Phase behaviour of the system (carbon dioxide + n-heptane + methylbenzene): a comparison between experimental data and SAFT-

γ-Mie predictions

Saif Z. S. Al Ghafri1,2, Geoffrey C. Maitland1, and J. P. Martin Trusler1*

(1) Qatar Carbonates and Carbon Storage Research Centre, Department of Chemical Engineering, Imperial College London,

South Kensington Campus, London SW7 2AZ UK.

(2) Fluid Science and Resources Division, School of Mechanical & Chemical Engineering, University of Western Australia, 35

Stirling Highway, Crawley WA 6009, Australia

* Corresponding author e-mail: m.trusler@imperial.ac.uk.

Abstract

In this work, we explore the capabilities of the Statistical Associating Fluid Theory for potentials

of the Mie form, with parameter estimation based on a group-contribution approach, SAFT-γ-Mie,

to model the phase behavior of the (carbon dioxide + n-heptane + methylbenzene) system. In

SAFT-γ-Mie, complex molecules are represented by fused segments representing the functional

groups from which the molecule may be assembled. All interactions between groups, both like

and unlike, were determined from experimental data on pure substances and binary mixtures

involving CO2. A high-pressure high-temperature variable-volume view cell was used to measure

the vapor-liquid phase behavior of ternary mixtures containing carbon dioxide, n-heptane, and

methylbenzene over the temperature range (298 and 423) K at pressures up to 16 MPa. In these

experiments, the mole ratio between n-heptane and methylbenzene in the ternary system was

fixed at a series of specified values, and the bubble-curve and part of the dew-curve was

measured under carbon dioxide addition along four isotherms.

Keywords: Phase behaviour; modelling; carbon dioxide; hydrocarbon; SAFT; heptane; toluene, methylbenzene

mailto:m.trusler@imperial.ac.uk

1

1. Introduction

Carbon dioxide (CO2) is recognized as the most significant anthropogenic greenhouse gas and a

major contributor to global climate change. There is an urgent need to reduce CO2 emissions

associated with the combustion of fossil fuels in power generation and other industrial processes,

and carbon capture and storage (CCS) is a viable means of achieving this. Captured CO2 might

also be used in enhanced oil recovery (EOR) processes, thereby realizing an economic benefit.

The miscibility of CO2 with hydrocarbons has an essential role in the design of both CCS

processes, when CO2 is to be stored in depleted oil or gas fields, and in CO2-EOR operations. In

both cases, CO2 would form mixtures with complex hydrocarbons, including both aliphatic and

aromatic molecules spanning several orders of magnitude in molecular weight, under conditions

of elevated temperature and pressure.1-5 In addition, high-pressure phase equilibria of systems

containing mixtures of CO2 with hydrocarbons are of interest for pyrolysis processes, degrading

of organic waste, and hydrotreatment in aqueous systems.6 CO2 is also important as a solvent in supercritical fluid extraction processes (SFE). CO2 has mild critical conditions (Tc = 304.16 K,

pc = 7.38 MPa), is inexpensive, nontoxic, non-flammable, and readily available7 and thus used as

a supercritical solvent to separate complex mixtures such as aromatic components.

Equilibrium data for binary (CO2 + alkanes) and (CO2 + aromatics) mixtures are plentiful while

fewer data exist for the binary mixture classes (CO2 + branched alkanes) and (CO2 + branched

naphthenes). Only scarce data exist regarding phase equilibria of (CO2 + hydrocarbon) mixtures

of three components or more. High-pressure High-temperature phase equilibrium data and

experimental methods have been reviewed by Fornari,8 Dohrn and Brunne,9 Christov and Dohrn10

and more recently Dohrn, Peper, and Fonseca.11, 12 From these reviews it is evident that

equilibrium data for ternary, or higher, (CO2 + hydrocarbon) mixtures are very limited, especially

for systems containing heavy hydrocarbons and/or hydrocarbons other than paraffins. To our

knowledge, there are no phase equilibria data reported in the literature for the ternary mixture

studied in this work. However, the constituent binary systems have been studied extensively.

The system xCO2 + (1 - x)C7H8 has been studied recently by Lay and coworkers13, 14 at pressures

up to 7.5 MPa, temperatures up to 313 K, and composition over the range x = (0.215 to 0.955)

using a pVT apparatus with a variable volume cell. Tochigi et al.15 also studied the system at

pressures up to 6.0 MPa, temperatures up to 333 K and composition over the range x = (0.080 to

0.889) using a static-type apparatus composed of an equilibrium cell, sampling and analysis

system. Wu et al.16 extended the conditions investigated up to p = 16.6 MPa and T = 572 K, for

x = (0.01 to 0.78), by using a dynamic-synthetic method based on a fiber optic reflectometer; this

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is the widest range studied for this mixture. All authors used the Peng-Robinson equation of

state17 as a modeling tool. Naidoo et al.18 studied the same mixture at pressures up to 12.1 MPa, temperatures up to 391 K and compositions in the range x = (0.0578 to 0.8871) using a static-

analytical apparatus equipped with a sapphire window for visual observation, liquid sampling

techniques and gas chromatography for composition analysis. Other studies reporting phase

equilibria of the (carbon dioxide + methylbenzene) system can be found in references.19-25

The system xCO2 +(1 - x)C7H16 has also been studied by Lay13 at pressures up to 7.4 MPa,

temperatures up to 313 K and composition in the range x = (0.503 to 0.904) using the same

apparatus mentioned above. Choi and Yeo26 studied the system at pressures up to 12.2 MPa,

temperatures up to 370 K and compositions in the range x = (0.885 to 0.958) using a high pressure

variable volume cell. Kalra et al.27 studied the same mixture at pressures up to 3.3 MPa, with

temperatures up to 477 K with x = (0.022 to 0.949); this represents the widest temperature range

investigated for this system. Fenghour et al.28 measured bubble points at pressures up to

55.5 MPa, temperatures up to 459 K, and x = (0.2918 to 0.4270) using an isochoric method; this

represents the widest pressure range investigated for this system. Mutelet et al.29 used a high-

pressure variable-volume cell to perform static phase equilibrium measurements at pressures up

to 13.40 MPa, temperatures up to 413 K and compositions in the range x = (0.183 to 0.914). The

data were compared against the predictive equation of state recently developed by Jaubert and

coworkers,30-37 which was based on the use of a group contribution approach to estimate

temperature-dependent binary interaction parameters in the Peng-Robinson equation of state.

Other studies reporting the phase equilibria of this system can be found in references.38-40

A considerable amount of effort has been dedicated to developing integrated modeling

approached for the prediction of phase behavior and other thermophysical properties of (CO2 +

hydrocarbon) mixtures. A variety of approaches have been used, ranging from empirical and

semi-empirical correlative models, such as cubic equations of state (EoS) with adjustable binary

parameters, to predictive cubic equations of state such as PPR7831 and PR2SRK36, 37 to

molecular-based models such as the Statistical Associating Fluid Theory (SAFT).41, 42 Cubic

equations of state rely on the availability of experimental data for a specific system in order to

determine binary interaction parameters, which are commonly taken to be temperature

dependent. They are widely applied and may provide accurate descriptions, limited however in

applicability by the availability of experimental data. These equations of state have the

disadvantage of often yielding inaccurate liquid densities and poor predictions of liquid-liquid

equilibria, especially in highly immiscible systems such as (water + alkanes). Furthermore, they

3

are less reliable for polar and associating fluids and for systems containing molecules that differ

greatly in size. On the other hand, SAFT may give better predictions for complex and associating

mixtures, without extensive fitting to experimental data. More so in the case of group contribution

approaches, where the group interaction parameters are transferrable between systems and

predictions can be made without further consideration of experimental data. The constituent

binary systems in this study, (CO2 + n-heptane) and (CO2 + methylbenzene), have been

compared already with the prediction from PPR78 EoS.43 Different SAFT versions have also been

used to model mainly (CO2 + n-alkane) binary systems: SAFT-VR,44 PC-SAFT,45-48 Soft-SAFT,49

and GC-SAFT.50 Results from SAFT-γ-Mie have not been reported previously for (CO2 + n-

heptane) and (CO2 + methylbenzene) and none of the modeling approaches discussed here have

been applied in the literature for the ternary mixture.

In this work, we implement SAFT with the generalized Mie potential and a group contribution

approach, SAFT-γ-Mie, to determine the phase behavior of the (CO2 + C7H16 + C7H8) system and

we compare the results with new experimental measurements also reported in this work. This

allows the predictive capability of the SAFT-γ-Mie approach to be tested in a ternary system and

under conditions at which one of the components (CO2) may be supercritical. The ternary mixture

(CO2 + C7H16 + C7H8) is chosen as representative of the family of (carbon dioxide + alkane +

aromatic) mixtures and is studied as a first approach to determining the conditions of phase

equilibria in multi-component (carbon dioxide + hydrocarbon) systems. New data for phase

equilibrium have been measured covering a wide range of conditions and compositions at

different fixed feed-liquid mole ratios between n-heptane and methylbenzene in the ternary

system. Coupled to the state-of-the-art modeling approach applied, this work facilitates accurate

phase-equilibrium predictions for (carbon dioxide + hydrocarbon) systems over wide ranges of

conditions, as validated by the comparisons presented in this paper.

2. Experimental

2.1 Apparatus

The apparatus used was previously described in detail;51 a summary is given here for

completeness. Figure 1 illustrates the configuration of the variable-volume static-synthetic

apparatus, which permits visual observation of the co-existing phases inside the equilibrium cell

under conditions of known overall composition. The apparatus supported working pressures and

4

temperatures up to 40 MPa and 473.15 K, respectively. The equilibrium cell was fitted with a

movable piston on one end and closed by a sapphire window on the other end, allowing for visual

observation of the entire equilibrium cell.

Mixing of the injected fluids was accomplished by means of an internal PTFE-coated magnetic

stirrer bar of ellipsoidal shape coupled to a rotating external magnet. Two high-pressure syringe

pumps were used for quantitative injection of the components of interest into the equilibrium cell.

One pump was used to inject CO2 and the other to inject a pre-prepared hydrocarbon mixture of

known composition. An insulated aluminum heating jacket attached to the body of the cell was

used to control the temperature, which was measured using a calibrated 4 wire platinum

resistance thermometer (Sensing Device Ltd, model SD01168). A pressure transducer (DJ

Instruments, model DF2) was used upstream of the equilibrium cell to measure the system pressure. A CCD camera was used to take still pictures and video of the mixture as an aid to

visual observations of the phase transitions. The apparatus was previously validated by

comparison with published isothermal vapor-liquid equilibrium data for the binary system (carbon

dioxide + n-heptane).51

2.2 Calibration and Uncertainty

The calibration and associated uncertainties have been described previously in detail.51 Here a

summary is given relevant to the system studied. The overall standard uncertainty of the cell

temperature was taken to be 0.5 K. This value is larger than reported previously51 and takes into

account non-uniformity that was found to exist at high temperatures. The pressure transducer

used to measure the sample pressure was calibrated against a hydraulic pressure balance and

the standard uncertainty of the pressure was estimated to be 35 kPa.

The uncertainty of the mass of fluid injected into the cell depends on the uncertainties of the

volume expelled from the syringe pump, the density under the pump conditions, and the dead

volume corrections required. For CO2, the density was obtained from the equation of state of Span

and Wagner52 with an estimated relative uncertainty between (0.03 and 0.05) %. The density of

the liquid hydrocarbon mixture was obtained from experimental data reported in reference53 where

a vibrating tube densimeter (DMA 60, Anton Paar) was used with estimated relative uncertainties

in the range from (0.023 to 0.057) %. Considering all factors, the standard relative uncertainty of

the mass injected was ≤ 0.13% and this leads to a standard uncertainty u(x1) of the mole fraction

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x1 of CO2 ≤ 0.0017x1(1 - x1). The mole fractions of x2 of heptane and x3 of methylbenzene are

given by

)1/()1( 12 YYxx −−= , (1)

and )1/()1( 13 Yxx −−= , (2)

where Y = x2/x3 is the mole ratio of heptane to methylbenzene in the liquid feed, which was

determined gravimetrically with a standard uncertainty u(Y) < 10-4. The uncertainties in x2 and x3

in the ternary mixture were therefore dominated by the uncertainty in x1 and are given

approximately by u(x2) = u(x1)Y/(1 + Y) and u(x3) = u(x1)/(1 + Y).

The uncertainties of the bubble- and dew-pressures was mainly affected by the subjective

uncertainty in observing the bubble- or dew-point condition and the uncertainty of the pressure

measurement itself. Except in the critical region, bubble points were easily observed visually

during isothermal measurements with variation of the cell volume. Dew points were generally

more difficult to observe by this method and were only measured at high pressures. Close to the

critical point, it became more difficult to detect both bubble- and dew-point conditions. Considering

these factors, the uncertainty in temperature and the uncertainty of the pressure, the standard

uncertainty of the bubble pressure pb was estimated to be 0.2 MPa at all temperatures, while the

standard uncertainties of the critical and dew pressures pd were estimated to be 0.3 MPa.

2.3 Materials

The materials used are detailed in Table 1.

2.4 Experimental Procedure

The experimental procedure was similar to that described in detail previously.51 The liquid

hydrocarbon mixture was prepared gravimetrically at ambient pressure and temperature and

loaded into one of the syringe pumps, while the other (refrigerated at 283 K) was loaded with pure

liquid CO2. Starting from a clean and evacuated system, the liquid mixture was introduced into

the cell followed by injection of carbon dioxide. The mass of fluid introduced in each injection step

was obtained from the syringe displacement and knowledge of the density at the pump

temperature and pressure. The overall composition of the system was calculated at every stage

of the experiment from the cumulative amounts of hydrocarbon liquid and carbon dioxide

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introduced from the pumps, allowing for the dead volume that remains in the connecting tubes

and fittings.

Following the injection of components, V-20 was closed (see Figure 1) and the pressure inside

the cell was adjusted by moving the piston until one homogenous phase was obtained at a fixed

temperature. The system was then allowed to equilibrate under continued stirring for at least one

hour. The pressure was then decreased in small decrements, each followed by a further

equilibration period, while simultaneously recording temperature, pressure and volume, and

observing the state of the system. This process continued until the appearance of a second phase.

Usually, after observing a bubble or dew point, additional carbon dioxide was injected and a new

measurement was initiated. A random selection of bubble-point measurements were repeated

three or more times to check the repeatability, which was found to be within 0.1 MPa and therefore

well within the overall claimed uncertainty. Other state points were measured once only. Visual

observation using the CCD camera was the primary means of detecting phase changes.

3. Theory

The SAFT, stemming from the first order perturbation theory of Wertheim,54-57 was implemented

in this work with a group contribution approach and the generalized Mie potential to represent

segment-segment interactions. In the resulting SAFT-γ-Mie approach, complex molecules are

represented by fused segments corresponding to the functional groups from which the molecule

may be assembled. SAFT-γ-Mie has been described in detail by Papaioannou et al.58 and here

we summarize only the interaction model and the nature and source of the parameters involved.

In SAFT-γ-Mie, each functional group from which a molecule is composed is characterized by one

or more identical segments. The potential energy of interaction ukl between non-associating

segments k and l present in two different molecules is given by

−

−=

− klklklklkl λ

kl

klλ

kl

kl

λλλ

kl

kl

klkl

klklklkl r

σrσ

λλ

λλελ

ru,a,r,a,r,a )/(

,a

,r

,a,r

,r)(, (3)

where rkl is the center-to-center distance between the groups, λr,kl is the repulsive exponent, λa,kl

is the attractive exponent, εkl is the energy-scaling parameter and σkl is the length-scaling

parameter. The parameters that characterize the interactions of identical functional groups are

therefore as follows: εkk, σkk, λr,kk, λa,kk and the number νk of segments that comprise the group. An

additional parameter, the shape factor Sk, is used to characterize the extent to which the group

7

contributes to the molecular properties of the system. The parameters εkl, σkl, λr,kl and λa,kl in the

unlike interaction energy may be estimated from the following combining rules:

( )llkkkl σσσ += 21

, (4)

llkk

kl

llkkkl εεσ

σσε 3

33

=, (5)

)3)(3(3 −−+= llkkkl λλλ , (6)

where the latter applies to both λr,kl and λa,kl.58, 59 The estimates from these combining rules may

not be sufficiently accurate but improved estimates may be obtained by regression against

experimental data. It is notable that in many, but not all, cases both like and unlike group

parameters can be obtained from the analysis of pure-substances properties. However, where a

molecule (such as CO2) is represented by a single group the interaction parameters between that

and other function groups must be either estimated or regressed against experimental mixture

data.

In the present case, the interaction parameters were determined from experimental data of

systems comprising the constituent groups, but not necessarily the constituent compounds or

sub-systems of the (carbon dioxide + n-heptane + methylbenzene) mixture itself. Thus, when

applied to the current system, the method is regarded as predictive. The source and values of the

parameters used for the individual groups are given in Table 2; these were all obtained in previous

work58, 60, 61 by fitting saturated vapor pressures and saturated liquid densities. Cross parameters

σkl and λa,kl were obtained from the combining rules, equations (4) and (6), while the source and

values of the cross parameters εkl and λr,kl are given in Table 3. Most of these were also obtained

from combining rules but it was found necessary to fit some of the unlike terms in order to

adequately describe binary (p, T, x, y) vapor-liquid equilibrium (VLE) data. In this work, the CO2-

aCH cross interaction parameters ε12 and λr,12 were determined by fitting experimental VLE data

for (carbon dioxide + benzene) at temperatures of 298 K,62 313 K,62 353 K,25 373 K,25 and 393 K.25

The CO2-aCCH3 cross-interaction energy parameter ε12 was determined by fitting experimental

VLE data for (carbon dioxide + methylbenzene) at temperatures of 283 K,18 311 K,19 353 K,19

394 K,19 and 413 K.21 In this case, λr,12 was obtained using the combining rule. The parameter

optimization involved minimization of the following objective function:

8

[ ]∑∑==

−+

−=

N

iiiiiii

yN

i iii

iiiiiip xTyxTyN

WxTp

xTpxTpN

Wχ

1

2calc,exp,

2

1 exp,

calc,exp,2 ),(),(),(

),(),( , (7)

where Ti and xi denote the ith experimental temperature and liquid-phase composition at which

the experimental bubble pressure and vapor-phase composition were pi,exp and yi,exp and the

corresponding calculated values are pi,calc and yi,cal, respectively. Additionally, N is the total number

of VLE data points, and Wp and Wy are weighting factors. The minimization of χ2 was achieved

using a gradient-based successive quadratic programming algorithm with multiple starting points

as detailed by Papaioannou et al.58 In principle, the weighting factors should be adjusted to reflect

the experimental uncertainties but it was found that satisfactory results were obtained in an un-

weighted fit; accordingly Wp and Wy were both taken as unity. In Figures 2 and 3, the SAFT-γ Mie

description of the phase behavior is compared with the experimental data for the temperatures

considered in the parameter estimation. The remaining cross interactions parameters between

unlike groups were taken from the literature.58, 60, 61

To further test the validity of the optimized interaction parameters for between CO2 and both the

aCH and aCCH3 groups, experimental VLE data for CO2 + xylene isomers were considered.

Specifically, the VLE data for binary mixtures of carbon dioxide with 1,2-dimethylbenzene, 1,3-

dimethylbenzene and 1,4-dimethylbenzene (ortho-, meta- and para-xylene) reported by Walther

et al.63 were compared with the predictions of SAFT-γ Mie with the parameter set described above.

These data were measured at T = (313, 333, 353, 373 and 393) K for each isomer and the

comparison with the predictions of SAFT-γ Mie is shown in Figures 4, 5 and 6 . According to the

group contribution hypothesis, all three isomers should exhibit the same VLE properties. In fact,

as shown in Figure 7 for the isotherms at T = 393 K some differences can be observed with bubble

pressures decreasing in the order 1,2-dimethylybenzene > 1,3-dimethylybenzene > 1,4-

dimethylybenzene. Given these differences, the agreement between the experimental data and

the model shown in Figures 4 to 6 is about as good as is possible under a group contribution

hypothesis and this serves to confirm the validity of the parameters used in the present work.

4. Results and Discussion

The (carbon dioxide + n-alkane) mixtures up to n-dodecane exhibit Type II phase behavior43, 64 in

the classification of Scott and van Konynenburg.65, 66 The binary mixture (carbon dioxide +

methylbenzene) exhibits type I phase behavior.16 The ternary mixture exhibits ternary class II

phase behavior according to the global ternary diagrams proposed by Bluma and Deiters.67 As a

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consequence, in addition to a liquid-gas critical surface a liquid-liquid critical plane exists at low

temperatures and a critical endpoint curve exists at low pressure connecting upper critical

endpoints.

The experimental bubble and dew pressures obtained are given in Table 4 for all isotherms

measured over the whole composition range of carbon dioxide at different mole ratios Y of n-

heptane to methylbenzene in the feed liquid: Y = (0.138, 0.371, 0.930, and 3.004). The

measurements were carried out at temperatures T/K = (298.15, 323.15, 373.15, and 423.15) over

a range of pressures up to 16 MPa.

The experimental results are plotted as pressure-composition (p, x1) diagrams in Figures 8, 9, 10

and 11, where x1 is the mole fraction of CO2, for all isotherms at each of the four mole ratios Y of

n-heptane in the feed liquid. Also shown in Figures 8 to 11 are the predictions of the SAFT-γ-Mie

theory (continuous curves). Here we observe generally good agreement between experiment and

the predictions of the theory. Figure 8 shows that the agreement is almost perfect at the lowest

temperature. Figures 9 to 11 show that, at higher temperatures, the predicted bubble-pressures

typically fall slightly below, and the predicted critical compositions slightly above, the experimental

values. However, these differences remain quite small even at the highest temperature

considered.

5. Conclusions

New experimental VLE data are reported for the ternary system (carbon dioxide + n-heptane +

methylbenzene) at temperature between (298 and 423) K and at pressures up to approximately

16 MPa. The results span four different fixed mole ratios of n-heptane to methylbenzene and, for

each fixed ratio, four isotherms was studied. Comparison between the predictions of the SAFT-γ-

Mie approach and the experimental data show very good agreement and demonstrate the

predictive capability of the theory.

Acknowledgments

The authors are pleased to acknowledge many helpful discussions with Simon Dufal and

Apostolos Georgiadis concerning application of the SAFT-γ-Mie approach.

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Funding

This work was carried out as part of the activities of the Qatar Carbonates & Carbon Storage

Research Centre (QCCSRC). We gratefully acknowledge the funding of QCCSRC provided jointly

by Qatar Petroleum, Shell, and the Qatar Science and Technology Park, and their permission to

publish this research.

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(17) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fun 1976, 15, 59-64. (18) Naidoo, P.; Ramjugernath, D.; Raal, J. D. A New High-Pressure Vapour–Liquid Equilibrium Apparatus. Fluid Phase Equilib. 2008, 269, 104-112. (19) Ng, H.-J.; Robinson, D. B. Equilibrium-Phase Properties of the Toluene-Carbon Dioxide System. J. Chem. Eng. Data 1978, 23, 325-327. (20) Sebastian, H. M.; Simnick, J. J.; Lin, H.-M.; Chao, K.-C. Gas-Liquid Equilibrium in Mixtures of Carbon Dioxide + Toluene and Carbon Dioxide + M-Xylene. J. Chem. Eng. Data 1980, 25, 246-248. (21) Morris, W. O.; Donohue, M. D. Vapor-Liquid Equilibria in Mixtures Containing Carbon Dioxide, Toluene, and 1-Methylnaphthalene. J. Chem. Eng. Data 1985, 30, 259-263. (22) Chang, C. J. The Solubility of Carbon Dioxide in Organic Solvents at Elevated Pressures. Fluid Phase Equilib. 1992, 74, 235-242. (23) Chang, C. J. Volume Expansion Coefficients and Activity Coefficients of High-Pressure Carbon Dioxide Dissolution in Organic Liquids at 298 K. J. Chem. Eng. Jpn. 1992, 25, 164-170. (24) Muhlbauer, A. L.; Raal, J. D. Measurement and Thermodynamic Interpretation of High-Pressure Vapour-Liquid Equilibria in the Toluene + CO2 System. Fluid Phase Equilib. 1991, 64, 213-236. (25) Kim, C.-H.; Vimalchand, P.; Donohue, M. D. Vapor-Liquid Equilibria for Binary Mixtures of Carbon Dioxide with Benzene, Toluene and P-Xylene. Fluid Phase Equilib. 1986, 31, 299-311. (26) Choi, E.-J.; Yeo, S.-D. Critical Properties for Carbon Dioxide + n-Alkane Mixtures Using a Variable-Volume View Cell. J. Chem. Eng. Data 1998, 43, 714-716. (27) Kalra, H.; Kubota, H.; Robinson, D. B.; Ng, H.-J. Equilibrium Phase Properties of the Carbon Dioxide-N-Heptane System. J. Chem. Eng. Data 1978, 23, 317-321. (28) Fenghour, A.; Trusler, J. P. M.; Wakeham, W. A. Densities and Bubble Points of Binary Mixtures of Carbon Dioxide and N-Heptane and Ternary Mixtures of N-Butane, N-Heptane and N-Hexadecane. Fluid Phase Equilib. 2001, 185, 349-358. (29) Mutelet, F.; Vitu, S.; Privat, R.; Jaubert, J.-N. Solubility of CO2 in Branched Alkanes in Order to Extend the PPR78 Model (Predictive 1978, Peng–Robinson EoS with Temperature-Dependent kij Calculated through a Group Contribution Method) to Such Systems. Fluid Phase Equilib. 2005, 238, 157-168. (30) Jaubert, J.-N.; Vitu, S.; Mutelet, F.; Corriou, J.-P. Extension of the PPR78 Model (Predictive 1978, Peng–Robinson EoS with Temperature Dependent kij Calculated through a Group Contribution Method) to Systems Containing Aromatic Compounds. Fluid Phase Equilib. 2005, 237, 193-211. (31) Jaubert, J.-N.; Mutelet, F. VLE Predictions with the Peng–Robinson Equation of State and Temperature Dependent kij Calculated through a Group Contribution Method. Fluid Phase Equilib. 2004, 224, 285-304. (32) Vitu, S.; Jaubert, J.-N.; Mutelet, F. Extension of the PPR78 Model (Predictive 1978, Peng–Robinson EoS with Temperature Dependent kij Calculated through a Group Contribution Method) to Systems Containing Naphtenic Compounds. Fluid Phase Equilib. 2006, 243, 9-28.

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(33) Vitu, S.; Jaubert, J.-N.; Pauly, J.; Daridon, J.-L.; Barth, D. Bubble and Dew Points of Carbon Dioxide + a Five-Component Synthetic Mixture: Experimental Data and Modeling with the PPR78 Model. J. Chem. Eng. Data 2007, 52, 1851-1855. (34) Vitu, S.; Jaubert, J.-N.; Pauly, J.; Daridon, J.-L.; Barth, D. Phase Equilibria Measurements of CO2 + Methyl Cyclopentane and CO2 + Isopropyl Cyclohexane Binary Mixtures at Elevated Pressures. J. Supercrit. Fluids 2008, 44, 155-163. (35) Vitu, S.; Jaubert, J.-N.; Pauly, J.; Daridon, J.-L. High-Pressure Phase Behaviour of the Binary System CO2 + cis-Decalin from (292.75 to 373.75) K. J. Chem. Thermodyn. 2008, 40, 1358-1363. (36) Jaubert, J.-N.; Qian, J.; Privat, R.; Leibovici, C. F. Reliability of the Correlation Allowing the kij to Switch from an Alpha Function to Another One in Hydrogen-Containing Systems. Fluid Phase Equilib. 2013, 338, 23-29. (37) Jaubert, J.-N.; Privat, R. Relationship between the Binary Interaction Parameters (kij) of the Peng–Robinson and Those of the Soave–Redlich–Kwong Equations of State: Application to the Definition of the PR2SRK Model. Fluid Phase Equilib. 2010, 295, 26-37. (38) Hayduk, W.; Walter, E. B.; Simpson, P. Solubility of Propane and Carbon Dioxide in Heptane, Dodecane, and Hexadecane. J. Chem. Eng. Data 1972, 17, 59-61. (39) Inomata, H.; Arai, K.; Saito, S. Measurement of Vapor-Liquid Equilibria at Elevated Temperatures and Pressures Using a Flow Type Apparatus. Fluid Phase Equilib. 1986, 29, 225-232. (40) Sako, T.; Sugeta, T.; Nakazawa, N.; Otake, K.; Sato, M.; Ishihara, K.; Kato, M. High Pressure Vapor-Liquid and Vapor-Liquid-Liquid Equilibria for Systems Containing Supercritical Carbon Dioxide, Water and Furfural. Fluid Phase Equilib. 1995, 108, 293-303. (41) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New Reference Equation of State for Associating Liquids. Ind. Eng. Chem. Res. 1990, 29, 1709-1721. (42) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. SAFT: Equation-of-State Solution Model for Associating Fluids. Fluid Phase Equilib. 1989, 52, 31-38. (43) Vitu, S.; Privat, R.; Jaubert, J.-N.; Mutelet, F. Predicting the Phase Equilibria of CO2 + hydrocarbon Systems with the PPR78 Model (PR Eos and kij Calculated through a Group Contribution Method). J. Supercrit. Fluids 2008, 45, 1-26. (44) Galindo, A.; Blas, F. J. Theoretical Examination of the Global Fluid Phase Behavior and Critical Phenomena in Carbon Dioxide + n-Alkane Binary Mixtures. J. Phys. Chem. B 2002, 106, 4503-4515. (45) García, J.; Lugo, L.; Fernández, J. Phase Equilibria, Pvt Behavior, and Critical Phenomena in Carbon Dioxide + N-Alkane Mixtures Using the Perturbed-Chain Statistical Associating Fluid Theory Approach. Ind. Eng. Chem. Res. 2004, 43, 8345-8353. (46) Fu, D.; Liang, L.; Li, X. S.; Yan, S.; Liao, T. Investigation of Vapor-Liquid Equilibria for Supercritical Carbon Dioxide and Hydrocarbon Mixtures by Perturbed-Chain Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 2006, 45, 4364-4370. (47) Arce, P.; Aznar, M. Modeling of Critical Lines and Regions for Binary and Ternary Mixtures Using Non-Cubic and Cubic Equations of State. J. Supercrit. Fluids 2007, 42, 1-26. (48) Arce, P. F.; Aznar, M. Computation and Modeling of Critical Phenomena with the Perturbed Chain-Statistical Associating Fluid Theory Equation of State. J. Supercrit. Fluids 2008, 43, 408-420.

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16

Table 1. Description of chemical samples

Chemical name Source Purity as supplied Additional purification

Carbon dioxide BOC 0.99995 None

heptane Sigma Aldrich 0.990 None

methylbenzene Sigma Aldrich 0.998 None

Table 2. Like group parameters used Sk (ε/kB) / K σ ⋅1010 / m λr λa Reference

CH3 0.5725 256.77 4.077 15.050 6.00 58

CH2 0.2293 473.39 4.880 19.871 6.00 58

aCH 0.3218 371.53 4.058 14.756 6.00 61

aCCH3 0.3166 651.41 5.487 23.627 6.00 60

CO2 0.8468 207.89 3.050 26.408 5.06 60

Table 3. Unlike group cross interaction energies, ε and lambda repulsive, λr.* Group 1 Group 2 (ε/kB) / K λr Reference

CH3 CH2 350.77 CR 58 CH3 aCH 305.81 CR 61 CH3 aCCH3 CR CR Current work CH3 CO2 205.70 CR 60 CH2 aCH 415.64 CR 61 CH2 aCCH3 CR CR Current work CH2 CO2 276.45 CR 60 aCH aCCH3 471.23 CR 60 aCH CO2 224.33 14.155 Current work

aCCH3 CO2 309.36 CR Current work

*CR denotes parameters obtained with a combining rule

17

Table 4. Experimentally VLE data for CO2 (1) + n-heptane (2) + methylbenzene (3) at temperatures T, pressures p, for different mole ratios Y of n-heptane to methylbenzene, where xi denotes the mole fraction of component i in the mixture at a bubble or dew point. a

p/MPa x1 x2 x3 Status Y

T = 298.15 K

0.503 0.0532 0.1149 0.8319 bubble 0.138

1.052 0.1215 0.1066 0.7719 bubble 0.138

1.755 0.2083 0.0961 0.6956 bubble 0.138

3.313 0.4163 0.0708 0.5129 bubble 0.138

4.352 0.5968 0.0489 0.3543 bubble 0.138

4.874 0.7108 0.0351 0.2541 bubble 0.138

5.254 0.8127 0.0227 0.1646 bubble 0.138

5.631 0.8972 0.0125 0.0903 bubble 0.138

5.892 0.9504 0.0060 0.0436 bubble 0.138

5.968 0.9588 0.0050 0.0362 bubble 0.138

6.062 0.9736 0.0032 0.0232 bubble 0.138

6.085 0.9769 0.0028 0.0203 bubble 0.138

6.126 0.9818 0.0022 0.0160 bubble 0.138

6.210 0.9893 0.0013 0.0094 bubble 0.138

6.223 0.9909 0.0011 0.0080 bubble 0.138

6.186 0.9909 0.0011 0.0080 bubble 0.138

6.256 0.9954 0.00055 0.0040 bubble 0.138

0.437 0.0479 0.2576 0.6945 bubble 0.371

0.695 0.0731 0.2508 0.6761 bubble 0.371

1.425 0.1705 0.2245 0.6050 bubble 0.371

2.901 0.3572 0.1739 0.4689 bubble 0.371

4.206 0.5627 0.1183 0.3190 bubble 0.371

5.250 0.8068 0.0523 0.1409 bubble 0.371

5.475 0.8661 0.0362 0.0977 bubble 0.371

5.625 0.8977 0.0277 0.0746 bubble 0.371

5.725 0.9172 0.0224 0.0604 bubble 0.371

5.792 0.9275 0.0196 0.0529 bubble 0.371

5.910 0.9546 0.0123 0.0331 bubble 0.371

6.175 0.9775 0.0061 0.0164 bubble 0.371

6.172 0.9897 0.0028 0.0075 bubble 0.371

0.473 0.0484 0.4586 0.4930 bubble 0.930

1.241 0.1507 0.4093 0.4400 bubble 0.930

18

p/MPa x1 x2 x3 Status Y 2.205 0.2767 0.3486 0.3747 bubble 0.930

3.825 0.5000 0.2410 0.2591 bubble 0.930

4.501 0.6244 0.1810 0.1946 bubble 0.930

4.850 0.7152 0.1373 0.1476 bubble 0.930

5.355 0.8460 0.0742 0.0798 bubble 0.930

5.525 0.8825 0.0566 0.0609 bubble 0.930

5.712 0.9157 0.0406 0.0437 bubble 0.930

5.805 0.9292 0.0341 0.0367 bubble 0.930

6.135 0.9743 0.0124 0.0133 bubble 0.930

6.230 0.9836 0.0079 0.0085 bubble 0.930

6.255 0.9865 0.0065 0.0070 bubble 0.930

0.782 0.0946 0.6793 0.2261 bubble 3.004

1.465 0.1847 0.6117 0.2036 bubble 3.004

2.319 0.2985 0.5263 0.1752 bubble 3.004

2.837 0.3652 0.4763 0.1585 bubble 3.004

3.575 0.4619 0.4037 0.1344 bubble 3.004

4.221 0.5680 0.3241 0.1079 bubble 3.004

4.762 0.6861 0.2355 0.0784 bubble 3.004

4.930 0.7325 0.2007 0.0668 bubble 3.004

5.012 0.7593 0.1806 0.0601 bubble 3.004

5.101 0.7822 0.1634 0.0544 bubble 3.004

5.222 0.8038 0.1472 0.0490 bubble 3.004

5.405 0.8583 0.1063 0.0354 bubble 3.004

5.585 0.8951 0.0787 0.0262 bubble 3.004

5.636 0.9163 0.0628 0.0209 bubble 3.004

5.875 0.9451 0.0412 0.0137 bubble 3.004

5.953 0.9592 0.0306 0.0102 bubble 3.004

6.045 0.9696 0.0228 0.0076 bubble 3.004

6.072 0.9732 0.0201 0.0067 bubble 3.004

6.123 0.9748 0.0189 0.0063 bubble 3.004

T = 323.15 K

0.297 0.0218 0.1188 0.8594 bubble 0.138

1.245 0.0976 0.1096 0.7928 bubble 0.138

2.400 0.1867 0.0987 0.7146 bubble 0.138

2.650 0.2082 0.0961 0.6957 bubble 0.138

19

p/MPa x1 x2 x3 Status Y 3.742 0.3081 0.0840 0.6079 bubble 0.138

4.815 0.4161 0.0709 0.5130 bubble 0.138

6.581 0.5956 0.0491 0.3553 bubble 0.138

7.497 0.7098 0.0352 0.2550 bubble 0.138

8.114 0.8122 0.0228 0.1650 bubble 0.138

8.775 0.9070 0.0113 0.0817 bubble 0.138

8.852 0.9297 0.0085 0.0618 bubble 0.138

8.965 0.9537 0.0056 0.0407 bubble 0.138

8.925 0.9669 0.0040 0.0291 bubble 0.138

8.824 0.9793 0.0025 0.0182 dew 0.138

8.756 0.9816 0.0022 0.0162 dew 0.138

8.217 0.9860 0.0017 0.0123 dew 0.138

0.254 0.0196 0.2653 0.7151 bubble 0.371

0.676 0.0482 0.2576 0.6942 bubble 0.371

1.678 0.1372 0.2335 0.6293 bubble 0.371

4.005 0.3401 0.1786 0.4813 bubble 0.371

6.015 0.5433 0.1236 0.3331 bubble 0.371

7.395 0.7143 0.0773 0.2084 bubble 0.371

8.142 0.8210 0.0484 0.1306 bubble 0.371

8.423 0.8669 0.0360 0.0971 bubble 0.371

8.625 0.8972 0.0278 0.0750 bubble 0.371

8.865 0.9256 0.0201 0.0543 bubble 0.371

8.916 0.9476 0.0142 0.0382 bubble 0.371

8.895 0.9660 0.0092 0.0248 dew 0.371

8.652 0.9801 0.0054 0.0145 dew 0.371

8.091 0.9856 0.0039 0.0105 dew 0.371

0.201 0.0199 0.4723 0.5078 bubble 0.930

1.285 0.1028 0.4324 0.4648 bubble 0.930

2.785 0.2288 0.3717 0.3995 bubble 0.930

4.115 0.3567 0.3100 0.3333 bubble 0.930

5.550 0.4995 0.2412 0.2593 bubble 0.930

6.402 0.6022 0.1917 0.2061 bubble 0.930

7.275 0.7035 0.1429 0.1536 bubble 0.930

7.650 0.7620 0.1147 0.1233 bubble 0.930

8.415 0.8722 0.0616 0.0662 bubble 0.930

20

p/MPa x1 x2 x3 Status Y 8.645 0.8992 0.0486 0.0522 bubble 0.930

8.767 0.9154 0.0408 0.0438 bubble 0.930

8.852 0.9568 0.0208 0.0224 bubble 0.930

8.885 0.9716 0.0137 0.0147 dew 0.930

8.675 0.9743 0.0124 0.0133 dew 0.930

8.264 0.9801 0.0096 0.0103 dew 0.930

0.234 0.0235 0.7326 0.2439 bubble 3.004

0.550 0.0535 0.7101 0.2364 bubble 3.004

1.889 0.1694 0.6232 0.2074 bubble 3.004

3.205 0.2777 0.5419 0.1804 bubble 3.004

3.910 0.3425 0.4933 0.1642 bubble 3.004

4.921 0.4415 0.4190 0.1395 bubble 3.004

5.950 0.5472 0.3397 0.1131 bubble 3.004

7.107 0.6836 0.2374 0.0790 bubble 3.004

7.536 0.7582 0.1814 0.0604 bubble 3.004

8.015 0.8238 0.1322 0.0440 bubble 3.004

8.395 0.8767 0.0925 0.0308 bubble 3.004

8.635 0.9067 0.0700 0.0233 bubble 3.004

8.736 0.9251 0.0562 0.0187 bubble 3.004

8.765 0.9275 0.0544 0.0181 bubble 3.004

8.795 0.9508 0.0369 0.0123 bubble 3.004

8.707 0.9648 0.0264 0.0088 dew 3.004

8.230 0.9784 0.0162 0.0054 dew 3.004

T = 373.15

1.025 0.0437 0.1161 0.8402 bubble 0.138

2.441 0.1138 0.1076 0.7786 bubble 0.138

3.765 0.1864 0.0987 0.7149 bubble 0.138

3.885 0.1937 0.0979 0.7084 bubble 0.138

4.115 0.2079 0.0961 0.6960 bubble 0.138

6.017 0.3091 0.0839 0.6070 bubble 0.138

7.768 0.4136 0.0712 0.5152 bubble 0.138

7.875 0.4199 0.0704 0.5097 bubble 0.138

10.162 0.5502 0.0546 0.3952 bubble 0.138

10.951 0.5955 0.0491 0.3554 bubble 0.138

12.547 0.7097 0.0352 0.2551 bubble 0.138

21

p/MPa x1 x2 x3 Status Y 13.747 0.8122 0.0228 0.1650 bubble 0.138

13.890 0.8447 0.0189 0.1364 bubble 0.138

13.678 0.8861 0.0138 0.1001 dew 0.138

13.052 0.9207 0.0096 0.0697 dew 0.138

11.872 0.9417 0.0071 0.0512 dew 0.138

0.497 0.0219 0.2647 0.7134 bubble 0.371

1.922 0.0925 0.2456 0.6619 bubble 0.371

3.786 0.1966 0.2174 0.5860 bubble 0.371

7.175 0.3850 0.1664 0.4486 bubble 0.371

10.435 0.5764 0.1146 0.3090 bubble 0.371

11.694 0.6627 0.0913 0.2460 bubble 0.371

13.256 0.7760 0.0606 0.1634 bubble 0.371

13.562 0.8337 0.0450 0.1213 bubble 0.371

13.532 0.8683 0.0356 0.0961 bubble 0.371

13.256 0.9011 0.0268 0.0721 dew 0.371

12.752 0.9234 0.0207 0.0559 dew 0.371

11.653 0.9408 0.0160 0.0432 dew 0.371

0.110 0.0000 0.4819 0.5181 bubble 0.930

0.750 0.0376 0.4638 0.4986 bubble 0.930

3.501 0.1878 0.3914 0.4208 bubble 0.930

5.432 0.2947 0.3399 0.3654 bubble 0.930

8.080 0.4473 0.2664 0.2863 bubble 0.930

10.880 0.6180 0.1841 0.1979 bubble 0.930

11.950 0.6919 0.1485 0.1596 bubble 0.930

13.040 0.7765 0.1077 0.1158 bubble 0.930

13.170 0.8510 0.0718 0.0772 bubble 0.930

13.100 0.8730 0.0612 0.0658 dew 0.930

12.250 0.9297 0.0339 0.0364 dew 0.930

10.761 0.9502 0.0240 0.0258 dew 0.930

0.933 0.0534 0.7102 0.2364 bubble 3.004

2.256 0.1298 0.6529 0.2173 bubble 3.004

4.450 0.2567 0.5577 0.1856 bubble 3.004

6.825 0.3987 0.4511 0.1502 bubble 3.004

9.351 0.5497 0.3378 0.1125 bubble 3.004

11.250 0.6744 0.2443 0.0813 bubble 3.004

22

p/MPa x1 x2 x3 Status Y 12.160 0.7449 0.1914 0.0637 bubble 3.004

12.653 0.7938 0.1547 0.0515 bubble 3.004

12.812 0.8503 0.1123 0.0374 bubble 3.004

12.702 0.8818 0.0887 0.0295 dew 3.004

12.431 0.9115 0.0664 0.0221 dew 3.004

12.152 0.9227 0.0580 0.0193 dew 3.004

11.735 0.9316 0.0513 0.0171 dew 3.004

10.576 0.9472 0.0396 0.0132 dew 3.004

T = 423.15 K

1.258 0.0335 0.1173 0.8492 bubble 0.138

3.454 0.1257 0.1061 0.7682 bubble 0.138

4.905 0.1860 0.0988 0.7152 bubble 0.138

5.415 0.2075 0.0962 0.6963 bubble 0.138

7.946 0.3092 0.0839 0.6069 bubble 0.138

10.364 0.4134 0.0712 0.5154 bubble 0.138

12.726 0.5221 0.0580 0.4199 bubble 0.138

14.287 0.5954 0.0491 0.3555 bubble 0.138

15.997 0.7096 0.0352 0.2552 bubble 0.138

16.065 0.7699 0.0279 0.2022 bubble 0.138

16.021 0.7996 0.0243 0.1761 dew 0.138

15.275 0.8328 0.0203 0.1469 dew 0.138

14.672 0.8527 0.0179 0.1294 dew 0.138

14.276 0.8596 0.0170 0.1234 dew 0.138

13.050 0.8792 0.0147 0.1061 dew 0.138

1.425 0.0482 0.2576 0.6942 bubble 0.371

4.323 0.1672 0.2254 0.6074 bubble 0.371

6.153 0.2491 0.2032 0.5477 bubble 0.371

9.956 0.4167 0.1578 0.4255 bubble 0.371

11.813 0.5003 0.1352 0.3645 bubble 0.371

14.225 0.6215 0.1024 0.2761 bubble 0.371

15.243 0.7026 0.0805 0.2169 bubble 0.371

15.536 0.7779 0.0601 0.1620 dew 0.371

15.075 0.8067 0.0523 0.1410 dew 0.371

14.052 0.8411 0.0430 0.1159 dew 0.371

13.832 0.8478 0.0412 0.1110 dew 0.371

23

p/MPa x1 x2 x3 Status Y 13.032 0.8667 0.0361 0.0972 dew 0.371

11.957 0.8792 0.0327 0.0881 dew 0.371

0.405 0.0000 0.4819 0.5181 bubble 0.930

1.256 0.0378 0.4637 0.4985 bubble 0.930

2.962 0.1170 0.4255 0.4575 bubble 0.930

4.545 0.1875 0.3916 0.4209 bubble 0.930

6.625 0.2868 0.3437 0.3695 bubble 0.930

10.320 0.4512 0.2645 0.2843 bubble 0.930

13.250 0.6018 0.1919 0.2063 bubble 0.930

14.595 0.7085 0.1405 0.1510 bubble 0.930

14.755 0.7702 0.1107 0.1191 dew 0.930

13.950 0.8206 0.0865 0.0929 dew 0.930

13.200 0.845 0.0747 0.0803 dew 0.930

11.587 0.8620 0.0665 0.0715 dew 0.930

2.150 0.0875 0.6846 0.2279 bubble 3.004

4.421 0.1980 0.6017 0.2003 bubble 3.004

7.615 0.3490 0.4884 0.1626 bubble 3.004

11.532 0.5420 0.3436 0.1144 bubble 3.004

13.625 0.6833 0.2376 0.0791 bubble 3.004

13.853 0.7198 0.2102 0.0700 bubble 3.004

13.792 0.7745 0.1692 0.0563 dew 3.004

13.350 0.7982 0.1514 0.0504 dew 3.004

12.375 0.8310 0.1268 0.0422 dew 3.004

11.052 0.8587 0.1060 0.0353 dew 3.004 a Expanded uncertainties are U(T) = 1 K, U(p) = 0.4 MPa for bubble points or U(p) = 0.6 MPa for dew points, U(x1) = 0.0034x1(1 - x1), U(x2) = U(x1)Y/(1 + Y), and U(x3) = U(x1)/(1 + Y) with coverage factor k = 2.

Figure 1. Schematic diagram of the variable volume cell apparatus: V-1, on/off valve; V-2, filter; V-3, check valve; V-4, on/off valve; V-5, reducer; V-6 valve; V-7 and V-8, filter; V-9 and

V-10, 5 way electrically actuated valves; V-11 and V-12, union crosses; V13 to V16, check

valves; V17, three way electrically actuated valve; V-18, tee; V-19, two way manual valve; V-

20, three way manual valve; V-21 safety head; V-22, two way air operated normally closed

valve; VVC, variable volume cell; E-1 and E-2, high pressure syringe pumps; notation P and T

indicates pressure transducer and temperature sensors respectively. Green colour indicates

gas paths, red colour indicates liquid paths, and blue colour indicates mixture paths

E-1V-6V-9

CO2

Gas

V-2V-1

V-4

V-3

V-10

V-5

Liq/

Sol

V-7

V-11

V-12

Vent

Vacuum

V-21

E-2

V-13

V-14

V-15

V-16

V-18

V-19Vent

V-17

Vent

Serv

o M

otor

V-20C VVC

P

T

Liq/

Sol V-8

V-22

25

Figure 2. Isothermal p-x diagram for CO2 + benzene, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data while the continuous curves represents the description with the SAFT-γ Mie approach at: T = 298 K (squares),62 313 K (circles),62 353 K (diamonds),25 373 K (crosses),25 and 393 K (triangles).25

Figure 3. Isothermal p-x diagram for CO2 + methylbenzene, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data while the continuous curves represents the description with the SAFT-γ Mie approach at: T = 283 K (diamonds),18 T = 311 K (crosses),19 T = 353K (squares),19 T = 394 K (circles),19 and T = 413 K (triangles).21

0

2

4

6

8

10

12

14

16

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

0

2

4

6

8

10

12

14

16

18

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

26

Figure 4. Isothermal p-x diagram for CO2 + 1,2-dimethylybenzene, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data of Walther et al. 63 while the continuous curves represents the description with the SAFT-γ Mie approach at: T = 313 K (circles), T = 333 K (triangles), T = 353 K (crosses), T = 373 K (diamonds), and T =393 K (squares).

Figure 5. Isothermal p-x diagram for CO2 + 1,3-dimethylybenzene, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data of Walther et al. 63 while the continuous curves represents predictions of the SAFT-γ Mie approach at: T = 313 K (circles), T = 333 K (triangles), T = 353 K (crosses), T = 372 K (diamonds), and T = 393 K (squares).

0

2

4

6

8

10

12

14

16

18

20

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

0

2

4

6

8

10

12

14

16

18

20

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

27

Figure 6. Isothermal p-x diagram for CO2 + 1,4-dimethylybenzene, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data of Walther et al. 63 while the continuous curves represents predictions of the SAFT-γ Mie approach at: T = 313 K (circles), T = 333 K (triangles), T = 353 K (crosses), T = 373 K (diamonds), and T =393 K (squares).

Figure 7. Isothermal p-x diagram for CO2 + 1,2-dimethylybenzene (circles), CO2 + 1,3-dimethylybenzene (squares), and CO2 + 1,4-dimethylybenzene (triangles) and at T = 393 K, where p is pressure and x is the mole fraction of CO2. Symbols represent the experimental literature data of Walther et al.63 while the continuous curves represents predictions of the SAFT-γ Mie approach.

0

2

4

6

8

10

12

14

16

18

20

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

0

2

4

6

8

10

12

14

16

18

20

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x

28

Figure 8. Bubble curve for the ternary mixture (CO2 + n-heptane + methylbenzene) at temperature T = 298.15 K, where p is pressure and x1 is the mole fraction of CO2. Symbols

represents experimental data at the following mole ratios Y of heptane to methylbenzene: (a) Y = 0.138; (b), Y = 0.371; (c), Y = 0.930; and (d), Y = 3.004. The solid line represents prediction

from SAFT-γ-Mie.

0

2

4

6

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

a

0

2

4

6

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

b

0

2

4

6

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

c

0

2

4

6

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

d

29

Figure 9. Bubble and dew curves for the ternary mixture (CO2 + n-heptane + methylbenzene) at temperature T = 323.15 K, where p is pressure and x1 is the mole fraction of CO2. Symbols

represents experimental data at the following mole ratios Y of heptane to methylbenzene: (a) Y = 0.138; (b), Y = 0.371; (c), Y = 0.930; and (d), Y = 3.004. The solid line represents prediction

from SAFT-γ-Mie.

0

3

6

9

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

a

0

3

6

9

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

b

0

3

6

9

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

c

0

3

6

9

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

d

30

Figure 10. Bubble and dew curves for the ternary mixture (CO2 + n-heptane + methylbenzene) at temperature T = 373.15 K, where p is pressure and x1 is the mole fraction of CO2. Symbols

represents experimental data at the following mole ratios Y of heptane to methylbenzene: (a) Y = 0.138; (b), Y = 0.371; (c), Y = 0.930; and (d), Y = 3.004. The solid line represents prediction

from SAFT-γ-Mie.

0

4

8

12

16

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

a

0

4

8

12

16

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

b

0

4

8

12

16

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

c

0

4

8

12

16

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

d

31

Figure 11. Bubble and dew curves for the ternary mixture (CO2 + n-heptane + methylbenzene) at temperature T = 423.15 K, where p is pressure and x1 is the mole fraction of CO2. Symbols

represents experimental data at the following mole ratios Y of heptane to methylbenzene: (a) Y = 0.138; (b), Y = 0.371; (c), Y = 0.930; and (d), Y = 3.004. The solid line represents prediction

from SAFT-γ-Mie.

0

6

12

18

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

a

0

6

12

18

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

b

0

6

12

18

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

c

0

6

12

18

0.0 0.2 0.4 0.6 0.8 1.0

p/M

Pa

x1

d

32

Graphical Abstract - For Table of Contents Use Only

E-1

V-11

V-12

Vent

Vacuum

V-21

E-2

V-13

V-14

V-15

V-16

V-18

V-19Vent

V-17

Vent

Serv

o M

otor

V-20

C VVC

P

T

V-22

Saif Z. S. Al Ghafri1,2, Geoffrey C. Maitland1, and J. P. Martin Trusler1*1. Introduction2. Experimental2.1 Apparatus2.2 Calibration and Uncertainty2.3 Materials2.4 Experimental Procedure3. Theory4. Results and Discussion5. ConclusionsAcknowledgmentsFunding