the

intercept on the Y-axis keeps decreasing with increasing temperature, suggesting an

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inverse relationship. The ‘B’ value ranges from –0.9 to −7.0 for different compounds.

The higher ‘B’ value indicates a sharper decrease in solubility of gas with increasing

temperature. However, solubility of liquids/ solids in supercritical fluids increases with

temperature at constant density for most compounds due to increase in vapor pressure of

the solid [13].

In case of higher-molecular weight compounds, the average deviation was about

4.6 %, with regression coefficients greater than 0.95 in most cases, with AARD (%)

varying from 0.9% to 11.7%. The A*, B* and D* values are represented in Table 3.

Contrary to the smaller molecular weight compounds, the A* values are all negative

ranging from −5 to −25. The value of A* decreases with increase in molecular weight of

the fatty acid ester, higher alcohols and ionic liquids. The B* values are also negative but

showed no specific trend; ranging from −0.4 to −5. As in case of smaller molecular

weight compounds, solubility decreases at higher temperatures at constant density

conditions.

Eq. (9a) and (9b) can be rearranged with the ln T on the left hand side, to yield

ln ln lnGasX B T A Dρ− = + (10a)

lnln *ln * *GasX B T A DPρ

− = + (10b)

In the above equations, the left hand side is a function of temperature and right hand side

is a function of density. When the left hand side of each of these equation was plotted

against ln ρ or lnPρ , a single straight line with slope A or A* and intercept D or D* is

obtained. All the isotherms fall onto this line. Thus the equation could be used to check

the self consistency of the experimental data.

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To illustrate this, liquid solubility values of various compounds were plotted.

Figures 1(a) and 1(b) represent the straight line plots for small molecular weight

compounds while Figures 2(a) and 2(b) show straight line plots for high-molecular

weight compounds. This model could be concomitant to the Mendez-Teja model [24]

used for correlating and checking self-consistency for solubility of solids in supercritical

fluids.

4. Conclusions

Two semi-empirical expressions with three parameters were used to correlate the

liquid phase data in vapor/supercritical fluid-liquid equilibria in a wide temperature and

pressure range. Several binary systems consisting of both lower and higher molecular

weight compounds were considered and an average deviation of around 5% was

obtained, with correlation coefficients greater than 0.95. The expressions were

represented graphically such that different isotherms fell on a single straight line for all

the binary systems tested. This expression could be used to test the self consistency of the

liquid phase data like the Mendez-Teja model, which is used to test the self-consistency

of the solubilities of solid phase in supercritical fluids.

Acknowledgments

The authors thank the Council of Scientific and Industrial Research (CSIR) for financial

support.

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5. References

[1] G. Madras, C. Erkey, A. Akgerman, M.A. McHugh, Supercritical extraction of organic contaminants from soil combined with adsorption onto activated carbon, Environ. Prog., 13 (1994) 45-50.

[2] M. Skerget, Z. Knez, M. Knez-Hrncic, Solubility of solids in sub-and supercritical fluids: a review, J. Chem. Eng. Data, 56 (2011) 694-719.

[3] R. Marr, T. Gamse, Use of supercritical fluids for different processes including new developments—a review, Chem. Eng. Process., 39 (2000) 19-28.

[4] F.P. Lucien, N.R. Foster, Solubilities of solid mixtures in supercritical carbon dioxide: a review, J. Supercrit. Fluids, 17 (2000) 111-134.

[5] W. Nilsson, J. Hudson, Solubility of simple and mixed triacylglycerols in supercritical CO2, J. Am. Oil Chem. Soc., 70 (1993) 749-754.

[6] G. Brunner, Selectivity of supercritical compounds and entrainers with respect to model substances, Fluid Phase Equilib., 10 (1983) 289-298.

[7] J. Chrastil, Solubility of solids and liquids in supercritical gases, J. Phys. Chem., 86 (1982) 3016-3021.

[8] C. Garlapati, G. Madras, Solubilities of solids in supercritical fluids using dimensionally consistent modified solvate complex models, Fluid Phase Equilib., 283 (2009) 97-101.

[9] H.-D. Sung, J.-J. Shim, Solubility of CI disperse red 60 and CI disperse blue 60 in supercritical carbon dioxide, J. Chem. Eng. Data, 44 (1999) 985-989.

[10] J.C. González, M.R. Vieytes, A.M. Botana, J.M. Vieites, L.M. Botana, Modified mass action law-based model to correlate the solubility of solids and liquids in entrained supercritical carbon dioxide, J. Chromatogr. A, 910 (2001) 119-125.

[11] J.-l. Li, J.-s. Jin, Z.-t. Zhang, X.-m. Pei, Equilibrium solubilities of a p-toluenesulfonamide and sulfanilamide mixture in supercritical carbon dioxide with and without ethanol, J. Supercrit. Fluids, 52 (2010) 11-17.

of 25

Accep

ted

Man

uscr

ipt

[12] Z.-R. Yu, B. Singh, S.S. Rizvi, J.A. Zollweg, Solubilities of fatty acids, fatty acid esters, triglycerides, and fats and oils in supercritical carbon dioxide, J. Supercrit. Fluids, 7 (1994) 51-59.

[13] Ö. Güçlü-Üstündag, F. Temelli, Correlating the solubility behavior of fatty acids, mono-, di-, and triglycerides, and fatty acid esters in supercritical carbon dioxide, Ind. Eng. Chem. Res., 39 (2000) 4756-4766.

[14] L.A. Blanchard, J.F. Brennecke, Recovery of organic products from ionic liquids using supercritical carbon dioxide, Ind. Eng. Chem. Res., 40 (2001) 287-292.

[15] S. Keskin, D. Kayrak-Talay, U. Akman, Ö. Hortaçsu, A review of ionic liquids towards supercritical fluid applications, J. Supercrit. Fluids, 43 (2007) 150-180.

[16] T. Fornari, E.J. Hernández, G. Reglero, Solubility of supercritical gases in organic liquids, J. Supercrit. Fluids, 51 (2009) 115-122.

[17] E.J. Hernández, G. Reglero, T. Fornari, Correlating the solubility of supercritical gases in high-molecular weight substances using a density-dependent equation, AIChE J., 57 (2011) 765-771.

[18] Á. Pérez-Salado Kamps, D. Tuma, J. Xia, G. Maurer, Solubility of CO2 in the ionic liquid [bmim][PF6], J. Chem. Eng. Data, 48 (2003) 746-749.

[19] D. Mackay, W.Y. Shiu, R.P. Sutherland, Determination of air-water Henry's law constants for hydrophobic pollutants, Environ. Sci. Technol., 13 (1979) 333-337.

[20] J. Staudinger, P.V. Roberts, A critical review of Henry's law constants for environmental applications, Crit.Rev.Env.Sci.Tec, 26 (1996) 205-297.

[21] I. Krichevsky, J. Kasarnovsky, Thermodynamical calculations of solubilities of nitrogen and hydrogen in water at high pressures, J. Am. Chem. Soc., 57 (1935) 2168-2171.

[22] G. Heron, T.H. Christensen, C.G. Enfield, Henry's law constant for trichloroethylene between 10 and 95 C, Environ. Sci. Technol., 32 (1998) 1433-1437.

of 25

Accep

ted

Man

uscr

ipt

[23] R. Span, W. Wagner, A new equation of state for carbon dioxide covering the fluid region from the triple�point temperature to 1100 K at pressures up to 800 MPa, J. Phys. Chem. Ref. Data, 25 (1996) 1509-1596.

[24] J. Méndez-Santiago, A.S. Teja, The solubility of solids in supercritical fluids, Fluid Phase Equilib., 158 (1999) 501-510.

[25] G.J. Besserer, D.B. Robinson, Equilibrium-phase properties of n-pentane-carbon dioxide system, J. Chem. Eng. Data, 18 (1973) 416-419.

[26] H. Kalra, H. Kubota, D.B. Robinson, H.-J. Ng, Equilibrium phase properties of the carbon dioxide-n-heptane system, J. Chem. Eng. Data, 23 (1978) 317-321.

[27] H.-S. Byun, T.-H. Choi, Vapor-Liquid equilibria measurement of carbon dioxide+ 1-hexene and carbon dioxide+ 2-ethyl-1-butene systems at high pressure, Korean J. Chem. Eng., 21 (2004) 1032-1037.

[28] L.E. Camacho-Camacho, L.A. Galicia-Luna, O. Elizalde-Solis, Z. Martínez-Ramírez, New isothermal vapor–liquid equilibria for the CO2+n-nonane, and CO2+n-undecane systems, Fluid Phase Equilib., 259 (2007) 45-50.

[29] M.K. Gupta, Y.H. Li, B.J. Hulsey, R.L. Robinson Jr, Phase equilibrium for carbon dioxide-benzene at 313.2, 353.2, and 393.2 K, J. Chem. Eng. Data, 27 (1982) 55-57.

[30] H.-J. Ng, D.B. Robinson, Equilibrium-phase properties of the toluene-carbon dioxide system, J. Chem. Eng. Data, 23 (1978) 325-327.

[31] H. Reamer, B. Sage, Phase Equilibria in Hydrocarbon Systems. Volumetric and Phase Behavior of the n-Decane-CO2 System, J. Chem. Eng. Data, 8 (1963) 508-513.

[32] R. Shaver, R. Robinson Jr, K. Gasem, An automated apparatus for equilibrium phase compositions, densities, and interfacial tensions: data for carbon dioxide+ decane, Fluid Phase Equilib., 179 (2001) 43-66.

[33] A.-D. Leu, S.Y.-K. Chung, D.B. Robinson, The equilibrium phase properties of (carbon dioxide+ methanol), J. Chem. Thermodyn., 23 (1991) 979-985.

of 25

Accep

ted

Man

uscr

ipt

[34] S.N. Joung, C.W. Yoo, H.Y. Shin, S.Y. Kim, K.-P. Yoo, C.S. Lee, W.S. Huh, Measurements and correlation of high-pressure VLE of binary CO2–alcohol systems (methanol, ethanol, 2-methoxyethanol and 2-ethoxyethanol), Fluid Phase Equilib., 185 (2001) 219-230.

[35] Ž. Knez, M. Škerget, L. Ilič, C. Lütge, Vapor–liquid equilibrium of binary CO2–organic solvent systems (ethanol, tetrahydrofuran, ortho-xylene, meta-xylene, para-xylene), J. Supercrit. Fluids, 43 (2008) 383-389.

[36] O. Elizalde-Solis, L.A. Galicia-Luna, L.E. Camacho-Camacho, High-pressure vapor–liquid equilibria for CO2+ alkanol systems and densities of n-dodecane and n-tridecane, Fluid Phase Equilib., 259 (2007) 23-32.

[37] D.W. Jennings, R.J. Lee, A.S. Teja, Vapor-liquid equilibria in the carbon dioxide+ ethanol and carbon dioxide+ 1-butanol systems, J. Chem. Eng. Data, 36 (1991) 303-307.

[38] M.V. da Silva, D. Barbosa, High pressure vapor–liquid equilibrium data for the systems carbon dioxide/2-methyl-1-propanol and carbon dioxide/3-methyl-1-butanol at 288.2, 303.2 and 313.2 K, Fluid Phase Equilib., 198 (2002) 229-237.

[39] A. Jónasson, O. Persson, P. Rasmussen, G.S. Soave, Vapor–liquid equilibria of systems containing acetic acid and gaseous components. Measurements and calculations by a cubic equation of state, Fluid Phase Equilib., 152 (1998) 67-94.

[40] C.-Y. Day, C.J. Chang, C.-Y. Chen, Phase equilibrium of ethanol+ CO2 and acetone+ CO2 at elevated pressures, J. Chem. Eng. Data, 41 (1996) 839-843.

[41] M. Akgün, N.A. Akgün, S. Dinçer, Phase behaviour of essential oil components in supercritical carbon dioxide, J. Supercrit. Fluids, 15 (1999) 117-125.

[42] C.-M.J. Chang, C.-C. Chen, High-pressure densities and P-T-x-y diagrams for carbon dioxide+ linalool and carbon dioxide+ limonene, Fluid Phase Equilib., 163 (1999) 119-126.

[43] D. Villanueva Bermejo, E. Ibáñez, R.P. Stateva, T. Fornari, Solubility of CO2 in Ethyl Lactate and Modeling of the Phase Behavior of the CO2+ Ethyl Lactate Mixture, J. Chem. Eng. Data, 58 (2013) 301-306.

of 25

Accep

ted

Man

uscr

ipt

[44] C. Lockemann, S. Munoz de Soto-Soliz, E.-U. Schlünder, High-pressure phase equilibria and densities of the binary system carbon dioxide/methyl laurate, Chem. Eng. Process., 34 (1995) 561-564.

[45] H. Inomata, T. Kondo, S. Hirohama, K. Arai, Y. Suzuki, M. Konno, Vapour—liquid equilibria for binary mixtures of carbon dioxide and fatty acid methyl esters, Fluid Phase Equilib., 46 (1989) 41-52.

[46] C. Lockemann, High-pressure phase equilibria and densities of the binary mixtures carbon dioxide—oleic acid, carbon dioxide—methyl myristate, and carbon dioxide—methyl palmitate and of the ternary mixture carbon dioxide—methyl myristate—methyl palmitate, Chem. Eng. Process., 33 (1994) 171-187.

[47] C.-m.J. Chang, M.-s. Lee, B.-c. Li, P.-y. Chen, Vapor–liquid equilibria and densities of CO2 with four unsaturated fatty acid esters at elevated pressures, Fluid Phase Equilib., 233 (2005) 56-65.

[48] R. Bharath, H. Inomata, K. Arai, K. Shoji, Y. Noguchi, Vapor-liquid equilibria for binary mixtures of carbon dioxide and fatty acid ethyl esters, Fluid Phase Equilib., 50 (1989) 315-327.

[49] J.-N. Jaubert, P. Borg, L. Coniglio, D. Barth, Phase equilibria measurements and modeling of EPA and DHA ethyl esters in supercritical carbon dioxide, J. Supercrit. Fluids, 20 (2001) 145-155.

[50] W.-H. Hwu, J.-S. Cheng, K.-W. Cheng, Y.-P. Chen, Vapor–liquid equilibrium of carbon dioxide with ethyl caproate, ethyl caprylate and ethyl caprate at elevated pressures, J. Supercrit. Fluids, 28 (2004) 1-9.

[51] O. Elizalde-Solis, L.A. Galicia-Luna, S. Sandler, J. Sampayo-Hernández, Vapor–liquid equilibria and critical points of the CO2+ 1-hexanol and CO2+ 1-heptanol systems, Fluid Phase Equilib., 210 (2003) 215-227.

[52] F. Fourie, C. Schwarz, J. Knoetze, Phase equilibria of alcohols in supercritical fluids: Part I. The effect of the position of the hydroxyl group for linear C8 alcohols in supercritical carbon dioxide, J. Supercrit. Fluids, 47 (2008) 161-167.

[53] C.J. Chang, K.-L. Chiu, C.-Y. Day, A new apparatus for the determination of P-x-y diagrams and Henry's constants in high pressure alcohols with critical carbon dioxide, J. Supercrit. Fluids, 12 (1998) 223-237.

of 25

Accep

ted

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uscr

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[54] W. Weng, M. Lee, Phase equilibrium measurements for the binary mixtures of 1-octanol plus CO2, C2H6 and C2H4, Fluid Phase Equilib., 73 (1992) 117-127.

[55] D.-S. Jan, C.-H. Mai, F.-N. Tsai, Solubility of carbon dioxide in 1-tetradecanol, 1-hexadecanol, and 1-octadecanol, J. Chem. Eng. Data, 39 (1994) 384-387.

[56] O.J. Catchpole, J.-C. von Kamp, Phase equilibrium for the extraction of squalene from shark liver oil using supercritical carbon dioxide, Ind. Eng. Chem. Res., 36 (1997) 3762-3768.

[57] P.J. Pereira, M. Goncalves, B. Coto, E.G. de Azevedo, M.N. da Ponte, Phase equilibria of CO2+ dl-α-tocopherol at temperatures from 292 K to 333 K and pressures up to 26 MPa, Fluid Phase Equilib., 91 (1993) 133-143.

[58] A. Bamberger, G. Sieder, G. Maurer, High-pressure (vapor+ liquid) equilibrium in binary mixtures of (carbon dioxide+ water or acetic acid) at temperatures from 313 to 353 K, J. Supercrit. Fluids, 17 (2000) 97-110.

[59] T. Charoensombut-Amon, R.J. Martin, R. Kobayashi, Application of a generalized multiproperty apparatus to measure phase equilibrium and vapor phase densities of supercritical carbon dioxide in n-hexadecane systems up to 26 MPa, Fluid Phase Equilib., 31 (1986) 89-104.

[60] A. Shariati, C.J. Peters, High-pressure phase behavior of systems with ionic liquids: measurements and modeling of the binary system fluoroform+ 1-ethyl-3-methylimidazolium hexafluorophosphate, J. Supercrit. Fluids, 25 (2003) 109-117.

[61] A. Shariati, C.J. Peters, High-pressure phase behavior of systems with ionic liquids: Part III. The binary system carbon dioxide+ 1-hexyl-3-methylimidazolium hexafluorophosphate, J. Supercrit. Fluids, 30 (2004) 139-144.

[62] A. Shariati, K. Gutkowski, C.J. Peters, Comparison of the phase behavior of some selected binary systems with ionic liquids, AIChE J., 51 (2005) 1532-1540.

[63] M.C. Kroon, A. Shariati, M. Costantini, J. van Spronsen, G.-J. Witkamp, R.A. Sheldon, C.J. Peters, High-pressure phase behavior of systems with ionic liquids: Part V. The binary system carbon dioxide+ 1-butyl-3-methylimidazolium tetrafluoroborate, J. Chem. Eng. Data, 50 (2005) 173-176.

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[64] M. Costantini, V.A. Toussaint, A. Shariati, C.J. Peters, I. Kikic, High-pressure phase behavior of systems with ionic liquids: Part IV. Binary system carbon dioxide+ 1-hexyl-3-methylimidazolium tetrafluoroborate, J. Chem. Eng. Data, 50 (2005) 52-55.

[65] K. Gutkowski, A. Shariati, C. Peters, High-pressure phase behavior of the binary ionic liquid system 1-octyl-3-methylimidazolium tetrafluoroborate+ carbon dioxide, J. Supercrit. Fluids, 39 (2006) 187-191.

[66] A.M. Schilderman, S. Raeissi, C.J. Peters, Solubility of carbon dioxide in the ionic liquid 1-ethyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide, Fluid Phase Equilib., 260 (2007) 19-22.

[67] W. Ren, B. Sensenich, A.M. Scurto, High-pressure phase equilibria of carbon dioxide (CO2)+n-alkyl-imidazolium bis (trifluoromethylsulfonyl) amide ionic liquids, J. Chem. Thermodyn., 42 (2010) 305-311.

[68] E.-K. Shin, B.-C. Lee, J.S. Lim, High-pressure solubilities of carbon dioxide in ionic liquids: 1-alkyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide, J. Supercrit. Fluids, 45 (2008) 282-292.

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Table 1: Regression analysis based on Eq. (9b) for the solubility of methyl oleate +

carbon dioxide. The statistical analysis (analysis of variance (ANOVA) and the parameter

fitting are presented.

Analysis of variance:

Parameter fitting: Parameter Value Error t-value Prob>|t|

A* -8.04170 0.16972 -47.3830 <0.0001B* -2.79578 0.18428 -15.1720 <0.0001C* 16.44249 1.07047 15.3600 <0.0001

Source of variation Degree of freedom Sum of squares Mean square F value Prob. >FModel 2 3.76280 1.88140 1138.55 0.0001Error 32 0.05288 0.00165 Total 34 3.81568

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Table 2: Regression parameters, A, B and C with standard error (S.E) for small molecular weight compounds using Eq. (9a)

Compound N P range(MPa) T range (K) Xgas range AARD(%) A S.E B S.E D S.E R2 Reference n-Pentane 46 0.2-1.0 277.5-377.6 0.03-1.00 13.0 1.06 0.02 -3.35 0.21 13.75 1.22 0.981 [25] n-Heptane 60 0.1-13.3 310.0-477.0 0.02-0.95 6.8 0.85 0.01 -0.79 0.09 -0.18 0.54 0.989 [26] n-Hexene 59 1.7-12.1 313.2-393.2 0.25-0.95 5.1 0.67 0.02 -1.01 0.11 2.04 0.66 0.972 [27] n-Nonane 36 2.0-15.6 315.1-418.8 0.14-0.93 4.7 0.74 0.01 -0.92 0.09 1.08 0.54 0.989 [28] Benzene 43 0.7-13.3 313.2-393.2 0.04-0.82 5.1 0.97 0.01 -2.48 0.10 8.96 0.60 0.995 [29] Toluene 31 3.3-15.3 311.1-476.9 0.03-0.97 9.5 0.93 0.02 -1.39 0.15 2.79 0.87 0.991 [30]

n-Decane 54 0.3-18.5 277.4-410.8 0.05-0.99 8.5 0.77 0.02 -1.41 0.12 3.74 0.68 0.976 [31] n-Decane 29 3.2-16.1 319.1-372.9 0.21-0.97 2.2 0.66 0.01 -1.36 0.09 3.99 0.51 0.995 [32] Undecane 40 2.3-19.2 314.9-418.3 0.11-0.92 5.5 0.70 0.01 -0.92 0.10 1.18 0.57 0.984 [28] Methanol 27 0.4-16.5 323.2-394.2 0.01-0.85 8.8 1.03 0.02 -2.36 0.29 7.41 1.67 0.991 [33] Ethanol 60 0.5-12.0 313.4-344.8 0.02-0.97 7.6 0.98 0.01 -3.59 0.35 14.92 2.01 0.992 [34] Ethanol 30 1.5-13.5 313.2-353.2 0.05-0.73 4.1 0.97 0.02 -2.69 0.28 9.63 1.49 0.992 [35]

1-Propanol 20 10.6-15.8 344.8-426.7 0.17-0.80 4.8 2.30 0.12 2.13 0.35 -26.47 2.71 0.977 [36]

1-Butanol 28 4.6-11.8 314.8-337.2 0.28-0.81 1.7 0.87 0.01 -2.50 0.16 9.15 0.92 0.995 [37] Isoamyl alcohol 54 1.2-8.2 288.2-313.2 0.13-0.94 4.9 0.80 0.01 -6.66 0.28 33.52 1.90 0.990 [38]

Acetic acid 50 2.7-7.4 298.0-348.0 0.01-0.75 2.2 0.98 0.00 -4.15 0.07 18.56 0.38 0.999 [39] Acetone 70 0.7-7.1 291.2-313.1 0.14-0.94 4.7 0.68 0.01 -3.61 0.27 17.05 1.54 0.988 [40]

Limonene 24 6.1-11.2 313.2-333.2 0.43-0.89 2.4 0.72 0.02 -4.07 0.26 19.16 1.45 0.979 [41] Linalool 28 1.4-11.1 313.2-333.2 0.15-0.94 4.6 0.67 0.01 -2.79 0.49 12.17 2.81 0.989 [42]

Ethyl lactate 22 2.0-8.1 311-323 0.06-0.42 5.0 0.85 0.02 -5.64 0.83 26.75 4.78 0.990 [43]

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Table 3: Regression parameters, A*, B* and C* with standard error (S.E) for high molecular weight compounds using Eq. (9b)

Compound P range (MPa) T range (K) Xgas range AARD(%) N A* S.E B* S.E D* S.E R2 Reference Methyl laurate 4.0-12.0 313.2-333.2 0.15-0.88 3.7 22 -13.32 0.34 -4.49 0.40 26.60 2.32 0.977 [44] Methyl stearate 2.1-20.4 313.2-343.2 0.75-0.93 2.3 24 -7.19 0.32 -2.17 0.23 12.79 1.37 0.961 [45]

Methyl myristate 0.8-12.0 313.2-333.2 0.34-0.94 4.7 22 -9.28 0.44 -3.17 0.36 18.70 2.07 0.976 [45] Methyl myristate 2.0-12.0 313.2-333.2 0.23-0.94 4.9 38 -9.61 0.24 -4.11 0.35 24.14 2.03 0.977 [46] Methyl palmitate 2.1-18.3 313.2-343.2 0.33-0.95 3.4 32 -8.99 0.25 -2.96 0.23 17.46 1.39 0.976 [45] Methyl palmitate 2.7-13.0 313.2-333.2 0.40-0.93 3.1 33 -8.96 0.26 -3.13 0.28 18.43 1.66 0.976 [46] Methyl linoleate 2.8-18.0 313.2-333.2 0.52-0.95 2.0 26 -7.80 0.29 -2.41 0.22 14.21 1.26 0.971 [47]

Methyl oleate 1.8-20.0 313.2-343.2 0.27-0.93 3.1 35 -8.04 0.17 -2.80 0.18 16.44 1.07 0.986 [45] Methyl oleate 2.8-18.0 313.2-333.2 0.48-0.94 2.1 25 -8.27 0.27 -2.38 0.20 14.10 1.17 0.978 [47] Ethyl Stearate 2.7-18.2 313.2-333.2 0.45-0.91 2.4 27 -7.57 0.26 -2.32 0.27 13.65 1.57 0.972 [48] Ethyl oleate 1.1-18.6 313.2-333.2 0.19-0.96 3.7 38 -7.26 0.19 -2.53 0.33 14.86 1.92 0.976 [48]

Ethyl linoleate 2.0-17.0 313.2-333.2 0.30-0.95 2.9 32 -8.07 0.17 -2.92 0.27 17.15 1.55 0.987 [48] Ethyl EPA 2.6-20.0 313.2-333.2 0.54-0.92 1.9 33 -5.78 0.20 -1.46 0.19 8.54 1.13 0.964 [48] Ethyl EPA 4.2-20.8 313.2-333.2 0.50-0.94 2.1 25 -8.16 0.31 -2.13 0.17 12.57 1.01 0.972 [47] Ethyl EPA 6.0-21.8 303.2-353.2 0.75-0.91 1.1 33 -6.15 0.33 -1.38 0.10 8.12 0.57 0.946 [49] Ethyl DHA 1.8-21.1 313.2-333.2 0.48-0.88 1.6 25 -4.51 0.15 -1.50 0.19 8.70 1.11 0.977 [48] Ethyl DHA 4.2-23.5 313.2-333.2 0.75-0.94 1.5 23 -4.89 0.36 -1.52 0.15 8.86 0.86 0.920 [47] Ethyl DHA 4.7-24.2 313.2-353.2 0.64-0.95 2.1 25 -7.26 0.31 -1.80 0.17 10.61 0.96 0.962 [49]

Ethyl caproate 1.7-9.2 308.2-328.2 0.21-0.85 3.9 29 -10.13 0.24 -4.08 0.36 24.01 2.10 0.985 [50] Ethyl caprylate 2.4-9.2 308.2-328.2 0.29-0.89 2.8 28 -10.45 0.23 -4.09 0.26 24.08 1.51 0.988 [50] Ethyl caprate 2.3-8.5 308.2-328.2 0.28-0.85 2.7 26 -10.30 0.23 -4.11 0.26 24.11 1.51 0.989 [50]

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Table 3: Continued Compound P range (MPa) T range (K) Xgas range AARD (%) N A* S.E B* S.E D* S.E R2 Reference

Hexanol 2.2-20.2 324.6-432.5 0.03-0.92 7.5 42 -25.93 0.71 -2.65 0.17 16.37 1.03 0.975 [51] 1-octanol 6.7-17.7 308.2-348.2 0.54-0.91 3.7 31 -14.96 0.95 -1.50 0.22 9.06 1.30 0.900 [52] 1-octanol 2.8-15.1 308.2-328.2 0.17-0.78 4.7 20 -15.05 0.40 -2.64 0.44 15.63 2.55 0.983 [53] 1-octanol 4.0-16.0 313.2-348.2 0.26-0.86 4.5 30 -18.45 0.58 -3.68 0.30 21.87 1.77 0.983 [54] 1-nonanol 2.8-15.6 308.2-328.2 0.21-0.76 3.9 31 -16.83 0.41 -4.34 0.39 25.53 2.29 0.984 [53] 1-decanol 2.8-15.6 308.2-328.2 0.18-0.76 3.6 31 -15.28 0.34 -3.10 0.36 18.31 2.09 0.988 [53]

Tetradecanol 1.0-5.1 373.2-473.2 0.06-0.27 6.4 15 -8.49 0.35 -1.55 0.22 8.56 1.40 0.981 [55] Hexadecanol 1.0-5.1 373.2-473.2 0.04-0.30 6.2 15 -8.97 0.34 -2.10 0.22 11.93 1.31 0.984 [55] Octadecanol 1.0-5.1 373.2-473.2 0.04-0.30 6.3 15 -8.42 0.37 -2.00 0.23 11.29 1.42 0.979 [55]

Squalene 10.0-25.0 313.2-333.2 0.77-0.82 6.7 8 -2.47 0.34 -0.38 0.13 2.07 0.78 0.913 [56] Tocopherol 9.1-26.1 313.2-333.2 0.68-0.76 0.9 28 -2.03 0.17 0.46 0.08 -2.92 0.47 0.897 [57]

Water 4.0-14.1 323.2-353.2 0.01-0.02 2.3 29 -12.69 0.32 -3.57 0.16 17.46 0.95 0.986 [58] n-hexadecane 6.9-25.8 313.2-343.2 0.06-0.97 6.8 55 -8.13 0.15 -1.98 0.35 11.65 2.05 0.982 [59] [Emim]-[PF6] 1.5-97.1 308.0-366.0 0.10-0.62 6.4 74 -8.68 0.18 -2.02 0.23 11.29 1.32 0.974 [60] [Hmim]-[PF6] 0.6-94.6 298.5-363.6 0.10-0.65 9.4 98 -6.91 0.12 -3.57 0.24 20.41 1.38 0.970 [61]

[Bmim]-[PF6]

5.9-73.5

293.3-363.5 0.09-0.73

9.3

99

-6.84

0.15

-3.77

0.23

21.50

1.33

0.957

[62]

[Bmim]-[BF4] 0.5-46.7 293.1-327.9 0.10-0.60 9.2 102 -7.47 0.16 -4.07 0.17 23.32 1.00 0.956 [63] [Hmim]-[BF4] 0.5-86.6 293.2-368.1 0.10-0.70 11.7 104 -6.89 0.17 -3.78 0.28 21.66 1.65 0.945 [64] [Omim]-[BF4] 1.0-85.8 307.7-363.3 0.10-0.75 9.3 100 -6.74 1.74 -2.93 0.25 16.78 1.48 0.962 [65]

[Emim]-[TF3N] 0.8-14.4 312.1-450.5 0.12-0.60 8.1 96 -8.08 0.20 -3.03 0.11 17.59 0.66 0.954 [66] [Emim]-[TF3N] 1.4-14.7 298.2-343.2 0.28-0.78 6.4 21 -6.23 0.36 -2.34 0.33 13.47 1.92 0.946 [67] [Dmim]-[TF3N] 1.4-14.8 298.2-343.2 0.35-0.85 5.3 22 -6.20 0.26 -2.00 0.25 11.68 1.42 0.968 [67] [Bmim]-[TF3N] 1-42.8 293.2-344.4 0.31-0.80 4.0 84 -5.06 0.12 -2.45 0.12 14.07 0.70 0.957 [68] [Hmim]-[TF3N] 1.4-39.0 303.7-344.4 0.32-0.83 4.9 90 -6.00 0.15 -2.34 0.16 13.53 0.91 0.947 [68] [Omim]-[TF3N] 0.6-34.8 297.4-344.4 0.30-0.85 4.8 96 -4.21 0.10 -2.04 0.15 11.75 0.84 0.951 [68]

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3.0 3.5 4.0 4.5 5.0 5.5 6.035.5

36.0

36.5

37.0

37.5

38.0

38.5

(a)

ln X

gas -

B ln

T

ln ρ

1 2 3 4 5 619

20

21

22

23

24

25

ln X

Gas

- B

lnT

ln ρ

(b)

Figure 1: (a) Carbon dioxide solubility in isoamyl alcohol [38] at ■, 323 K; ●, 333 K;

▲, 353 K. (b) Carbon dioxide solubility in acetic acid [39] at ■, 298 K; ●, 323 K; ▲,

348 K. The solid lines represent the correlation on Eq. (9a).

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0.04 0.06 0.08 0.10 0.1216.0

16.2

16.4

16.6

16.8

17.0

ln X

Gas

- B* l

nT

lnρ/P

(a)

0.06 0.09 0.12 0.15 0.18

24.3

24.6

24.9

25.2

25.5

25.8

26.1

ln X

Gas

- B* l

nT

ln ρ / P

(b)

Figure 2: (a) Carbon dioxide solubility in methyl laurate [44] at ■, 313 K; ●, 323 K; ▲,

333 K. (b) Carbon dioxide solubility in water [58] at ■, 323 K; ●, 333 K; ▲, 353 K.

The solid lines represent the correlation on Eq. (9b).

Simple three parameter equations for correlating liquid phase compositions in subcritical and...

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